#  s-process Enriched Evolved Binaries in the Galaxy and the Magellanic Clouds

Meghna Menon  School of Mathematical and Physical Sciences, Macquarie
University, Balaclava Road, Sydney, NSW 2109, Australia  [ Devika Kamath
School of Mathematical and Physical Sciences, Macquarie University, Balaclava
Road, Sydney, NSW 2109, Australia  Maksym Mohorian  School of Mathematical and
Physical Sciences, Macquarie University, Balaclava Road, Sydney, NSW 2109,
Australia  Hans Van Winckel  Instituut voor Sterrenkunde, K.U.Leuven,
Celestijnenlaan 200D bus 2401, B-3001, Leuven, Belgium  Paolo Ventura  INAF,
Observatory of Rome, Via Frascati 33, I-00077 Monte Porzio Catone (RM), Italy

###### Abstract

Post-asymptotic giant branch stars (post-AGB) in binary systems, with typical
orbital periods between $\sim\\!100$ to $\sim\\!1000$ days, result from a
poorly understood interaction that terminates their precursory AGB phase. The
majority of these binaries display a photospheric anomaly called ‘chemical
depletion’, thought to arise from an interaction between the circumbinary disc
and the post-AGB star, leading to the reaccretion of pure gas onto the star,
devoid of refractory elements due to dust formation. In this paper, we focus
on a subset of chemically peculiar binary post-AGBs in the Galaxy and the
Magellanic Clouds (MCs). Our detailed stellar parameter and chemical abundance
analysis utilising high-resolution optical spectra from VLT+UVES revealed that
our targets span a $T_{\rm eff}$ of 4900 - 7250 K and [Fe/H] of -0.5 - -1.57
dex. Interestingly, these targets exhibit a carbon ([C/Fe] ranging from 0.5 -
1.0 dex, dependant on metallicity) and s-process enrichment
([s/Fe]$\,\geq\\!1$dex) contrary to the commonly observed chemical depletion
pattern. Using spectral energy distribution (SED) fitting and period-
luminosity-colour (PLC) relation methods, we determine the luminosity of the
targets (2700 $-$ 8300 $\rm L_{\odot}$), which enables confirmation of their
evolutionary phase and estimation of initial masses (as a function of
metallicity) (1 - 2.5 $\rm M_{\odot}$). In conjunction with predictions from
dedicated ATON stellar evolutionary models, our results indicate a predominant
intrinsic enrichment of carbon and s-process elements in our binary post-AGB
targets. We qualitatively rule out extrinsic enrichment and inherited
s-process enrichment from the host galaxy as plausible explanations for the
observed overabundances. Our chemically peculiar subset of intrinsic carbon
and s-process enriched binary post-AGBs also hints at potential variation in
the efficiency of chemical depletion between stars with C-rich and O-rich
circumbinary disc chemistries. However, critical observational studies of
circumbinary disc chemistry, along with specific condensation temperature
estimates in C-rich environments, are necessary to address gaps in our current
understanding of disc-binary interactions inducing chemical depletion in
binary post-AGB systems.

###### keywords:

stars: evolution - binaries - AGB and post-AGB - chemically peculiar -
abundances, techniques: spectroscopic, galaxies: Magellanic Clouds

Astrophysics and Space Technologies Research Centre, Macquarie University,
Balaclava Road, Sydney, NSW 2109, Australia Meghna
<EMAIL_ADDRESS>Astrophysics and Space
Technologies Research Centre, Macquarie University, Balaclava Road, Sydney,
NSW 2109, Australia INAF, Observatory of Rome, Via Frascati 33, I-00077 Monte
Porzio Catone (RM), Italy Astrophysics and Space Technologies Research Centre,
Macquarie University, Balaclava Road, Sydney, NSW 2109, Australia

##  1 Introduction

Standard stellar evolutionary models, describing the evolution of low- and
intermediate-mass (LIM, 1-8 $\rm M_{\odot}$) single stars, predict the
occurrence of the slow neutron capture process (s-process ) during their
Asymptotic Giant Branch (AGB) phase (Maurizio2001; Herwig2005; karakas14a,
see). The s-process results in the production of approximately half of the
elements heavier than iron (Gallino1998; Kappeler2011; kobayashi20, see). The
other half is thought to be due to the rapid neutron capture process
(r-process) happening in massive stars ($>\\!8\mbox{\,$\rm M_{\odot}$}$)
(Wanajo2011; Kajino2019, see). Recent investigations suggest the existence of
additional nucleosynthetic processes such as the intermediate neutron capture
process (Choplin2021; Choplin2022; Choplin2023, i-process, see), contributing
to the production of heavy elements in low-mass (1-3 $\rm M_{\odot}$) AGB
stars. The validity of these predictions has been observationally verified
through studies of AGB stars (Abia2002; Jonsell2006; Straniero2014; Cseh2019;
Shetye2020, e.g.,) and post-AGB stars (Vanwinckel2000; Reyniers2003;
Kamath2014; kamath15, e.g.,).

Post-AGB stars serve as superior tracers of AGB nucleosynthesis and dredge-up
compared to AGB stars. (vanwinckel03; kamath20; Kamath2022Universe, see).
Notably, their higher photospheric temperatures ($\sim\\!3000$ K to
$\sim\\!30000$ K) compared to their preceding AGB phase ($\sim\\!2000$ K to
$\sim\\!4000$ K) ensure that the optical spectra of post-AGB stars allow for
the detection of atomic transitions of a wide range of elements from CNO up to
the heaviest s-process elements, well beyond the Ba peak (Vanwinckel2000;
desmedt12; desmedt2016, e.g.,).

Post-AGB stars exhibit a distinctive Infrared (IR) excess, indicative of their
dusty circumstellar environment vanwinckel03. Detailed investigations of the
spectral energy distribution (SED) in optically bright post-AGB stars have
revealed two main categories based on the nature of their IR excess: ‘shell-
source’ and ‘disc-source’ vanwinckel03; Gezer2015; Manick2018. The shell-
sources represent single post-AGB stars with a distinctive double-peaked SED.
The first peak (near-IR) corresponds to the photospheric component, while the
second peak (mid-IR) characterises a detached and expanding shell of cold
dust—an AGB dust shell remnant. However, the disc-sources display a broad IR
excess, commencing in the near-IR region, indicating the existence of a stable
compact dusty disc (Gezer2015, see). Observational studies have now firmly
established that the presence of the stable compact disc (circumbinary disc)
around the disc-sources is attributed to their binary nature (vanwinckel09;
oomen18; Kluska2022, e.g.,).

Observational studies of post-AGB stars in the Galaxy (Vanwinckel2000; rao12;
deSmedt2015; Kamath2022, e.g.,) and the Magellanic Clouds (MCs) (Kamath2014;
kamath15, e.g.,) have shown that they are far more chemically diverse than
anticipated. Typically, low-mass single post-AGB stars are carbon and
s-process enriched, a reflection of the nucleosynthetic processes that occur
during and prior to their AGB phase (Reyniers2003, eg). Notably, some single
post-AGB stars (shell-sources) stand out as the most s-process enriched
objects known to date (Reyniers2004; desmedt12, e.g.,). By and large,
theoretical single-star low-mass AGB models are in agreement with observations
(vanaarle11; Desmedth2014; deSmedt2015; desmedt2016, e.g.,). However, a study
by kamath17 reported a subset of luminous single post-AGB stars (one in the
Small Magellanic Cloud (SMC) and two in the Galaxy) that exhibited neither
traces of carbon enhancements nor s-process elements, suggesting a likely
failure of the third dredge-up (TDU). Further expanding on this, a recent
investigation by Kamath2022 categorised single post-AGB stars with similar
atmospheric parameters into two groups: those displaying s-process enrichment
and those exhibiting no s-process enrichment.

Additionally, the majority of the post-AGB stars in binary systems (disc-
sources) exhibit a chemical anomaly in their photosphere known as ‘chemical
depletion’ (oomen18; kamath19, see). This phenomenon arises from the
interaction between the binary post-AGB star and the surrounding circumbinary
disc (disc-binary interaction). Their photospheric abundance pattern resembles
the gas phase of the interstellar medium, with volatile elements like Zn and S
maintaining their initial abundances, while refractory elements, including
s-process elements, are notably underabundant, making them extrinsically
metal-poor.

In this paper, we focus on a subset of chemically peculiar post-AGB disc-
sources that show carbon and s-process enrichment in their photospheric
chemical composition, contrary to the commonly observed photospheric chemical
depletion typically observed in disc-sources. We present a detailed
atmospheric parameter and chemical abundance analysis of J005107.19-734133.3
(hereafter referred to as J005107), which represents the first known post-AGB
disc-source in the SMC with an s-process enrichment. The s-process enrichment
of this star was initially identified in the SMC survey by Kamath2014. In
addition, we incorporate two previously recognised s-process enriched post-AGB
disc-sources: MACHO 47.2496.8 in the Large Magellanic Cloud (LMC) Reyniers2007
and HD 158616 in our Galaxy desmedt2016. This provides an overview of carbon
and s-process enriched binary post-AGB stars across both the Galaxy and the
MCs. The unusual s-process enrichment in these stars suggests that the disc-
binary interaction did not induce a photospheric chemical depletion. Through
this study, we aim to understand the efficiency of chemical depletion in these
systems and the effects of binarity on their peculiar chemical composition. We
also investigate the underlying mechanism responsible for this chemical
peculiarity.

This paper is structured as follows: Section 2, presents an overview of the
targets in this study, providing detailed information on the photometric and
spectroscopic data associated with each target. In Section 3, we provide a
detailed description of our spectral analysis, to derive the atmospheric
parameters and chemical abundances of the target stars. In Section 4, we
detail SED fitting, luminosity derivation and initial mass estimation of the
targets. Finally, in Section 5, we investigate the chemical peculiarity of our
targets and their underlying mechanism by comparing the observationally
derived chemical abundances with theoretical predictions from the ATON
evolutionary models ventura98.

##  2 Targets and Observations

The target sample for this study consists of three chemically peculiar objects
previously classified as post-AGB stars, that have a ‘disc-type’ SED (see
Figure 6) and lie within the ‘disc box’ of Gezer2015 (see Figure 1). The three
targets are J005107 from the SMC Kamath2014, MACHO 47.2496.8 from the LMC
reyniers05, and HD 158616 desmedt2016 from the Galaxy. We note that HD 158616
is a confirmed binary according to orbital parameter studies conducted by
oomen18. With regards to J005107 and MACHO 47.2496.8, taking into account a
combination of their SED characteristics and pulsation features (as detailed
below for each of the targets), we conclude that these two stars also reside
in binary systems.

