© The Authors 2023

1 Introduction

The origin of the peculiar chemical composition of carbon-enhanced-metal-poor stars enriched in both s and r elements (CEMP-rs stars) is an unsolved problem. Some of the scenarios that have been invoked to explain their overabundances (Jonsell et al. 2006; Masseron et al. 2010; Hampel et al. 2016) include (i) a primordial origin (the pollution of the birth cloud by an r-process source), (ii) pollution of the binary by a third massive star (triple system), (iii) pollution by the primary (type 1.5 supernova or accretion-induced collapse), and finally (iv) the intermediate neutron-capture process or i-process. This nucleosynthesis process leads to neutron densities of the order of N_n ~ 10¹⁵ cm⁻³, which is intermediate between those of the s-process (N_n ~ 10⁸ cm⁻³) and those required by the r-process (Nn ≫ 10²⁰ cm⁻³). Recently, Karinkuzhi et al. (2021a) studied a sample of CEMP-s and -rs stars in our Galaxy and suggested that the abundance pattern in CEMP-rs stars can be produced by a thermally pulsing asymptotic giant branch (TP-AGB) star experiencing i-process nucleosynthesis after proton ingestion during its first convective thermal pulse, with this material being transferred to a close-by companion. From a comparison of the abundance profiles of CEMP-s and CEMP-rs stars, Karinkuzhi et al. (2021a) noticed an abundance continuum rather than dichotomic patterns. Therefore, the i-process could be a manifestation of the s-process at low ([Fe/H] ~ −2) metallicities, when proton injection takes place. Our previous identification and analysis (Karinkuzhi et al. 2018) of a star enriched in s and r elements at higher metallicity ([Fe/H] ~ 0.7) hint at an i-process not limited to metal-poor environments. The literature contains other pieces of evidence in line with this hypothesis, such as the barium star subsamples of Cui et al. (2014) and den Hartogh et al. (2023), and the born-again phase of the Sakurai’s object, which also seems to display an i-process pattern (Herwig et al. 2011). These observations suggest it may be possible for a given object to produce this rs pattern without resorting to a “two-event” scenario (independent and cumulative pollution episodes by an r-process and an s-process).

In this paper, we use a sample of 15 stars from Norfolk et al. (2019) reanalyzed in Karinkuzhi et al. (2021b, hereafter K21) to check for potential hybrid profiles at close-to-solar metallicities. This paper is organized as follows. Section 2 describes the sample selection and Sect. 3 the method used to derive the atmospheric parameters and abundances. In Sect. 4 we classify the stars on the basis of their [s/r] ratio, while in Sect. 5 we use a classification based on a larger number of heavy elements. Section 6 presents AGB models and nucleosynthesis reproducing the measured abundances with an i-process triggered by a proton-injection episode (PIE) very similar to the one found in metal-poor stellar models. In Sect. 7 we show that the i-process provides better agreement with the measured abundances than a superposition of two independent s and r pollution episodes. Conclusions are presented in Sect. 8.

2 Sample selection

Our sample consists of 15 bright barium stars selected from the 895 objects from Norfolk et al. (2019) and for which high-resolution HERMES (Raskin et al. 2011) spectra are available. A first analysis of this sample was presented in K21. The metallicities range from [Fe/H] = 0.02 to −0.61. Among the 15 programme stars, 4 show no s-process overabundances ([X/Fe] < 0.2 dex), 8 show mild s-process overabundances (at least three heavy elements with 0.2 ≤ [X/Fe] < 0.8), and 3 have strong overabundances (at least three heavy elements with [X/Fe] ≥ 0.8), as listed in Table 1.

The binarity of these stars was investigated by K21 from which it appears that 2 out of the 3 strong barium stars show a clear binary signature from radial-velocity (RV) variations. The results for the other classes are intriguing, because only 1 out of the 8 mild barium stars diagnosed exhibits statistically significant RV variations, and on the contrary, 2 out of the 4 “no-s” stars show a binary signature.

