s-Process in Low Metallicity Stars. III. Individual analysis of CEMP-s and CEMP-s/r with AGB models

We provide an individual analysis of 94 carbon enhanced metal-poor stars showing an s-process enrichment (CEMP-s) collected from the literature. The s-process enhancement observed in these stars is ascribed to mass transfer by stellar winds in a binary system from a more massive companion evolving faster toward the asymptotic giant branch (AGB) phase. The theoretical AGB nucleosynthesis models have been presented in Paper I. Several CEMP-s stars show an enhancement in both s and r-process elements (CEMP-s/r). In order to explain the peculiar abundances observed in CEMP-s/r stars, we assume that the molecular cloud from which CEMP-s formed was previously enriched in r-elements by Supernovae pollution. A general discussion and the method adopted in order to interpret the observations have been provided in Paper II. We present in this paper a detailed study of spectroscopic observations of individual stars. We consider all elements from carbon to bismuth, with particular attention to the three s-process peaks, ls (Y, Zr), hs (La, Nd, Sm) and Pb, and their ratios [hs/ls] and [Pb/hs]. The presence of an initial r-process contribution may be typically evaluated by the [La/Eu] ratio. We found possible agreements between theoretical predictions and spectroscopic data. In general, the observed [Na/Fe] (and [Mg/Fe]) provide information on the AGB initial mass, while [hs/ls] and [Pb/hs] are mainly indicators of the s-process efficiency. A range of 13C-pocket strengths is required to interpret the observations. However, major discrepancies between models and observations exist. We highlight star by star the agreements and the main problems encountered and, when possible, we suggest potential indications for further studies. These discrepancies provide starting points of debate for unsolved problems ...

has been presented by Bisterzo et al. (2010a, hereafter Paper I) and Bisterzo et al. (2011, hereafter Paper II). Theoretical results are obtained with a post-process nucleosynthesis method (Gallino et al. 1998), based on full evolutionary FRANEC (Frascati Raphson-Newton Evolutionary Code, Chieffi & Straniero 1989) models, following the prescriptions by Straniero et al. (2003), as described in Paper I. AGB models with initial masses M = 1.3, 1.4, 1.5, 2 M⊙, metallicities −3.6 [Fe/H] −1.5, and a range of 13 C-pockets are adopted. The 13 C-pocket is a thin 13 C-rich layer, which forms when few protons diffuse after a thermal instability, once the bottom of the convective envelope penetrates into the top layers of the radiative He-intershell (the zone between the H-and He-shells). This recurrent phenomenon is called third dredge-up (TDU). At H-shell re-ignition, protons are captured by the abundant 12 C and the 13 C-pocket is produced at the top of the He-intershell. Subsequently, when the temperature increases up to 1 × 10 8 K, neutrons are released in radiative conditions via the 13 C(α, n) 16 O reaction. This is the major neutron source in low mass AGB stars. The physical environments involved in the formation of the 13 C-pocket are still affected by large uncertainties. According to the description of our AGB models provided in Paper I, we assumed a range of 13 C-pocket strengths. This assumption is based on the spectroscopic observations of different stellar populations (MS, S, C(N), Ba stars, CEMP-s stars): for a given metallicity, they show a spread that may be reproduced by AGB models if a range of s-process efficiencies is assumed (Busso et al. 1995Abia et al. 2001Abia et al. , 2002Sneden et al. 2008;Käppeler et al. 2011). Starting from the case ST defined by Gallino et al. (1998) in order to reproduce the solar main s-process component (Arlandini et al. 1999), we multiply or divide the 13 C (and 14 N) abundance in the pocket by different factors: from a minimum fraction of ST, below which the sprocess contribution becomes negligible 1 , up to a maximum (ST×2), because further proton ingestion gives rise to 14 N instead of 13 C. Note that in our approximation, we did not account for a likely decrease in mass of the 13 C-pocket with the number of TDUs, as obtained by recent FRANEC models (see Cristallo et al. 2011, and references therein). They introduced a physical algorithm for the treatment of the transition region between the convective envelope and the radiative H-exhausted core, based on a non-diffusive mixing scheme Cristallo et al. 2009a). This allows the formation of a tiny 13 C-pocket, which decreases in mass with the number of TDUs. The interpretation of the s-process spread observed in different stars with new FRANEC models ) is under investigation. A second neutron source is driven in the convective thermal pulse by the partial activation of the 22 Ne(α, n) 25 Mg reaction. When neutrons are released, both in the pocket and in the convective TP, a fraction is captured via the resonant reaction 14 N(n, p) 14 C. As discussed in Paper I, a complex chain of proton captures occurs, affecting in particular the production of F (Lugaro et al. 2008;Abia et al. 2010;Gallino et al. 2010, and references therein). Besides the formation of the 13 C-pocket, additional uncertainties that affect AGB models and s-process nucleosynthesis are the evaluation of the mass loss and the efficiency of the TDU. Mass loss plays a key role during the AGB phase, and it affects several stellar properties, as the efficiency of the TDU (in which the surface is enriched with freshly synthesised 12 C and s-process elements), the number of thermal pulses and, therefore, the duration of this evolutionary phase. In Paper I, we discussed these topics and their effects on our theoretical predictions.
With the recent discovery of peculiar stars showing both s and r-process enhancements (CEMP-s/r) incompatible with a pure s-process nucleosynthesis, a highly debated issue has begun. Indeed, the two processes are synthesised in different astrophysical conditions. Several hypotheses have been proposed in order to justify the presence of the products of both processes in the same star (e.g., Cohen et al. 2003;Jonsell et al. 2006;Lugaro et al. 2009, and references therein). Our working scenario, already presented by Sneden et al. (2008) and Bisterzo et al. (2009), has been discussed in detail in Paper II. Considering the large spread observed for [Eu/Fe] in field halo stars, we follow the hypothesis that the molecular cloud from which a given binary system formed was initially enriched in different proportions in r-process elements. The astrophysical site and physical conditions of the rprocess are not understood and several theoretical models have been advanced in order to estimate the r component. As discussed in Paper II, a good approximation of the rprocess contribution to isotopes from Ba to Bi is evaluated with the residual method, Nr = N⊙ -Ns, starting from the solar main and strong s-process contributions. According to the spread observed for [Eu/Fe] in Galactic halo stars with [Fe/H] −2 (e.g., Paper II, Fig. 2), where Eu is a typical r-process element, observations of CEMP-s and CEMP-s/r stars may be interpreted under the hypothesis of a range of initial r-enhancements ([r/Fe] ini ∼ 0.0, 0.5, 1.0, 1.5, 2.0, scaled to Eu). The [La/Eu] ratio provides a good indicator of the initial r-process contribution in these stars. Indeed, 70% of solar La is synthesised by the s-process, while less than 5% of solar Eu is produced by the s-process. On the basis of the initial r-enhancement adopted, we consider as CEMP-s/r those stars that need an [r/Fe] ini from 1.0 to 2.0, while CEMP-s are those stars that require an [r/Fe] ini < 1. If not differently specified, CEMP-s stars are interpreted by assuming an [r/Fe] ini = 0.5, in agreement with the average of [Eu/Fe] observed in field halo stars (Paper II, Section 3).
The goal of this paper is to provide a first step toward our understanding of these puzzling CEMP-s and CEMPs/r stars, through a comparison between the AGB models presented in Paper I and the spectroscopic observations of each individual star. This analysis is of fundamental importance in order to account for the uncertainties, number of lines, resolution spectra obtained by different authors. This highlights possible agreements or discrepancies between theory and observations and suggests starting points for future investigations. A general discussion of the sample considered here has been provided in Paper II, in which we pre-sented an extensive analysis of the sample of a hundred of CEMP-s stars collected from the literature (Aoki et al. 2002a(Aoki et al. ,c,d, 2006; Barbuy et al. 2005; Barklem et al. 2005;Behara et al. 2010;Cohen et al. 2003Cohen et al. , 2006Goswami et al. 2006;Goswami & Aoki 2010;Ivans et al. 2005;Ishigaki et al. 2010;Israelian et al. 2001;Jonsell et al. 2006;Johnson & Bolte 2002Junqueira & Pereira 2001;Lucatello et al. 2003Lucatello et al. , 2011Masseron et al. 2006Masseron et al. , 2010Pereira & Drake 2009;Preston & Sneden 2001;Roederer et al. 2008Roederer et al. , 2010aSneden et al. 2003b; Thompson et al. 2008;Tsangarides 2005;Van Eck et al. 2003;Zhang et al. 2009). At halo metallicities, major constraints on the AGB initial mass are provided by the observed [Na/Fe] (and [Mg/Fe]) and, in some cases, by [hs/ls] (see Paper II). As described in Paper I, the predicted [Na/Fe], [Mg/Fe] and [ls/Fe] mainly depend on the number of TDUs. Indeed, by decreasing the metallicity, an increasing amount of primary 22 Ne in the advanced thermal pulses is produced starting from primary 12 C (via 14 N(α, γ) 18 F(β + ν) 18 O and 18 O(α, γ) 22 Ne; see e.g., Mowlavi et al. 1999;Gallino et al. 2006). In our models, 23 Na is mainly synthesised via neutron capture on the abundant 22 Ne during the thermal pulses (Paper I). Starting from 23 Na, Mg is also produced during the advanced TPs, via the reactions 23 Na(n, γ) 24 Mg, 22 Ne(α, n) 25 Mg and 22 Ne(α, γ) 26 Mg (Mowlavi et al. 1999;Gallino et al. 2006;Husti et al. 2007). Goriely & Mowlavi (2000) firstly suggested an additional important source of Na. It derives from their choice of the proton profile in the pocket: they considered an exponentially decreasing proton profile, starting from the envelope abundance (X(H) ∼ 0.7) down to ∼ 10 −6 . A similar range of H abundance has been introduced by new FRANEC (Cristallo et al. 2009a, their Fig. 13). In the outer layer of the pocket, when 12 C get destroyed by the very high hydrogen fraction introduced in the pocket, and 22 Ne becomes more abundant than 12 C, proton capture on 22 Ne feeds 23 Na at a temperature close to 40 MK. Instead, in our prescriptions, we adopted an H profile limited to the range X(H) < 1.8 × 10 −3 , as described by Gallino et al. (1998) (their Fig. 1), which excludes the region in which a large amount of protons reaches the He-intershell. Consequently, we do not have in the pocket the 14 N-rich and 23 Na-rich regions. However, we have accounted for the contribution to 23 Na by 22 Ne that comes from the ashes of the H-burning shell. As anticipated above, during the TP almost all 14 N left by H-burning is converted to primary 22 Ne. This primary 22 Ne, which is mixed with the envelope by subsequent TDU episodes, also affects the final 23 Na production. Indeed, in the interpulse phase the H-burning shell advances in mass. By adopting the reaction rates by NACRE, about 20% of 22 Ne is converted to 23 Na via 22 Ne(p, γ) 23 Na during the H-shell. This implies an increase of the [Na/Fe] on the surface by ∼ 0.1 dex. As well as 23 Na, the large amount of primary 22 Ne also produces Sr, Y and Zr via the 22 Ne(α, n) 25 Mg neutron source. This results in an increase of the predicted [ls/Fe] with the AGB initial mass. Note that, by decreasing the metallicity, the reduced abundance of the major seed 56 Fe, together with large amount of primary 22 Ne, highlights the effect of the 22 Ne(n, γ) reaction, which acts as efficient seed, besides as neutron poison (see Gallino et al. 2006; Section 6). The two s-process indicators [hs/ls] and [Pb/hs] provide information about the choice of the 13 C-pocket 2 . A dilution factor dil (defined as the logarithm of the mass of the convective envelope of the observed star, M obs ⋆ , over the mass transferred from the AGB to the companion, M trans AGB ) is adopted in order to simulate the mixing occurring in the envelope after the mass transfer from the AGB. The [hs/Fe] ratio gives the first assessment of the dilution of the C and s-rich material transferred from the AGB. For subgiants/giants having suffered the first dredge-up (FDU, a large mixing involving about 80% of the mass of the star), dil 1 dex is needed. The method adopted to interpret the spectroscopic observations has been described in Paper II for three stars taken as example: the CEMP-s giant HD 196944, the main-sequence CEMP-s/r HE 0338-3945, and a CEMP-s HE 1135+0139 for which no lead is measured. We extend this analysis here to 94 CEMP-s and CEMP-s/r stars following the classification adopted in Paper II, in agreement with the s-and r-process enhancements observed: • CEMP-sII stars show high s-process enhancement with [hs/Fe] 1.5 (Section 2.1); • CEMP-sI stars show mild s-process enhancement with [hs/Fe] < 1.5 (Section 2.2); • CEMP-sII/r are high s-process enhanced stars, also showing an r-process contribution not compatible with a pure AGB nucleosynthesis ([hs/Fe] 1.5; 0.0 [La/Eu] 0.4). Similarly to the s-process enhancement, we may distinguish two subgroups among CEMP-sII/r stars, according to the initial r-process enhancement (Section 3): -CEMP-sII/rII with 1.5 [r/Fe] ini 2.0 -CEMP-sII/rI with [r/Fe] ini ∼ 1.0.
One would expect a further class of stars with both mild sand r-process contributions, the CEMP-sI/rI. None of the stars of the sample belongs to this group probably because these stars cannot be distinguished from Galactic halo stars due to their low initial r-enhancement. Moreover, we consider in a separate category those stars without Eu detection, because a possible initial r-process enrichment can not be excluded: among them, we separate CEMP-sII/− (Section 4.1) and CEMP-sI/− (Section 4.2) stars. At the beginning of each Section we list the name of the stars analysed in alphabetical order, with a distinction between main-sequence/turnoff subgiant stars before the FDU and subgiants/giants having suffered the FDU. Stars with a large number of observations (collected in Table 2 and 10 of Paper II) are analysed in Sections 2, 3, and 4. Stars with a limited number of s-process observations (Table 3 and 11 of Paper II) are discussed in Appendix A. A summary of the results is given in Section 7. For convenience, we report in Tables 1 and 2 a list of the stars studied here, with their references, metallicity, classification provided in Paper II, the number of the Figure associated to the theoretical interpretation.

