Chemical Homogeneity of Wide Binary Systems: An Approach from Near-Infrared Spectroscopy

Our spectroscopic observations were conducted during two observing runs in the 2021B and 2023A semesters. For each observing run, we selected target wide binaries from two different catalogs, each serving different purposes.

The targets for the 2021B observing run were selected from the catalog of Jiménez-Esteban et al. (2019), which reported 3741 comoving groups based on Gaia DR2 (Gaia Collaboration et al. 2018). After cross-matching this catalog with NIR photometric data from the Two Micron All Sky Survey (2MASS) catalog (Skrutskie et al. 2006), we selected 28 bright comoving pair candidates (8.0 < Gaia G < 12.0; 7.0 < 2MASS K_s < 10.0) with a separation between the component stars larger than 10,000 au. These selection criteria were defined to investigate the chemical homogeneity of wide binaries with wider separation, as well as to validate the NIR spectroscopic technique.

For the 2023A observing run, we focused on wide binaries suspected to have an accretion origin (see, e.g., Lim et al. 2021; Nissen et al. 2021). To do this, we selected target candidates exhibiting large proper motion and with observable conditions at the Gemini-South telescope (6.0 < Gaia G < 15.0; μ > 50 mas yr⁻¹) from the SUPERWIDE catalog of Hartman & Lépine (2020). This catalog reported 99,203 wide binary systems based on Gaia DR2, providing an advantage in tracing accreted wide binaries due to its inclusion of a higher number of comoving pair candidates with large proper motions than the catalog of Jiménez-Esteban et al. (2019). After updating the astrometric solution with the Gaia EDR3 (Gaia Collaboration et al. 2021) and incorporating NIR photometric data from 2MASS, we pre-estimated the orbital energy (E) and angular momentum (L_Z ) of the comoving stars with the Galactic potential of McMillan (2017), assuming a line-of-sight velocity of 0 km s⁻¹. We note that while the line-of-sight velocities of many target stars have recently been updated by Gaia DR3 (Gaia Collaboration et al. 2023), this information was not available during the preparation of our observation. Finally, we selected eight comoving pairs in the dynamical domains of various accretion events, such as Sequoia, Gaia–Enceladus, and Helmi-streams, referring to the criteria of Massari et al. (2019).

However, due to the telescope schedule and unfavorable weather conditions, only 10 and one comoving pairs were actually observed during the 2021B and 2023A semesters, respectively, and five pairs were analyzed in this study (see Section 2.2).

The high-resolution NIR spectroscopy for our targets was conducted using the IGRINS instrument at the Gemini-South telescope under Programs GS-2021B-Q-310 and GS-2023A-Q-309 (PI: Seungsoo Hong). These observations were carried out as part of the K-GMT science program. We note that although observing time was also allocated for the 2022A semester (GS-2022A-Q-219), no observations were conducted during that period. The IGRINS instrument consists of two separate spectrograph arms, covering the H and K bands, respectively, with a spectral resolving power of R ∼ 45,000 (Park et al. 2014; Mace et al. 2018). The observations were performed in service mode over nine nights between 2021 August and November and one night in 2023 April under Band 3 conditions (image quality ∼85, cloud cover ∼80). Each spectrum was obtained from an ABBA nod sequence observation with an estimated exposure time to achieve a signal-to-noise ratio (S/N) of ∼100, as referred from the IGRINS website. ⁴ However, the derived S/N, estimated from the variances of each spectrum, varied from 60 to 120 depending on the star.

Out of the 20 stars observed during the 2021B semester, the spectroscopic analysis could not be performed on nine of them. This was primarily due to their weak or unobservable absorption features in the NIR region, which can be attributed to the high temperature of their stellar atmospheres. In Figure 1, the observed targets are plotted on color–magnitude diagrams (CMDs), with open symbols indicating the stars for which chemical abundance measurements were not feasible. It is evident from the diagram that the study of stellar chemical abundances using NIR spectroscopy (H and K bands) is not suitable for stars with (BP − RP > 0.65) or (J − K_s > 0.3). Therefore, the five pairs, including SVO 2357, for which spectroscopic analysis was not available, have been excluded from our analysis (see Figure 1).

