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S stars and s-process in the Gaia era I. Stellar parameters and chemical abundances in a sub-sample of S stars with new MARCS model atmospheres

S stars are transition objects between M-type giants and carbon stars on the asymptotic giant branch (AGB). They are characterized by overabundances of s-process elements. Roughly half of them are enhanced in technetium (Tc), an s-process element with no stable isotope, while the other half lack technetium. This dichotomy arises from the fact that Tc-rich S stars are intrinsically producing s-process elements and have undergone third dredge-up (TDU) events, while Tc-poor S stars owe their s-process overabundances to a past pollution by a former AGB companion. Our aim is to analyse the abundances of S stars and gain insights into their evolutionary status and on the nucleosynthesis of heavy s-process elements taking place in their interior. In particular, the location of extrinsic and intrinsic S stars in the HR diagram will be compared with the theoretical onset of the TDU on the thermally-pulsing AGB. A sample of 19 S-type stars was analysed by combining HERMES high-resolution spectra, accurate Gaia Data Release 2 (GDR2) parallaxes, stellar-evolution models, and newly-designed MARCS model atmospheres for S-type stars. Combining the derived parameters with GDR2 parallaxes allows a joint analysis of the location of the stars in the Hertzsprung-Russell diagram and of their surface abundances. For all 19 stars, Zr and Nb abundances are derived, complemented by abundances of other s-process elements for the three Tc-rich S stars. These abundances agree within the uncertainties with nucleosynthesis predictions for stars of corresponding mass, metallicity and evolutionary stage. Most extrinsic S stars lie close to the tip of the red giant branch (RGB), and a few are located along the early AGB. The location of intrinsic S stars in the HR diagram is compatible with them being thermally-pulsing AGB stars.


Introduction
S stars are late-type giants displaying, as the most characteristic feature of their optical spectra, ZrO bands (Merrill 1922) along with the usual TiO bands present in stars of similar temperatures (approximately 3000-4000 K, as M-type stars). The spectra show overabundances of s-process elements (Smith & Lambert 1990) produced by the slow capture of neutrons on elements heavier than Fe (Burbidge et al. 1957;Käppeler et al. 2011) during the thermally-pulsing AGB phase (TP-AGB). These elements are then brought to the surface of the AGB star through mixing processes called third dredge-ups (TDU). The carbon over oxygen (C/O) ratio of S stars is in the range 0.5 to 0.99 which makes them transition objects between M-type (C/O ∼ 0.4) and carbon (C/O >1) stars (Iben & Renzini 1983).
Another important characteristic of the S star family is the technetium (Tc) dichotomy. Tc is an element produced by the s-process and which has no stable isotope. Its isotope 99 Tc has a half-life of 210 000 yrs. The puzzling detection of Tc in some S stars but not in others was solved after realizing that the S stars without Tc (i.e. Tc-poor S stars) belong to binary systems. They are called extrinsic S stars (Smith & Lambert 1988;Jorissen et al. 1993) because they owe their s-process abundances to mass transfer from a former AGB companion which is now a white dwarf. Therefore, the extrinsic S stars show s-process overabundances, except for Tc, which has decayed since the termination of the AGB phase of the companion. On the contrary, Tcrich S stars, called intrinsic, are producing s-process elements including Tc and transporting them to their surface via ongoing, recurrent TDU episodes.
We recently discovered a third class of S stars, the bitrinsic S stars (Shetye et al. 2020, S20 hereafter) that share properties with both the intrinsic and extrinsic classes: they are Tcrich and as such are located on the TP-AGB, but they also show overabundances of Nb, a signature of extrinsically-enriched stars (Neyskens et al. 2015;Shetye et al. 2018;Karinkuzhi et al. 2018). Indeed, the unstable 93 Zr isotope (produced by the sprocess) decays into 93 Nb, the only stable isotope of Nb, in 1.53 Myr. Therefore a niobium enrichment is expected in extrinsic stars, while it is not in TP-AGB stars.
The intrinsic S stars play an important role in our understanding of AGB nucleosynthesis and in particular of the TDU. They are the first objects on the AGB to show clear signatures (Tc and ZrO) of the TDU occurrences. They constrain the minimum luminosity of the TDU as well as its mass and metallicity dependence. The recent discovery of intrinsic, low-mass (initial mass < 1.5 M ), solar metallicity S stars (Shetye et al. 2019, S19 hereafter) provided an observational evidence of the operation of TDUs even in low-mass stars.
In a previous paper (Shetye et al. 2018, S18 hereafter) we introduced a new method for the parameter and abundance determination in S-type stars. However, the number of intrinsic S stars available at the time of that study was limited by the bias of the Tycho-Gaia astrometric solution against extremely red sources (Michalik et al. 2015). In the current work we investigate the chemical composition and evolutionary status of 13 intrinsic S stars from Gaia DR2 for which we could obtain high-resolution spectra. This paper is a follow up on the investigation of the evolutionary status of S stars conducted in the pioneering work of Smith & Lambert (1990). We introduce the observational sample in Section 2 and discuss the Tc detection in Section 3. Sections 4 and 5 are dedicated to the description of the parameter and abundance determination. In Section 6 we present the Gaia EDR3 HR diagram of intrinsic and extrinsic S stars. We discuss the derived elemental abundances of the sample stars and compare them with nucleosynthesis predictions in Section 7. Finally, we conclude with a summary of the most important results.