3 Derivation of atmospheric parameters and abundances

The derivation of atmospheric parameters is presented in K21, but the stellar parameters are repeated here (Table 1). Abundances were derived through spectral synthesis using the local thermodynamic equilibrium (LTE) TURBOSPECTRUM code (Alvarez & Plez 1998). We used solar abundances from Asplund et al. (2009) and the line lists of Heiter et al. (2015); Heiter (2020) as in Karinkuzhi et al. (2018, 2021a). Table A.1 presents the derived Pr, Nd, Sm, and Eu abundances, while we refer to Tables A.1 and A.2 of K21 for the remaining abundances. The complete abundance profiles are also presented in Figs. B.1 and B.2. Mashonkina et al. (2000) and Mashonkina & Christlieb (2014) studied the non-LTE (NLTE) corrections for the Eu II 6645.135 Å line and showed that they are negligible (≈0.06 to 0.08 dex for metallicities higher than −3.0). For the other elements, we were not able to find information about NLTE corrections at the metallicities of our objects. The isotopic shifts and hyperfine splitting (HFS) of the atomic lines were included while deriving the Eu abundances. For other elements, the isotopic shifts and HFS splitting are not available for the lines we used. Figure 1 presents the spectral fitting of Eu lines in a few sample stars. Though many Nd lines are available throughout the spectral coverage, we used the Nd II lines in the range 5200–5400 Å because these are relatively free from molecular blends. For Pr and Sm, we used all the measurable lines as listed in Karinkuzhi et al. (2018, 2021a). Details of the error estimates are presented in K21. Table 2 presents the changes in the abundances resulting from variation of the atmospheric parameters T_eff, log ɡ, micro-turbulence ξ, and [Fe/H] by 100 K, 0.5, 0.5 km s⁻¹, and 0.5 dex, respectively. The final errors are calculated using Eqs. (1) and (2) of K21 and are presented in Table A.1.

4 Classification based on [Ba/Eu] and [La/Eu] abundance ratios

Various abundance thresholds have been used for the classification of CEMP-s and -rs stars (see discussion in Sect. 5 of Karinkuzhi et al. 2021a). Figures 2 and 3 present typical (s,r) planes using lanthanum and barium as the prototype s-element, respectively, and europium as a representative r-element. The different colored regions correspond to commonly accepted limits (Beers & Christlieb 2005) for CEMP-s stars ([Ba/Eu] or [La/Eu] > 0.5, blue region), CEMP-rl stars ([Ba/Eu] or [La/Eu] < 0, 0 < [Eu/Fe] < +1, light green region), and CEMP-rII stars ([Ba/Eu] or [La/Eu] < 0, [Eu/Fe] > +1, dark green region). Finally, the intermediate region between the blue CEMP-s and the green CEMP-r regions has been colored in red. A growing number of stars enriched in both r and s elements (CEMP-rs) has been found in the past decade to occupy this region. In Figs. 2 and 3, CEMP-r, -s, and -sr stars from Masseron et al. (2010), and Karinkuzhi et al. (2021a) are shown as green, blue, and red dots, respectively. In addition, barium stars analyzed by Roriz et al. (2021, for which the barium abundance is not available) are plotted as small blue crosses in Fig. 2.

The majority of barium stars analyzed by Roriz et al. (2021) and also the majority of CEMP-s stars are located in the blue-shaded region, as expected. However, we note that especially at low enrichment levels ([La/Fe] and [Eu/Fe] < 0.7), many barium and CEMP-s stars occupy the red-shaded region. Actually, if the enrichment is low, the pristine composition might not be erased by the pollution from the companion and the current abundance profile might also reflect an enrichment due to Galactic chemical evolution. Alternatively, the abundances could be biased because of the difficulty in determining weak line abundances in blended spectra¹.

The 15 stars of the current sample are identified in Fig. 2 with black symbols surrounding the corresponding dots: black crosses for the “no s-process enrichment”, black squares for the “mild enrichment”, and plus symbols for the “strong enrichment” of Table 1. Interestingly, these stars all fall in the CEMP-rs (red) or r-I (green) regions. This is reminiscent of the barium stars analyzed by den Hartogh et al. (2023): these authors detect the signature of an i-process activation in about 25% of the evolved companions of the barium star.

Fig. 1 Spectral fitting of the 6437.640 and 6645.135 Å EuII lines for four sample stars. Red lines correspond to spectral syntheses with the abundance for Eu listed in Table A.1. Blue and green lines represent syntheses with abundances deviating by ±0.3 dex from the adopted abundance. The magenta line corresponds to the synthesis with a null abundance for Eu.