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The target IDs are derived from the original catalogs using specific naming conventions. For the targets selected from Jiménez-Esteban et al. (2019), the IDs consist of the prefix "SVO" followed by the group ID. Similarly, for targets from Hartman & Lépine (2020), the IDs consist of the prefix "SWB" followed by the catalog ID. In Table 1, we provide the IDs, coordinates, parallax, proper motions, magnitudes, and radial velocities (RVs) for the targets, updated by the recent Gaia DR3. In addition, the angular and physical separations between the component stars listed in the table have been re-estimated using Gaia DR3, whereas the original catalogs were based on Gaia DR2.

The 1D spectrum was extracted using the IGRINS Pipeline Package (Lee et al. 2017b). This process involved flat-fielding correction, subtraction of the sky background, and wavelength calibration using OH emission and telluric lines. To create a single continuous spectrum spanning from 1.5 to 2.4 μm, we merged the spectra from 28 and 26 echelle orders for the H and K arms, respectively, leaving a gap between 1.81 and 1.94 μm. The final spectra were obtained after normalizing the continuum and converting the wavelengths from vacuum to air using the specutils package of Astropy (Astropy Collaboration et al. 2013, 2018). A more detailed description of the data reduction process can be found in Lim et al. (2022).

Then, we measured RV of each star using cross-correlation with the synthetic spectrum from the Pollux database (Palacios et al. 2010) through the IRAF RV package. The heliocentric RV (RV_helio), derived through the rvcorrect task, and the corresponding measurement error for each star are provided in Table 2. It is important to note that the RVs for these stars have been updated in Gaia DR3 after our observations (see Table 1). The RVs obtained from Gaia DR3 and our measurements demonstrate good agreement, with a typical difference of ∼0.3 km s⁻¹, except for SWB 111893b. Furthermore, the RV discrepancies between the component stars of each target pair, as estimated by both our measurements and Gaia, are found to be smaller than 0.8 km s⁻¹. This suggests that these paired stars share a common proper motion in 3D space, indicating a current or past physical binding in wide binary systems. However, a more detailed kinematic analysis is necessary to further investigate the orbital properties of these comoving pairs. For a simple task, we estimated the future trajectories of our samples within the Milky Way based on their current positions and 3D motions using the Gala package (Price-Whelan 2017). The component stars of SVO 2448 and SVO 3206 will move closer together, while the stars in the other pairs will move farther apart.

Table 2. Heliocentric RV and Atmospheric Parameters

ID	RVhelio	Teff	$\mathrm{log}g$	vt	[Fe/H]model
	(km s−1)	(K)	(dex)	(km s−1)	(dex)
SVO 2324a	19.58 ± 0.67	5883	4.19	1.04	0.18
SVO 2324b	19.13 ± 0.67	6113	4.26	1.12	0.18
SVO 2448a	−31.33 ± 0.24	5683	4.34	0.87	0.22
SVO 2448b	−31.51 ± 0.43	5804	4.10	1.03	0.28
SVO 2684a	−25.40 ± 0.37	5738	4.17	0.97	0.22
SVO 2684b	−25.07 ± 0.33	5860	4.05	1.08	0.29
SVO 2759a	24.62 ± 1.15	6091	4.15	1.21	−0.43
SVO 2759b	24.02 ± 1.05	5998	4.13	1.18	−0.51
SVO 3206a	32.56 ± 0.29	4896	3.22	1.03	−0.02
SVO 3206b	33.03 ± 0.35	4896	3.19	1.04	−0.02
SWB 111893a	−189.91 ± 2.24	⋯	⋯	⋯	⋯
SWB 111893b	−58.12 ± 1.03	⋯	⋯	⋯	⋯

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However, in the case of the SWB 111893 pair, the two component stars exhibit a significant difference in our RV estimate beyond the measurement uncertainties. Although Gaia DR3 provides RV only for the SWB 111893b star (−191.64 km s⁻¹), it is also in disagreement with our estimate (−58.12 km s⁻¹), but it aligns with the RV of SWB 111893a (−189.91 km s⁻¹). We suspect that the RV of SWB 111893b obtained from Gaia DR3 is contaminated by the nearby SWB 111893a due to their small angular separation of only ≲5''. The similarity in proper motion between the two stars is also doubtful due to relatively large measurement errors in parallax and proper motion in the R.A. and decl. directions, which are 0.06 mas, 0.08 mas yr⁻¹, and 0.06 mas yr⁻¹ for SWB 111893a. This is in contrast to the typical errors observed in other samples, 0.02 mas in parallax and 0.02 mas yr⁻¹ in proper motion for both directions. Even if their proper motions are accurate, it is difficult to consider them as a comoving system due to the substantial difference in space motion. SWB 111893a has (U, V, W) velocities of (−51.9, −226.8, −120.3) km s⁻¹, while SWB 111893b has (−91.6, −100.8, −120.5) km s⁻¹, which dynamically places them in the halo and thick disk, respectively. A more precise understanding of their motion and orbit will be necessary once a more accurate astrometric solution becomes available in future Gaia data releases. Furthermore, in addition to this substantial kinematic discrepancy between the two stars, their spectra also display notably distinct absorption features. These differences indicate that SWB 111893 is not a wide binary, and therefore we have excluded this pair from our analysis as they are not suitable for our intended purpose.