In Table 1, we present our target sample including their other names and two
sets of stellar parameters. The stellar parameters under "This Study"
represent the spectroscopically derived atmospheric parameters in this study.
The stellar parameters under "Literature" represent the spectroscopically
determined atmospheric parameters from previous Literature analysis.

Table 1: Target sample along with two sets of stellar parameters. The final
column lists the references to the previous literature analysis.

#ID | Object Name | Other Name |  | $T_{\rm eff}$
---
(K)
| $\log g$
---
(dex)
| [Fe/H]
---
(dex)
| $\xi_{\rm t}$
---
(km s-1)
|  | $T_{\rm eff}$
---
(K)
| $\log g$
---
(dex)
| [Fe/H]
---
(dex)
| $\xi_{\rm t}$
---
(km s-1)
Ref.
| This Study | Literature |
1 | J005107.19-734133.3 | OGLE SMC-T2CEP-18 | 5768 $\pm$ 85 | 0.21 $\pm$ 0.10 | -1.57 $\pm$ 0.10 | 4.08 $\pm$ 0.05 |  | 5267 $\pm$ 250 | 0.72 $\pm$ 0.50 | -1.56 $\pm$ 0.50 | … | 1
2 | MACHO 47.2496.8 | OGLE LMC-T2CEP-15 | 4898 $\pm$ 100 | 0.00 $\pm$ 0.50 | -1.42 $\pm$ 0.16 | 4.00 $\pm$ 1.00 |  | 4900 $\pm$ 250 | 0.00 $\pm$ 0.50 | -1.50 $\pm$ 0.50 | 3.50 $\pm$ 1.00 | 2
3 | HD 158616 | IRAS 17279-1119 | 7379 $\pm$ 110 | 1.47 $\pm$ 0.25 | -0.50 $\pm$ 0.20 | 2.97 $\pm$ 0.25 |  | 7250 $\pm$ 125 | 1.25 $\pm$ 0.25 | -0.64 $\pm$ 0.12 | 3.00 $\pm$ 0.50 | 3

  * •

Notes: The stellar parameters under "This study" represent the
spectroscopically determined atmospheric parameters obtained using the
$Python$ wrapper of iSpec (E-iSpec) (see section 3) whereas the stellar
parameters under the title "Literature" represent the spectroscopically
determined atmospheric parameters from the Literature analysis. Note that the
low-resolution spectral analysis of J005107.19-734133.3 did not provide an
estimated $\xi_{\rm t}$ value. Detailed information on the tabulated
information can be found in the individual studies in column ’Ref’. The column
’Ref.’ indicates the individual study: 1 - Kamath2014, 2 - Reyniers2007, 3 -
desmedt2016

In the following paragraphs, we discuss the individual targets of our study in
detail.

Figure 1: The WISE colour-colour diagram for the sample stars along with the
stars studied in Gezer2015 is depicted here. The different types of SED
characteristics among the post-AGB stars are represented here with different
symbols and colours. The Non-IR box represents the non-dusty stars that show
no IR excess in their SEDs. The sample stars are numbered according to their
position in Table 1 for reference.

J005107 has been classified as a post-AGB star and an RV Tauri pulsator in the
photometric study conducted by Manick2018. Additionally, Manick2018
categorised J005107 as an RVa type due to the lack of prominent long-term
variability, based on its OGLE III light curve (LC). The fundamental period of
this star is approximately 39.67 days according to the latest OGLE IV
database, Soszy2018. In Figure 2 (left), we present the LC of J005107 from the
latest data release: OGLE IV. Furthermore, Manick2018 also identified J005107
as a disc-source due to the presence of a characteristic IR excess in its SED
(see Figure 6), consistent with the presence of a circumbinary disc, which is
typical in binary post-AGB stars. Notably, the prominent Ba II features in the
low-resolution optical AAOmega spectra presented in Kamath2014 recognised
J005107 as the first s-process enriched RV Tauri star in the SMC.

MACHO 47.2496.8 was initially classified both as a post-AGB star and as an RV
Tauri pulsator in the MACHO Project: LMC Variable Star Inventory VII,
conducted by Alcock_1998 on optically bright post-AGB stars in the LMC.
Additionally, Manick2018 classified MACHO 47.2496.8 as an RVa type, based on
its OGLE III LC. The fundamental period of this star is approximately 56.48
days according to the latest OGLE IV database Soszy2018. In Figure 2 (right),
we present the LC of MACHO 47.2496.8 from the latest data release: OGLE IV.
Manick2018 also identified MACHO 47.2496.8 as a disc-source due to the
presence of a characteristic IR excess in its SED. In a series of low-
resolution spectra described by Pollard_2000, MACHO 47.2496.8 exhibited strong
C2 bands and Ba II features, leading to its identification as the first carbon
and s-process enriched RV Tauri star. This classification was further
confirmed by a subsequent high-resolution spectral analysis by Reyniers2007.

HD 158616 has been classified as an optically bright post-AGB star with a
carbon enrichment, as determined by the spectroscopic study of Hans1997.
Additionally, the high-resolution spectroscopic studies by rao12 and
desmedt2016 established HD 158616 as the first post-AGB star rich in s-process
elements discovered to be in a spectroscopic binary. HD 158616 is confirmed to
be a binary star with an orbital period of 365.0 days, and additional orbital
properties can be found in oomen18. desmedt2016 also identified this star as a
disc-source due to a characteristic IR excess in its SED.

The SED fitting of the target stars is detailed in Section 4.1.

Figure 2: The phased LCs of the RV Tauri targets J005107 (left) and MACHO
47.2496.8 (right). The fundamental pulsation period used to phase the LC of
each target is mentioned in the text. The LCs are scattered due to their semi-
regular nature; they usually show considerable variations from cycle to cycle.
This behaviour is typically more pronounced for the longer-period RV Tauri
stars. The photometric data for J005107 and MACHO 47.2496.8 have been sourced
from the latest OGLE IV database of Type II Cepheids Soszy2018.

###  2.1 Photometric Data

To construct the SEDs in Section 4.1, we collected the photometric data from
the Vizier database Vizier2000. Photometry at optical and near-IR wavelengths
characterises the photospheric emission of the post-AGB star. Subsequently,
the post-AGB photosphere is fitted using these data points (see Section 4.1).
The most significant photometry bands we used at these wavelengths are the
UBVRI Johnson-Cousins bands Bessell1990. For one of the targets, we also used
photometry from Geneva Geneva1999 and SDSS SDSS2017. Emission at longer
wavelengths is dominated by low-temperature emission from the dusty disc.
Therefore, photometry at mid- and far-IR wavelengths defines the circumstellar
environment. To characterise this we use the photometric data from the 2MASS
All-Sky Catalog of Point Sources Cutri2003, the WISE All-Sky Data catalogue
Cutri2012, the AKARI/IRC mid-IR all-sky survey Ishihara2010, and the IRAS
catalogue of Point Sources IRAS.

Table 2: Photometric data of the targets. See text for full details.

Object Name | RA (deg) | Dec (deg) | U | B | SDSS.RP | V | R | I | J | H | K | W1 | W2 | AKARI.S9W | IRAS.F12 | W3 | W4 | IRAS.F25 | IRAS.F60 | IRAS.F100
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
J005107 | 12.780083 | -73.692598 | 16.65 | 16.657 | 99.99 | 15.84 | 15.45 | 14.85 | 14.33 | 13.65 | 12.93 | 11.39 | 10.44 | 99.99 | 99.99 | 8.365 | 6.926 | 99.99 | 99.99 | 99.99
MACHO 47.2496.8 | 73.930267 | -67.852718 | 17.31 | 16.23 | 99.99 | 15.08 | 14.28 | 14.00 | 13.19 | 12.67 | 12.57 | 12.09 | 11.79 | 99.99 | 99.99 | 10.26 | 9.248 | 99.99 | 99.99 | 99.99
HD 158616 | 262.695520 | -11.368968 | 11.92 | 10.09 | 9.368 | 9.642 | 99.99 | 99.99 | 7.845 | 7.299 | 6.525 | 5.178 | 4.029 | 3.301 | 3.520 | 2.600 | 1.234 | 2.900 | 1.600 | 1.980

  * •

Notes: The RA and DEC coordinates are given for the J2000 epoch. Null
magnitudes are listed as 99.999.

The photometric magnitudes of all the objects covering the optical, near-IR,
and mid-IR bands are presented in Table 2. As these stars are pulsating,
multiple measurements for magnitude values within the same photometric bands
are available. Hence, we provide the mean value of each measurement in Table
2. We refer to the Appendix A of oomen18 for the list of the most common
catalogs used.

Figure 6 shows the SEDs of all the targets in our sample. As mentioned in
Section 2, the SEDs of our target stars are of ‘disc-type’.

###  2.2 Spectroscopic Observations and Data Reduction

The high-resolution optical spectra of the three targets: J005107, MACHO
47.2496.8 and HD 158616 were taken from the Ultraviolet and Visual Echelle
Spectrograph (UVES, UVES), which is the echelle spectrograph mounted on the 8
m UT2 Kueyen Telescope of the Very Large Telescope (VLT) array at the Paranal
Observatory of European Southern Observatory (ESO) in Chile, aiming to obtain
comprehensive data on a large sample of post-AGB objects. The dichroic beam-
splitter was used to get maximum wavelength coverage resulting in a wavelength
coverage from approximately 3280 Å to 4560 Å for the blue arm of UVES, and
from approximately 4726 Å to 5800 Å and 5817 Å to 6810 Å for the lower and
upper part of the red arm of the UVES CCD chip respectively. There are small
spectral gaps between 4560 Å and 4726 Å and between 5800 Å and 5817 Å due to
the spatial gap between the three UVES CCDs. Each wavelength range is observed
separately with a specific exposure time. The resolving power of the UVES
spectra varies between $\sim\\!60,000$ and $\sim\\!65,000$. In Figure 3, two
spectral snippets are presented, illustrating the quality of the spectral data
and highlighting the identification of certain s-process elements in the
target stars.

Figure 3: Comparison of the normalised and radial velocity corrected spectra
of all target stars. The spectra have been shifted in flux for clarity. Red
and black vertical lines mark the positions of s-process elements (and also
carbon) and non-s-process elements, respectively. For more information, see
the text. Table 3: Observational logs of the target stars. The references for
previous high-resolution spectroscopic studies utilising the spectra presented
in this table are provided.

