Observational evidence of third dredge-up occurrence in S-type stars with initial masses around 1 Msun

TL;DR

This study provides observational evidence that low-mass (~1 solar mass) AGB stars can undergo third dredge-up events, confirmed by Gaia data and stellar models, with implications for understanding s-process nucleosynthesis in such stars.

Contribution

First direct observational evidence of third dredge-up in low-mass (~1 Msun) S-type AGB stars using Gaia parallaxes and stellar evolution models.

Findings

Six Tc-rich S stars are consistent with initial masses around 1 Msun.

Third dredge-up occurs at low luminosity and early in the thermally-pulsing AGB phase.

Reasonable agreement between observed and predicted s-process abundances.

Abstract

Context- S stars are late-type giants with spectra showing characteristic molecular bands of ZrO in addition to the TiO bands typical of M stars. Their overabundance pattern shows the signature of s-process nucleosynthesis. Intrinsic, technetium (Tc)-rich S stars are the first objects, on the Asymptotic Giant Branch (AGB), to undergo third dredge-up (TDU) events. Gaia exquisite parallaxes now allow to precisely locate these stars in the Hertzsprung-Russell (HR) diagram. Here we report on a population of low-mass, Tc-rich S stars, previously unaccounted for by stellar evolution models. Aims- Our aim is to derive parameters of a sample of low-mass Tc-rich S stars and then, by comparing their location in the HR diagram with stellar evolution tracks, to derive their masses and to compare their measured s-process abundance profiles with recently derived STAREVOL nucleosynthetic predictions for low-mass AGB stars. Methods- The stellar parameters were obtained using a combination of HERMES high-resolution spectra, accurate Gaia Data Release 2 (Gaia-DR2) parallaxes, stellar-evolution models and newly-designed MARCS model atmospheres for S-type stars. Results- We report on 6 Tc-rich S stars lying close to the 1 Msun (initial mass) tracks of AGB stars of the corresponding metallicity and above the predicted onset of TDU, as expected. This provides direct evidence for TDUs occurring in AGB stars with initial masses as low as ~ 1 Msun and at low luminosity, i.e. at the start of the thermally-pulsing AGB. We present AGB models producing TDU in those stars with [Fe/H] in the range -0.25 to -0.5. There is a reasonable agreement between the measured and predicted s-process abundance profiles. For 2 objects however (CD -29 5912 and BD +34 1698), the predicted C/O ratio and s-process enhancements do not match simultaneously the measured ones.

Tables

Table 1. Table B1: Basic data of our sample stars. Column 1 lists the entry number in the General Catalog of S Stars (Stephenson 1984 ) , and column 2 lists various other identifiers. Column 3 gives the observation date and column 4 the S/N ratio in the V 𝑉 V band (around 500 nm). Columns 5, 6, 7, and 8 list the spectral type, the V 𝑉 V magnitude, the V − K 𝑉 𝐾 V-K color index, and the 2MASS K 𝐾 K magnitude, respectively, retrieved from the SIMBAD database (Wenger et al. 2000 ) . Column 9 displays the Gaia DR2 parallax and its error. Column 10 lists the adopted reddening (Gontcharov 2012 ) .

CSS	Name	Observation date	S/N	Sp. type	$V$	$V-K$	$K$	$\varpi \pm {\sigma }_{\varpi }$	$E_{B-V}$
								(mas)
1190	HD 357941	17 June 2018	90	M4S	9.41	6.636	2.774	1.71 $\pm$ 0.11	0.057
154	IRAS 05387+0137	2 February 2017	40	S5*3	10.79	6.997	3.793	0.85 $\pm$ 0.08	0.138
182	IRAS 06000+1023	3 February 2017	60	S4	10.38	6.119	4.261	0.81 $\pm$ 0.12	0.066
489	CD $-{29}^{\circ }$5912	17 February 2018	50	S4, 4	10.79	5.751	5.039	0.59 $\pm$ 0.04	0.162
1099	V915 Aql	27 May 2016	50	S5+/2	8.4	6.3	2.1	1.97 $\pm$ 0.06	0.17
413	BD $+{34}^{\circ }$1698	23 April 2016	40	M4S	10.67	6.965	3.705	0.93 $\pm$ 0.11	0.102

Table 2. Table B2: Atmospheric parameters of the sample stars. The values in parentheses list the range spanned by the log ⁡ g 𝑔 \log g  iterations (Sect.  4 ), except for [Fe/H], where they list the uncertainties on [Fe/H] as derived from the abundance analysis (Sect.  5 ). The last column provides the current mass of the S star, provided by the evolutionary track going through the current T eff subscript 𝑇 eff T_{\mathrm{eff}}   and luminosity of the star, for the corresponding metallicity. In all cases, the initial mass was 1 M ⊙ .

