Spectroscopic study of four metal-poor carbon stars from the Hamburg/ESO Survey: On confirming the low-mass nature of their companions ¹¹1Based on data collected using Mercator/HERMES, SUBARU/HDS

The low- and intermediate-mass stars (0.8 - 10 M_⊙) are the predominant stellar population of our Galaxy (Karakas & Lattanzio, 2014). These stars are the main sites of various nucloesynthesis and important participants of chemical evolution of the Universe (Travaglio et al., 2001, 2004; Romano et al., 2010; Kobayashi et al., 2011, 2020). As they evolve through different stages of stellar evolution, they enriched the ISM through stellar outflows or winds. The pollution from these low- and intermediate- mass stars account for about 90% of the ISM dust and the massive stars account for the rest (Sloan et al., 2008). Majority of the elements heavier than Fe are produced by these stars through slow- (s-) and rapid- (r-) neutron-capture processes. The origin and evolution of these heavy elements still remains poorly understood. This underscores the need for detailed studies on different classes of stars enhanced in heavy elements, for instance Ba, CH, carbon-enhanced metal-poor (CEMP) stars etc. The last two decades had witnessed a significant increase in the high-resolution spectroscopic studies of these groups of stars.

Ba and CH stars show enhanced abundances of s-process elements. The CEMP-stars are metal-poor counterparts ([Fe/H]$<$$-$1) of CH stars (e.g. Lucatello et al. 2005; Abate et al. 2016). A fraction of them show enrichment of s- and/or r-elements. They are classified into four sub-classes: CEMP-r (enhanced in r-process elements), CEMP-s (enhanced in s-process elements), CEMP-r/s (enhanced in both s- and r-process elements), and CEMP-no (little or no enhancement of heavy elements) (Beers & Christlieb, 2005). The suggested origin for CEMP-r stars is that they were formed from the ISM pre-enriched by events, such as, core-collapse SNe, neutron star mergers, neutron star - black hole mergers (Surman et al., 2008; Arcones & Thielemann, 2013; Rosswog et al., 2014; Drout et al., 2017; Lippuner et al., 2017). The suggested progenitors for the origin of carbon enhancement of CEMP-no stars, that polluted ISM, are faint SNe, spinstar, metal-free massive stars, binary mass-transfer from extremely metal-poor AGB stars (Heger & Woosley, 2010; Nomoto et al., 2013; Chiappini, 2013; Tominaga et al., 2014).

CEMP-s stars are metal-poor analog of CH and Ba stars, and binary mass-transfer from former AGB companion stars have been identified as the source of their observed abundance pattern (e.g. Jorissen et al. 1998; Lucatello et al. 2005; Starkenburg et al. 2014; Jorissen et al. 2016a; Hansen et al. 2016b). However, the exact origin of CEMP-r/s stars is an open question (Jonsell et al., 2006; Masseron et al., 2010; Koch et al., 2019). Studies have shown that almost half of the CEMP-s stars are CEMP-r/s stars (Sneden et al., 2008; Käppeler et al., 2011; Bisterzo et al., 2011). Just like the CEMP-s stars, CEMP-r/s stars are also found to belong to binary systems (Lucatello et al., 2005; Starkenburg et al., 2014; Hansen et al., 2016b). The scenarios proposed to explain the origin of CEMP-r/s stars include: self-pollution of a star formed from r-element enriched ISM, pollution from AGB companion in a binary system formed from r-element enriched ISM, binary system polluted from the massive primary in a tertiary system, secondary star polluted from the primary exploded as Type 1.5 SN or intermediate neutron-capture (i-) process (Jonsell et al. 2006 and references therein, Hampel et al. 2016). The i-process, originally proposed by Cowan & Rose (1977), produces neutron density intermediate between s- and r-process, of the order of 10^15-17 cm^-3. There are a number of sites proposed to host the i-process, such as Rapidly Accreting White Dwarfs (Denissenkov et al., 2017), super-AGB stars of low-metallicity (Doherty et al., 2015; Jones et al., 2016), metal-poor massive (M $\geq$ 20 M_⊙) stars (Banerjee et al., 2018), extremely low-metallicity (z $\leq$ 10^-5) low-mass AGB stars (Fujimoto et al., 1990; Hollowell et al., 1990; Lugaro et al., 2009), low-mass (M $\leq$ 2M_⊙) very low-metallicity (z $\leq$ 10^-4) AGB stars (Fujimoto et al., 2000; Campbell & Lattanzio, 2008; Lau et al., 2009; Cristallo et al., 2009; Campbell et al., 2010; Stancliffe et al., 2011). etc., though exact site(s) is not confirmed yet. Several studies used i-process in low-mass low-metallicity AGB stars to successfully explain the abundances of CEMP-r/s stars (Hampel et al., 2016; Karinkuzhi et al., 2021; Goswami et al., 2021; Shejeelammal et al., 2021; Shejeelammal & Goswami, 2021; Purandardas & Goswami, 2021).

