Elemental Abundances in the Diffuse Interstellar Medium from Joint Far-ultraviolet and X-Ray Spectroscopy: Iron, Oxygen, Carbon, and Sulfur

Oxygen is the most abundant cosmic element after H and He, and the amount depleted into dust grains is highly variable with ISM phase. The overall estimate of the oxygen budget in the ISM remains highly uncertain, as noted by Jenkins (2009). Although it is anticipated that oxygen may experience some depletion into dust, a considerable portion of it appears to be absent from the gaseous phase, without a comprehensive explanation. The combined contribution of carbon monoxide (CO), ices, silicate, and oxide dust particles is insufficient to fully account for the missing oxygen in the denser regions of the ISM, particularly at the interface where the diffuse and dense ISM meet, as highlighted by Whittet (2010) and Poteet et al. (2015). Oxygen has been extensively studied in the literature using high-resolution X-ray spectroscopy of the O K-edge (Takei et al. 2002; Juett et al. 2004; de Vries & Costantini 2009; Pinto et al. 2010, 2013; Costantini et al. 2012; Gatuzz et al. 2014, 2016; Joachimi et al. 2016; Eckersall et al. 2017). In Psaradaki et al. (2020, 2023), we studied the oxygen abundance in both gas and solids through the O K-edge. We found that about 10%–20% of the neutral oxygen is depleted into dust, and that in the diffuse sight lines, the oxygen abundance is consistent with or slightly above the solar value. In this work, we examine the X-ray and UV features simultaneously.

Iron is a major constituent in most dust grain models, as more than 90% of the total iron is depleted from the gas phase; the remainder is presumably locked up in dust grains (e.g., Savage & Bohlin 1979; Jenkins et al. 1986; Snow et al. 2002; Jenkins 2009). More than 65% of the iron is injected into the ISM in gaseous form by Type Ia supernovae; therefore, most of the Fe dust growth is expected to take place in the ISM (Dwek 2016). However, the exact composition of Fe-bearing grains as well as the exact amount and form that iron takes in the ISM is still unclear. Iron is expected to be present in silicate dust grains, but it could also exist in pure metallic nanoparticles (e.g., Kemper et al. 2002) or even as metallic inclusions in glass with embedded metal and sulfides (GEMS), suspected to be of interstellar origin (e.g., Bradley 1994; Altobeli et al. 2016; Ishii et al. 2018). The possibility of iron sulfides is discussed in more detail below.

UV and optical observations find that the remaining gas-phase Fe is primarily in the form of Fe ii in neutral regions of the ISM (Snow et al. 2002; Jensen & Snow 2007; Miller et al. 2007). This is because the ionization potential of Fe i is 7.87 eV, and it can be ionized by photons coming from the interstellar radiation field (ISRF) with energies between 7.87 eV and the Lyman limit at 13.6 eV. The ionization potential of Fe ii is 16.18 eV, which lies above the cutoff energy of the ISRF and is thereby unlikely to get ionized. In H II regions, the gas-phase iron should be a mix of Fe ii, Fe iii, and Fe iv. In H ii regions, some Fe i may exist, but due to depletion rates as high as 99% found in cold neutral regions (e.g., Savage & Sembach 1996), it is more likely to be in dust grains.