Star
Ref.
[  François et al. 2004). Note that Bergemann & Gehren (2008) found that the observed Mn may increase up to [Mn/Fe] ∼ −0.1 due to NLTE corrections. Concerning Cu, we assume an initial solar-scaled value if no observations are provided. Actually, because AGBs marginally produce Cu, a better choice would be [Cu/Fe] ini ∼ −0.7, which represents the average ratio observed in unevolved halo stars (Bisterzo et al. 2004;Romano & Matteucci 2007). We accounted for this effect when discussing the four CEMP-s stars for which Cu has been detected (HE 0338-3945 discussed in Paper II, Section 5.2, CS 30322-023, CS 31062-050 and HD 206983). The comparison between theoretical predictions and observations may help to establish the efficiency of non-convective mixing occurring in the envelope of the observed star during their main-sequence phase (e.g., thermohaline, gravitational settlings, radiative levitation, see Richard et al. 2002;Vauclair 2004;Stancliffe et al. 2007;Stancliffe & Glebbeek 2008;Stancliffe et al. 2009;Thompson et al. 2008;Theado & Vauclair 2010). For stars on the red giant branch, having undergone the FDU, all mixing processes occurred during the main-sequence phase are erased.

CEMP-S STARS
In this Section we provide an individual analysis of CEMP-sII and CEMP-sI stars (with Eu measured). As anticipated in Section 1, CEMP-s are generally interpreted with an initial r-process enhancement [r/Fe] ini = 0.5, on the basis of an average of the [Eu/Fe] observed in halo field stars (see Paper II, Fig. 2). Different [r/Fe] ini from −1.0 to 0.7 are adopted for some peculiar stars, as discussed below.

CEMP-sII stars
There are six stars with an s-process enhancement higher than [hs/Fe] 1.5. One star having not suffered the FDU, CS 22881-036 by Preston & Sneden (2001), and a second star with uncertain occurrence of the FDU, HE 0336+0113 by Cohen et al. (2006), (see discussion in Paper II, Section 2); two giants, HE 1509-0806 and HE 2158-0348 by Cohen et al. (2006). Note that the low Eu upper limit detected for HE 1509-0806 excludes a high initial r-process enhancement, and classifies this star as a CEMP-sII. In addi- . C and N are not included because they may be affected by deep-mixing (see text). The range between the two lines corresponds to a typical model uncertainty of 0.2 dex. An initial r-process enrichment of [r/Fe] ini = 0.5 is adopted. Here and in the following Figures, both theoretical and spectroscopic abundances have been normalised to the solar photospheric values by Lodders, Palme & Gail (2009). This explains possible discrepancies with respect to the observations listed in Paper II (Tables 2  and 3), in which we adopted the normalisations provided by the different authors. tion, we describe in this Section the CEMP-sII subgiant BS 16080-175, for which spectroscopic data have been analysed by Tsangarides (2005) (PhD Thesis). HD 26 (Van Eck et al. 2003;Masseron et al. 2010), which shows a higher metallicity ([Fe/H] = −1), is discussed separately in Section 5.
2.1.1 CS 22881-036 ( Fig. 1) This turnoff star with [Fe/H] = −2.06, T eff = 6200 K and log g = 4.0, was studied by Preston & Sneden (2001). After the first radial velocity study by Preston & Sneden (2000), Preston et al. (2009) find variations over a period of 16 years, with P = 378 days. Following the method explained in Paper II (Section 5), the choice of the 13 C-pocket is made according to the observed s-process indicator [hs/ls] = 0.76. Preston & Sneden (2001) suggest typical uncertainties of 0.2 -0.3 dex for species with many transitions. No lead is detected in this star. In Fig. 1, we show possible solutions with AGB models of M AGB ini = 1.3 M⊙, cases ST/6, ST/8 and ST/9, and no dilution. Here and in the following Figures the name of the star, its metallicity, the literature of the spectroscopic data, and the characteristics of the AGB models adopted (i.e. initial mass, 13 Cpocket, dilution factor and initial r-process enhancement) are given in the caption. In the lower panel the differences between observations and AGB predictions [El/Fe] obs−th are represented. The two lines placed at ± 0.2 dex are to indicate possible uncertainties of the model or of the initial abundances of light elements. As discussed in Paper II, Section 5, the [C/Fe], [N/Fe] and 12 C/ 13 C ratios measured in CEMP-s stars are largely overestimated by AGB models. Indeed, AGB models predict a large amount of 12 C in the envelope already after the first thermal pulses with TDU (Paper I). The occurrence of extra-mixing like the cool bottom processing (CBP) have been hypothesised in order to interpret observations in AGB stars and pre-solar grains of AGB origin (Nollett et al. 2003;Domínguez et al. 2004a,b;Wasserburg et al. 2006;Zinner et al. 2006;Cristallo et al. 2007;Busso et al. 2010). Several physical processes may concur in this mixing (e.g., rotation, magnetic fields, thermohaline mixing), and their efficiency is difficult to estimate. An additional deep mixing may reduce the 12 C/ 13 C ratio and increase 14 N in low-mass low-metallicity AGB stars ([Fe/H] −2.5): during the first fully developed TP, an ingestion of protons from the envelope down to the convective He-intershell occurs (Hollowell et al. 1990;Iwamoto et al. 2004;Campbell & Lattanzio 2008;Cristallo et al. 2009b;Campbell, Lugaro, Karakas 2010). This leads to efficient proton captures on CNO isotopes, with a large production of 13 C and, at lower level, of 14 N. This episode may also modify the s-process pattern. There is a maximum mass (which increases with decreasing the metallicity) below which AGB models undergo proton ingestion. The assumption of an initial enhanced distribution (e.g., of α-elements compatible with observations of metal-poor stars) would further decrease this mass limit . Further studies on this topic are desirable. For these reasons, C and N are not included in the lower panel of Fig. 1 and in the following Figures. We refer to Paper II for a general discussion about C and N. We are planning to reconsider this topic in a forthcoming study. However, we underline that high uncertainties affect the spectroscopic determination of C and N, because of NLTE or 3D model corrections (Asplund 2005;Collet et al. 2007;Grevesse et al. 2007;Asplund et al. 2009;Caffau et al. 2009;Frebel & Norris 2011). The AGB models displayed in Fig. 1  The range of dilution accounts for the spread observed in the hs elements: indeed, with a slightly lower 13 C-pocket efficiency and dil = 0.3 dex, we may still interpret the two s-peaks. This indicates that mixing during the main-sequence phase were not efficient in this CEMP-s. In order to estimate plausible variations of the dilution resulting from the uncertainties of the 13 C-pocket, we test the effect on the abundances of a variation of the mass involved in the pocket. We recall that in our models, the mass of the pocket is 5 × 10 −4 M⊙, that is about 1/20 of the typical mass involved in a thermal pulse. A mass of the pocket of the order of 1/10 of the mass involved in the thermal pulse can be considered as an extreme case. This would increase the [El/Fe] of the s-process elements of about 0.3 dex. Therefore, we found that the uncertainty of the mass of the 13 C-pocket only marginally affects the dilution (up to ∼ 0.2 dex, given that the previous example is an extreme case). AGB models with low initial mass undergo a limited number of thermal pulses. In these models, the [El/Fe] abundances predicted in the envelope after two subsequent TDUs differ by ∼ 0.2 dex, corresponding to an increase of the initial mass of about +0.025 M⊙. This is not the case of AGB models with initial mass M > 1.4 M⊙, for which negligible differences are observed in the s-process distribution after the 12 th TDU (see Paper I,Fig. 4,top panel). Summing up, for lower AGB initial masses, the dilution may increase up to ∼ 0.4 dex, owing to a plausible increase of the mass of the pocket, or to an additional TDU. This value may be considered in agreement with a moderate mixing.

HE 0336+0113 (Fig. 2)
HE 0336+0113 was analysed by Cohen et al. (2006), who found [Fe/H] = −2.7, T eff = 5700 (± ∼ 150) K and log g = 3.5 (± ∼ 0.4). As anticipated in Paper II (Section 2), the onset of the FDU for subgiants may involve marginal mixing of the accreted AGB wind material with the original envelope of the observed star, unless efficient thermohaline mixing is at play. The high Mg observed ([Mg/Fe] ∼ 1 dex) can be interpreted only by AGB models with initial masses higher than 1.3 M⊙. A high [Na/Fe] is predicted. Observations of Na lines are highly desirable. Among ls elements, Zr is not detected, and among hs elements no Sm is measured, making the [hs/ls] ratio very uncertain. The low upper limit detected for Pb ([Pb/hs] 0.2) indicates low 13 C-pocket efficiencies. In case of very low 13 C-pocket choices, the predicted [hs/Fe] does not exceed ∼ 2 dex, in agreement with a low dilution. In Fig. 2, we show solutions with M AGB ini = 1.4 and 2 M⊙, cases close to ST/50, and dil = 0.0 -0.3 dex. The low dilution suggests that the envelope did not reach yet its maximum penetration during the FDU episode. For these stars we can not properly quantify the efficiency of mixing during the main-sequence phase (see Section 2.1.1). We adopt an initial r-process enrichment [r/Fe] ini = 0.5 in agreement with the average of field halo stars to obtain [Eu/Fe] s+r th = 1.03. A similar value within 0.1 dex is predicted by a model without initial r-process enhancement. C and N are very uncertain for this star and no systematic errors are provided by Cohen et al. (2006). Solutions with M AGB ini = 1.5 M⊙ give even worse interpretations for C, N and Mg.