To determine the atmosphere parameters, effective temperature (T_eff), surface gravity ($\mathrm{log}g$), and microturbulence (v_t ) for each star, we employed canonical photometric methods. It is important to mention that, in the case of NIR spectroscopy, the spectroscopic determination of atmosphere parameters through the ionization equilibrium between Fe i and Fe ii abundances is limited due to the absence of Fe ii lines. In our previous study employing IGRINS data, we derived T_eff and $\mathrm{log}g$ for giant stars using the line-depth ratio (LDR) and equivalent width (EW) of the CO band (Lim et al. 2022). However, these methods are not applicable in the present study because the LDR method for the NIR region has not been validated for subdwarf stars, and the CO feature is not observable in our target stars due to their high T_eff.

Therefore, we determined the photometric T_eff of our target stars using the (J − K_s ) color from the 2MASS catalog (Skrutskie et al. 2006) and the color–temperature relations of González Hernández & Bonifacio (2009). Since this relation includes a metallicity term, we assumed solar metallicity ([Fe/H] = 0.0 dex) as an initial value for all stars in the first iteration. Although we also measured T_eff using the relation of Mucciarelli et al. (2021) for Gaia photometric data, we adopted T_eff obtained from (J − K_s ) in our analysis due to its lower susceptibility to extinction. The reddening factors for each star were obtained from various sources: Schlegel et al. (1998), Schlafly & Finkbeiner (2011), Bayestar 17 (Green et al. 2018), Bayestar 19 (Green et al. 2019), and Stilism (Lallement et al. 2018). Although these values were generally similar, we finally the adopted E(B − V) value from Schlafly & Finkbeiner (2011), along with their extinction coefficients (R_J = 0.723; R_H = 0.460; ${R}_{{K}_{s}}$ = 0.310), which are available for all sample stars. However, for the SVO 2759 pair, we utilized E(B − V) values obtained from Stilism due to the significant variations among reddening sources for these stars, which could lead to substantial differences in chemical abundance measurements (for more details, see Section 4.1).

With the initial determination of T_eff, we calculated $\mathrm{log}g$ using the canonical relation

$$\begin{eqnarray*}\begin{array}{rcl}\mathrm{log}{g}_{* } & = & \mathrm{log}{g}_{\odot }+\mathrm{log}\displaystyle \frac{{M}_{* }}{{M}_{\odot }}+4\mathrm{log}\displaystyle \frac{{T}_{\mathrm{eff},* }}{{T}_{\mathrm{eff},\odot }}\\ & & +0.4({M}_{\mathrm{bol},* }-{M}_{\mathrm{bol},\odot }),\end{array}\end{eqnarray*}$$

where $\mathrm{log}{g}_{\odot }$ = 4.44 dex, T_eff,⊙ = 5777 K, and M_bol,⊙ = 4.74 for the Sun. The bolometric correction for each star was computed using the code provided by Casagrande & VandenBerg (2018), and stellar mass and distance were obtained from Gaia. We then estimated v_t from the relation provided by Mashonkina et al. (2017):

$$\begin{eqnarray*}&&\begin{array}{c}{v}_{t}=0.14-0.08\times [{\rm{Fe}}/{\rm{H}}]+4.90\\ \,\times ({T}_{{\rm{eff}}}/{10}^{4}\,{\rm{K}})-0.47\times {\rm{log}}{\rm{g}}.\end{array}\end{eqnarray*}$$

After the first iteration of the above procedure, we obtained the second estimate of metallicity using the newly derived T_eff, $\mathrm{log}g$, and v_t parameters. We repeated the whole process with the newly derived metallicity until the output matched the input. The final values of T_eff, $\mathrm{log}g$, v_t , and [Fe/H] for the atmospheric models are provided in Table 2.