Name |  | Date
---
(YYYY-MM-DD)
| UTC Start
---
(hh:mm:ss)
| Exp Time
---
(s)
| Telescope+
---
Spectrograph
| Wavelength Coverage
---
(Å)
S/N | References
J005107.19-734133.3 | 2017-06-28 | 08:53:42 | All: 3 × 3005(1,2) | VLT + UVES | 3281.91-6832.27 | 80 | -
| 2017-07-16 | 08:09:24 | All: 3 × 3005(3) | VLT + UVES | 3281.91-6832.27 | 80 |
MACHO 47.2496.8 | 2005-02-09 | 00:30:00 | Blue: 7200 | VLT + UVES | 3758-4983 | 40 | a
| 2005-02-08 | 02:49:00 | RedL: 7200 | VLT + UVES | 4780-6808 | 70 |
| 2005-02-09 | 00:30:00 | RedU: 7200 | VLT + UVES | 6705-10084 | 80 |
HD 158616 | 2014-09-18 | 00:00:00 | All: 1 × 65 | VLT + UVES | 3280-6810 | 80 | b

  * •

Notes: The exposure times of UVES spectra are split into four categories:
exposure times for the Blue arm, Red Lower arm, Red Upper arm or all three
arms; the latter is indicated with “All”. The wavelength coverage for the
"Blue" UVES arm is from approximately 3280 to 4530 Å and the "RedL" and "RedU"
UVES arms are from approximately 4780 to 5770 Å and from 5800 to 6810 Å,
respectively.
(1,2) The log details are for Observation one (OB1) and Observation two (OB2)
together. (see text for details on OB1, OB2 and OB3).
(3) The log details are for Observation three (OB3).

  * •

References: a - Reyniers2007, b - desmedt2016

Table 3 gives the log of the observations, the spectral intervals covered and
the signal-to-noise (S/N) ratio for each object. In general, the signal-to-
noise (S/N) ratio is lower at blue wavelengths. We note that the echelle data
does not have a consistent S/N because it depends on the blaze function. The
S/N is higher at the blaze wavelengths, where the spectrograph works most
efficiently, compared to other parts of the spectrum. The "References" column
points to the literature of the previous high-resolution studies.

In the following paragraphs, we only discuss the spectral reduction,
normalisation, radial velocity correction and weighted average merging of
J005107 in detail. Similar steps of the other two targets: MACHO 47.2496.8 and
HD 158616 are explained in detail by Reyniers2007 and desmedt2016,
respectively.

The UVES spectral reduction of the raw data of J005107 was performed using the
UVES reduction pipeline from EsoReflex on the default optimal settings. The
EsoReflex software allows the user to choose from a variety of pipelines that
correspond to the various telescopes available at ESO. The reduction process
involves the standard steps of extracting frames, determining wavelength
calibration and applying this scale to flat-field divided data. As part of the
reduction, cosmic clipping was also taken into account.

The normalisation of the reduced spectrum was done by fitting in small
spectral windows with fifth-order polynomials through interactively defined
continuum points. We note that normalisation is the most delicate step in the
reduction procedure, especially in the blue part of the spectrum, where the
spectrum is so crowded that the continuum is rarely reached. The most
significant source of uncertainty for the abundances calculated from lines in
this region is the continuum location. Three observations were taken for
J005107 with an exposure time of 3005 s for each UVES arm. Since the third
observation (OB3) of J005107 was taken after 19 days (see Table 3) from
observation one (OB1) and observation two (OB2), and considering the target to
be an RV Tauri pulsator, the phase of OB3 is different from that of OB1 and
OB2. Hence, we decided to treat the OB3 as an independent spectrum for the
rest of our analysis. However, the OB3 spectra had minimal lines to be useful
for both atmospheric parameter analysis as well as abundance derivation.
Therefore, we chose to use only OB1 and OB2 for the rest of our analysis.

To determine the radial velocity of J005107, several well-identified atomic
lines in the spectrum were fitted with a Gaussian curve to find their centre
wavelength. The Doppler shift equation was used to compute the shifted
velocity. This yields a heliocentric radial velocity of $v=160\pm$8 km s-1 for
OB1 and OB2, which is precise enough for line identification purposes. This is
also in good agreement with the radial velocity value $v=187.5\pm 4.3$ km s-1
estimated by Kamath2014 using the low-resolution spectra. Furthermore, the
velocity of J005107 validates the membership of the SMC, with the heliocentric
radial velocity of the SMC being $\sim\\!160$ km s-1 Richter1987.

Once all three spectra (Blue, RedL and RedU) of OB1 and OB2 were normalised
and radial velocity corrected, a weighted mean average merging was performed,
thereby obtaining a single final spectrum, which was used to perform a
detailed spectral analyses of J005107. A significant portion of the Blue
spectrum (wavelength range $3280-4560$ Å) has a signal-to-noise ratio (S/N)
that is too low to be useful for a precise spectral abundance analysis; as a
result, these wavelength ranges are not used for the spectral analyses of
J005107.

##  3 Spectroscopic Analysis

We performed a systematic spectral analysis for all our target stars, which
included: (a) precise estimation of atmospheric parameters: effective
temperature ($T_{\rm eff}$), surface gravity ($\log g$), metallicity ([Fe/H]),
and microturbulant velocity ($\xi_{\rm t}$) and (b) chemical abundance
derivation for all identifiable elements from the final prepared spectrum of
each star. The atmospheric parameter determination, as well as the abundance
analysis, are carried out using E-iSpec, our own $Python-$based semi-automated
spectral analysis tool for optical and NIR spectra, serving as a wrapper for
iSpec Blanco2014a; Blanco2019. E-iSpec offers enhanced capabilities for
determining atmospheric parameters, elemental abundances, and isotopic ratios
in evolved stars with complex atmospheres, utilising 1D local thermal
equilibrium (LTE) model atmospheres, MOOG radiative transfer code sneden1973,
and comprehensive line lists. A detailed description of E-iSpec and our
spectral analysis procedure is presented in Mohorian et al. 2024.

In brief, there are two modules in E-iSpec: one for determining atmospheric
parameters (using the equivalent width (EW) method, see Section 3.1) and the
other for determining abundances (using EW and synthetic spectral fitting
(SSF), see Section 3.2). For the spectral analyses, the latest LTE model
atmospheres, ATLAS9 castelli03 or MARCS MarcsModel2008, chosen depending on
the $T_{\rm eff}$ of the star, were used in combination with the LTE abundance
calculation routine MOOG (version July 2009) by sneden1973. The model
atmospheres were uniquely determined by the $T_{\rm eff}$, $\log g$, [Fe/H]
and $\xi_{\rm t}$. Line lists from the Vienna Atomic Line Database (VALD)
VALDLinelist with a range of 3000 Å to 11000 Å were used to identify the
spectral lines of the target stars. This covers the full wavelength coverage
of UVES spectra and allows for identifying spectral lines of about 160 ions
ranging from He (Z = 2) up to U (Z = 92).

We note that the atmospheric parameters and chemical abundances of all our
targets were derived aiming at isolated, unblended and non-saturated lines,
the identification of which was challenging due to the small-amplitude
pulsations and pulsation-driven shocks commonly observed in RV Tauri pulsating
stars Reyniers2007. We avoided spectral noise by using lines with EW greater
than 5 mÅ. Additionally, we avoided lines with EW greater than 150 mÅ since
they are saturated. We note that non-LTE effects were not taken into account
for our analysis.

In the following subsections, we briefly describe our spectral analyses:
atmospheric parameter determination (see Section 3.1) and derivation of
chemical abundances (see Section 3.2).

###  3.1 Atmospheric parameter determination

We derived the atmospheric parameters of all the target stars using Fe I and
Fe II lines (see Section 3 for more details on line selection). Fe was chosen
due to its large number of unblended lines, covering a broad range of
excitation potential. The EWs were calculated for each line using an iterative
procedure in which the theoretical EWs of individual lines were compared to
the calculated EWs. The atmospheric parameter determination method is outlined
below.

The effective temperature ($T_{\rm eff}$) was estimated using excitation
analysis, wherein the abundances derived from Fe I lines are imposed to be
independent of their excitation potential (EP). An accurate derivation of
$T_{\rm eff}$ is promoted by the wide range in EP (0.5 - 5 eV) and the
sufficiently large number of lines. The surface gravity (log g) is determined
using ionisation analyses, imposing the abundances to be independent of the
lines being from neutral or ionised Fe. The microturbulent velocity ($\xi_{\rm
t}$) was derived by imposing the independence of the abundance derived from
individual Fe lines of the reduced equivalent width (RW). Concerning the error
estimation for atmospheric parameters, they are determined from the covariance
matrix generated by the non-linear least-squares fitting algorithm in E-iSpec.

We note that the atmospheric parameter analysis can be verified using other
species like Ti or Cr, provided there is a substantial number of lines for
certain species. However, due to a large number of blends, the majority of the
elements only have less than three useful lines to perform the analysis.

The results of the atmospheric parameter analysis of our targets are presented
in Table 1 and discussed in Section 3.3.

###  3.2 Abundance Analysis

We derived chemical abundances using both the EW method and the SSF technique
- which are modules of E-iSpec. In the EW method, observed EWs were compared
with predictions from theoretical model atmospheres (ATLAS9 castelli03 or
MARCS MarcsModel2008), involving an iterative adjustment of assumed abundances
until observed and predicted EWs converged, yielding best-fit abundance
values. The SSF technique involved comparing observed stellar spectra with
synthetic spectra generated by theoretical model atmospheres, employing chi-
square fitting to iteratively refine model parameters and derive precise
chemical abundances.

We note that the lines used for the abundance derivation are as per the
criteria mentioned in Section 3. The complete linelists of the target stars
are provided as online supporting material.

The uncertainties associated with the derived abundances are determined using
the procedure outlined by Deero2005. E-iSpec provides the errors of the
derived abundances only as standard deviations of the measured values
($\sigma_{\rm|121|}$). However, the total error $\sigma_{\rm tot}$ is the
quadratic sum of $\sigma_{\rm|121|}$, uncertainties in abundances due to
atmospheric parameters and the [Fe/H] error. To determine the sensitivity of
the abundances to the stellar parameters, the abundances were recalculated
changing $T_{\rm eff}$, $\log g$ and $\xi_{\rm t}$ with their calculated error
(see Table 1 for atmospheric parameter errors). We impose a
$\sigma_{\rm|121|}$ of 0.20 dex for all the ions for which only one line was
available. The chosen uncertainty of 0.2 dex corresponds to the allowed
standard deviation for the line-to-line scatter, indicating the range within
which all individual line abundances are expected to lie.

