A&A 670, A111 (2023)
https://doi.org/10.1051/0004-6361/202244849© The Authors 2023

Astronomy&
Astrophysics

HyGAL: Characterizing the Galactic ISM with observationsof hydrides and other small molecules
II. The absorption line survey with the IRAM 30 m telescope
W.-J. Kim1 , P. Schilke1 , D. A. Neufeld2 , A. M. Jacob2 , Á. Sánchez-Monge1 , D. Seifried1 , B. Godard3 ,K. M. Menten4 , S. Walch1 , E. Falgarone5 , V. S. Veena4 , S. Bialy6 , T. Möller1 , and F. Wyrowski4
1

I. Physikalisches Institut, Universität zu Köln, Zülpicher Str. 77, 50937 Köln, Germany
e-mail: wonjukim@ph1.uni-koeln.de2
William H. Miller III Department of Physics & Astronomy, Johns Hopkins University, Baltimore, MD 21218, USA
3
LERMA, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Université, 75014 Paris, France
4
Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, 53121 Bonn, Germany
5
Laboratoire de Physique de l’ENS, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, 24 rue Lhomond,
75005 Paris, France
6
Department of Astronomy, University of Maryland, College Park, MD 20742-2421, USA
Received 31 August 2022 / Accepted 8 December 2022
ABSTRACTAs a complement to the HyGAL Stratospheric Observatory for Infrared Astronomy Legacy Program, we report the results of a groundbased absorption line survey of simple molecules in diffuse and translucent Galactic clouds. Using the Institut de Radioastronomie
Millimétrique (IRAM) 30 m telescope, we surveyed molecular lines in the 2 mm and 3 mm wavelength ranges toward 15 millimeter
continuum sources. These sources, which are all massive star-forming regions located mainly in the first and second quadrants of the
Milky Way, form the subset of the HyGAL sample that can be observed by the IRAM 30 m telescope. We detected HCO+ absorption
lines toward 14 sightlines, toward which we identified 78 foreground cloud components, as well as lines from HCN, HNC, C2 H, andc-C3 H2 toward most sightlines. In addition, CS and H2 S absorption lines are found toward at least half of the continuum sources. The
spectral line data obtained were analyzed to characterize the chemical and physical properties of the absorbing interstellar medium
statistically. The column density ratios of the seven molecular species observed are very similar to values found in previous absorption
line studies carried out toward diffuse clouds at high latitudes. As expected, the C2 H and c-C3 H2 column densities show a tightcorrelation with that of N(HCO+ ), because of these all these molecules are considered to be proxies for the H2 column density toward
diffuse and translucent clouds. The HCN and HNC column densities, by contrast, exhibit nonlinear correlations with those of C2 H,
c-C3 H2 , and HCO+ , increasing rapidly at Av ≈ 1 in translucent clouds. Static Meudon photodissociation region (PDR) isobaric models
that consider ultraviolet-dominated chemistry were unable to reproduce the column densities of all seven molecular species by justa factor of a few, except for H2 S. The inclusion of other formation routes driven by turbulent dissipation could possibly explain theobserved high column densities of these species in diffuse clouds. There is a tentative trend for H2 S and CS abundances relative to H2
to be larger in diffuse clouds (X(H2 S) and X(CS) ∼ 10−8 −10−7 ) than in translucent clouds (X(H2 S) and X(CS) ∼ 10−9 −10−8 ) toward asmall sample; however, a larger sample is required in order to confirm this trend. The derived H2 S column densities are higher than thevalues predicted from the isobaric PDR models, suggesting that chemical desorption of H2 S from sulfur-containing ice mantles may
play a role in increasing the H2 S abundance.
Key words. astrochemistry – techniques: spectroscopic – ISM: molecules

1. Introduction
Our understanding of the interstellar medium (ISM) has
significantly improved in the past decade, through extensive
observational efforts in absorption line spectroscopy performedat 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 evenpolyatomic molecules (e.g., C3 H+ , CH2 , H2 O, HCO+ , C2 H,
c-C3 H, l-C3 H, HCN, HNC, CH3 CN, NH3 , H2 CO, and c-C3 H2 ;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 acold 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 thosein which the local fraction of gas-phase carbon in C+ , fCn+ ,exceeds 0.5) and translucent clouds (defined as those in whichnfCn+ < 0.5 but the local fraction of gas-phase carbon in CO, fCO,
remains less than 0.9) in the Milky Way are excellent laboratories to study the formation and destruction of molecular clouds.
A111, page 1 of 41

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A&A 670, A111 (2023)

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 andmolecular gas. Differing in their physical and chemical properties, diffuse and translucent clouds have, for example, different
molecular gas fractions and different abundances of carbonbearing species (see Snow & McCall 2006, and references
therein). In particular, if only the total visual extinction (Av ) is
known, distinguishing translucent clouds from the superpositionof multiple diffuse clouds yielding similar fractions of integrated
column densities for atomic ( fHN ) or molecular ( fHN2 ) hydrogenis not straightforward. Nonetheless, the chemistry in the two
types of clouds is certainly different as the primary reservoirs ofgas-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 andthe 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, thatare higher column densities. As carbon is a key element ininterstellar chemistry, we also explored absorption by carbonbearing molecules (HCN, HNC, C2 H, and c-C3 H2 ) that havebeen 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 enhancedby the dissipation of interstellar turbulence; this creates small
regions of elevated temperature and large ion-neutral drift thatenables 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 H2 S, CS, SO,
and SH) greatly exceed values predicted by standard models ofcold diffuse molecular clouds, providing further evidence forthe 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 beenpossible 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 formationand destruction of molecular hydrogen in a turbulent medium(e.g., Bialy et al. 2017, 2019; Bialy & Burkhart 2020), as thediffering abundances and kinematics of these molecules studied
here demonstrate the importance of considering gas dynamical
A111, page 2 of 41

