© The Authors 2023

1 Introduction

Our understanding of the interstellar medium (ISM) has significantly improved in the past decade, through extensive observational efforts in absorption line spectroscopy performed at millimeter (mm) and submillimeter (submm) wavelengths toward background continuum sources. These observations have revealed both physical complexity and chemical richness as evidenced by the detection of various diatomic (e.g., CN, CO; Liszt & Lucas 2001; Liszt et al. 2019), triatomic, and even polyatomic molecules (e.g., C₃H⁺, CH₂, H₂O, HCO⁺, C₂H, c-C₃H, 1-C₃H, HCN, HNC, CH₃CN, NH₃, H₂CO, and c-C₃H₂; Polehampton et al. 2005; Flagey et al. 2013; Gerin et al. 2011, 2019; Godard et al. 2010; Liszt et al. 2006, 2014, 2018). The ISM has been shown to consist of multiphase gas combining a cold neutral medium (CNM) and warm neutral medium (WNM; Bialy & Sternberg 2019; Bellomi et al. 2020) in diffuse clouds where chemistry begins with the formation of simple molecules. These diffuse clouds contain CO-dark H₂ gas, in which CO is not detected in emission, but it can still be detected at a low abundance in absorption. Thus, diffuse clouds (defined as those in which the local fraction of gas-phase carbon in C⁺, $f_{{\text{C}}^{+}}^n$, exceeds 0.5) and translucent clouds (defined as those in which $f_{{\text{C}}^{+}}^n<0.5$ but the local fraction of gas-phase carbon in CO, $f_{\text{CO}}^n$, remains less than 0.9) in the Milky Way are excellent laboratories to study the formation and destruction of molecular clouds. The very different conditions in dense molecular clouds, where eventually star formation occurs, lead to a substantially different molecular composition. Significant efforts have been undertaken to determine the physical parameters that characterize the gas properties of high latitude diffuse clouds and solar neighborhood clouds (e.g., Liszt & Lucas 2001, 2004; Lucas & Liszt 2000, 2002) as well as for a few specific sightlines in the Galactic plane (e.g., Godard et al. 2010; Gerin et al. 2011; Neufeld et al. 2015). In contrast to high latitude clouds, the ISM in the disk of the Milky Way has many more complicated structures of atomic and molecular gas. Differing in their physical and chemical properties, diffuse and translucent clouds have, for example, different molecular gas fractions and different abundances of carbon-bearing species (see Snow & McCall 2006, and references therein). In particular, if only the total visual extinction (A_v) is known, distinguishing translucent clouds from the superposition of multiple diffuse clouds yielding similar fractions of integrated column densities for atomic $\left(f_{\text{H}}^N\right)$ or molecular $\left(f_{{\text{H}}_2}^N\right)$ hydrogen is not straightforward. Nonetheless, the chemistry in the two types of clouds is certainly different as the primary reservoirs of gas-phase carbon vary from diffuse clouds to translucent clouds.

Absorption lines of HCO⁺ sample low-density regions, which can neither be observed in molecular emission nor in CO millimeter absorption because of both low excitation and the absence of CO (Hogerheijde et al. 1995; Liszt et al. 2018, 2019), making them an excellent tracer of H₂ (Gerin et al. 2019) that is not directly detectable except through ultraviolet (UV) observations toward nearby hot stars in very diffuse clouds. At millimeter and submillimeter wavelengths, where observations are unaffected by dust absorption, background sources (and foreground clouds) can be observed at large distances within the Galactic plane, and at higher visual extinctions, that are higher column densities. As carbon is a key element in interstellar chemistry, we also explored absorption by carbon-bearing molecules (HCN, HNC, C₂H, and c-C₃H₂) that have been observed to be surprisingly as abundant (e.g., Godard et al. 2010; Gerin et al. 2011) as HCO⁺ in diffuse and translucent clouds. Their observed abundances are much higher than predicted from simple photodissociation region (PDR) models (e.g., Godard et al. 2010; Gerin et al. 2011).

The unexpectedly large column densities and broad line widths of the HCO⁺ and HCN molecules observed at millimeter wavelengths can be explained by their formation being enhanced by the dissipation of interstellar turbulence; this creates small regions of elevated temperature and large ion-neutral drift that enables endothermic reactions not possible under the standard conditions typical of the CNM (e.g., Hogerheijde et al. 1995; Godard et al. 2010, 2014). For similar reasons, the observed abundances of sulfur-bearing molecules (such as H₂S, CS, SO, and SH) greatly exceed values predicted by standard models of cold diffuse molecular clouds, providing further evidence for the enhancement of endothermic reaction rates by elevated temperatures or ion-neutral drift (Neufeld et al. 2015). Therefore, observations of these molecules provide important constraints on shock and turbulent dissipation region (TDR) models.

By combining observations of multiple species, examining correlations and measuring abundance ratios, it has been possible to determine the distribution function for the H₂ fraction within the diffuse and translucent ISM. This provides an important constraint on global models for the formation and destruction of molecular hydrogen in a turbulent medium (e.g., Bialy et al. 2017, 2019; Bialy & Burkhart 2020), as the differing abundances and kinematics of these molecules studied here demonstrate the importance of considering gas dynamical processes that enhance the formation rate of some of their progenitor species.

This paper presents an absorption line survey, in the 2 mm and 3 mm wavelength regions, carried out using the Institut de Radioastronomie Millimétrique (IRAM) 30 m telescope, as a complement to the HyGAL Stratospheric Observatory for Infrared Astronomy (SOFIA) Legacy Program (see Jacob et al. 2022, hereafter Paper I, for an overview of the HyGAL program) that surveys six hydride species (i.e., ArH⁺, OH⁺, H₂O⁺, SH, OH, and CH), C⁺, and O toward 25 bright Galactic continuum background sources at submillimeter wavelengths. This millimeter absorption line program surveys 15 sightlines targeted by the HyGAL program. Here we will explore the absorption line data and investigate associations between simple molecules and the hydrides studied in Paper I. Section 2 describes the acquisition of the spectroscopic data, and the calibration and data reduction procedures employed. In Sect. 3, we present the spectra of lines from HCO⁺, HCN, HNC, CS, H₂S, C₂H, and c-C₃H₂ that are detected in absorption toward the different sightlines; here we discuss both their general properties and the CO emission counterparts that have previously been observed along some of these sightlines. The determination of the column densities of these molecular species will be explained in Sect. 4, together with a principal component analysis for all species reported both in this paper and in Paper I toward W3(OH) and W3 IRS5. In Sect. 5, we discuss the results of the principal component analysis and the derived observational quantities (column densities and abundances), and we compare these measurements with the results of isobaric PDR models, trying to understand the chemical and physical properties of diffuse and translucent clouds across the Milky Way. Finally, we conclude and summarize all the results from this study in Sect. 6.

2 Observations and data reduction

We carried out observations of a molecular absorption line survey (Project ID: 003–20) in the 2 and 3 mm wavelength regions, during the period of 2020 June 23–30, with the Eight MIxer Receiver (EMIR)¹ on the IRAM 30 m telescope, toward the 15 HyGAL continuum sources listed in Table 1. The continuum sources observed here cover slightly more than half of the entire HyGAL source sample (see Paper I) and are mostly located in the first and second quadrants of the Milky Way as shown in Fig. 1, except for two sources, NGC 6334 I and G357.558−00.321, which are located in the fourth quadrant. For a given column density of a target species, the signal-to-noise ratio for absorption line features is proportional to the continuum flux at the relevant wavelength. The Herschel InfraRed Galactic Plane Survey (Hi-GAL, Molinari et al. 2016) provides a compact source catalog (Elia et al. 2017, 2021) with continuum fluxes at 70, 160, 250, 350, and 500 µm coinciding with the wavelengths of transitions targeted with HyGAL (approximately spanning 149–194 µm). The HyGAL program selected 25 submillimeter sources with flux limits over 2000 Jy at 160 µm for sources in the inner Galaxy and >1000 Jy for sources in the outer Galaxy (see Paper I for more details on the source selection).

The observations were done with two different receiver setups: the first configuration combines the E090 and E150 receivers (covering 92–99.7 GHz and 166.5–174.2 GHz) and the other uses the E090 receiver alone (covering 83.2–90.9 GHz and 98.9–106.6 GHz). These setups allowed us to target a number of molecular transitions with a total bandwidth coverage of 15 GHz (including a 1 GHz bandwidth overlap between the two setups); they proved ideal for obtaining widespread absorption line features arising from foreground clouds at different velocities. Table 2 shows the observed molecular transitions within the coverage and provides the line information. Both receiver setups are connected to the FTS200 backend offering a frequency channel resolution of 200 kHz (equivalent to Δυ ~ 0.35 km s⁻¹ for H₂S and 0.62–0.66 km s⁻¹ for the other transitions). For our analysis, we resampled all the spectral line data to a fixed velocity resolution of 0.8 km s⁻¹, except H₂S for which we use a better resampled resolution of 0.36 km s⁻¹. We utilized the Continuum and Line Analysis Single-dish Software (CLASS) software² of the Grenoble Image and Line Data Analysis Software (GILDAS) package (Pety 2005) for the initial data reduction of the molecular line data, and further post-processed the data using Python (e.g., when combining the observations made in two different switching modes).

Fig. 1 Positions of fifteen sightlines (black dots with names) from the HyGAL program in the Galactic plane. This distribution plot is reproduced based on the Fig. 3 of Paper I. Colored curves represent different Milky Way spiral arms; the 3-kpc arm is in yellow, the Norma and outer arms are in red, the Scutum-Centaurus arm is in blue, the Sagittarius-Carina arm is in purple, the Perseus arm is in black, and the local arm is in cyan. The Sun and the Galactic center (GC) are marked with the red Sun and asterisk symbols, respectively. The gray-shaded ellipse around the GC represents the long bar.

Calibration for PSw and WSw mode observations

The observed data sets consist of wobbler switching (WSw) and position switching (PSw) On-Off mode observations. For WSw mode observations, all sources were observed with throw angles of ±120″. In active star-forming regions, which often exhibit extended emission structures, these relatively small throw angles can result in reference positions that are significantly contaminated by emission in the stronger lines such as HCO⁺ (1→0). This causes artificial absorption features in the final calibrated spectra. On the other hand, standing waves are often generated in the PSw mode as the telescope slews to distant reference positions while the WSw mode provides reliable continuum level measurements and flat baselines. Since standing waves distort the emission and absorption line profiles, we carefully investigated all the PSw spectra and excluded those scans that are severely affected by standing wave effects before averaging all observational scans.

Figure 2 shows an example of the HCO⁺ spectra obtained with WSw and PSw mode observations toward G29.96−0.02. In the top panel of Fig. 2, the WSw spectrum shows additional apparent absorption features; these are found, for example, at LSR velocities of 50 and 85 km s⁻¹, the latter lying close to the velocity of the background continuum source (97 km s⁻¹). These components are not detected in the PSw spectrum, implying that they may be dismissed as artifacts arising from contamination in the reference position. To identify such artifacts, we rescaled the PSw spectrum to the WSw spectrum, allowing for both multiplicative and additive offsets, by using the relationship of $\text{A}{T}_{\text{a}}^{*}\left(\text{PSw}\right)+\text{B}$, where A and B are constants, representing the slope and y-intercept, respectively, of the linear least-squares regression on both the spectra. We note that there are some values of A that are lower than 1, which may be caused by the significant contamination from the WSw reference positions or the less flat baselines from the PSw modes. The coefficients used for rescaling the PSw spectra are listed in Table 3. We have examined if any excessive residual spectral features remain after subtracting a rescaled PSw spectrum from a WSw spectrum, as shown in the green profile in the middle panel of Fig. 2. If the residual value in any velocity channel exceeds three times the rms value (marked by black horizontal dashed lines), the WSw value at the selected velocity channel is replaced by the PSw value at the same velocity because the high residual components are regarded not to be real but due to the reference position contamination. The continuum levels and rms noise of the spectra for the seven species toward each source are listed in Table 4. Subsequently, we combined the rescaled PSw and the WSw spectra corrected to exclude the WSw spectral range with the counterfeit absorption features. Since the WSw mode was used as the primary observing mode, observations made in this mode have a longer integration time (about 1.5 h per source) and in turn a larger number of scans than observations taken in the PSw mode. Thus, before combining both data sets, the spectra are weighted by the inverse squares of their measured rms noise levels. The plot in the bottom panel shows the combined spectrum in black along with the WSw and PSw spectra in blue and red, respectively. The combined spectrum appears to be well-calibrated, with a higher signal-to-noise ratio than spectra obtained in the individual modes, and without any false absorption features (like the 50 km s⁻¹ component). We used the combined spectra of all observed transitions in all following analyses.

Fig. 2 Comparison of the HCO+ spectra from observations with wobbler switching and position switching modes. The top panel shows the HCO+ spectra (velocities relative to the local standard of rest, LSR) taken with WSw (blue) and PSw (red) modes toward G29.96−0.02. The middle panel shows the residual spectrum (green) after fitting the WSw and PSw spectra. Black horizontal dashed lines mark the 3 rms level. The bottom panel presents the combined spectrum (black) of the WSw and rescaled PSw ($\text{A}{T}_{\text{a}}^{*}(\text{PSw})+\text{B}$, where A and B are the slope and y-intercept of a linear least-squares regression fit, respectively), with the individual WSw and PSw spectra in the same colors as in the top panel.

3 Results

3.1 Detected absorption lines

Table 5 lists the molecular species detected in absorption observed toward 14 out of the 15 millimeter continuum sources. The spectra obtained toward the last target listed in Table 1, G357.558−00.321, are not shown because the observations were not sensitive enough to detect the millimeter wave continuum from this weakest of the 15 sources. Some continuum sources have broad emission features of HCO⁺, HCN, HNC, CS, and H₂S at their υ_sys, spanning a few tens of km s⁻¹. Several absorption lines are detected at the LSR velocities of such emission line wings and/or emission lines at υ_sys. It is not clear if the absorption lines arise from physically unrelated foreground clouds or if they are associated with the molecular gas of the star forming regions in which the continuum sources reside, in particular their dense envelopes. In some cases (see for e.g., G19.61−0.23 and G32.80+0.19) the absorption line components have distinct offsets in velocity from the emission lines and these components unambiguously trace foreground diffuse or translucent clouds.