Observational sample
From the General Catalogue of Galactic S-Stars (Stephenson 1984, CGSS), we selected the ones with a Gaia Data Release 2 (DR2) parallax matching the condition σ / ≤ 0.3 and with available HERMES high-resolution spectra (Raskin et al. 2011). From this sample we distinguished the intrinsic S stars from the extrinsic ones using Tc lines (Section 3) and kept only the Tc-rich S stars. Among these, the Tc-rich S stars with initial masses smaller than 1.5 M were studied in S19. The cases of BD +79 • 156 and o 1 Ori, two bitrinsic stars, were discussed in S20. In the current work we derive parameters and abundances for the remaining Tc-rich S stars and also compile the Tc-rich S star results from S18 (3 stars), S19 (5 stars), S20 (2 stars) to increase the size of our sample.
Though the sample was designed using the Gaia DR2, Gaia early Data Release 3 (EDR3) became public during the course of our analysis. Hence the stellar parameters and luminosities were derived using Gaia EDR3. The relative parallax difference between the two releases | DR2 − EDR3 |/ EDR3 is usually smaller than 12% (except for V812 Oph, CSS 151, and CSS 454 which show the largest relative deviations of 22%, 33% and 57.5%, respectively). The cause of the large parallax difference of some stars between DR2 and EDR3 is not yet clear. However, to make a consistent comparison of the present study with the previously studied samples (S18, S19 and S20), we re-computed the luminosities of all the extrinsic and intrinsic stars of S18, S19 and S20 using EDR3 (Table D.1). As a result, some stars previously identified (using DR2 parallaxes) as low-mass S stars (BD +34 • 1698 = CSS 413 and HD 357941 = CSS 1190; see S19) turn out to have higher masses (M ini = 1.4 and 3.5 M respectively) according to their location in the HR diagram using EDR3 parallaxes (Sect. 6). This change in their masses required to adopt a log g value different from the one used for their abundance anal- Notes. Columns 1 and 2 list the CGSS (Stephenson 1984) and AAVSO identifiers, respectively. Column 3 contains the V amplitude from AAVSO.
ysis in S19 (both stars had log g ∼ 1 in S19; with EDR3 we find instead log g ∼ 0 for both of them). Hence, in the current work we also re-computed the stellar parameters and abundances of BD +34 • 1698 and HD 357941, along the guidelines described in Sections. 4 and 5 using the EDR3 parallaxes (Table D.2). A last criterion to define the Tc-rich S-star sample relates to the photometric variability. Large convective cells and/or pulsations are responsible for the photometric variability of TP-AGB stars. The thermal structure of these pulsating atmospheres can be significantly different from time-independent, hydrostatic atmospheres used to derive their stellar parameters, which can therefore be quite unreliable. We checked the time series data obtained by the American Association of Variable Star Observers (AAVSO) and removed from our sample the Tc-rich S stars with photometric variability ∆V > 1 mag (see Table 1) except for V812 Oph. The HERMES spectra of V812 Oph, despite its high variability (∆V > 1.4 mag), matched well the atmospheric models all over the optical range, hence we included it in the current sample. The sample of newly analyzed stars is listed in Table 2.