In this work, we have presented the results of a detailed high-resolution spectroscopic analysis of four carbon stars identified from the HES. The structure of the paper is as follows. The stellar sample, source of the spectra and data reduction are discussed in Section 2. Section 3 provides a discussion on radial velocity. Estimation of stellar atmospheric parameters, along with the discussion on stellar mass, is provided in Section 4. In Section 5, we have presented the discussion on abundance determination, followed by a discussion on abundance uncertainties in Section 6. Classification of program stars is presented in Section 7. A detailed discussion on various abundance ratios of the program stars are provided in Section 8. A discussion on the origin of the program stars, along with the parametric model based analysis, is also given in the same section. This section also contains a discussion on individual stars. Conclusions are drawn in Section 9.

All the four objects, HE 0457$-$1805, HE 0920$-$0506, HE1241$-$0337, and HE 1327$-$2116 analysed in this study are selected from the candidate metal-poor stars identified from the Hamburg/ESO survey (HES) (Christlieb, 2003). The stars HE 0457$-$1805 and HE 1241$-$0337 are listed in the catalog of carbon stars identified from the Hamburg/ESO survey (HES) by Christlieb et al. (2001). The object HE 0457$-$1805 is also listed in the list of potential CH star candidates by Goswami (2005). The objects HE 0920$-$0506 and HE 1327$-$2116 are listed in the catalog of bright metal-poor candidates from the HES by Frebel et al. (2006). The wavelength calibrated, high-resolution (R$\sim$50,000) spectrum of HE 1241$-$0337 is taken from SUBARU/HDS archive (http://jvo.nao.ac.jp/portal/v2/). The wavelength coverage of this spectrum is 4100 - 6850 Å with a wavelength gap between 5440 and 5520 Å. The high-resolution (R$\sim$86,000) spectra of the objects HE 0457$-$1805, HE 0920$-$0506, and HE 1327$-$2116 were obtained using the High-Efficiency and high-Resolution Mercator Echelle Spectrograph (HERMES) attached to the 1.2m Mercator telescope at the Roque de los Muchachos Observatory in La Palma, Canary Islands, Spain, operated by the Institute of Astronomy of the KU Leuven, Belgium (Raskin et al., 2011). The data were reduced using the HERMES pipeline. The HERMES spectra cover the wavelength range 3770 - 9000 Å. Multiple frames of each object were taken on different nights: 15 frames with exposure of 1800 and 2100 sec for HE 0457$-$1805 during the period 2013 - 2016, 10 frames with exposure ranging from 750 - 1800 sec for HE 0910$-$0506 during 2018 - 2020, and 3 frames with exposure of 1200 sec for HE 1327$-$2116 on 31/01/2019 and 01/02/2019. To maximize the S/N ratio, all these frames were co-added after the Doppler correction. The co-added spectra are then continuum fitted for further analysis, using IRAF²²2IRAF (Image Reduction and Analysis Facility) is distributed by the National Optical Astronomical Observatories, which is operated by the Association for Universities for Research in Astronomy, Inc., under contract to the National Science Foundation software. Table 1 provides basic information about the program stars, and the sample spectra are shown in Figure 1.