The continuum sources observed here are H II regions and massive star-forming regions (see Paper I for the details of the HyGAL program). Some of them (e.g., G31.41+0.31) are chemically rich environments whose submillimeter and millimeter spectra exhibit a multitude of molecular emission lines associated with star-formation (e.g., outflows and hot molecular cores, Nony et al. 2018; Gorai et al. 2021). The CS, H₂S, and c-C₃H₂ spectra are severely contaminated molecular lines emitted by the background continuum source, various of them unidentified. As a result, the detection rates of absorption features for these transitions are lower than those of the other species. Moreover, the c-C₃H₂ transition we targeted lies close to the HCS⁺ (J = 2 → 1) transition at 85.3479 GHz (Margulès et al. 2003), with a velocity separation of only −31.6 km s⁻¹, and the H₂S transition is relatively close to the ³⁴SO (J = 4₄ → 3₃) transition at 168.8151 GHz. At negative velocities with respect to the source systemic velocity, some c-C₃H₂ and H₂S absorption components – the presence of which is suggested by corresponding absorption lines of the other molecular species (mainly HCO⁺) – are blended with the emission lines of HCS⁺ and ³⁴SO. For these cases, we simultaneously fit the HCS⁺ and ³⁴SO emission lines with the c-C₃H₂ and H₂S absorption lines, respectively. In total, we have detected HCO⁺ absorption features in the spectra of all 14 sightlines listed in Table 5 and so velocities of HCO⁺ absorption components were used as a reference for identifying absorption line features in the six other molecular line transitions studied. A significant number of sightlines also have detectable absorption lines of HCN (12 sightlines), HNC (11 sightlines), C₂H (12 sightlines), and c-C₃H₂ (nine sightlines) transitions. CS and H₂S are only detected toward eight and six sources, respectively, because of the poorer S/N at the higher H₂S transition frequency or significant emission line contamination.

Figures 3–9 present the observed spectra, normalized with respect to the continuum flux and displayed as a function of υ_LSR Fits to the spectra, obtained with the extended CASA Line Analysis Software Suite (XCLASS, Möller et al. 2017), are overlaid in red. The shaded areas designate the velocity intervals of specific spiral arms, inter-arm regions, and unidentified foreground clouds or the envelope layers of dense molecular cloud associated with the continuum sources; their velocity intervals, defined by previous observational studies (see Paper I and references therein), are tabulated in Table 6. In emission, HCN (J = 1 ← 0) has three hyperfine components (F = 1 ← 1, F = 2 ← 1, and F = 0 ← 1) that are completely blended, leading to even broader observed line widths. In absorption, however, the narrower intrinsic line widths in diffuse and translucent clouds often permit all three hyperfine structure (hfs) components to be individually discerned. We see blended HCN hfs profiles in absorption toward some sightlines because several superposed foreground clouds have similar velocity ranges. C₂H (J = 1 ← 0) is another molecular transition with multiple hyperfine components. This line has six hfs components, with the two weakest components being well separated and each of the two brightest components being blended to the remaining two components. We defined the frequency of the brightest component (J = 3/2 ← 1/2, F = 2 ← 1, 87.3168 GHz) of C₂H as the rest frequency for purposes of computing the υ_LSR C₂H is found to be ubiquitous in the Milky Way, and thus it often traces multiple velocity components. HCO⁺ (µ_A = 3.90), HCN (µ_A = 2.984) and HNC (µ_A = 3.04) have much larger dipole moments than CO (µ_A = 0.110) and can therefore be detected in absorption far more easily than CO in low-density clouds.

3.2 Detected absorption line profiles

3.2.1 W3 IRS5, W3(OH), and NGC 7538 IRS1

The second quadrant sources W3 IRS5, W3(OH), and NGC 7538 IRS1 are located in the Perseus arm in the outer Galaxy. W3 IRS5 and W3(OH) harbor high mass young stellar objects in different evolutionary stages that belong to the W3 molecular clouds and H II region complex, while NGC 7538 IRS1 is the most prominent of several such sources in the NGC 7538 region. As in the host arm of the background sources, the Perseus arm, the sightlines toward these three sources are also aligned along the local arm where they cover a velocity range from approximately −16 km s⁻¹ to 7 km s⁻¹. In the spectra toward W3 IRS5 shown in the left panel of Fig. 3, three components in HCO⁺ absorption are detected at velocities of −20, −3, and 0.7 km s⁻¹, respectively, where the −20 km s⁻¹ component is the deepest one. Only the −20 km s⁻¹ component appears in HCN, C₂H, and c-C₃H₂. Toward W3(OH) (the middle panel of Fig. 3), we find three HCO⁺ components at velocities (−20, −2 and 0 km s⁻¹) similar to those seen toward W3 IRS5 and also notice an additional component at −10 km s⁻¹, not detected in the sightline to W3 IRS5. The deepest feature along this sightline is at 0 km s⁻¹, with that at −10 km s⁻¹ being the next deepest. These velocity components are also detected in the spectra of the six other species except for the −20 km s⁻¹ feature, which is not observed in the HNC and H₂S spectra.

Toward NGC 7538 IRS1, we only detect a single HCO⁺ component at −10 km s⁻¹, as shown in the right panel of Fig. 3. All the detected absorption components toward these three sightlines are associated with the local arm, except for the −20 km s⁻¹ component toward W3 IRS5. This −20 km s⁻¹ feature likely arises from diffuse clouds belonging to the Perseus arm rather than the envelope of the molecular cloud as C₂H and c-C₃H₂ absorption lines show a clear separation from the background emission. In addition, the spectra of CH, OH, OH⁺, O, C⁺, and ArH⁺ from the SOFIA HyGAL observations in Paper I all show absorption line dips around this velocity. The hydride, O, and C⁺ absorption lines show variations in absorption line profiles for W3(OH) and W3 IRS5, also seen here in the millimeter spectra.

Fig. 3 Observed spectra (black) and the XCLASS modeled spectra (red) in a $T_{\text{a}}^{*}/T_c$ scale, toward W3 IRS5, W3(OH), and NGC 753 8 IRS1 from left to right. The spectra in each panel correspond to HCO+, HCN, HNC, CS, H2S, C2H, and c-C3H2, from top to bottom. The shaded areas indicate velocity intervals of the local arm in cyan and the Perseus arm in gray. The υsys of the continuum sources are indicated using vertical dashed lines.

3.2.2 NGC 6334 I and DR21

NGC 6334 I and DR21 are in the vicinity of the solar neighborhood with heliocentric distances of 1.3 and 1.5 kpc, respectively. However, these sources reside in different spiral arms, namely the Sagittarius arm and the local arm, respectively. Toward NGC 6334 I (upper panel of Fig. 4), we find two distinct HCO⁺ absorption components at +7 km s⁻¹ and +14 km s⁻¹, respectively, of which the first is the most prominent one, while the latter has a significantly broader profile (Δυ ~ 8 km s⁻¹). HF (an excellent tracer of molecular gas, including CO-dark gas) absorption at 243 µm (van der Wiel et al. 2016), shows foreground clouds at +6 and +8 km s⁻¹ that are not considered to be physically associated to the NGC 6334 molecular cloud. The HCO⁺ absorption component at +7 km s⁻¹ is believed to arise from the same clouds in which HF is detected. The richness of molecular emission lines prohibits a convincing absorption line detection in the CS and H₂S spectral windows while the other species show an absorption feature close to the +7 km s⁻¹ velocity of HCO⁺.

Toward DR21 (lower panel of Fig. 4), we detected absorption features for all seven species, of which the two small hydrocarbons (C₂H, c-C₃H₂) show a broader line shape than the other species without a red-shifted emission wing indicating an outflow as traced by HCN, CS, and H₂S. The deepest absorption lines seen at +8.4 km s⁻¹ for all species originate from diffuse, extended gas surrounding the W75N cloud for which the majority of the emission is seen at +9 km s⁻¹ (Schneider et al. 2010).

3.2.3 HGAL0.55–0.85 and G09.62+0.19

HGAL0.55–0.85 is located in the Galactic Center region and shows broad emission wings in lines from the HCO⁺, HCN, and CS molecules. As seen in the upper panel of Fig. 5, only two narrow absorption components are found in the HCO⁺ spectrum at −7 and −10 km s⁻¹, respectively, in the blue-shifted HCO⁺ emission wing.

G09.62+0.19 lies in the Norma spiral arm near the expanding 3 kpc arm. In addition, the sightline crosses the Scutum-Centaurus and Sagittarius arms over a range of velocities from + 10 to +40 km s⁻¹. Our mm band survey detected three distinct HCO⁺ absorption features at +16, +23, and +69 km s⁻¹ as shown in the lower panel of Fig. 5 toward G09.62+0.19. The first two features have a large velocity shift from the systemic velocity of the embedded H II regions (−5−0 km s⁻¹), which is close to velocities of dense molecular cores (+2 to +5 km s⁻¹, Liu et al. 2017, 2020) belonging to the Scutum-Centaurus arm. For all other transitions except for CS and c-C₃H₂ which we fail to fit because of the broad line emission from the background source, only a single absorption component is detected at +23 km s⁻¹. The weak absorption feature at +69 km s⁻¹ only appears in HCO⁺ and does not match any identified spiral arm.

Fig. 4 Same as Fig. 3 but toward NGC 6334 I and DR21. The brown shaded areas indicate velocity intervals of the molecular cloud envelope layers or unidentified foreground clouds toward these sightlines.

Fig. 5 Same as Fig. 3 but toward HGALO.55–0.85 and G09.62+0.19. The brown and blue shaded areas indicate velocity intervals corresponding to the molecular cloud envelope layers or unidentified foreground clouds, and the Scutum-Centaurus arm, respectively.

Fig. 6 Same as Fig. 3 but toward G10.47 +0.03. The shaded areas indicate the velocity intervals of specific spiral arms (Sagittarius-Carina arm in magenta, Scutum-Centaurus arm in blue, inter-arm gas in orange, the GC/bar in yellow, and the 135 km s−1 arm located beyond the GC in blue-green).

3.2.4 G10.47+0.03

This background source lies in the inner Galaxy, behind the GC and the Galactic bar. Thus, several spiral arms pass through its sightline and they cause HCO⁺ absorption features spanning a wide velocity range from −28 to +179 km s⁻¹, while background emission ranges between +52 and +83 km s⁻¹, as shown in Fig. 6. Such widespread absorption line features are also detected in the hydrides (ArH⁺, o-H₂O⁺, OH⁺, and CH; Jacob et al. 2020), but the hydride absorption lines are broadly continuous, unlike what is seen in the HCO⁺ absorption line profiles, which shows well separated components in distinct velocity intervals. The millimeter absorption lines in the velocity interval between −28 and +52 km s⁻¹ originate from foreground clouds in inter-arm gas (−28 to +2.4 km s⁻¹), the near-side crossing of the Sagittarius arm (+3.2 to +20 km s⁻¹), and the Scutum-Centaurus arm (+20 to +52 km s⁻¹). Surprisingly, the inter-arm HCO⁺ absorption feature shows a similar absorption depth, $T_{\text{a}}^{*}/T_c$, when compared to absorption lines arising in the spiral arms. However, the HCO⁺ absorption lines belonging to the Scutum-Centaurus arm and the near-side of the Sagittarius arm display flat absorption dip profiles close to being saturated. Such broad features are also seen in the HCN spectra, while the spectra of the other species have mostly narrow absorption features. We notice that these HCO⁺ absorption line features cover similar velocities as the OH⁺line at 1033 GHz line (Jacob et al. 2020) but have much narrower widths. The absorption around 120 km s⁻¹ is likely related to diffuse gas in the 3 kpc arm and the Galactic bar (υ > +80 km s⁻¹), whereas the components at velocities greater than 120 km s⁻¹ are believed to be associated with the +135 km s⁻¹ spiral arm (Sormani & Magorrian 2015) located beyond the GC. Between these two velocity features, the HCO⁺ 154 km s⁻¹ feature is deeper than that belonging to the 3 kpc arm, while the deepest absorption component of OH⁺ is at 120 km s⁻¹ (Jacob et al. 2020). The 154 km s⁻¹ component identified in HCO⁺ is also detected in the spectra of HCN, HNC, C₂H, CS, and H₂S. However, the 120 km s⁻¹ feature is barely seen in HCN, CS, and C₂H partly due to emission line contamination. As a well known hot core source, G10.47+0.03 is rich in complex molecules (Widicus Weaver et al. 2017). For the H₂S and c-C₃H₂ spectra, we detect multiple, strong emission components that further complicates the assignment and fitting of absorption line features.

Fig. 7 Same as Fig. 3 but toward G45.07+0.13. The shaded areas indicate the velocity intervals of specific spiral arms (local arm in cyan and Sagittarius-Carina arm in magenta), and the molecular cloud envelope or unidentified foreground clouds in brown.

3.2.5 G45.07+0.13

This background source lies in the Sagittarius arm and has an outflow, causing a broad blue-shifted wing (Hunter et al. 1997) in the emission profiles of lines from the HCO⁺, HCN, and CS molecules. The absorption feature seen at 24 km s⁻¹ in the millimeter transitions, displayed in Fig. 7 is believed to belong to its host spiral arm spanning a velocity interval between 20 and 60 km s⁻¹. The conspicuous absorption component at 67 km s⁻¹ being red-shifted from the υ_sys (60 km s⁻¹) in HCO⁺, HCN, and HNC likely traces infalling foreground gas toward the continuum source as it is similar to that of the CS (2←1) absorption feature (Hunter et al. 1997) near 65–67.3 km s⁻¹ obtained from interferometric observations revealing infalling gas motion. In addition, we also detect weak absorption lines related to the local arm (0−20 km s⁻¹) at 1, 8, and 15 km s⁻¹ in the HCO⁺ spectrum.

Fig. 8 Same as Fig. 3 but toward G29.96−0.02, W43 MM1, and G31.41+0.31. The shaded areas indicate the velocity intervals of specific spiral arms (local arm in cyan, Sagittarius-Carina arm in magenta, Aquila-Rift in green), and the molecular cloud envelope or unidentified foreground clouds in brown.