The results of the abundance analysis of our targets are presented in Table 4
and Table 7 and discussed in Section 3.3.

###  3.3 Results of Spectroscopic Analysis: Atmospheric Parameters and
Chemical Abundances

In this section, we present the results of the spectral analyses of J005107.
We note that this study marks the first high-resolution spectral analyses of
J005107. However, for MACHO 47.2496.8 and HD 158616 similar high-resolution
spectral analyses have been previously carried out by Reyniers2007 and
desmedt2016, respectively. For benchmarking our methodology (i.e., the E-iSpec
Code) we repeated the spectral analyses for these two objects (see A for the
final results). Since the derived atmospheric parameters and abundances of
MACHO 47.2496.8 and HD 158616 align closely with values reported in the
literature (refer to Table 1 and Table 7), we opted to adopt the literature
values of both atmospheric parameters and abundances for the rest of our
analysis.

The various atmospheric parameters of J005107 are displayed in Table 1, under
the title "This study". The atmospheric parameters of J005107 clearly fall
within the range of typical post-AGB parameter values.

Table 4: Spectroscopically determined abundance results for J005107.

Ion | Z | $\log\varepsilon_{\odot}$ | N | [X/Fe] | $\sigma_{\rm tot}$ | $\log\varepsilon$ | $\sigma_{\rm|121|}$
---|---|---|---|---|---|---|---
C I | 6 | 8.43 | 1 | 1.09 | 0.217 | 7.95 | 0.20
O I | 8 | 8.69 | 1 | 1.06 | 0.212 | 8.18 | 0.20
Mg I | 12 | 7.60 | 2 | 0.77 | 0.160 | 6.79 | 0.15
Si I | 14 | 7.51 | 3 | 0.61 | 0.081 | 6.54 | 0.07
Ca I | 20 | 6.37 | 3 | 0.43 | 0.114 | 5.19 | 0.04
Sc II | 21 | 3.15 | 1 | 0.33 | 0.215 | 1.91 | 0.20
Ti I | 22 | 4.95 | 2 | 0.59 | 0.205 | 4.25 | 0.18
Cr I | 24 | 5.64 | 2 | 0.43 | 0.197 | 4.49 | 0.19
Fe I | 26 | 7.50 | 37 | 0 | 0.132 | 5.92 | 0.09
Fe II | 26 | 7.50 | 6 | 0 | 0.171 | 5.92 | 0.12
Ni I | 28 | 6.22 | 1 | 0.53 | 0.241 | 5.17 | 0.20
Zn I | 30 | 4.56 | 1 | 0.48 | 0.246 | 3.46 | 0.20
Y II | 39 | 2.12 | 5 | 1.13 | 0.115 | 1.76 | 0.03
Zr II | 40 | 2.58 | 2 | 0.74 | 0.101 | 1.74 | 0.02
La II | 57 | 1.10 | 3 | 1.52 | 0.133 | 1.04 | 0.04
Ce II | 58 | 1.58 | 7 | 1.44 | 0.138 | 1.44 | 0.04
Pr II | 59 | 0.72 | 3 | 1.66 | 0.211 | 0.8 | 0.20
Nd II | 60 | 1.42 | 15 | 1.69 | 0.146 | 1.53 | 0.07
Sm II | 62 | 0.96 | 4 | 1.70 | 0.147 | 1.08 | 0.07
Gd II | 64 | 1.07 | 2 | 1.66 | 0.113 | 1.15 | 0.05

  * •

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 Asplund2009. N
represents the number of lines used for each ion, [X/Fe] is the element-over-
iron ratio, $\sigma_{\rm tot}$ is the total uncertainty on [X/Fe],
$\log\varepsilon$ is the derived 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.

Table 4 presents the final derived abundances for different elements of
J005107. Unfortunately, all Ba lines were severely saturated (see Figure 3 at
6141.7324 Å), making it impossible to accurately determine the abundance of
one of the significant s-process species. Except for the species where all
observable lines turned out to be blended, the other s-process elemental
abundances were derived from isolated single lines. We list the elements by
their atomic number (Z), the solar abundances ($\log\varepsilon_{\odot}$)
retrieved from Asplund2009, the number of lines identified for each element
(N), the element-over-iron ratio ([X/Fe]), the total uncertainty on [X/Fe]
($\sigma_{\rm tot}$), the determined abundance ($\log\varepsilon$), and the
line-to-line scatter ($\sigma_{\rm|121|}$). Although the abundances of several
useful elements for nucleosynthesis studies could not be determined, Table 4
still provides quantified abundances of a range of s-process elements. See
Section 3 for details on atmospheric parameters and derived abundance
uncertainties.

Figure 4: Spectroscopically derived abundances of J005107. The error bars
represent the total uncertainties $\sigma_{\rm tot}$. Some elements are
labelled for reference. The black colour data points represent CNO elements,
the blue represents Fe peak elements, the magenta represents Zn and S, and the
red represents s-process elements.

Combining the results of both atmospheric parameter analysis and abundance
derivation we interpret the characteristics of J005107. J005107 is an F-type
star ($T_{\rm eff}$ = $5764\pm 85$ K) with a low surface gravity ($\log g$ =
$0.21\pm 0.10$ dex) and an iron abundance ([Fe/H] = $-1.57\pm 0.10$). The iron
abundance of J005107 is low compared to the mean metallicity of the SMC [Fe/H]
= -0.7 dex luck1998. This categorises J005107 as a low-metallicity star, which
is commonly recognised as an astrophysical production site producing heavy
s-process elements provided the TDU occurs bisterzo2010. Figure 4 shows the
abundance distribution ([X/Fe]) for J005107 as a function of atomic number
(Z). From the abundance plot, it is clear that J005107 is strongly enriched in
s-process elements with an [s/Fe] = $1.52\pm 0.20$ dex. Moreover, it also has
a carbon enrichment with [C/Fe] = $1.09\pm 0.21$ dex. However, we note that
owing to the observed blending in the single available carbon line (located at
4817.373 Å as detailed in the linelist), accurately determining the carbon
abundance posed a significant challenge.

##  4 Photometric Analysis

In this section, we present details on the SED fitting (Section 4.1) and the
luminosity derivation (Section 4.2) of our target stars.

###  4.1 SED Fitting

Most of our targets are RV Tauri pulsators that often show large amplitude
pulsations that can go up to several magnitudes in V. One of the greatest
challenges in fitting the SEDs of these stars is that these pulsations cause a
scatter in the photometric data points. Therefore reddening is difficult to
determine. To overcome this issue, it is crucial to have full coverage of all
photometric bands in the same pulsation phase. However, since the same
pulsation phase data is unavailable, we have utilised all the accessible
photometric data points (see Section 2.1) to construct the SEDs. We determined
the SED of all the targets of this study in a strictly homogeneous way, as
explained below.

We adopted the same approach described in Kluska2022 and Kamath2022 to
construct all the SEDs in this study. In summary, we began by determining the
total line-of-sight reddening or extinction parameter ($E(B-V)$) by minimising
the difference between the optical fluxes and the reddened photospheric
models. The total reddening includes both interstellar and circumstellar
reddening. We assume that the total reddening in the line of sight has the
wavelength dependency of the interstellar-medium extinction law cardelli89
with Rv = 3.1. The extinction law in the circumstellar environment likely
differs from the interstellar extinction law. However, investigating this
aspect falls outside the scope of our current study. For the atmospheric
models, we used the appropriate Kurucz atmospheric models castelli03, the
parameters of which were taken from the spectroscopic analysis presented in
Section 3.1 (see Table 1). We interpolated in the $\chi^{2}$ landscape between
the models centred around the spectroscopically determined parameters and
applied ranges of $\Delta$$T_{\rm eff}$ $\pm 500$ K, $\Delta$$\log g$ $\pm
0.5$ dex, $\Delta$[Fe/H] $\pm 0.5$ dex (see Figure 5). The SEDs of our three
target stars are presented in Figure 6.

Figure 5: An example of $\chi^{2}$ plot of J005107 to obtain the reddening
parameter $E(B-V)$ after the parameter grid search. This plot illustrates the
correlation between $T_{\rm eff}$ and $E(B-V)$ of the targets.

Figure 6: SEDs of J005107 (top left), MACHO 47.2496.8 (top right) and HD
158616 (bottom). The data points represent the dereddened photometry. The red
line represents the best-fitting scaled model atmosphere (see text for
details). Table 5: Luminosities of the targets derived using the SED fitting
method and PLC relation method.

Object |  | $P_{0}$
---
(days)
|  $\rm L_{SED}$
---
( $\rm L_{\odot}$)
|  $\Delta$ $\rm L_{SED}$
---
( $\rm L_{\odot}$)
|  $\rm L_{PLC}$
---
( $\rm L_{\odot}$)
|  $\Delta$ $\rm L_{PLC}$
---
( $\rm L_{\odot}$)
| $E(B-V)$
---
(mag)
SED type | Comments
J005107.19-734133.3 | 39.67 | 2702 | ${}^{+5108}_{-1747}$ | 2868 | ${}^{+6449}_{-1405}$ | $0.22^{+0.47}_{-0}$ | Disc | post-AGB, RV Tauri
MACHO 47.2496.8 | 56.48 | 3001 | ${}^{+4051}_{-2775}$ | 2208 | ${}^{+4087}_{-1877}$ | $0.05^{+0.24}_{-0}$ | Disc | post-AGB, RV Tauri
HD 158616 | - | 8256 | ${}^{+10301}_{-6288}$ | - | - | $0.53^{+0.63}_{-0.48}$ | Disc | post-AGB, Binary,  $\rm P_{Orb}$=363.3 days

  * •

Notes: $P_{0}$ is the fundamental pulsation period of the RV Tauri targets and
are shown in Col. 2. The luminosities derived from SED along with their
corresponding upper and lower limits are displayed in Col. 3 and 4
respectively. Similarly, the luminosities obtained using the PLC relation
along with their corresponding upper and lower limits are displayed in Col. 5
and 6 respectively. Note that the target HD 158616 does not have luminosity
derived from the PLC relation as it is not an RV Tauri star. The reddening
derived from the SED model along with their corresponding upper and lower
limits are shown in Col. 7, and the SED type of the targets are presented in
Col. 8 (see text for details).

