The first measurements of carbon isotopic ratios in post-RGB stars: SZ Mon and DF Cyg
E-iSpec: A spectral analysis tool to derive elemental abundances and isotopic ratios for evolved stars

SZ Mon is a spectral type F8 star showing broad infrared excess in the SED. The very first studies of SZ Mon (Lloyd Evans, 1968; Stobie, 1970) classified this object as a Type II Cepheid with a double period¹¹1Double period is the empirically best-fit value for phase curves of Type II Cepheids, yet the fundamental pulsation period is twice shorter (Stobie, 1970). of 32.686 days. Maas et al. (2007) classified SZ Mon as RVa photometric type, i.e., an RV Tau variable without a detected secondary variation of its phase curve with significant amplitude and long period $\sim 1000$d (referred to as the RVb phenomenon).

In the recent studies (Maas et al., 2007; Oomen et al., 2019), SZ Mon was classified as a post-AGB star with a disc-type SED. Oomen et al. (2019) presented the SED modelling for SZ Mon and derived the SED luminosity $L_{\textrm{SZ Mon, SED}}=2400^{+2000}_{-1000}L_{\odot}$.

Furthermore, chemical abundance studies by Maas et al. (2007) showed that SZ Mon is an evolved post-AGB binary star showing photospheric chemical depletion – characteristic of post-AGB and post-RGB binary stars (see Section 1).

We note that, while SZ Mon was classified as a post-AGB RV Tauri (RV Tau) variable in the literature, in this study we re-classified the evolutionary nature of this target. Based on the newly derived luminosity of SZ Mon (see Section 3.2), its disc-type SED, and the confirmation of photospheric chemical depletion (see Section 4.3), we conclude that SZ Mon is a post-RGB binary star. Furthermore, given that the observed fundamental pulsation period is less than 20 days (i.e., 16.336 days; Soszyński et al., 2008), SZ Mon rather belongs to the W Virginis (W Vir) subclass of Type II Cepheid family (instead of RV Tau subclass). We adopted this new classification of SZ Mon (i.e., a post-RGB binary star and W Vir variable) for the rest of this study.

DF Cyg is a star of G6/7Ib/IIa spectral type. DF Cyg exhibits a broad infrared excess in the SED (i.e., disc-type de Ruyter et al., 2006). Manick et al. (2019) derived the luminosity of DF Cyg from SED fitting, wherein $L_{\textrm{DF Cyg, SED}}=1010^{+150}_{-140}L_{\odot}$).

Giridhar et al. (2005) conducted an extensive abundance analysis of DF Cyg and identified a rather steep depletion pattern with an unusually negative volatile-refractory abundance ratio ([Zn/Ti]=$-0.7$ dex). In our current study (see Section 4.3), we performed an independent abundance analysis, which resulted in a standard depletion pattern with ([Zn/Ti]=$+0.35$ dex).

DF Cyg was classified as an RV Tau variable with a fundamental pulsation period of 24.91 days (Kiss & Bódi, 2017). Using the pulsation period, Manick et al. (2019) derived a more reliable estimate of DF Cyg luminosity from period-luminosity-colour (PLC) relation for Type II Cepheids $L_{\textrm{DF Cyg, PLC}}=990\pm 190L_{\odot}$), and classified DF Cyg as a post-RGB star.

Previous studies have suggested that DF Cyg could be a binary system due to the very strong RVb phenomenon in the light curve, as discussed by Bódi et al. (2016) and Vega et al. (2017), or due to the presence of a disc, as mentioned by de Ruyter et al. (2005) and explained in Van Winckel (2018). Orbital parameter analysis (Oomen et al., 2018) confirmed the binary nature of DF Cyg with an orbital period of 784 days (see Table 1).

In this paper, we validated the binary post-RGB nature of DF Cyg (see Section 3.2).

In Table 2, we present the photometric magnitudes of SZ Mon and DF Cyg in various wavelength bands, including optical, NIR, and mid-infrared (MIR). The UBVRI photometry is taken from the Johnson-Cousins system (Johnson & Morgan, 1953; Cousins, 1976), and the I-band filters from the Sloan Digital Sky Survey (SDSS, York et al., 2000). The Two Micron All Sky Survey (2MASS) provides magnitudes in the J, H, and K bands (1.24, 1.66, and 2.16 $\mu$m, respectively; Skrutskie et al., 2006). WISE (Wright et al., 2010) contains the magnitudes in the W1, W2, W3, and W4 bands (3.4, 4.6, 12, and 22 $\mu$m, respectively). The mid-infrared (MIR) was complemented by fluxes from the MSX, AKARI, and IRAS catalogues (Egan et al., 2003; Ishihara et al., 2010; Neugebauer et al., 1984).