HE 1509-0806 (Fig. 3)
This is one of the coolest giants studied by Cohen et al. (2006)  with TDU (e.g., n3, n4, n5 for M AGB ini ∼ 1.2 -1.3 M⊙ models) and, consequently, the [El/Fe] distribution predicted in the envelope is low. Therefore, low dilutions must be applied, in contrast with a giant after the FDU. By increasing the AGB initial mass, plausible interpretations are found, as shown in Fig. 3

CEMP-sI
Twelve stars show mild s-process enhancement. The turnoff star CS 22964-161 by Thompson et al. (2008); two stars for which the occurrence of the FDU is uncertain, CS 22880-074 by Aoki et al. (2002cAoki et al. ( ,d, 2007 and CS 29513-032 by Roederer et al. (2010a); seven giants, CS 22942-019 by Aoki et al. (2002c,d); Preston & Sneden (2001), CS 30301-015 by Aoki et al. (2002cAoki et al. ( ,d, 2007, CS 30322-023 by Masseron et al. (2006); Aoki et al. (2007), HD 196944 by Aoki et al. (2002cAoki et al. ( ,d, 2007; Masseron et al. (2010) (already discussed in Paper II, Section 5), HE 0202-2204 and HE 1135+0139 by Barklem et al. (2005) (already discussed in Paper II, Section 5), HK II 17435-00532 by Roederer et al. (2008). In addition, we described in this Section a further CEMP-sI giant, BS 17436-058, for which spectroscopic data have been analysed by Tsangarides (2005) (PhD Thesis). Similarly to HD 26, the giant HD 206983 studied by Junqueira & Pereira (2001) and Masseron et al. (2010) has metallicity [Fe/H] ∼ −1 and will be discussed in Section 5.   Thompson et al. (2008). ). An initial r-process enrichment of [r/Fe] ini = 0.5 is adopted. log g = 3.7 and 4.1, for primary and secondary, respectively, Thompson et al. 2008), with enhanced lithium (log ǫ (Li) = 2.0 ± 0.2). The abundances of the secondary star are more uncertain, but an s-process enhancement is observed in both stars, with [Pb/Fe] ∼ 2 dex. Theoretical interpretations with AGB models have been widely discussed by Thompson et al. (2008). Satisfactory solutions for the three s-process peaks are found with 1.3 M/M⊙ 2. The close to solar [Na/Fe] agrees with AGB models of initial mass M = 1.3 M⊙, cases ST/9, ST/12, ST/15, and dil = 0.9 dex, as displayed in Fig. 6. A large dilution is applied in order to interpret the mild s-process enhancement observed ([ls/Fe] ∼ 0.5 and [hs/Fe] ∼ 1). However, theoretical interpretations with lower dilution (dil ∼ 0.4 dex) may be obtained by AGB models with M AGB ini ∼ 1.2 M⊙ at the 3 rd pulse (case ST/15). Thompson et al. (2008) conclude that only moderate thermohaline mixing could occur in this star. Indeed, gravitational settling, which involved the star in the first 3 -4 Gyr before the mass accretion of the AGB, offsets the thermohaline efficiency, producing a mean molecular weight (µ) barrier below the convective zone, which confined the thermohaline convection (see also Richard et al. 2002). This is sustained by the high Li observed (log ǫ (Li) = +2.09 ± 0.20), which otherwise would be depleted, because of the higher temperature reached in the inner layers of the star. However, these computations do not include radiative levitation, hence they do not represent the conclusive step of investigations of mixing on the secondary star.

CS 22880-074 (Fig. 7)
This subgiant ([Fe/H] = −1.93, T eff = 5850 K and log g = 3.8) was analysed by Aoki et al. (2002c,d). CS 22880-074 lies in the region of the HR diagram in which the occurrence of the FDU is uncertain. We remind that in very metal-poor stars Na may be affected by strong uncertainties due to non-local thermodynamic equilibrium (NLTE) corrections (Andrievsky et al. 2007;Aoki et al. 2007;Barbuy et al. 2005 and references therein). For this star, the NLTE correction for the Na I D lines decreases the [Na/Fe] abundance by 0.7 dex . We show in Fig. 7

CS 29513-032 (Fig. 8)
This subgiant with [Fe/H ] = −2.08, T eff = 5810 K and log g = 3.3, has been recently studied by Roederer et al. (2010a). The occurrence of the FDU is uncertain in this star. It is a member of a stellar stream identified by Helmi et al. (1999), probably originating from the disruption of a former Milky Way satellite galaxy. Roederer et al. (2010a) studied twelve of these stars, but only CS 29513-032 is s-process enhanced. The authors firstly have hypothesised a contribution from an AGB companion. Despite the presence of a definite, albeit moderate, s-process signature, CS 29513-032 shows [C/Fe] = 0.63 (± 0.2 dex), lower than usually observed in CEMP-s stars. Actually, some authors consider CEMP those stars with [C/Fe] 1, according to the definition of Beers & Christlieb (2005); we include among CEMP all objects with [C/Fe] 0.5. For this mild s-rich star a very large dilution is necessary in order to interpret the observations ([ls/Fe] ∼ 0, [hs/Fe] ∼ 0.5, [Pb/Fe] ∼ 1.6) even for AGB models with low initial mass: already at the 5 th TDU (with M AGB ini = 1.3 M⊙) a dilution of 1.4 dex is needed. Lower dilutions may be obtained at the 2 nd TDU (M AGB ini ∼ 1.2 M⊙; dil = 0.3 dex). This may imply that efficient mixing have taken place in this subgiant (e.g., FDU or thermohaline, gravitational settling; see Section 1). The low observed [Na/Fe] accounts for NLTE corrections. Owing to the large dilution applied, a low [Na/Fe] is also predicted by models with M AGB ini = 1.5 and 2 M⊙. For this star, Na and can not provide constraints on the AGB initial mass and all AGB models in the range 1.3 M/M⊙ 2 may equally fit the observations. In Fig. 8, two solutions are shown, M AGB ini = 1.3 and 1.5 M⊙ models, cases ST/9 and ST/3, dil = 1.4 and 2.4 dex, respectively. We adopt a negative initial [Y/Fe] ini = −0.5, which is compatible with the spread of [Y/Fe] observed in field halo stars (e.g., François et al. 2007)  . The observed [hs/Fe] shows a spread of about 0.6 dex. AGB models with low 13 C-pockets predict a slightly decrease, by increasing the atomic number, of the abundances from Ba to Sm. The observed Ba and Sm are overestimated by models. We consider Ce and Nd (6 and 7 lines detected, respectively) more reliable than La and Sm (2 and 1 lines, respectively) 3 . A dilution of 0.7 dex is applied. AGB models with lower initial mass (M AGB ini 1.5 M⊙) would need dil 0.5 dex, which disagrees with the large mixing occurring in a giant. An upper limit for fluorine is detected by Lucatello et al. (2011) ([F/Fe] < 2.1). AGB models predict higher [F/Fe] abundance (almost at the same order than [C/Fe], see Paper I). Further spectroscopic investigations are desirable in order to constrain theoretical predictions.
2.2.5 CS 30301-015 ( Fig. 10) The spectra of cool giants are highly contaminated by molecular bands. This is the case of CS 30301-015, showing [Fe/H] = −2.64, T eff = 4750 K and log g = 0.8 (Aoki et al. 2002c(Aoki et al. ,d, 2007. The CN molecular bands are too strong for a reliable N abundance determination. The high [Na/Fe] and [Mg/Fe] observed by Aoki et al. (2007) Aoki et al. (2002c), N is very uncertain in this star.
2.2.6 CS 30322-023 ( Fig. 11) The giant CS 30322-023 is the most metal-poor star of the sample ([Fe/H] = −3.5, −3.39 Masseron et al. 2006Masseron et al. , 2010 [Fe/H] = −3.25 Aoki et al. 2007). Due to its low surface gravity (T eff = 4100 K; log g = −0.3) 4 , the hypothesis of an intrinsic AGB star at the beginning of its TP-AGB phase was advanced by Masseron et al. (2006). Aoki et al. (2007) measured T eff = 4300 ± 100 K and log g = 1.0 ± 0.3 dex, supporting instead the binary scenario. The uncertainties of the atmospheric parameters (∆T eff = 250 K and ∆log g = 1.0 dex) is due to the use of LTE instead of NLTE atmospheric models. In fact, the gravities of metal-poor giants derived from LTE iron-line analysis are most probably underestimated by 0.5 up to 1 dex (Thévenin & Idiart 1999;Israelian et al. 2001Israelian et al. , 2004Korn et al. 2003). 5 The condition M AGB ini > 2 M ⊙ comes from the hypothesis of the Hot Bottom Burning process in order to explain [N/Fe] > [C/Fe], while the condition M AGB ini < 4 M ⊙ was adopted by the authors to justify the absence of an r-process overabundance, for which the AGB companion cannot evolve as Type 1.5 Supernova. 6 Note that the observed Na accounts for NLTE and 3D corrections ). −0.6), requiring a negative initial r-process composition of the molecular cloud ([r/Fe] ini = −1). A dil = 2.5 dex means that the mass transferred from the AGB is 300 times lower than the mass of the convective envelope of the secondary star; then, the s-process contribution is very low, and negative values for [Sr,Y/Fe], as well as for r-process elements as [Eu,Gd,Tb,Dy/Fe] are obtained. Otherwise, for dil ∼ 1 dex the negative initial [El/Fe] abundances are overcome by the s-process contribution. Because of the peculiarity of this star, caution in the interpretation of the spectroscopic data is suggested. In fact, due to the very low metallicity, the AGB nucleosynthesis may differ from the canonical scenario due to the occurrence of a proton ingestion episode (see Section 2.1.1).

HE 0202-2204 (Fig. 13)
The giant HE 0202-2204 ([Fe/H] = − 1.98, T eff = 5280 K and log g = 1.65) was studied by Barklem et al. (2005). In No initial r-process enhancement is adopted. This star was discussed in Paper II as representative of the CEMP-s stars (see Fig. 12), and it is reported here for completeness.  Barklem et al. (2005). The [La/Eu] obs is better interpreted by a pure s-process distribution ([r/Fe] ini = 0.0, as shown here); however, the initial rprocess enhancement [r/Fe] ini = 0.5 generally adopted in this paper for CEMP-s stars agrees within the errors with the observations. These models predict  Barklem et al. (2005), who found [hs/ls] = 0.48. We predict [Pb/Fe] th ∼ 1.0 -1.8. No initial r-process enrichment is assumed. The differences [El/Fe] obs−th displayed in the lower panel refer to the AGB model represented with solid line. This star was discussed in Paper II as representative of those CEMP-s stars without Pb detection (see Fig. 14), and it is reported here for completeness. and ST/6 (solid and dashed lines, respectively). Both cases are in agreement with a giant having suffered the FDU because of the high dilutions applied (dil = 0.7 -1.7 dex). These models predict [Pb/Fe] th ∼ 2. With higher s-process efficiencies (case ST) and M AGB ini = 1.5 M⊙ (dil = 0.9 dex), the estimated Pb is very high ([Pb/Fe] th ∼ 3.2): this solution is discarded because [Mg/Fe] would be largely overestimated ([Mg/Fe] th = 0.7). No initial r-process enhancement is adopted in Fig. 13, but an [r/Fe] ini = 0.5, generally assumed for CEMP-s stars, still agrees within the [La/Eu] uncertainty.

HK II 17435-00532 (Fig. 15)
A complete analysis of this mild s-process giant was provided by Roederer et al. (2008) ([Fe/H] = −2.23, T eff = 5200 K and log g = 2.15). They found an unexpected high amount of lithium. So far HK II 17435-00532 does not seem to be member of a binary system. Further radial velocity measurements are required because the observation was done over a time span of about 180 days, which does not permit to discover very long periods. Theoretical interpretations with AGB models have been widely discussed by Roederer et al. (2008). In Fig. 15, we show solutions with M AGB ini = 1.5 M⊙ models. The solid line represents the case ST/12 and dil = 1.8 dex examined by Roederer et al. (2008) (Tsangarides 2005). AGB models with an initial mass from 1.3 to 2 M⊙ (dil = 0.7 -1.6 dex) may equally interpret the observations. Measurement of Na and Mg are highly desirable. In bital axis inclination which does not permit observations of velocity variations (Tsangarides 2005).