Name	$T_{\mathrm{eff}}$	$L$	$\log g$	[Fe/H]	C/O	[s/Fe]	Mcur
	(K)	(L⊙)				(dex)	(M⊙)
HD 357941	3400	1357	1	-0.27	0.5	0	0.7
	(100; 100)	(1193; 1558)	(0; 1)	($\pm$ 0.23)	(0.5; 0.75)	(0; 1)
CSS 154	3400	2128	1	-0.29	0.5	0	0.9
	(100; 100)	(1774; 2599)	(1; 3)	($\pm$0.20)	(0.5; 0.89)	(0; 1)
CSS 182	3500	1635	1	-0.4	0.5	1	0.9
	(100; 100)	(1236; 2266)	(1; 3)	($\pm$0.21)	(0.5; 0.89)	(1; 1)
CD $-{29}^{\circ }$5912	3600	1667	1	-0.4	0.5	1	0.8
	(100; 100)	(1446; 1943)	(1; 3)	($\pm$0.22)	(0.5; 0.89)	(1; 1)
V915 Aql	3400	1958	0	-0.5	0.75	0	0.7
	(3400; 3400)	(1832; 2098)	(0; 1)	($\pm$ 0.15)	(0.65; 0.75)	(0; 1)
BD +34∘1698	3400	1967	1	-0.54	0.5	1	0.7
	(200; 200)	(1564; 2548)	(1; 3)	($\pm$0.27)	(0.5; 0.89)	(1; 1)

Table 3. Table B3: 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 𝑁 N lists the number of lines used to derive the abundance. The σ [ X / Fe ] subscript 𝜎 delimited-[] X Fe \sigma_{\rm[X/Fe]} column lists the total uncertainty on the abundances calculated using the method described in Sect.  5 . The abundances and total error budget for V915 Aql have been retrieved from S18.

			BD +34∘1698					HD 357941					CSS 154
	$Z$	$\log ϵ_{}^a{}_{\odot }{}^{}$	$\log ϵ$	$N$	[X/H]	[X/Fe]	${\sigma }_{\left[X/\mathrm{Fe}\right]}$	$\log ϵ$	$N$	[X/H]	[X/Fe]	${\sigma }_{\left[X/\mathrm{Fe}\right]}$	$\log ϵ$	$N$	[X/H]	[X/Fe]	${\sigma }_{\left[X/\mathrm{Fe}\right]}$
C	6	8.43	8.059	-	-0.371	0.169	-	8.059	-	-0.371	-0.101	-	8.359	-	-0.071	0.219	-
N	7	7.83	9.6	-	1.77	2.31	-	9.1	-	1.27	1.54	-	9.6	-	1.77	2.06	-
O	8	8.69	8.36	-	-0.33	0.21	-	8.36	-	-0.33	-0.06	-	8.66	-	-0.03	0.26	-
Fe	26	7.5	6.96 $\pm 0.27$	13	-0.54	-	0.3	7.23 $\pm 0.23$	13	-0.27	-	0.2	7.21$\pm 0.20$	10	-0.29	-	0.2
Y I	39	2.21	-	-	-	-	-	2.3$\pm$ 0.00	1	0.09	0.36	0.5	2.5$\pm$ 0.00	1	0.29	0.58	0.5
Y II	39	2.21	-	-	-	-	-	2.5$\pm$ 0.00	1	0.29	0.56	0.5	-	-	-	-	-
Zr I	40	2.58	2.7$\pm$ 0.07	2	0.12	0.66	0.4	2.45 $\pm$ 0.21	2	-0.13	0.14	0.4	2.6$\pm$ 0.42	2	0.02	0.31	0.6
Nb I	41	1.46	0.95 $\pm$ 0.05	3	-0.51	0.03	0.3	1.2$\pm$ 0.00	2	-0.26	0.01	0.3	1.2 $\pm$ 0.00	1	-0.26	0.03	0.3
Ba I	56	2.18	2.5$\pm$ 0.00	1	0.29	0.86	0.4	2.2$\pm$ 0.00	1	0.02	0.29	0.4	2.2 $\pm$ 0.00	1	0.02	0.31	0.4
Ce II	58	1.58	1.62$\pm$ 0.15	4	0.04	0.58	0.2	1.4 $\pm$ 0.00	2	-0.18	0.09	0.2	1.35 $\pm$ 0.07	2	-0.23	0.06	0.2
Pr II	59	0.72	-	-	-	-	-	-	-	-	-	-	0.7 $\pm$ 0.00	1	-0.02	0.27	0.1