The SEDs of SZ Mon and DF Cyg are shown in Fig. 1 (top and bottom, respectively). We note that in the case of DF Cyg, we specifically excluded the $V$ and $I$ band magnitudes (which come from the ASAS Catalogue of Variable Stars in the Kepler Field), since they were obtained during the minima in the RVb period, which is out of phase with all the other photometric data points (see Fig. 8 of Manick et al. (2018). This significantly improves the $\chi^{2}$ value of the SED fitting and provides a more accurate luminosity estimate (see Section 3.2).

The SEDs of SZ Mon and DF Cyg exhibit characteristics of a disc type (Oomen et al., 2018), suggesting the possible presence of a circumbinary disc, which is indicative of binarity in post-RGB and post-AGB stars (Kamath et al., 2016; Kluska et al., 2022).

In this study, we calculated luminosities of SZ Mon and DF Cyg using two methods: i) by fitting the SED (SED luminosity, $L_{\rm SED}$); and ii) by using the PLC relation (PLC luminosity, $L_{\rm PLC}$). We briefly describe these two methods below.

To compute the SED luminosities, we followed the procedure described in Oomen et al. (2018); Kluska et al. (2022). In short, we started by assuming the appropriate Kurucz model atmospheres (Castelli & Kurucz, 2003) to fit the initial photometric data points. Following this, we accurately computed a dereddened SED model for SZ Mon and DF Cyg. This model took into account the overall reddening or extinction parameter $E(B-V)$ that yielded the lowest $\chi^{2}$ value from our extensive parameter grid search. The total reddening considered here encompassed both interstellar and circumstellar reddening. We made the assumption that the total reddening along the line of sight follows the wavelength dependence described by the interstellar-medium extinction law (Cardelli et al., 1989) with an $R_{V}$=3.1. We incorporated the more accurate Bailer-Jones geometric distances, denoted as $z_{\rm BJ}$, along with their respective upper and lower limits, represented as $z_{\rm BJU}$ and $z_{\rm BJL}$, sourced from the research conducted by Bailer-Jones et al. (2021). These geometric distances were computed based on Gaia EDR3 parallaxes, taking into consideration a direction-dependent prior distance. It is important to note that in all our calculations, we assumed that the emission of flux from the stars followed an isotropic radiation pattern. We also note that stellar variability was not considered, and this omission resulted in an increased $\chi^{2}$ value for high-amplitude variables.

To calculate the PLC luminosity, we used the PLC relation, which was obtained following the similar procedure as in Manick et al. (2018), but updated with OGLE-IV data for RV Tau pulsating variables in the LMC (Menon et al., submitted). In short, this relation uses the colour-corrected V-band magnitude known as the Wesenheit index (${\rm WI}=V-2.55(V-I)_{0}$; see Ngeow & Kanbur, 2005) and is given as

where $M_{bol,{\rm WI}}$ is the absolute Wesenheit magnitude, $P_{0}$ is the observed fundamental pulsation period in days, $\mu=18.49$ is the distance modulus for the LMC, $(V-I)_{0}$ is the intrinsic colour of each star. $m=-3.59$ is the slope, and $c=18.79$ is the intercept of the linear fit of the relation (see Fig. 5 in Manick et al. (2018)). Bolometric corrections $BC$ for SZ Mon and DF Cyg were calculated based on their observed effective temperatures, $T_{\rm eff}$ = 5 460 K for SZ Mon (see Table 4) and $T_{\rm eff}$ = 5 770 K for DF Cyg (see Table 5), following the tabulated relation from Flower (1996), corrected by Torres (2010).

We would like to highlight that due to the exclusion of the only available I-band magnitude (as discussed in Section 3.1), the calculation of the PLC luminosity for DF Cyg is not feasible. Nevertheless, our refined photometric selection for the SED fit provides a more reliable luminosity in comparison to the SED and PLC luminosity values reported by Manick et al. (2018).

In Table 1, we provide the final values and corresponding uncertainties in the SED and the PLC luminosities for SZ Mon and the SED luminosity for DF Cyg. The uncertainties in the SED luminosities were determined by calculating the standard deviation of the upper and lower luminosity limits, taking into consideration the uncertainties associated with distances ($z_{\rm BJU}$ and $z_{\rm BJL}$) and reddening ($E(B-V)$) for each respective target. On the contrary, the uncertainties in the PLC luminosities were dominated by the uncertainties of the reddening.