The degree to which interstellar sulfur is depleted is still a matter of debate (Jenkins 2009). In the diffuse ISM, sulfur is expected to have modest depletion (Costantini et al. 2019 and references therein). However, in denser regions, such as molecular clouds, sulfur can be included in aggregates such as H₂S and SO₂ (Duley et al. 1980). Sulfur in dust has been detected near C-rich asymptotic giant branch stars, planetary nebulae (Hony et al. 2002), and protoplanetary disks (Keller & Messenger 2013). Solid Fe–S compounds are abundant in planetary system bodies, such as interplanetary dust particles, meteorites, and comets (e.g., Wooden 2008). The presence of sulfur in dust grains can also be associated with GEMS (Bradley 1994), where the FeS particles are concentrated on the surface of the glassy silicate. Metallic Fe particles embedded in a silicate matrix have become a popular model for explaining the depletion patterns of the ISM (e.g., Zhukovska et al. 2018). The Stardust mission revealed sulfur in the form of FeS, suspected to be of ISM origin (Westphal et al. 2014). This evidence revitalizes the idea that sulfur could be present in dust species, as well as in less dense ISM environments (Costantini et al. 2019). However, it has been shown that GEMS are a less-favored candidate of interstellar dust (Keller & Messenger 2011, 2013; Westphal et al. 2019).

In recent X-ray studies of interstellar Fe absorption, appreciable quantities of iron sulfide material like troilite (FeS), pyrite Peru (FeS₂), and ferrous sulfate (FeSO₄) are not found (Psaradaki et al. 2023; Corrales et al. 2024, submitted). Moreover, Gatuzz et al. (2024) carried out a recent X-ray study of the sulfur K-edge. The authors estimated column densities of ionic species of sulfur along with column densities of dust compounds for a sample of 36 low-mass X-ray binaries. Upper limits were obtained for most sources including the dust components. However, they found that the cold–warm column densities tend to decrease with the Galactic latitude, with no correlation with distance or Galactic longitude. S i has an ionization potential of 10.36 eV, below the Lyman limit, so the majority of gas-phase S in the neutral medium is expected to be in the form of S ii. This work examines S ii gas through the far-UV (FUV) triplet transition at 1250.6, 1253.8, and 1259.5 Å.

Carbon is also suspected to be a major constituent of interstellar dust grains; however, we have limited knowledge about the amount of carbon that is locked up in dust grains (Jenkins 2009). It has been suggested that carbon constitutes around 20% of the total depleted mass in the Galaxy (Whittet 2003; Draine & Hensley 2021). Its depletion covers a relatively narrow range of values, showing that it is not a strong function of environmental density (Costantini et al. 2019). The majority of carbon should be locked in graphite grains, providing a likely explanation for the 2175 Å emission feature (Draine 1989, 2003, and references therein). However, concerns have been raised regarding the insufficiency of carbon depletion to account for the observed optical properties of interstellar dust (Kim & Martin 1996; Dwek 1997; Mathis 1998). A broad interstellar absorption feature at 2175 Å as well as narrow-band emission features in the far-IR are attributed to polycyclic aromatic hydrocarbons (e.g., Draine 1989, 2003). Various carbonaceous grain compositions proposed include graphite, hydrogenated amorphous carbon, and silicates with carbonaceous mantles (Duley et al. 1989; Weingartner & Draine 2001; Zubko et al. 2004; Jones et al. 2017; Costantini et al. 2019). Carbon could also be locked in nanodiamonds, which could be created from graphite and amorphous carbon grains in high-pressure ISM environments, for example, around shocks (Tielens et al. 1987). Nanodiamonds are also found in meteoritic material, and isotopic ratios imply that they are not from the solar system. However, our knowledge of the actual depletion of carbon—and thereby the total amount of carbonaceous interstellar dust—is still an enigma.

Carbon spectroscopy of Galactic sources is usually challenging in the X-ray due to very high absorption as well as the relative insensitivity of modern X-ray instruments near the C K photoelectric absorption edge at 0.3 keV. However, it is possible for very low column density sight lines. Gatuzz et al. (2018) studied the C K-edge using high-resolution Chandra spectra of four novae during their super-soft-source phase. The authors detected resonances of C ii Kα as well as the C iii Kα and Kβ transitions. Moreover, simultaneous examination of the X-ray and UV spectrum of the extragalactic source Mrk 509 (Pinto et al. 2012) suggests that most of the neutral carbon is locked up in dust, while the bulk of C ii comes from the warm photoionized phase. In this work, we study gas-phase carbon in the FUV through the C i and C ii transition at 1328.8 and 1335.7 Å, respectively.