Tc detection
Three Tc I resonance lines located at 4238.19, 4262.27 and 4297.06 Å were used. A signal to noise ratio (S/N) of at least 30 in the V-band is needed to detect the Tc lines in S-star spectra (Van Eck et al. 1998, S18, S19). The spectra of our sample stars all have a S/N (listed in Column 11 of Table 2) equal to or larger than 40 in the V band and 30 in the B band. The Tc absorption features of our sample stars around the three Tc lines are presented in Fig. 1.
We confirm all previous Tc-rich classifications except for one target, HD 288833, classified as Tc-poor by Jorissen et al. (1993), despite the fact that its IRAS excess ([12] -[25]) is larger than −1.3 while extrinsic stars have [12] -[25] < −1.3 according to their classification criterion. This criterion was designed by Jorissen et al. (1993) to diagnose the expected lower infrared excess of the extrinsic stars with respect to that of (more evolved) intrinsic stars. The three Tc absorption features can be readily identified for this object in Fig. 1.
For all other stars our classification is in agreement with previous findings when they exist. HR Peg, AA Cam, V1139 Tau, V679 Oph and HD 64147 were indeed classified as intrinsic S stars in Smith & Lambert (1988), Smith & Lambert (1990) and Jorissen et al. (1993). We agree with Otto et al. (2011) classification of CSS 1152 as an intrinsic S star based on AKARI photometry and also confirm the results of Neyskens et al. (2015) that KR CMa and CSS 454 are intrinsic S stars. We could not use the Tc line at 4238.19 Å for CD -27 • 5131, as the region around Shreeya Shetye et al.: S stars and s-process in the Gaia era  (Stephenson 1984) entry number and HD, BD or other names. Columns 3, 4, 5, and 6 indicate spectral type, V, K and J magnitudes, respectively, extracted from the SIMBAD Astronomical Database (Wenger et al. 2000). Column 7 lists the Gaia EDR3 parallax and its error. Z 5 is the five-parameter zero-point correction on the parallax from Lindegren et al. (2020). The reddenning E B−V has been obtained from the Gontcharov (2017) extinction maps. BC K is the bolometric correction in the K band as computed from the MARCS model atmospheres. Columns 10 and 11 document the HERMES observation dates and their signal-to-noise (S/N) ratio around 500 nm. this line is dominated by a cosmic ray hit. From its other two Tc lines we assess the Tc-rich nature of this object, in agreement with SVE17. For V812 Oph, CSS 151 and BD-18 • 2608, that we classify as Tc-rich, no literature classification is available.

Derivation of the atmospheric parameters
Disentangling the intricate parameter space of S stars has always been a challenging task because their spectra are dominated by molecules. The atmospheres of S stars are complex as the thermal structure is dependent on their chemical composition (C/O and, to a lesser extent, heavy elements). Different methods have been used in the past for the stellar parameters determination. For instance, in their pioneering work, Smith & Lambert (1985) derived T eff from the (V − K) colors and log g from the standard log g -mass relationship where they estimated the masses by comparing the positions of the S stars in the HR diagram with the evolutionary tracks. However, the T eff -(V − K) relation valid for M-type giants has been shown to be inappropriate for S-type stars (SVE17) because of the spectral energy distribution (SED) alteration (mainly by ZrO, LaO and YO bands) induced by the non-standard chemical composition of S stars. New MARCS model atmospheres (Gustafsson et al. 2008) were designed to cover the full parameter range of S stars, with T eff from 2700 K to 4000 K, log g from 0 to 5, In the current study, the stellar parameters are determined as in S18. In summary, the high-resolution HERMES spectra are compared with a grid of ∼ 3500 synthetic spectra computed from the S star MARCS models to obtain atmospheric parameter estimates T eff , log g and [Fe/H]. The fitting is undertaken over small spectral windows (listed in Appendix Table E.1) because HER-MES spectra cannot be considered as flux-calibrated over their whole wavelength range. The fit with the lowest total χ 2 value then identifies the best-fitting model, providing a first estimate of the atmospheric parameters.
The stellar luminosities were calculated using the distances derived from the Gaia EDR3 parallaxes after applying the zeropoint correction from Lindegren et al. (2020), the reddening E B−V computed from Gontcharov (2017) and the bolometric correction in the K band as computed from the MARCS model atmospheres. Combining the T eff , metallicity and luminosity, we located the stars in the HR diagram and compared them with STAREVOL (Siess 2006) evolutionary tracks to estimate their current stellar masses.
A new surface gravity was then computed and the procedure iterated (as described in Fig. 5 of S18) until the log g retrieved from spectral fitting was consistent with the one obtained from the HR diagram. The uncertainties on the stellar parameters were obtained from the variations of the atmospheric parameters while iterating for log g. Our final set of parameters and the corresponding uncertainties are presented in Table 3. A further discussion of the reliability of the stellar masses thus found, based on their correlation with the height above the galactic plane and with 2MASS photometry, may be found in Appendix A.

Chemical abundance determination
The abundance determination methodology is the same as the one adopted in S18 and S19. We compared the observed spectra with synthetic spectra generated using Turbospectrum v15.1 (Plez 2012) and MARCS model atmospheres of S stars with the parameters derived in Sect. 4. We have made use of the same Fig. 1. The spectral region around the three (4238.19, 4262.27 and 4297.06 Å) Tc I lines in our sample of Tc-rich S stars. For comparison purposes, the spectrum of a Tc-poor S star (HD 233158, in blue in the top panels) from S18 is also plotted. The spectra have been arbitrarily normalized and binned by a factor of 1.5 to increase the S/N ratio. The Tc I line at 4238.19 Å could not be used for CD -27 • 5131 as local normalization was hampered by a nearby cosmic ray hit. input molecular line lists as in SVE17, atomic line list as in the Gaia-ESO survey (Heiter et al. 2020) and varied the abundances till a satisfactory agreement could be found.