Fig. 2 [La/Fe] as a function of [Eu/Fe], The figure includes CEMP-s stars, CEMP-rs stars, and r-process-enriched stars from Masseron et al. (2010) and Karinkuzhi et al. (2021 a) as well as the Ba stars of Roriz et al. (2021). The dashed green line corresponds to abundance-ratio scaling with a pure solar r-process (Goriely 1999), whereas the continuous blue line corresponds to s-process nucleosynthesis abundance ratio scaling with the predictions from the fifth pulse of a 1.5 M⊙ star at [Fe/H] = −1.

Fig. 3 Same as Fig. 2, but with [Ba/Fe] as a function of [Eu/Fe],

Fig. 4 Histogram of the signed distance (Eq. (1)) of the star samples. Upper panel: star sample of the present study (considering only those with mild and strong enrichments, meaning 11 stars out of 15). Middle panel: Karinkuzhi et al. (2021a) sample of CEMP-rs (red) and -r (green) stars. Lower panel: Karinkuzhi et al. (2021a) sample of CEMP-s stars. The dashed line represents the dS = 0.6 limit between CEMP-s and CEMP-rs stars, as defined in Karinkuzhi et al. (2021a).

5 Classification based on s- and r- elements

We used seven elemental abundances (Y, Zr, Ba, La, Ce, Nd, Sm) to compute a signed distance to a reference abundance pattern, which was chosen to be the solar r-process scaled to the europium abundance of the star (see Eq. (3) of Karinkuzhi et al. 2021a): $$d_{\text{S}}=\frac{1}{N}{\displaystyle \sum _{x_i}\left({\log }_{10}{ϵ}_{x_i,*}-{\log }_{10}{ϵ}_{x_i,\text{norm}\left(\text{r,*}\right)}\right)},$$(1)

where {x₁…x_N} are the N considered heavy elements, and we employ the commonly used notation ${\log }_{10}{ϵ}_{x_i}={\log }_{10}\left(n_{x_i}/n_{\text{H}}\right)+12$, with n_Xi being the number density of element x_i. We denote ${\log }_{10}{ϵ}_{x_i,\text{*}}$ the abundance of element Xi for the program stars, and ${\log }_{10}{ϵ}_{x_i,\text{norm}\left(\text{r,*}\right)}$ the standard r-process abundance profile $\log {ϵ}_{x_i,r}$ normalized to the star abundance profile with respect to europium: $$\text{log\hspace{0.17em}}{ϵ}_{x_i,\text{norm}\left(\text{r,*}\right)}=\log {ϵ}_{x_i,r}+\left(\text{log\hspace{0.17em}}{ϵ}_{Eu,*}-\log {ϵ}_{Eu,r}\right),$$(2)

where the adopted r-process abundances $\log {ϵ}_{x_i,r}$ are listed in Table B.4 of Karinkuzhi et al. (2021a). Figure 4 presents the histogram of this signed distance together with the limit adopted in Karinkuzhi et al. (2021a) to separate CEMP-s from CEMP-rs stars (at d_S = 0.6). This limit is certainly somewhat arbitrary. However, Fig. 4 shows that most of our sample stars strongly enriched in heavy elements appear to have an rs pattern.

6 Comparison with nucleosynthesis predictions

We computed AGB nucleosynthesis predictions by coupling the STAREVOL code (Siess & Arnould 2008) with an extended reaction network of 1160 species linked by 2123 nuclear reactions. More details on the nuclear network and input physics can be found in Choplin et al. (2021) and Goriely et al. (2021). The solar abundances are taken from Asplund et al. (2009), which correspond to a metallicity of Z = 0.0134. The Reimers (1975) mass-loss rate with η_R = 0.4 is used from the main sequence up to the end of core helium burning and that of Vassiliadis & Wood (1993) is used during the AGB phase. We computed dedicated models with an initial mass of 2 M_⊙ and a metallicity of [Fe/H] = −0.5, which is close to the metallicity derived from the observations as explained below.

In the present calculations, a diffusion equation is used to compute the partial mixing of protons in the C-rich layers at the time of the third dredge up (TDU). We follow Eq. (9) of Goriely & Siess (2018) and use in our standard case the same diffusive mixing parameters in our simulations as in Shetye et al. (2019), namely ƒ_env = 0.14, D_min = 10⁷cm² s⁻¹, and p = 1/2, where ƒ_env controls the extent of the mixing, D_min the value of the diffusion coefficient at the base of the envelope, and p is a free parameter describing the shape of the diffusion profile. In addition to this diffusive mixing at the base of the envelope, a similar prescription is applied at the top of the thermal pulse, where a coefficient ƒ_pulse governs the diffusive transport. Two different values of the ƒ_pulse coefficient, triggering an s-process or i-process nucleosynthesis, are considered here, as explained below.