In Figure 2, we present the Kiel diagram showing the T_eff and $\mathrm{log}g$ values for our target stars, along with the connection between each pair of stars. As shown in this figure, SVO 3026a, b are identified as subgiant stars, while the others are subdwarf stars. It is important to note that while the component stars of our wide binary samples happen to be located at the same evolutionary stage, wide binaries comprising different types of stars, such as main-sequence and white dwarf pairs, are also reported in the literature (e.g., El-Badry et al. 2021; Zhao et al. 2023). Furthermore, the component stars of each wide binary demonstrate similarities in all atmospheric parameters, with differences of ≲200 K in T_eff, ≲0.2 dex in $\mathrm{log}g$, and ≲0.1 km s⁻¹ in v_t . In particular, SVO 3206a and SVO 3206b exhibit almost identical characteristics, with ΔT_eff = 0 K, ${\rm{\Delta }}\mathrm{log}g$ = 0.03 dex, and Δv_t = 0.01 km s⁻¹. These similarities suggest that the two stars in each wide binary were formed together and have evolved equally so far.

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On the other hand, since SVO 3206a and b are subgiant stars, we were able to measure T_eff using the LDR relations suggested by Fukue et al. (2015), as utilized in Lim et al. (2022). The LDR T_eff is estimated to be 4980 K for both stars, which is only 84 K larger than the value derived from the (J − K_s ) color. In addition, T_eff values measured using the relation with the EW of the CO-overtone band at 2.293 μm, suggested by Park et al. (2018), are also close to the other estimations, being 4898 K for SVO 3206a and 4891 K for SVO 3206b. The consistency of T_eff values obtained from three different methods further supports the reliability of our parameter determination.

The chemical element abundances of each star were determined using the spectral synthesis method with the synth driver of the 2019NOV version of the local thermodynamic equilibrium (LTE) code MOOG (Sneden 1973). Model atmospheres were constructed by interpolating a grid of plane-parallel MARCS models (Gustafsson et al. 2008) based on the parameters determined in the previous section. The chemical abundances of Fe, Na, Mg, Al, Si, S, K, Ca, Ti, Cr, Ni, and Ce were measured from absorption lines listed in Lim et al. (2022), referring to Afşar et al. (2018). In addition, atomic and molecular lines generated using the recent version of linemake ⁵ (Placco et al. 2021) were used to make synthetic spectra. The chemical abundances were measured from each absorption line, and the final values were determined as the mean of the measurements for each element.

For the SVO 3206a and SVO 3206b stars, we were able to measure the abundances of C, N, and O from CO, CN, and OH features, respectively. However, these molecular features were not observed in other stars due to their high T_eff. The abundances of O, C, and N were sequentially measured, and the measurements were repeated with the updated abundances in the model atmosphere since these elements are bound in molecules. The derived abundances for SVO 3206a and SVO 3206b are as follows: [C/Fe] = −0.139; −0.168 dex, [N/Fe] = +0.030; +0.121 dex, and [O/Fe] = −0.021; +0.011 dex, respectively.

Furthermore, we applied line-by-line non-LTE (NLTE) abundance corrections for Fe, Mg, Si, Ca, Ti, and Cr using previous studies by Mashonkina et al. (2007), Bergemann & Cescutti (2010), and Bergemann et al. (2012, 2013, 2015) for 1D plane-parallel atmospheric models. ⁶ The comparison between LTE and NLTE abundances shows that the differences are very small for Fe and Mg. However, the NLTE effects generally lead to an increase in the abundances of Ca, Ti, and Cr elements by ∼0.06 dex on average, whereas the abundance of Si is decreased by ∼0.01 dex.

The LTE and NLTE chemical abundances, represented as [X/H] adopting the solar scale of Asplund et al. (2009), the line-to-line scatter (σ), and the number of lines (N) for each element, are presented in Tables 3 and 4. We note that the Ti abundances for SVO 2759a, b stars were not measured due to the absence of absorption lines caused by their high T_eff. The statistical measurement error for the abundance ratios can be estimated as σ/$\sqrt{N}$ for each element. The typical errors on the [Fe/H] measurements are less than 0.02 dex, and those on the [Mg/H] measurements are ≲0.03 dex.