3.2.6 G29.96−0.02, W43 MM1, and G31.41 +0.31

The sightlines toward these three background sources, located in the Scutum-Centaurus arm, are in a similar direction. Along the sightline toward G29.96−0.02 (left panel of Fig. 8), we detected broad, deep absorption features from −0.6 to +23 km s⁻¹ in the HCO⁺ spectrum, related to the Aquila Rift (Paper I), while multiple absorption components in the range from +49 to + 79 km s⁻¹ correspond to the near-side crossings of the Sagittarius spiral arm. All of these components are found in other millimeter transitions, except those originating in the Sagittarius arm, which are not detected in the H₂S, and c-C₃H₂ spectra at rms levels, 12.5 and 7.5 mK, respectively. The HCO⁺ absorption line at 8 km s⁻¹ has a significantly broader profile, while the absorption profiles of HNC, CS, and the two small hydrocarbons show multiple dips within the velocity interval of the Aquila-Rift region. Such multiple dips are also found in H I absorption spectrum (Fish et al. 2003) between −0.6 and +23 km s⁻¹, showing at least four well separate absorption components. All detected absorption features in these millimeter transitions have counterparts of absorption components in the spectrum of o-H₂Cl+ (Neufeld et al. 2015).

W43 MM1 and G31.41+0.31 are situated in the Scutum-Centaurus spiral arm and classified as hot cores (Nony et al. 2018; Widicus Weaver et al. 2017) which give rise to a variety of emission line features at millimeter wavelengths. Due to forests of emission lines blending into the absorption features, we only fit certain absorption features, causing that the model fits to some of the absorption features have greater uncertainties others. HCO⁺ absorption features toward W43 MM1 (the middle panel of Fig. 8) appear intermittently from +1 to +85 km s⁻¹ and among them, the absorption components with a dip at 11 km s⁻¹ traces diffuse gas from the Aquila Rift. Some of the HCO⁺ absorption features within this velocity range partly correspond to the near-side crossing of the Sagittarius arm (roughly +24 to +50 km s⁻¹) and are possibly related to local diffuse gas from its host spiral arm, the Scutum-Centaurus arm (+50 to +100 km s⁻¹) with υ_sys = +98 km s⁻¹. It is, however, not clear whether all the absorption features arise in the Scutum-Centaurus arm or partly related to inter-arm gas or to some other region.

Several absorption lines in the observed transitions are detected along the sightline toward G31.41+0.31 (right panel of Fig. 8), but we have only fit components associated with the local arm (0−20 km s⁻¹) because its velocity range is less affected by emission contamination. In the HCO⁺ spectra, both absorption components at 7 and 13 kms have a similar depth, but for other molecular species, the features at 7 km s⁻¹ are much weaker than those at 13 km s⁻¹.

3.2.7 G19.61−0.23 and G32.80+0.19

These two sources are inferred to lie in the first quadrant of the Milky Way in the Perseus and Sagittarius-Carina spiral arms at distances of 12.6 and 9.7 kpc respectively. Such large distances allow several spiral arms to be intercepted by the sightlines, resulting in multiple absorption components in the molecular spectra observed toward these sources. Along the sightline toward G19.61–0.23 (upper panel of Fig. 9), the HCO⁺ spectrum shows absorption features spanning a wide velocity range from –7 to 130 km s^–1. Several features absorb parts of the emission line arising from the molecular gas related to the background continuum source, which drives an outflows that produces broad red- and blue-shifted emission wings for optically thick transitions (Furuya et al. 2011). The HCO⁺ absorption dip at 46 km s^–1 appears at the velocity of an absorption component of C¹⁸O (3←2) (Furuya et al. 2011), observed with the Submillimeter Array (SMA), implying infalling gas in the low-density outer layers of the central core, which may be interpreted as self-absorption in the background source. On the other hand, another prominent feature at 51 km s^–1 in the absorption spectrum of HCO+ is absent in the ¹³CO (3←2) absorption spectrum, unlike that at 46 km s^–1. Prominent absorption components at 51 km s^–1 and also at higher velocities, 71, 100, and 119 km s^–1, have corresponding HI absorption features (Kolpak et al. 2003). Absorption features at these four velocities appear in millimeter transitions and, therefore, seem to be arising in intervening clouds along the sightline. The first two features at 51 and 71 km s^–1 are associated with the near- and far-side crossings of the Sagittarius spiral arm (spanning from ~ 35 to 74 km s^–1), and the latter, at 100 and 119 km s^–1, are believed to be located on the 3 kpc arm. We also find red-shifted absorption features with respect to the v_sys of 41.8 km s^–1 for this source and assume that these absorption lines are unrelated-foreground clouds as HI absorption line components are also detected in this velocity range (Kolpak et al. 2003). The HCN, HNC, C₂H, and c-C3H₂ lines show similar absorption features as the HCO⁺ spectrum. In the CS and H₂S spectra fewer absorption features are identified, for H₂S spectrum this is caused by its ragged baseline, possibly the result of a number of emission lines.

Toward G32.80+0.19 (lower panel of Fig. 9), for all seven species, we detect widespread absorption features spanning a broad range of velocities from 2 to 110 km s^–1 with the v_sys of 15 km s^–1 and emission spanning 1–28 km s^–1 from the background source. Apart from the red-shifted components with respect to v_sys, the blue-shifted absorption features in the HCO⁺, HCN, C₂H, and c-C₃H₂ spectra are detected in the velocity interval between 4 and 15 km s^–1 which is close to the velocity range of the Aquila-Rift. These absorption lines are possibly associated with foreground cloud components. As seen in the HCO⁺ spectra toward the other background continuum sources, the HCO⁺ spectrum toward G32.80+0.19 clearly shows absorption features that are broader than those of the other six species. Absorption features in the velocity interval between 58 and 120 km s^–1 trace the Scutum-Centaurus spiral arm and show four prominent dips at 70, 81, 85, and 89 km s^–1. The deepest dip for HCO⁺, HCN, HNC, and the two small hydrocarbons are at 89 km s^–1. On the other hand, CS and H₂S show the deepest dips at 85 km s^–1. Absorption in the $N_{{\text{k}}_{\text{a}},{\text{k}}_{\text{c}}}=1_{1,0}\leftarrow 1_{1,1}$ line of H₂CO at a frequency of 4.83 GHz (wavelength 6.2 cm) is observed by (Araya et al. 2002) against the radio continuum emission of the same background source at similar velocities as the CS and H₂S line with its deepest absorption appearing at ~85 km s^–1. The Sagittarius arm and the Aquila Rift also cross this sightline and correspond to velocity ranges of 15–57 km s^–1 and 5–6 km s^–1, respectively. The red-shifted absorption features with respect to the source’s systemic velocity at 15 km s^–1 could arise from low-density diffuse gas associated with the molecular clouds of the continuum source as the H₂CO absorption features (Araya et al. 2002) correspond to the features seen in the HCO⁺, C₂H, and c-C3H₂ spectra. However, as its velocities correspond to Aquila Rift as well.

Fig. 9 Same as Fig. 3 but toward G19.61–0.12 and G32.80+0.19. The shaded areas indicate velocity intervals of specific spiral arms (Aquila-Rift in green, Sagittarius-Carina arm in magenta, Scutum-Centaurus arm in blue, inter-arm gas in orange, the GC/bar in yellow), and the molecular cloud envelope or unidentified foreground clouds in brown. Toward G32.80+0.19, the insert in the HCN panel zooms in on the HCN absorption features on top of the emission within a velocity window between –10 and 30 km s–1.

3.3 CO emission counterparts

As described in the previous section, the millimeter absorption components of simple molecules detected in this survey generally have narrower line features than those those of the hydride molecular ions (e.g., OH⁺ or ArH⁺, Schilke et al. 2014; Jacob et al. 2020), whose submillimeter absorption spectra have continuous broad line profiles over wide velocity ranges. Such narrow spectral line shapes might imply that the millimeter absorption lines of neutral species and HCO⁺ trace denser gas than that traced by hydride molecular ions. To investigate whether any of the CO emission from dense molecular clouds is detected at the velocities of HCO⁺ absorption, we utilized archival data from available CO emission surveys: for ¹³CO (2→1) data mapped with an angular resolution of 30”, the Structure, Excitation and Dynamics of the Inner Galactic Interstellar Medium (SEDIGSM, Schuller et al. 2021) program obtained with the SHeFI single-pixel instrument at the 12 m diameter Atacama Pathfinder Experiment submillimeter telescope; for ¹³CO (1→0) data obtained with an angular resolution of 46” in the inner Galaxy, the Boston University-FCRAO Galactic Ring Survey (GRS, Jackson et al. 2006) that used the SEcond QUabbin Optical Imaging Array (SEQUOIA) at the Five College Radio Astronomy Observatory 14 m telescope; and for ¹²CO (1→0) and ¹³CO (1→0) observed with an angular resolution of 20” the FOREST Unbiased Galactic plane Imaging survey performed with the Nobeyama 45 m telescope (FUGIN, Umemoto et al. 2017) and the telescope’s four-beam, dual-polarization, sideband-separating SIS receiver. Figure 10 displays the CO emission spectra toward eight of our sources obtained from the surveys mentioned above; they are G09.62+0.19, G10.47+0.03, G19.61–0.23, G29.96–0.02, W43 MM1, G31.41+0.31, G32.80+0.19, and G45.07+0.13. The upper panels show the ¹²CO (1→0) emission (in black) and ¹³CO (1→0) or (2→1) (in red) on the main–beam temperature (T_mb) scale, and the lower panels show HCO⁺ absorption spectra (in blue) normalized relative to the continuum. The vertical dotted lines indicate representative absorption dips. For G09.62+0.19, only the ¹³CO (2→1) data from the SEDIGIM survey is available, and G10.47+0.03 is observed only in the FUGIN survey, but not the GRS survey. Since the rms noise level of the FUGIN ¹³CO (1→0) data is higher than that of the GRS survey, we mainly use the ¹³CO (1→0) data of the GRS survey for the remaining sightlines observed in our survey. After extracting the CO spectrum within an area covered by a 20 “ radius, we resampled the spectral data to 0.6 km s^–1 velocity bins that are 2.4–6 times broader than the original spectral resolutions of the SEDIGIM and GRS surveys. For the FUGIN data, we smoothed the spectral channel resolution to 1.3 km s^–1 to improve S/N levels.

In Fig. 10, the most prominent absorption features have CO emission counterparts while weak absorption lines tend be not to have a detection of CO emission except for the absorption features around 0–20 km s^–1 toward G45.07+0.13. In addition, not all deep absorption features have clear CO emission lines at their velocity ranges. For some velocity components toward some sources, CO emission features have different intensities, although the HCO⁺ absorption line depths are comparable. For example, toward G10.47+0.03, the depth of the absorption feature at around 154 km s^–1 is similar to that of the absorption components spanning 0–50 km s^–1, but its CO emission counterpart is weaker. Frequently, compared to HCO⁺ with narrow line profiles, broad HCO⁺ absorption features tend to have CO emission counterparts.

4 Analysis

4.1 Line parameter determination with XCLASS

The spectral lines observed were modeled using the extended CASA Line Analysis Software Suite (XCLASS³, Möller et al. 2017) by solving the 1-dimensional radiative transfer equation with the assumption of local thermal equilibrium (LTE) for an isothermal source. The myXCLASSFit program computes synthetic spectra, by fitting the spectral lines with Gaussian profiles, thereby ensuring that opacity effects on the line shapes are properly taken into account. The fit is performed using optimization package MAGIX (Möller et al. 2013), which provides an interface between the input codes and an iterating engine. It minimizes the deviation between the modeled outputs from the observational data. Molecular properties (e.g., Einstein A coefficients, partition functions, etc.) are taken from an embedded SQLite database containing entries from the Cologne Database for Molecular Spectroscopy (CDMS, Müller et al. 2001, 2005) and the Jet Propulsion Laboratory database (JPL, Pickett et al. 1998) in its Virtual Atomic and Molecular Data Center (VAMDC, Endres et al. 2016) implementation, along with an extended set of partition function calculations. The parameter set fitted for each absorption line component consists of the excitation temperature (T_ex), the total column density (N_tot), the line width (Ay), and the velocity offset (v_off) from the systemic velocity. The column density per velocity interval, dN/dv for each velocity channel, i, is related to the optical depth, τ_i, (Paper I) by $${\left(\frac{\text{d}N}{\text{d}\upsilon }\right)}_i=\frac{8\pi v^3}{c^3}\frac{Q\left(T_{\text{ex}}\right)}{g_{\text{u}}{A}_{\text{ul}}}\frac{\exp \left(E_{\text{u}}/k{T}_{\text{ex}}\right)}{\exp \left(hv/k{T}_{\text{ex}}\right)-1}{\tau }_i,$$(1)

where E_u is the energy of the upper state for the selected transition, g_u is the upper state degeneracy, and v is the frequency of a molecular transition. The quantity A_ul is the Einstein coefficient for spontaneous emission, and Q(T_ex) and k are the partition function and Boltzmann constant, respectively. For the absorption components, we adopt a fixed excitation temperature for all observed molecular transitions equivalent to the cosmic microwave background temperature of 2.73 K. This is motivated by the high dipole moments of most of the species, which lead to critical densities for the observed transitions that lie a few orders of magnitude above the typical number density of hydrogen molecules ($n_{{\text{H}}_2}$) in translucent clouds of a few hundred cm^–3 (e.g., Snow & McCall 2006; Gerin et al. 2016). Thus, the excitation temperature of these transitions are determined by the 2.73 K cosmic background radiation field. XCLASS offers various algorithms to find the best-fit parameters by minimizing the x² value, and in this work, we used the Levenberg-Marquardt algorithm. In addition, in the fitting procedure, all the hfs splitting transitions of HCN and C₂H are taken into account, and the fitting deconvolves the hfs of these molecular transitions. We note that we only consider the ortho transitions of H₂S and c-C₃H₂, and thus the derived column densities of these molecules only apply to their ortho species, not to the sum of their ortho and para species. The spectral line profiles observed are the combination of emission and absorption features. We have performed simultaneous fitting of the emission and absorption lines to determine the background for the absorption lines and derive accurate physical properties for the absorption components. However, since the focus of this paper is the absorption system (rather than deriving reliable physical parameters of the emission lines), we do not present the fit parameters of the emission lines. For uncertainties of column densities derived here, we perform the error estimation by sampling a posterior distribution of the optical depths $\left(\propto \ln \left(T_{\text{a}}^{*}/T_{\text{c}}\right)\right)$ The sampling was performed using XCLASS fits to multiple realizations of sample spectra that were generated by adding independent pseudorandom noise to the observed spectra. For the XCLASS fits, as done to the main fitting for the original data sets, we also fit emission and absorption components simultaneously on the noise–added spectra in order to take into account variability of the posterior distributions caused by emission components.

Figures 11 and A.1–A.5 display the column density per velocity interval, dN(X)/dv, determined for all seven species studied and toward all sources, with uncertainties indicated as blue shaded areas. The gray parts indicate the velocity ranges of the emission lines that partly overlap with the absorption lines. As a result, the column densities of the absorption components within the gray velocity ranges might have higher uncertainties than those implied by the blue shaded areas because of additional errors that may arise when emission components are simultaneously fitted with the absorption components.