Table 4. Table B4: Sensitivity of the elemental abundances of CD − 29 ∘ superscript 29 -29^{\circ} 5912 on variations of the atmospheric parameters. A dash in the Δ Δ \Delta columns indicates that because of a degraded agreement between the observed and the synthetic spectrum, the (unique) line usually providing the abundance for the considered element had to be rejected.

model	$T_{\mathrm{eff}}$	$\log g$	[Fe/H]	C/O	[s/Fe]	${\chi }_t$
	(K)	(dex)	(dex)		(dex)	(km s -1)
A	3600	1	-0.5	0.5	1	2
B	3700	1	-0.5	0.5	1	2
C	3500	1	-0.5	0.5	1	2
D	3600	0	-0.5	0.5	1	2
E	3600	1	-0.5	0.5	1	1.5
F	3600	1	-0.5	0.75	1	2
G	3600	1	0.0	0.5	1	2
H	3500	1	-0.5	0.9	1	2

Table 5. Table E1: Atomic line list. The last column identifies the stars where the corresponding line was used for abundance determination (A: HD 357941; B: CSS 154; C: CSS 182; D: CD − 29 ∘ superscript 29 -29^{\circ} 5912; E: BD +34 ∘ 1698).

Species	$\lambda$ [Å]	$\chi$ [eV]	$\log gf$	Reference	Star
Fe I	7389.398	4.301	-0.460	Kurucz (2007)	ACDE
	7418.667	4.143	-1.376	O’Brian et al. (1991)	ABCDE
	7443.022	4.186	-1.820	Martin et al. (1988)	ABCD
	7461.263	5.507	-3.059	Kurucz (2007)	ABCDE
	7498.530	4.143	-2.250	Martin et al. (1988)	ABCDE
	7540.430	2.727	-3.850	Martin et al. (1988)	ABCDE
	7568.899	4.283	-0.773	Kurucz (2007)	ACDE
	7583.787	3.018	-1.885	O’Brian et al. (1991)	E
	7586.018	4.313	-0.458	Kurucz (2007)	ACDE
	8108.320	2.728	-3.898	Kurucz (2007)	ABCDE
	8248.129	4.371	-0.887	Kurucz (2007)	D
	8471.743	4.956	-1.037	Kurucz (2007)	D
	8515.108	3.018	-2.073		D
	8616.280	4.913	-0.655	Kurucz (2007)	D
	8621.601	2.949	-2.320		D
	8698.706	2.990	-3.452	Kurucz (2007)	ABCDE
	8699.454	4.955	-0.380	Nave et al. (1994)	ABCDE
	8710.404	5.742	-5.156	Kurucz (2007)	ABCDE
	8729.144	3.415	-2.871	Kurucz (2007)	ABCDE
Y I	6402.006	0.066	-1.849	Kurucz (2007)	CD
	6435.004	0.066	-0.820	Hannaford & Lowe (1985)	C
	6557.371	0.000	-2.290	Kurucz (2007)	CD
	6793.703	0.066	-1.601	Kurucz (2007)	CD
	8800.588	0.000	-2.240	Corliss & Bozman (1962)	ABCD
Y II	7881.881	1.839	-0.570	Nilsson et al. (1991)	ACD
Zr I	7819.374	1.822	-0.380	Biémont et al. (1981)	ABCDE
	7849.365	0.687	-1.300	Biémont et al. (1981)	ABCDE
Nb I	5189.186	0.130	-1.394	Duquette & Lawler (1982)	ABCDE
	5271.524	0.142	-1.240	Duquette & Lawler (1982)	AE
	5350.722	0.267	-0.862	Duquette & Lawler (1982)	CDE
Ba I	7488.077	1.190	-0.230	Miles & Wiese (1969)	ABCDE
Ce II	7580.913	0.327	-2.120		CE
	8025.571	0.000	-1.420	Meggers et al. (1975)	CDE
	8404.133	0.704	-1.670		C
	8716.659	0.122	-1.980	Meggers et al. (1975)	ABCDE
	8772.135	0.357	-1.260	Palmeri et al. (2000)	ABCDE
Pr II	5322.772	0.483	-0.141		CD
Nd II	5276.869	0.859	-0.440	Meggers et al. (1975)	CD
	5293.160	0.823	0.100	Den Hartog et al. (2003)	CD
	5319.810	0.550	-0.140	Den Hartog et al. (2003)	CD
	5385.888	0.742	-0.860	Meggers et al. (1975)	CD
	5431.516	1.121	-0.470		D
	7513.736	0.933	-1.241	Meggers et al. (1975)	CD
Sm II	7042.206	1.076	-0.760		D
Eu II	6437.640	1.320	-1.998		D
	6645.061	1.380	-0.516		D