Li
We used the Li i line at 6707.8 Å to derive the Li abundance. This line is known to be blended with a neighboring Ce ii line at 6708.099 Å in the warmer post-AGB stars (Reyniers et al. 2002). However, we did not identify any dominating blend from this line to the Li i line in our sample stars. In Fig. 2  The Li abundances of all the intrinsic S stars of our sample are generally low except for HR Peg. HR Peg was found to be a Li-rich star also by Vanture et al. (2007) who classified the star as a high-mass star (M > 3 M ) with hot bottom burning (HBB) as an explanation for the Li abundance. However, our mass estimate for HR Peg is M curr = 2.2 M , in agreement with the 2.0 M value found by Neyskens et al. (2015). Therefore, HR Peg does not appear to be massive enough to be producing Li through HBB. Other plausible explanations involve some extra mixing in low-mass AGB stars (e.g. Charbonnel & Balachandran 2000;Uttenthaler et al. 2007;Uttenthaler & Lebzelter 2010) or the engulfment of planets/brown dwarfs (Siess & Livio 1999).

C, N, O
We used the CH bands around 4250 Å to determine the C abundance. The sensitivity of these bands to the carbon abundance is limited in S-star spectra because CH bands are blended with mainly TiO and ZrO (as can be seen from Fig. 16 of SVE17). It was not possible to derive the O abundance because the λ 6300.3 Å O i line lies in a severely blended region. We used the solar oxygen abundance (Asplund et al. 2009) scaled with respect to the metallicity and included an alpha enhancement The uncertainty on C/O was estimated from the range of values of the C/O providing an acceptable fit to the CH G-band.
The N abundance was then determined from the CN lines available in the region 8000-8100 Å. The line list for these CN lines was taken from Sneden et al. (2014).

[Fe/H]
We used the same line lists as S18 and S19 (see also Appendix Table F.1) for Fe line synthesis. Between 9 and 15 Fe lines were used to derive the metallicity for all the sample stars, except for the star Vy 12, for which only six Fe lines could be used, as the other lines were strongly blended by molecules because of the high C/O of this object (0.97). The derived metallicity as well as the standard deviation due to line-to-line scatter are listed in Table 3.

Light s-process elements (Sr, Y, Zr, Nb)
The line list of S18 was used and complemented as documented in Appendix Table F.1. The strontium abundance could be derived only for HD 288833, BD-18 • 2608, and V679 Oph. The Y abundance was measured for all the sample stars. The Zr abundance was measured for all stars except KR CMa using the two Zr i lines at 7819.37 and 7849.37 Å with transition probabilities from laboratory measurements (Biémont et al. 1981). Some Nb i lines from Appendix Table F.1 could not be used in some stars. In fact, none of the Nb i lines could be used for CSS 151 because of the low S/N of its spectrum. The Nb abundance could therefore not be derived for this star.

Heavy s-process elements (Ba, Ce, Nd)
We derived the barium abundance using only one Ba i line located at 7488.07 Å. The cerium abundance was determined using the Ce ii lines from S18 together with some new lines located at 7580.91, 8025.57, 8394.51, 8405.25, and 8769.91 Å. There is a huge scatter in the Ce abundances for HR Peg, o 1 Ori, KR CMa, BD+79 • 156, and HD 64147 despite the use of Ce ii lines displaying satisfactory fits. The bottom panel of Fig. 3 illustrates the fact that even neighboring Ce ii lines (at 8769.91 and 8772.13 Å) can provide discrepant abundances (by ∼ 0.4 dex in this case). As explained in Karinkuzhi et al. (2018), cerium abundances derived using only Ce ii lines above 7000 Å are ∼ 0.3 dex lower than the ones derived from Ce ii lines in the range 4300-6500 Å. These authors mention that this difference might be imputable to non-LTE (non-local thermodynamic equilibrium) effects. This could be the reason for the sub-solar cerium abundances in some of our stars, as they were determined using only red Ce ii lines (λ > 7000 Å). These uncertain abundances are marked with a colon in Tables C.2 and C.3.

Other heavy elements (Pr, Sm, Eu)
Good Eu ii and Pr ii lines are located in the bluer part of the spectrum and could be used in some stars where the blending was weak. The Sm abundance was derived when possible using the Sm ii 7042.20 and 7051.55 Å lines. These lines are well fitted and yield consistent abundances.

Tc
All three Tc i resonance lines at 4238.19, 4262.27 and 4297.06 Å are heavily blended (Little-Marenin & Little 1979). We first derived the other s-process abundances in order to reproduce these blends as precisely as possible. The 4262.27 Å line is the best reproduced by our spectral synthesis. Its blends, consisting in two neighbouring lines of Nb i (at 4262.050 Å) and Gd ii (at 4262.087 Å) were identified in Van Eck & Jorissen (1999). The Tc abundance was derived from the 4262.27 Å Tc i line in our sample stars as well as in all intrinsic S stars from S18 and S19 (Table C.1).