###  4.2 Luminosity Determination

Accurately determining the luminosities of post-AGB stars and combining them
with their effective temperatures ($T_{\rm eff}$) allows us to investigate
their positions in the Hertzsprung-Russell (HR) diagram. This helps us better
understand the evolutionary stage of the target post-AGB objects. However,
accurately deriving the luminosities of post-AGB stars remains a significant
challenge due to multiple factors. These include the impact of reddening—both
circumstellar and interstellar—on observational photometric data, along with
complexities arising from variability, particularly for the RV Tauri
pulsators. Moreover, concerning binary post-AGB stars with orbital periods
ranging from 100 to 700 days, systematic errors in parallax determination
affect distances and consequently, luminosities Kamath2022. This issue arises
because Gaia EDR3 does not account for the orbital motion of binaries, often
resulting in an underestimation of parallax. Consequently, this oversight
impacts the derived distances and the luminosities of these stars
Pourbaix2019.

To estimate the luminosity of our targets, it is imperative to address the
limitations above. We, therefore, use two methods discussed in the following
subsections, i.e., the SED fit ( $\rm L_{SED}$) (Section 4.2.1) and the
period-luminosity-colour (PLC) relation ( $\rm L_{PLC}$) (Section 4.2.2). We
find  $\rm L_{PLC}$ to offer greater precision and reliability when compared
to  $\rm L_{SED}$. This preference arises due to significant variations in
$T_{\rm eff}$ across the pulsation cycle in our target stars, which are RV
Tauri pulsators (see Section 2). These fluctuations also lead to notable
changes in the model fitting of stellar atmospheres (illustrated by the red
lines in Figure 6). Additionally, as mentioned above, for stars in binary
systems, the uncertainties in distances obtained from parallax measurements
are markedly influenced by binary orbital motion, which adds to the
uncertainties in  $\rm L_{SED}$.

####  4.2.1 Deriving the Luminosity using SED

The bolometric luminosities ( $\rm L_{SED}$) of the targets were derived by
integrating the flux under the dereddened photospheric SED model (see Section
4.1). To achieve this, we assumed an average distance of $62.1\pm 1.9$ kpc to
the SMC graczyk and $49.97\pm 1$ kpc to the LMC Walker2012; Pietrzy2013
respectively. For our Galactic target HD 158616, we utilised the more precise
Bailer-Jones geometric distances (i.e., $z_{\rm BJ}$) and their associated
upper and lower limits ($z_{\rm BJU}$ and $z_{\rm BJL}$ respectively) from the
study by BailerJones2021A. The geometric distances were determined using Gaia
EDR3 parallaxes, incorporating a direction-dependent prior distance.
Throughout this computation, we assumed that the flux emitted by the stars is
radiated isotropically. The derived SED luminosities ( $\rm L_{SED}$) along
with their corresponding upper and lower limits ($\Delta$ $\rm L_{SED}$) for
the targets are presented in Col. 3 and 4 of Table 5, respectively. To
calculate these upper and lower limits for the SED luminosities ($\Delta$ $\rm
L_{SED}$), we utilised the corresponding upper and lower limits of the
reddening values, as derived and outlined in Col 7 of Table 5.

####  4.2.2 Deriving the Luminosity using PLC Relation

One of the greatest benefits of type II Cepheids is that their pulsations can
be used to determine their luminosities due to the correlation between their
pulsational periods and luminosities. Unlike the previous SED fitting method
(see Section 4.2.1), this approach does not rely on distance dependencies,
providing a valuable advantage for accurate luminosity derivation.

Many post-AGB stars, specifically RV Tauri stars exhibit strong radial
pulsations because they are located in the long-period segment of the type II
Cepheid instability strip. The radial modes of these stars can be directly
linked to their physical sizes. By incorporating a colour or temperature
factor, one can establish a connection between the star’s luminosity and its
pulsation period. This relationship is referred to as the period-luminosity-
colour (PLC) relation, as shown in studies by Alcock_1998 and Ripepi2015.

Figure 7: The reddening-free Wesenheit index plotted with the log ($P_{0}$) of
the RV Tauri stars in the LMC and SMC from Soszy2015; Soszy2017.
Note: We excluded stars from the analysis if their standard deviation exceeded
$1\sigma$ of the fit.

We determined the luminosities of the two RV Tauri stars: J005107 and MACHO
47.2496.8, by adopting the PLC relation calibration method as established by
Manick2018. The PLC relation was calibrated separately for the LMC and SMC
stars using the photometric data in the latest OGLE IV database Soszy2018.
This relation uses the colour-corrected V-band magnitude known as the
Wesenheit index (WI) (Ngeow2005 and is given by

$M_{bol,WI}=m\cdot log(P_{0})+c-\mu+BC+2.55(V-I)_{0}$ (1)

where $P_{0}$ is the observed fundamental pulsation period in days, m is the
slope and c is the intercept of the linear regression in the Wesenheit plane
(see Figure 7). We obtained $m=-3.59$ and c = 18.79 for the LMC and $m=-2.45$
and c = 17.45 for SMC respectively. $\mu$ is the distance modulus for the LMC
and SMC and have values of 18.49 Walker2012; Pietrzy2013 and 18.965 graczyk,
respectively. The value BC is the bolometric correction for each star computed
using the relation between BC and effective temperature provided by
Flower1996. The intrinsic colour $(V-I)_{0}$ of each star in the SMC and LMC
is calculated using the reddening $E(V-I)$ and the observed colour $(V-I)$.
The reddening $E(V-I)$ is determined by the conversion of the total reddening
$E(B-V)$ derived from the SED (see Section 4.2.1) using the conversion
equation by Tammann2003 and Haschke2011.

$E(V-I)=1.38E(B-V)$ (2)

The derived PLC luminosities ( $\rm L_{PLC}$) along with their corresponding
upper and lower limits ($\Delta$ $\rm L_{PLC}$) of the RV Tauri targets are
displayed in Col. 5 and 6 of Table 5 respectively. To calculate these upper
and lower limits for the PLC luminosities ($\Delta$ $\rm L_{PLC}$), we utilise
the corresponding upper and lower limits of the reddening values, as outlined
in Col 7 of Table 5, and also incorporate the error propagation values
obtained through the PLC calibration fit.

We once again note that  $\rm L_{PLC}$ offers greater precision and
reliability when compared to  $\rm L_{SED}$, as detailed in the last paragraph
of Section 4.2. However, for HD 158616 we had to consider  $\rm L_{SED}$ as
there is no  $\rm L_{PLC}$ (this is not an RV Tauri star).

The luminosities of the target stars are presented in Table 5, and the derived
luminosities fall within the typical post-AGB luminosity range. Consequently,
we investigate the chemical peculiarities of the target stars, within the
context of the post-AGB evolutionary phase.

###  4.3 Initial Mass Estimates

The evolution of LIM stars during the post-He-burning life is characterised by
the gradual increase in the luminosity, in turn, related to the growth of the
mass of the degenerate core, due to the continuous flux of H-free matter,
favoured by the CNO nuclear activity. As far as AGB stars are concerned, a
classic relation between core mass and luminosity was found by paczynski. As
stars with different masses evolve through the AGB with different core masses,
the luminosity of AGB stars serves as a reliable indicator of the mass of the
progenitor. On the chemical side, the surface composition is exposed to
changes during the AGB lifetime, primarily connected to the occurrence of
several TDU events, which raise the surface carbon, and potentially lead to
the formation of carbon stars iben74. The increase in the surface carbon takes
place in parallel with the growth of the core mass (hence of the luminosity)
and is accompanied by the surface s-process enrichment. Based on these
reasons, the combined knowledge of the luminosity and the surface chemical
composition can be tentatively used to identify the progenitors of the sources
considered and the evolutionary stage when the AGB evolution was halted, and
the contraction to the post-AGB phase began.

Table 6: Overview of the $T_{\rm eff}$, metallicity, [C/Fe], s-process
indices, C/O ratio and initial mass of our target stars.

Object | $T_{\rm eff}$ | [Fe/H] | [C/Fe] | [s/Fe] | C/O | Initial mass range
---|---|---|---|---|---|---
J005107 | 5768 $\pm$ 85 | -1.57 $\pm$ 0.10 | 1.09 $\pm$ 0.21 | 1.52 $\pm$ 0.20 | 0.58 $\pm$ 0.37 | 0.8-1  $\rm M_{\odot}$
MACHO 47.2496.8 | 4900 $\pm$ 250 | -1.50 $\pm$ 0.50 | - | 1.96 $\pm$ 0.20 | $>2$ | 1-1.2  $\rm M_{\odot}$
HD 158616 | 7250 $\pm$ 125 | -0.64 $\pm$ 0.12 | 0.47 $\pm$ 0.14 | 0.96 $\pm$ 0.17 | 0.94 $\pm$ 0.22 | 2.5  $\rm M_{\odot}$

  * •

Notes: $T_{\rm eff}$, [Fe/H], [C/Fe], [s/Fe] and C/O of MACHO 47.2496.8 and HD
158616 are taken from the high resolution spectroscopic analysis conducted by
Reyniers2007 and desmedt2016 respectively.
Although an accurate abundance derivation for carbon ([C/Fe]) is absent for
MACHO,47.2496.8, it is still categorised as a carbon-enriched object due to
its high C/O and carbon isotopic ratio, as indicated by Reyniers2007. The C/O
ratio for J005107 should be treated as a lower limit as the precise
determination of carbon was not feasible (see Section 3.3).
The C/O ratio for MACHO 47.2496.8 is a lower limit, as the precise
determination of carbon and oxygen abundances was not feasible (see
Reyniers2007 for additional details).

Figure 8: AGB evolution of stars of different mass and metallicity $\rm
Z=0.001$, in the $\rm C/O$ vs. luminosity plane. The target stars J005107 and
MACHO 47.2496.8 are marked. See text for more details. Figure 9: Time
variation of the luminosity and the surface $\rm C/O$ of a $\rm
2.5\leavevmode\nobreak\ M_{\odot}$ model star of $Z=0.004$. The grey-shaded
region indicates the evolutionary phase of HD 158616 during which both the
luminosity and the C/O are consistent with those derived from the
observations. See text for more details.

In this section, we use ATON code for stellar evolution modelling ventura98 to
estimate the mass of the progenitors of our target stars and their formation
epoch. While the ATON evolutionary models are designed for single AGB stars,
we explore the potential of employing these single AGB models to characterise
the chemical composition of our binary post-AGB target stars, based on the
assumption that the photospheric chemical abundance pattern observed in binary
post-AGB stars is a reflection of the AGB nucleosynthesis that occurred before
the termination of the AGB phase due to the binary interaction. By comparing
our observations with predictions from the ATON stellar evolution models, we
can indeed confirm whether binary interactions impact the stellar chemical
composition. We used evolutionary tracks with an initial metallicity of Z =
0.001 for J005107 and MACHO 47.2496.8, and Z = 0.004 for HD 158616. The
observationally derived values of [C/Fe], [s/Fe], and C/O, along with the
corresponding initial mass range as determined in this section, are presented
in Table 6. Note that the initial mass range indicated here refers to the mass
at the beginning of the AGB.