When considering a relatively weak diffusive mixing at the top of the thermal pulse characterized by ƒpulse = 0.03, the AGB phase of our 2 M_⊙ [Fe/H] = −0.5 model star is found to follow a standard evolution with the occurrence of eight thermal pulses and a regular surface enrichment at the time of the TDU. In addition, the diffusive mixing at the bottom of the envelope gives rise to a radiative s-process during the interpulse phases similar to what is found in Goriely & Siess (2018). The corresponding abundance pattern found at the surface at the end of the AGB evolution is illustrated in Fig. 5 (blue curve).

The ingestion of protons in the convective helium-burning zone can lead to a rich i-process nucleosynthesis that can explain the surface enrichment of CEMP-rs stars relatively successfully (e.g., Hampel et al. 2019; Karinkuzhi et al. 2021a; Choplin et al. 2021). However, as detailed in Choplin et al. (2022), when no extra mixing is included, the PIE is restricted to model stars of metallicity lower than typically [Fe/H] ~ −2. When considering diffusive mixing below the envelope and at the top of the thermal pulse, it is found that a possible PIE can be triggered in a way very similar to those found in very metal-poor stars. In particular, mixing parameters ƒ_env = 0.06 and ƒ_pulse = 0.06 lead to a PIE at the time of the third thermal pulse, with a maximum neutron density reaching 10¹⁴cm⁻³. The resulting surface abundance distribution is shown in Fig. 5 (red profile) and is rather similar to the one obtained in low-metallicity stars (Choplin et al. 2022).

In summary, depending on the strength of the overshoot mixing imposed both at the bottom of the envelope and at the top of the pulse, either a standard s-process or an i-process can be simulated in a 2 M_⊙ [Fe/H] = −0.5 model star. Despite progress in multi-dimensional simulations of convective boundary mixing (e.g., in low-mass stars, Mocák et al. 2011; Herwig et al. 2014; Woodward et al. 2015), no firm conclusions can be drawn as to the strength of the mixing. Our approach is to explore these possibilities and compare our results with the present observations.

We pay particular attention to the most strongly enriched s-process stars of Table 1, because their abundances must reflect genuine pollution and not the chemical enrichment of the Galaxy, contrarily to the situation that might prevail for stars with weak enrichments. In particular, TYC 2250–1047–1 and TYC 591–1090–1 show an [Eu/Fe] of 0.88 and 0.93 dex, respectively, which cannot be explained by Galactic chemical evolution alone. Very few stars are found with [Eu/Fe] > 0.4 among disk stars with [Fe/H] > −0.4 (Tautvaišienė et al. 2021; Van der Swaelmen et al. 2023). Therefore, the abundance pattern of these two stars must result from extra pollution(s). TYC 2955–408–1, with [Eu/Fe] = 0.52, is difficult to classify and the abundances of additional elements are needed to decide whether it is an i-process star or a barium star with a europium abundance corresponding to the high-europium tail of the Galactic distribution. A comparison of their measured and predicted abundances is given in Fig. 6, where a dilution factor is applied to the surface abundances shown in Fig. 5 to match the overabundances observed in the La-Ba region. This dilution factor is required to simulate the mixing of the nucleosynthesis yields from the primary star onto its companion (assumed to be of the same initial composition).

The overall accuracy of the model predictions can be quantified for each star through the reduced χ² indicator: $${\chi }^2=\frac{1}{N}{\displaystyle \sum _X\frac{{\left({\left[\text{X}/\text{Fe}\right]}_{\text{obs}}-{\left[\text{X}/\text{Fe}\right]}_{\mathrm{mod}}\right)}^2}{{\sigma }_{\text{X,obs}}^2},}$$(3)

where [X/Fe]_obs and [X/Fe]_mod are respectively the measured and predicted abundances of a given element X, and σ_X,obs is the associated uncertainty on the measured abundance. We consider the N = 10 elements available in all stars, namely Sr, Y, Zr, Ba, La, Ce, Pr, Nd, Sm, and Eu.