Full text

*Aims. *Our aim is to derive parameters of a sample of low-mass Tc-rich S stars and then, by comparing their location in the HR diagram with stellar evolution tracks, to derive their masses and to compare their measured s-process abundance profiles with recently derived STAREVOL nucleosynthetic predictions for low-mass AGB stars.

*Methods. *The stellar parameters were obtained using a combination of HERMES high-resolution spectra, accurate Gaia Data Release 2 (Gaia-DR2) parallaxes, stellar-evolution models and newly-designed MARCS model atmospheres for S-type stars.

*Results. *We report on 6 Tc-rich S stars lying close to the 1 M⊙  (initial mass) tracks of AGB stars of the corresponding metallicity and above the predicted onset of TDU, as expected. This provides direct evidence for TDUs occurring in AGB stars with initial masses as low as $\sim$1 M⊙  and at low luminosity, i.e. at the start of the thermally-pulsing AGB. We present AGB models producing TDU in those stars with [Fe/H] in the range $-0.25$ to $-0.5$ There is a reasonable agreement between the measured and predicted s-process abundance profiles. For 2 objects however (CD -29∘5912 and BD +34∘1698), the predicted C/O ratio and s-process enhancements do not match simultaneously the measured ones.

1 Introduction

S-type stars are characterized by the presence of ZrO molecular bands on top of the TiO bands typical of M-type giants (Merrill, 1922), along with a carbon/oxygen (C/O) ratio in between the ones of M-type stars ($\sim$0.5) and those of carbon stars ($>$1). S-process elements, produced during the Asymptotic Giant Branch (AGB) phase, are overabundant in their atmospheres (Smith & Lambert, 1990). The fact that technetium (Tc), an s-process element with no stable isotopes, is detected in some but not all S stars, remained a puzzle until it was discovered that Tc-rich S stars are thermally-pulsing AGB (TP-AGB) stars undergoing s-process nucleosynthesis and third dredge-up (TDU) events, while Tc-poor S stars are less evolved stars owing their s-process enrichment to a pollution from a former AGB companion which has now turned into an undetected white dwarf (Jorissen & Mayor, 1988; Smith & Lambert, 1988; Jorissen et al., 1993; Van Eck & Jorissen, 1999, 2000; Van Eck et al., 2000). Enough time elapsed since the mass transfer for Tc to decay completely. Hence, S stars can be divided into two groups, the intrinsic, Tc-rich ones and the extrinsic, binary ones with no Tc. S stars serve as important probes to understand the AGB nucleosynthesis, since intrinsic S stars are the first stars on the AGB to show signatures of TDU.

An intriguing challenge in our understanding of AGB nucleosynthesis and TDU episodes is the growing series of observations pointing at dredge-up occurring in low-mass stars (¡1.5 M⊙). Such evidences are now more solid thanks to Gaia parallaxes (Gaia Collaboration et al., 2018) allowing to precisely locate objects in the Hertzsprung-Russell diagram (HR diagram; e.g., for S-type stars, Shetye et al., 2018, S18 hereafter). V915 Aql is an example of such a low-mass (initial mass $\sim$1 M⊙) intrinsic S star from the sample of S18 exhibiting s-process element enrichment (including Tc).

There were previous mentions of low-mass stars experiencing dredge-up. For example van Aarle et al. (2013) and De Smedt et al. (2015) reported strongly s-process-enriched and moderately metal-poor low-luminosity post-AGB stars as an evidence of TDU in stars of low initial masses ($\sim$1 M⊙).

