1. Introduction
The origin of heavy elements beyond iron (
$A\,\gt\,60$
) is primarily attributed to neutron-capture nucleosynthesis, with the slow neutron-capture process (s-process) playing a dominant role in low- and intermediate-mass stars (
$\sim$
0.8–8
$\rm M_{\odot}$
). The s-process operates under lower neutron densities (
$n\,\lesssim10^{12}$
cm
$^{-3}$
) and over longer timescales, allowing unstable nuclei to undergo
$\beta$
-decay between successive neutron captures (see Iben Reference Iben1974; Busso, Gallino, & Wasserburg Reference Busso, Gallino and Wasserburg1999; Lugaro et al. Reference Lugaro, Pignatari, Reifarth and Wiescher2023, references therein). Asymptotic giant branch (AGB) stars are well established as the primary astrophysical site for the s-process (e.g. Gallino et al. Reference Gallino1998; Lugaro et al. Reference Lugaro, Herwig, Lattanzio, Gallino and Straniero2003; Herwig Reference Herwig2005; Karakas & Lattanzio Reference Karakas and Lattanzio2014). The detection of technetium (Tc), a short-lived radioactive element produced by the s-process, in the atmospheres of AGB stars provides compelling observational evidence of ongoing s-process nucleosynthesis during this phase (Merrill Reference Merrill1952; Werner et al. Reference Werner and Rauch2015; Shetye et al. Reference Shetye2020). The s-process proceeds along the valley of
$\beta$
-stability and is typically categorised into three components based on neutron exposure: the weak component synthesises light s-process (ls) elements (e.g. Sr, Y, Zr), the main component synthesises heavier s-process (hs) elements (e.g. Ba, La, Nd); and the strong component is responsible for the heaviest stable s-process elements, including Pb and Bi (e.g. Lugaro et al. Reference Lugaro, Karakas, Stancliffe and Rijs2012; Karakas & Lattanzio Reference Karakas and Lattanzio2014). The
$\textrm{[hs/ls]}$
ratio is widely used as a diagnostic of neutron exposure and s-process efficiency during AGB nucleosynthesis.
However, observationally constraining AGB nucleosynthesis remains challenging due to the extended, pulsating atmospheres, strong mass loss, molecular opacities, and circumstellar dust envelopes of AGB stars (Abia, de Laverny, & Wahlin Reference Abia, de Laverny and Wahlin2008; Pérez-Mesa et al. Reference Pérez-Mesa2019). Post-asymptotic giant branch (post-AGB) stars offer a valuable alternative. These luminous, short-lived objects have recently departed the AGB and retain surface compositions reflective of their prior nucleosynthetic histories (see Van Winckel Reference Van Winckel2003; Kamath et al. Reference Kamath2022, Reference Kamath2023). Their relatively high photospheric temperatures (
$T_{\rm eff}$
$\sim$
3 000–30 000 K) allows access to a wide range of atomic lines in the optical regime, enabling detailed chemical abundance analyses of elements from CNO to heavy s-process elements well beyond the Ba peak (e.g. Van Winckel & Reyniers Reference Van Winckel and Reyniers2000; van Aarle et al. Reference van Aarle2011; De Smedt et al. Reference De Smedt2012, Reference De Smedt, Van Winckel, Kamath and Wood2015, Reference De Smedt2016; Kamath et al. Reference Kamath2022). These properties make post-AGB stars exquisite targets for constraining stellar evolution and nucleosynthesis models (Kamath & Van Winckel Reference Kamath and Van Winckel2022).
To date,
$\sim$
18 single s-process enriched post-AGB stars have been well studied in the Galaxy (see Kamath et al. Reference Kamath2022, and references therein)
$\sim$
1 in the Small Magellanic Cloud (SMC) (e.g. De Smedt et al. Reference De Smedt2012) and
$\sim$
6 in the Large Magellanic Cloud (LMC) (e.g. van Aarle et al. Reference van Aarle2011; De Smedt et al. Reference De Smedt2012, Reference De Smedt, Van Winckel, Kamath and Wood2015). Analyses of these stars have uncovered significant discrepancies between observed surface abundances and those predicted by theoretical nucleosynthesis models. These discrepancies have sparked renewed interest in alternative neutron-capture processes. This has motivated the proposal of the intermediate neutron-capture process (i-process), which operates at neutron densities between those of the s-process and r-process (
$n~\sim10^{13}$
–
$10^{15}$
cm
$^{-3}$
) (see Hampel et al. Reference Hampel, Stancliffe, Lugaro and Meyer2016; Choplin, Siess, & Goriely Reference Choplin, Siess and Goriely2021; Choplin et al. Reference Choplin, Siess, Goriely and Martinet2024, references therein). These models show promising agreement for elements between the first and second s-process peaks. However, the success of such models often hinges on finely tuned parameters such as overshoot efficiencies or neutron exposures, limiting their general applicability. Notably, even in models that match the general abundance trends, significant discrepancies remain for lead (Pb), highlighting its role as a particularly sensitive diagnostic of neutron-capture processes – especially in metal-poor environments (Kamath & Van Winckel Reference Kamath and Van Winckel2021).
Previous abundance studies of single s-process enriched post-AGB stars have been valuable but often piecemeal. A recent study by Kamath et al. (Reference Kamath2022) analysed a larger, comprehensive Galactic sample of
$\sim$
30 single post-AGB stars, with luminosities and initial masses derived from Gaia DR3 parallaxes. This study exemplifies the remarkable chemical diversity among stars with similar stellar parameters and luminosities, revealing both s-process enriched and non-enriched stars, and challenging existing paradigms of AGB nucleosynthesis. Furthermore, the discovery of s-process enriched post-AGB binaries in both the Galaxy and the MCs further complicates the picture (Menon et al. Reference Menon, Kamath, Mohorian, Van Winckel and Ventura2024). Together, these findings point to a more nuanced and diverse range of neutron-capture signatures than previously appreciated.
The growing body of observational and theoretical work on post-AGB stars highlights that each star may reflect a distinct nucleosynthetic history (see e.g. Kamath et al. Reference Kamath2022, Reference Kamath2023; Menon et al. Reference Menon, Kamath, Mohorian, Van Winckel and Ventura2024). While large-sample studies reveal population-wide trends, detailed studies of individual stars remain essential for decoding the complex interplay of processes that shape surface abundances.
In this work, we present a detailed chemical abundance analysis of J003643.94
$-$
723722.1 (hereafter J003643), the most carbon-rich and one of the most s-process enriched post-AGB stars identified in the Small Magellanic Cloud (SMC). We compare the derived abundances with predictions from a range of theoretical stellar evolutionary models to investigate the underlying enrichment processes. J003643’s well-constrained luminosity and initial mass, coupled with its unique chemical fingerprint, provide fresh insight into s-process nucleosynthesis in post-AGB stars. To better understand the chemical diversity observed in post-AGB stars, we compare some of the key abundance ratios of J003643 with a broader sample of post-AGB stars, including single s-process enriched, non-s-process enriched, and binary s-process enriched post-AGB stars. In addition, we aim to investigate Pb abundances in post-AGB stars using both local thermodynamic equilibrium (LTE) and a toy model to make a preliminary estimate of non-local thermodynamic equilibrium (NLTE) effects, thereby refining Pb abundance estimates and addressing longstanding discrepancies between observational data and theoretical nucleosynthesis predictions.
This paper is organised as follows: Section 2 presents an overview of the target and describes the photometric and spectroscopic datasets. Section 3 outlines the derivation of atmospheric parameters and chemical abundances. Section 4 describes the luminosity derivation. Section 5 introduces the stellar evolutionary models used in this study. Section 6 compares J003643 to the comparative sample of post-AGB stars and explores its nucleosynthetic origin by comparing with theoretical model predictions. We also assess the Pb discrepancy using both LTE and NLTE techniques. Section 7 summarises the main findings and implications of this study.
2. Target details
The primary target of this study, J003643, was first identified as a post-AGB candidate in the SMC through a comprehensive low-resolution spectroscopic survey by Kamath, Wood, & VanWinckel (Reference Kamath, Wood and Van Winckel2014). In the same study, J003643 was classified as a shell-source based on its characteristic double-peaked spectral energy distribution (SED; see Figure 1). Shell-sources are typically thought to be single post-AGB stars that exhibit a distinct double-peaked SED, where the first peak in the near-IR corresponds to the stellar photosphere, while the second peak in the mid-infrared is attributed to thermal emission from a detached, expanding shell of cold circumstellar dust material ejected during the AGB phase (Van Winckel Reference Van Winckel2003; Gezer et al. Reference Gezer2015).
SED of J003643. The data points represent dereddened photometry, while the red line corresponds to the best-fitting scaled model atmosphere. See Section 4 for details on the SED fitting.
2.1 Photometric data
Photometric data for J003643 were retrieved from the Vizier database (Ochsenbein, Bauer, & Marcout Reference Ochsenbein, Bauer and Marcout2000) to construct its SED (see Figure 1). The optical and near-IR photometry characterises the photospheric emission of the post-AGB star, while mid- and far-IR photometry provides insight into the properties of the circumstellar environment.
For the optical and near-IR regime, we utilised data from the UBVRI Johnson-Cousins photometric system (Bessell Reference Bessell1990). Mid- and far-IR fluxes were obtained from the 2MASS All-Sky Catalog of Point Sources (Cutri et al. Reference Cutri2003) and the WISE All-Sky Data Catalog (Cutri et al. Reference Cutri2012). The full set of photometric magnitudes for J003643 is presented in Table 1. A comprehensive list of commonly used photometric catalogues can be found in Appendix A of Oomen et al. (Reference Oomen2018).
Photometric data used for the SED of J003643. See text for full details.
Notes: A standard error of 0.05 mag is adopted for the SED fitting. IRAC and MIPS are instruments aboard the Spitzer satellite.
The resulting SED of J003643 is shown in Figure 1. Details of the SED fitting procedure are described in Section 4.