We note that we considered the PLC luminosity to be more precise and more reliable than the SED luminosity, mainly due to the significant $T_{\rm eff}$ fluctuations in our targets throughout the pulsation cycle (leading to significant changes in model fitting of stellar atmospheres shown as red lines in Fig. 1) and the uncertainty of distances obtained from parallax measurements, which were heavily affected by the binary orbital motion (Kamath et al., 2022).

In this subsection, we provide details of the optical and NIR spectral observations used in our study.

iSpec is an integrated spectroscopic software framework, which is capable of determining atmospheric parameters such as effective temperature, surface gravity, metallicity, micro/macroturbulence, rotation and individual elemental abundances for AFGKM stars. The full details of iSpec are presented in Blanco-Cuaresma et al. (2014); Blanco-Cuaresma (2019). In brief, iSpec integrates MARCS (Gustafsson et al., 2008) and different ATLAS9 (i.e., Kurucz, Castelli & Kurucz, KuruczODFNEW; Castelli & Kurucz, 2003) one-dimensional (1D) model atmospheres with assumed local thermodynamic equilibrium (LTE) together with the following radiative transfer codes: SPECTRUM (Gray & Corbally, 1994), Turbospectrum (Alvarez & Plez, 1998; Plez, 2012), SME (Valenti & Piskunov, 1996), MOOG (Sneden, 1973), and Synthe/WIDTH9 (Kurucz, 1993; Sbordone et al., 2004). These radiative transfer codes are implemented in iSpec to work in two different approaches: equivalent widths (EW) method and synthetic spectral fitting (SSF) technique. Furthermore, to carry out the spectral analyses, iSpec provides several line lists with a wide wavelength coverage (overall, from 300 nm to 4 $\mu$m). The line lists included are: the VALD3 line list (Kupka et al., 2011), the APOGEE line list (Smith et al., 2021), the Gaia-ESO line list (Heiter et al., 2021), the ATLAS9 line lists (Kurucz & Bell, 1995), and the original SPECTRUM line list, which contains atomic and molecular lines obtained mainly from the NIST Atomic Spectra Database (Ralchenko, 2005). Additionally, iSpec provides a collection of ready-to-use solar abundances from Anders & Grevesse (1989); Grevesse & Sauval (1998); Asplund et al. (2005); Grevesse et al. (2007); Asplund et al. (2009).

We note that iSpec offers two usability modes: a GUI version and a Python version. E-iSpec (see Section 4.2) exclusively utilises the Python version, which offers enhanced functionality.

While iSpec is capable of the spectral analysis of a wide range of targets, we note that it is not specifically designed for our goal. Firstly, iSpec routine for automatic continuum normalisation performs poorly for evolved stars, the spectra of which contain prominent molecular bands. Secondly, the molecular line lists presented in iSpec (especially for NIR regime) were not up-to-date. Thirdly, the error estimation of elemental abundances in iSpec only takes into account line-to-line (L2L) scatter completely ignoring the systematic errors caused by uncertainties of atmospheric parameters. Finally and most importantly, the isotopic ratios were not addressed in chemical analysis routines of iSpec. To overcome these limitations, we developed a Python wrapper for iSpec: E-iSpec.

E-iSpec⁴⁴4Accessible via https://github.com/MaksTheUAstronomer/E-iSpec.git is a semi-automated spectral (optical and NIR) analysis tool implemented in Python, primarily derived from iSpec but enhanced with extended capabilities described below. E-iSpec allows for the determination of atmospheric parameters, elemental abundances (from both atomic lines and molecular lines), and isotopic ratios, particularly for evolved stars with complex atmospheres.

E-iSpec uses 1D LTE model atmospheres (from MARCS and ATLAS9 grids)⁵⁵5We note that spherically-symmetric MARCS model atmospheres generally perform better for cool giants (Mészáros et al., 2012). and relies on the following radiative transfer codes, which were chosen due to their performance and reliability: Turbospectrum (Plez, 2012) for synthetic spectral fitting technique and Moog (Sneden, 1973) for equivalent width method. Line lists for atomic and molecular transitions, as detailed in Appendix B, are drawn from VALD3 for optical spectra ($\lambda\sim 300-1100$ nm) and DR17 APOGEE for NIR spectra ($\lambda\sim 1500-1700$ nm) (Kupka et al., 2011; Hayes et al., 2022). Solar abundances are derived from LTE values provided by Asplund et al. (2009).