CEMP-sII/rII with [r/Fe] ini ∼ 2
We discuss in this Section six stars showing very high s-and r-process enhancements ([hs/Fe] ∼ [Eu/Fe] ∼ 2) interpreted with an initial r-enrichment of the molecular cloud [r/Fe] ini ∼ 2. Five are main-sequence/turnoff stars, CS 22898-027 by Aoki et al. (2002cAoki et al. ( ,d, 2007  This turnoff star ([Fe/H] = −2.26; T eff = 6250 K and log g = 3.7, before the occurrence of the FDU) has been analysed by Preston & Sneden (2001), Aoki et al. (2002c,d), and Aoki et al. (2007).  A theoretical interpretation of the spectroscopic abundances was presented by Sneden, Cowan & Gallino (2008). In Fig. 17, we provide similar solutions with updated models. The observed [Na/Fe] is low while the second s-peak is high ([hs/Fe] 2), as in several main-sequence stars. This agrees with a M AGB ini ∼ 1.3 M⊙ model, ST/12 and no dilution. Three thermal pulses with TDU are shown. They represent a plausible decrease (n4) or increase (n6) in mass of about 0.025 M⊙ for M AGB ini ∼ 1.3 M⊙ models (see Section 2.1.1). An additional TDU corresponds to an increase of the abundances of ∼ 0.2 dex. The model with 4 TDUs seems to better interpret the low [Na/Fe] and [Y/Fe] observed. However, only one line has been detected for Na, while 2 lines for Y (as for Sr and Zr), and both elements agree with theoretical predictions within an uncertainty of 0.2 dex. An initial r-enrichment [r/Fe] ini = 2.0 is adopted in order to interpret the average among Eu, Dy and Er (3, 2 and 4 lines, respectively). By increasing the number of TDUs (M AGB ini = 1.5 or 2 M⊙; case ST/4.5; dil ∼ 1 dex), the observed [Na/Fe] and [ls/Fe] would be overestimated by AGB models. This excludes the possibility that the star underwent efficient mixing during its main-sequence phase.  For the first time in metal-poor stars Bi is detected, with a high overabundance, in agreement with AGB predictions at these low metallicities: stars with a huge amount of lead are also expected to exhibit a high s-process abundance of bismuth. In fact, despite the solar bismuth is mainly produced by the r-process (∼ 80%), at [Fe/H] ∼ −2.6 and for a given 13 C-pocket, the number of neutrons per iron seed is ∼ 400 times higher than solar, directly feeding the third s-process peak (Paper I). Also Nb was detected in this star supporting the binary scenario ([Zr/Nb] ∼ 0; Ivans et al. 2005, see also Paper I). [Na/Fe] is overestimated by AGB models in Fig. 18. We recall that Na may have a large uncertainty (of 0.6 dex or more) due to poorly understood NLTE effects on Na line formation and for 3D atmospheric models. By increasing the AGB initial mass, and therefore the number of TDUs, a dilution factor must be applied in order to reproduce the observed values, but both Na and Mg would be highly overestimated by theoretical models (Bisterzo et al. 2008b). Interpretations with negligible dilutions are compatible with moderate mixing during the main-sequence phase. An initial r-enrichment of 2 dex is assumed. Note that only an upper limit has been detected for Ag and at present we do not adopt initial r-process contributions for isotopes lower than Ba (see Paper II, Section 3). The low [Y/Fe] observed does not agrees with AGB predictions. The hypothesis of We assumed an initial [Cu/Fe] = −0.7, in agreement with unevolved halo stars at this metallicity (see Section 1). This star was discussed in Paper II as representative of the CEMP-s/r stars (see Fig. 15), and is reported here for completeness.
an initial subsolar [Y/Fe] does not change sensibly the final [Y/Fe] prediction, because of the high s-process contribution to Y together with no dilution (Ivans et al. 2005 Kurucz (1995), which, according to Sneden et al. (1996), are rescaled laboratory data from Corliss & Bozman (1962). Tm should be reconsidered with the high-quality gf -values published by Wickliffe & Lawler (1997). A negative [Cu/Fe] is observed, in agreement with unevolved halo stars (see Section 1).  A Na measurement is highly desirable. [Mg/Fe] (0.5 ± 0.24) agrees within the errors with both AGB models, even if the solution with a lower number of TDUs better interprets the observations. [Ba/Fe] obs (with 2 lines detected) is underestimated by models. La (6 lines) and Nd (9 lines) are considered more reliable ([hs/ls] = 1.15). We predict [Pb/Fe] th ∼ 3. An r-process enrichment of [r/Fe] ini = 1.8 dex is adopted.

CEMP
This class includes ten stars showing very high s-process enhancement ([hs/Fe] ∼ 2) and an initial r-enrichment [r/Fe] ini ∼ 1.5. Three are main-sequence stars, CS 29526-110, CS 31062-012 by Aoki et al. (2002cAoki et al. ( ,d, 2007, and SDSS J1349-0229 by Behara et al. (2010). One star is a subgiant having not suffered the FDU, CS 31062-050 by  and Aoki et al. (2007). Five stars are giants, CS 22948-27 and CS 29497-34 by Barbuy et al. (2005) and Aoki et al. (2007), HD 187861 and HD 224959 by Van Eck et al. (2003) and Masseron et al. (2010), LP 625-44 by Aoki et al. (2002aAoki et al. ( ,d, 2006. For the last star CS 22183-015, discrepant atmospheric parameters have been estimated by different authors (Johnson & Bolte 2002;Cohen et al. 2006), and the occurrence of the FDU remains uncertain. The main-sequence star CS 29526-110 was subject to different studies (Aoki et al. 2002c(Aoki et al. ,d, 2007. It is a singlelined binary (Aoki et al. 2002d;Tsangarides 2005), although its period remains unknown. Different effective temperatures are estimated from V−K and B−V (T eff (B − V ) = 6500 K; T eff (V − K) = 6800 K). We report the most recent values by Aoki et al. (2008) Aoki et al. 2002c) is based on two new red lines which are suitable for abundance determination, as well as the two very strong resonance lines previously considered ). The solution shown in Fig. 23 corresponding to the 6 th TDU seems to better interpret the recent s-process measurements by Aoki et al. (2008)  The main-sequence star CS 31062-012 ([Fe/H] = −2.55; T eff = 6250 K; log g = 4.5) has been analysed by Norris et al. (1997), Aoki et al. (2001), Israelian et al. (2001), Aoki et al. (2002cAoki et al. ( ,d, 2007Aoki et al. ( , 2008. CS 31062-012 does not show significant radial velocity variations (Norris et al. 1997;Aoki et al. 2002c), even with the extended period of 6000 days of observation . Despite that, the high [hs/Fe] (∼ 2) and the detection of [Pb/Fe] = 2.4, implies a significant contribution from an AGB companion. Spectroscopic data are interpreted with AGB models of M AGB ini = 1.3 M⊙, case ST/30 and no dilution (Fig. 24). Because of the high [hs/ls] observed (∼ 1.5 dex), the first s-peak is about 0.5 dex lower than theoretical predictions. No improvement may be obtained under the hypothesis of an initial [Sr,Y/Fe] ini = −1, compatible with the spread observed in field stars (e.g., François et al. 2007), because the s-process contribution prevails if no dilution is applied. Moreover, with an initial r-process enhancement of [r/Fe] ini = 1.5, the [hs/ls] ratio does not increase appreciably (Paper II). However, only 2 lines for Sr and 1 line for Y have been detected. The Na measured in 2007 is lower with respect to the value detected in 2008, due to NLTE corrections (∆[Na/Fe]LTE−NLTE 0.7 dex, see Aoki et al. 2007,   . It shows evidence for highly enhanced neutron capture elements, from both s-and r-process contributions. In Fig. 25 Fig. 25 as representative of the hs peak. However, we underline the large discrepancy affecting the elements of the second s-peak and the s-process indicators [hs/ls] = 0.57 and [Pb/hs] = 1.09. We weight the initial r-enhancement on the observed [Eu/Fe], because the other r-elements (Gd, Tb, Dy and Er) are generally affected by larger uncertainties. An initial r-process enrichment of [r/Fe] ini = 1.5 is adopted. However, we underline the enhancement observed in the r-elements as Gd, Tb, Dy and Er with respect to Eu ([e.g., [Er/Eu] ∼ 1). Note that about 60% of solar Hf is produced by the s-process (Arlandini et al. 1999 However, both N and Na are affected by large uncertainties in CEMP-s stars. The present study suggests that no efficient mixing had occurred in this star. Further investigations are strongly desirable for this star. Indeed, serious problems are found in the theoretical intepretation with AGB models of both hs and r-process elements. 3.2.4 CS 31062-050 (Fig. 26) The subgiant CS 31062-050 was examined by Aoki et al. (2002cAoki et al. ( ,d, 2006Aoki et al. ( , 2007 and , ([Fe/H] = −2.42; T eff = 5600 K; log g = 3.0). The occurrence of the FDU is uncertain for this star. Many elements have been observed, among them Os and Ir lines were detected by Aoki et al. (2006) for the first time in CEMP-s stars. Moreover, Aoki et al. (2003) and Tsangarides (2005) found radial velocity variations, confirming the binary scenario. Ba is higher than the other hs elements, even if the result of  is reduced by 0.2 dex according to Aoki et al. (2006), who used two weaker lines, which are less sensitive to hyperfine splitting. CS 31062-050 has been discussed in detail in the review by Käppeler et al. (2011). The low [Na/Fe] (which accounts for NLTE corrections) agrees with a M AGB ini = 1.3 M⊙ model with dil = 0.2 dex (Fig. 26), according to a star before the FDU and in  ] is about 1 dex higher than observed. Despite only one line was detected for Na, which is affected by a high uncertainty because of the severe contamination from interstellar Na absorption, Aoki et al. (2007) excluded [Na/Fe] observations higher than 0.8 dex. Os and Ir, whose r-process fractions in the solar system material are 88% and 98%, respectively (see Paper II), are an important confirmation of the r-process enhancement. The initial r-process enrichment [r/Fe] ini = 1.6 accounts for the observed low [Ir/Fe] with correspondingly lower estimates for [Er,Tm,Yb,Lu/Fe]. The observed [Hf/Fe] is higher than our theoretical prediction. We recall that Hf is mainly produced by the s-process (about 60% of solar Hf, Paper II). Therefore, larger initial r-process enhancements would not affect the [Hf/Fe] prediction. This is the only star among CEMPs and CEMP-s/r with a measurement among the light-relements from Mo to Cs: [Pd/Fe] = 0.98 . About 50% of solar Pd is produced by the s-process (see Paper II, Table 5), while 50% of solar Pd is ascribed to the r-process. An [r/Fe] ini = 1.6 would provide [Pd/Fe] th = 1.4, about 0.4 dex higher than observed. Lower initial light-r-enhancements are assumed in order to interpret Pd, [light-r/Fe] ini = 0.5 -1.0, corresponding to [Pd/Fe] th = 0.8 -1.0, respectively. In Fig. 26, a [light-r/Fe] ini = 0.5 is shown for elements from Mo to Cs. The exact site of nucleosynthesis of the r-process remains still unknown and a possible explanation of this difference comes from the hypothesis of a multiplicity of the r-process contributions (see Paper II, Section 3; Travaglio et al. 2004, Qian & Wasserburg 2008, Sneden et al. 2008. Cu and Al are not produced in AGB stars, as confirmed by the observations. In particular, the negative [Cu/Fe] value is consistent with the observations of unevolved halo stars in the same range of metallicity (see Section 1).
3.2.5 CS 22948-27 (≡ HE 2134-3940), (Fig. 27) Barbuy et al. (1997) and Hill et al. (2000), analysed the spectrum of this cool giant, which is heavily contaminated by CH, CN, and C2 molecular bands. Recently, Barbuy et al. (2005) reviewed this star using high-resolution spectra that permit the detection of lead. Na and Al lines are sensitive to NLTE effects, which decreases the abundance of Na by 0.5 dex and increases the abundance of Al by 0.65 dex (Barbuy et al. 2005). Aoki et al. (2007) confirmed the results by Barbuy et al. (2005), providing updated values for Na and Mg and adopting a slightly higher effective temperature (T eff = 5000 K instead of T eff = 4800 K; log g = 1.8).  (Preston & Sneden 2001). This very cool giant (T eff = 4800 K and log g = 1.8), affected by strong C2 and CH molecular bands, was analysed by Barbuy et al. (1997), Hill et al. (2000),  and Barbuy et al. (2005). Aoki et al. (2007) adopted a slightly higher effective temperature (T eff = 4900 K), confirming the results by Barbuy et al. (2005), and provided updated values for Na and Mg. In Fig. 28 we show theoretical interpretations with M AGB ini = 2 M⊙ (ST/6, ST/9 and ST/12) and dil = 1 dex, in agreement with the observed [hs/ls] = 0.81 and [Pb/hs] = 0.93. The abundances found by the two studies are in agreement within the uncertainties with the exception of Na and Mg, for which Aoki et al. (2007) found 0.4 and 0.5 dex higher values than Barbuy et al. (2005). Aoki et al. (2007) exclude that these discrepancies are due to the small differences in the atmospheric parameters adopted, and highlight the uncertainty of the Na abundance, for which only two very strong lines are available. However, an excess in [Na/Fe] is confirmed by both authors. The enhanced Na observed ([Na/Fe] = 1.37, Aoki et al. 2007) is about 0.2 dex lower than that predicted by the AGB model shown in Fig. 28.  (Barbuy et al. 2005;Aoki et al. 2007). Solutions with AGB models of low initial mass and negligible dilution are excluded for this giant having suffered the FDU. As for CS 22948-27 (see also Paper I; Section 2.2.4), AGB models predict a [F/Fe] lower than the value detected by Lucatello et al. (2011). Further measurement are desirable.