2.2 Spectroscopic observations and data reduction
High-resolution optical spectra of J003643 were obtained using the Ultraviolet and Visual Echelle Spectrograph (UVES) (Dekker et al. Reference Dekker, D’Odorico, Kaufer, Delabre, Kotzlowski, Iye and Moorwood2000), mounted on the 8 m UT2 Kueyen Telescope of the Very Large Telescope (VLT) array at the European Southern Observatory’s (ESO) Paranal Observatory in Chile (Program ID: 092.D-0485). These observations were part of a broader effort to obtain high-quality spectroscopic data for post-AGB stars. To maximise wavelength coverage, the dichroic beam-splitter was employed, yielding spectra that span 3 280–4 560 Å for the blue arm and 4 726–5 800 Å and 5 817–6 810 Å for the lower and upper regions of the red arm CCD chip, respectively. Due to the physical separation between the three UVES CCDs, small spectral gaps exist between 4 560–4 726 Å and 5 800–5 817 Å. Each spectral range was observed separately with a consistent exposure time. The resolving power of UVES for these observations ranges between
$\sim$
60 000 and
$\sim$
65 000.
Figure 2 presents a spectral region of the target star J003643 (upper) alongside J004441 (lower), one of the most s-process enriched post-AGB stars from De Smedt et al. (Reference De Smedt2012), for comparison. This figure illustrates the quality of the UVES spectra and highlights the detection of specific s-process elements in J003643.
Normalised spectra of the target star J003643 (upper) and one of the most s-process enriched post-AGB stars, J004441 (lower), from De Smedt et al. (Reference De Smedt2012) for comparison. The spectra have been normalised and shifted to zero velocity for illustrative purposes. The red and black vertical lines mark the positions of selected s-process and non-s-process elements, respectively.
The observational details, including spectral coverage and signal-to-noise (S/N) ratios per observation, are provided in Table 2. The S/N ratio is lower at blue wavelengths due to increased atmospheric extinction, reddening effect and reduced detector sensitivity. Additionally, the echelle spectra exhibit non-uniform S/N owing to the blaze function, which results in a higher S/N near blaze wavelengths where the spectrograph operates most efficiently. The final weighted mean spectrum has an S/N of 30 in the blue region and 55 in the red region.
Observational logs of the J003643.
Notes: The final S/N after the weighted mean merging of similar observations is approximately 30 in the blue region and 55 in the red region of the spectrum.
The pre-reduced UVES spectra of J003643 were retrieved from the ESO Archive Science Portal. The normalisation of the reduced spectrum was performed by fitting fifth-order polynomials within small spectral windows using interactively selected continuum points. This step is particularly crucial in the blue spectral region, where significant line crowding makes continuum placement challenging. The primary source of measurement uncertainty in abundance determinations for lines in this region arises from continuum placement errors.
The radial velocity of J003643 was determined by measuring the central wavelengths of several well-identified atomic lines using Gaussian profile fitting. The Doppler shift equation was then applied to derive a heliocentric radial velocity of
$v= 133.9 \pm 0.26$
km s
$^{-1}$
, which is consistent with SMC membership, given the mean heliocentric velocity of the SMC being
$\sim$
160 km s
$^{-1}$
(Richter, Tammann, & Huchtmeier Reference Richter, Tammann and Huchtmeier1987).
After normalisation and radial velocity correction of all the spectra (blue and red), a weighted mean merging was performed to obtain a single final spectrum, which was subsequently used for a detailed spectroscopic analysis of J003643. A significant portion of the blue spectrum (3 280–4 560 Å) exhibits an S/N too low (
$\lt$
30) for reliable abundance determination. Consequently, these wavelength ranges were excluded from the spectroscopic analysis of J003643.
3. Spectroscopic analysis of J003643
The spectroscopic analysis of J003643, including the determination of accurate atmospheric parameters and the derivation of chemical abundances for all identifiable elements, was conducted using E-iSpec (Mohorian et al. Reference Mohorian2024), a custom Python wrapper for iSpec (Blanco-Cuaresma et al. 2014; Blanco-Cuaresma Reference Blanco-Cuaresma2019). E-iSpec interfaces with the LTE spectrum synthesis tool MOOG (Sneden Reference Sneden1973). A detailed description of E-iSpec and the spectroscopic analysis methodology is provided in Mohorian et al. (Reference Mohorian2024). Our approach closely follows the methods outlined in Menon et al. (Reference Menon, Kamath, Mohorian, Van Winckel and Ventura2024) and Mohorian et al. (Reference Mohorian2024).
The atmospheric parameters and elemental abundances were determined using carefully selected spectral lines that are isolated, unblended, and non-saturated. To minimise spectral noise, we included only lines with equivalent widths (EW) greater than 5 mÅ, while excluding those exceeding 150 mÅ to avoid saturation effects.
A summary of the atmospheric parameter determination and chemical abundance derivation is presented in Sections 3.1 and 3.2, respectively.
3.1 Atmospheric parameter determination
The atmospheric parameters of J003643 were determined using Fe I and Fe II lines, following the approach described in Mohorian et al. (Reference Mohorian2024) and Menon et al. (Reference Menon, Kamath, Mohorian, Van Winckel and Ventura2024). The EWs for each line were computed iteratively by comparing the theoretical EWs with the observed values.
The effective temperature (
$T_{\rm eff}$
) was derived through excitation equilibrium, ensuring that Fe I abundances remain independent of excitation potential (EP). The surface gravity (
$\log g$
) was determined via ionisation equilibrium, enforcing consistency between Fe I and Fe II abundances. The microturbulent velocity (
$\xi_{\rm t}$
) was obtained by requiring that the derived Fe abundances are independent of the reduced equivalent width (RW) of individual lines. Uncertainties in the atmospheric parameters were estimated using the covariance matrix from the non-linear least-squares fitting algorithm in E-iSpec.
The results of the atmospheric parameter analysis for J003643 are presented in Table 3 and discussed in Section 3.3. The values in the last column of Table 3 correspond to the atmospheric parameters derived from low-resolution AAOmega spectra by Kamath et al. (Reference Kamath, Wood and Van Winckel2014).
Spectroscopically derived atmospheric parameters of J003643.
Notes: Atmospheric parameters from Kamath et al. (Reference Kamath, Wood and Van Winckel2014) were derived using low-resolution AAOmega spectra.
3.2 Derivation of chemical abundances
The chemical abundances of different elements of J003643 were derived using both the EW method and spectral synthesis fitting (SSF), both implemented in E-iSpec, following a similar approach to Menon et al. (Reference Menon, Kamath, Mohorian, Van Winckel and Ventura2024). In the EW method, the observed EWs were compared with theoretical EWs based on synthetic spectra from a model atmosphere (ATLAS9; Castelli & Kurucz Reference Castelli, Kurucz, Piskunov, Weiss and Gray2003). The assumed abundances were iteratively adjusted until the observed and predicted EWs converged, yielding the best-fit values.
The SSF method involved comparing the observed spectra with synthetic spectra generated from model atmospheres, using a chi-square fitting procedure to iteratively refine the model parameters and determine precise chemical abundances. Instrumental and macroturbulent broadening were incorporated through Gaussian convolution, consistent with the UVES resolving power (
$R\approx 60\,000$
) and with macroturbulent velocities expected in cool, low-gravity stellar atmospheres. Examples of SSF applied to the spectral lines of four elements are shown in Figure 3: O I at 6 155.971 Å, 6 156.755 Å, and 6 158.187 Å, Y II at 6 613.731 Å, Eu II at 6 437.640 Å and Pb II at 5 608.853 Å. These illustrate the sensitivity of the derived abundances to both line strength and local continuum placement. SSF was performed alongside the EW method for these elements to ensure consistency and to validate the robustness of the derived abundances.
SSF of the O I lines at 6 155.971, 6 156.755, and 6 158.187 Å (top left), Y II line at 6 613.731 Å (top right), Eu II line at 6 437.640 Å (bottom left), and Pb II line at 5 608.853 Å (bottom right) for J003643. Here, A(X) denotes the logarithmic absolute abundance
$\log\epsilon(X)$
of the respective element, and A(X)
$=\,-10$
indicates a synthetic spectrum computed with zero abundance of that element.
The lines used for abundance derivation were selected based on the line selection criteria outlined in Section 3. The linelist used for the spectroscopic analysis of J003643 is provided in Table A1.
The uncertainties in the derived abundances were estimated using the method outlined in Deroo et al. (Reference Deroo, Reyniers, van Winckel, Goriely and Siess2005). E-iSpec calculates the errors as standard deviations (
$\sigma_{\rm |121|}$
) for each line, while the total error (
$\sigma_{\rm tot}$
) is computed as the quadratic sum of
$\sigma_{\rm |121|}$
, uncertainties due to atmospheric parameters, and the
$\textrm{[Fe/H]}$
error. To assess the sensitivity of the abundances to stellar parameters, we recomputed the abundances by varying
$T_{\rm eff}$
,
$\log g$
, and
$\xi_{\rm t}$
within their respective uncertainties (see Table 3). A
$\sigma_{\rm |121|}$
of 0.20 dex was adopted for species with only a single measurable line, reflecting the expected line-to-line scatter.
The derived chemical abundances for J003643 are presented in Table 4, and the result of the analysis is discussed in Section 3.3. The elements in Table 4 are arranged by atomic number (Z), with the corresponding solar abundances (
$\log\varepsilon_{\odot}$
) taken from Asplund et al. (Reference Asplund, Grevesse, Sauval and Scott2009). The table also includes the number of identified lines per element (N), the element-to-iron ratio (
$\textrm{[X/Fe]}$
), the total uncertainty on
$\textrm{[X/Fe]}$
(
$\sigma_{\rm tot}$
), the absolute abundance (
$\log\varepsilon$
), and the line-to-line scatter (
$\sigma_{\rm |121|}$
). Despite the inability to determine the abundances of several key nucleosynthesis elements, Table 4 presents quantified abundances for a wide range of s-process elements.
Spectroscopically determined abundance results for J003643.
Notes: The ions that were detected and their corresponding atomic number (Z) are listed in columns 1 and 2, respectively. The solar abundances (
$\log\varepsilon_{\odot}$
) in column 3 are retrieved from Asplund et al. (Reference Asplund, Grevesse, Sauval and Scott2009). N represents the number of lines used for each ion,
$\textrm{[X/Fe]}_{\rm LTE}$
is the element-over-iron ratio derived considering LTE,
$\sigma_{\rm tot}$
is the total uncertainty on
$\textrm{[X/Fe]}$
,
$\log\varepsilon$
is the determined abundance, and
$\sigma_{\rm |121|}$
is the line-to-line scatter. We impose a
$\sigma_{\rm |121|}$
of 0.20 dex for all ions for which only one line is available for the abundance determination.