In addition, systematic errors in the chemical abundance measurements can arise from uncertainties in the determination of atmospheric parameters. To assess the impact of these systematic errors, we used Monte Carlo sampling to estimate the uncertainties in T_eff, $\mathrm{log}g$, and v_t . The uncertainty in [Fe/H] was initially obtained from the statistical measurement error. Then, the uncertainties in T_eff, $\mathrm{log}g$, and v_t were computed by taking into account the errors in magnitudes, mass, and distance from Gaia and 2MASS data, along with the error in [Fe/H] and the fitting error of each equation. The typical uncertainties for our samples were determined to be ±190 K in T_eff, ±0.06 dex in $\mathrm{log}g$, ±0.07 km s⁻¹ in v_t , and ±0.02 dex in [Fe/H]. We then re-estimated the chemical abundances by adopting eight-atmosphere models with different parameters that varied in their uncertainties for SVO 2448b, which has the median T_eff among the samples. The systematic errors for each element, presented in Table 5, were obtained by comparing the newly estimated abundances with the original values. The abundance variations were found to be less than 0.2 dex for all elements, with the effect of T_eff being the most significant, as expected given the large uncertainty in T_eff measurement.

Table 5. Systematic Error Due to the Uncertainty in the Atmospheric Parameters for SVO 2448b

Species	Teff		$\mathrm{log}g$		vt		[Fe/H]
	(5804 K)		(4.10 dex)		(1.03 km s−1)		(+0.27 dex)
	−208 K	+208 K	−0.07 dex	+0.07 dex	−0.07 km s−1	+0.07 km s−1	−0.01 dex	+0.01 dex
Fe	−0.13	+0.13	+0.01	−0.01	+0.01	−0.01	+0.00	−0.00
Na	−0.17	+0.16	+0.01	−0.03	+0.00	−0.02	−0.01	−0.01
Mg	−0.16	+0.16	+0.02	−0.02	+0.01	−0.01	+0.00	+0.00
Al	−0.13	+0.13	+0.01	−0.01	+0.01	−0.00	+0.00	+0.00
Si	−0.10	+0.11	+0.01	−0.02	+0.01	−0.01	−0.00	−0.00
S	+0.08	−0.08	−0.02	+0.01	−0.00	−0.01	−0.01	−0.00
Ca	−0.15	+0.14	+0.01	−0.01	+0.01	−0.01	−0.00	−0.00
Ti	−0.20	+0.17	−0.00	−0.00	−0.00	−0.01	−0.00	−0.00
Cr	−0.17	+0.15	+0.02	+0.00	+0.02	+0.00	+0.01	+0.00
Ni	−0.10	+0.11	+0.00	+0.00	+0.01	−0.01	+0.00	+0.00

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The RV and chemical abundances of some sample stars were compared with data from spectroscopic surveys. Specifically, the data for SVO 2759b were obtained from the Large Sky Area Multi-object Fiber Spectroscopic Telescope (LAMOST) medium-resolution spectroscopic survey (R ∼ 7500; Liu et al. 2020), and the data for SVO 2448a and SVO 2448b were obtained from Galactic Archaeology with HERMES (GALAH, R ∼ 28,000; Buder et al. 2021).

The estimates in this study show good agreement with the survey data. The differences in RV between our estimations and the survey data are less than 1 km s⁻¹. In this study, the RVs are estimated to be 24.02, −31.33, and −32.12 km s⁻¹ for SVO 2759b, SVO 2448a, and SVO 2448b, respectively, while 23.59, −31.51, and −31.66 km s⁻¹ are obtained from the survey data.

In the case of [Fe/H] ratio, our estimations and values obtained from the GALAH survey are similar, being 0.22/0.28 dex versus 0.23/0.30 dex for SVO 2448a/SVO 2448b. The differences in chemical abundances for other elements between this study and GALAH for these two stars are also less than 0.1 dex, with an average difference of 0.05 dex, except for Mg. However, our estimations of Mg abundances are approximately 0.2 dex lower than those from GALAH in both stars. For SVO 2759b, although the [Fe/H] value obtained from LAMOST (−0.35 dex) is somewhat larger than that from our study (−0.51 dex), this discrepancy could be attributed to the lower resolution of the LAMOST survey or uncertain determination of atmospheric parameters.