Uncertainties on the abundances
The uncertainties on the abundances have been computed using the ones of the S star V915 Aql investigated in S18. The atmospheric parameters of V915 Aql are representative of those of most of our sample stars, hence we computed the elemental abundance error by quadratically adding the elemental standard deviation due to line-to-line scatter, the abundance errors due to parameter uncertainties of V915 Aql as derived in S18 (see also Appendix B), and a term of 0.1 dex to take into account continuum placement errors. For abundances that were derived using only one line, an arbitrary line-to-line scatter of 0.1 dex was assumed. Error bars on Tc abundances were estimated as the range of Tc abundances providing an acceptable fit of the Tc i 4262.27 Å line. The final elemental uncertainties on abundances are listed in Appendix Tables C.2, C.3, and C.4.

HR diagram of S stars
In Fig. 4 we present an HR diagram collecting Tc-rich S stars studied in S18, S19, and S20 as well as those of the present work, together with Tc-poor stars from S18. We used the final stellar parameters presented in Table 2. The errors on T eff are taken from Table 2. For HD 288833, V812 Oph, AA Cam, and V679 Oph for which T eff did not change during the log g iterations, we imposed a standard symmetric error of 100 K on their T eff . The asymmetric error on the luminosity was derived after propagating the error on the parallax. The evolutionary tracks displayed in Fig. 4 were computed with the STAREVOL code (Siess et al. 2000) and are described in detail in Escorza et al. (2017). Briefly, we use standard input physics with a mixing-length parameter α = 1.75, grey surface boundary conditions and the Asplund et al. (2009) solar mixture. Opacity enhancement due to the formation of molecules in carbon-rich atmospheres is also accounted for following the formulation of Marigo (2002). The Schröder & Cuntz (2007) mass-loss prescription is activated up to the end of core helium burning followed by the Vassiliadis & Wood (1993) formulation during the  AGB phase. We also consider overshooting below the convective envelope following the exponential decay expression of Herwig Article number, page 7 of 22 A&A proofs: manuscript no. aa et al. (1997) with the parameter f over = 0.01. Models were computed for various metallicities, including [Fe/H] = 0, -0.25 and -0.5.
There is a clear segregation between the location of intrinsic and extrinsic S stars in the HR diagram. Indeed, whatever the considered metallicity range, intrinsic S stars are always located above the black dotted line (see Fig. 4) marking the predicted onset of TDU for masses above 1.5 M . Whereas it is obvious that Tc-rich stars must be TP-AGB stars (because of the Tc detection), such a consistency between the luminosity of the third dredge-up onset in theoretical models, and the luminosity of observed intrinsic S stars, which are the least evolved objects identified as TP-AGB stars, was not as clearly demonstrated so far. Table 4 summarizes the observational constraints on the TDU first occurrence in terms of luminosity, initial mass and metallicity. For each mass and metallicity bins, we indicate the lowest luminosity of intrinsic S stars from our so-called large sample collecting stars from S18, S19, S20 and from the current work. These luminosities represent an observational upper limit on the TDU first occurrence in AGB stars, in the sense that Tcrich stars are observed at such luminosities, so that TDU must have already occurred by the time the star reaches this position in the HR diagram. However, since S stars are the first objects on the AGB to show clear signatures of TDU events (Tc and ZrO), this upper limit must be quite close to the genuine TDU occurrence line. It can be used as an observational constraint to be satisfied by the stellar evolutionary models of the corresponding masses and metallicities.

Discussion on the abundances and comparison with STAREVOL nucleosynthesis predictions
The elemental abundances derived following the methodology presented in Sect. 5 allow us to investigate nucleosynthesis in intrinsic S stars. We compare the measured abundance profiles of our sample stars with the nucleosynthesis calculations of the STAREVOL code (Goriely & Siess 2018) which uses an extended network of 411 species. The predicted and measured abundance distributions are presented in Fig. 5. The pulse number is chosen in order to optimally match both the overabundance level and the location in the HR diagram. We find a good overall agreement between the predicted and measured distributions of heavy elements. In particular, the peak of heavy s-elements is well reproduced in all stars. However, problems persist with the light elements such as carbon or oxygen, as discussed in Sect. 7.1, and with some heavy elements, e.g. Ce as discussed in Sect. 5.4. The models do account for most of the derived Tc abundances; however, we note that abundance predictions for Tc are extremely sensitive to the pulse number and to the amount of dilution in the stellar envelope due to the initial absence of Tc in the star. Hence, the agreement between predicted and measured abundances may be poor in some cases, for e.g., CSS 151, BD -18 • 2608, and CSS 454. We now investigate specific element ratios.