The radial velocities of the program stars are estimated from the measured shift in wavelengths of several spectral lines using the Doppler equation. Then, the obtained radial velocity is corrected for heliocentric motion. The average value of these heliocentric motion corrected velocities is taken as the radial velocity of the object. The detailed radial velocity data of the objects analyzed in this study are to be published in a summary paper on orbits of CEMP stars (Jorissen et al., in preparation). The estimated radial velocities, along with the values from the Gaia DR2 (Gaia Collaboration et al., 2018) and RAVE DR4 (Kordopatis et al., 2013), are given in Table 2. The object HE 0457$-$1805 is a confirmed binary with an orbital period of 2724$\pm$23 days (Jorissen et al., 2016a). Our radial velocity estimate of this object differ from the Gaia value by $\sim$2 km s^-1 and from the RAVE value by $\sim$9 km s^-1. For the object HE 0920$-$0506, our estimate shows a difference of $\sim$3 km s^-1 from the Gaia value. This may indicate that this star is likely a binary. For the other object, HE 1327$-$2116, our estimates show a difference of $\sim$0.7 km s^-1 from the Gaia and RAVE values. The radial velocity estimates for the object HE 1241$-$0337 is not available in Gaia and RAVE.

The stellar atmospheric parameters of the program stars are derived from the measured equivalent widths of the clean Fe I and Fe II lines with excitation potential and equivalent width, respectively, in the range of 0 - 6.0 eV and 10 - 180 mÅ. The radiative transfer code MOOG (Sneden, 1973) is used for our analysis under the assumption of local thermodynamic equilibrium (LTE). The model atmosphere is selected from the Kurucz grid of model atmospheres with no convective overshooting (Castelli & Kurucz 2003, http://kurucz.harvard.edu/grids.html). To select the initial model atmosphere to start with, we have used the photometric temperature estimates calculated from the calibration equations given by Alonso et al. (1999, 2001) and a guess of typical log g value for giants. Using the usual excitation balance and ionization balance method, the final model atmosphere is obtained through an iterative process from the initial one. The detailed procedure is described in our earlier papers Shejeelammal et al. (2020, 2021); Shejeelammal & Goswami (2021). Derived Fe abundances of the program stars are shown in Figure 2, and their derived atmospheric parameters are given in Table 2. The literature values of these atmospheric parameters are also provided in the same table. The comparison of our estimates of stellar atmospheric parameters with the literature values is discussed in Section 8.5.

The surface gravity is also calculated from the parallax method using
log (g/g_⊙)= log (M/M_⊙) + 4log (T_eff/T_eff⊙) - log (L/L_⊙)
The adopted solar values are log g_⊙ = 4.44, T_eff⊙ = 5770 K, and M_bol⊙ = 4.74 mag. The masses of the program stars are found from their positions on the H-R diagram (log T_eff - log (L/L_⊙) diagram) generated using the evolutionary tracks of Girardi et al. (2000). This procedure is discussed in detail in Shejeelammal et al. (2020). For the objects HE 0457$-$1805 and HE 1327$-$2116, z = 0.0004 ([Fe/H]$\sim$$-$1.7) tracks were used and z = 0.004 ([Fe/H]$\sim$$-$0.7) tracks for HE 0920$-$0506. The positions of the program stars on the H-R diagram are shown in Figure 3. We could find only an upper limit to the mass of the star HE 0457$-$1805. We could not estimate the mass of the star HE 1241$-$0337 since its parallax value is not available. The estimated mass and log  g values of the program stars are given in Table 3. For the star HE 0920$-$0506, the spectroscopic log  g is $\sim$0.8 dex lower than that estimated from the parallax method. In some carbon stars, such an inconsistency between the spectroscopic atmospheric parameters and those derived from the evolutionary tracks could arise as their evolutionary tracks shift towards lower temperatures (Marigo, 2002; Jorissen et al., 2016b). The spectroscopic log  g values have been used for our analysis.

The elemental abundances were estimated from two methods: (i) using the equivalent widths of the spectral lines and (ii) by comparison of observed spectra and synthetic spectra generated with MOOG (spectral synthesis calculation), using Kurucz model atmospheres (http://kurucz.harvard.edu/grids.html). The spectral synthesis calculation is performed to derive the abundances of elements with hyper-fine splitting (HFS) as well as for molecular bands. The hyper-fine components of each atomic line, whenever available, are considered for the abundance estimation. In the case of abundance determination using the equivalent width method, the spectral line identification is performed by comparing the stellar spectra with the Doppler corrected spectrum of Arcturus. The line parameters are taken from linemake ³³3linemake contains laboratory atomic data (transition probabilities, hyperfine and isotopic substructures) published by the Wisconsin Atomic Physics and the Old Dominion Molecular Physics groups. These lists and accompanying line list assembly software have been developed by C. Sneden and are curated by V. Placco at https://github.com/vmplacco/linemake. atomic and molecular line database (Placco et al., 2021).