We report a typo in Eq. (6) of Karinkuzhi et al. (2021a), where the normalizing factor 1/N was erroneously omitted, though it was included when computing the χ² listed in the Table 1 of that paper (see Corrigendum in Karinkuzhi et al. 2023). Equation (3) above is the correct expression used to provide the numbers given in the tables of both papers.

In Karinkuzhi et al. (2021a), reduced χ² values for CEMP-s stars (when compared to an s-process) ranged between 2.7 and 10.9. Similarly, reduced χ² values for CEMP-rs stars (when compared to an i-process) ranged between 1.3 and 10.6. Here, for the two most enriched stars (TYC 2250-1047-1 and TYC 591–1090–1), we find a reduced χ² of between 6.4 and 7.6 (depending on the exact number (8 or 10) of considered chemical elements, but including Eu; see Table 3) when comparing to an i-process, but in the range between 11.2 and 23.7 when comparing to an s-process. The chemical pattern of these two most-enriched stars is therefore better reproduced by an i-process than by an s-process.

We note that the first peak s-process element abundances (Sr, Y, Zr) are always difficult to reproduce (either by an s- or i-process; Fig. 6), and this strongly impacts the χ². The results from the χ² are therefore less clear with the seven elements than with a metric using eight (i.e., including Eu) or ten elements (including Sr, Pr and Eu). Considering Eu in addition to Sm is therefore crucial when assessing an i- or r- contribution. We note that of these two stars, only TYC 2250–1047–1 is classified as rs-enriched according to the signed distance criterion (d_S <0.6). The reason for this partially lies in the fact that the 0.6 threshold on the signed distance is a somewhat arbitrary value and, as seen in Fig. 4, values up to d_S = 0.75 might still be encountered for some CEMP-rs stars falling in the intermediate (red) regions of Figs. 2 and 3.

In summary, in this paper we use two different indicators to assess the s- or i-character of a measured stellar abundance profile: the distance indicator (using seven heavy elements plus Eu, which serves to normalize the measured Eu abundance to the solar-scaled “universal” r-process abundance; this has the advantage of being model-independent) and the reduced χ² (computed between the measured profile and a nucleosynthetic prediction, either s or i). Table 3 shows that these two indicators are consistent when the comparison is based on the same set of chemical elements, as can be seen by comparing the reduced χ² for seven elements (6.0, 2.6) and the d_S distance, which uses the same seven elements (0.63, 0.56) for the two stars (TYC 591–1090–1, TYC 2250–1047–1), ordered by increasing contribution of an i-process. The eight and ten-element χ² show that including Sr as well as Pr and Eu is very important in order to obtain clearly different s-process χ² and i-process χ², and therefore to obtain a clear diagnostic concerning the s- or rs-character of the abundance profile.

We demonstrate in the next section that replacing the i-process pattern with any superposition of two independent sand r-pollutions deteriorates the agreement with the measured abundances.

Fig. 5 Comparison of the final elemental surface distributions [X/Fe] (solid lines) obtained after the development of the neutron-capture processes in a 2 M⊙ AGB star of metallicity [Fe/H] = −0.5. The blue line is obtained with diffusive mixing characterized by ƒenv = 0.14 and ƒenv = 0.03, which gives rise to s-process nucleosynthesis, while the red line results from mixing with ƒenv = 0.06 and ƒpulse = 0.06 leading to a PIE, i.e., to a i-process nucleosynthesis.

Fig. 6 Comparison of the measured abundances with nucleosynthesis predictions from the STAREVOL code. The abundances obtained at the surface of the 2 M⊙ [Fe/H] = −0.5 model with two different sets of the diffusive mixing parameters, (the blue line corresponding to an s-process, and the red line to an i-process) as shown in Fig. 5, are compared with the abundances of the 3 most enriched barium stars (black squares).