[C/Fe] and [s/Fe]
The surface composition of TP-AGB stars should reflect the addition of 12 C originating from the He-burning shell and s-process material produced either radiatively in the interpulse or in the convective thermal pulses for more massive objects. The TDU is then responsible for transporting these products to the stellar surface. As the star evolves on the TP-AGB, its carbon abundance should thus increase along with its s-process over-abundances. Eventually the star becomes carbon-rich when the C/O ratio exceeds unity. However, massive AGB stars with M ini > ∼ 4 M experience HBB and can efficiently burn the dredged-up carbon to produce mainly 14 N. In the top panel of Fig. 6 we present the carbon abundance as a function of s-process abundance for our intrinsic S star sample. The [s/Fe] index has been calculated using the Y, Zr and Ba abundances and is listed in Table C.5. In order to compare this trend with that of the stars from the next evolutionary stage, we added in Fig. 6 the Tc-rich carbon stars from Abia et al. (2002). The [C/Fe] abundances in this work were derived from the C/O ratios assuming solar oxygen abundance scaled with respect to metallicity and taking into account an α-element enhancement (Sect. 5.2). The determination of [C/Fe] is therefore quite indirect. We thus present in the bottom panel of Fig. 6 the C/O ratios. Their determination is very robust, given the high sensitivity of molecular bands to the C/O ratio. As expected, there is no overlap between C/O ratio of C stars and S-type stars. We note that 3 S-type stars have C/O ratios close to, but definitely lower than 1: indeed their C/O of 0.899, 0.971, and 0.998, produces an observed spectrum markedly different from the spectrum of an SC star (characterized by C/O = 1).
A common misunderstanding is that S stars have C/O = 1. This statement is often encountered in the literature even as a definition of S-type stars. Once again (see also Van Eck et al.  Table 4. Observed lowest luminosities of intrinsic S stars in different mass and metallicity bins (collected from this work, S18, S19 and S20  Table C.5, Figure 4 and Table A.1 from S20 for individual heavy-element abundances). This star is an-other example of the "Stephenson M-type stars" uncovered by Smith & Lambert (1990). Nevertheless, it shows clear Tc signatures (Figure 1 of S20 7. The distribution of [hs/ls] as a function of metallicity for the intrinsic S stars of our study (filled squares). The hs-index has been calculated using Ba and Nd, and the ls-index using Y and Zr. The symbols are color-coded with respect to the initial mass in the bins M ini < 1.5 M (blue), 1.5 ≤ M ini < 2.5 M (red), and M ini ≥ 2.5 M (green). Note that these mass bins are designed to match the [hs/ls] STAREVOL predictions only available for M ini = 1.5, 2, 2.5 M . Open circles denote the predictions from pulse to pulse for the different initial masses.

[hs/ls] and metallicity
We now investigate the potential correlations between the heavy (hs) to light (ls) s-process element ratio [hs/ls], mass and metallicity. The neutron irradiation index [hs/ls] is actually expected to increase with decreasing metallicity (Goriely & Mowlavi 2000), as the number of neutrons per iron seed increases.  From our measured abundances we find a large scatter in [hs/ls] with respect to metallicity (Fig. 7), within our limited range of metallicity. De Smedt et al. (2015Smedt et al. ( , 2016) also reported such a scatter in the [hs/ls] -[Fe/H] plane from their study of sprocess enriched post-AGB stars. However, the evolutionary link between post-AGB stars and intrinsic stars remains to be firmly established. Figure 7 also shows the absence of a clear correlation between the [hs/ls] ratio and the initial stellar masses.
When compared with the theoretical predictions accounting for the pulse-to-pulse variation, plotted in the top panel of Fig. 7, we find that the overall range covered by our measured [hs/ls] indices is compatible with that of the predicted abundances of the theoretical models. However, the [hs/ls] model predictions are not available for the complete metallicity range covered by our measured [Fe/H]. Tc abundances are also the ones with the highest C/O ratios, which is consistent with expectations from TP-AGB evolution. However, it is worth mentioning that whereas [s/Fe] is predicted to monotonically increase as the star ascends its AGB (see Fig. 6, this is also true for C/O if there is no HBB, and for luminosity, set aside the luminosity variations during thermal pulses), the technetium abundance has a more complex behaviour, because the 99 Tc half life (210 000 yrs) is not totally negligible with respect to the TP-AGB duration. For example, the evolution of the technetium-to-zirconium abundance ratio is not flat but shows a non-trivial evolution displayed in Fig. 2 of Neyskens et al. (2015). The lack of a clear trend in Fig. 8 is therefore not surprising.