We use the joined information from X-ray data through the Chandra and XMM-Newton satellites and FUV data from the Cosmic Origins Spectrograph (COS) on board the Hubble Space Telescope (HST) in order to understand the abundance and depletion of oxygen, iron, sulfur, and carbon. In the last decades, high-resolution X-ray absorption spectroscopy has proven to be a powerful tool for studying the ISM (e.g., Wilms et al. 2000; Takei et al. 2002; Juett et al. 2004; Ueda et al. 2005; Pinto et al. 2010; García et al. 2011; Costantini et al. 2012; Pinto et al. 2013; Gatuzz et al. 2016; Joachimi et al. 2016; Schulz et al. 2016; Yang et al. 2022). In particular, in the X-ray, we are able to study the solid-phase composition of highly depleted elements, such as iron in the line of sight toward a bright background source.

X-ray absorption fine structures are spectroscopic features observed near the photoelectric absorption edges of solid material (dust), and their shape is the ultimate footprint of the chemical composition, size, and crystallinity (e.g., Newville 2014; Lee & Ravel 2005; Corrales et al. 2016; Zeegers et al. 2017; Rogantini et al. 2018, 2019; Corrales et al. 2019; Zeegers et al. 2019; Psaradaki et al. 2020; Costantini & Corrales 2022; Psaradaki et al. 2023). However, the abundance and absorption strength of Fe ii, likely the largest repository of gas-phase iron, is difficult to constrain from the X-ray band alone (Psaradaki et al. 2023; Corrales et al. 2024, submitted). In this pilot study, we use the joint information of the FUV and X-ray absorption spectra of the low-mass X-ray binary Cygnus X-2 to study both the gas and dust components of the ISM, providing the most comprehensive means possible to determine the abundances and depletion of prevalent interstellar elements. Cygnus X-2 is a bright X-ray source with a moderate column density (2 × 10²¹ cm⁻²) and high flux (2.3 × 10⁻⁹ erg s⁻¹ cm⁻² in the 0.3–2 keV band), making it an excellent target to study the diffuse ISM in the O K- and Fe L-edges. This sight line also exhibits a rich FUV spectrum with absorption signatures from the ISM. The distance of the source has been estimated to be around 7–12 kpc (Cowley et al. 1979; McClintock et al. 1984; Smale 1998; Yao et al. 2009). This paper is organized as follows. In Section 2, we present the HST/COS, Chandra, and XMM-Newton data used in this study and their reduction processes. In Section 3, we describe the adopted method for analyzing the FUV spectra, and in Sections 4 and 5, we discuss the spectral fitting to the X-ray data. Finally, in Section 6, we discuss the results, and we give our conclusions in Section 7.

In Table 5, we report the abundance of O, Fe, C, S, and Ne among the different values found in the literature in standard units of $\mathrm{log}({\rm{X}}/{\rm{H}})+12$, where X/H represents the abundance of each element with respect to hydrogen. Anders & Grevesse (1989) present abundance tables for both meteoric and solar photosphere data. For our comparisons, we assume the photospheric values, although the two sets are generally consistent with each other, except for a few elements. For Fe, the solar value is 7.67 ± 0.03, while the meteoric is 7.51 ± 0.01. Similarly, the tabulated values from Grevesse & Sauval (1998), Lodders (2003), and Asplund et al. (2009, 2021) refer to the solar photospheric values. Wilms et al. (2000) present a model for the absorption of X-rays in the ISM. The selected values come from the adopted abundance of the ISM based on Cardelli et al. (1996), Snow & Witt (1996), and Meyer et al. (1998). Lastly, we also include in the comparison B-type star elemental abundances from Nieva & Przybilla (2012). In this study, our spectral models are based on the protosolar abundances as provided by Lodders & Palme (2009), which serve as the default abundance set in SPEX. In Figure 6, we present a comparative analysis of the elemental abundances listed in Table 5 for the elements under investigation in our study. Variations in the reported values make it important to note that the choice of the reference abundance table can have an impact on the resulting measured abundances.