7 Testing the scenario of two independent pollution episodes

To check that the abundance patterns of the two i-process stars, TYC 2250–1047–1 and TYC 591–1090–1, are better fitted with an i-process than with a superposition of two independent pollution episodes, one by an s-process and another one by an r-process, we performed the following test. A mixed r+s profile was added to a solar abundance profile scaled to the metallicity of the considered star. The r+s profile was built summing an r- and an s-contribution, each one varied independently from zero to values producing overabundances largely exceeding the measured abundances. We assume a solar-like pattern for the r-process (Table B.4 of Karinkuzhi et al. 2021a) and an AGB pattern for the s-process at the corresponding stellar metallicity (blue line in Fig. 6; see also Goriely & Siess 2018). The agreement between the resulting abundance profile (plotted in faded colors in Fig. 7) and the measured profile was quantified by computing a χ² as in Eq. (3). For the two stars, a pure s-process produces better agreement with the measured abundances than an r+s mixture. An r-process contribution is never favored because the slope of the r-process is quite steep (i.e., it is more rapidly decreasing with increasing Z than the s-process), and so matching the high europium (as well as samarium) abundances would inevitably lead to significant overestimation of the light-s (Sr, Y, Zr) abundances. The resulting ${\chi }_S^2$ (between the s-profile and the measured abundances) is very similar to the ${\chi }_i^2$ (between the i-proflle and the measured abundances), but the s-proflle never explains the high europium abundance measured in TYC 2250–1047–1 and TYC 591–1090–1. The present analysis indicates that these two enriched stars are better explained by an i-process than by a superposition of two independent s and r processes.

Some deviations between the measured and i-process abundances can still be noted, in particular for light s-elements, but also for Eu, which, in contrast to Sm, tends to be underestimated by the model. The absence of an odd–even effect between the measured Sm and Eu abundances is puzzling.

Fig. 7 Comparison of the measured abundance profiles (black squares) with a series of synthetic profiles made by a superposition of s- (as plotted in blue in Fig. 6) and r-process profiles, both varied independently and continuously from a solar-scaled profile with a very low s+r enrichment (purple faded lines) to large s+r enrichments (green faded lines). The synthetic “s+r” profile best matching the measured abundances is plotted as a thick violet line. For both stars, this latter corresponds to a pure s-process contribution (therefore, any r-process contribution would deteriorate the agreement regardless of the s-process contribution). For reference, the i-process profile best matching the measured abundances is plotted in red as in Fig. 6.

8 Conclusions

Our reanalysis of 15 stars classified as s-process-enriched by Norfolk et al. (2019) indicates that their abundances seem to be rather characterized by a hybrid sr pattern rather than by a pure s-process pattern, as inferred from the distance indicator which quantifies the deviation of the star’s abundance profile from a pure r-process distribution. For the two most enriched stars of our sample (which have [Eu/Fe] ≳ 0.75 and cannot be explained by Galactic chemical evolution models), the comparison of the abundance profile with detailed calculations shows that an i-process nucleosynthesis (resulting from the occurrence of a PIE) is a better fit to the observed abundances than a pure s-process or than any combination of r- and s-patterns. At low enrichment levels, the primordial composition resulting from the galactic chemical evolution blurs the picture. This can be seen in Fig. 2, where the barium stars enter the r+s region below [s/Fe] = 0.5 dex.

It is possible that a non-negligible fraction of the stars previously identified as barium stars (because barium enhancement is relatively easy to identify) also present an r-element enrichment, but it is only recently that r-element abundances have been systematically investigated among barium stars. A population of rs-enriched objects (with [La/Eu] < 0.5) seems to emerge, not only at low-metallicities where it was first noticed (among CEMP-rs stars), but also at close-to-solar metallicities, as also found in other samples of barium stars (Karinkuzhi et al. 2018; den Hartogh et al. 2023) and in Sakurai’s object (Herwig et al. 2011; van Hoof et al. 2017). If the i-process is indeed active in objects such as AGB stars of close-to-solar metallicity, important impacts on nucleosynthesis and galactic chemical evolution can be expected. In particular, the i-process contribution to our Solar System would need to be revisited.

Acknowledgements

D.K. acknowledges the financial support from University of Calicut through seed money grant with file number U.O.No.14449/2022/Admn. S.V.E. thanks the Fondation ULB for its support. The Mercator telescope is operated thanks to grant number G.0C31.13 of the FWO under the “Big Science” initiative of the Flemish governement. Based on observations obtained with the HERMES spectrograph, supported by the Fund for Scientific Research of Flanders (FWO), the Research Council of KU Leuven, the Fonds National de la Recherche Scientifique (F.R.S.- FNRS), Belgium, the Royal Observatory of Belgium, the Observatoire de Genève, Switzerland and the Thüringer Landessternwarte Tautenburg, Germany. L.S. and S.G. are senior research associates from F.R.S.- FNRS (Belgium). This work was supported by the F.R.S.- FNRS Grant No IISN 4.4502.19.