Fig. 10 Spectra lines of CO and HCO+ toward the eight sightlines. The upper panel for each plot shows 12CO emission lines (1 → 0) in black, obtained from the FUGIN survey (Umemoto et al. 2017), and 13CO (1 → 0) emission lines in red from the GRS survey (Jackson et al. 2006). For only G09.62+0.19, the 12CO (2 → 1) is taken from the SEDIGISM survey (Schuller et al. 2021). The lower panel for each plot shows absorption and emission lines in HCO+ spectra in blue from this survey. In the both panels, the vertical dotted lines indicate significant absorption features.

4.2 Principal component analysis

Principal component analysis (PCA) has been used to investigate differences and similarities in the distributions of multiple species detected in absorption spectra (e.g., Sect. 4.2 in Neufeld et al. 2015). Here, we carried out PCA of our W3(OH) data for 13 species (HCO⁺, HCN, HNC, CS, H₂S, C₂H, c-C₃H₂, CH, OH, O, C⁺, H₂O⁺, and OH⁺) and for W3 IRS5 for 11 species (same as for W3(OH) except with the addition of ArH⁺ and the omission of HNC, CS, and H₂S). The lattermost six species listed for W3(OH) were observed with SOFIA (Paper I). The SOFIA results published to date provide spectra of these species toward three sightlines, W3(OH), W3 IRS5, and NGC 7538 IRS1. Since only HCO⁺ was detected toward NGC 7538 IRS1 in the present work, this sightline was not considered in our PCA analysis. Moreover, the SH absorption features detected with SOFIA toward these sightlines are all associated with the background continuum source; toward them foreground absorption is detected. Therefore, SH is not included in this PCA analysis. Instead of using transmission $\left(T_{\text{a}}^{*}/T_{\text{c}}\right)$ or optical depth spectra, we used column densities, dN/dv, as the input to the PCA, thereby minimizing contributions from the emission features and avoiding complications caused by hfs. All the column density spectra were computed with a common channel width of 0.8 km s^–1. As discussed further below, we also accounted for uncertainties in the derived column densities, which can significantly affect the results of the PCA.

Prior to performing the PCA analysis, standardization is imperative: this involves rescaling the spectra so that their variations have a mean of zero and a variance of unity. PCA involves writing the column density for each species, i, as a linear combination of orthogonal eigenfunctions (a.k.a. principal components), f_j(v) $$N_i\left(\upsilon \right)=a_i+b_i{\displaystyle \sum _{j=1}^k{C}_{ij}{f}_j\left(\upsilon \right),}$$(2)

where a_i and b_i and C_ij are coefficients, and k is the number of species included (13 for W3(OH) or 11 for W3 IRS5). The C_ij obey a normalization constraint, ${\text{Σ}}_{j=1}^k{C}_{ij}^2=1$ To examine the reliability of the PCA results, uncertainty estimates are essential. Therefore, we made use of 1000 realizations obtained by random sampling within the column density probability distribution function and then for each realization of the 1000 realizations, we created a data set containing PCA results for all used species from the each PCA performance toward W3(OH) and W3 IRS5, respectively. From these multiple realizations, we obtained a distribution of the PCA results for each species. Using the posterior distributions for all considered species from the PCA performances for the 1000 realization, we obtained 2σ confidence intervals for all the PCA results; these are included in the results presented in the following section.

In Figs. 12 and C.1, the left panels show eigen spectra of principle components with percentage of variances and uncertainties (2σ), toward W3(OH) and W3 IRS5, respectively. As the first component (f₁(v), labeled PC-1) accounts for more than half of the variance for each source, its profile resembles the column density distributions of most of the species included in the PCA. However, there are significant differences between the W3(OH) (Fig. 12) and W3 IRS5 (Fig. C.1) sightlines in regard to the fraction of the variance accounted for by each component. For W3(OH), PC–1 and PC–2 account respectively for 71.5±2.6% and 13.4±2.0% of the total variance, Toward W3 IRS5, PC-2 accounts for a more significant fraction of the total variance, 22.6±2.0%, and PC-1 accounts for only slightly more than half (56.9±2.2%) of the total. The right panel of Figs. 12 and C.1 represent scaled channel-wise column density spectra as black curves for the observed species (for W3(OH), HCO⁺, HCN, HNC, CS, H₂S, C₂H, c-C₃H₂, CH, OH, O, C⁺, H₂O⁺, and OH⁺; for W3 IRS5, HCO⁺, HCN, C₂H, c-C₃H₂, CH, OH, O, C⁺, H₂O⁺, OH⁺, and ArH⁺). The column density spectra reproduced (red and blue dotted lines) by summing the first three terms in the expansion, for most of the species but for C⁺, H₂O⁺, OH⁺, and ArH⁺ by summing up to the first five terms: C_i1 f₁(v), C_i2 f₂(v) and C_i3 f₃(v), and additionally C_i4 f₄(v) and C_i5f₅(v) for the mentioned species above. For both sources, the first three principal components account for ~90% of the total variance, and the sum of their contributions provides a reasonable approximation to the column densities of the observed species.

Fig. 11 Channel-wise column density spectra (dN/dv) as a function of velocity toward G29.96–0.02 and G32.80+0.19. The dN/dv in each panel shows HCO+, HCN, HNC, CS, H2S, C2H, and c-C3H2 from top to bottom. The gray shaded area indicates velocity range of the HCO+ emission lines. The blue shaded regions represent 2σ confidence intervals for the derived column densities (per velocity interval).

5 Discussion

5.1 Correlations between species for W3(OH) and W3 IRS5

Figures 13 and 14 show the coefficients C_ij in the PCA expansion for each observed species. These are sometimes referred to as h-plots (e.g., Ungerechts et al. 1997). Figure 13 shows the coefficients, C_i1 and C_i2, for the first and second components, PC-1 and PC-2, obtained for W3(OH) (left panel) and W3 IRS5 (right panel), while Fig. 14 shows the coefficients for the second and third terms in the expansion. Each colored vector corresponds to a different species as indicated, and the normalization condition for the C_ij coefficients implies that all the plotted vectors must lie within the unit circle (black). Colored ellipses indicate the uncertainties (corresponding to 2σ confidence intervals) for each vector.

The angle (θ) between any two vectors (corresponding to two different species) indicates how well the two species of a given pair are correlated with each other. The similarity between any two vectors may be characterized by the cosine of the angle between the vectors (known as cosine similarity); cos θ = A·B/||A|| ||B||. Figures 15 and 16 present similarity coefficients estimated for each pair of species, with cos 9 represented as percentages; acute angles in the h–plots indicate a strong similarity (~100% as noted in Figs. 15 and 16), orthogonal (90°) angles mean no similarity (0%, i.e., lack of correlation), and opposite vectors with an angle of 180° represent negative similarity (–100%, i.e., anticorrelation). Although the sets of species detected are not exactly identical toward these sightlines, the relative positions of the vectors appear to be similar for most of the species, as shown in Fig. 13. In addition, we note that when we recompute the vector positions for the same set of species (HCO⁺, HCN, C₂H, c-C₃H₂, CH, OH, O, C⁺, H₂O⁺, and OH⁺) for both sightlines, the relative positions stay almost the similar as shown as in Figs. 13 and 14, and the PCA h-plots for the recomputed results are presented in Fig. D.1. From these plots, which present the PCA results, we observe three notable trends summarized below.

First, the molecular ions OH⁺, H₂O⁺, and ArH⁺ and C⁺ lie away from neutral molecular species HCN, HNC, CS, H₂S, C₂H, and C-C₃H₂ and HCO⁺ in the h-plots. The first three mentioned molecular ions and C⁺ are considered to be tracers of gas with small molecular fractions, especially ArH⁺, which traces gas with a molecular fraction ≲10^–3 (Schilke et al. 2014; Jacob et al. 2020). In Figs. 15 and 16, the similarity coefficients between the group of hydride ions and the group of neutral molecules show that these two groups are poorly correlated (cooler colors). On the other hand, all the species within each group have very similar distributions, as shown by the warm colors in the heat maps. Clearly, HCO⁺ traces the same gas as that traced by neutral molecules, showing correlation coefficients higher than 92% in the PC-1 versus PC-2 heat map.

Second, the sulfur-bearing species, CS and H₂S, lie close to the neutral molecular species rather than to the molecular ions in the h-plots, and exhibit significant similarities as shown in Figs. 15 and 16. Such a pattern is also found for other sight-lines, W31C and W49N (Neufeld et al. 2015). In agreement with Neufeld et al. (2015), we find the abundances of these two sulfur-bearing species to peak in regions of larger molecular fraction rather than in regions traced by C⁺ and the hydride ions OH⁺, H₂O⁺, and ArH⁺.

Third, the vectors for CH and OH lie very close to each other in all the h-plots shown in Figs. 13 and 14. Their correlation coefficients exceed 99.9% (Figs. 15 and 16). In addition, these molecules lie reasonably close to oxygen in the h-plots. The vectors corresponding to these three species lie between the neutral and ion molecules in both the h-plots, with the vectors for CH and OH located closer to those for the other neutral species and the vector for O located closer to those for the ionized species. CH is considered a good tracer for H₂ because it is present in gas dominated by both atoms and molecules (Gerin et al. 2010; Wiesemeyer et al. 2018; Jacob et al. 2019). On the other hand, the vector for O tends to lie closer to those of the molecular ions that are found in gas with small molecular fractions.

Fig. 12 Left: Eigen spectra of thirteen principal components with percentage of variances as well as uncertainties (2σ), toward W3(OH). Right: scaled channel-wise column density spectra for the thirteen species (HCO+, HCN, HNC, CS, H2S, C2H, c-C3H2, CH, OH, O, C+, H2O+, and OH+) as a function of vLSR. Black curves represent the observational data, and red dotted curves are the spectra reproduced with only the first three principal components (PC-1, PC-2, and PC-3). For C+, H2O+, and OH+, the reproduced spectra indicated by blue dotted curves include one or two more PCs, i.e., PC-4 and PC-5.

Fig. 13 Variable correlation circle plots for the first and second PCs toward W3(OH) in the left panel and W3 IRS5 in the right panel. The solid straight lines close to the unit circle imply PC-1 and PC-2 contain the most information about the variables. Different colors are used to denote the different species analyzed. Each colored ellipse is a 2σ confidence interval for the uncertainty of the PCA results for the corresponding species.

Fig. 14 Same as Fig. 13 but for the second and third PCs (PC-2 and PC-3) toward the same sources, from left to right.

Fig. 15 Cosine similarities showing correlation between two pairs of species in the circle plots for PC-1 versus PC-2 toward W3(OH) (top) and W3 IRS5 (bottom).

Fig. 16 Cosine similarities showing correlation between two pairs of species in the circle plots for PC-2 versus PC-3 toward W3(OH) (top) and W3 IRS5 (bottom).

Fig. 17 Comparisons of column densities in 0.8 km s–1 velocity channel bins for seven molecular species; (a) HCN versus HCO+, (b) HNC versus HCO+, (c) C2H versus HCO+, (d) c-C3H2 versus HCO+, (e) CS versus HCO+, and (f) H2S versus HCO+. The color codes correspond to specific spiral arms (local arm in cyan, Perseus arm in black, Aquila-Rift in blue, Sagittarius-Carina arm in magenta, Scutum-Centaurus arm in green, inter-arm regions in orange). All symbols without black edges indicate upper limits for nondetections, while the data points above the detection threshold are marked with black edges. In addition, the blue-green colored points indicate clouds that belong to the 135 km s–1 arm located beyond the Galactic center, toward G10.47 + 0.03. The black dotted lines represent the median value of the column density ratio in each panel. Uncertainties in the derived channel-wise column densities are presented as error bars. The red lines present a best-fit taking into account uncertainties of column densities. The gray areas are 2σ confidence interval for the best fit (red lines) with errors.

5.2 Column densities and abundances

In Fig. 17, we compare channel-wise column densities for all sightlines – except for NGC 7538 IRS1 and HGAL0.55–0.85, toward which only HCO⁺ is detected – to investigate whether the column densities show a linear relationship and whether there is any noticeable variation associated with specific spiral- or inter-arm regions. Due to high noise levels and contamination by emission lines, we have fewer detections for H₂S and CS. To obtain a reasonable number of data points required for reliable statistical results, we constrain the detection thresholds of their column densities to the 1.5 rms and 2 rms levels for H₂S and CS, respectively, while for the remaining five molecules, we adopt a 2.5 rms threshold to mitigate uncertainties caused by poor sensitivity.

The comparison of dN(HCN)/dv and dN(HCO⁺)/dv in Fig. 17a shows the best correlation, with a Pearson correlation coefficient (r) of 0.81. dN(C₂H)/dv in Fig. 17c has the second-best correlation with dN(HCO⁺)/dv, r = 0.78: both these values differ from zero at a very high level of statistical significance. Along the sightlines toward extragalactic sources, both HCN and C₂H also show such good correlations and are considered to be proxies for the total column density of H₂ (Liszt & Lucas 2001; Lucas & Liszt 2000). In Figs. 17b,d, dN(HNC)/dv and dN(c-C₃H₂)/dv show moderate correlations (r = 0.66–0.71) with dN(HCO⁺)/dv. In contrast, the two sulfur-bearing molecules appear to be less correlated (r = 0.45–0.62) with dN(HCO⁺)/dv, as shown in Figs. 17e,f. On the other hand, all the species show better correlations between the same chemical families as seen in the subplots of Fig. 18, with correlation coefficients which are 0.85 for (a) dN(HCN)/dv versus dN(HNC)/dv 0.79 for (b) dN(C₂H)/dv versus dN(c-C₃H₂)/dv and 0.77 for (c) dN(CS)/dv versus dN(H₂S)/dv Such strong correlations between the same chemical families (HCN and HNC, C₂H and c-C₃H₂, as well as CS and H₂S, in Fig. 18) have also been found in other diffuse and translucent clouds in the galactic plane and the solar neighborhood (Lucas & Liszt 2000, 2002; Liszt & Lucas 2001; Gerin et al. 2011; Godard et al. 2010; Neufeld et al. 2015).