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Table 5. Literature Standard Abundances for the Elements in This Study

References	$\mathrm{log}({\rm{O}}/{\rm{H}})+12$	$\mathrm{log}(\mathrm{Fe}/{\rm{H}})+12$	$\mathrm{log}({\rm{C}}/{\rm{H}})+12$	$\mathrm{log}({\rm{S}}/{\rm{H}})+12$	$\mathrm{log}(\mathrm{Ne}/{\rm{H}})+12$	log(O/Ne)	log(Fe/Ne)	log(S/Ne)
Anders & Grevesse (1989)	8.93 ± 0.035	7.67 ± 0.03	8.56 ± 0.04	7.21 ± 0.06	8.09 ± 0.10	0.84 ± 0.10	−0.42 ± 0.10	−0.88 ± 0.01
Grevesse & Sauval (1998)	8.83 ± 0.06	7.5 ± 0.05	8.52 ± 0.06	7.33 ± 0.11	8.08 ± 0.06	0.75 ± 0.08	−0.58 ± 0.08	−0.75 ± 0.11
Wilms et al. (2000) a	8.69	7.43	8.38	7.09	7.94	0.75	−0.51	−0.85
Lodders (2003)	8.69 ± 0.05	7.47 ± 0.03	8.39 ± 0.04	7.19 ± 0.04	7.95 ± 0.10	0.74 ± 0.11	−0.48 ± 0.10	−0.76 ± 0.10
Lodders & Palme (2009) b	8.73 ± 0.07	7.45 ± 0.08	8.39 ± 0.04	7.14 ± 0.01	8.05 ± 0.10	0.68 ± 0.12	−0.6 ± 0.13	−0.91 ± 0.10
Asplund et al. (2009) c	8.69 ± 0.05	7.5 ± 0.04	8.43 ± 0.05	7.12 ± 0.03	7.93 ± 0.10	0.76 ± 0.11	−0.43 ± 0.1	−0.81 ± 0.10
Nieva & Przybilla (2012) d	8.76 ± 0.04	7.52 ± 0.03	8.33 ± 0.04	⋯	8.09 ± 0.05	0.67 ± 0.06	−0.57 ± 0.06	⋯
Asplund et al. (2021)	8.69 ± 0.04	7.46 ± 0.04	8.46 ± 0.04	7.12 ± 0.03	8.06 ± 0.05	0.63 ± 0.10	−0.60 ± 0.06	−0.94 ± 0.06
This study e						0.81 ± 0.03	−0.41 ± 0.11	$-{1.35}_{0.05}^{0.04}$

Notes. The standard abundances are expressed in logarithmic units, with hydrogen 12.0 by definition.

^a Note that these values come from the adopted abundance of the ISM based on Cardelli et al. (1996), Snow & Witt (1996), and Meyer et al. (1998). ^b Used in this study and default set of abundances in SPEX. ^c We refer to the photospheric values. ^d Abundances derived from B-type stars. ^e The log(O/Ne) ratio is the sum of the predicted O i abundance that we obtain from a simultaneous X-ray and FUV fit and the solid-phase oxygen. For the log(Fe/Ne) ratio, we used the combined contribution of solid iron and atomic Fe ii. The log(S/Ne) ratio comes from the S ii value only resulting from the FUV fit. The Ne abundance is determined through the fit of the Ne K-edge in the X-ray spectrum from Psaradaki et al. (2023); in particular, it represents the summed abundance of Ne i, Ne ii, and Ne iii.