HD 187861 (Fig. 29)
This giant was firstly studied by Vanture (1992b). Subsequently, high-resolution spectra were analysed by Van Eck et al. (2003) and Masseron et al. (2010).  3. An initial r-process enhancement of 1.6 dex is adopted. In Fig. 30, we show theoretical interpretations with AGB models of initial mass 1.5 M⊙ and dil = 1 dex (case ∼ ST/3), compared with both spectroscopic studies (Van Eck et al. 2003;Masseron et al. 2010). Analogous interpretations are obtained by AGB models of initial mass 2 M⊙ (ST/3 and dil = 1 dex). Solutions with initial masses M < 1.5 M⊙ and lower dilutions are discarded, because they would be in contrast with a giant after the FDU. T eff = 5500 K; log g = 2.5) with the High Dispersion Spectrograph (HDS) of the Subaru Telescope, subsequently improved by the detection of upper limits for two r-process elements, Os and Ir ). The binarity was confirmed by radial velocity monitoring (Norris et al. 1997;Aoki et al. 2000), strongly supporting the mass transfer scenario. The period has not been estimated yet, and further measurements of the radial velocity are required to infer orbital parameters for this star.    Fig. 5, bottom panel). Moreover, these models require negligible dilution, in contrast with a giant after the FDU. is 0.6 dex higher. Note that the error bar shown for La accounts for uncertainties due to fitting of synthetic spectra and atmospheric parameters. The [Pb/hs] ratio is low in this star (∼ 0.46 dex), and low 13 C-pockets are needed in order to interpret the s-process distribution. A similar solution is obtained with M AGB ini = 2 M⊙, but the observed [Na/Fe] is slightly higher than AGB prediction. To match the r-process abundances, we adopt an [r/Fe] ini = 1.5 dex. This choice was assessed on the observed [Eu/Fe] (Aoki et al. 2002a, as well as on the recent Yb detection and on the upper limit of Ir ). The observed r-process elements Gd, Er and Tm (7, 6 and 3 lines) are underestimated with the initial r-enhancement assumed in Fig. 31. We underline that four among the neutron capture elements (Y, Ba, Gd, Er) are not interpreted by AGB models. The interpretation of this star remains problematic and further investigations both on spectroscopic and on theoretical point of view are desirable.

HE 0143-0441 (Fig. 33)
This is a main-sequence/turnoff star ([Fe/H] = −2.31; T eff = 6240 K; log g = 3.7), analysed by Cohen et al. (2004Cohen et al. ( , 2006. Only the most recent data by Cohen et al. (2006) are considered here. We present possible theoretical interpretations with AGB models of different initial masses. Two solutions are shown in . This would also provide information about the efficiency of the mixing during the main-sequence phase. An initial r-process enrichment [r/Fe] ini = 1 is adopted. (Fig. 34) This main-sequence star was studied by Behara et al. (2010) with R = 30 000 ([Fe/H] = −2.5; T eff = 6500 K; log g = 4.5 dex). The neutron capture elements are highly enhanced. Large differences are detected among the hs peak elements (e.g., [Ce/La] ∼ 1) and among the r-elements (e.g., [Gd/Eu] ∼ 1.5), similarly to the star SDSS J1349-0229 (Section 3.2.3). We assess the initial r-enhancement by the observed [Eu/Fe], while La is chosen as the most representative among the hs peak. In Fig. 34, SDSS J0912+0216 is inter- preted with a M AGB ini = 1.3 M⊙ model (case ST/18 and dil = 0.6 dex). This star lies on the main-sequence, and the dilution provided by this model suggests that mixing has been efficient during this phase. However, the large spread affecting the hs elements leave this conclusion very uncertain. Solutions with negligible dilutions may be obtained by decreasing the number of TDUs (e.g., M AGB ini = 1.2 M⊙, pulse number 3), but the predicted [Na/Fe] would be 0.3 dex lower than that observed. The detected [La/Eu] ratio needs an initial r-process enhancement of [r/Fe] ini = 1 dex. However, we are not able to interpret the discrepancy observed among Eu and the other r-elements. Similarly, Ru is highly enhanced, at the same level of Gd and Tb. The low [Na/Fe] would exclude models with M AGB ini 1.5 M⊙. Note that by increasing the AGB initial mass and with a proper choice of the 13 C-pocket and dilution factor, we may find theoretical solutions for the high [Ce,Pr/Fe] observed, but several observed elements ([Na, Mg, Sr, Y, Ba, La, Nd, Eu/Fe]) would be overestimated by models. Behara et al. (2010) provide 3D atmospheric model corrections for C and N, which decrease the observations shown in Fig. 34 by 0.5 and 0.67 dex, respectively. Further investigations are strongly desirable for this star, especially in the light of the large discrepancies outlined both among hs and r-elements that can not be explained by AGB models.

HD 209621 (≡ HIP 108953, BD +205071), (Fig. 35)
This giant with [Fe/H] ∼ −1.93 (T eff = 4500 K and log g = 2.0) has been recently observed by Goswami & Aoki (2010). HD 209621 was one of the CH stars analysed by Vanture (1992b) with lower resolution spectra (R = 20 000 instead of 50 000 by Goswami & Aoki 2010 = 2 M⊙ models with a large dilution in agreement with a giant (dil = 0.9 dex) are shown. The low [Na/Fe] is calculated with the resonance doublet Na I D lines at 5890 and 5896Å with a LTE analysis. Lower AGB initial mass and lower dilutions are discarded because in contrast with a giant after the FDU (e.g., a model of M AGB ini = 1.5 M⊙ and ST/15 would imply a dil = 0.6 dex). An [r/Fe] ini = 1 is adopted to interpret the [hs/Eu] ratio. The observed [Er/Fe] is lower than theoretical predictions, but only one line is detected for this element. Note that W, similarly to Hf, is mostly an s-process element (∼ 60% of solar W is produced by the main-s process). Therefore, our theoretical prediction would not be largely affected by higher initial r-process enhancements. However, Goswami & Aoki (2010) explicitly mention a potential overestimation of the [W/Fe] abundance owing to a possible blending. Goswami & Aoki (2010) provided theoretical interpretations with a parametric model, based on the solar system s and r-process isotopic abundances (scaled to the metallicity of the star) of each isotope provided by Arlandini et al. (1999). This method does not account for the dominant contribution to Pb and Bi by the strong component at low metallicities. Indeed, in order to estimate the solar r-process percentage of Pb and Bi, we adopt a Galactic Chemical Evolution model, which accounts for the s-process contribution of all AGB masses and all metallicities (Travaglio et al. 2004, Paper II). (Fig. 36) CS 22887-048, with [Fe/H] = −1.7, was studied by Tsangarides (2005), PhD thesis. This star shows an effective temperature typical of main-sequence/turnoff stars (T eff = 6500 K), while its surface gravity is rather low (log g = 3.35). Johnson et al. (2007) included this star in a sample of metal-poor N-rich candidates. They estimated a metallicity 1 dex lower than Tsangarides (2005) Observations are from Goswami & Aoki (2010). A spread in the ls elements is observed, while [Pb/hs] ∼ 0. For discussions about differences between observed and predicted Na, Y, Er and W see text. An initial r-process enrichment of [r/Fe] ini = 1.0 is adopted. lower than AGB models: a smaller [hs/Fe] th value would be obtained by a lower 13 C-pocket efficiency (e.g. the case ST/3 for M AGB ini = 1.5 M⊙), with a significant decrease in lead ([Pb/Fe] th = 2.7). Note that [La/Eu] = 0.24 would require a higher initial r-process enrichment. Further AGB model constraints may be obtained by detecting Na and additional hs elements.

CEMP-S STARS WITH NO EU MEASUREMENT
In this Section, we analyse CEMP-sII and CEMP-sI stars with no Eu detection. These stars are interpreted by an initial r-process enrichment [r/Fe] ini = 0.5, chosen as representative of the average of [Eu/Fe] observed in halo field stars (see Section 1).
4.1.6 HE 0212-0557 (Fig. 42) This giant HE 0212-0557 ([Fe/H] = −2.27; T eff = 5075 K; log g = 2.15) has been analysed by Cohen et al. (2006). It is a cool star, affected by molecular absorption from CH and CN bands (Cohen et al. 2006). The Na I D line is too strong for a reliable abundance determination. Concerning the ls elements, Zr is not detected, one line is available for Sr, and three lines for Y.

CEMP-sI with no Eu
Eleven stars show mild s-process enhancement ([hs/Fe] < 1.5) for which Eu measurements are not available. Four stars lie before the occurrence of the FDU: HE 0231-4016, HE 0430-4404 and HE 2150-0825 by Barklem et al. (2005), HE 2232-0603 by Cohen et al. (2006). Six stars are giants: BD +04 • 2466 by (Pereira & Drake 2009;Zhang et al. 2009;Ishigaki et al. 2010), HD 189711, HD 198269 andV Ari by Van Eck et al. (2003), HE 1031-0020, HE 1434-1442 by Cohen et al. (2006). Similarly to HD 26 and HD 206983, the giant HE 1152-0355, with [Fe/H] = −1.3 (Goswami et al. 2006), will be discussed in Section 5. (Fig. 43), HE 0430-4404 (Fig. A3) and HE 2150-0825 (Fig. A4) These three stars, analysed by Barklem et al. (2005)  Observations are from Cohen et al. (2006). The first s-peak is very uncertain, because Zr is not measured and only one line is available for Sr. Three lines are detected for Y. An [r/Fe] ini = 0.5 is adopted. 2 M⊙ can equally interpret the spectroscopic observations with a proper 13 Cpocket and dilution. Similar 13 C-pocket efficiencies and dilutions are adopted for HE 0430-4404 and HE 2150-0825 (see Fig. A3 and A4, Appendix A). For these three stars we predict [Pb/Fe] th ∼ 1.6 -2.2. A Na investigation may help to discriminate the AGB initial mass and the efficiency of mixing during the main-sequence phase.