$\textrm{[X/Fe]}_{\rm NLTE}$
is the element-over-iron ratio derived considering NLTE along with uncertainty eNLTE (see Section 3.2.1 for details).
Notably, this study presents the first direct measurement of the Pb abundance in a post-AGB star, derived from the Pb II line at 5 608.853 Å, which was the only detectable Pb line in J003643 (further details on Pb are provided in Section 6.3). In contrast, previous studies of post-AGB stars have only been able to derive upper limits on Pb abundance using SSF (e.g. De Smedt et al. Reference De Smedt2016), primarily due to the intrinsic weakness of Pb lines and line blending effects, which have hindered precise abundance measurements.
3.2.1 NLTE effects
Departures from LTE, if not accounted for, can introduce inaccuracies in spectroscopic analyses and lead to biased conclusions. To assess their impact, we tested possible NLTE effects on spectral lines of C I, O I, Mg I, and Ca I. Weak lines of Ti II (Mallinson et al. Reference Mallinson, Lind, Amarsi and Youakim2024) and Fe II (Lind, Bergemann, & Asplund Reference Lind, Bergemann and Asplund2012) are expected to show relatively mild departures from LTE. Therefore, we adopted
$\textrm{[Fe/H]}$
derived from Fe II lines as the metallicity and applied NLTE corrections to the elemental abundances of C, O, Mg, and Ca accordingly. The results, including uncertainties, are presented in Table 4 under the column ‘
$\textrm{[X/Fe]}_{\rm NLTE}$
’. To calculate the uncertainties of the NLTE abundances, we adopt the same systematic error as in the LTE analysis, the component that quantifies the sensitivity of the abundances to uncertainties in
$T_{\rm eff}$
,
$\log g$
, and
$\xi_{\rm t}$
by recomputing them within their quoted errors, since the NLTE corrections themselves are essentially invariant to these parameter shifts. We then compute the
$\sigma_{\rm |121|}$
of the NLTE abundances (eNLTE), which is found to be very similar to that in LTE. Consequently, the total uncertainty
$\sigma_{\rm tot}$
for the NLTE abundances matches the LTE value to two decimal places.
The NLTE calculations were performed using Balder (Amarsi et al. Reference Amarsi2018b), which is based on Multi3D (Leenaarts & Carlsson Reference Leenaarts, Carlsson, Lites, Cheung, Magara, Mariska and Reeves2009). These calculations were carried out using the same ATLAS model atmosphere of J003643 employed for LTE abundance determinations in this study. The abundances were computed for five values in steps of 0.5 dex around the 1D LTE value. The model atoms were adopted from Amarsi et al. (Reference Amarsi, Barklem, Collet, Grevesse and Asplund2019) for C I, Amarsi et al. (Reference Amarsi, Barklem, Asplund, Collet and Zatsarinny2018a) for O I, and Asplund et al. (Reference Asplund, Amarsi and Grevesse2021) for Mg I and Ca I.
A caveat of this test is that the adopted model atoms were originally calibrated for stars with lower effective temperatures and higher atmospheric densities than J003643. Nevertheless, the results provide insight into the extent to which departures from LTE might affect our abundance determinations.
3.3 Results of spectroscopic analysis: Atmospheric parameters and chemical abundances
In this section, we present the results of the spectroscopic analysis of J003643.
The atmospheric parameters derived for J003643 are summarised in Table 3. Our analysis confirms that J003643 is an A-type post-AGB star with an effective temperature of
$T_{\rm eff}$
=
$7\,552\pm91$
K. It has a low surface gravity (
$\log g$
=
$1.04\pm0.16$
dex) and an iron abundance of
$\textrm{[Fe/H]}$
=
$-0.97\pm0.11$
dex. Although the iron abundance of J003643 is low, it is comparable to the mean metallicity of the SMC (
$\textrm{[Fe/H]}\,= -0.7$
dex) (Luck et al. Reference Luck, Moffett and Barnes1998).
The derived chemical abundances for J003643 are presented in Table 4. Figure 4 illustrates the abundance distribution (
$\textrm{[X/Fe]}$
) as a function of atomic number (Z).
Spectroscopically derived abundances of J003643. The error bars represent the total uncertainties (
$\sigma_{\rm tot}$
). The data points are colour-coded: black for CNO elements, blue for Fe-peak elements, and red for s-process elements. Circles represent LTE abundances, while triangles represent NLTE abundances (for details on NLTE, see Section 3.2.1). Some elements are labelled for reference.
In Figure 4, the circles represent LTE abundances, while the triangles correspond to NLTE abundances (for details on NLTE, see Section 3.2.1). The NLTE abundances, where available, generally agree with the LTE results within the uncertainties.
Figure 4 shows that J003643 has a
$\textrm{[C/Fe]}$
of 1.33
$\pm$
0.14 dex and an
$\textrm{[O/Fe]}$
of -0.08
$\pm$
0.20 dex. Notably, it has a C/O ratio of
$12.58\pm0.25$
based on LTE abundances and
$16.21\pm0.22$
from NLTE-corrected abundances. This is relatively higher than the typical C/O ratios of s-process enriched post-AGB stars (
$\approx1$
–3), primarily driven by J003643’s low oxygen abundance, relative to typical post-AGB stars (see Section 6.1 for details).
Additionally, Figure 4 also shows that J003634 is enriched in s-process elements. The s-process distributions and overabundances of LIM stars are commonly described using four observational indices:
$\textrm{[ls/Fe]}$
,
$\textrm{[hs/Fe]}$
,
$\textrm{[s/Fe]}$
, and
$\textrm{[hs/ls]}$
. To maintain consistency, we use the same elemental abundances as in De Smedt et al. (Reference De Smedt2016) for calculating these indices. We define the hs index as the average of La, Ce, Nd, and Sm; the ls index as the average of Y and Zr; and the overall
$\textrm{[s/Fe]}$
index as the mean of all six s-process elements. For J003643, we derive
$\textrm{[ls/Fe]}$
= 1.72
$\pm$
0.17 dex,
$\textrm{[hs/Fe]}$
= 2.19
$\pm$
0.11 dex,
$\textrm{[hs/ls]}$
= 0.48
$\pm$
0.12 dex and
$\textrm{[s/Fe]}$
=
$2.09\pm0.20$
dex.
Furthermore, while previous studies of s-process enriched post-AGB stars have only reported upper limits for Pb abundances based on SSF (e.g. De Smedt et al. Reference De Smedt2016), this study provides the first direct Pb abundance measurement in a post-AGB star using both EW and SSF methods. The clearly detected Pb II line at 5 608.853 Å yields a consistent Pb abundance of
$\textrm{[Pb/Fe]}$
= 3.16 dex from EW fitting and
$\textrm{[Pb/Fe]}$
= 3.20 dex from SSF (see Figure 3d), enabling a more robust comparison with theoretical nucleosynthesis predictions.
4. Luminosity determination through SED fitting
Accurately determining the luminosity of a post-AGB star and combining it with its derived atmospheric parameters and elemental abundances provides valuable insights into its evolutionary stage and facilitates the estimation of its initial mass. However, deriving the luminosities of post-AGB stars remains challenging due to several factors, including the effects of circumstellar and interstellar reddening on observational photometry (see e.g. Kamath et al. Reference Kamath2022, Reference Kamath2023).
To determine the luminosity of J003643, we utilised its SED fitting parameters, following the approach outlined in Kluska et al. (Reference Kluska2022) and Kamath et al. (Reference Kamath2022). In summary, the total line-of-sight reddening or extinction parameter (
$E(B-V)$
) was determined by minimising the difference between the observed optical fluxes and the reddened photospheric models. This total reddening accounts for both interstellar and circumstellar extinction. We assumed that the total reddening follows the wavelength dependency of the interstellar extinction law (Cardelli, Clayton, & Mathis Reference Cardelli, Clayton and Mathis1989) with
$R_V\,= 3.1$
. While the extinction law in the circumstellar environment likely differs from the interstellar law, investigating this aspect is beyond the scope of this study.
For the atmospheric models, we adopted the Kurucz models (Castelli & Kurucz Reference Castelli, Kurucz, Piskunov, Weiss and Gray2003) with parameters derived from the spectroscopic analysis in Section 3.1 (see Table 3). The SED fitting was performed by interpolating within the
$\chi^2$
landscape, using models centred on the spectroscopically determined parameters and applying variations of
$\Delta T_{\rm eff}$
$\pm 500$
K,
$\Delta\log g$
$\pm 0.5$
dex, and
$\Delta \textrm{[Fe/H]}$
$\pm 0.5$
dex (see Section 3.1). The resulting SED of J003643 is shown in Figure 1.
The bolometric luminosity or SED luminosity (
$\rm L_{SED}$
) of J003643 was derived by integrating the flux under the dereddened photospheric SED model, assuming an average distance of
$62.1 \pm 1.9$
kpc to the SMC (Graczyk et al. Reference Graczyk2012). The derived SED luminosity (
$\rm L_{SED}$
) and its corresponding upper and lower limits for J003643 are
$7\,623^{8\,606}_{5\,761}L_{\bigodot}$
. To estimate the uncertainties in luminosity, we incorporated the upper and lower limits of the reddening values, as outlined in Table 5.
Overview of the effective temperature, metallicity, C/O ratio, s-process indices, derived luminosity and initial mass estimate of J003643.
Notes: See Section 3.2 for details on chemical abundances presented here. See Section 4 for details on luminosity derivation.
5. Stellar evolutionary models: ATON, MONASH and FRUITY
Comparing the derived chemical abundances of a star with stellar evolutionary models is key to understanding its evolution and nucleosynthesis. In this section, we compare the spectroscopically derived abundances of J003643 with predictions from three independent stellar evolutionary models: ATON (Section 5.1), MONASH (Section 5.2) and FRUITY (Section 5.3), to assess nucleosynthetic efficiency and constrain parameters such as initial mass and mixing.
5.1 ATON
To facilitate meaningful comparison with theoretical stellar evolutionary models, we first estimated the initial mass of J003643, a key parameter that governs stellar evolution and chemical yields. For this, we utilised evolutionary tracks computed with the ATON stellar evolution code (Ventura et al. Reference Ventura, Zeppieri, Mazzitelli and D’Antona1998).