On the contrary, standard stellar-evolution models at solar metallicity produce TDUs only in stars with initial masses larger than 1.4 – 1.5 M⊙ (Straniero et al., 2003; Bisterzo et al., 2010; Cristallo et al., 2015; Karakas & Lugaro, 2016), with the exception of Weiss & Ferguson (2009) which found TDU already at 1 M⊙ for $Z=0.02$, but allowing for some overshooting below the convective pulse. This minimum initial mass for the occurrence of TDU actually depends on the chemical composition, mass-loss rate, mixing prescriptions and numerics. For example, the models of Lugaro et al. (2012) and Fishlock et al. (2014) make TDU at $\sim$1 M⊙ but for metallicities as low as [Fe/H] $\sim-2.3$ and $-1.2$, respectively. Similarly, the AGB models of Stancliffe et al. (2005) and Weiss & Ferguson (2009) give rise to TDU at 1 M⊙ for the LMC and SMC metallicities (respectively $Z=0.008$ and 0.004, as adopted for these computations, which for $Z_{\odot}=0.02$ translates to [Fe/H]${}_{\rm LMC}=-0.4$ and [Fe/H]${}_{\rm SMC}=-0.7$). We moreover stress that Stancliffe et al. (2005) did not consider any mass loss at any stage of the evolution.

Here, we report on the analyses of 6 Tc-rich S stars in the solar neighbourhood. Thanks to the Gaia DR2 parallaxes, we compare the location of the sample stars in the HR diagram with the new AGB models computed using the STAREVOL code to determine their evolutionary masses. We further discuss the agreement between the measured s-process abundances and the nucleosynthesis predictions.

2 Observations

Among the Tc-rich S stars with an accurate Gaia DR2 parallax (i.e., matching the condition $\sigma_{\varpi}/\varpi$ $\leq 0.3$) that we observed with the HERMES high-resolution spectrograph (Raskin et al., 2011), we selected the stars that appeared to have an initial mass around 1 M⊙. Our sample includes 6 low-mass Tc-rich S stars; V915 Aql, which was analysed in S18, is among them. Only spectra with a S/N ratio larger than or equal to 30 in the $V$ band were used, to ensure Tc-line detectability. The observation log can be found in Table B1. Stellar masses were obtained from the position of the stars in the HR diagram (with luminosities obtained from the Gaia DR2 parallaxes and stellar parameters as derived in Sect. 4) compared with the STAREVOL evolutionary tracks (see also S18 for more details about the way masses were derived). The parallaxes and other basic data of the sample stars can be found in Table B1.

3 Technetium detection

The radio-isotope pairs Tc-Mo and Zr-Nb give a precise diagnostic to decide whether a star is currently experiencing s-process nucleosynthesis and dredge-ups (Mathews et al., 1986; Neyskens et al., 2015). Intrinsic S stars can thus be identified without ambiguity if they are enriched in Tc (Merrill, 1952) but not in Nb (Neyskens et al., 2015; Karinkuzhi et al., 2018). We use the three strong Tc I resonance lines located at $4238.19$ Å, $4262.27$ Å, and $4297.06$ Å. Though these lines are heavily blended with other (s-process) lines, their combination can be used reliably for the intrinsic/extrinsic classification. Fig. C1 displays the absorption features produced by the three lines for our sample stars and illustrates that they are all intrinsic S stars. Wang & Chen (2002) classified BD +34∘1698 and HD 357941 as extrinsic S stars based on their location in the $(K-[12],[12]-[25])$ color-index plane (where [12] and [25] are the IRAS magnitudes); however, our high-resolution spectra demonstrate without ambiguity that they are Tc-rich. The classification of CD $-29^{\circ}5912$ as an intrinsic S star is in agreement with the classification by Van Eck et al. (2017). There was no former classification available in the literature for CSS 182 and CSS 154.

The second diagnostic, based on the Nb abundance, is in perfect agreement with the Tc diagnostic, as will be shown in Sect. 5.

4 Stellar parameter determination

The atmospheric parameters {Teff, $\log g$, [Fe/H], C/O, [s/Fe]}, where [s/Fe]111The abundance of element X is defined as $\mathrm{[X/Y]}=\log_{10}(n_{\rm X}/n_{\rm Y})_{*}-\log_{10}(n_{\rm X}/n_{\rm Y})_{\odot}$ where $n_{i}$ is the number density of element $i$, and Y is a normalising element (usually H or Fe). The exact meaning of [s/Fe] in the grid of S-star MARCS model atmospheres is described in Appendix A.1. is the s-process enhancement with respect to the (metallicity-scaled) solar s-process contribution, were derived as in S18. In summary, this method performs a $\chi^{2}$ adjustment between a grid of S-star MARCS synthetic spectra (Van Eck et al., 2017) and observed HERMES spectra within carefully selected spectral regions, also considering synthetic and observed photometric color indices. Luminosity was calculated using the distances derived from the Gaia DR2 parallaxes, the reddening $E_{B-V}$ (retrieved from Gontcharov 2012) and the bolometric correction in the $K$-band as computed from the MARCS model atmospheres. The luminosity combined with $T_{\rm eff}$ leads to a constrain on the stellar mass by comparing with STAREVOL evolutionary tracks, allowing to re-evaluate the surface gravity. The parameter selection was iterated till the surface gravity derived from the spectroscopic adjustment matched the value derived from the stellar position in the HR diagram. The variations of the atmospheric parameters while iterating for $\log g$ are used as an estimate of the parameter uncertainty, as listed in Table B2.