HE 2232-0603 (Fig. 44)
The mild s-process subgiant HE 2232-0603 ([Fe/H] = −1.85; T eff = 5750 K; log g = 3.5, with uncertain FDU) has been analysed by Cohen et al. (2006) firstly identified as a metal-poor star by Bond (1980), and afterwards it was classified as CH star or "metal-deficient barium star" by Luck & Bond (1991). Jorissen et al. (2005) confirm the binary scenario, finding radial velocity variations with a period P = 4593 days. Large dilutions are needed in order to interpret the mild s-process observed ([ls/Fe] = 0.6, [hs/Fe] = 1.2, [Pb/Fe] = 1.9), even using AGB models with low initial mass. In Fig. 45, we show solutions with M AGB ini = 1.3 M⊙, cases ST/6, ST/9, ST/12, and dil = 0.9 dex. Among the hs elements, the observed [Ce/Fe], with 5 detected lines, is about 0.3 dex lower than the AGB predictions. Nd is the most reliable with 12 detected lines. The [Na/Fe] ∼ 0 observed by Ishigaki et al. (2010), would be slightly overestimated by AGB models with higher initial mass, although the s-process elements are equally well interpreted: for instance, M AGB ini = 1.5 M⊙ predicts [Na/Fe] th = 0.3 (case ST/3; dil = 1.8 dex). The observed [C/Fe] is ∼ 0.6 dex lower than the AGB prediction. The low 12 C/ 13 C ratio detected (15 +5 −3 ) confirms that efficient mixing has taken place. The predicted [O/Fe] is ∼ 0.5 dex higher than observed. Note that the uncertainty shown for [O/Fe] in Fig. 45, may be underestimated, because C, N, and O measured by Pereira & Drake (2009) are interdependent. (Fig. 46) The mild s-process enhanced giant HD 198269, with [Fe/H] ∼ −2.2, T eff = 4800 K and log g = 1.3, has been studied by Van Eck et al. (2003). Only Zr is measured among the ls elements, while the hs peak is better determined with La, Ce, Nd and Sm ([hs/ls] = 0.94). One line is detected for Pb ([Pb/hs] = 1.07). As said by the authors, the derived abundances may be uncertain owing to the presence of molecular We analyse these two mild s-process enhanced stars together, because they show similar s-process distributions ([hs/ls] ∼ 0.2; [Pb/hs] ∼ −0.3). As said before, the abundances by Van Eck et al. (2003) are uncertain because only few lines are available in a very crowded region of the spectrum, veiled by molecular lines. The difficulties increase for the coolest stars, as the giants HD 189711 ([Fe/H] ∼ −1.8; T eff = 3500 K; log g = 0.5) and V Ari ([Fe/H] ∼ −2.4; T eff = 3580 K; log g = −0.2), for which the abundance determination represent a real challenge for the spectroscopists, and the errors are of the order of ± 0.4 dex. Caution is suggested for these stars. An attempt to interpret the [El/Fe] observations is given in Figs. A1 and A2 (Appendix A). Very low s-process efficiencies are adopted (ST/24 and ST/30), in order to obtain [Pb/hs] ∼ −0.42 and −0.22, respectively. For HD 189711, Kipper et al. (1996) measured [Eu/Fe] = 1.45, which may suggest a possible initial r-process enhancement. However, the metallicities detected by Van Eck et al. (2003) and Kipper et al. (1996) are discrepant ([Fe/H] = −1.8 and −1.15, respectively), and further Eu investigations are desirable in this star. 4.2.6 HE 1031-0020 (Fig. 47) The giant HE 1031-0020 is one of the coolest stars analysed by Cohen et al. (2006), ([Fe/H] = −2.86; T eff = 5080 K; log g = 2.2). It is affected by molecular absorption from CH and CN bands, and the metallicity is probably underestimated. The Na I D line is too strong and no reliable abundance can be obtained. A large uncertainty is reported by Cohen et al. (2006) for Ti (±0.4 dex) with 15 detected lines.

HD 198269
The detection of Mg is, in general, accurate, with an uncertainty of about ± 0.2 dex. Caution is suggested by Cohen et al. (2006)  = 2 M⊙ a dil = 1.6 dex is adopted (dotted line). A case ST/5 is needed for both models. AGBs with lower initial mass may equally interpret the spectroscopic data: M AGB ini = 1.3 M⊙, case ST/15 and dil = 0.8 dex, in agreement with a giant after the FDU. Among the hs elements, a difference of about 0.5 dex is observed between La and Nd (four lines detected for both elements). This discrepancy contrasts with AGB predictions. In Fig. 47 we consider La as more reliable among the hs elements. With a proper choice of the 13 C-pocket and dilution factor, we may find theoretical solutions for the ob-  4.2.7 HE 1434-1442 (Fig. 48) The giant HE 1434-1442 has [Fe/H] = −2.39, T eff = 5420 K and log g = 3.15 (Cohen et al. 2006). As other stars studied by Cohen et al. (2006), it is affected by molecular absorption from CH and CN bands. A limited number of s elements is observed: Ba (three lines), Y and Nd (two lines), and Pb (one line). 1.4 M⊙ models. However, Na is explicitly mentioned by the authors as very uncertain for this cool star. C and N are not very reliable, because no error bars are provided by Cohen et al. (2006). s-process elements. All these stars show enhanced [C/Fe] and s-process elements. Their metallicity is close to disc stars and their atmospheric parameters are far from the TP-AGB phase. These stars may be considered as a link between CEMP-s and s-rich giants or dwarfs of disc metallicity (e.g., barium stars 12 , CH stars, MS/S stars with no Tc, symbiotic stars), because the carbon and s-enrichment on their surface is commonly ascribed to a binary scenario with mass transfer by stellar winds. Some of these stars are not CH stars, and, starting from Luck & Bond (1991), they have been classified as "metal-poor barium stars".

HD 26 (Fig. 49)
Vanture (1992,b) studied for the first time HD 26, deriving spectroscopic abundances for C, N, O, and heavier elements. They classified this giant as a CH star. Later on, Van Eck et al. (2003) and Masseron et al. (2010) reported spectroscopic observations obtained with high-resolution spectra. We discuss here only these most recent values. A model constraint is given by the occurrence of the FDU (T eff = 5170 K and log g = 2.2 by Van Eck et al. 2003; T eff = 4900 K and log g = 1.5 by Masseron et al. 2010), which requires a dilution of the order of 1 dex. The abundances by Van Eck et al. (2003) are uncertain because only few lines veiled by molecular bands are available; they refer to Ce as 12 Barium stars are giants (and dwarfs) showing Ba and Sr overabundances by the presence of singly ionised barium, Ba II, at λ = 4554Å and Sr II (λ = 4077Å, λ = 4215Å), as well as CH G band and CN bands also enhanced (Allen & Barbuy 2006;Smiljanic et al. 2007). Values of [Pb/Fe] > 1 dex have been observed for the first time in barium stars by Allen & Barbuy (2006), explained with efficient 13 C-pockets in the AGB companion. Theoretical interpretations of barium stars have been discussed by Husti et al. (2008Husti et al. ( , 2009). the most reliable element among the hs-peak. Besides five neutron capture elements (Zr, La, Ce, Nd, and Sm), they detected the Pb I line at 4057.812Å, clearly resolved thanks to the high-resolution R = λ/∆λ = 135 000. Masseron et al. (2010) provided new observations for C, N, O, Mg, and Eu, as well as updated results for Ba, La, Ce, and Pb ([hs/ls] = 0.5; [Pb/hs] = 0.7). In Fig. 49 we show theoretical interpretations with AGB models of M AGB ini = 1.5 M⊙, cases ST/1.5, ST/2, ST/2.5, and dil = 1 dex. Similar solutions are obtained with higher AGB initial masses (e.g., M AGB ini = 2 M⊙). No initial r-process enhancement is adopted for this star. The observed [Mg/Fe] is higher than the AGB predictions. The observations by Masseron et al. (2010) shown in Fig. 49 will be discussed by the authors in Masseron et al., in preparation. 5.2 HD 206983 (Fig. 50) This giant (T eff ∼ 4200 K, log g = 0.6) has been analysed by Masseron et al. (2010), Drake & Pereira (2008) (who studied C, N, O), and Junqueira & Pereira (2001). In Fig. 50, we show theoretical interpretations using AGB models of initial masses M = 1.3 and 1.5 M⊙, case ST, dil = 0.7 and 1.6 dex, respectively. We considered Y (seven detected lines) more reliable than Zr (four lines available), (Junqueira & Pereira 2001). Discrepant [C/Fe] and [O/Fe] ratios are found by Drake & Pereira (2008) and Masseron et al. (2010): note that Drake & Pereira (2008) adopted the stellar parameters obtained by Junqueira & Pereira (2001), which provided a metallicity 0.4 dex lower than [Fe/H] = −0.99 by Masseron et al. (2010). In Fig. 50, we display solutions with AGB models of [Fe/H] th = −1, which agree with [C/Fe] detected by Masseron et al. (2010). Instead, the observed [N/Fe] is about 0.7 dex higher than AGB predictions. Note that, by decreasing metallicity, a larger primary amount of [C/Fe] is predicted. C and N are also affected by uncertainty in 3D atmosphere models that may decrease the observations   Goswami et al. (2006) could not estimate Na for the highly blended lines present in the spectra. A possible interpretation is shown in Fig. 51

CS 29503-010
This main-sequence star (T eff ∼ 6500 K and log g = 4.5; [Fe/H] = −1.06) has only Ba detected among the s-elements, with [Ba/Fe] = 1.5. AGB models with initial mass in the range 1.3 M/M⊙ 2 may equally interpret the observations, by adopting different 13 C-pockets and dilutions. However, at present, this star seems not to belong to binary system (Tsangarides 2005), and further spectroscopic investigations are desirable.

HE 0507-1653
Only barium among the s-process elements is measured for this giant with T eff ∼ 5000 K and log g = 2.4 ([Fe/H] = −1.38, −1.42; Aoki et al. 2007;.  detected C and N, in agreement with previous results by Aoki et al. (2007). Due to the limited number of spectroscopic observations, a range higher than 1 dex may be predicted for the ls peak and Pb.

EFFECT OF 22 NE, 12 C AND 1O AT LOW METALLICITY
The aim of this Section is to provide a more detailed discussion about the impact of the 22 Ne(n, γ) 23 Ne reaction, both as neutron poison and as neutron seed, and about the effect of the 12 C(n, γ) 13 C and 16 O(n, γ) 17 O reactions as neutron poisons. Additional tests with respect to Paper I (see Section 4 and Appendix C) are presented, by changing the AGB initial mass and the 13 C-pocket. The s-process distribution observed in several stars can be interpreted by AGB models with different initial masses and a proper choice of the 13 C-pocket. In particular, at [Fe/H] ∼ −2.5, comparable [hs/ls] and [Pb/hs] are obtained with M = 1.3 M⊙ model and ∼ST/12 or M = 1.5 M⊙ and case ∼ST/3. This is mainly due to the large amount of primary 22 Ne at low metallicities, which acts both as neutron poison and as neutron seed. In addition to 22 Ne, neutron poisons by primary 12 C and 16 O also affect the s-process abundances. This result highlights the importance of a study focused on the production of the light elements, the reactions involved and their uncertainties, as well as their effects on the s-process path.

22 Ne
At low metallicities, 22 Ne has two effects: it acts both as neutron seed and as neutron poison. The first effect leads to a production of 56 Fe by neutron captures on 22 Ne; then, 56 Fe becomes seed for the nucleosynthesis of the s-elements. Therefore, both iron seeds and the number of neutrons released change. Concerning the effect of 22 Ne as neutron seed, we report in Fig. 52, left panel, a comparison of the envelope abundances for an AGB model of M = 1.5 M⊙ at [Fe/H] = −2.6 and a case ST/3 (red solid line), with a test case in which we set to zero the initial abundances of all isotopes from 56 Fe to 209 Bi (blue dotted line). Owing to the abundant primary 22 Ne, the 22 Ne(n, γ) 23 Ne reaction drives a neutron chain that extends up to 56 Fe and beyond, producing a large amount of s-elements. A similar effect is obtained for an AGB model of initial mass M = 1.3 M⊙ and case ST/12 (Fig. 52,right panel). Concerning the effect of neutron poison, we made additional tests by setting to zero the 22 Ne(n, γ) 23 Ne reaction. We report in Fig. 53, the results of AGB models of M = 1.5 M⊙ (20 TDUs) at [Fe/H] = −2.6 (red solid lines), compared with a test case in which the 22 Ne(n, γ) 23 Ne channel is set to zero (blue dotted lines). Two 13 C-pockets are considered: ST/12 (left panel) and ST/3 (right panel). By excluding the 22 Ne(n, γ) 23 Ne channel, the production of the three s-process peaks in general increases. When a case ST/3 is adopted, major effects are observed for the ls elements, while the hs peak is almost unchanged; for case ST/12, the effect on Pb is large. For AGB models with M = 1.4 M⊙ (10 TDUs) we obtain results similar to M = 1.5 M⊙ models. For AGB models of initial mass M = 1.3 M⊙, the effect of the 22 Ne(n, γ) 23 Ne reaction is marginal owing to the limited number of thermal pulses (5 TDUs). For AGB models with M ∼ 1.35 M⊙ at the 6 th and 7 th TDU, we obtain results similar to M = 1.3 M⊙ models.