ATON stellar evolution code models the structure and nucleosynthesis of LIM stars, employing the Full Spectrum of Turbulence (FST) model for convective mixing (Ventura et al. Reference Ventura, Zeppieri, Mazzitelli and D’Antona1998; Ventura, D’Antona, & Mazzitelli Reference Ventura, D’Antona and Mazzitelli2008; Ventura et al. Reference Ventura, Karakas, Dell’Agli, Garca-Hernández and Guzman-Ramirez2018). It includes treatments of mass loss, convective boundary mixing, and thermal pulses during the AGB phase. The code tracks the evolution of light-element surface abundances, particularly C, N, and O, shaped by internal mixing processes. Although it does not compute detailed heavy-element nucleosynthesis, ATON provides robust predictions for CNO enrichment and structural evolution relevant to AGB modelling (see e.g. Kamath et al. Reference Kamath2023).
In this study, we adopt an initial metallicity of
$Z=0.0014$
, and use ATON to model the stellar evolution of J003643 based on its spectroscopically derived luminosity, atmospheric parameters, and surface carbon and oxygen abundances, following the methodology of Kamath et al. (Reference Kamath2023).
Figures 5 and 6 illustrate the luminosity evolution and surface
$\textrm{[C/Fe]}$
abundance variation as functions of the AGB lifetime (normalised to the total duration of the AGB phase) for stars with initial masses of
$2M_{\bigodot}$
(black),
$2.5M_{\bigodot}$
(red), and
$3M_{\bigodot}$
(green). In Figure 5, the blue horizontal line represents the SED-derived luminosity of J003643 (see Section 4), while in Figure 6, the grey-shaded region indicates the spectroscopically derived carbon abundance of J003643 with its uncertainty (see Section 3.2). We use
$\textrm{[C/Fe]}$
rather than
$\textrm{[O/Fe]}$
to constrain AGB evolution because carbon is gradually enhanced through third dredge-up (TDU) episodes, making it highly sensitive to the progenitor mass and internal nucleosynthesis. In contrast, oxygen shows little surface variation during the AGB phase for low-mass stars (
$\lt$
3
$\rm M_{\odot}$
) and primarily reflects the composition of the progenitor gas. This distinction is confirmed by Kamath et al. (Reference Kamath2023), demonstrating that
$\textrm{[C/Fe]}$
correlates more tightly with stellar mass and TDU efficiency, while
$\textrm{[O/Fe]}$
remains largely unaffected in the mass range relevant to post-AGB stars. Nevertheless, the
$\textrm{[O/Fe]}$
predicted by the 2
$\rm M_{\odot}$
model assuming no
$\alpha$
-enhancement is
$\sim$
0.2 dex, which is slightly higher but still consistent within uncertainties with the spectroscopically derived oxygen abundance of J003643 (
$\textrm{[O/Fe]}$
=
$-0.08 \pm 0.20$
dex).
Luminosity evolution as a function of AGB lifetime for stars with an initial metallicity of
$Z = 0.0014$
. The models correspond to initial masses of
$2M_{\bigodot}$
(black),
$2.5M_{\bigodot}$
(red), and
$3M_{\bigodot}$
(green). The blue horizontal line represents the derived SED luminosity of J003643 (see Section 4). See text for more details.
Surface
$\textrm{[C/Fe]}$
abundance evolution as a function of AGB lifetime for stars with an initial metallicity of
$Z = 0.0014$
. The models correspond to initial masses of
$2M_{\bigodot}$
(black),
$2.5M_{\bigodot}$
(red), and
$3M_{\bigodot}$
(green). The grey-shaded region indicates the spectroscopically derived carbon abundance of J003643 with its uncertainty (see Section 3.2). See text for more details.
The evolutionary tracks show that all three models cross evolutionary phases consistent with the estimated luminosity of J003643. Specifically, in the
$2M_{\bigodot}$
model, the observed luminosity is reached toward the end of the AGB phase. In the
$2.5M_{\bigodot}$
model, it occurs in the first half of the AGB lifetime and in the
$3M_{\bigodot}$
model, the luminosity is attained at the beginning of the AGB phase. However, within the ATON grid, higher masses (
$\geq3M_{\bigodot}$
) can be ruled out, as hot-bottom burning (HBB) would prevent carbon enrichment, which contradicts the observed high
$\textrm{[C/Fe]}$
in J003643. Similarly, within the ATON grid, lower masses (
$\lt$
2
$\rm M_{\odot}$
) are also excluded, as they fail to reach the derived luminosity of J003643 (indicated by the blue line in Figure 5) (Dell’Agli et al. Reference Dell’Agli2015).
Furthermore, examining the surface carbon abundance evolution in Figure 6, we find that the observed carbon abundance of J003643 aligns best with the final phases of the AGB. This suggests that J003643 most likely originated from a star with an initial mass of about
$2M_{\bigodot}$
, corresponding to a formation epoch of approximately 1 billion years ago. We note that the initial mass estimated here refers to the mass at the ZAMS, before the star evolved into its post-AGB phase.
5.2 MONASH
The MONASH stellar evolution code (Lattanzio Reference Lattanzio1986; Karakas Reference Karakas2014) was used to construct detailed stellar evolution models of J003643. The stellar evolutionary sequences allow us to calculate the detailed nucleosynthesis, including s-process elements, using a post-processing nucleosynthesis code. We refer to Karakas & Lugaro (Reference Karakas and Lugaro2016) for further details. For this study, we used the same version of the code and input physics described in Karakas et al. (Reference Karakas2018). The main uncertainties that we examined include the amount of TDU, which we can change by including convective overshoot at the base of the convective envelope (e.g, see Kamath, Karakas, & Wood Reference Kamath, Karakas and Wood2012), and the size of the partially mixed zone (PMZ) in the post-processing calculations. In our post-processing calculations, the 13C pocket is formed by inserting protons into the top layers of the He-intershell during the deepest extent of each TDU event. The extent of the protons in the He-shell is called the PMZ. Observations of barium stars show a range of s-process abundances which likely indicate some natural variation in the size of 13C pockets (e.g. Cseh et al. Reference Cseh2018). For this reason, we experiment with calculating models with different size PMZ (we refer to Buntain et al. (Reference Buntain2017) for a detailed study of 13C pockets in our models, including a comparison to other studies).
We experiment with models with initial masses between 1.5 to 2
$\rm M_{\odot}$
with
$Z = 0.001$
and find that the best match to the luminosity of J003643 near the end of the TP-AGB phase occurs in a 1.7
$\rm M_{\odot}$
model. This is similar to the result from the ATON code (2
$\rm M_{\odot}$
, see Section 5.1), given that these are two independent stellar evolution codes and there is a slight difference in metallicity. We note that a 0.3
$\rm M_{\odot}$
offset is well within the typical systematic uncertainties of TP-AGB modelling. For the nucleosynthesis predictions (Figure 11, green line), we adopt a PMZ mass of 0.006
$\rm M_{\odot}$
, which provides the best overall match to the observed s-process enrichment.
The results and the interpretation of our comparison between the spectroscopically derived abundances of J003643 and the MONASH models, including the impact of PMZ on s-process abundances, are discussed in Section 6.2.
5.3 FRUITY
To explore the impact of differences in input physics and numerical treatments across stellar evolution codes, we also utilised the stellar evolution and nucleosynthesis framework: FRUITY (Full-Network Repository of Updated Isotopic Tables and Yields) (Cristallo et al. Reference Cristallo2011). FRUITY is designed to simulate the evolution and chemical enrichment of LIM stars, with a particular focus on s-process nucleosynthesis. These models span a range of initial masses (1.3–6.0
$\rm M_{\odot}$
) and metallicities (
$Z = 0.00002$
to
$Z = 0.03$
), making them well-suited for comparisons with stars observed in different galactic environments.
For this study, we use the s-process distribution from the latest FRUITY models, which incorporate the effects of mixing triggered by magnetic fields (Vescovi et al. Reference Vescovi, Cristallo, Busso and Liu2020), to compare with the spectroscopically derived abundances of J003643. These updated FRUITY models incorporate a magnetic mixing mechanism as a new driver for the formation of the 13C pocket, the primary neutron source for s-process nucleosynthesis. Unlike previous versions (Cristallo et al. Reference Cristallo2011; Piersanti, Cristallo, & Straniero Reference Piersanti, Cristallo and Straniero2013; Cristallo et al. Reference Cristallo, Straniero, Piersanti and Gobrecht2015), where the 13C pocket was formed via convective overshoot, this new approach accounts for buoyancy-driven magnetic instabilities, which naturally induce mixing within the He-intershell. This results in a self-consistent 13C pocket formation, influencing both neutron exposure and the overall efficiency of the s-process.
In addition to this revised mixing mechanism, several other updates have been implemented in the latest FRUITY models, including the equation of state (EOS) and the nuclear reaction network (see Vescovi et al. Reference Vescovi, Cristallo, Palmerini, Abia and Busso2021, for more details). For the models presented in this work, an updated initial chemical composition from Lodders (Reference Lodders2021) and revised values for C, N, O, and Ne from Magg et al. (Reference Magg2022) were used. Additionally, mass-loss prescriptions were updated using a revised period-mass-loss relation calibrated to the latest Galactic O- and C-rich giant data (Höfner & Olofsson Reference Höfner and Olofsson2018), with pulsation periods derived from the period-mass-radius relation of Trabucchi & Mowlavi (Reference Trabucchi and Mowlavi2022). The updated mass-loss rate is less efficient than that previously adopted in Vescovi et al. (Reference Vescovi, Cristallo, Busso and Liu2020, Reference Vescovi, Cristallo, Palmerini, Abia and Busso2021), further enhancing predictions of carbon and heavy-element abundances.
We tested models with initial masses between 1.5 and 2
$\rm M_{\odot}$
at
$Z = 0.001$
and found that the 2
$\rm M_{\odot}$
magnetic-mixing FRUITY model provides the best match to the observed heavy-element abundances (see Figure 12, black line). We also explore the magnetic-mixing FRUITY model with an initially r-process enhanced composition, adopting a solar r-process distribution prescribed by Prantzos et al. (Reference Prantzos, Abia, Cristallo, Limongi and Chieffi2020) scaled by +2 dex ([r/Fe] = +2 dex) from Ga to Bi (see Figure 12, magenta line).