Appendix A Individual abundances

Table A.1 lists the elemental abundances.

Appendix B Abundance pattern in program stars

Figures B.1 and B.2 show the abundance patterns for stars showing no, mild, or strong s-process enrichment. Figure 3 displays the ([Ba/Fe], [Eu/Fe]) diagram.

Fig. B.1 Abundance profiles of the program stars color coded according to the adopted classification criteria. The upper panel shows the abundance pattern in stars with no s-process enhancements. The lower panel shows the abundance pattern in three stars with strong s-process enrichments.

Fig. B.2 Same as B.1 but for the eight mildly s-process-enriched stars.

References

All Tables

All Figures

	Fig. 1 Spectral fitting of the 6437.640 and 6645.135 Å EuII lines for four sample stars. Red lines correspond to spectral syntheses with the abundance for Eu listed in Table A.1. Blue and green lines represent syntheses with abundances deviating by ±0.3 dex from the adopted abundance. The magenta line corresponds to the synthesis with a null abundance for Eu.
In the text

Fig. 2 [La/Fe] as a function of [Eu/Fe], The figure includes CEMP-s stars, CEMP-rs stars, and r-process-enriched stars from Masseron et al. (2010) and Karinkuzhi et al. (2021 a) as well as the Ba stars of Roriz et al. (2021). The dashed green line corresponds to abundance-ratio scaling with a pure solar r-process (Goriely 1999), whereas the continuous blue line corresponds to s-process nucleosynthesis abundance ratio scaling with the predictions from the fifth pulse of a 1.5 M⊙ star at [Fe/H] = −1.

In the text

	Fig. 3 Same as Fig. 2, but with [Ba/Fe] as a function of [Eu/Fe],
In the text

Fig. 4 Histogram of the signed distance (Eq. (1)) of the star samples. Upper panel: star sample of the present study (considering only those with mild and strong enrichments, meaning 11 stars out of 15). Middle panel: Karinkuzhi et al. (2021a) sample of CEMP-rs (red) and -r (green) stars. Lower panel: Karinkuzhi et al. (2021a) sample of CEMP-s stars. The dashed line represents the dS = 0.6 limit between CEMP-s and CEMP-rs stars, as defined in Karinkuzhi et al. (2021a).

In the text

Fig. 5 Comparison of the final elemental surface distributions [X/Fe] (solid lines) obtained after the development of the neutron-capture processes in a 2 M⊙ AGB star of metallicity [Fe/H] = −0.5. The blue line is obtained with diffusive mixing characterized by ƒenv = 0.14 and ƒenv = 0.03, which gives rise to s-process nucleosynthesis, while the red line results from mixing with ƒenv = 0.06 and ƒpulse = 0.06 leading to a PIE, i.e., to a i-process nucleosynthesis.

In the text

Fig. 6 Comparison of the measured abundances with nucleosynthesis predictions from the STAREVOL code. The abundances obtained at the surface of the 2 M⊙ [Fe/H] = −0.5 model with two different sets of the diffusive mixing parameters, (the blue line corresponding to an s-process, and the red line to an i-process) as shown in Fig. 5, are compared with the abundances of the 3 most enriched barium stars (black squares).

In the text

Fig. 7 Comparison of the measured abundance profiles (black squares) with a series of synthetic profiles made by a superposition of s- (as plotted in blue in Fig. 6) and r-process profiles, both varied independently and continuously from a solar-scaled profile with a very low s+r enrichment (purple faded lines) to large s+r enrichments (green faded lines). The synthetic “s+r” profile best matching the measured abundances is plotted as a thick violet line. For both stars, this latter corresponds to a pure s-process contribution (therefore, any r-process contribution would deteriorate the agreement regardless of the s-process contribution). For reference, the i-process profile best matching the measured abundances is plotted in red as in Fig. 6.

In the text

	Fig. B.1 Abundance profiles of the program stars color coded according to the adopted classification criteria. The upper panel shows the abundance pattern in stars with no s-process enhancements. The lower panel shows the abundance pattern in three stars with strong s-process enrichments.
In the text

	Fig. B.2 Same as B.1 but for the eight mildly s-process-enriched stars.
In the text