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Because it is a noble gas, neon will not deplete into dust grains. Thus, it can serve as a suitable reference for comparing the observed abundance of elements, providing an alternative to hydrogen, which does not provide any spectral features in the X-ray band. The last four columns of Table 5 display the calculated X/Ne ratio for each of the literature abundance tables. The Ne abundance is determined through the fit of the Ne K-edge in the X-ray spectrum from Psaradaki et al. (2023), and it represents the summed abundance of Ne i, Ne ii, and Ne iii, which is 2.1 × 10¹⁷ cm⁻². In the final row of Table 5, we present our computed value for log(X/Ne). In Figure 6, we visualize the results of Table 5, showing the deviations of the literature standard abundance tables for Fe, O, and S compared to neon, with the values of this work derived from FUV and X-ray observations. We will revisit this comparison of elemental abundances with neon in the following sections, where we will explore individual discussions of the elements under study.

We further use the spectral synthesis code Cloudy (version 2017; Ferland et al. 2017) and run a grid of models over a wide range of ionization parameters (ionizing photon density) and metallicity values for a neutral hydrogen column density of 2 × 10²¹ cm⁻². The ionization parameter U is defined as the ratio between the number densities of ionizing photons and hydrogen (U ≡ n_γ /n_H), and we allow this parameter to vary from $\mathrm{log}U=-4$ to 0 by 0.25 dex. We also vary $\mathrm{log}Z/{Z}_{\odot }=-2$ to +0.5 in steps of 0.1 dex. We adopt a photoionizing spectrum from the Milky Way that includes a contribution from the extragalactic UV background (Fox et al. 2005) and assume thermal and ionization equilibrium for a plane-parallel slab geometry with a uniform density. We use the "grains ISM" command to specify grains with a size distribution and abundance consistent with those in the Milky Way and additionally employ the "metals deplete" command in our models to deplete elements that are included in grains, e.g., Fe, according to the work of Jenkins (2009). We utilize the Cloudy grids to compare between the ratios of the ions investigated in this study and the corresponding values predicted by Cloudy. We found that the relative abundances of each gas-phase ion were relatively insensitive to the magnitude of ionization parameter U for the photoionizing spectrum used in this run. We use logU = −5 as our fiducial value in the discussion below.

First, we compare our observed ion abundances for oxygen with those predicted by Cloudy in scenarios where elements are not depleted into dust. This approach allows us to assess the predicted ion quantities in the case of excluding the influence of the dust phase, thereby discerning any disparities. Using Cloudy, we have determined that O ii/O i = 4.62 × 10⁻⁴ and O iii/O i = 1.2 × 10⁻⁷. Neutral oxygen gas is thereby expected to significantly dominate the neutral ISM abundance when compared to O ii and O iii, with O iii being the least abundant among these ions. However, Cloudy functions as a photoionized model, diverging from the primarily collisionally ionized models used in the hot model of SPEX, and one should exercise caution when comparing to the absolute value of the ionic ratios. Through simultaneous fitting of both X-ray and UV data, we established upper limits for the ionic column densities of O ii, O iii, and O iv ions (Table 4). With the exception of O iii, these upper limits are consistent with the derived values of Gatuzz et al. (2018) for the same source.