5 Abundance determination and uncertainties

The atomic abundances were derived by comparing observed and synthetic spectra generated by the Turbospectrum (Alvarez & Plez, 1998, Plez, 2012) spectral synthesis code on MARCS model atmospheres of S-type stars (Van Eck et al., 2017) with matching parameters. For V915 Aql, the stellar parameters and abundances from S18 were used.

C, N, O: The C/O ratio is obtained from the stellar parameter determination (Sect. 4). The oxygen abundance cannot be derived from the optical spectrum in S-type stars, hence its solar-scaled value at the stellar metallicity was adopted, thereby fixing the C abundance. The nitrogen abundance was derived from the CN lines in the 7900-8100 Å range. In particular, the lines listed in Merle et al. (2016) were used.

[Fe/H]: The metallicity was derived using 10 or more Fe lines in the range 7300-8700 Å, as listed in Table E1. The metallicities of the sample stars are listed in column 5 of Table B2, along with their standard deviation.

Heavy elements: The spectra of S stars are dominated by molecular bands and unblended atomic s-process lines are rare (Smith & Lambert, 1990). This is why a spectral-synthesis approach is required, as opposed to relying solely on equivalent widths. As in Neyskens et al. (2015), Karinkuzhi et al. (2018) and S18, we only used the two Zr I lines at 7819.37 Å and 7849.37 Å with transition probabilities from laboratory measurements (Biémont et al., 1981). The Y I and Y II available lines lie in regions subject to blending by molecular lines of ZrO. The Y abundance of BD +34∘1698 could not be derived, presumably because of its higher Zr abundance coupled with a low temperature ([Zr/Fe]=2.7, $T_{\mathrm{eff}}$=3400 K; see Tables B2 and B3). The Ba abundance was derived for all stars using the 7488.077 Å Ba I line. We could not find any good Nd lines for BD +34∘1698, HD 357941 and CSS 154, but for CSS 182 and CD $-29^{\circ}$5912 at least 5 good lines were available. The other s-process element abundances were derived using the lines from Table E1 and are listed in Table B3.

All the sample stars show an overall mild enrichment of s-process elements. These results are also consistent with the moderate C/O ratios of these stars (0.5 – 0.75), indicating that they are at the very beginning of the TP-AGB.

Finally, Table B3 confirms the Tc – Nb anti-correlation encountered in S stars (Neyskens et al., 2015), since all the Tc-rich stars of our sample are devoid of any significant Nb enhancement, whereas they show genuine Zr overabundances. This is evidence that the freshly produced 93Zr did not have time yet to decay to (mono-isotopic) Nb. Our classification (based on the Tc lines) of these objects as intrinsic TP-AGB stars is thus fully corroborated by the Nb diagnostic.

Abundance uncertainties. The atmospheric parameters of S stars are unfortunately degenerated, in the sense that different combinations of $T_{\rm eff}$, $\log g$ and C/O may lead to similar line strengths. The effects of changing the stellar parameters may thus compensate each other, so that the impact on abundances may be limited (see the discussion in S18 and Sect. 7). Therefore, quadratically adding the abundance uncertainties induced by each atmospheric-parameter variation within its uncertainty range would crudely overestimate the total error. To evaluate the abundance uncertainties, we used instead the method of Cayrel et al. (2004). This method involves finding a model (tagged ‘model H’ in the list of Table B4) that provides an almost equally good spectral fit as our best model (tagged ‘model A’) in a representative spectral region (around Zr I lines at 7819 Å and 7849 Å). The difference between the abundances derived from models H and A, together with the line-to-line scatter and the error due to continuum placement (0.1 dex), were quadratically added to estimate the total uncertainty on each elemental abundance. When only one spectral line was available for a given element, a standard line-to-line scatter of 0.1 dex was adopted. The effect on the abundances of the variation of individual atmospheric parameters can be found in Table B4.