The results and the interpretation of our comparison between the spectroscopically derived abundances of J003643 and the magnetic mixing FRUITY models are discussed in Section 6.2.
6. Discussion
In this section, we place the photospheric chemical composition of J003643 in a broader astrophysical context. We first compare its CNO and s-process abundance ratios with a relevant and comprehensive sample of post-AGB stars to investigate chemical trends and diversity (Section 6.1). We then explore the origin of its chemical enrichment by comparing its abundance pattern against predictions from various stellar evolutionary models (Section 6.2). Finally, we assess the longstanding Pb abundance discrepancy, including a first exploration of possible NLTE effects on Pb (Section 6.3).
6.1 Comparative analysis of key abundance ratios in post-AGB stars
The detailed spectroscopic analysis of J003643 revealed a relatively high C/O ratio (16.21) compared to other post-AGB stars (
$\sim$
1–3). To investigate this anomaly, we compared some of the key abundance ratios of J003643 (C/O,
$\textrm{[C/Fe]}$
,
$\textrm{[O/Fe]}$
,
$\textrm{[s/Fe]}$
,
$\textrm{[hs/ls]}$
) with a comprehensive sample of post-AGB stars, including single s-process enriched stars, single non-s-process enriched stars, and binary s-process enriched stars, spanning different galactic environments, the LMC, SMC and Galaxy. The full post-AGB sample (referred to hereafter as the ‘comparative sample’) considered in this study, including their references, is summarised in Table B1.
Figure 7a shows the spectroscopically derived C/O ratios versus
$\textrm{[s/Fe]}$
for the comparative sample of post-AGB stars. The data points are symbol- and colour-coded to distinguish between different groups (see caption for details). J003643 stands out as an outlier, displaying the highest C/O ratio (16.21) in the comparative sample, making it the first spectroscopically confirmed post-AGB star with such a high C/O ratio.
Comparison of key abundance ratios for the comparative sample of post-AGB stars. Red represents single s-process enriched post-AGB stars, blue corresponds to single non-s-process enriched post-AGB stars, and green denotes binary s-process enriched post-AGB stars. The target J003643 is highlighted with a black circle. LMC stars are shown as circles, SMC stars as squares, and Galactic stars as triangles. The numbers correspond to the index values listed in Table 8.
To investigate the high C/O ratio of J003643, we compared its
$\textrm{[C/Fe]}$
–
$\textrm{[s/Fe]}$
,
$\textrm{[O/Fe]}$
–
$\textrm{[C/Fe]}$
and
$\textrm{[O/Fe]}$
–
$\textrm{[Fe/H]}$
distributions with the comparative sample (Figures 7b, c and d respectively). Figure 7b reveals a strong positive correlation with an increase of
$\textrm{[C/Fe]}$
with
$\textrm{[s/Fe]}$
consistent with expectations from TDU during the AGB phase. J003643 clearly falls along this correlation, indicating its carbon enhancement scales with its s-process enrichment, similar to other s-process enriched post-AGB stars. This suggests a typical TDU history and implies that the high C/O ratio of J003643 is not due to an unusually high carbon abundance.
Figure 7c reveals a positive correlation between
$\textrm{[O/Fe]}$
and
$\textrm{[C/Fe]}$
, where stars with higher
$\textrm{[C/Fe]}$
generally also exhibit higher
$\textrm{[O/Fe]}$
. Similarly, Figure 7d shows a negative correlation between
$\textrm{[O/Fe]}$
and
$\textrm{[Fe/H]}$
, indicating that
$\textrm{[O/Fe]}$
tends to increase with decreasing metallicity. J003643 stands out as a distinct outlier in both figures, exhibiting a relatively low
$\textrm{[O/Fe]}\,=-0.08\pm0.20$
dex compared to stars with similar
$\textrm{[C/Fe]}$
and
$\textrm{[Fe/H]}$
. Given that oxygen is not substantially altered during the RGB or AGB phases (e.g. Karakas & Lattanzio Reference Karakas and Lattanzio2014), this oxygen deficit is likely a reflection of the initial chemical composition of its natal gas.
To investigate the oxygen abundance of J003643 and the comparative sample, we examined the chemical evolution trends of the Galaxy and the MCs. Chemical evolution studies of Galactic field giant stars show that
$\textrm{[O/Fe]}$
generally increases with decreasing metallicity, reaching values up to
$\sim$
1 dex at
$\textrm{[Fe/H]}\,\lesssim -1.5$
dex (see, e.g. Bensby et al. Reference Bensby, Feltzing, Lundström and Ilyin2005; Reddy, Lambert, & Prieto Reference Reddy, Lambert and Prieto2006; Mucciarelli et al. Reference Mucciarelli2023a). This trend is reflected in our Galactic comparative sample, where metal-poor stars show similarly enhanced oxygen abundances and consequently C/O ratios within the typical range of
$\sim$
1–3. In the LMC,
$\textrm{[O/Fe]}$
is as low as 0 dex at
$\textrm{[Fe/H]}\,\approx$
-0.5 dex and rises to
$\sim$
0.5 dex at
$\textrm{[Fe/H]}\,\approx$
-1.5 dex (e.g. Van der Swaelmen et al. Reference Van der Swaelmen, Hill, Primas and Cole2013). Our LMC comparative sample generally follows this trend at low metallicities, though some stars with
$\textrm{[Fe/H]}\,\lesssim-1$
dex show high
$\textrm{[O/Fe]}$
values up to 0.8 dex (see Figure 7d). This may reflect observational biases due to the limited number of low-metallicity LMC field giants available for comparison. In the SMC, field giant stars at
$\textrm{[Fe/H]}\approx -1.0$
dex exhibit
$\textrm{[O/Fe]}$
values ranging from
$-0.1$
to
$+0.4$
dex with a mean of
$\approx +0.2$
dex, although with a scatter (see Figure 8 of Mucciarelli et al. Reference Mucciarelli2023a). At
$\textrm{[Fe/H]}\approx -1.5$
dex, the mean
$\textrm{[O/Fe]}$
rises to
$\approx +0.8$
dex. Our SMC comparative sample, including J003643, generally follows this trend. Some stars with
$\textrm{[Fe/H]}\,\lesssim-1.5$
dex exhibit elevated
$\textrm{[O/Fe]}$
up to 1 dex (see Figure 7d), which may again reflect observational biases from the limited number of low-metallicity SMC field giants available for comparison.
The relatively low
$\textrm{[O/Fe]}\,=-0.08\pm0.2$
dex, compared to the comparative sample of post-AGB stars at similar
$\textrm{[Fe/H]}$
and
$\textrm{[C/Fe]}$
, together with
$[\alpha$
/Fe]
$\,\approx0$
dex of J003643 indicates that it likely formed from an interstellar medium (ISM) that was intrinsically oxygen-poor. Additionally, recent APOGEE observations of
$\approx$
3 600 RGB stars in the LMC and SMC by Nidever et al. (Reference Nidever2020) further confirm both
$[\alpha$
/Fe] and
$\textrm{[O/Fe]}$
remain essentially solar at
$\textrm{[Fe/H]}\, \approx$
-1, demonstrating that oxygen-poor,
$\alpha$
-solar abundance patterns are indeed present in SMC star-forming regions. Therefore, the relatively high C/O ratio observed in J003643 primarily reflects formation from oxygen-poor gas, rather than resulting from an unusually high carbon abundance.
Having established the likely chemical origin of J003643’s high C/O ratio, we next examined its s-process efficiency in the context of the comparative sample, using the
$\textrm{[hs/ls]}$
–
$\textrm{[s/Fe]}$
plane. Figure 8 shows the spectroscopically derived
$\textrm{[hs/ls]}$
ratios plotted against
$\textrm{[s/Fe]}$
for the comparative sample. Previous studies (Van Winckel & Reyniers Reference Van Winckel and Reyniers2000; Reyniers et al. Reference Reyniers, Van Winckel, Gallino and Straniero2004; van Aarle et al. Reference van Aarle, Van Winckel, De Smedt, Kamath and Wood2013) have reported a positive correlation between
$\textrm{[s/Fe]}$
and
$\textrm{[hs/ls]}$
, where stars with higher
$\textrm{[s/Fe]}$
tend to exhibit higher
$\textrm{[hs/ls]}$
ratios, reflecting a shift in the s-process path toward heavier elements at higher neutron exposures. Our analysis confirms this correlation and supports the theoretical expectation that stronger s-process enrichment corresponds to a greater relative production of hs elements compared to ls elements, due to increased neutron flux per iron seed. However, there is a
$2\sigma$
scatter. This is unlikely to arise from observational uncertainties, which are relatively well constrained, but may reflect variations in neutron exposure, the structure and extent of the 13C pocket, initial stellar mass, or other processes not fully captured by current models. Additionally, J003643 fits well within the least-squares relation derived from the comparative sample. This indicates that its heavy-to-light s-process element production is typical for its overall
$\textrm{[s/Fe]}$
value. Furthermore, as in the C/O-
$\textrm{[s/Fe]}$
plane, no systematic trend is observed with galactic environment, as stars from the Galaxy, LMC, and SMC remain evenly distributed.
$\textrm{[hs/ls]}$
as a function of
$\textrm{[s/Fe]}$
for the comparative sample of post-AGB stars. Colours, symbols and numbering remain the same as in Figure 6. The black line represents the least-squares fit, while the grey-shaded region indicates the
$2\sigma$
standard deviation.
$\textrm{[hs/ls]}$
ratio as a function of
$\textrm{[Fe/H]}$
for the comparative sample of post-AGB stars. Colours, symbols and numbering remain the same as in Figure 6. The black dotted line represents the theoretical prediction from a 2
$\rm M_{\odot}$
FRUITY model (Cristallo et al. Reference Cristallo, Straniero, Piersanti and Gobrecht2015). The dark brown solid line represents the least-squares linear fit to the combined observational data.