In Figs. 17 and 18 the black dotted straight lines have a slope that represents the average column density ratio between any two given species. The red solid lines are the best fits to the data (only including the data points above the detection thresholds), including column density uncertainties, shown as error bars on the plots. The gray areas represent the 2σ confidence interval of the best-fit uncertainties. These uncertainties are obtained by resampling the data points and then iteratively fitting the resampled data sets. Comparing dN(HCO⁺)/dυ versus dN(HCN)/dυ we find that the median value and the best-fit agree fairly well. For the other cases, comparing different chemical groups, the best fit lines are not as steep as the lines representing the median. Such discrepancies become significant when comparing sulfur-containing molecules (CS and H₂S) with HCO⁺, shown in plots e and f of Fig. 17 since their relationships are weakly correlated. In addition, each color represents a different spiral-arm or intermediate arm region, or an unassigned foreground clouds, as tabulated in Table 6. For HCN, HNC, and the two small hydrocarbons, there is no apparent difference in column densities between clouds associated with the different environments. However, in panel e of Fig. 17 for CS, the cloud components belonging to the 135 km s⁻¹ arm, marked in blue-green color, have higher dN(CS)/dυ compared to the other spiral arms that have dN(HCO⁺)/dυ ≈ 1–9 × 10¹¹ cm⁻² km⁻¹ s.

In panel b of Fig. 18, the two small hydrocarbons, have a nonlinear relationship for values of dN(C₂H)/dυ < 1 × 10¹³ cm⁻² km⁻¹ s, which plateaus as dN(c-C₃H₂)/dυ increases (≈1–4 × 10¹¹ cm⁻² km⁻¹ s). As dN(C₂H)/dυ increases beyond the inflection point from ≈1 × 10¹³ cm⁻² km⁻¹ s to higher C₂H column densities, the column densities of these small hydrocarbons follow a linear relationship. Taking into account fitting uncertainties, the flat slope between the column densities of the two small hydrocarbons at lower values of N(C₂H) remains constant.

Figure 19 shows kernel density estimate (KDE) plots to examine distributions of channel-wise column density ratios. With the KDE method the probability density function of sample data can be estimated based on kernels as weights. KDE provides smooth profiles of the density, unlike histograms. Here we used a Gaussian kernel placed on each ratio data point as marked by the short vertical lines (in green, blue, and orange colors). The KDEs, shown as solid curves, are the sum of all kernels at each column density ratio. The solid and dashed vertical lines are median and mean values, respectively, of the distributions. The values for the median and mean as well as the standard deviations (SDs) are listed in Table 7. We compare the values with ratios obtained from previous absorption line studies (Lucas & Liszt 2000, 2002; Godard et al. 2010; Gerin et al. 2011; Neufeld et al. 2015), which are marked by black and gray bars. From this work we get mean ratios of 1.78, 0.49, and 0.27 for N(HCN)/N(HCO⁺), N(HNC)/N(HCO⁺) and N(HNC)/N(HCN), respectively. The mean ratios of N(HCN)/N(HCO⁺) (Fig. 19a1) and N(HNC)/N(HCO⁺) (Fig. 19a2) are very similar to values from the previous studies, while the mean ratio of N(HNC)/N(HCN) (Fig. 19a3) is slightly higher than that derived by Liszt & Lucas (2001) and Godard et al. (2010) of (0.21 ±0.71) but within the error range. The median N(HNC)/N(HCN) ratio of 0.22 from this survey agrees well with the other studies. According to Liszt & Lucas (2001), a small N(HNC)/N(HCN) ratio such as 0.2 is expected to indicate warmer gas at higher A_v or denser gas conditions. In addition, this ratio distribution is very similar to the distribution of HNC/HCN, between 0.01 and 1.0, toward star-forming regions (e.g., Graninger et al. 2014) and Orion-KL/the OMC regions (e.g., Schilke et al. 1992; Hacar et al. 2020; HNC/HCN ~ 0.013–0.2). Toward some sightlines, N(HNC)/N(HCN) ratios are between 0.2 and 1.0. This range might imply that the observed HCN and HNC trace warmer regions and/or inner parts of diffuse molecular clouds since the high ratio of these two molecules are found toward TMC-1 (ratio of 1, Ohishi et al. 1992).

The mean ratios of the column densities of C₂H and c-C₃H₂ to N(HCO⁺) (Figs. 19b1,b2) and N(C₂H)/N(c-C₃H₂) (Fig. 19b3) are 19.81, 0.57, and 30.26. The mean value of the column density ratios of the two small hydrocarbons agrees well with previously measured values of 27.7±0.8 and 28.2±1.4 from Lucas & Liszt (2000) and Gerin et al. (2011), as shown in Fig. 19b3. For N(CS) versus N(HCO⁺), N(H₂S) versus N(HCO⁺) and N(CS) versus N(H₂S), the mean ratios are 1.99, 2.07, and 0.73, respectively. Like other species, these two sulfur-containing molecules have mean ratios greater than their median values (Figs. 19c1,c2,c3, and Table 7). The previously measured mean ratios of 2±1 for N(CS)/N(HCO⁺) (Lucas & Liszt 2002) and 0.32–0.61 for N(CS)/N(H₂S) (Neufeld et al. 2015) come very close to the measurements obtained here.

The detected absorption features of simple molecular species studied in this work have different velocity components, and some of them have CO emission counterparts, shown in Fig. 10. Therefore, to characterize the properties of individual diffuse and translucent foreground clouds, we integrated column densities over given velocity intervals to identify individual cloud components and list the average column densities for all 14 line-of-sight sources in Tables 8 and B.1. Figure 20 shows the column densities (upper and middle image) of HCN, HNC, C₂H, c-C₃H₂, CS, and H₂S and column density ratios (lower panel) as a function of N(H₂). The H₂ column density is derived from N(HCO⁺) using a HCO⁺ abundance of 3 × 10⁻⁹ relative to H₂ (N(H₂) = N(HCO⁺)/3 × 10⁻⁹) (Lucas & Liszt 2000; Liszt et al. 2010) for N(HCO⁺) < 2.8 × 10¹² cm⁻², 2 × 10⁻⁸ (N(H₂) = N(HCO⁺)/2 × 10⁻⁸) for N(HCO⁺) > 9.4 × 10¹³ cm⁻², and an interpolated value between these two ranges of N(HCO⁺), log(N(H₂)) = log(N(HCO⁺))× 1.64, because N(HCO⁺) and N(H₂) does not follow a linear correlation in regions with higher H₂ column density (Thiel et al. 2019). Visual extinctions of 1 and 5 are marked with vertical blue dotted lines and estimated using A_v (mag) = N(H₂)/(9.4 × 10²⁰ cm⁻²) (Thiel et al. 2019). In Fig. 20, symbols of the same color indicate foreground clouds in the same direction, and the black diagonal lines represent lines of constant abundance for each individual molecular species presented. We exclude the cloud component in the velocity range between 9.0 and 20.2 km s⁻¹ for G09.62+0.19 as its extremely large N(HCO⁺) value of 9.2 × 10¹⁴ cm⁻² indicates that the component does not originate from either diffuse or translucent clouds.

On the left-hand side of Fig. 20, N(HCN) and N(HNC) increase as N(H₂) (A_v) increases, but slightly nonlinearly. In particular, the HCN abundance increases briefly relative to H₂ at N(H₂) ≳ 10²¹ cm⁻², regions considered to be translucent clouds. Liszt & Lucas (2001) also reported such nonlinear relationships of the column densities of CN-bearing molecules. They show a rapid increase in abundances of both the CN-bearing molecules detected toward sightlines with N(HCO⁺) ≳ 10¹² cm⁻² equivalent to N(H₂) ~ 0.3–0.5 × 10²¹ cm⁻² by assuming an abundance of 3 × 10⁻⁹ relative to H₂, against extra-galactic continuum sources. The lower-left panel shows the column density ratios of HCN and HNC as a function of N(H₂), and these ratios tend to increase slightly toward higher molecular hydrogen column densities, tracing higher visual extinction regions of molecular clouds.

As expected, in the middle plots of Fig. 20, the column densities of the two small hydrocarbons (C₂H and c-C₃H₂) show tight linear correlations with N(H₂), and their abundance varies only a little across different environments from diffuse (A_v < 1) gas to dense molecular gas (A_v > 5), through translucent molecular gas regions in between. The C₂H abundance measured here lies in an approximate range from 10⁻⁸ to 10⁻⁷, while that of c-C₃H₂ is pretty much within 10⁻⁹−10⁻⁸. These abundances relative to H₂ agree well with the X(C₂H) ~ 4–7 × 10⁻⁸ (Lucas & Liszt 2000; Gerin et al. 2011) and X(c-C₃H₂) ~ 2–3 × 10⁻⁹ (Liszt et al. 2012) in diffuse gas, measured in previous absorption line studies. As seen in the bottom plot, the N(C₂H)/N(c-C₃H₂) ratios in individual cloud components of our targets are constant over the values of N(H₂) probed, with an average column density ratio of N(C₂H)/N(c-C₃H₂) ~ 30.26 indicated by the gray horizontal dashed line. This average ratio agrees well with the values obtained by Lucas & Liszt (2000).

As already seen in Fig. 17, N(CS) and N(H₂S) also show poor correlations with N(H₂) in Fig. 20, in contrast to the column densities of HCN, HNC, C₂H and c-C₃H₂, although N(CS) has some degree of correlation with N(H₂). The abundances of CS and H₂S derived in diffuse clouds are higher >10⁻⁸ than those in translucent clouds (10⁻⁹ < abundance <10⁻⁸). However, apart from the fitting uncertainties, the derived column densities of CS and H₂S probably contain higher uncertainties than the lines of the other species, for example, due to poor sensitivities, as seen in Fig. 8. Therefore, it is difficult to conclude that the abundance of these sulfur-bearing species is higher toward diffuse clouds than toward translucent clouds. We need more observational data points with higher sensitivity toward more diffuse clouds to confirm this hypothesis since we only have a small sample (10 for CS and 4 for H₂S). The CS abundances toward the Galactic translucent clouds are in good agreement with X(CS) ~ 4 × 10⁻⁹ determined for high latitude diffuse clouds in the solar neighborhood (Lucas & Liszt 2002) in spite of the sulfur chemistry being different in these environments. Likewise, the abundances of H₂S are similar with X(H₂S) determined from diffuse clouds in different parts of the Galactic plane (Neufeld et al. 2015). In the plot of N(CS)/N(H₂S), a majority of the foreground clouds with detections for both these molecules are identified as translucent clouds but still associated with relatively less dense regions (A_v ~ 1–3 mag). In addition, the column density ratios do not show any correlation with the total hydrogen column density in the sightlines studied here.

Fig. 18 Same as Fig. 17 but for (a) HCN versus HNC, (b) C2H versus c-C3H2, and (c) CS versus H2S.

Fig. 19 Kernel density estimate (KDE) distributions of the channel-wise column density ratios. Black and gray bars indicate unweighted mean ratio values measured from previous studies of absorption lines (Lucas & Liszt 2000, 2002; Godard et al. 2010; Gerin et al. 2011; Neufeld et al. 2015). Median and mean values of the KDE distributions are marked by solid and dashed vertical lines (in lime, cyan, and fuchsia).

5.3 Variation of abundances along the sightline

Figures 21, E.1 and E.2 show variations in molecular abundance relative to N(H₂) in the lower panel and N(H₂) in the upper panel as a function of velocity along 12 sightlines. Two sightlines, HGAL0.55–0.85 and NGC 7538 IRS1, are not plotted here because only the HCO⁺ transition is seen in absorption toward these two sources. The column density of H₂ and the abundance of the molecules relative to H₂ are average values over given velocity ranges (see Tables 8 and B.1). In the upper panel, visible extinctions of 1 and 5 are indicated with horizontal dotted lines separating the three types of molecular gas clouds; diffuse clouds below A_v < 1.0, translucent clouds in 1.0 < A_v < 5.0, while regions with A_v > 5 are considered to be dense molecular clouds. The black arrows imply that the derived column densities and abundances may be underestimated within the velocity ranges marked with gray shaded areas that are affected by spectral emission features. Abundances of the considered species are shown in the lower panels with different colored markers; green circles for HCN, purple asterisks for HNC, orange up triangles for CS, red left triangles for H₂S, cyan cross for C₂H, and gray hexagons for c-C₃H₂.

Overall, some variations in abundance along the selected sightlines are found. These variations are not attributed to variable rms levels since the variability of abundances appears in all the sightlines, nor fitting uncertainties. Despite potential uncertainties, the abundances of C₂H and c-C₃H₂ change little and are instead consistent in both velocity ranges or between diffuse and translucent clouds. In Table 9 the mean abundances of these small hydrocarbons are surprisingly similar, while N(H₂) of diffuse clouds is smaller than that of translucent clouds by a factor of 4. We note that all calculations for the median values do not include the absorption features associated with background continuum sources. The median abundances of HCN and HNC do not show significant changes from diffuse to translucent clouds. In contrast, we note that X(H₂S) (with a median of 2.5 × 10⁻⁸) and X(CS) (with a median of 9.3 × 10⁻⁹) in diffuse clouds are significantly higher than in translucent clouds; median values of X(H₂S) and X(CS) are 2.8 × 10⁻⁹ and 6.6 × 10⁻⁹, respectively. These species’ higher abundances in diffuse clouds are already noticeable in Figs. 20, 21, E.l, and E.2. Overall, the mean or median abundances of the discussed species fit well within the ranges of values derived for high-altitude clouds or other clouds in the Galactic plane, considering the uncertainties. The abundance variations toward individual clouds may signify the influences of their environments which might be affected by, for example, pristine infalling gas in low metallicity (De Cia et al. 2021), the high UV fields (~5 × 10⁵ in Habing units, Rizzo et al. 2003) from embedded massive star-forming regions, or outflows, or the feedback from young high mass stars at the late stage of molecular clouds (e.g., influence of turbulence and shocks caused by expanding HII regions and stellar winds). All these effects could, to different degrees, mix gas from star-forming regions with diffuse or/and translucent gas, and result in significant time dependent chemistry (e.g., Pilleri et al. 2013).