In Figure 8 we show the AGB evolution of stars of different mass and
metallicity $\rm Z=0.001$, in the (surface) $\rm C/O$ vs. luminosity plane.
This is similar to the plane used by devika23 to interpret the sample of
Galactic AGBs presented in Kamath2022. The single evolutionary sequences run
towards the right upper part of the plane, as both luminosity and the surface
$\rm C/O$ increase as a consequence of the growth in the core mass and of the
effects of TDU. The role of the initial mass is seen in the largest $\rm C/O$
reached, which is seen to be higher the larger the initial mass of the star,
as higher mass stars experience more TDU events than their lower mass
counterparts, thus reach higher carbon mass fractions in the surface regions
flavia15. The $\rm 2.5\leavevmode\nobreak\ M_{\odot}$ model star partly
escapes from this trend, as the surface carbon enrichment is less efficient in
stars with mass close to the threshold to experience hot bottom burning
flavia15. We also note that the luminosity at which a given value of $\rm C/O$
is reached is sensitive to the initial mass of the star. This is particularly
evident for $\rm M>1.5\leavevmode\nobreak\ M_{\odot}$ (see Figure 8), above
the threshold mass to start helium burning under quiescent conditions; indeed
all the stars undergoing the helium flash develop cores of similar mass. Thus
they start the AGB phase with similar luminosities Ventura2021.

The dashed horizontal line in Figure 8 refers to J005107. It is located in
correspondence with the lower limit for the surface C/O$\sim\\!0.58$, while
the width indicates the luminosity  $\rm L_{PLC}$ along with the upper and
lower limits $\Delta$ $\rm L_{PLC}$ (see Table 5). Unfortunately, the latter
quantity is very large, of the order of $\rm 5000\leavevmode\nobreak\
L_{\odot}$, thus preventing a tight derivation of the mass of the progenitor.
The comparison with the evolutionary tracks shows compatibility with
progenitors of $\rm 1-2\leavevmode\nobreak\ M_{\odot}$, corresponding to the
formation epoch from 1 Gyr to 3 Gyr ago. This explanation holds provided that
the luminosity is above $\rm 4000\leavevmode\nobreak\ L_{\odot}$. Taking into
account the recommended value of the base luminosity $\rm
2868\leavevmode\nobreak\ L_{\odot}$ (see Table 5) poses severe problems in the
interpretation of this source, because, as shown in Figure 8, no occurrence of
TDU events is expected according to the results based on standard stellar
evolution modelling in the low luminosity domain. A possible explanation,
similar to the one proposed by devika23 to interpret a few low-luminosity
sources in the sample by Kamath2022, is that J005107 descends from a low-mass
($\rm 0.8-1\leavevmode\nobreak\ M_{\odot}$) progenitor, which is currently
contracting to the blue after losing the external envelope, before the start
of the thermal pulses phase. The carbon and s-process enrichment would be
favoured by the occurrence of deep mixing during the helium flash, similarly
to the mechanism invoked by schwab to explain the presence of lithium-rich
clump stars. A further possibility is that J005107 suffered a late thermal
pulse after the beginning of the post-AGB contraction iben84 so that it is
nowadays re-expanding to the red, at a luminosity significantly lower than
that characterising the contraction phase. Examples of such an evolution are
shown in blocker95 (see Figure 14) and tosi22 (see Figure 3).

The grey-shaded region in Figure 8 refers to MACHO 47.2496.8, based on the
lower limit of $\sim 2$ of the surface $\rm C/O$ Reyniers2007, and the
luminosity  $\rm L_{PLC}$ range reported in Table 5. We find consistency with
the predictions from AGB modelling only if the luminosity is close to the
upper limit given in Table 5, as no carbon enrichment is expected at lower
luminosities. According to this interpretation MACHO 47.2496.8 descends from a
progenitor of mass in the $\rm 0.8-1\leavevmode\nobreak\ M_{\odot}$ range,
which left the AGB after one or two thermal pulses after the C-star stage was
reached. We once again note that the values indicated above refer to the mass
at the beginning of the AGB. If we consider a typical mass loss during the
ascending of the red giant branch of $\rm\sim 0.2\leavevmode\nobreak\
M_{\odot}$, we deduce that the progenitor mass was in the $\rm
1-1.2\leavevmode\nobreak\ M_{\odot}$ range, which corresponds to an age range
for MACHO 47.2496.8 of $3-6$ Gyr.

To study HD 158616 we use the $Z=0.004$ tracks published in devika23. The
luminosity range reported in Table 5 rule out very low-mass progenitors, thus
shifting the attention to $\rm M>1.5\leavevmode\nobreak\ M_{\odot}$ stars. In
Figure 9, we show the time variation of the luminosity and the surface $\rm
C/O$ of a $\rm 2.5\leavevmode\nobreak\ M_{\odot}$ model star of $Z=0.004$. The
grey-shaded region indicates the evolutionary phase during which both the
luminosity and the $\rm C/O=0.94\pm 0.22$ desmedt2016 are consistent with
those derived from the observations. Based on these results, we propose that
HD 158616 descends from a $\rm 2.5\leavevmode\nobreak\ M_{\odot}$ progenitor,
formed around half Gyr ago, which left the AGB after experiencing a few
thermal pulses, two out of which after the first TDU event. The estimated mass
interval for the progenitor is pretty narrow in this case since the initial
mass vs luminosity trend is very tight in the $\rm M>2\leavevmode\nobreak\
M_{\odot}$ domain (see Figure 8).

##  5 Discussion

In the following subsections, we employ the obtained stellar parameters,
chemical abundances, derived luminosities, and initial masses to explore the
chemical peculiarity of our target stars (Section 5.1). We also investigate
whether the observed s-process enrichment of our targets has an extrinsic or
intrinsic nature (see Section 5.2).

###  5.1 Investigating the chemical peculiarity of Targets

We compared the chemical compositions of our target stars to appropriate
binary post-AGB stars and single post-AGB stars with similar stellar
parameters: $T_{\rm eff}$, $\log g$ and [Fe/H] (see Figure 10 legends). This
comparative analysis is aimed at discerning whether there exists a composite
signature reflecting both chemical depletion, commonly observed in binary
post-AGB stars, and s-process enrichment, typically seen in low-mass single
post-AGB stars. Identifying both chemical patterns concurrently might suggest
the likelihood of s-process enrichment, consequently leading to the observed
chemical depletion pattern.

To investigate any hidden signatures of chemical depletion in our targets, we
make use of the ratio [Zn/Ti] (see kamath19 for more details). Since Ti is
likely to be more strongly depleted than Zn, [Zn/Ti] is an ideal indicator of
chemical depletion in O-rich environments. We note that the abundance of CNO
elements may undergo changes as a result of prior AGB nucleosynthesis and
dredge-up. Consequently, understanding the true effect of depletion on these
elements poses a challenge and falls outside the scope of this study. Our
analysis mainly focuses on examining the effect of depletion on the refractory
elements.

Figure 10 shows the abundance of the element over hydrogen ([X/H]) as a
function of the equilibrium condensation temperature ($T_{\rm condensation}$)
for a solar photospheric composition, which is oxygen-rich, (Lodders2003,
taken from) for the individual target stars (left panels) and their comparison
binary stars (middle panels) and their comparison single stars (right panels).
The stellar parameters ($T_{\rm eff}$, $\log g$ and [Fe/H]), luminosities,
[Zn/Ti], [s/Fe] and C/O for each of the stars are listed in their respective
legends.

Figure 10: Comparison plots illustrating the abundance pattern in terms of
element over hydrogen ([X/H]) ratios as a function of condensation temperature
($T_{\rm condensation}$) (Lodders2003, taken from) of the target stars with
post-AGB binary stars and post-AGB single stars from the literature that have
similar stellar parameters. The stellar parameters along with other necessary
parameters are provided in the legend. To distinguish between the different
elements, we continue to use the same colour coding and symbols as before. The
black colour data points represent CNO elements, the blue represents Fe peak
elements, the magenta represents Zn and S, and the red represents s-process
elements.
Left: [X/H] Vs $T_{\rm condensation}$ of target stars.
Middle: [X/H] Vs $T_{\rm condensation}$ of post-AGB binary stars from
kamath19, Gielen2009 and Waelkens1992 with similar stellar parameters of the
target sample in the respective left panel. Right: [X/H] Vs $T_{\rm
condensation}$ of post-AGB single stars from desmedt2016 that has similar
stellar parameters of the target sample in the respective left panel.

For J005107 we use J050304.9-684024.7 kamath19 as our comparison binary post-
AGB star and IRAS 22272+5435 desmedt2016 as our comparison single post-AGB
star. For MACHO 47.2496.8 we use J051418.1-691234.9 Gielen2009 as our
comparison binary post-AGB star and IRAS 05113+1347 desmedt2016 as our
comparison single post-AGB star. For HD 158616 we use HD 44179 Waelkens1992 as
our comparison binary post-AGB star and IRAS 07134+1005 desmedt2016 as our
comparison single post-AGB star.

From Figure 10, it becomes evident that the chemical patterns of our targets
align consistently with their comparison single post-AGB stars (as expected
for post-TDU objects), indicating that our targets show notable enrichment in
s-process elements with no signs of chemical depletion unlike their comparison
binary post-AGB stars. The value of [Zn/Ti]$\,<\\!0.5$ for our target stars
(see legends of Figure 10) further confirms the absence of a photospheric
chemical depletion. Therefore, we dismiss the possibility of an s-process
enrichment following a chemical depletion.