In summary, E-iSpec allows to prepare the stellar spectra for chemical analysis and to determine atmospheric parameters along with elemental abundances and isotopic ratios. In the following subsections, we describe the capabilities of E-iSpec. The final atmospheric parameters, elemental abundances, and carbon isotopic ratio for SZ Mon and DF Cyg derived with E-iSpec are provided in Tables 4 and 5, respectively. Additionally, we present an extensive benchmarking of E-iSpec in Appendix D.

In this study, we used E-iSpec to determine atmospheric parameters, elemental abundances, and carbon isotopic ratios for two binary post-RGB stars: SZ Mon and DF Cyg. We found that the derived atmospheric parameters and elemental abundances are in good agreement with the previous studies of SZ Mon (Maas et al., 2007) and DF Cyg (Giridhar et al., 2005), which is expected given the proximity of pulsation phases in our study and the corresponding literature (see Tables 4 and 5, as well as Fig. 6). We calculated more accurate elemental abundances and increased the amount of analysed species for SZ Mon (9 newly studied species) and DF Cyg (8 newly studied species), including ¹³C.

Similarly to Maas et al. (2007) and Giridhar et al. (2005), we detected the chemical depletion profiles for both targets. To quantitatively describe the chemical depletion, we used [Zn/Ti] abundance ratio and the turn-off temperature $T_{\rm turn-off}$ (Oomen et al., 2019; Kluska et al., 2022). Due to its volatile nature, Zn ($T_{\rm cond,~{}Zn}=726$ K; Lodders, 2003) is anticipated to exhibit lesser depletion or non-depletion. In contrast, Ti ($T_{\rm cond,~{}Ti}=1582$ K; Lodders, 2003) is a refractory element expected to be significantly more depleted for post-RGB/post-AGB binary stars, causing [Zn/Ti] ratio to grow up to 3.4 dex (as in case of AF Crt; Kluska et al., 2022). We found that our targets exhibit a rather mild depletion with [Zn/Ti] values of 0.4 dex for SZ Mon and 0.3 dex for DF Cyg, as opposed to more extreme literature values of 0.8 dex and –0.7 dex, respectively.

The turn-off temperature $T_{\rm turn-off}$ (Oomen et al., 2019) marks the onset of chemical depletion pattern, separating the relatively non-depleted elements (i.e., volatile elements like Zn and S) and the elements affected by the depletion process (i.e., refractory elements like Fe and Ti). It is worth noting that when comparing the elemental abundances of SZ Mon and DF Cyg to those of the post-AGB sample (roughly selected from Oomen et al. (2019) by their SED luminosity $L_{\rm SED}>2\,500~{}L_{\odot}$; see Section 3.2), we notice that $T_{\rm turn-off}$ in SZ Mon and DF Cyg ($\approx 1\,400$ K; see Fig. 6) is higher than the median $T_{\rm turn-off}$ in binary post-AGB sample ($\approx 1\,100$ K; see Oomen et al. (2019) and references therein).

Regarding carbon isotopic ratios, our study marks the first attempt at estimating them in post-RGB stars. Using E-iSpec, as explained in Section 4.2.3, we derived ¹²C/¹³C=8$\pm$4 for SZ Mon and ¹²C/¹³C=12$\pm$3 for DF Cyg. To better understand the implications, we compared these values with theoretical predictions from the ATON evolutionary models, outlined in Section 5.

To interpret the CNO abundances of SZ Mon and investigate its evolution, we modelled the evolution of $\rm 1~{}M_{\odot}$ star of metallicity $\rm Z=0.004$, which corresponded to initial metallicity of $\approx-0.7$ dex as traced by observed [S/H] and [Zn/H] (see Fig. 6). We note that the horizontal part of the evolutionary tracks shown in Fig. 7 represents the initial pre-Main Sequence phase, during which the luminosity decreases and the surface chemistry is unchanged. During the RGB phase the luminosity increases, and the different sequences bifurcate after the RGB bump, when changes (due to extra mixing) in the surface chemical composition take place. In Fig. 7, we show the calculated models with no extra mixing (black lines), in which the only modification of the surface chemistry took place after the first dredge-up (FDU). We also assumed some further mixing after the bump, either moderate (red lines) or deep (blue lines). The grey boxes represent the corresponding observed values for SZ Mon within their uncertainties.

The upper subplot of Fig. 7 shows the evolution of the surface carbon isotopic ratio. It is clear that the assumption that no extra-mixing takes place after the RGB bump, thus the surface chemistry of the star is unchanged after the FDU (black line), is not consistent with the measured value (indicated with a grey box). The agreement of theoretical and experimental values of ¹²C/¹³C becomes satisfactory, when moderately deep extra mixing is considered.