Luminosity and Tc
In Fig. 9 we compare the Tc abundances and the luminosities of the sample stars. A large scatter in luminosity is present for each Tc abundance. If we focus on a specific mass bin, there is a loose trend of increasing Tc abundance with increasing luminosity, represented by the dashed least-square fit lines in Fig. 9. We also find that the most luminous and massive star in Fig. 9 has a relatively moderate Tc overabundance. A likely explanation is the larger dilution of s-elements in the bigger envelope of more massive AGB stars. Besides, with increasing stellar mass, the mass of the 13 C pocket responsible for the s-process, as well as that of the thermal pulses, are reduced because of the stronger compression of the shells induced by the larger core mass. Lower surface abundances of s-process elements are thus expected in higher-mass TP-AGB stars (García-Hernández et al. 2013).

The Zr-Nb plane and intrinsic/extrinsic stars segregation
A particular attention can also be paid to the Zr and Nb abundances that can be used as extrinsic/intrinsic star markers (Neyskens et al. 2015). As already mentioned in Sect. 1, niobium is mono-isotopic and can only be produced by the decay of 93 Zr (with a half-life of 1.53 × 10 6 yr). Intrinsic S stars are freshly producing s-process elements including 93 Zr, and there is not enough time on the TP-AGB for a significant production of 93 Nb. On the contrary, in extrinsic S stars, enough time has elapsed since the end of the nucleosynthesis in the companion for 93 (Neyskens et al. 2015, S18). The Zr -Nb plane has been studied extensively for extrinsically-enriched objects: the high Nb abundance in extrinsic stars has been demon-Article number, page 11 of 22 A&A proofs: manuscript no. aa Fig. 10. [Zr/Fe] as a function of [Nb/Fe] for the intrinsic S stars (black filled triangles) and extrinsic S stars (open squares) from S18 compared with the nucleosynthesis predictions for different initial masses and metallicities. The bitrinsic S stars from S20 are plotted with a blue star symbol. The "ext" and "int" labels next to the model parameters refer to extrinsic (respectively intrinsic) model abundances. strated in various extrinsic-star families among which CH and CEMP stars (Karinkuzhi et al. 2018(Karinkuzhi et al. , 2021. The apparent shift of extrinsic stars from the STAREVOL 2 -3 M predictions by a few tenths of a dex is as well discussed in Karinkuzhi et al. (2018). These authors speculated that this shift could arise due to the oscillator strengths of the two Zr lines used to derive the Zr abundance of the extrinsic S stars, which have a tendency to yield abundances that are about 0.1 dex too low in the benchmark stars of their sample (Arcturus and V762 Cas). Here we populate the high-Zr, low-Nb region of this plane, adding constraints from the Tc-rich S stars. Figure 10 confirms, on the basis of our so-called large sample of intrinsic S stars, the nice segregation between extrinsic and intrinsic stars in the [Zr/Fe] -[Nb/Fe] plane (with one exception discussed below). We also compare the measured Zr and Nb abundances with nucleosynthesis predictions from STAREVOL for intrinsic and extrinsic stars of 2 and 3 M , and metallicities [Fe/H] = 0.0 and -0.2. In Fig. 10, the intrinsic S stars from our sample have [Zr/Fe] < 1.6 and follow the trend predicted for TP-AGB stars (open squares in red and green). It is worth mentioning that some 93 Zr decay (inducing some 93 Nb production) is both predicted and observed, as can be seen from the fact that highly-enriched (high-Zr) intrinsic stars, which are the most evolved S stars on the TP-AGB, tend to have the largest Nb enrichments, and nicely follow the STAREVOL inclined trend in the [Zr/Fe] -[Nb/Fe] plane.
The two Tc-rich S stars o 1 Ori and BD+79 • 156 are 'bitrinsic' S stars as they are Tc-rich (intrinsic) but show signs of binarity together with a large Nb enrichment (for the corresponding [Zr/Fe] ratio), two evidences that they are also extrinsic stars, as discussed in S20. In addition to these two stars, the use of Gaia EDR3 parallaxes revealed a potentially new 'bitrinsic' candidate, BD +34 • 1698. We re-computed the s-process abundances of this star as its stellar parameters (mainly mass and log g) changed when Gaia DR2 parallaxes were replaced by Gaia EDR3. The revised s-process abundances of BD+34 • 1698 are presented in Appendix Table D.2. It has a [Zr/Nb] ratio close to unity, along with clear signatures of Tc (see Fig. C1 of S19), hence it qualifies as a 'bitrinsic' candidate. Wang & Chen (2002) classified it as a candidate extrinsic S star based on its IRAS photometry. Two spectra taken with the Hermes spectrograph revealed a clear radial-velocity variation: V r = 18.59 ± 0.05 km s −1 on JD 2 457 502.44 and V r = 22.59 ± 0.09 km s −1 on JD 2 459 289.51. Our detection of the binary motion associated to a clear Tc enrichment and a [Zr/Nb] ratio close to unity unambiguously classify BD +34 • 1698 as a member of the restricted family of bitrinsic stars (S20). Lastly, Fig. 10 confirms that the Zr-Nb analysis successfully serves as an additional test (apart from Tc) for the classification of S stars as intrinsic or extrinsic.