Lastly, to examine how neutron exposure varies with stellar metallicity, Figure 9 presents the spectroscopically derived
$\textrm{[hs/ls]}$
ratio as a function of
$\textrm{[Fe/H]}$
for the comparative sample. The colours and symbols follow the same scheme as in Figure 6, and the black and green dotted line shows the theoretical prediction from a 2
$\rm M_{\odot}$
FRUITY model (Cristallo et al. Reference Cristallo, Straniero, Piersanti and Gobrecht2015) and 1.5
$\rm M_{\odot}$
MONASH model (see Karakas Reference Karakas2014; Karakas & Lugaro Reference Karakas and Lugaro2016; Karakas et al. Reference Karakas2018) respectively. Previous studies (e.g. De Smedt et al. Reference De Smedt2016) did not report a clear correlation between
$\textrm{[Fe/H]}$
and
$\textrm{[hs/ls]}$
, likely due to the limited number (
$\sim$
14) of well-characterised post-AGB stars. However, with the inclusion of a more comprehensive sample of s-process enriched stars (
$\sim$
29), we now find a negative correlation between
$\textrm{[Fe/H]}$
and
$\textrm{[hs/ls]}$
. To explore the significance of this correlation, we performed a Pearson correlation test. Although the test gives a statistically significant negative correlation between
$\textrm{[Fe/H]}$
and
$\textrm{[hs/ls]}$
(slope=
$-0.35$
,
$r=-0.42$
,
$p=0.024$
), the object-to-object scatter is large, with objects 3,4, and 29 falling outside the
$2\sigma$
errors. Additionally, a significant fraction of the current sample does not match the model predictions. Although this trend supports theoretical predictions that lower-metallicity stars have higher neutron-to-seed ratios, favouring the production of heavier s-process elements and yielding elevated
$\textrm{[hs/ls]}$
ratios (see Gallino et al. Reference Gallino1998; Busso et al. Reference Busso, Gallino, Lambert, Travaglio and Smith2001), a more complete sample is required to confirm the correlation. Additionally, J003643 agrees with the model prediction, further reinforcing that its s-process efficiency is consistent with expectations for its metallicity. However, the persistent disagreement between model predictions and observations for the majority of stars, especially at
$\textrm{[Fe/H]}\,\lesssim-0.5$
dex, suggests that factors beyond metallicity, such as initial mass, TDU efficiency, dominant neutron source (13C vs. 22Ne), and mass-loss history, may significantly influence the resulting
$\textrm{[hs/ls]}$
ratios. This disagreement does not appear to depend on galactic environment, as stars from the Galaxy, LMC, and SMC are distributed uniformly in the
$\textrm{[hs/ls]}$
–
$\textrm{[Fe/H]}$
plane.
Comparison of the spectroscopically derived abundances of J003643 with stellar evolutionary model predictions reproduced from De Smedt et al. (Reference De Smedt2012), originally used for the post-AGB star J004441. Selected elements are labelled for reference. See text for details.
6.2 Understanding the nucleosynthetic origin of J003643 using predictions from different stellar evolutionary models
To investigate the nucleosynthetic origin of the heavy-element enrichment observed in J003643, we first assess whether its chemical composition could reflect pre-enrichment from its birth environment in the SMC. The SMC’s chemical evolution is distinct from that of the Galaxy, characterised by low metallicities and modest enhancements in s-process elements. For example, Mucciarelli et al. (Reference Mucciarelli2023a) report that the average [Zr/Fe], [Ba/Fe], and [La/Fe] abundances in SMC field giants remain below
$\sim$
0.5 dex, even at low metallicities. In contrast, J003643 exhibits significantly higher values for these s-process indicators, pointing toward substantial intrinsic enrichment during its AGB phase. Additionally, studies of SMC field stars and clusters have revealed signs of enhanced r-process contributions, particularly in elements like europium (Eu), with [Eu/Fe] often exceeding typical Galactic values at comparable metallicities (e.g. Reggiani et al. Reference Reggiani, Schlaufman, Casey, Simon and Ji2021; Mucciarelli et al. Reference Mucciarelli2023b).
To further explore the intrinsic nucleosynthesis, we compared the spectroscopically derived abundances of J003643 with predictions from various stellar evolutionary models previously applied to the most s-process enriched post-AGB star, J004441 (see De Smedt et al. Reference De Smedt2012, references therein). As shown in Figure 10, adapted from De Smedt et al. (Reference De Smedt2012), the best-fitting model for J004441 is the STAREVOL model with a late thermal pulse. However, despite J003643 having similar stellar parameters and
$\textrm{[s/Fe]}$
, this model fails to reproduce its observed abundances, particularly for C, O, several hs and ls elements, and most notably Pb. Other models considered in the same study similarly fail to simultaneously match the full abundance pattern of J003643.
Comparison of the spectroscopically derived abundances of J003643 with predictions from the MONASH stellar evolution code. The y-axis represents the elemental abundance ratio
$\textrm{[X/Fe]}$
, and the x-axis denotes the atomic number Z. The red squares and triangles with error bars show the LTE and NLTE-corrected abundances of J003643 derived in this study (see Section 3.2). The blue line with dots corresponds to the predicted abundance pattern from the standard MONASH model with no convective overshoot, with an initial mass of 1.7
$\rm M_{\odot}$
and metallicity
$Z=0.0014$
. The green line with dots corresponds to the predicted abundance pattern from the MONASH model with an initial mass of 1.7
$\rm M_{\odot}$
and metallicity
$Z = 0.0014$
, incorporating a large PMZ of 0.006
$\rm M_{\odot}$
. Some elements are labelled for reference. See text for details.
To perform a more targeted analysis of the heavy-element abundance of J003643, we strategically employed two sets of stellar evolution and stellar evolutionary models: the MONASH (Section 5.2) and FRUITY (Section 5.3) grids.
MONASH: The standard MONASH model (see Section 5.2 and Figure 11; blue line) significantly underpredicts the derived heavy-element abundances of J003643. However, the MONASH model, assuming a large PMZ of 0.006
$\rm M_{\odot}$
(see Section 5.2 and Figure 11; green line), predicts an s-process distribution that is very similar to the derived abundance of J003643, particularly for Fe-peak, the light s-process (ls) peak (Y, Zr) and the second peak (Ce, Nd). Despite this improvement, the predicted Pb abundance remains lower than derived. Additionally, elements such as Er and Hf are also underpredicted. The model attains a final C/O = 12.5, slightly overestimating the oxygen abundance.
FRUITY:The new magnetic mixing FRUITY model (see Section 5.3 and Figure 12; black line) slightly overestimates the abundances of CNO while the Fe-peak, ls and second s-process peak elements are well reproduced. The FRUITY model also underpredicts the derived Pb abundance. Additionally, it underpredicts the derived abundances of Eu, Er, Lu, Yb, and Hf. To explore this, we considered a modified version of the model that includes an initially r-process enhanced composition, adopting a solar r-process distribution as prescribed by Prantzos et al. (Reference Prantzos, Abia, Cristallo, Limongi and Chieffi2020), scaled by +2 dex ([r/Fe] = +2 dex) from Ga to Bi (see Figure 12, magenta line). While the pre-enrichment scenario improves the fit for several r-process sensitive elements, particularly Eu, Er, and Hf, it does not broadly affect the overall abundance pattern. This raises the possibility that J003643 may have formed from a locally r-process enriched ISM. This is supported by studies of the SMC, where field stars at low metallicities show systematically elevated [Eu/Fe] ratios compared to their Galactic counterparts, indicating a more efficient early r-process enrichment in the SMC (Reggiani et al. Reference Reggiani, Schlaufman, Casey, Simon and Ji2021; Mucciarelli et al. Reference Mucciarelli2023a). Although the average [Eu/Fe] in the SMC remains below +0.5 dex, the possibility of localised enrichment episodes, e.g. from neutron star mergers, remains plausible.
i
-process Models: Additionally, studies by Hampel et al. (Reference Hampel, Karakas, Stancliffe, Meyer and Lugaro2019) suggest that the abundance patterns of some Pb-poor post-AGB stars (
$\textrm{[Pb/Fe]}$
$\lt2.5$
dex) may be better explained by i-process nucleosynthesis (Cowan & Rose Reference Cowan and Rose1977; Malaney Reference Malaney1986; Hampel et al. Reference Hampel, Stancliffe, Lugaro and Meyer2016). At intermediate neutron densities, the i-process boosts the ls and hs elements without producing large amounts of Pb. Although J003643 is not Pb-poor, we tested whether i-process nucleosynthesis could nonetheless reproduce its observed abundance pattern. The i-process model of Choplin et al. (Reference Choplin, Siess, Goriely and Martinet2024), computed for a 1.5
$\rm M_{\odot}$
,
$Z = 0.001$
AGB star (Figure 13; cyan line), substantially overestimates the abundances of the ls elements while severely underpredicting the hs elements, including Pb. Similarly, the best-fitting i-process model from Hampel et al. (Reference Hampel, Karakas, Stancliffe, Meyer and Lugaro2019), assuming a neutron density of
$n\,= 10^{11}$
cm
$^{-3}$
(Figure 13; orange line), overestimates many of the heavy elements but still fails to reproduce the observed Pb abundance. These discrepancies suggest that i-process nucleosynthesis is unlikely to account for the observed abundance pattern of J003643.
Comparison of the spectroscopically derived abundances of J003643 with theoretical nucleosynthesis predictions from the new magnetic mixing FRUITY model. The y-axis represents the elemental abundance ratio
$\textrm{[X/Fe]}$
, and the x-axis denotes the atomic number Z. The red squares and triangles with error bars show the LTE and NLTE-corrected abundances of J003643 derived in this study (see Section 3.2). The black line corresponds to the predicted abundance pattern from the new magnetic mixing FRUITY model with an initial mass of 2
$\rm M_{\odot}$
and metallicity
$Z = 0.001$
. The magenta line represents a version assuming a pre-enriched r-process component with [r/Fe] = 2 dex, applied from Ga to Bi. Some elements are labelled for reference. See text for details.