The lower left subplot of Fig. 7 shows the evolution of the nitrogen abundance. We find that some extra mixing is required to fit the observations, as the FDU can account for a N enhancement of only $\sim 0.2$ dex, against the $\sim 0.4$ dex range derived from the spectroscopic analysis. Given that the efficiency of deep mixing affects the luminosity, at which a given surface nitrogen is reached, we deduce that use of a moderate deep mixing leads to a better agreement with the observations for [N/H].

Finally, in the lower right subplot of Fig. 7, we show the evolution of C/O ratio. The central value is more consistent with models without extra mixing, but the significant uncertainty in C/O of 0.11 (which is mostly caused by the uncertainty in oxygen abundance of 0.14 dex) does not allow us to draw any certain conclusions from this tracer.

Overall, the results presented so far indicate that SZ Mon evolved along the RGB until the core mass grew to $\rm\sim 0.36-0.37~{}M_{\odot}$, and the luminosity reached the nowadays value, in the $\rm 400-500~{}L_{\odot}$ range. At this evolutionary stage, mass transfer to the companion favoured the loss of the external mantle, an early departure from the RGB, and the beginning of the general contraction of the structure, until the current status was reached. The derived surface chemical composition, particularly the carbon isotopic ratio and nitrogen, suggests the combined effects of the FDU and deep mixing occurred after the RGB bump.

An alternative possibility is that the contraction to the blue started during the early AGB phase, after the exhaustion of central helium, before the occurrence of the first thermal pulse. Nevertheless, we contend that the evolution of both our targets was terminated during the RGB phase rather than the early-AGB phase. This is plausible, given the larger radius of a star at the tip of the RGB compared to an early AGB star. Additionally, RGB timescales are about three times longer than early AGB timescales. Furthermore, if the star evolved until the tip of the RGB, the mixing mechanism would act for a longer duration, favouring a more pronounced modification of surface chemistry, such as a smaller carbon isotopic ratio and a higher abundance of nitrogen.

To model the evolution of DF Cyg, we constructed evolutionary sequences of a 1 $M_{\odot}$ star of solar metallicity. Similarly to SZ Mon, the initial metallicity of DF Cyg ($\approx 0$ dex) was chosen according to [Zn/H] serving as a proxy (see Fig. 6). We note that the horizontal part of the evolutionary tracks shown in Fig. 8 represents the initial pre-Main Sequence phase, during which the luminosity decreases and the surface chemistry is unchanged. In Fig. 8, the black lines indicate the results obtained by assuming only FDU, without any further extra mixing. The red and blue solid lines indicate the models involving extra mixing (moderately deep and very deep, respectively). The grey boxes in the different panels represent the observed range of the corresponding values within the errors.

The upper subplot of Fig. 8 shows the evolution of the carbon isotopic ratio. The observed value of DF Cyg agrees well with the model predictions when some moderately deep extra mixing is considered (red line).

The lower left subplot of Fig. 8 shows the evolution of the nitrogen abundance. The substantial uncertainty of observed [N/H] for DF Cyg (0.11 dex) prevents us from making definitive conclusions. However, we can deduce that experimental values of [N/H] agree with theoretical predictions from models involving either no extra mixing or moderately deep extra mixing.

In the lower right subplot of Fig. 8, we show the evolution of the C/O with luminosity. Significant uncertainty in C/O (caused by uncertainty in [O/H] of 0.2 dex) does not allow us to use C/O as an indicator of extra mixing efficiency. However, for DF Cyg, the surface carbon was found to be super-solar (see Table 5 and Fig. 6). Since the surface carbon content is known to decrease during the RGB phase, we conclude that the matter, from which the star formed was slightly enhanced in carbon, with $\rm[C/Zn]_{0}\approx+0.3$. This value of initial carbon enhancement is within the scatter for Galactic solar type stars, as observed in the Galactic chemical history of carbon by Nissen et al. (2020).

We find an overall consistency between the results from stellar evolution modelling and the observations. The analysis of the behaviour of the surface carbon suggests that even a higher initial carbon would be consistent with the derived carbon abundance. However this would create some tension with the behaviour of nitrogen, which in that case would grow to values in excess of those consistent with the spectroscopic analysis.

Similarly to SZ Mon, we argue that DF Cyg underwent an early departure of the RGB, after the luminosity reached $\rm\sim 600-700~{}L_{\odot}$. In comparison with the evolution of SZ Mon, we note that the effects of deep mixing are softer here, as clear in the slope of the ¹²C/¹³C vs luminosity trends of the two stars. This is explained by the difference in the metallicity, as the temperature gradients in lower metallicity stars are higher, resulting in a more efficient transport process (Lagarde et al., 2012).