As mentioned in Section 1, the chemical depletion pattern observed in binary
post-AGB stars with circumbinary discs is attributed primarily to the disc-
binary system interaction. Since our target stars do not show the expected
signatures of chemical depletion, it appears that the disc-binary interaction
inducing chemical depletion failed in our systems. To explain this anomaly, it
is worth noting that the majority of the binary post-AGB stars that display
photospheric chemical depletion have a photospheric chemical composition that
reflects a C/O$\,<\\!1$ dex (the majority having a C/O$\,\lessapprox\\!0.6$)
and circumbinary disc chemistry that is O-rich (Gielen2011; Cava2023;
Mass2005, see). Accordingly, the condensation temperatures typically utilised
(as also in this study, as mentioned above) are based on a solar photospheric
composition characterised by an O-rich nature Lodders2003. However, our target
stars display a photospheric chemical composition that is enhanced in carbon
with C/O$\,>\\!1$ dex, [C/Fe] ranging between 0.5 - 1.0 dex (dependant on
metallicity) and s-process elements with [s/Fe]$\,>\\!1$ dex. This points to a
possibility of the circumbinary disc around our target stars possessing a
C-rich dust chemistry rather than the atypical O-rich dust chemistry.
Unfortunately, we do not have observations of the circumstellar disc chemistry
of our target stars to verify their C-rich nature. However, it is well known
that the mechanisms governing processes such as molecular formation and dust
condensation are likely to exhibit significant differences Dell2021 resulting
in likely variations to chemical depletion efficiencies in C-rich environments
when compared to O-rich environments. Consequently, dust condensation
temperatures based on an O-rich disc composition, as used in this study, will
not be suitable for our targets. To fully grasp the impact of C-rich
circumstellar chemistry on chemical depletion in binary post-AGB stars, we
would also need condensation temperatures specific to a C-rich environment.
Unfortunately, these estimates are not currently available, making the
qualitative investigation of this aspect outside the scope of our study.

To examine potential variations in the disc morphologies of the circumbinary
discs around our target stars, we utilise the colour-colour diagram as
introduced by Kluska2022, which is based on the characteristics of the IR
excess. This approach aids in identifying the circumbinary disc type
associated with our targets. Figure 11 displays the IR colour-colour diagram
of the target stars along with the stars studied in Kluska2022. J005107 and HD
1586161 exhibit a "full-disc" model. This implies continuous dust extension
from the dust sublimation radius to the outer edge. In contrast, MACHO
47.2496.8 features a "transition-disc" model, indicating a lack of dust within
a radius significantly larger than the theoretical dust sublimation radius
(for further insights, refer to Kluska2022). These observations clarify that
the circumbinary disc of our target stars closely resembles that of depleted
binary post-AGB stars, presenting either as a full-disc or a transition-disc.
Therefore, there is no apparent deviation in the circumbinary disc morphology
or characteristics from the typical traits observed in a binary post-AGB star.
This indicates that the observed chemical peculiarity of the target stars is
not attributed to their disc structure.

Figure 11: Wise colour-colour diagram for the target stars along with the
stars studied in Kluska2022. The dashed black lines represent the boundaries
between the different categories defined in Kluska2022. The targets of this
study are given in magenta colour and are numbered according to their position
in Table 1 for reference.

###  5.2 Extrinsic or Intrinsic Enrichment?

The observed enrichment in s-process (and carbon) elements within our target
stars is likely to be due to three possibilities: 1) extrinsically from the
binary companion, 2) intrinsically through nucleosynthesis processes occurring
within the star during its AGB phase, and 3) from the host galaxy, through
intrinsic enrichment from the chemical composition of the interstellar medium
(ISM) from which the star originated. We investigate each of these
possibilities in detail.

Extrinsic enrichment: Observational investigations of low-mass binary stars,
such as Barium stars and Carbon-Enhanced Metal-Poor (CEMP) stars, indicate
that the observed carbon and s-process enrichment in their photospheres
results from interactions with their evolved companions (AGB or white dwarf
(WD)) (Jorissen2019; Escorza2023; Goswami2023, e.g.,). The companion star,
having undergone or undergoing AGB nucleosynthesis, transfers carbon and
s-process elements to the photosphere of these stars, making them
extrinsically enriched. We investigated a similar possibility for our targets.
However, previous studies of Galactic binary post-AGB stars (oomen18, see)
show that most of these stars do not have a dim WD as a companion. We present
some of the arguments favouring this hypothesis below.

The first is a statistical argument. It is supported by the robust analysis of
the companion mass ($\rm M_{2}$) distribution conducted by oomen18. From their
analysis, it was found that the companion mass distribution function (see
Figure 4 of oomen18) peaks at $\sim\\!1\mbox{\,$\rm M_{\odot}$}$. To explore
the possibility of a WD companion population, oomen18 fitted a double Gaussian
profile to the mass distribution. However, this adjustment did not result in a
better fit, and the mass distribution shifted towards higher masses rather
than peaking at lower masses comparable to WDs. Consequently, they refrained
from incorporating the WD population into the mass distribution. Additionally,
data from the Gaia DR2 catalogue indicates that the observed distribution of
WD mass peaks at $0.6\mbox{\,$\rm M_{\odot}$}$ Jim2018. Therefore, the
cumulative mass-function distribution fit by oomen18 does not convincingly
support the possibility that the majority of the binary post-AGB stars have a
WD companion as the mass distribution of companion masses does not have a peak
around $0.6\mbox{\,$\rm M_{\odot}$}$.

The second is an observational argument. The majority of the binary post-AGB
systems have jets launched from their circum-companion (Bollen2017;
Bollen2021; Bollen2022, e.g.). The velocities of these jets can be used to
constrain the nature of the jet-launching object, i.e. the companion in these
binary systems. The velocity of these jets ranges from $\sim\\!150$ to 400 km
s-1 Bollen2021; Bollen2022. The escape velocity of a WD ($\sim\\!5000$ km s-1)
is about one order of magnitude larger than the jet velocities determined for
the post-AGB binary systems. On the other hand, the jet velocities from the
binary post-AGB system are all around the escape velocity of MS stars
($\sim\\!100$ to 1000 km s-1). This suggests that the companion of the
majority of the binary post-AGB stars are MS.

The third argument is based on the observations of binary post-AGB stars by
oomen18, where they did not detect any symbiotic activities in the spectra.
This lack of symbiotic activities, when considered alongside the two
aforementioned points, serves as an additional indication supporting the
absence of a compact object, such as a WD, within the binary system.

All the above-mentioned arguments are, therefore, a strong indication that the
companions in the majority of the binary post-AGB systems are likely to be MS
stars rather than WDs. With regard to the targets in our study, the absence of
orbital parameter data for two targets (J005107 and MACHO 47.2496.8) limits
the extent of our argumentation. However, the confirmed binary star HD 158616
in our study has a detected mass function of 0.022 $\rm M_{\odot}$, which
translates to a companion mass of 0.26 $\rm M_{\odot}$ assuming a mass of 0.6
$\rm M_{\odot}$ for the primary star and an inclination of 75 degrees (too
small companion mass to be a WD at 75 degrees inclination) (oomen18, see). As
the light curve is not affected by variable reddening, the inclination may be
larger, leading to an even higher companion mass. Additionally, HD 158616 has
an orbital period of $363.3$ days, which means that the full orbital phase
coverage is difficult to obtain given the observations are always covering the
same phase. Yet we have accumulated enough data to show that the jets as
observed in this object ($\sim\\!150$ km s-1) do not trace the escape velocity
of a WD but that of a MS star (see Figure 14). Therefore, based on HD158616,
and extrapolating the arguments observed for the majority of the binary post-
AGB stars to our sample objects where orbital data is unavailable, we can
conclude that extrinsic enrichment is highly unlikely for our targets.

Intrinsic enrichment: To investigate the possibility of intrinsic enrichment,
we used ATON code for stellar evolution modelling ventura98 to trace the
nucleosynthetic history of our target stars (see Section 4.3 for more
details). We once again note that while the ATON evolutionary models are
designed for single AGB stars, we explore the potential of employing these
models to predict $\rm C/O$ for each of the target stars (as tracers of TDU).
We then compared the theoretically predicted C/O with the observed $\rm C/O$
of our target stars. The results from the models predict that our target stars
have experienced thermal pulses during their AGB phase (see Figure 8 and
Figure 9, respectively). For J005107, this result is explained using the upper
limit luminosity range  $\rm L_{PLC}$ (see Table 5). We note that the observed
O abundance of J005107 ([O/Fe]$\ =1.06\pm 0.21$ dex) is also mainly intrinsic
and influenced by the dredge-up in the prior AGB phase. During the TDU, even
if the C enrichment is the most outstanding consequence, some O enrichment
occurs too. Especially in the metal-poor domain, the increase in [O/Fe] is
relevant due to the low oxygen content of the gas from which the star was
formed. Concerning the Z = 0.001 models used in this paper for J005107 (see
Section 4.3), we find that the largest increase in [O/Fe] is achieved during
the evolution of the 2.5 $\rm M_{\odot}$ model star, for which [O/Fe]
increases by 0.9 dex. For lower initial masses we still find O enrichment,
down to 0.2 dex for the stars of initial mass around 0.9 $\rm M_{\odot}$.

Consequently, the above arguments show the likely occurrence of AGB
nucleosynthesis and hence strongly suggest the likelihood of an intrinsic
carbon and s-process enrichment of our targets (see Section 4.3 for more
details).

Inherited enrichment from the host galaxy: We also investigated whether the
observed s-process enrichment of the target stars originated from the initial
chemical composition of the ISM from which it was formed. To assess this, we
compared the local initial s-process abundances of the SMC, LMC and the
Galaxy. The initial s-process abundances of the SMC were determined by
comparing the s-process abundances of SMC red giant stars Mucciarelli2023. For
the LMC, initial s-process abundances were derived from the s-process
abundances of LMC field red giant stars VanderSwaelmen2013. In the case of the
Galaxy, the initial s-process abundances were determined by comparing the
s-process abundances of F and G dwarfs within the Galactic discs, as reported
by Simmerer2004, Bensby2005, Brewer2006 and Reddy2003; Reddy2006. Based on the
above comparisons, it becomes evident that the standard enrichment of
s-process elements in the SMC, LMC, and the Galaxy is typically
$\sim\,$[s/Fe]$\,\leq\\!0.5$ dex. V453 Oph, a post-AGB star in the Galaxy,
exhibits a mild s-process enrichment which is attributed to the initial
inherited s-process enrichment from the Galaxy Deero2005. Drawing insights
from the abundance analysis of V453 Oph Deero2005, we conclude that the mild
s-process enrichment of the order of [s/Fe]$\ =0.50\pm 0.21$ dex can reflect
the inherited s-process abundance of the Galaxy at its birthplace, rather than
being a result of its internal nucleosynthesis (see B for additional details
regarding V453 Oph). Additionally, it is worth noting that, unlike our
targets, V453 Oph exhibits a very metal-poor composition, with [Fe/H]$\
=-2.23\pm 0.12$ dex, where the inherited galactic enrichments are typically
more prominent. Consequently, for our post-AGB target stars, the impact of
inherited galactic enrichment (i.e., a maximum of $\sim\,$[s/Fe]$\,\leq\\!0.5$
dex) cannot solely explain the strong s-process enrichment observed (i.e.,
[s/Fe]$\,\gtrapprox\\!1$ dex).