Although the abundance estimation is performed under the assumption of LTE, we have applied the non-LTE (NLTE) corrections whenever available. The solar abundance values are adopted from Asplund et al. (2009). The details of the abundances of each elements and the details of NLTE corrections as well as HFS are discussed in this section. The estimated elemental abundances in the program stars are given in Tables 4 and 5. The atomic lines used to derive the abundances of each elemental species are given in Tables 9 - 11.

The uncertainty in the abundances of each element is calculated following the procedure in Shejeelammal et al. (2020) using;

$\sigma_{log\epsilon}^{2}$ = $\sigma_{ran}^{2}$ + $(\frac{\partial log\epsilon}{\partial T})^{2}$ $\sigma_{T\rm_{eff}}^{2}$ + $(\frac{\partial log\epsilon}{\partial logg})^{2}$ $\sigma_{logg}^{2}$ + $(\frac{\partial log\epsilon}{\partial\zeta})^{2}$ $\sigma_{\zeta}^{2}$ + $(\frac{\partial log\epsilon}{\partial[Fe/H]})^{2}$ $\sigma_{[Fe/H]}^{2}$

Here, $\sigma_{log\epsilon}$ is the total uncertainty in the absolute abundance of the particular element. The $\sigma_{ran}$ is the random error which is calculated from the standard deviation ($\sigma_{s}$) of the abundances derived from N lines of the particular element using $\sigma_{ran}$ = $\frac{\sigma_{s}}{\sqrt{N}}$. The $\sigma_{T\rm_{eff}}$, $\sigma_{logg}$, $\sigma_{\zeta}$ and $\sigma_{[Fe/H]}$ are the typical uncertainties in the stellar atmospheric parameters, which are $\sigma_{T\rm_{eff}}$$\sim$$\pm$100 K, $\sigma_{logg}$$\sim$$\pm$0.2 dex, $\sigma_{\zeta}$$\sim$$\pm$0.2 km s^-1 and $\sigma_{[Fe/H]}$$\sim$$\pm$0.1 dex. The abundance uncertainty in the abundance ratio of an element, X, is calculated from;
$\sigma_{[X/Fe]}^{2}$ = $\sigma_{X}^{2}$ + $\sigma_{Fe}^{2}$.

We made the calculation simple by assuming that the parameters are independent. Hence, the uncertainties calculated here are taken to be the upper limits. The changes in the abundances of each element with the variation in different atmospheric parameters are given in Table 7. We have evaluated the differential abundances in the specific case of the star HE 0920$-$0506.

Among our stellar sample, HE 0457$-$1805, HE 1241$-$0337, and HE 1327$-$2116 are found to be metal-poor objects with [Fe/H]$<$$-$1, whereas HE 0920$-$0506 is moderately metal-poor with [Fe/H]$\sim$$-$0.75. CEMP stars are traditionally being classified as the metal-poor stars with [C/Fe]$>$1 (Beers & Christlieb, 2005). This classification criteria is being refined and many authors use different threshold values for [C/Fe] to define CEMP stars. However, the carbon abundance is related to the evolutionary stages of the stars. In the case of evolved metal-poor giant stars, the surface carbon abundance could be altered through CNO cycle as a result of internal mixing. This internal mixing processes are First Dredge-Up (FDU) on the giant branch and some extra mixing at the tip of RGB (Charbonnel, 1995; Charbonnel et al., 1998; Gratton et al., 2000; Shetrone, 2003; Jacobson et al., 2005; Spite et al., 2005, 2006; Aoki et al., 2007; Placco et al., 2014). Hence, using a fixed [C/Fe] value to define CEMP stars without considering the evolutionary effects would be incomplete. Here, we have adopted the empirical definition of Aoki et al. (2007) to distinguish the CEMP stars of our sample. This definition is shown schematically in Figure 6. As seen from this figure, while HE 0457$-$1805 and HE 1327$-$2116 are CEMP stars, HE 0920$-$0506 is a non-CEMP star. From the C/O value ($>$1) of HE 0920$-$0506, we found that it is a CH star. We could not locate the star HE 1241$-$0337 in this diagram as we could not find its luminosity due to the unavailability of parallax. However, the higher [C/Fe] value ($\sim$2.57) of this star place it in the CEMP category.