To understand the abundance variations along the sightlines in relation to molecular gas structures, we plot position-position-velocity images of two selected sightlines (G19.61−0.23 and G32.80+0.19). Compared with other sightlines, these two sightlines have absorption features well separated from the background emission lines. As a result, absorption lines of all seven transitions are clearly detected (see Fig. 9). Figure 22 displays position-position-velocity images of ¹³CO emission extracted over an area of 12′ × 12′ from the GRS survey with the original spectral resolution (0.2 km s⁻¹). Toward both sightlines, we notice complex structures of dense molecular gas rather than simple shapes like spheres or cylinders. We can clearly see dense and clumpy molecular gas structures at the systemic velocities of these sightlines (for G19.61−0.23, υ_sys = 41.8 km s⁻¹, and for G32.80+0.19, υ_sys = 15 km s⁻¹). Some foreground clouds (velocity ranges of 28–40 km s⁻¹ and 58.5–70.8 km s⁻¹ for G19.61−0.23 and 90–110 km s⁻¹for G32.80+0.19) show an open ring structure. We need to study the association and interaction between diffuse material filling voids of dense molecular gas and the dense material by combining absorption and emission spectral analyses to address the abundance variations found in this work.

Fig. 20 Comparison of the column density of the presented molecular species and N(H2). Each colored symbol represents different individual clouds in the sightline toward the observed background continuum sources (DR2l: red X, G09.62+0.19: blue circle, G10.47 +0.03: green up-triangle, G19.61−0.23: cyan square, G29.96−0.02: yellow left-triangle, G31.41+0.31: lime hexagon, G32.80+0.19: magenta star, G45.07+0.13: orange cross, NGC 6334 I: black down-triangle, W3 IRS5: aquamarine thin diamond, W3(OH): light-coral pentagon, W43 MM1: dodger-blue octagon). Filled and unfilled markers indicate foreground components and molecular envelope components, respectively. For the molecular envelope components, only lower limits are marked by arrows instead of fitting uncertainty bars. Black diagonal dotted lines represent abundances of given molecules on the y-axis relative to N(H2) with their values labeled. In each panel, two vertical blue dotted lines indicate the visual extinction of 1 and 5, respectively. In the plot of N(C2H)/N(c-C3H2), the gray horizontal dashed line indicates a mean value of 30.26 in the column density ratio.

Fig. 21 N(H2) and N(X)/N(H2) ratio integrated over specific velocity intervals from top to bottom toward W3(OH), G29.96−0.02, G19.61−0.23, and G32.80+0.19. Different species are labeled with different symbols and colors as shown in the legend displayed in the right-hand corner of the top panel. The gray areas indicate the velocity ranges of the emission lines. In the upper panels, the dotted horizontal lines correspond to Av of 1 and 5, respectively. In the lower panels, the black horizontal arrows indicate the velocity ranges in which CO emission features have been detected from archival data at its given sensitivity. All the other sources are displayed in Figs. E.1 and E.2.

Fig. 22 Position-position-velocity images of 13CO emission using data taken from the GRS survey toward two selected sightlines; G19.61−0.23 (approximately 90° angle difference between left two images) and G32.80+0.19 (approximately 90° angle difference between right two images).

5.4 UV-dominated chemistry

We used the Meudon PDR code⁴ (Le Petit et al. 2006; Goicoechea & Le Bourlot 2007; Gonzalez Garcia et al. 2008) to study the physical conditions of diffuse and translucent clouds in which the molecules are studied in this investigation and are produced. The Meudon PDR code simulates a plane-parallel slab cloud illuminated on both sides by assuming that the cloud is in a static state. Throughout the model cloud, the thermal and chemical profiles are computed by assuming thermal and chemical equilibrium for every location. All models simulated here are isobaric models that consider constant thermal pressure. The calculated temperature and density profiles show that the temperature in the cloud decreases with increasing density. Self and mutual shielding for H, H₂, CO, isotopologues of CO (i.e., ¹³CO and ¹⁸CO), and HD becomes vital for models of diffuse clouds. Thus, toward the foreground clouds studied in this work, the H/H₂ transition should be considered in PDR models in detail with regard to the shielding processes. Therefore, we have applied an exact radiative transfer method described in Goicoechea & Le Bourlot (2007) to the PDR models rather than the analytical approximation to the self-shielding process in a line, described by Federman et al. (1979; FGK approximation). In the exact method, the spherical harmonics method (Goicoechea & Le Bourlot 2007) is implemented to solve for the far-ultraviolet (FUV) radiation fields in externally and internally illuminated clouds, considering gas absorption and scattering properties by dust grains.

Table 10 shows the fixed and free parameters used in the simulated PDR models. We used default values for initial abundances of elements, extinction curve (R_v), and dust properties and considered them to be fixed parameters. However, we have changed the values for the interstellar radiation field (G₀ in Mathis units), which for the solar neighborhood is G₀ = 1 and for FUV illuminated PDRs such as the Horsehead Nebula is G₀ = 100 (Pety et al. 2005). The value of G₀ only changes on the observer side and is fixed to 1 for the backside of the cloud in all models. Since the observed galactic sightlines pass over different parts of the Milky Way, we assume that diffuse clouds along the sightlines are controlled by various cosmic ray ionization rate (ζ) values where ζ is the total ionization rate by cosmic rays per H₂ molecule. Therefore, we varied ζ to 5 × 10⁻¹⁷, 1 × 10⁻¹⁶ and 1 × 10⁻¹⁵ s⁻¹ in our models. In addition, we have assumed typical values of interstellar pressure in diffuse and translucent clouds of 1000, 3000, 5000, and 10 000 K cm⁻³ and chosen total extinctions along the plane-parallel slab of A_v = 0.1, 1, 5, and 10 mag. We note that in the Meudon PDR isobaric models, each velocity-integrated component listed in Tables 8 and B.1 is a separate cloud (diffuse or translucent clouds) with a uniform pressure.

Figures 23–25 show comparisons of N(X) for each species X studied and column density ratios with N(HCO⁺), from top to bottom, and the predicted column densities and ratios from isobaric PDR models are marked with colored symbols and lines. For the predicted values from the models, different colors indicate various radiation field strengths and cosmic-ray ionization rates; G₀ = 1 and ζ = 5 × 10⁻¹⁷ s⁻¹ in red, G₀ = 100 and ζ = 5 × 10⁻¹⁷ s⁻¹ in green, G₀ = 1 and ζ = 1 × 10⁻¹⁶ s⁻¹ in blue, G₀ = 100 and ζ = 1 × 10⁻¹⁶ s⁻¹ in orange, and G₀ = 100 and ζ = 1 × 10⁻¹⁵ s⁻¹ in purple. Initial pressures of 1000, 3000, 5000, and 10 000 K cm⁻³ are indicated with dotted-, dashed-, dashed-dotted-, and solid-lines, respectively. In addition, the results with different visual extinctions are represented by colored triangles (A_v = 1 mag), colored squares (A_v = 5 mag), and colored circles (A_v = 10 mag). We note that all the predicted column densities at A_v = 0.1 mag fall outside the range of column densities shown in Figs. 23–25.

5.4.1 HCO⁺, HCN, and HNC

The top and middle plots of Fig. 23 show comparisons of two CN-bearing molecules (i.e., HCN and HNC) with N(HCO⁺) as well as the column densities predicted from the isobaric PDR models. For HCN, most of the models underestimate the observed quantities, only those models with ζ = 5 × 10⁻¹⁷−1 × 10⁻⁶ s⁻¹ and an initial pressure of 10 000 Kcm⁻³ result in values close to the lower limit of the observed column densities by a factor of a few higher. The modeled gas conditions are at n_H ~ 1400–2000 cm⁻³ and decrease in gas temperature at A_v ~ 1 mag. For HNC, all models fit reasonably within the observed column density ranges. In addition, models with G₀ = 1 (red and blue colors) make better predictions than those with G₀ = 100. The predicted N(HCN), N(HNC), and N(HCO⁺)from the isobaric models result from regions of higher visual extinction between 1 and 10 mag. In contrast, the estimated H₂ column densities from the observations correspond to lower than A_v ≤ 5 mag. These models provide reasonable predictions of column densities of these species. However, the models underestimate column densities by roughly an order of magnitude, especially for HCN₊ and HCO⁺. The modeled N(HCN)/N(HNC) against N(HCO⁺) as shown in the bottom-left panel of Fig. 23, is lower than the ratios from the observations due to an underestimation of N(HCN) in the isobaric PDR models.

In the isobaric PDR models, there are two main formation pathways for HCO⁺ and the two CN-bearing molecules (see Godard et al. 2009; Gerin & Liszt 2021 for details). For HCO⁺, the first one involves the chains, from OH + C⁺ → CO⁺ + H to CO⁺ + H₂ → HCO⁺ + H, and the second pathway is via H₂O + C+ → HCO⁺ + H. The latter reaction can also lead to the production of HOC⁺ that can produce HCO⁺ via hydrogenation. The formation of HCN and HNC involves nitrogen via the reaction NH + C⁺ → CN⁺ + H₂ or H → HCN⁺ or HNC⁺ + H₂ → HCNH⁺; NH₂ + C⁺ → HCN⁺ + H₂ → HCNH⁺. The dissociative recombination of HCNH⁺ forms HCN and HNC. Additionally, HCN can be produced via the neutral-neutral reaction of CH₂ + N. As seen in Fig. 23, the chemistry involving only the UV-dominated chemistry cannot reproduce the observed column densities of these species in diffuse and translucent clouds. In the turbulence-dominated chemistry (Godard et al. 2009, 2010, 2014) involving turbulent dissipation rate, relaxation and ion-neutral drift (Valdivia et al. 2017), several crucial endoenergetic reactions can significantly increase the abundances of important precursors of HCN, HNC, and HCO⁺, such as CH⁺, ${\text{CH}}_2^{+}$, ${\text{CH}}_3^{+}$ as well as NH. The TDR models from Godard et al. (2009, 2014) show a considerable increase in the formation of these three species via ion-neutral reactions, CH⁺+ N → CN⁺ + H₂ → HCN⁺ or HNC⁺ + H₂ →HCNH⁺; ${\text{CH}}_2^{+}$ + N → HCN⁺ + H₂ → HCNH⁺; ${\text{CH}}_3^{+}$ + N → HCNH⁺; ${\text{CH}}_3^{+}$ + O → HCO⁺ + H₂. Additionally, the reaction of CH⁺ with oxygen enhances the abundance of CO⁺, leading to HCO⁺.

Fig. 23 Column densities of HCN and HNC and their column density ratio as a function of N(HCO+), with predictions from isobaric PDR models overlaid. Filled and unfilled black markers indicate foreground components and molecular envelope components observed, respectively. The arrows refer to lower limits of N(X), and the markers are as same as Fig. 20. Each color represents different radiation field strengths and cosmic-ray ionization rates; red: G0 = 1 and ζ = 5 × 10−17 s−1 green: G0 = 100 and ζ = 5 × 10−17 s−1 blue: G0 = 1 and ζ = 1 × 10−16 s−1 orange: G0 = 100 and ζ = 1 × 10−16 s−1 and purple: G0 = 100 and ζ = 1 × 10−15 s−1 Initial pressures of 1000, 3000, 5000, 10 000 K cm−3 are indicated with dotted-, dashed-, dashed-dotted-, and solid-lines, respectively. Av =1, 5, and 10 mag are marked with colored triangles, squares, and circles, respectively.

Fig. 24 Column densities of C2H and c-C3H2 and their column density ratio as a function of N(HCO+), with predictions from isobaric PDR models overlaid. All symbols and lines used to represent the models are the same as Fig. 23.

5.4.2 C₂H and c-C₃H₂

Figure 24 shows comparisons between column densities predicted from isobaric PDR models and observations for C₂H and c-C₃H₂. Similar to the HCN and HCO⁺ results, the models underestimate the column densities of these two small hydrocarbons in these foreground cloud components. Nevertheless, their observed column densities are in better agreement with values from the isobaric models corresponding to low-density gas in n_H ~ 100–500 cm⁻³ up to 1000 cm⁻³. The N(C₂H) toward the diffuse clouds with N(HCO⁺) < 2 × 10¹² cm⁻² (corresponding to an observed A_v ~ 1) is close to the column densities from the isobaric models with moderate pressure values (dashed and dash-dotted green lines) of 3000–5000 K cm⁻³ giving n_H ≈ 500–1000 cm⁻³ and strong UV radiation of G₀ = 100 and ζ = 5 × 10⁻¹⁷ s⁻¹, for less shielded regions A_v < 5 (colored square symbols). By contrast, in denser regions having N(HCO⁺) > 2 × 10¹² cm⁻², the low-density models (dashed lines, n_H ≈ 100–500 cm⁻³) with lower G₀ of 1 (red and blue colors) at high A_v > 5 mag seem to fit the observed column densities better. For c-C₃H₂, the low-density PDR models with G₀ = 1 only in the direction of translucent clouds predict results near the low end of the column densities obtained from the observational data, as in the case of C₂H. The comparison between N(C₂H)/N(c-C₃H₂) and N(HCO⁺) for the models and observations show a better match than those for N(HCN)/N(HNC) versus N(HCO⁺) but still have some discrepancy. Overall, the models with lower density and the solar neighborhood G₀ generate column densities of these hydrocarbons close to the observed values, unlike the cases of HCN, HNC, and HCO⁺ which are associated better with high density gas materials. Nevertheless, the predicted column densities of the small hydrocarbons are underestimated by a factor of a few. In particular, for c-C₃H₂, toward diffuse clouds with N(c-C₃H₂) < 2 × 10¹² cm⁻², the discrepancy is more than about a factor of 10. In the isobaric PDR models, the predicted column densities of c-C₃H₂ are total column densities of ortho and para species without separate spin symmetries (with a spin-weight ratio of 3/1 for ortho/para). Thus, with consideration of this fact, the discrepancies between the observations and the models become larger.

In the PDR chemistry, C₂H is mainly produced by the recombination of ${\text{C}}_2{\text{H}}_2^{+}$+ and ${\text{C}}_2{\text{H}}_3^{+}$ with electrons (e.g., Godard et al. 2009; Mookerjea et al. 2012). In addition, it is formed by the photodissociation of C₂H₂ (Lee 1984) as well as by the neutralneutral reaction of CH₂ with atomic carbon (Turner et al. 2000; Sakai et al. 2010). For the formation of c-C₃H₂, once C₃H⁺ is formed by reactions of C₂H₂ with C⁺, C₃H⁺ produces the linear and cyclic ${\text{C}}_3{\text{H}}_3^{+}$ isomers via reactions with H₂ (Maluendes et al. 1993). The resulting isomers produce linear and cyclic-C₃H₂ by dissociative recombination (Fossé et al. 2001). In addition, the recombination of C₃H⁺ also contributes to the abundances of C₂H (Guzmán et al. 2015).