As mentioned in Section 1, previous studies have reported similar metallicities of the component stars in many wide binary pairs based on optical spectroscopic observations (e.g., Andrews et al. 2018; Hawkins et al. 2020). In this study, we also find that the five wide binary pairs show nearly identical [Fe/H] abundance ratios in their component stars, which is consistent with the relatively similar atmospheric parameters within each pair (see Table 2). The differences in [Fe/H] between the component stars are 0.002, 0.059, 0.072, 0.073, and 0.001 dex for the SVO 2324, SVO 2448, SVO 2684, SVO 2759, and SVO 3206 pairs, respectively. These differences are comparable to the statistical error on the Fe abundance measurement (∼0.02 dex). It is noteworthy that the SVO 3206a and SVO 3206b stars exhibit a remarkable similarity in Fe abundances, as well as equivalent T_eff and other similar parameters, as shown in Figures 1 and 2. When considering the NLTE [Fe/H] ratios, the differences remain small, with Δ[Fe/H] of 0.001, 0.058, 0.062, 0.059, and 0.008 dex for each wide binary pair, respectively.

However, in the case of the SVO 2759 pair, the difference in [Fe/H] between the two component stars varies with the applied reddening values. As discussed in Section 3.1, noticeable variations in E(B − V) are derived from different sources for the SVO 2759a and SVO 2759b stars, whereas other stars show similar values. In particular, 3D extinction maps from Bayestar and Stilism demonstrate that the E(B − V) values for these two stars are highly dependent on their respective location (see Figure 3). It appears that these variations in E(B − V) values may be attributed to the two stars being located either in front of or behind a highly obscured region. These differences in E(B − V) can lead to variations in T_eff, which, in turn, affect the [Fe/H] measurements. The [Fe/H] ratios were measured as −0.08/−0.20 dex using Schlafly & Finkbeiner (2011), −0.20/−0.49 dex using Bayestar 17 (Green et al. 2018), and −0.43/−0.51 dex using Stilism (Lallement et al. 2018) for the SVO 2759a/SVO 2759b stars, respectively. Among these estimates, we have adopted the E(B − V) values of Stilism for the SVO 2759 pair. This choice was based on these values being the smallest, with the least difference in E(B − V) and [Fe/H] between the two stars, assuming that both stars evolved in a similar environment. We note that the reddening values of Schlafly & Finkbeiner (2011) were applied for other stars, because the Stilism reddening map is not available for distant stars.

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Figure 4 displays a comparison of the observed spectra of component stars in each wide binary pair in the H- and K-band regions. As shown in this figure, the two stars comprising a wide binary system exhibit remarkably similar features throughout the entire spectral region, including the absorption lines of Fe, Si, and Ni. The fact that the observed spectra of the component stars overlap so closely reinforces the notion that our target stars are not randomly comoving pairs but rather widely separated binary systems. Furthermore, the striking similarity in the spectral features of the two stars with similar atmospheric and chemical properties demonstrates the stability and effectiveness of the NIR spectroscopic observation using IGRINS and the data reduction technique utilized in this study.

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The metallicity of our samples ranges from −0.5 dex to +0.3 dex in terms of [Fe/H] ratio, which falls within the range where a large number of wide binaries are reported in the literature (see Hwang et al. 2021). Most of the known wide binaries within this metallicity range are associated with the Galactic disk (e.g., Andrews et al. 2018; Hawkins et al. 2020). Similarly, our five wide binary samples are also dynamically associated with the thin disk, as shown in Figure 5, with a vertical distance (Z_max) of less than 0.5 kpc. Therefore, these samples can be considered typical metal-rich disk wide binaries. While Hwang et al. (2021) suggested that plenty of wide binaries in this metallicity range may be influenced by radial migration of stars, drawing a firm conclusion about their formation mechanism is challenging.

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Figure 6 presents the abundance ratios and measurement errors for each element in terms of [X/H], together with the differences between the component stars of each wide binary system. The typical measurement error is less than 0.03 dex for all elements, except for Al and Cr, where it is somewhat larger at 0.07 and 0.05 dex, respectively. Our sample stars do not show any peculiar chemical abundance patterns compared to the general field stars in the Milky Way. However, our measurements of the [Mg/H] abundance ratio appear to be underestimated when compared to the other elements, as suspected from the comparison with GALAH data (see Section 3.3). Further investigation of the origin of this underestimation with a larger sample is necessary, while the systematic uncertainties from the absorption line information or our measurements are speculated.