We have adopted the classification scheme given by Goswami et al. (2021) to sub-classify our CEMP stars. This classification scheme considers [Ba/Eu] and [La/Eu] ratios of the stars, which is given as;

The results of a detailed spectroscopic analysis of four potential CH/CEMP star candidates selected from the Hamburg/ESO Survey are presented. We present the first ever abundance analysis for the object HE 1241$-$0337. Although the abundances of Fe and C (and O for HE 0920$-$0506) derived from medium-resolution spectra are available in the literature, we present for the first time a high-resolution spectroscopic analysis for the objects HE 0457$-$1805, HE 0920$-$0506, and HE 1327$-$2116. We have estimated the stellar atmospheric parameters as well as the abundances of twenty-eight elements along with the carbon isotopic ratio.

Our analysis has shown that the objects HE 0457$-$1805 and HE 1241$-$0337 are CEMP-s stars, HE 0920$-$0506 is a CH star, and HE 1327$-$2116 is a CEMP-r/s star. The radial velocity estimate shows that HE 0457$-$1805 and HE 0920$-$0506 are low-radial velocity objects ($<$ 100 km s^-1), whereas HE 1241$-$0337 and HE 1327$-$2116 are high-radial velocity ($>$ 100 km s^-1) objects. While HE 0457$-$1805 is a confirmed binary, the difference noted in the radial velocity of HE 0920$-$0506 from literature value may indicate that it is likely a binary. Our analysis based on absolute carbon abundance has revealed that all these stars belong to the region of binary stars.

The positions of program stars on the A(C) - [Fe/H] diagram suggest that the observed enhancement in the abundances of the neutron-capture elements may be due to the pollution from binary companions. We have investigated the nature of the companion AGB stars of our program stars using several diagnostics such as C, N, Na, and Mg abundances, [hs/ls] and [Rb/Zr] ratios. From the analysis based on these diagnostics, we have found that none of the program stars are polluted by massive AGB stars. Our analysis based on different abundance ratios and abundance profiles confirmed the low-mass AGB companions of the program stars.

We have carried out a parametric model based analysis for the CEMP-s (HE 0457$-$1805 and HE 1241$-$0337) and CH (HE 0920$-$0506) stars in our sample. A comparison of the observed abundances in these stars with the predictions from the FRUITY models of AGB stars by means of a dilution factor incorporated parametric model function confirmed that the AGB stars that polluted them were low-mass stars with masses M $\leq$ 2.5 M_⊙.

The observed abundance pattern in the CEMP-r/s star of our sample, HE 1327$-$2116, is well reproduced with the i-process parametric models in low-mass, low-metallicity AGB stars. The neutron density responsible for its observed abundance is found to be n$\sim$10¹¹ cm^-3. Our analysis for HE 0457$-$1805 using these same models has shown that the neutron density n$\sim$10¹⁰ cm^-3 in low-mass AGB stars could reproduce its observed abundance. Thus, the parametric model based study for the program stars corroborates the results we have obtained from the abundance profile analysis.

Funding from the DST SERB project No. EMR/2016/005283 is gratefully acknowledged. We are thankful to the referee for useful comments and suggestions. We are thankful to Melanie Hampel for providing us with the i-process yields in the form of number fractions. We thank Alain Jorissen for sharing the HERMES spectra used in this study. The HERMES spectrograph is supported by the Fund for Scientific Research of Flanders (FWO), the Research Council of K.U.Leuven, the Fonds National de la Recherche Scientifique (F.R.S.- FNRS), Belgium, the Royal Observatory of Belgium, the Observatoire de Genéve, Switzerland and the Thüringer Landessternwarte Tautenburg, Germany. This work made use of the SIMBAD astronomical database, operated at CDS, Strasbourg, France, and the NASA ADS, USA. 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).