Similar to HCN, HNC, and HCO⁺, turbulence-dominated chemistry can considerably increase the abundances of C₂H and c-C₃H₂ by enhancing abundances of their precursor, C₂H which is formed from CH₂ via hydrogenation reactions. Not only that, but also the endoenergetic reaction of ${\text{C}}_2^{+}+{\text{H}}_2$ with −ΔE/k = 1260 K (Godard et al. 2009) increases the abundance of C₂H. Aside from the contribution of turbulent dissipation, the formation of small hydrocarbons possibly involves the top-down hydrocarbon chemistry that describes polycyclic aromatic hydrocarbons (PAHs) and small carbonaceous grains being broken down by UV erosion into small hydrocarbons that react in the gas phase (e.g., Pety et al. 2005; Gerin et al. 2011; Guzmán et al. 2015).

Fig. 25 Column densities of CS and H2S and their column density ratio as a function of N(HCO+), with predictions from isobaric PDR models overlaid. All markers and lines for the models are same as Fig. 23.

5.4.3 CS and H₂S

Figure 25 shows comparisons of the column densities of the two sulfur-bearing species and their column density ratios with N(HCO⁺). The top panel shows a good agreement between the predicted and derived column densities of CS. All the models with a wide range of physical parameters (G₀ = 1 and 100, ζ = 5 × 10⁻¹⁷ and 1 × 10⁻¹⁶ s⁻¹, and gas pressures of 1000–10 000 Kcm⁻³) broadly fit the derived column densities. In particular, toward translucent cloud components, the models with G₀ = 1, ζ = 1 × 10⁻¹⁶ s⁻¹, and pressure of 3000–5000 K cm⁻³ (blue dashed- and dashed-dotted-lines) well fit the derived values from the observations. The primary pathway of CS formation is the dissociative recombination reaction of HCS⁺ and electrons, which, however, leads to CS + H in 19% of reactions (Montaigne et al. 2005). There are two formation routes for HCS⁺, either through CH + S⁺ → CS⁺; CS⁺ + H₂ → HCS⁺ in the PDR route or through $\text{S}+{\text{CH}}_3^{+}\to {\text{HCS}}^{+}$ in the TDR route (Neufeld et al. 2015). We have found that the results of our PDR models are obtained in more shielded gas (n_H ~ 100–1000 cm⁻³ and A_v > 1 mag) compared to the more diffuse gas (n_H = 50 cm⁻³ and A_v = 0 ·4 mag) considered in the TDR and shock models presented in Neufeld et al. (2015). The destruction of CS reacting with ${\text{H}}_3^{+}$ directly contributes to the formation of HCS⁺ alongside other CS destruction pathways driven by photoionization and ion-exchange reactions.

The middle panel in Fig. 25 shows that the isobaric PDR models underestimate the observed column densities of H₂S. We also note that, as in the case of c-C₃H₂, the H₂S column densities predicted from the models show the total column densities of both ortho and para species, while the observational measurements refer to the column densities of only ortho-H₂S. In UV-dominated chemistry, reactions of S⁺ + H₂ → H₂S⁺ + e⁻ → H₂S is the main pathway to form H₂S. However, in low A_v (<0.5 mag) regions, the endothermic reaction of SH + H₂ → H₂S + hv (with -δE/k = 6862 K) becomes the predominant formation pathway for H₂S (e.g., Sternberg & Dalgarno 1995; Neufeld et al. 2015). In addition, the abundances of H₂S⁺, which is the precursor of H₂S, can be enhanced by two other endothermic reactions: SH⁺ + H₂ → H₂S⁺ + H (−δE/k = 6380 K), and S⁺ + H₂ → H₂S⁺ + hv (−δE/k = 9860 K). Similar to the species discussed in the previous sections, these endothermic reactions activated by turbulent dissipation or shocks (Neufeld et al. 2015) could significantly enhance the abundances of H₂S toward the observed sightlines. However, TDR or shock models alone cannot address the high observed column densities (Neufeld et al. 2015). This implies that another route for the formation of H₂S is needed. This route could be related to dust grain-surface chemistry (e.g., Navarro-Almaida et al. 2020; Cazaux et al. 2022). Sulfur is depleted onto dust grains (Ruffle et al. 1999) because sulfur mainly exists as S⁺ (Sternberg & Dalgarno 1995) and most dust grains are negatively charged. According to the gas-grain models of Navarro-Almaida et al. (2020), the chemical desorption of H₂S (via solid-H + solid-HS → H₂S) can explain the high H₂S abundances observed in translucent clouds (cloud edges, n(H₂) < 10⁴ cm⁻³) surrounding the dark clouds TMC-1 and Barnard 1b. Although the clouds in our sample have different physical conditions to these objects, the addition of chemical desorption may also help explain the high H₂S abundances derived toward the Galactic sightlines in our sample.

6 Summary and conclusions

Using the IRAM 30 m telescope, we have studied seven simple molecular species – HCO⁺, HCN, HNC, C₂H, c-C₃H₂, CS, and H₂S – in absorption toward 15 submillimeter sources in the Milky Way. We have detected HCO⁺ absorption lines in the direction of all 14 sources that show detectable millimeter wave continuum radiation, identifying 78 foreground gas components. A significant number of sightlines also have detectable absorption lines of HCN (12 sightlines), HNC (11 sightlines), C₂H (12 sightlines), and c-C₃H₂ (9 sightlines), CS (8 sightlines) and H₂S (6 sightlines). Our sensitivity to CS and H₂S is reduced by the presence of significant emission line contamination near the CS frequency and the poorer S/N ratios achieved at the higher H₂S transition frequency.

Using principal component analysis to investigate correlations among the species observed with the IRAM 30 m telescope and 7 other species observed with SOFIA (Paper I), we find that C⁺ and the hydride ions OH⁺, H₂O⁺, and ArH⁺ are poorly correlated with neutral molecules and HCO⁺. Sulfur-bearing molecules, CS and H₂S, appear to be better correlated with the neutral molecules than with hydride ions, which are tracers of gas with small molecular fractions. In addition, CH, OH, and O tend to be partially associated with both mostly molecular and predominantly atomic gas.

For the column densities, we find that N(HCN) and N(HNC) increase nonlinearly with N(H₂). While the abundances of the two molecules increase linearly in diffuse clouds (A_v < 1), their abundances suddenly increase in regions with N(H₂) ≳ 10²¹ cm⁻², where gas is further shielded against ultraviolet radiation. In contrast, C₂H and c-C₃H₂ do not increase as rapidly, and their column densities show a close correlation with N(HCO⁺). Moreover, the column density ratios of the two small hydrocarbons remain constant over the N(H₂) range probed and lie close to the ratios measured previously toward external galaxies. Interestingly, we find that the abundances of CS and H₂S in diffuse clouds are 5–10 times higher than in translucent clouds (A_v ≈ 1). This might imply the onset of sulfur depletion at around A_v of 1. Variations in the abundances of observed species along sightlines exist, but finding specific patterns is difficult as the abundances are influenced by the surrounding environment.

We reasonably reproduce column densities of HNC and CS using isobaric PDR models, but the column densities of the other molecular species observed here, except for H₂S, are underestimated by a factor of 2–10. Any of the models failed to reproduce the column densities of H₂S. As explored in previous studies on diffuse clouds, TDR models, which include pathways involving endoenergetic chemical reactions, could explain the discrepancy between the predicted and observed column densities of HCN, HCO⁺, C₂H, and c-C₃H₂. For H₂S, additional formation routes, for example grain-surface production and chemical desorption of H₂S, may play an important role in increasing the abundance of H₂S in diffuse and translucent clouds.

Acknowledgements

We would like to thank the referee for their constructive comments and suggestions that have helped to improve this paper. This work is based on observations made with the Institut de Radioastronomie Millimétrique (IRAM) 30 m telescope and used the data from Paper I obtained with the NASA/DLR Stratospheric Observatory for Infrared Astronomy (SOFIA). SOFIA is jointly operated by the Universities Space Research Association, Inc. (USRA), under NASA contract NNA17BF53C, and the Deutsches SOFIA Institut (DSI) under DLR contract 50 OK 0901 to the University of Stuttgart. This work was supported by DLR/Verbundforschung Astronomie und Astrophysik Grant 50 OR 2007. We gratefully acknowledge the excellent support provided by the SOFIA Operations Team, the GREAT Instrument Team, and the staff of the IRAM 30 m telescope.

Appendix A Channel-wise column density spectra of the detected molecular species

Figures A.1–A.5 show the column density per velocity interval for each detected molecular species in each observed source.

Fig. A.1 Channel-wise column density spectra (dN/dυ) as a function of velocity toward W3(OH) and DR21. The dN/dυ in each panel shows HCO+, HCN, HNC, CS, H2S, C2H, and c-C3H2 from top to bottom. The gray shaded area indicates dispersion of HCO+ emission lines from continuum sources, and the blue shaded regions represent 2σ confidence intervals for the derived column densities (per velocity interval).

Fig. A.2 Channel-wise column density spectra (dN/dυ) as a function of velocity toward G19.61−0.23 and G31.41+0.31 The dN/dυ in each panel shows HCO+, HCN, HNC, CS, H2S, C2H, and c-C3H2 from top to bottom. The gray shaded area indicates dispersion of HCO+ emission lines from continuum sources, and the blue shaded regions represent 2σ confidence intervals for the derived column densities (per velocity interval).

Fig. A.3 Channel-wise column density spectra (dN/dυ) as a function of velocity toward G45.07+0.13 and G09.62+0.19. The dN/dυ in each panel shows HCO+, HCN, HNC, CS, H2S, and C2H from top to bottom, but no C2H toward G09.62+0.19. The gray shaded area indicates dispersion of HCO+ emission lines from continuum sources, and the blue shaded regions represent 2σ confidence intervals for the derived column densities (per velocity interval).

Fig. A.4 Channel-wise column density spectra (dN/dυ) as a function of velocity toward W43 MM1 and NGC 63341. The dN/dυ in each panel shows HCO+, HCN, HNC, CS, and H2S from top to bottom. The gray shaded area indicates dispersion of HCO+ emission lines from continuum sources, and the blue shaded regions represent 2σ confidence intervals for the derived column densities (per velocity interval).

Fig. A.5 Channel-wise column density spectra (dN/dυ) as a function of velocity toward NGC 7538 IRS1, HGAL0.55–0.85, and W3 IRS5. Toward NGC 7538 IRS1 and HGAL0.55–0.85, HCO+ is only detected. For W3 IRS5, the dN/dυ in each panel shows HCO+, HCN, C2H, and c-C3H2 from top to bottom. The gray shaded area indicates dispersion of HCO+ emission lines from continuum sources, and the blue shaded regions represent 2σ confidence intervals for the derived column densities (per velocity interval).

Appendix B Derived column densities of the detected molecular species

Table B.1 lists integrated column densities over given velocity interval for each detected molecule in each observed source.

Appendix C Principal component analysis toward W3 IRS5

Figure C.1 shows the principal components in the left panel, and in the right panel, the rescaled column density profiles of observed absorption line (black curves) and the reproduced column density profiles (red and blue dotted lines) for each detected species, toward W3 IRS5.

Fig. C.1 Left: Eigen spectra of the eleven principle components with percentage of variances as well as uncertainties, toward W3 IRS5. Right: Scaled channel-wise column density spectra of the eleven species (HCO+, HCN, C2H, c-C3H2, CH, OH, O, C+, H2O+, OH+, and ArH+) as a function of υLSR. Black curves represent the observational data, and red dotted curves are the spectra reproduced with only the first three principal components (PC-1, PC-2, and PC-3). For C+, H2O+, OH+, and ArH+, the reproduced spectra indicated by blue dotted curves include one or two more PCs, i.e., PC-4 and PC-5.

Appendix D H-plots for the ten considered species (HCO⁺, HCN, C₂H, c-C₃H₂, CH, OH, O, C⁺, H₂O⁺, and OH⁺) toward W3(OH) and W3 IRS5

Figure D.1 shows the h-plots for ten considered species toward W3(OH) and W3 IRS5 as like as Figs. 13 and 14, but these h-plots only consider ten species that are commonly detected toward these two sightlines.

Fig. D.1 Upper: Variable correlation circle plots for the first and second PCs toward W3(OH) in the left panel and W3 IRS5 in the right panel. The solid straight lines close to the unit circle imply PC-1 and PC-2 contain the most information about the variables. Different colors are used to denote the different species analyzed. Each colored ellipse is a 2σ confidence interval for the uncertainty of the PCA results for the corresponding species. Lower: Same as the upper panel but for the second and third PCs (PC-2 and PC-3) toward the same sources, from left to right.

Appendix E Variations of N(H₂) and N(X)/N(H₂) ratios

Figures E.1 and E.2 show variations in molecular abundance relative to N(H₂) in the lower panel and N(H₂) in the upper panel as a function of velocity in each source.

Fig. E.1 N(H2) and N(X)/N(H2) ratio integrated over specific velocity intervals from top to bottom toward W3 IRS5, NGC 63341, DR21, and G09.62+0.19. Different species are labeled with different symbols and colors as shown in the legend displayed in the right corner of the W3(OH) diagram. The gray areas indicate the velocity ranges of the emission lines. In the upper panels, the dotted horizontal lines correspond to Av of 1 and 5, respectively. In the lower panels, the black horizontal arrows indicate the velocity ranges in which CO emission features have been detected from archival data at its given sensitivity.

Fig. E.2 N(H2) and N(X)/N(H2) ratio integrated over specific velocity intervals from top to bottom, toward G10.47+0.03, W43 MM1, G31.41+0.31, and G45.07+0.13. All symbols and lines are same as Fig. E.1.

References

All Tables

All Figures

Fig. 1 Positions of fifteen sightlines (black dots with names) from the HyGAL program in the Galactic plane. This distribution plot is reproduced based on the Fig. 3 of Paper I. Colored curves represent different Milky Way spiral arms; the 3-kpc arm is in yellow, the Norma and outer arms are in red, the Scutum-Centaurus arm is in blue, the Sagittarius-Carina arm is in purple, the Perseus arm is in black, and the local arm is in cyan. The Sun and the Galactic center (GC) are marked with the red Sun and asterisk symbols, respectively. The gray-shaded ellipse around the GC represents the long bar.

In the text

Fig. 2 Comparison of the HCO+ spectra from observations with wobbler switching and position switching modes. The top panel shows the HCO+ spectra (velocities relative to the local standard of rest, LSR) taken with WSw (blue) and PSw (red) modes toward G29.96−0.02. The middle panel shows the residual spectrum (green) after fitting the WSw and PSw spectra. Black horizontal dashed lines mark the 3 rms level. The bottom panel presents the combined spectrum (black) of the WSw and rescaled PSw ($\text{A}{T}_{\text{a}}^{*}(\text{PSw})+\text{B}$, where A and B are the slope and y-intercept of a linear least-squares regression fit, respectively), with the individual WSw and PSw spectra in the same colors as in the top panel.