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Regarding the abundance differences within each wide binary system, as anticipated from the small differences in [Fe/H] and the spectral similarities shown in Figure 4, the two component stars exhibit almost identical chemical compositions for all the elements measured in this study. The average abundance difference among all elements ranges from 0.05 to 0.09 dex for SVO 2324, SVO 2448, SVO 2684, and SVO 2759 pairs, while for the SVO 3206 pair it is 0.03 dex. In the case of the SVO 3206 pair, [C, N, O/H] abundance ratios are also indicated in the lower panel of Figure 6, with differences between SVO 3206a and SVO 3206b estimated to be 0.029, 0.091, and 0.032 dex for C, N, and O elements, respectively. These small differences are consistent with those for the other elements within the same pair.

The small differences in all abundance ratios, as well as the comparable atmospheric parameters, between the two stars in each wide binary indicate that they formed simultaneously in the same environment and have undergone similar evolutionary processes. Thus, although the two stars are currently separated by a large distance (>10,000 au), they were likely formed simultaneously in close proximity or from a single, large, homogeneous gas cloud. This aligns with various scenarios proposed for the formation of wide binary systems, as introduced in Section 1.

Furthermore, the Δ[X/H] values for the wide binaries in the sample are comparable to those estimated in other studies based on high-resolution optical spectroscopy with R ≳ 45,000 (Δ[X/H] = 0.05–0.10 dex; Hawkins et al. 2020; Nelson et al. 2021). This suggests that high-resolution NIR spectroscopy can effectively conduct a detailed chemical abundance study with a comparable level of reliability to typical optical spectroscopy. In addition, assuming the identical chemical properties of wide binary components, our results support the notion that IGRINS can be used for the chemical tagging of stars in the Milky Way with an accuracy of ≲0.1 dex.

Most wide binary pairs, including the ones in this study, show a homogeneous chemical composition between the component stars. However, determining the origin of wide binary pairs solely based on this chemical similarity is challenging, as multiple scenarios have been suggested based on this characteristic (e.g., Kouwenhoven et al. 2010; Elliott & Bayo 2016). The possibility of various formation channels depending on the wide binary is also one of the main problems in understanding their origin.

To better understand the origin of wide binary systems, Hwang et al. (2021) suggested examining the mass ratios and orbital eccentricity of wide binary systems as a function of metallicity for a large sample. In addition, Ramírez et al. (2019) proposed that studying the correlation between the differences in chemical abundances and the separation between the component stars would provide important insights into the formation scenarios for wide binaries. They demonstrated that the absolute differences in chemical abundances tend to increase with increasing separation, and this trend has also been reported by Liu et al. (2021). This observed trend can be attributed to the notion that larger star-forming clouds may be less homogeneous than smaller clouds, assuming that stars in a wide binary pair are formed from a single cloud. The larger differences in chemical abundances in wide binaries with larger separations may arise from the local inhomogeneities within the cloud during the star formation process.

Since our samples were selected from wide binary candidates with separations larger than 10,000 au (see Section 2.1), they can provide significant constraints on the trend of chemical differences with binary separation. In Figure 7, we present the absolute difference in [Fe/H] as a function of projected binary separation for our samples and data from the literature. Notably, SVO 2759 (represented by the red circle) exhibits a moderate difference in [Fe/H] at the largest separation (∼100,000 au). The correlation between ∣Δ[Fe/H]∣ and separation is not clearly evident from this figure. While there appears to be a trend of increasing variation in ∣Δ[Fe/H]∣ for wide binaries with larger separations, it is important to note that there are samples with small differences in [Fe/H] even at large separations. In particular, two of our sample pairs, SVO 2324 and SVO 3206, exhibit remarkably tiny differences in [Fe/H] (<0.01 dex) compared to other wide binaries with separations larger than 10,000 au. This finding suggests that the difference in Fe abundance between the component stars may be influenced by the specific properties of each wide binary pair, which could arise from different formation mechanisms. For instance, wide binary systems showing smaller differences in [Fe/H] between their component stars, such as SVO 2324 and SVO 3206, may have formed closer together and then drifted apart through, for example, dynamical unfolding from a higher-order system (Elliott & Bayo 2016). Our result highlights the importance of individual characteristics of wide binary pairs based on the assumption that the formation and evolution mechanisms can vary depending on the individual wide binary system (see also Oh et al. 2018; Lim et al. 2021). On the other hand, it is necessary to be cautious when combining data from multiple sources, because the differences in precision according to data should be taken into account.