Therefore, the above arguments point to the possibility that the observed
carbon and s-process enrichment of our target stars is most likely intrinsic
in nature. This implies that the observed carbon and s-process enrichment is
likely to be a result of the AGB nucleosynthesis that occurred before the
termination of the AGB phase via binary interaction. However, what remains
unclear is that unlike the majority of binary post-AGB which display a disc-
binary driven photospheric chemical depletion, our target star’s chemical
depletion seems to have failed, causing retention of the signature of the
nucleosynthesis that occurred during and before the AGB evolution of these
objects.

##  6 Summary and Conclusions

In this study, we present detailed stellar parameter and chemical abundance
studies of a subset of chemically peculiar binary post-AGB stars (disc-
sources) in the Galaxy and the MCs that exhibit a carbon and s-process
enrichment in their photospheric chemical composition, contrary to the
commonly observed photospheric chemical depletion typically observed in binary
post-AGB stars.

Our investigation into the carbon and s-process enrichment observed in our
target stars has provided valuable insights. By considering extrinsic,
intrinsic, and inherited galactic enrichment scenarios, we have effectively
ruled out extrinsic and inherited galactic s-process enrichment as
explanations for the observed overabundance of carbon and s-process elements
in our target stars.

Based on our observationally derived stellar parameters and chemical
abundances combined with predictions from dedicated ATON stellar evolutionary
models (Ventura et al., 1998), we propose that the carbon and s-process
enrichment in our target stars is predominantly intrinsic in nature. Our
target stars display an abundance pattern consistent with expectations for a
post-TDU system (as depicted in Figure 10) with C/O$\,>\\!1$ dex, [C/Fe]
ranging between 0.5 - 1.0 dex and [s/Fe]$\,>\\!1$ dex. This photospheric
chemical composition suggests the presence of a circumstellar disc with C-rich
chemistry. The differences in molecular formation and dust condensation
processes that occur in C-rich versus O-rich circumstellar environments
(atypical of the majority of binary post-AGB stars displaying photospheric
chemical depletion) strongly indicate potential variations in chemical
depletion efficiencies. Furthermore, the standard dust condensation
temperatures, based on O-rich compositions, are not suitable for our analysis.
However, the absence of observations regarding the circumstellar dust
chemistry of our targets, coupled with the lack of condensation temperature
estimates specific to C-rich environments, limits our ability to confirm this
hypothesis.

Conducting observational studies on the circumbinary disc chemistry of our
target stars, especially in comparison to other binary post-AGB stars
displaying chemical depletion, is crucial. This effort will uncover potential
peculiarities in our target stars and address gaps in our current
understanding of the disc-binary interaction that leads to varying
efficiencies and/or the lack of chemical depletion in binary post-AGB systems.

MM acknowledges the financial support provided by the International Macquarie
Research Excellence Scholarship (iMQRES) program for the duration of this
research. MM, DK, and MM also acknowledge the ARC Centre of Excellence for All
Sky Astrophysics in 3 Dimensions (ASTRO 3D). 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
number C14/17/082. This study is based on observations collected with the Very
Large Telescope at the ESO Paranal Observatory (Chile) of program numbers
099.D-0536, 074.D-0619 and 094.D-0067.

##### Data Availability Statement

The data underlying this article is made available online.

##  Appendix A Spectroscopic Analysis of MACHO 47.2496.8 and HD 158616

We performed a similar atmospheric parameter analysis and abundance analysis
as described in Section 3.1 and Section 3.2 respectively, for MACHO 47.2496.8
and HD 158616.

The results of the atmospheric parameters are presented in Table 1 under the
title "This study". The results of the abundance analysis are presented in
Table 7. We note that since the derived atmospheric parameters and abundances
of MACHO 47.2496.8 and HD 158616 align closely with values reported in the
literature (see Table 1 for atmospheric parameter details and Table 7 for
abundance details), we opted to adopt the literature values of both
atmospheric parameters and abundances for the rest of our analysis.

Table 7: Spectroscopically determined abundance results for MACHO 47.2496.8
and HD 158616 along with their literature values.

| MACHO 47.2496.8 | HD 158616
---|---|---
Ion | Z | [X/Fe] | [X/Fe]Literature | [X/Fe] | [X/Fe]Literature
C I | 6 | - | - | 0.51$\pm$0.20 | 0.47$\pm$0.14
N I | 7 | - | <0.88$\pm$0.20 | - | -0.07$\pm$0.35
O I | 8 | - | - | 0.19$\pm$0.14 | 0.24$\pm$0.16
Na I | 11 | 0.28$\pm$0.21 | 0.30$\pm$0.20 | 0.47$\pm$0.22 | 0.52$\pm$0.11
Mg I | 12 | 0.32$\pm$0.20 | 0.30$\pm$0.20 | 0.19$\pm$0.11 | 0.16$\pm$0.12
Si I | 14 | - | - | 0.37$\pm$0.26 | 0.36$\pm$0.20
S I | 16 | - | - | 0.33$\pm$0.25 | 0.33$\pm$0.18
Ca I | 20 | -0.30$\pm$0.20 | -0.50$\pm$0.20 | 0.16$\pm$0.23 | 0.17$\pm$0.09
Sc II | 21 | - | - | 0.13$\pm$0.17 | 0.10$\pm$0.12
Ti I | 22 | -0.09$\pm$0.20 | -0.05$\pm$0.05 | 0.20$\pm$0.19 | 0.18$\pm$0.12
V II | 23 | - | - | 0.54$\pm$0.15 | 0.53$\pm$0.13
Cr I | 24 | - | - | 0.05$\pm$0.19 | 0.04$\pm$0.11
Mn II | 25 | - | - | 0.18$\pm$0.21 | 0.13$\pm$0.15
Fe I | 26 | -0.05$\pm$0.14 | -0.11$\pm$0.10 | 0$\pm$0.18 | 0$\pm$0.06
Co I | 27 | - | - | -0.23$\pm$0.20 | -0.20$\pm$0.17
Ni I | 28 | 0.05$\pm$0.01 | 0$\pm$0.20 | 0.36$\pm$0.19 | 0.43$\pm$0.12
Zn I | 30 | 0.17$\pm$0.20 | 0.20$\pm$0.20 | 0.29$\pm$0.21 | 0.23$\pm$0.31
Y II | 39 | 1.17$\pm$0.24 | 1.13$\pm$0.10 | 0.72$\pm$0.12 | 0.71$\pm$0.12
Zr II | 40 | 1.37$\pm$0.20 | 1.30$\pm$0.20 | 0.78$\pm$0.25 | 0.77$\pm$0.12
Ba II | 56 | - | - | 1.20$\pm$0.22 | 1.16$\pm$0.31
La II | 57 | 2.10$\pm$0.24 | 2.14$\pm$0.09 | 0.86$\pm$0.11 | 0.92$\pm$0.17
Ce II | 58 | 2.12$\pm$0.21 | 2.08$\pm$0.10 | 1.08$\pm$0.11 | 0.98$\pm$0.15
Pr II | 59 | 2.19$\pm$0.20 | 2.17$\pm$0.15 | 1.07$\pm$0.19 | 1.17$\pm$0.21
Nd II | 60 | 2.16$\pm$0.11 | 2.12$\pm$0.09 | 0.75$\pm$0.23 | 0.75$\pm$0.19
Sm II | 62 | 2.08$\pm$0.13 | 1.91$\pm$0.15 | 0.98$\pm$0.17 | 1.03$\pm$0.19
Lu II | 71 | - | - | 0.89$\pm$0.18 | 0.94$\pm$0.27
Hf II | 72 | 2.12$\pm$0.20 | 2.00$\pm$0.20 | 0.76$\pm$0.20 | 0.72$\pm$0.25
W I | 74 | <1.71$\pm$0.20 | <1.60$\pm$0.20 | - | -
Pb I | 82 | <2.17$\pm$0.20 | <2.10$\pm$0.20 | - | -

  * •

Notes: The detected ions and their corresponding atomic number (Z) are listed
in columns 1 and 2, respectively. [X/Fe] is the element-over-iron ratio along
with the total uncertainty (see Section 3.2 for more details on error
estimations). The abundances in italics are derived using the SSF method. The
literature values are taken from desmedt2016 and Reyniers2007 respectively.

##  Appendix B Target details of V453 Oph

Figure 12: SED of V453 Oph. The data points represent the dereddened
photometry. The red line represents the best-fitting scaled model atmosphere
(see Section 4.1 for details).

V453 Oph has been classified as a post-AGB star based on its high luminosity
Rao2011, determined using the PLC relation of RV Tauri variables in the LMC as
established by Alcock_1998. It has also been identified as an RV Tauri
pulsator with a fundamental pulsation period of 40.52 days and a spectral type
Fp, based on the Combined General Catalogue of Variable Stars survey by
kholopov1998. Additionally, Pollard1995 categorised V453 Oph as an RVa type
based on its reasonably regular LC variations (see Figure 13). The high-
resolution spectroscopic study conducted by Deero2005 recognised V453 Oph as
the first s-process enriched but carbon-deficient RV Tauri star in the Galaxy.
However, the SED of this star does not exhibit any IR excess, leading to its
position in the Non-IR box (see Figure 12). Drawing insights from the
abundance analysis and metal-poor nature ([Fe/H] = $-2.23\pm 0.12$ dex) of
V453 Oph Deero2005, we conclude that the mild s-process enrichment ([s/Fe]$\
=0.50\pm 0.21$ dex) of V453 Oph reflects the intrinsic local s-process
enrichment of the Galaxy at its birthplace.

Figure 13: The phased LC of the V453 Oph. The fundamental pulsation period
used to phase the LC is 40.52 days. The LCs are scattered due to their semi-
regular nature; they usually show considerable variations from cycle to cycle.
This behaviour is typically more pronounced for the longer-period RV Tauri
stars. The photometric data for V453 Oph is taken from ASAS-SN Variable Stars
Database II Shappee2014; Jayasinghe2019.

##  Appendix C Dynamic Spectra of HD 158616

Figure 14: The dynamic spectra for the $H\alpha$ line of HD 158616. The
spectra are shown as a function of the orbital phase (Bollen2021, see).