In the text

Fig. 3 Observed spectra (black) and the XCLASS modeled spectra (red) in a $T_{\text{a}}^{*}/T_c$ scale, toward W3 IRS5, W3(OH), and NGC 753 8 IRS1 from left to right. The spectra in each panel correspond to HCO+, HCN, HNC, CS, H2S, C2H, and c-C3H2, from top to bottom. The shaded areas indicate velocity intervals of the local arm in cyan and the Perseus arm in gray. The υsys of the continuum sources are indicated using vertical dashed lines.

In the text

	Fig. 4 Same as Fig. 3 but toward NGC 6334 I and DR21. The brown shaded areas indicate velocity intervals of the molecular cloud envelope layers or unidentified foreground clouds toward these sightlines.
In the text

	Fig. 5 Same as Fig. 3 but toward HGALO.55–0.85 and G09.62+0.19. The brown and blue shaded areas indicate velocity intervals corresponding to the molecular cloud envelope layers or unidentified foreground clouds, and the Scutum-Centaurus arm, respectively.
In the text

	Fig. 6 Same as Fig. 3 but toward G10.47 +0.03. The shaded areas indicate the velocity intervals of specific spiral arms (Sagittarius-Carina arm in magenta, Scutum-Centaurus arm in blue, inter-arm gas in orange, the GC/bar in yellow, and the 135 km s−1 arm located beyond the GC in blue-green).
In the text

	Fig. 7 Same as Fig. 3 but toward G45.07+0.13. The shaded areas indicate the velocity intervals of specific spiral arms (local arm in cyan and Sagittarius-Carina arm in magenta), and the molecular cloud envelope or unidentified foreground clouds in brown.
In the text

	Fig. 8 Same as Fig. 3 but toward G29.96−0.02, W43 MM1, and G31.41+0.31. The shaded areas indicate the velocity intervals of specific spiral arms (local arm in cyan, Sagittarius-Carina arm in magenta, Aquila-Rift in green), and the molecular cloud envelope or unidentified foreground clouds in brown.
In the text

Fig. 9 Same as Fig. 3 but toward G19.61–0.12 and G32.80+0.19. The shaded areas indicate velocity intervals of specific spiral arms (Aquila-Rift in green, Sagittarius-Carina arm in magenta, Scutum-Centaurus arm in blue, inter-arm gas in orange, the GC/bar in yellow), and the molecular cloud envelope or unidentified foreground clouds in brown. Toward G32.80+0.19, the insert in the HCN panel zooms in on the HCN absorption features on top of the emission within a velocity window between –10 and 30 km s–1.

In the text

Fig. 10 Spectra lines of CO and HCO+ toward the eight sightlines. The upper panel for each plot shows 12CO emission lines (1 → 0) in black, obtained from the FUGIN survey (Umemoto et al. 2017), and 13CO (1 → 0) emission lines in red from the GRS survey (Jackson et al. 2006). For only G09.62+0.19, the 12CO (2 → 1) is taken from the SEDIGISM survey (Schuller et al. 2021). The lower panel for each plot shows absorption and emission lines in HCO+ spectra in blue from this survey. In the both panels, the vertical dotted lines indicate significant absorption features.

In the text

	Fig. 11 Channel-wise column density spectra (dN/dv) as a function of velocity toward G29.96–0.02 and G32.80+0.19. The dN/dv in each panel shows HCO+, HCN, HNC, CS, H2S, C2H, and c-C3H2 from top to bottom. The gray shaded area indicates velocity range of the HCO+ emission lines. The blue shaded regions represent 2σ confidence intervals for the derived column densities (per velocity interval).
In the text

Fig. 12 Left: Eigen spectra of thirteen principal components with percentage of variances as well as uncertainties (2σ), toward W3(OH). Right: scaled channel-wise column density spectra for the thirteen species (HCO+, HCN, HNC, CS, H2S, C2H, c-C3H2, CH, OH, O, C+, H2O+, and OH+) as a function of vLSR. Black curves represent the observational data, and red dotted curves are the spectra reproduced with only the first three principal components (PC-1, PC-2, and PC-3). For C+, H2O+, and OH+, the reproduced spectra indicated by blue dotted curves include one or two more PCs, i.e., PC-4 and PC-5.

In the text

Fig. 13 Variable correlation circle plots for the first and second PCs toward W3(OH) in the left panel and W3 IRS5 in the right panel. The solid straight lines close to the unit circle imply PC-1 and PC-2 contain the most information about the variables. Different colors are used to denote the different species analyzed. Each colored ellipse is a 2σ confidence interval for the uncertainty of the PCA results for the corresponding species.

In the text

	Fig. 14 Same as Fig. 13 but for the second and third PCs (PC-2 and PC-3) toward the same sources, from left to right.
In the text

	Fig. 15 Cosine similarities showing correlation between two pairs of species in the circle plots for PC-1 versus PC-2 toward W3(OH) (top) and W3 IRS5 (bottom).
In the text

	Fig. 16 Cosine similarities showing correlation between two pairs of species in the circle plots for PC-2 versus PC-3 toward W3(OH) (top) and W3 IRS5 (bottom).
In the text

Fig. 17 Comparisons of column densities in 0.8 km s–1 velocity channel bins for seven molecular species; (a) HCN versus HCO+, (b) HNC versus HCO+, (c) C2H versus HCO+, (d) c-C3H2 versus HCO+, (e) CS versus HCO+, and (f) H2S versus HCO+. The color codes correspond to specific spiral arms (local arm in cyan, Perseus arm in black, Aquila-Rift in blue, Sagittarius-Carina arm in magenta, Scutum-Centaurus arm in green, inter-arm regions in orange). All symbols without black edges indicate upper limits for nondetections, while the data points above the detection threshold are marked with black edges. In addition, the blue-green colored points indicate clouds that belong to the 135 km s–1 arm located beyond the Galactic center, toward G10.47 + 0.03. The black dotted lines represent the median value of the column density ratio in each panel. Uncertainties in the derived channel-wise column densities are presented as error bars. The red lines present a best-fit taking into account uncertainties of column densities. The gray areas are 2σ confidence interval for the best fit (red lines) with errors.

In the text

	Fig. 18 Same as Fig. 17 but for (a) HCN versus HNC, (b) C2H versus c-C3H2, and (c) CS versus H2S.
In the text

Fig. 19 Kernel density estimate (KDE) distributions of the channel-wise column density ratios. Black and gray bars indicate unweighted mean ratio values measured from previous studies of absorption lines (Lucas & Liszt 2000, 2002; Godard et al. 2010; Gerin et al. 2011; Neufeld et al. 2015). Median and mean values of the KDE distributions are marked by solid and dashed vertical lines (in lime, cyan, and fuchsia).

In the text

Fig. 20 Comparison of the column density of the presented molecular species and N(H2). Each colored symbol represents different individual clouds in the sightline toward the observed background continuum sources (DR2l: red X, G09.62+0.19: blue circle, G10.47 +0.03: green up-triangle, G19.61−0.23: cyan square, G29.96−0.02: yellow left-triangle, G31.41+0.31: lime hexagon, G32.80+0.19: magenta star, G45.07+0.13: orange cross, NGC 6334 I: black down-triangle, W3 IRS5: aquamarine thin diamond, W3(OH): light-coral pentagon, W43 MM1: dodger-blue octagon). Filled and unfilled markers indicate foreground components and molecular envelope components, respectively. For the molecular envelope components, only lower limits are marked by arrows instead of fitting uncertainty bars. Black diagonal dotted lines represent abundances of given molecules on the y-axis relative to N(H2) with their values labeled. In each panel, two vertical blue dotted lines indicate the visual extinction of 1 and 5, respectively. In the plot of N(C2H)/N(c-C3H2), the gray horizontal dashed line indicates a mean value of 30.26 in the column density ratio.

In the text

Fig. 21 N(H2) and N(X)/N(H2) ratio integrated over specific velocity intervals from top to bottom toward W3(OH), G29.96−0.02, G19.61−0.23, and G32.80+0.19. Different species are labeled with different symbols and colors as shown in the legend displayed in the right-hand corner of the top panel. The gray areas indicate the velocity ranges of the emission lines. In the upper panels, the dotted horizontal lines correspond to Av of 1 and 5, respectively. In the lower panels, the black horizontal arrows indicate the velocity ranges in which CO emission features have been detected from archival data at its given sensitivity. All the other sources are displayed in Figs. E.1 and E.2.

In the text

	Fig. 22 Position-position-velocity images of 13CO emission using data taken from the GRS survey toward two selected sightlines; G19.61−0.23 (approximately 90° angle difference between left two images) and G32.80+0.19 (approximately 90° angle difference between right two images).
In the text

Fig. 23 Column densities of HCN and HNC and their column density ratio as a function of N(HCO+), with predictions from isobaric PDR models overlaid. Filled and unfilled black markers indicate foreground components and molecular envelope components observed, respectively. The arrows refer to lower limits of N(X), and the markers are as same as Fig. 20. Each color represents different radiation field strengths and cosmic-ray ionization rates; red: G0 = 1 and ζ = 5 × 10−17 s−1 green: G0 = 100 and ζ = 5 × 10−17 s−1 blue: G0 = 1 and ζ = 1 × 10−16 s−1 orange: G0 = 100 and ζ = 1 × 10−16 s−1 and purple: G0 = 100 and ζ = 1 × 10−15 s−1 Initial pressures of 1000, 3000, 5000, 10 000 K cm−3 are indicated with dotted-, dashed-, dashed-dotted-, and solid-lines, respectively. Av =1, 5, and 10 mag are marked with colored triangles, squares, and circles, respectively.

In the text

	Fig. 24 Column densities of C2H and c-C3H2 and their column density ratio as a function of N(HCO+), with predictions from isobaric PDR models overlaid. All symbols and lines used to represent the models are the same as Fig. 23.
In the text

	Fig. 25 Column densities of CS and H2S and their column density ratio as a function of N(HCO+), with predictions from isobaric PDR models overlaid. All markers and lines for the models are same as Fig. 23.
In the text

Fig. A.1 Channel-wise column density spectra (dN/dυ) as a function of velocity toward W3(OH) and DR21. The dN/dυ in each panel shows HCO+, HCN, HNC, CS, H2S, C2H, and c-C3H2 from top to bottom. The gray shaded area indicates dispersion of HCO+ emission lines from continuum sources, and the blue shaded regions represent 2σ confidence intervals for the derived column densities (per velocity interval).

In the text

Fig. A.2 Channel-wise column density spectra (dN/dυ) as a function of velocity toward G19.61−0.23 and G31.41+0.31 The dN/dυ in each panel shows HCO+, HCN, HNC, CS, H2S, C2H, and c-C3H2 from top to bottom. The gray shaded area indicates dispersion of HCO+ emission lines from continuum sources, and the blue shaded regions represent 2σ confidence intervals for the derived column densities (per velocity interval).

In the text

Fig. A.3 Channel-wise column density spectra (dN/dυ) as a function of velocity toward G45.07+0.13 and G09.62+0.19. The dN/dυ in each panel shows HCO+, HCN, HNC, CS, H2S, and C2H from top to bottom, but no C2H toward G09.62+0.19. The gray shaded area indicates dispersion of HCO+ emission lines from continuum sources, and the blue shaded regions represent 2σ confidence intervals for the derived column densities (per velocity interval).

In the text

	Fig. A.4 Channel-wise column density spectra (dN/dυ) as a function of velocity toward W43 MM1 and NGC 63341. The dN/dυ in each panel shows HCO+, HCN, HNC, CS, and H2S from top to bottom. The gray shaded area indicates dispersion of HCO+ emission lines from continuum sources, and the blue shaded regions represent 2σ confidence intervals for the derived column densities (per velocity interval).
In the text

Fig. A.5 Channel-wise column density spectra (dN/dυ) as a function of velocity toward NGC 7538 IRS1, HGAL0.55–0.85, and W3 IRS5. Toward NGC 7538 IRS1 and HGAL0.55–0.85, HCO+ is only detected. For W3 IRS5, the dN/dυ in each panel shows HCO+, HCN, C2H, and c-C3H2 from top to bottom. The gray shaded area indicates dispersion of HCO+ emission lines from continuum sources, and the blue shaded regions represent 2σ confidence intervals for the derived column densities (per velocity interval).

In the text

Fig. C.1 Left: Eigen spectra of the eleven principle components with percentage of variances as well as uncertainties, toward W3 IRS5. Right: Scaled channel-wise column density spectra of the eleven species (HCO+, HCN, C2H, c-C3H2, CH, OH, O, C+, H2O+, OH+, and ArH+) as a function of υLSR. Black curves represent the observational data, and red dotted curves are the spectra reproduced with only the first three principal components (PC-1, PC-2, and PC-3). For C+, H2O+, OH+, and ArH+, the reproduced spectra indicated by blue dotted curves include one or two more PCs, i.e., PC-4 and PC-5.

In the text

Fig. D.1 Upper: Variable correlation circle plots for the first and second PCs toward W3(OH) in the left panel and W3 IRS5 in the right panel. The solid straight lines close to the unit circle imply PC-1 and PC-2 contain the most information about the variables. Different colors are used to denote the different species analyzed. Each colored ellipse is a 2σ confidence interval for the uncertainty of the PCA results for the corresponding species. Lower: Same as the upper panel but for the second and third PCs (PC-2 and PC-3) toward the same sources, from left to right.

In the text

Fig. E.1 N(H2) and N(X)/N(H2) ratio integrated over specific velocity intervals from top to bottom toward W3 IRS5, NGC 63341, DR21, and G09.62+0.19. Different species are labeled with different symbols and colors as shown in the legend displayed in the right corner of the W3(OH) diagram. The gray areas indicate the velocity ranges of the emission lines. In the upper panels, the dotted horizontal lines correspond to Av of 1 and 5, respectively. In the lower panels, the black horizontal arrows indicate the velocity ranges in which CO emission features have been detected from archival data at its given sensitivity.

In the text

	Fig. E.2 N(H2) and N(X)/N(H2) ratio integrated over specific velocity intervals from top to bottom, toward G10.47+0.03, W43 MM1, G31.41+0.31, and G45.07+0.13. All symbols and lines are same as Fig. E.1.
In the text