SUMMARY AND CONCLUSIONS
We have presented a detailed discussion of 94 CEMP-s and CEMP-s/r stars collected from the literature. This paper is strictly related to Paper II, in which we provided a general description of the sample and the main results obtained. The theoretical interpretation of CEMP-s/r stars is still largely debated, because the s and r-processes are ascribed to different physical environments. We remind the hypothesis adopted here and described in Paper II: we assumed an initial r-process enhancement in the molecular cloud from which the binary system formed, followed by s-process nucleosynthesis during the TP-AGB phase.
In the analysis we followed the star classification provided in Paper II. We considered all single species, the number of lines detected and the error bars determined by the authors, with particular attention to the three s-process peaks, ls, hs and Pb. For each star, AGB models that better interpret the observations have exhaustively discussed (a summary of the results has already been presented in Paper II, Tables 10 and 11). We considered separately those stars for which a limited number of observations among the s-process elements are available (Appendix A). Five stars with [Fe/H] > −1.5 were discussed in a separate Section: HD 206983, HD 26 and HE 1152-0355, as well as CS 29503-010 and HE 0507-1653, which have a limited number of s-element observations. Note that some CEMP-s stars analysed here were previously classified as CH stars (e.g., Van Eck et al. 2003). As firstly suggested by McClure (1990) and Luck & Bond (1991), these objects, showing strong features of CN and CH bands as well as high s-process abundances, may be considered a link between barium stars (with disk metallicity) and CEMP-s stars (with halo metallicity). Indeed, they all belong to binary systems with mass transfer from the most evolved companion having already undergone the TP-AGB phase.
As discussed in Paper II, interpretations of spectroscopic data are obtained for AGB initial masses in the range M ∼ 1.3 to 2 M⊙, provided that different dilutions and 13 Cpocket strengths are chosen. The AGB initial mass is mainly defined by the occurrence of the FDU (which implies a dilution of at least 1 dex) and by the observed [Na/Fe] (and [Mg/Fe]). Major information on the efficiency of the 13 Cpocket is provided by both [hs/ls] and [Pb/hs]. For a given metallicity, a range of 13 C-pocket strengths is required in order to interpret observations of CEMP-s and CEMP-s/r stars: for models with M AGB ini ∼ 1.3 M⊙, 13 C-pockets close to case ST/12 (with a range from cases ST/6 to ST/15) are needed, while for M AGB ini ∼ 1.5 M⊙, 13 C-pockets close to case ST/3 (with a range from cases ST/2 to ST/12) 13 are required (see Section 6). However, as highlighted in this study, such a classification is only indicative. Indeed, the analysis of individual stars provided in this paper is necessary in order to point out the peculiar characteristics of each star. For instance, several stars do not have Na or Pb detected, which are useful to constrain the AGB initial mass or the models including rotation, magnetic fields or gravity waves) are object of study (Herwig et al. 1997;Langer et al. 1999;Herwig et al. 2003;Denissenkov & Tout 2003;Siess et al. 2004;Straniero et al. 2006;Cristallo et al. 2009a 1.3 M⊙). On the other side, two stars among the sample show an extremely large s-process enhancement ([ls/Fe] ∼ 2 and [hs/Fe] ∼ 3), about 1 dex higher than the average of the CEMP-sII (or CEMP-sII/r) stars: CS 29528-028 and SDSS 1707+58. Both stars can only be interpreted by AGB models with initial mass M = 2 M⊙, which undergo a larger number of TDUs. Further investigations are strongly suggested, especially for SDSS 1707+58, which has a limited number of observations available. Among the sample listed in Table 1 (in which stars with a large number of observations are reported), 17 stars lie on the main-sequence/turnoff. The degree of dilution obtained for these stars may provide information on the effect of mixing as thermohaline, gravitational settlings and radiative levitation. We find that ten of them (CS 22881-036, CS 22898-027, CS 29497-030, CS 29526-110, CS 29528-028, CS 31062-012, HE 0338-3945, HE 2148-1247, SDSS 0216+06, SDSSJ1349-0229) have only one theoretical interpretation with negligible dilution, from which we may hypothesise that low mixing had occurred. Three stars (HE 0143-0441, HE 0430-4404, HE 1152+0027) may have different theoretical interpretations with different AGB initial masses (in the range of 1.2 -2 M⊙). For each star, a solution with dil = 0.0 dex may be found: HE 0143-0441 and HE 1152+0027 with M = 1.3 M⊙; HE 0430-4404 with M = 1.2 M⊙. Higher dilutions can be found with higher initial masses. Two stars, CS 22887-048 and BS 16080-175, were analysed by Tsangarides (2005), PhD Thesis. CS 22887-048 has solutions with different AGB models, but with low or negligible dilution: M = 1.4 M⊙ and dil = 0 dex, M = 1.5 or 2 M⊙ and dil = 0.3 dex. Tsangarides (2005) estimated a metallicity 1 dex higher than Johnson et al. (2007). A more detailed analysis is desirable. The main goal of this paper is to present a detailed study of spectroscopic observations star by star, through an analysis of the AGB models presented in Paper I and II. In general, we found possible agreements between theoretical predictions and spectroscopic data. The major discrepancies are summarised here below. This aims to provide potential indications for future studies, also of spectroscopic nature, and suggests important starting points of yet unsolved issues. One of the main problems concerns C and N. As highlighted in Paper II (Section 5.3), the observed [C/Fe], [N/Fe] and the carbon isotopic ratio 12 C/ 13 C can not be interpreted by AGB models. Large uncertainties are present in both spectroscopic (NLTE and 3D atmospheric models; Collet et al. 2007Collet et al. , 2009Grevesse et al. 2007;Asplund et al. 2009;Caffau et al. 2009;Frebel & Norris 2011) and AGB models, as extra-mixing processes (CBP), thermohaline, or rotation and magnetic fields which may induce the mixing Stancliffe 2010;Charbonnel & Lagarde 2010). The hypothesis of the CBP, in order to reconcile theoretical predictions and observations in stars (or SiC presolar grains), has been remarked by different authors (Nollett et al. 2003;Domínguez et al. 2004a,b;Cristallo et al. 2007;Busso et al. 2010;Palmerini et al. 2011). The effects of the CBP on 12 C and 14 N cannot be exactly quantified by models and the physical processes involved are not clear yet. In several CEMP-s stars the predicted [C/Fe] is much higher than reported by spectroscopic observations. The contemporary measurement of a very low 12 C/ 13 C ratio observed, in the typical range 4 to 10, indicates the impact of a strong extra-mixing, which have not been included in our AGB models nor in our treatment of the envelope of the observed low mass star after mass accretion by the more massive AGB companion. This will imply a concomitant reduction of the expected [C/Fe] and 12 C/ 13 C ratio, but at the same time a strong increase of the predicted [N/Fe]. In several cases one would expect CEMP-s stars to be even more N-rich than C-rich. A discussion of this issue is deferred to further work (Bisterzo et al., in preparation). An additional process that may increase 13 C and 14 N is the proton ingestion episode occurring in low mass AGBs of low metallicity (see Section 2.1.1). Among the light elements, also fluorine is largely produced by AGB models, while recent spectroscopic determinations in CEMP-s stars provide [F/Fe] about 1 dex (or more) lower than theoretical predictions (Lucatello et al. 2011). Note that recently, Palmerini et al. (2011) studied the effect of extra-mixing in AGB stars on the light-elements, suggesting a possible decrease of [F/Fe] at low metallicities. However, further studies both on the theoretical and spectroscopic point of view are strongly desirable. Another discrepancy concerns the elements belonging to the ls and hs peaks. AGB models predict (within 0.3 dex) similar abundances for the first s-peak (Sr, Y, and Zr) and for the second s-peak (for Ba, La, Ce, Pr and Nd), (with a slightly increasing or decreasing trend of [El/Fe] with atomic number depending on the 13 C-pocket, see Paper I, Appendix B). This is strongly supported by the reliable neutron cross section measurements and solar abundances in the ls and hs regions. Instead, some CEMP-s stars show an internal spread among ls and hs elements greater than 0.5 dex. In several stars the observed [Ba/Fe] is higher than the average of [hs/Fe] (e.g., HD 26, CS 30301-015, HE 0143-0441, HE 0336+0113, LP 625-44); the most evident example is CS 31062-050 , where [Ba/Fe] is about 0.5 dex higher than the other hs elements (Section 3.2.4). In general, Sr is more uncertain than other ls elements, with a limited number of lines detected. In our analysis, we exclude Sr from the ls elements and Ba from the hs peak, which are mainly affected by higher spectroscopic uncertainties (Busso et al. 1995) due to NLTE effects (Andrievsky et al. 2009(Andrievsky et al. , 2011Mashonkina et al. 2008;Short & Hauschildt 2006) . This may be due to non homogeneous or incomplete mixing of the gas in the Galactic halo or to a multiplicity of primary r-process components (see Travaglio et al. 2004, Qian & Wasserburg 2008, Sneden et al. 2008. Therefore, the hypothesis of an extreme initial deficiency of Sr, Y and Zr in the molecular cloud seems plausible. In some CEMP-s stars, we assumed an [Sr,Y,Zr/Fe] ini (or one of them) = −1, in order to interpret the observations (e.g., the CEMP-sI star CS 30322-023 by Masseron et al. 2006 and CS 29513-032 by Roederer et al. 2010a). However, in general, the s-process contribution is large and overcomes initial deficient compositions (e.g., CS CS29497-030 by Ivans et al. 2005 or CS 31062-012 Aoki et al. 2002dAoki et al. , 2007Aoki et al. , 2008. Then, the discrepancy within the ls elements remains an open problem. From the theoretical point of view, the nucleosynthesis of the ls elements is highly debated. Specifically, a primary contribution of about 20% to solar Sr, Y and Zr (lighter element primary process, LEPP Travaglio et al. 2004) has been hypothesised in order to interpret the observations of [Sr,Y,Zr/Fe] versus [Fe/H] in of Galactic metal-poor stars 15 . However, the exact contribution from this primary process to individual ls elements is not well established and its origin is still under investigation (e.g., Montes et al. 2007; see also the recent Arcones & Montes 2011 and references therein). Among CEMP-s/r stars, five stars (CS 22898027, CS 29497030, HE 03383945, HE 1305+0007 and HE 21481247) require the highest r-enhancement [r/Fe] ini = 2.0, with an observed [La/Eu] ∼ 0, together with [La/Fe] ∼ 2. As discussed in Paper II (Section 3), the hypothesis of an initial r-process enhancement is adopted in the region between Ba and Bi. Indeed, observations of elements between Mo and Cs 15 Galactic Chemical Evolution models (Travaglio et al. 2004;Serminato et al. 2009), that account for the main and strong sprocess in low and intermediate mass AGB stars of different stellar populations, predict s contributions of ∼ 64%, ∼ 67%, and ∼ 60% to solar Sr, Y, and Zr, respectively. The weak-s process in massive stars is estimated to contribute to ∼ 9% to solar Sr, ∼ 10% to solar Y, and ∼ 0% to solar Zr. The r-process contribution is ∼ 12%, 8% and 15% for solar Sr, Y and Zr, respectively. are lacking. For neutron-capture elements lighter than Ba, different initial r-process enrichment could be introduced under the assumption of a multiplicity of r-process components (Sneden et al. 2003a). Only  detected Pd for CS 31062-050. About 50% of solar Pd is produced by the s-process (see Paper II, Table 5); the remaining 50% is ascribed to the r-process. The [r/Fe] ini = 1.6, adopted in order to interpret the observed r-elements from Eu to Ir, would overestimate the [Pd/Fe] obs by ∼ 1 dex. Lower initial light-r-enhancements [light-r/Fe] ini ∼ 0.5 -1.0 are assumed (Section 3.2.4), likely confirming a multiplicity of the r-processes. This is the only reliable detection among the elements included between Mo and Cs in CEMP-s or CEMP-s/r stars. The upper limits for Ag in CS 29497-030 (Ivans et al. 2005) and HE 0338-3945 (Jonsell et al. 2006) do not provide significant constraints. When allowed, further investigations on the light-r elements are desirable. Behara et al. (2010) detected a very enhanced Ru in the main-sequence star SDSS J0912+0216 ([Ru/Fe] = 2.6). Even if no error bar is provided by the authors, the Ru observed in this star seems to agree with some among the heavy-r process elements, as Gd and Tb. The abundances observed in SDSS J0912+0216 are peculiar, both for s-and r-process elements: indeed, in addition to the already mentioned large spread among the hs peak, this star shows a large spread among the r-elements (e.g., [Gd/Eu] ∼ 1.5). A similar behaviour is found in SDSS J13490229, studied by the same authors. The spread is confirmed in both stars, and highlights a crucial problem from the point of view of the theoretical interpretation. Other three stars show discrepancies of about 0.5 dex between observed and predicted r-elements: CS 31062-050 (Er, Yb, Lu), LP 625-44 (Gd, Er) and HE 0338-3945 (Dy, Tm). These stars may be considered important starting point for future studies. In general, further investigations on the r-elements in CEMP-s and CEMP-s/r stars would be strongly useful.
We recall that the theoretical interpretations presented here are thought as test for AGB models, obtained with post-process nucleosynthesis models based on old FRANEC models (Gallino et al. 1998;Straniero et al. 2003). A new generation of FRANEC code is developing. These new full evolutionary models account for new opacities, updated reaction rates, a mixing algorithm to obtain the 13 C-pocket, a new evaluation of the mass loss rate based on the observed correlation with the pulsational period Cristallo et al. 2009bCristallo et al. ,a, 2011. Future investigations are planned in order to update our predictions accounting for low metallicity fully FRANEC models, once a whole spectrum of masses and metallicities will be completed. Table 3. Summary of theoretical interpretations for six CEMP-s and CEMP-s/r stars that need low 13 C-pocket efficiencies ( case ST/24). The AGB initial mass, 13 C-pocket, dilution factor, and initial r-enhancement are reported. Asterisks in column 9 indicate that no Eu has been observed. The Figure number associated to the theoretical interpretation is given in column 10.