Conclusions
Thanks to the combination of Gaia EDR3 parallaxes and the high-resolution HERMES spectra, we have determined the stellar parameters of a sample of 13 intrinsic S stars with metallicities in the range -0.7 < [Fe/H] < 0. We then derived their s-process element abundances. The heavy-element abundances of intrinsic S stars reveal their rich nucleosynthetic history. The main results from our study can be summarized as follows: (i) The Gaia EDR3 HR diagram of S stars confirms that intrinsic S stars are more evolved than their extrinsic counterparts. (ii) The luminosity lower limits for the occurrence of TDU in different mass and metallicity ranges provided in Table 4 can be used to constrain AGB evolutionary models. (iii) The objects from our sample with the largest C/O ratios are also the ones with the largest [s/Fe], which is consistent with TP-AGB evolution predictions. (iv) However, we clearly demonstrate the too rapid increase of the C/O ratio with respect to [s/Fe] in model predictions.
(v) The measured s-process abundances of intrinsic S stars are in good agreement with the AGB nucleosynthesis predictions for models of the corresponding mass and metallicity. In particular, the Zr and Nb abundances are matching very well the predicted trend for intrinsic S stars, confirming our previous finding (S18, S20) that the Nb abundance can be used as an intrinsic/extrinsic diagnostic as efficient as the Tc presence/absence. (vi) We present Tc abundances for a large sample of intrinsic S stars (20 stars). We find that the stars with the highest C/O ratios tend to be the ones with the highest Tc abundances.
In conclusion, the current investigation of a sample of intrinsic S stars has extended our understanding of their properties, in particular their location in the HR diagram and their chemical characterization considering ∼ 10 chemical elements, including C/O ratio and the radioactive element technetium. land and the Thüringer Landessternwarte Tautenburg, Germany. This work has made use of data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC,https://www.cosmos.esa.int/ web/gaia/dpac/consortium). Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement. This research has also made use of the SIMBAD database, operated at CDS, Strasbourg, France. LS & SG are senior FNRS research associates. Fig. A.1. Height above the galactic plane for the sample intrinsic stars and for the intrinsic stars from S18, S19 and S20, as a function of their initial mass (left panel) or luminosity (right panel).
. with the abundance from model A and these differences are listed as columns ∆ B−A , ..., ∆ G−A in the bottom panels of Table B.1. Model H is the one used to compute the error on the abundances of V915 Aql as described in Section 5.8 (or Section 4.4 of S18). The contribution from the atmospheric parameter uncertainties on the error on the Li and Tc abundances is given by ∆ H−A in Table B.1 as described in Sect. 5.8.

Appendix C: Elemental abundances of sample stars
In this section we present the tables listing the elemental abundances for the stars of our current study. Table C.1 lists the Tc and Li abundances in our sample stars and also in Tc-rich stars from S18, S19 and S20 which we computed during the current study. Tables C.2, C.3, and C.4 provide the full list of elemental abundances in our sample stars. for our sample stars as well as for Tc-rich stars from S18, S19, and S20.  Notes. The atmospheric parameters of V915 Aql are adopted from S18. A dash in the ∆ column indicates that the agreement between the observed and the synthetic spectra was too poor and that the (unique) line usually providing the abundance for the considered element could not be used for that purpose. Column χ t corresponds to the microturbulence.
Appendix D: Revised stellar parameters and abundances of stars from S18, S19, S20 As explained in Sect. 2, the Gaia EDR3 parallaxes became available in the course of our current study. Hence, we revised the stellar parameters of Tc-rich and Tc-poor stars from S18, S19 and S20 using the Gaia EDR3 parallaxes. In Table D.1 we list these revised stellar parameters which were derived using the same method as described in Sect. 4. In Table D.2 we present the re-computed elemental abundances of BD+34 • 1698 and HD 357941, which are the only two stars for which the EDR3 parallaxes imposed a revision of log g (see Table D.1).
Notes. A dash indicates that the agreement between the observed and the synthetic spectra was too poor and that the (unique) line usually providing the abundance for the considered element had to be rejected. The "<" symbol is used when the line is still usable but only provides an upper limit on the abundance.
Appendix E: Spectral windows used for spectral fitting in Sect. 4 Table E.1 lists the different spectral windows used in the spectral fitting routine to derive an initial estimate of the stellar parameters.     Elemental abundances for the sample stars, along with the standard deviation due to line-to-line scatter. Solar abundances (third column) are from Asplund et al. (2009). The column labelled N lists the number of lines used to derive the abundance. The σ [X/Fe] column lists the total uncertainty on the abundances calculated using the method described in Sect. 5.8. The abundances and total error budget for V915 Aql were retrieved from S19.   Meggers et al. (1975)