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Furthermore, Ramírez et al. (2019) reported increasing trends in abundance differences between stars in wide binary pairs with increasing separation, not only for Fe but also for other elements. These trends are more pronounced among elements with lower absolute abundance in the Sun, indicating that these elements were less homogeneous in the gas cloud where the wide binary formed. Ramírez et al. (2019) categorized elements into seven groups based on their absolute abundance in the Sun: for example, elements having solar abundance from 2 to 3 are classified as "Abd group 2" (see their Table 7). In this study, we also classified the elements we measured according to these criteria and plotted the average abundance differences as a function of binary separation in Figure 8. However, we limited our analysis to three abundance groups, Abd 4 & 5 (Ti, Cr), Abd 6 (Na, Al, Ca, Ni), and Abd 7 (Mg, Si, S, Fe), due to a shortage of measured elements.

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Figure 8 shows trends of increasing variation in absolute differences for the three groups with larger separations, although clear correlations are not evident. These trends are comparable to the observed trend in Fe abundance (see Figure 7). In addition, the least-squares-fitted lines for each group reveal that elements with lower solar abundances (Abd 4 & 5) exhibit a stronger correlation than the other groups (Abd 6 and Abd 7). We performed a Pearson correlation test on wide binaries with a separation of less than 50,000 au, as more distant samples could significantly affect the test. The Pearson correlation coefficients and their p-values, indicated in each panel of Figure 8, also support weaker correlations in the group of elements with higher solar abundance. Our results remain consistent even when excluding two samples with larger differences in chemical abundances at separations of around 10⁴ au. These findings suggest that the variation in trends with separation, depending on chemical elements, is a general characteristic of wide binary systems, corroborating the claims made by Ramírez et al. (2019). However, it is essential to note that the effect of precision in abundance measurement among element groups should not be disregarded, as the average abundance difference for Abd group 4 & 5 is derived from two elements, while the other groups include four elements.

An intriguing aspect that can be explored with wide binary systems is the investigation of their star-to-planet interactions. Since the component stars of wide binaries possess similar chemical properties and are far enough apart not to influence each other, the observed variations in abundance differences depending on the condensation temperature of elements can provide valuable insights into the properties of any potential hosting planet(s). In this regard, numerous studies have been conducted to examine the existence, formation, and chemical composition of planets or planetary engulfment events (e.g., Oh et al. 2018; Ramírez et al. 2019; Jofré et al. 2021; Liu et al. 2021; Ryabchikova et al. 2022). A key component of these investigations is comparing the abundance differences between volatile elements (with low condensation temperature, e.g., C, N, O) and refractory elements (with high condensation temperature, e.g., Fe, Ca, Mg), which, in turn, compose gaseous and terrestrial planets. Wide binary systems, affected by gaseous or terrestrial planets, exhibit noticeable trends in such comparisons.

In this study, we were able to measure the chemical abundances of C, N, and O elements only for SVO 3206 pair stars due to the high T_eff of other samples. Figure 9 displays Δ[X/H] for SVO 3206 (SVO 3206a − SVO 3206b) as a function of the condensation temperature of elements obtained from Lodders (2003). This plot reveals the absence of any correlation within this wide binary system, as confirmed by a large p-value of the Pearson correlation test (p-value = 0.914 with coefficient = −0.033). Our result suggests that these two stars have similar planetary system scales, including cases without planets, or that both stars are not significantly affected by star-to-planet interactions. It is worth noting that no planets have been reported for either star thus far. In addition, apart from the lack of correlation with condensation temperature, SVO 3206b is consistently more enhanced in chemical abundances than SVO 3206a by an average of ∼0.02 dex, which is a small value compared to those of other wide binary systems.

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Although we found no trend in chemical abundance differences corresponding to the condensation temperature of elements, our result demonstrates the capability of NIR spectroscopy for planet-hosting stars. In particular, the NIR region contains numerous CN, CH, and OH molecular features, which enable more accurate chemical abundance measurements for C, N, and O elements than optical spectroscopy, which relies on only a few spectral lines. The advantage of NIR spectroscopy for cool stars is also encouraging, given that many exoplanet studies focus on FGK-type stars. Therefore, the utilization of NIR high-resolution spectroscopy, combined with optical data, will be a powerful tool for studying wide binary systems hosting exoplanets based on a large number of chemical element abundances with high precision.