Understanding the exact reservoirs of iron in the diffuse ISM is still an open question. Our X-ray fits yield a column density of solid-phase iron of 3.9 × 10¹⁶ cm⁻². The atomic component is in Fe ii and contributes to the total column density through two distinct absorption systems (Table 3), amounting to 2 × 10¹⁵ cm⁻². Our Cloudy simulations, detailed in Section 6.1, indicate that the Fe i/Fe ii ratio should be approximately 2.5 × 10⁻³, while the Fe iii/Fe ii ratio is on the order of 10⁻⁶. These findings suggest that Fe ii is the dominant form of gas-phase iron in the neutral ISM, with Fe i and Fe iii concentrations being negligible. The abundance of Fe ii is still relatively small compared to the abundance of iron in solid form, accounting for merely 4% of the total iron content. The remaining 96% resides in solid-state structures in the form of amorphous pyroxene (Mg_0.75Fe_0.25SiO₃) and metallic iron. This dust grain mineralogy was previously found in Psaradaki et al. (2023), and it is assumed in this study. However, the dust column density of each compound is free, and it is found to be <6.1 × 10¹⁷ and <1.2 × 10¹⁶ cm⁻² for the amorphous pyroxene and metallic iron, respectively. Additionally, we examined the scenario where Fe exists principally in its metallic form, as detailed in Westphal et al. (2019) for the observation of Cygnus X-1. However, when applying this model to the case study of Cygnus X-2, we observed a less optimal fit. The suggestion of metallic iron as a compound needs further investigation, primarily due to uncertainties in the energy calibration across various measurements of this compound in the literature (Psaradaki 2021; E. Costantini et al. 2024, in preparation; Corrales et al. 2024).

The selection of the MRN dust size distribution could potentially have an effect on the calculation of the dust column density. In particular, the phenomenon of self-shielding may play a role in diminishing the overall iron column available for photoelectric absorption (Wilms et al. 2000). In this case, strong absorption prevents X-rays from penetrating the inner portions of the dust grain, and a smaller fraction of the total metal column contributes to the absorption edge (Corrales et al. 2016). Our study incorporates self-shielding, and we have considered the extinction (scattering + absorption) cross section in our spectral modeling. However, this effect is anticipated to be particularly noticeable in regions of the ISM containing large grains, approaching the upper limit of the dust size distribution employed in our investigation. Consequently, it is plausible that some of the depleted iron is located within populations of large grains, specifically those exceeding 0.25 μm in size. Other size distributions beyond the MRN, such as those employed in Zubko et al. (2004) and Weingartner & Draine (2001), will be examined in a future study.

We extend our calculations to determine the combined abundance of iron in both gaseous and dust components, comparing it to established standard abundance values found in the literature. The third column in Table 5 presents a comparison of the iron abundance figures, denoted in units of $\mathrm{log}(\mathrm{Fe}/{\rm{H}})+12$. Taking into account the associated uncertainties, our iron abundance estimation from our best fit is 7.38 ± 0.33, which takes into consideration iron in dust (comprising silicates and metallic iron) and Fe ii. This result is in agreement with the standard abundance tables. Moreover, in Table 5 and Figure 7 (left panel), we show a comparison of the iron abundance tables compared to neon. Overall, there is consistent behavior between our calculated $\mathrm{log}(\mathrm{Fe}/\mathrm{Ne})$ value, derived from spectral fitting of X-ray and UV data, and the standard abundance tables reported in the literature, with the exception of the most recent work of Asplund et al. (2021).

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In the COS spectrum of Cygnus X-2, we have identified singly ionized atomic sulfur lines (S ii) at wavelengths of 1250.58 and 1253.81 Å. These spectral lines are associated with two distinct velocity clouds. The first cloud exhibits a column density of approximately (7.4 ± 0.5) · 10¹⁵ cm⁻², and the second cloud shows a weaker transition with a column density of approximately (1.9 ± 0.1) · 10¹⁵ cm⁻². When examining Table 5 and the right panel of Figure 7, we observe that the S ii/Ne ratio derived from our analysis is underabundant compared to the total S/Ne ratio calculated from the literature. This suggests that there should be another reservoir of sulfur other than S ii in the diffuse sight line of Cygnus X-2.