Comparison of the spectroscopically derived abundances of J003643 with theoretical nucleosynthesis predictions from various stellar evolutionary models. The y-axis represents the elemental abundance ratio
$\textrm{[X/Fe]}$
, and the x-axis denotes the atomic number Z. The red squares and triangles with error bars show the LTE and NLTE-corrected abundances of J003643 derived in this study (see Section 3.2). The green and black lines correspond to predictions from the best-fitting MONASH and FRUITY models, respectively, while the magenta line represents a version assuming a pre-enriched r-process component with [r/Fe] = 2 dex, applied from Ga to Bi. Additional comparisons include the ATON model (brown line; Ventura et al. Reference Ventura, Zeppieri, Mazzitelli and D’Antona1998), an s-process model (yellow line; Lugaro et al. Reference Lugaro2015), and i-process models (cyan Choplin et al. Reference Choplin, Siess, Goriely and Martinet2024 and orange lines; Hampel et al. Reference Hampel, Karakas, Stancliffe, Meyer and Lugaro2019). Some elements are labelled for reference. See text for details.
Figure 13 summarises the best-fitting models, including ATON, MONASH, and FRUITY, as well as the i-process models from Hampel et al. (Reference Hampel, Karakas, Stancliffe, Meyer and Lugaro2019) and Choplin et al. (Reference Choplin, Siess, Goriely and Martinet2024) for comparison. Overall, the comparison between the observed abundances of J003643 and predictions from various stellar evolutionary models indicates that its heavy element enrichment results from an intrinsic s-process nucleosynthesis involving efficient TDU. However, the observed Pb abundance remains higher than predicted by all current models, despite varying nucleosynthetic assumptions. This persistent discrepancy highlights a gap in our understanding of Pb production in AGB stars. As the first post-AGB star with a direct and precise Pb abundance measurement, J003643 offers a valuable benchmark for refining theoretical models of heavy-element nucleosynthesis.
6.3 Investigating the Pb abundances and the longstanding Pb discrepancy in post-AGB stars
Pb is expected to be a major product of the s-process in low-mass AGB stars (
$\lt$
$3M_{\bigodot}$
), particularly at low metallicities where the neutron exposure is higher (e.g. Gallino et al. Reference Gallino1998; Goriely & Mowlavi Reference Goriely and Mowlavi2000). As the endpoint of the s-process chain, theoretical models predict that Pb should be strongly overabundant relative to the ls and hs peaks, resulting in high
$\textrm{[Pb/hs]}$
and
$\textrm{[Pb/ls]}$
ratios (e.g. Busso et al. Reference Busso, Gallino, Lambert, Travaglio and Smith2001; Lugaro et al. Reference Lugaro, Karakas, Stancliffe and Rijs2012). Accurate Pb measurements are thus essential to constrain the efficiency and termination of the s-process in these stars.
Despite these predictions, observational studies of s-process enriched post-AGB stars have consistently failed to detect Pb at the expected levels. In most cases, only upper limits have been obtained using SSF, due to the weakness of Pb lines in the optical, blending issues, and uncertainties in atomic data (e.g. De Smedt et al. Reference De Smedt2016; Kamath & Van Winckel Reference Kamath and Van Winckel2021). Depending on stellar temperature, Pb is probed using either the Pb I 4 057.807 Å line or the Pb II 5 608.853 Å line. Upper limits of derived Pb abundance for both single and binary s-process enriched post-AGB stars, compiled from the literature, are summarised in Table 6. For J003643, however, we derive the first direct Pb abundance measurement.
LTE and NLTE abundance ratios of lead (
$\textrm{[Pb/ls]}$
and
$\textrm{[Pb/hs]}$
) for s-process enriched single and binary post-AGB stars in the Galaxy and MCs, where lead abundance measurements are available. The table also includes their effective temperature and metallicity. See text for details.
Notes: All lead abundances and ratios, except for J003643, are upper limits derived using the SSF technique and have been adopted from De Smedt et al. (Reference De Smedt2016) and Kamath & Van Winckel (Reference Kamath and Van Winckel2021). NLTE-corrected Pb abundance ratios are presented in the last two columns. See text for details.
Previous studies have shown that for post-AGB stars with low metallicities (
$\textrm{[Fe/H]}$
$\lt-0.5$
dex), the derived
$\textrm{[Pb/hs]}$
and
$\textrm{[Pb/ls]}$
upper limits were significantly lower than theoretical predictions, with the discrepancy growing at lower metallicities (see Van Winckel & Reyniers Reference Van Winckel and Reyniers2000; De Smedt et al. Reference De Smedt2012, Reference De Smedt, Van Winckel, Kamath and Wood2015, Reference De Smedt2016). This persistent disagreement between predicted and deduced Pb abundances remains one of the key unresolved challenges in s-process nucleosynthesis (Kamath & Van Winckel Reference Kamath and Van Winckel2021).
Proposed explanations for this discrepancy include incomplete or inaccurate atomic data for Pb lines, limitations in spectral modelling, poor S/N in the blue region near the Pb I line, and incomplete treatment of physical processes governing the s-process in low-mass stars (e.g. Lugaro et al. Reference Lugaro, Karakas, Stancliffe and Rijs2012; Karakas & Lugaro Reference Karakas and Lugaro2016; De Smedt et al. Reference De Smedt2016). Additional effects – such as rotation, internal mixing (e.g. gravity-wave induced), and enhanced mass loss during or prior to the thermally-pulsing AGB phase – may add further uncertainty to the results (e.g. Herwig Reference Herwig2005; Siess, Goriely, & Langer Reference Siess, Goriely and Langer2004; Karakas & Lattanzio Reference Karakas and Lattanzio2014; Piersanti et al. Reference Piersanti, Cristallo and Straniero2013).
NLTE effects may also contribute to the discrepancy, particularly in warm, low-gravity post-AGB stars. As discussed in Kamath & Van Winckel (Reference Kamath and Van Winckel2021), NLTE calculations by Mashonkina et al. (Reference Mashonkina, Ryabtsev and Frebel2012) for the Pb I line at 4 057.807 Å in the Sun and a sample of metal-poor stars (
$-2.95\,\lt\,$
[Fe/H]
$\,\lt\,-0.7$
) showed that NLTE effects lead to systematically lower line absorption, resulting in positive abundance corrections of
$\Delta_{\mathrm{NLTE}}\sim$
0.2–0.45 dex. These effects become more pronounced at lower metallicities. However, the calculations were performed for stars with lower
$T_{\mathrm{eff}}$
and higher surface gravity than typical post-AGB stars.
Comparison of
$\textrm{[Pb/hs]}$
versus
$\textrm{[Fe/H]}$
for post-AGB stars with and without NLTE corrections. The left panel shows LTE-based upper limits of Pb abundances, while the right panel includes NLTE-corrected upper limits of Pb abundances derived in this study. Red symbols represent single s-process enriched post-AGB stars, while green symbols indicate binary s-process enriched post-AGB stars. LMC stars are shown as circles, SMC stars as squares, and Galactic stars as triangles. Downward arrows denote upper limits for all stars except J003643. The error bars along the x-axis indicate uncertainties in
$\textrm{[Fe/H]}$
. Theoretical predictions from FRUITY, STAREVOL, MSE, and MONASH stellar evolutionary models are overlaid for reference. See text for more details.
In this study, we perform an exploratory NLTE calculation using a simplified toy model for neutral Pb I to estimate NLTE effects on Pb abundance determinations. We focus on the neutral Pb I line, as Pb II – the dominant ionisation stage – is expected to remain close to LTE due to its stronger coupling with the local radiation field, making NLTE effects less significant (Mashonkina et al. Reference Mashonkina, Ryabtsev and Frebel2012).
As in Section 3.2.1, the NLTE calculations were performed using Balder (Amarsi et al. Reference Amarsi2018b), based on Multi3D (Leenaarts & Carlsson Reference Leenaarts, Carlsson, Lites, Cheung, Magara, Mariska and Reeves2009). The calculations were performed on a grid of MARCS model atmospheres (see Amarsi et al. Reference Amarsi2020 for details), for a range of microturbulence values (1, 2, and
$5\,\mathrm{km\,s^{-1}}$
) and
$\textrm{[Pb/Fe]}$
(from
$-1.5$
to
$+3.5$
in steps of
$0.5$
dex). The abundance corrections were interpolated or extrapolated (taking the edge values) onto the stellar parameters of interest.
For this test, a simple ‘toy’ model atom was constructed for neutral lead (Pb I). Energy levels and bound-bound transition rates were taken from the National Institute of Standards and Technology Atomic Spectra Database (NIST ASD; Ralchenko & Kramida Reference Ralchenko and Kramida2020). Photoionisation cross-sections were assumed to be hydrogenic. Inelastic electron collisions were estimated using the recipe of van Regemorter (Reference van Regemorter1962) for excitation and Allen (Reference Allen1973) for ionisation. Inelastic hydrogen collisions were estimated using the Drawin recipe Lambert (Reference Lambert1993); hydrogen collisional ionisation was assumed to be negligible (Barklem et al. Reference Barklem2011). For the collisional excitation recipes,
$\log gf$
was assumed to be
$-1.5$
for permitted lines (if missing from NIST ASD), and
$-3$
for forbidden lines.
This toy model is somewhat simpler than that used in Mashonkina et al. (Reference Mashonkina, Ryabtsev and Frebel2012). Possibly the main limitation here relative to that work is the absence of bound-bound transitions of high excitation potential (where Mashonkina et al. Reference Mashonkina, Ryabtsev and Frebel2012 include these via their own calculations using the Cowan code). Nevertheless, the resulting abundance corrections for the non-detected and hence upper limit of the Pb I 4 057.807 Å line are of the same order of magnitude as those presented in their Table 1, taking into account different assumptions about the inelastic hydrogen collisions. This could be because the NLTE effects are controlled by the photoionisation transitions as well as the radiative pumping of UV lines, which are included in our toy model. The
$\textrm{[Pb/Fe]}$
after applying the NLTE corrections for the post-AGB stars are presented in the last column of Table 6.