6 Comparison with STAREVOL nucleosynthesis predictions

We computed low-mass AGB models in order to compare the measured s-process overabundances and C/O ratios with their predicted values. These AGB models have been generated with the STAREVOL code (Siess & Arnould, 2008) using an extended s-process reaction network of 411 species and the same input physics as described in Goriely & Siess (2018). The reference solar composition is taken from Asplund et al. (2009) which corresponds to a metallicity $Z=0.0134$. To describe the mass-loss rate on the red giant branch (RGB), we use the Reimers (1975) prescription with $\eta_{R}=0.4$ (in Sect. 7.2, we evaluate the impact of this choice on the derived masses for our sample S stars) from the main sequence up to the beginning of the AGB and then switch to the Vassiliadis & Wood (1993) rate. Dedicated models with an initial mass of 1 M⊙ have been computed for [Fe/H] $=-0.3$ and $-0.5$. In the present calculations, a diffusion equation is used to compute the partial mixing of protons in the C-rich layers at the time of the TDU. Following the formalism of Eq. (9) of Goriely & Siess (2018), the diffusive mixing parameters adopted in our simulations are $f_{\rm over}=0.14$, $D_{\rm min}=10^{7}\,{\rm cm^{2}\,s^{-1}}$ and $p=1/2$, where $f_{\rm over}$ controls the extent of the mixing, $D_{\rm min}$ the value of the diffusion coefficient at the innermost boundary of the diffusive region and $p$ is an additional free parameter describing the shape of the diffusion profile. It should be stressed that a careful study of the parameter space for $f_{\rm over}$, $D_{\rm min}$ and $p$ has been carried out and only the above-mentioned values have been found to give rise to early TDU episodes and s-process enrichments compatible with observations (see below). While TDU is definitely needed to ensure a proper surface enrichment for the star to become an S star, the diffusive mixing should be strong enough to produce a significant amount of s-elements. But, on the other hand, the diffusive mixing should not be too efficient, to avoid large s-overabundances in the relatively thin envelope of the 1 M⊙ models. More details will be given in a forthcoming paper.

As shown in Fig. 1, the location of our 6 stars in the HR diagram matches well the tracks corresponding to the model star with initial mass 1 M⊙  (the estimated current mass is listed in the last column of Table B2), It can also be noted (see insert of Fig. 1) that within the error bars on the effective temperatures and luminosities, observations are compatible with the theoretical tracks corresponding to the first 3 pulse-interpulse cycles of the 1 M⊙ model star. Note that an uncertainty of about 100 K on the model effective temperature should also be considered (Cassisi, 2017). The inclusion of an efficient diffusive mixing (with a relatively large value of $f_{\rm over}$) at the bottom of the stellar envelope triggers not only TDU at the end of the first fully developed thermal pulse, but also the mixing of protons into the C-rich layers, hence an s-process nucleosynthesis strong enough to account for the surface enrichment of our 6 stars. For those with [Fe/H] $\simeq-0.3$ (HD 357941 and CSS 154), the measured abundances displayed in Fig. 2 are compatible with the occurrence of 3 thermal pulses, allowing the star to keep a relatively low C/O ratio (C/O = 0.75, compatible with observations; see Tables B2 and B3). Among the lower-metallicity stars which are compared with [Fe/H] $=-0.5$ models, CSS 182 and V915 Aql are compatible with a 2-pulse enrichment leading to C/O = 0.88. On the contrary, more TDU episodes seem to be required to explain the large surface abundances of s-elements measured in CD $-29^{\circ}$5912 and BD +34∘1698. However, these many TDU episodes then induce a C/O ratio above unity which is incompatible with the measured C/O ratios of 0.5 in these two objects.

7 Robustness of the derived stellar masses

Here we evaluate the sensitivity of the derived stellar masses on two key factors: (i) the adopted atmospheric parameters (Sect. 7.1), and (ii) the mass-loss rate on the RGB (Sect. 7.2).

7.1 Sensitivity to the adopted atmospheric-parameter set

The somewhat degenerate parameter space of S stars is well illustrated by the comparison of models A and H in Table B4. For example, a change of $T_{\mathrm{eff}}$ by +100 K or -100 K in model A can be compensated by an adjustment of the other stellar parameters (as in model H), in order to yield an equally acceptable fit of the global spectrum. Since the location of the stars in the HR diagram is parameter-dependent, so could in principle be the derived masses. The example of CD $-29^{\circ}$5912, which is representative of the other stars, shows that this is not the case however (Fig. D1). Models A and H differ in $T_{\mathrm{eff}}$ and C/O, and this difference induces a change in metallicity as derived from the Fe lines ([Fe/H] $=-0.27$). However, when compared with evolutionary tracks of the corresponding metallicity, the location in the HR diagram implied by models A or H in both cases falls along the track corresponding to the model with initial mass 1 M⊙.