Cloudy modeling further predicts that the S i/S ii ratio is 2.8 × 10⁻⁴, implying that the remaining sulfur is not in the neutral gas phase. Similarly, the S ii/S iii ratio is 7.1 × 10⁻⁴. These predictions imply that the remaining sulfur is not expected to be in the form of S i or S iii; instead, it could be bound within molecules or dust particles. However, it is essential to exercise caution when utilizing the Cloudy ratios in this context. Cloudy operates as a photoionized model, presenting a contrast to the predominantly collisionally ionized models employed in the hot model of SPEX and widely adopted in previous studies. Moreover, in Gatuzz et al. (2024), the S K-edge has been examined using high-resolution Chandra/HETGS spectra of 36 low-mass X-ray binaries. In the case of Cygnus X-2, their ionic column density estimates appear to disagree with the Cloudy predictions. However, only upper limits of the ionic column densities were able to be provided.

Sulfur in dust species can take on various forms, including FeS or FeS₂, or even exist within GEMS (Bradley 1994), where the FeS particles would be more concentrated on the surface of the glassy silicate. However, studies have demonstrated that GEMS are less favored as a plausible component of interstellar dust (Keller & Messenger 2011, 2013; Westphal et al. 2019). In Psaradaki et al. (2023), we used newly computed dust extinction models of astrophysical dust analogs for the Fe L-edges including FeS or FeS₂. However, strong evidence for these species was not found in those works. It has been discussed in the literature that sulfur does not appear to change depletion in the diffuse ISM, suggesting that it does not easily get incorporated into dust (Sembach & Savage 1996). However, in molecular clouds, sulfur can be included in aggregates such as H₂S or SO₂ (Duley et al. 1980). Inclusion into simple atomic sulfur or sulfur ices has been proposed to solve the missing-sulfur problem in dense molecular clouds (Vidal et al. 2017). We examined the three-dimensional maps of interstellar dust reddening, which are based on Pan-STARRS 1 and Two Micron All Sky Survey photometry and Gaia parallaxes ¹⁸ (Green et al. 2019 and references therein). These maps trace the dust reddening as a function of both angular position on the sky and distance. Using these maps, we did not find any steep jump in the line-of-sight reddening. This could suggest that the line of sight toward Cygnus X-2 is rather diffuse and does not cross a dense molecular cloud. Thus, the nature of the missing sulfur in the Cygnus X-2 sight line, as determined in this study, is still a mystery.

A comprehensive understanding of sulfur depletion within dust particles can be achieved through the examination of the sulfur K-edge at 2.48 keV in X-ray spectra. Unfortunately, the column density toward Cygnus X-2 falls short in providing the necessary optical depth to study the photoabsorption edge of sulfur. Moreover, the current X-ray instruments utilized in this study lack sufficient energy resolution at this critical energy range. The recently launched X-ray Imaging and Spectroscopy Mission (XRISM) will enable us to directly study the photoabsorption edge of sulfur (e.g., Costantini et al. 2019) and determine the dust inclusion of this element.

The gas-phase carbon in the neutral ISM could be primarily in the form of singly ionized species, C ii, because the C i ionization energy is lower than that of H I, and the C ii ionization energy is above that of H I. Using Cloudy, we indeed find that the C i/C ii ratio is 3.1 × 10⁻³. Surprisingly, we measure comparable column densities of C i and C ii from the FUV spectral fit. We find that the total column density of the C ii absorbers in the line of sight is (4.7 ± 0.3) × 10¹⁴ cm⁻², while for C i, we find ${3.6}_{-0.6}^{+1.1}\times {10}^{14}\ {\mathrm{cm}}^{-2}$.