To further investigate the impact of NLTE effects on Pb abundance determinations, we compare the derived
$\textrm{[Pb/hs]}$
and
$\textrm{[Pb/ls]}$
upper limits by incorporating the derived NLTE corrections from the toy model for the Pb I lines. Figures 14 and 15 present the
$\textrm{[Pb/hs]}$
and
$\textrm{[Pb/ls]}$
upper limits (except for J003643) as a function of metallicity (
$\textrm{[Fe/H]}$
), respectively, adapted from De Smedt et al. (Reference De Smedt2016), for the comparative sample. These figures also include predictions from various stellar evolutionary models:
$2M_{\bigodot}$
FRUITY model (Cristallo et al. Reference Cristallo, Straniero, Piersanti and Gobrecht2015),
$2M_{\bigodot}$
STAREVOL code (Goriely & Siess Reference Goriely and Siess2004; Siess Reference Siess2007, and references therein),
$2M_{\bigodot}$
Mount-Stromlo Evolutionary (MSE) predictions (Fishlock et al. Reference Fishlock, Karakas, Lugaro and Yong2014; Karakas Reference Karakas2010, and references therein), and 1.5
$\rm M_{\odot}$
MONASH model (Karakas Reference Karakas2014; Karakas & Lugaro Reference Karakas and Lugaro2016; Karakas et al. Reference Karakas2018, see). In both cases, the left figure shows LTE-based upper limits of Pb abundances, while the right figure includes NLTE-corrected upper limits of Pb abundances derived in this study. We note that NLTE corrections have been derived and applied exclusively to the upper limits of Pb abundances derived using Pb I lines, with no corrections applied to Pb II lines. For all stars except J003643, the
$\textrm{[Pb/hs]}$
and
$\textrm{[Pb/ls]}$
ratios represent upper limits. The error bars along the x-axis indicate uncertainties in the metallicity (
$\textrm{[Fe/H]}$
) of the stars.
Same as Figures 14, but for
$\textrm{[Pb/ls]}$
versus
$\textrm{[Fe/H]}$
.
The comparison reveals that even after applying NLTE corrections, the majority of post-AGB stars at low metallicities (
$\textrm{[Fe/H]}$
$\lt-0.5$
dex) exhibit significantly lower upper limits of
$\textrm{[Pb/hs]}$
and
$\textrm{[Pb/ls]}$
values than theoretical predictions. Figure 14 shows that roughly half of the existing sample with
$\textrm{[Fe/H]}$
$\lt-0.5$
dex are compatible with the theoretical predictions within the error bars. This, however, may reflect observational bias because the current sample is far from complete. Although NLTE corrections tighten the upper limits of the Pb abundances, they do not fully resolve the disagreement at low metallicities. Additionally, at higher metallicities, the NLTE corrections lead to an overall increase in the derived upper limits of
$\textrm{[Pb/hs]}$
and
$\textrm{[Pb/ls]}$
compared to their LTE-based values. This result suggests that NLTE effects must be accounted for in Pb abundance determinations, but they are insufficient to explain the observed discrepancies at low metallicities. Furthermore, J003643 is the first post-AGB star with a clear detection and precise derivation of Pb abundance, rather than an upper limit, which is significantly higher than that of the comparative sample (see Table 6). Yet, even this robust detection remains markedly underpredicted by current nucleosynthesis models. This underscores persistent shortcomings in our theoretical understanding of s-process nucleosynthesis, particularly in the context of explaining Pb production at low metallicities.
7. Summary and conclusions
In this paper, we expand the known chemical diversity among s-process enriched post-AGB stars, presenting a detailed abundance analysis of J003643, a single post-AGB star in the SMC. Using high-resolution VLT/UVES spectra and detailed analysis with E-iSpec, we derived the atmospheric parameters and elemental abundances of J003643. J003643 exhibits a C/O ratio of 16.21
$\pm$
0.22. With a
$\textrm{[s/Fe]}$
= 2.09 dex, J003643 also provides the first direct Pb abundance measurement in a post-AGB star (
$\textrm{[Pb/Fe]}$
= 3.16
$\pm$
0.18 dex) using the Pb II 5608 Å line, consistent across both EW and SSF methods.
To investigate the origin of J003643’s relatively high C/O ratio, we compared its key abundance ratios with those of
$\sim$
28 comparative sample of post-AGB stars from the Galaxy, LMC, and SMC. While J003643 follows the expected
$\textrm{[C/Fe]}$
–
$\textrm{[s/Fe]}$
trend, consistent with a typical TDU history, it stands out as a clear outlier when compared in both the
$\textrm{[O/Fe]}$
–
$\textrm{[C/Fe]}$
and
$\textrm{[O/Fe]}$
–
$\textrm{[Fe/H]}$
planes. J003643 exhibits a relatively low
$\textrm{[O/Fe]}$
= -0.08
$\pm$
0.20 dex and [
$\alpha$
/Fe]
$\approx$
0 dex compared to its Galactic and LMC counterparts with similar
$\textrm{[C/Fe]}$
and
$\textrm{[Fe/H]}$
, which typically show
$\textrm{[O/Fe]}$
$\approx$
0.5–1.0 dex. This relatively low
$\textrm{[O/Fe]}$
and
$\alpha$
-abundance of J003643 is consistent with the chemical evolution of SMC at
$\textrm{[Fe/H]}\,\approx$
-1 dex, and contrasts with the
$\alpha$
-enhanced trend observed in the Galaxy and LMC at the same metallicity. These comparisons suggest that the high C/O ratio in J003643 arises primarily from an oxygen-poor natal environment, rather than from an unusually high carbon enrichment.
Additionally, to investigate the nucleosynthetic origin of J003643’s heavy-element abundances, we first considered whether they could reflect its birth environment in the SMC. However, its abundance pattern differs markedly from that of typical SMC field giant stars, which are commonly used to trace the chemical evolution of the SMC. We then compared its abundances with predictions from various stellar evolutionary models: ATON, MONASH, and FRUITY, the latter two incorporating post-processing nucleosynthesis. While the models reproduce the observed abundance of CNO,
$\alpha$
, Fe-peak and s-process elements, they systematically underpredicts Pb abundance, despite the varying nucleosynthetic assumptions. This highlights persistent gaps in our understanding of lead production in AGB stars.
To explore this, we analysed Pb abundances across the comparative sample of s-process enriched post-AGB stars using NLTE-corrected values from a simplified toy model. While NLTE corrections bring the upper limits a bit nearer to the model predictions, improving consistency in some cases, major discrepancies remain for stars with
$\textrm{[Fe/H]}\,\lesssim$
-0.5 dex, further reinforcing our limited understanding of lead production.
In summary, J003643 with its high C/O ratio and the first precise measurement of Pb abundance presents a valuable benchmark for advancing our understanding of CNO and s-process nucleosynthesis, providing critical constraints on AGB nucleosynthesis, dredge-up efficiency, and the development of improved model prescriptions for key heavy elements.
Acknowledgement
This study is based on observations collected with the Very Large Telescope at the ESO Paranal Observatory (Chile) of program number 092.D-0485. MM1 acknowledges the financial support provided by the International Macquarie Research Excellence Scholarship (iMQRES) program for the duration of this research. MM1, DK, and MM2 also acknowledge the ARC Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D). DK and HVW acknowledge the support of the Australian Research Council Discovery Project DP240101150. AMA acknowledges the support from the Swedish Research Council (VR 2020-03940) and from the Crafoord Foundation via the Royal Swedish Academy of Sciences (CR 2024-0015). SC acknowledges the funding by the European Union – NextGenerationEU RFF M4C2 1.1 PRIN 2022 project ‘2022RJLWHN URKA’ and the INAF Theory Grant ‘Understanding Rprocess & Kilonovae Aspects (URKA)’. DV acknowledges the financial support from the German-Israeli Foundation (GIF No. I-1500-303.7/2019). AK acknowledges the support of the Australian Research Council Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D), through project number CE170100013. P.V. acknowledges the support received from the PRIN INAF 2019 grant ObFu 1.05.01.85.14 (‘Building up the halo: chemodynamical tagging in the age of large surveys’, PI. S. Lucatello). HVW acknowledges support from the Research Council, KU Leuven, under grant numbers IRI-I000225N and I000325N.
Supplementary material
The supplementary material for this article can be found at https://doi.org/10.1017/pasa.2025.10085.
Data availability statement
The data underlying this article is made available online.
Appendix A. Linelist of J003643
Linelist of J003643.
Notes: Linelist used for the abundance determination of J003643. The last column shows the calculated equivalent width (EW). The full line list used for the spectroscopic analysis of J003643 is provided as online supplementary material.
Appendix B. Comparative Sample of Post-AGB Stars
In this appendix, we present the comparative sample of post-AGB stars discussed in this study. Table 8 provides a comprehensive list of single s-process enriched post-AGB stars, single non-s-process enriched post-AGB stars, and binary s-process enriched post-AGB stars, spanning different galactic environments, including the LMC, SMC, and the Galaxy. This dataset serves as the basis for our comparative analysis of heavy-element enrichment, neutron irradiation efficiency, and the dependence of chemical signatures on stellar parameters, as discussed in Section 6.1.
Fundamental properties, chemical abundances, and s-process indices of the entire sample of s-process -rich single post-AGB stars, s-process non-enriched single post-AGB stars, and s-process -rich binary post-AGB stars in the Galaxy and MCs.
Notes: References: 1 – Kamath et al. (Reference Kamath2022), 2 – De Smedt et al. (Reference De Smedt2012), 3 – van Aarle et al. (Reference van Aarle, Van Winckel, De Smedt, Kamath and Wood2013), 4 – De Smedt et al. (Reference De Smedt, Van Winckel, Kamath and Wood2015), 5 – Reddy et al. (Reference Reddy, Bakker and Hrivnak1999), 6 – Van Winckel & Reyniers (Reference Van Winckel and Reyniers2000), 7 – De Smedt et al. (Reference De Smedt2016), 8 – Pereira et al. (Reference Pereira, Sales Silva, Chavero, Roig and Jilinski2011), 9 – Klochkova & Kipper (Reference Klochkova and Kipper2006), 10 – Reyneirs (Reference Reyneirs2000), 11 – Rao et al. (Reference Rao, Giridhar and Lambert2012), 12 – Van Winckel (Reference Van Winckel1997), 13 – Molina et al. (Reference Molina, Pereira and Arellano Ferro2019), 14 – Şahin et al. (2011), 15 – Pereira et al. (Reference Pereira, Lorenz-Martins and Machado2004), 16 – Arellano Ferro et al. (Reference Arellano Ferro, Giridhar and Mathias2001), 17 – Reyniers & Cuypers (Reference Reyniers and Cuypers2005), 18 – Kamath et al. (Reference Kamath2017), 19 – Menon et al. (Reference Menon, Kamath, Mohorian, Van Winckel and Ventura2024).
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