7.2 Sensitivity to the RGB mass-loss rate

The RGB mass-loss rate has a strong impact on the minimum initial mass for the occurrence of TDUs. Increasing the mass-loss rate by a factor of two along the RGB (in agreement with the typical uncertainty on observed RGB mass-loss rates; see Table 8 of Schröder & Cuntz, 2007), we find that a star with initial mass 1.2 M⊙ and $\eta_{R}=0.8$ will reach the same TP-AGB location in the HR diagram as a 1 M⊙ model with the standard $\eta_{R}$ value of 0.4. This simple argument suggests to adopt an uncertainty of 0.2 M⊙ on the determination of the stellar mass on the basis of its location in the HR diagram, hence on the minimum initial mass for the occurrence of TDU.

8 Conclusion

The combination of dedicated MARCS model atmospheres with the Gaia DR2 parallaxes allows to derive stellar parameters of S stars and to locate them in the HR diagram. Their (initial) masses have been derived as well, comparing these locations with STAREVOL evolutionary tracks. A subsample of 6 low-mass (1 – 1.2 M⊙), intrinsic (Tc-rich, Nb-poor) S stars could be identified, and points at the occurrence of TDU in low-mass AGB stars at relatively low luminosity, i.e. at the start of the TP-AGB. Here, we present AGB models that can produce TDUs for initial stellar masses as low as 1 M⊙ and metallicities [Fe/H] of $-0.3$ and $-0.5$, provided that a very efficient overshoot with $f_{\mathrm{over}}=0.14$ is applied at the base of the convective envelope. In the HR diagram, our low-mass intrinsic S stars are nicely located just above the predicted onset of TDU events.

We obtain a reasonable agreement between the measured and predicted s-process abundance profiles. However, some stars like CD $-29^{\circ}$5912 and BD +34∘1698 are puzzling since their level of s-process enrichment requires a number of TDU episodes that would bring the C/O ratio well above the measured value. Nevertheless, for the four remaining targets, the agreement between s-process abundances and C/O ratios is satisfactory.

In summary, our results on intrinsic low-mass S stars definitely prove that the TDU is active in stars with masses as low as 1 – 1.2 M⊙ with [Fe/H] in the range $-0.3$ to $-0.5$. The new AGB STAREVOL models can now account for the measured s-process abundances of low-mass AGB stars. These new observations and models improve our understanding of the onset of TDU and its mass and metallicity dependence.

Acknowledgements.

The authors thank the referee for very constructive comments. This research has been funded by the Belgian Science Policy Office under contract BR/143/A2/STARLAB. S.V.E. thanks Fondation ULB for its support. Based on observations obtained with the HERMES spectrograph, which is supported by the Research Foundation - Flanders (FWO), Belgium, the Research Council of KU Leuven, Belgium, the Fonds National de la Recherche Scientifique (F.R.S.-FNRS), Belgium, the Royal Observatory of Belgium, the Observatoire de Genève, Switzerland and the Thüringer Landessternwarte Tautenburg, Germany. 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.

Appendix A [s/Fe] in the MARCS grid

As a complement to Van Eck et al. (2017), we give here details about the exact meaning of the [s/Fe] parameter in the MARCS grid of S stars, which provides models with [s/Fe] = 0, +1, and +2 dex. This parameter adjusts the abundances $\log\epsilon_{X}$ for elements from Ga to Bi in the following way:

$X_{s}=\log_{10}\left[(n_{\rm X}/n_{\rm H})_{\odot}\times 10^{\mathrm{[Fe/H]}}\times 10^{[\mathrm{s}/\mathrm{Fe}]}\times f_{X,s}\right]\;,$

$X_{r}=\log_{10}\left[(n_{\rm X}/n_{\rm H})_{\odot}\times 10^{\mathrm{[Fe/H]}}\times 10^{[\mathrm{r}/\mathrm{Fe}]}\times(1-f_{X,s})\right]\;,$

$\log\epsilon_{X}=\log_{10}(10^{X_{s}}+10^{X_{r}}$).

The fractional s-process abundance of element $X$ (denoted $f_{X,s}$) is taken from Arlandini et al. (1999). The fractional r-process contribution of that element is then simply given by $f_{X,r}=1-f_{X,s}$. The parameter [r/Fe] is included in the above formulae for the sake of completeness, but it is set to 0 in the S-star grid.

Appendix B Basic data, atmospheric parameters and abundances of our sample stars

Appendix C Example spectra

Appendix D HR diagram

Appendix E Linelist