We compare these values with carbon-related results available in the existing literature. Gatuzz et al. (2018) studied the C K-edge using high-resolution Chandra spectra of four novae during their super-soft-source state. They found column densities of C ii in the range of (1.8–3.5) × 10¹⁷ cm⁻², which is inconsistent with our values in Table 3. Moreover, in the study by Sofia et al. (1997), the C ii (2325 Å) equivalent width was measured in an absorption system directed toward the diffuse sight line of the τ Canis Majoris star. The results indicated a column density of (7.57 ± 2.52) × 10¹⁶ cm⁻² for this system (and 10⁶ C ii/H i = 135 ± 46). This finding was later complemented by Sofia & Parvathi (2009), who investigated various sight lines in the ISM with known hydrogen abundances utilizing HST/STIS data. Through the modeling of the strongest lines, they found C ii column densities in the range (1.97–6.19) × 10¹⁷ cm⁻² across different lines of sight. In addition, Cardelli et al. (1993) detected C ii in diffuse clouds toward ζ Oph using the Goddard High Resolution Spectrograph, reporting a column density of 1.8 × 10¹⁷ cm⁻². Similarly, Cardelli et al. (1991) examined observations of ultraviolet interstellar absorption lines of dominant ion stages arising in the diffuse clouds in the direction of ξ Persei and focused on the same C ii line, reporting a column density of 5 × 10¹⁷ cm⁻². Collectively, these studies offer insights into the variations of C ii column densities across different interstellar absorption systems. The column density of C ii absorption observed in this study is significantly lower compared to the values reported above. One explanation could be that we are most likely probing C ii that has been ionized by the ambient ISRF at the edges of the S ii-bearing cloud, rather than a large photoionization region, as is expected around the massive O-type stars examined in the above works.

The C i in our study shows a different trend compared to the other ions studied here. The first and most dominant component shows a velocity shift of −25 km s⁻¹ between that of the nearer S ii and Fe ii absorbing region. Perhaps this stronger C i absorption could be arising from denser regions of the ISM that are shielded from the ISRF. The second, weaker component is redshifted compared to the rest-frame velocity. The source of this redshifted C i is unknown. Jenkins & Tripp (2011) studied the UV spectra of 89 stars using HST data. Based on the integrated C i absorption across all velocities, they determined that the column density of the C i absorbers falls within the range of approximately 2.4 × 10¹³–5.7 × 10¹⁴ cm⁻² (lower limit). Our findings align with these results.

There are still uncertainties around the abundance and depletion of carbon within dust grains. Although carbon is a substantial element in grains, our understanding of the mechanisms through which dust grains incorporate carbon remains rather incomplete (Jenkins 2009). This topic continues to be an active area of study. Future advancements, including upcoming X-ray missions and innovative concepts like Arcus (Smith 2016), hold the potential to carry out in-depth spectroscopic analysis around the C K-edge, in particular the features of dust as well as C i (Costantini et al. 2019).

In high-resolution X-ray spectroscopy, the choice of atomic data plays a crucial role in the analysis of the data and the interpretation of the results. In Psaradaki et al. (2020), we discussed the discrepancy between the atomic databases of SPEX and XSTAR for the oxygen ions from O i to O iv. We found out that the calibration of the energy scale of the different models can differ, and this can have an effect on the results, especially with future X-ray telescopes.

In this section, we examine the discrepancy in the atomic database for iron. We compare the atomic data implemented in SPEX with the available data of Fe i–Fe iv ions presented in the recent work of Schippers et al. (2021). The Fe i, Fe ii, and Fe iv data in Schippers et al. (2021) have been taken from Richter et al. (2004), Schippers et al. (2017), and Beerwerth et al. (2019), respectively. In Figure 8, we compare the databases. From the plots, it is evident that there is a shift of about 2.7 eV between the SPEX atomic data and the models presented in Schippers et al. (2021), which is detectable with the energy resolution of the Chandra HETGS instrument.

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We tested how the discrepancy between the atomic databases can affect the X-ray spectral fitting of Cygnus X-2. We shifted the absolute energy of the Fe i–Fe iv transitions in SPEX according to the energy calibration reported in Schippers et al. (2021). We kept the same model described in Section 4 and repeated the fit. Around the Fe L-edges, the X-ray absorption is dominated by the dust, while iron in atomic form is too weak to constrain the X-ray fits. We therefore achieved similar results. These discrepancies, however, will be more evident with future X-ray instruments, such as the spectral resolution capabilities demonstrated by the grating spectrometers of Arcus (Smith 2016).