Star
Ref.
[   Table 3) The number of elements detected for the stars discussed in Sections 2 and 3 provide important constraints for AGB models. Unfortunately, many CEMP-s stars have a limited number of s-process elements available. For instance, only Ba is detected in nineteen stars Cohen et al. 2006); for other stars, Sr among the ls and Ba among the hs elements are measured. Possible solutions have been provided in Paper II, Table 11. These theoretical interpretations have to be considered as indicative examples, because many AGB models may interpret the observations as well.

A2 CEMP-sII
Three main-sequence stars with a limited number of data belong to this group: HE 0024-2523 by Lucatello et al. (2003), CS 22967-07 and CS 30323-107 by , for which a very low upper limit is reported for Eu, excluding high initial r-process enhancements.  Gratton et al. (1999). The lines of C, N, Eu, La, and Pb were derived from spectral synthesis, because they are very weak or somewhat blended with nearby lines of other species (Lucatello et al. 2003). Only Sr with two lines is detected among the ls elements, while for Y and Zr upper limits are provided. The authors estimated an uncertainty of 0.1 dex for Pb because hyperfine structure and isotopic splitting were not included in the analysis. Fig. A5 shows possible theoretical interpretations with AGB models of initial mass M AGB ini = 1.3 M⊙, case ST/9 and no dilution. No initial r-process enrichment is necessary to interpret the observed [La/Eu] 0.7. For higher initial masses (M AGB ini = 1.5 -2 M⊙) dilutions higher than 1 dex are necessary. With these models, Mg and the neutron capture elements Ba, La and Pb would be equally fitted, while the observed [Na/Fe] approaches to the solution with M AGB ini = 1.3 M⊙. The low carbon isotopic ratio 12 C/ 13 C = 6 ± 1 sustains the hypothesis of efficient mixing.

A3 CEMP-sI
In this Section we describe three giants, CS 29495-42 by , HE 1001-0243 and HE 1419-1324 by Masseron et al. (2010), without observations of ls elements, and one star with uncertain occurrence of the FDU, CS 30315-91 ).

A3.1 CS 29495-42
CS 29495-42 is classified as a CEMP-sI star, with [Sr/Fe] = 0.2, [La/Fe] = 1.3 and [Pb/Fe] = 1.3. As observed in other stars, Ba (three lines) is about 0.5 dex higher than La and Ce (three and two lines, respectively). This star has T eff = 5544 K and log g = 3.4 , ([Fe/H] = −1.88). The occurrence of the FDU is uncertain in this star. Recently, Johnson et al. (2007) obtained T eff = 5400 K and log g = 3.3 with low resolution spectra, surely after the occurrence of the FDU. Solutions are found with AGB models of initial mass 1.3 M⊙ and dil = 0.9 dex. A low 13 C-pocket is needed to interpret the negative [Pb/hs] (ST/18), but the observed [Sr/Fe] (one detected line) is overestimated by the models. Higher 13 C-pockets agree with the observed [hs/Sr], but the predicted [Pb/Fe] would be higher than observed. The [Na/Fe] prediction may be considered in agreement with the observed value within an uncertainty of 0.2 dex. AGB models with higher initial mass would overestimate the observed [Na/Fe] and [Sr/Fe].
A3.2 HE 1001-0243 and HE 1419-1324 (Fig.s A6, A7) These two newly discovered giants have been recently studied by Masseron et al. (2010). Unfortunately no ls elements have been published so far. Observations by Masseron et al. (2010) will be discussed by the authors in a forthcoming paper. Both stars are giants with very low metallicity: HE 1001-0243 has [Fe/H] = −2.88, T eff = 5000 K and log g = 2.0, while HE 1419-1324 shows [Fe/H] = −3.05, T eff = 4900 K and log g = 1.8. For HE 1001-0243 the hs elements are very low ([hs/Fe] = 0.6) and only an upper limit for Pb is measured, but HE 1419-1324 shows high lead ([Pb/Fe] = 2.15; [Pb/hs] = 1.31) in accordance with an efficient s-process. We present here possible theoretical interpretations in Figs. A6 and A7.
AGB models with higher initial mass (M AGB ini = 1.5 and 2 M⊙) agree with the observed [Na/Fe] ∼ 0. No initial r-process enrichment is needed in order to interpret the observed [La/Eu] < 0.89.
A4 CEMP-sII/rII with [r/Fe] ini ∼ 1.5 The turnoff star HE 0131-3953 observed by Barklem et al. (2005), with a limited number of spectroscopic data among the ls elements (only Sr with one detected line), may belong to this group due to the high s-and r-process enhancement. For the giant CS 22891-171 by Masseron et al. (2010) no observations are available among the ls elements, but the authors detected Ba, La, Ce and Eu, adding this star to the CEMP-sII/rII class. The giant CS 30338-089 has been detected by  and by Aoki et al. (2007), with discrepant metallicities (∆[Fe/H] ∼ 0.7 dex).  found a high Eu enhancement, not confirmed by Aoki et al. (2007), who detected only Ba and Na. At the state of the art this star belongs to CEMP-sII/rII, but further measurements are needed. uncertain because it depends strictly on the ls elements, for which only Sr is observed. At this state, we predict [Pb/Fe] th ∼ 3. An initial r-process enrichment of [r/Fe] ini = 1.5 is needed in order to predict [La/Eu] = 0.3.
A4.2 CS 22891-171 (Fig. A9) The giant CS 22891-171 ([Fe/H] = −2.25; T eff = 5100 K; log g = 1.6) has been analysed by Masseron et al. (2010). No ls elements have been detected, while the observed [Pb/hs] ∼ 0 suggests a low s-process efficiency. In Fig. A9 we provide a possible theoretical interpretation with an AGB model of initial mass M = 2 M⊙ and a very low 13 C-pocket efficiency (case ST/45). High [hs/Fe] ( 2 dex), together with a low [Pb/hs] ratio ( 0), can not be obtained by AGB models with low initial mass (M AGB ini = 1.3 -1.4 M⊙), which undergo a lower number of thermal pulses with TDU. Even for the case shown in Fig. A9 a low dilution is applied, dil = 0.3 dex, hardly compatible with a giant having suffered the FDU. The low upper limit for oxygen is about 1 dex lower than the predictions. No satisfactory theoretical interpretations may be found for the observed C, N and O. However, we highlight that in CEMP stars these light elements are affected by large uncertainties. A high initial r-process enhancement [r/Fe] ini = 1.8 is required to explain the the observed [La/Eu] ratio (∼ 0.4). For a further discussion of this star, Masseron et al. (2010) refer to a paper in preparation.

A4.3 CS 30338-089
For this giant, discrepant metallicities have been detected by Aoki et al. (2007)    found lower [Fe/H] ratios also for other stars compared to other authors. This may be due to a systematic effect. The high [Eu/Fe] detected by  classifies this star as a possible CEMP-sII/r, but further investigations are desirable. We considered here the spectroscopic data by Aoki et al. (2007). The occurrence of the FDU (T eff = 5000 K and log g = 2.1) together with a high s-process enhancement, would exclude solutions with AGB models of M AGB ini = 1.3 M⊙. Indeed, the large mixing occurring during the FDU are simulated by a large dilution, which can not be applied if the AGB undergoes a limited number of TDUs. Possible solutions are listed in Paper II, Table 11, for M AGB ini = 1.5 and 2 M⊙ with dil = 0.5 dex (case ST/2). However, these models disagree with the low observed [Na/Fe] (∼ 0.46).

A5.2 Ten CEMP-sII giants
Ten giants studied by Aoki et al. (2007) (HE 0206-1916, HE 0400-2030, HE 1157-0518, HE 1319-1935, HE 1429-0551, HE 1447+0102, HE 1523-1155, HE 1528-0409, HE 2221-0453, HE 2228 are briefly discussed here. All stars have [Fe/H] −2.0, with the exception of HE 0400-2030 ([Fe/H] = −1.73). Among the s-process elements only barium has been measured. Due to the barium uncertainty, a range higher than 1 dex may be predicted for the ls peak and for lead. The only indication about the AGB initial mass may come from Na. However, we underline the spectroscopic uncertainties which affects Na via NLTE and 3D corrections. As for similar cases, further studies are required because presently several AGB masses may equally fit the observations by changing the 13 C-pocket and the dilution. A constraint derives from the occurrence of the FDU, for which a dilution of about 1 dex is needed. All these stars are giants, with the exception of HE 0400-2030, for which the FDU is uncertain. Possible theoretical interpretations have been provided in Paper II, Table 11.
Because of the limited number of elements analysed, all initial masses included in the range 1.3 M/M⊙ 2 can equally interpret HE 1443+0113. The high Mg ([Mg/Fe] = 0.9, with 4 lines) observed in HE 0012-1441, a double lined spectroscopic binary, rules out solutions with models of M AGB ini 1.3 M⊙. Also for this star the spectroscopic data are too scarce for speculations about possible AGB solutions.

A6.3 CS 29509-027
The few data measured for this main-sequence star by Sneden et al. (2003b)  We suggest to interpret this star with caution, because C and N have not been detected and no conclusive evidence of its binary nature has been found. Further investigations on this star would be desirable and any possible AGB contribution (e.g., Paper II, Table 11) needs to be confirmed by carbon and europium detections.

A6.5 Four CEMP-sI stars
Among the s-process elements only Ba is measured  and no accurate theoretical predictions may be provided for these stars. In similar cases further studies are required, and at present all the AGB initial mass may equally fit the observations. Possible solutions for these star are listed in Paper II, Table 11, (CS 22960-053, HE 0441-0652, HE 1005-1439, HE 2330-0555).

A6.6 HE 2227-4044 and HE 2240-0412
For the subgiant HE 2227-4044 only the s-process elements Sr, Ba, and La were detected by Barklem et al. (2005). Similar spectroscopic data and a similar metallicity were reported for the subgiant HE 2240-0412. All AGB models in the range between 1.3 M AGB ini /M⊙ 2 may equally interpret the observations, with dilutions of ∼ 0.8 -1.7 dex. We can give a lead estimation of [Pb/Fe] th ∼ 2, but this prediction is very uncertain. Similar spectroscopic data and metallicity are measured for another subgiant, HE 2240-0412. The same solutions can be adopted for both stars.

A6.7 HE 1305+0132
A preliminary discussion about this star has been provided by Gallino et al. (2010). This giant (T eff = 4462 ± 100 K; log g = 0.80 ± 0.30) was studied by Schuler et al. (2007. Discrepant metallicities ([Fe/H] = -2.5 ± 0.5; [Fe/H] = -1.9 with higher resolution in 2008) were found by the authors. Probably the [F/Fe] = 2.9 detected by Schuler et al. (2007) is overestimated. No further investigations were provided ever since. As well as an overabundant [Ba/Fe] = 0.9 dex, no informations about the other s-process elements are available for this star.