processes that enhance the formation rate of some of theirprogenitor 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, asa 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+ , H2 O+ , 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 dataand investigate associations between simple molecules and thehydrides studied in Paper I. Section 2 describes the acquisitionof 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, H2 S, C2 H, and c-C3 H2 that aredetected 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 thesesightlines. The determination of the column densities of thesemolecular species will be explained in Sect. 4, together with aprincipal component analysis for all species reported both in thispaper and in Paper I toward W3(OH) and W3 IRS5. In Sect. 5,
we discuss the results of the principal component analysis andthe derived observational quantities (column densities and abundances), and we compare these measurements with the resultsof isobaric PDR models, trying to understand the chemical andphysical properties of diffuse and translucent clouds across theMilky Way. Finally, we conclude and summarize all the resultsfrom 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 thefirst 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 149–494 µm).
The HyGAL program selected 25 submillimeter sources withflux 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 theother 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 of1

http://www.iram.es/IRAMES/mainWiki/
EmirforAstronomers

W.-J. Kim et al.: HyGAL: Characterizing the Galactic ISM with observations of hydrides and other small molecules. II.
Table 1. Source summary.

SourceRA (J2000)(hh:mm:ss)

Dec (J2000)(dd:mm:ss)

Gal. Long.
(deg)

Gal. Lat.
(deg)

d
(kpc)

RGAL
(kpc)

3sys
(km s−1 )W3 IRS5
W3(OH)NGC 6334 I
HGAL0.55−0.85
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*G45.07+0.13
DR21
NGC 7538 IRS1
G357.558−00.321

02:25:40.5
02:27:04.1
17:20:53.4
17:50:14.5
18:06:14.9
18:08:38.4
18:27:38.0
18:46:03.7
18:47:47.0
18:47:34.1
18:50:30.6
19:13:22.0
20:39:01.6
23:13:45.3
17:40:57.2+62:05:51.4+61:52:22.1−35:47:01.5−28:54:30.7−20:31:37.0−19:51:52.0−11:56:39.5−02:39:21.2−01:54:28.0−01:12:49.0−00:02:00.0+10:50:54.0+42:19:37.9+61:28:11.7−31:10:59.3

133.715133.948351.4170.546
9.620
10.47219.60829.95430.81731.41132.79645.07181.681111.542357.557+1.215+1.064+0.645−0.851+0.194+0.026−0.234−0.016−0.057+0.307+0.191+0.133+0.537+0.777−0.3212.3
2.0
1.3
7.7−9.2
5.2
8.6
12.6
4.8
3.1
3.7
9.7
7.8
1.5
2.6
9.0−11.8

9.9
9.6
7.0
0.4−1.0
3.1
1.6
4.4
4.7
5.7
5.4
5.3
6.1
7.4
9.8
1.0−3.6

–39.0
–47.0
–7.6
17.5
4.4
66.9
41.8
97.0
98.0
97.0
15.0
60.0
–3.0
–59.0
5.3

Notes. Except for the sources whose names are preceded by an asterisk, heliocentric and galactocentric distances are the values listed by Paper I.
For those five sources, revised distances are taken from Reid et al. (2019), who cite the primary references. The systemic velocity, 3sys , refers to thevelocity at which the H 13CO+ emission line peaks, for each source in our sample as per the observations presented here.

15
10

W3(OH)NGC 7538 IRS1
DR21
NGC 6334 I
W43 MM1
G31.41+0.31 G45.07+0.13
G09.62+0.03 G29.96-0.02
W3 IRS5

Q3
Q4

Y [kpc]

5
0

Q2
Q1

G32.80+0.19
G10.47+0.03

HGAL0.55-0.85
G357.558-00.321

G19.61-0.23

5
10
15

15

10

5

0

X [kpc]51015Fig. 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 outerarms are in red, the Scutum-Centaurus arm is in blue, the SagittariusCarina arm is in purple, the Perseus arm is in black, and the local arm isin cyan. The Sun and the Galactic center (GC) are marked with the red
Sun and asterisk symbols, respectively. The gray-shaded ellipse aroundthe GC represents the long bar.

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 linefeatures 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 ∆3 ∼ 0.35 km s−1
for H2 S and 0.62−0.66 km s−1 for the other transitions). For
our analysis, we resampled all the spectral line data to a fixedvelocity resolution of 0.8 km s−1 , except H2 S for which we use
a better resampled resolution of 0.36 km s−1 . We utilized theContinuum 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).
Calibration for PSw and WSw mode observations. The
observed data sets consist of wobbler switching (WSw) andposition 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 thatare severely affected by standing wave effects before averaging
all observational scans.
Figure 2 shows an example of the HCO+ spectra obtainedwith 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 ).
2https://www.iram.fr/IRAMFR/GILDAS/doc/html/
class-html/class.html
A111, page 3 of 41

A&A 670, A111 (2023)
Table 2. Observed molecular transitions.

Molecule

Transition

Rest frequency(GHz)

Beam size
(′′ )

Eu /k
(K)

El /k
(K)

Aul
(s−1 )

HCO+
HCN

J=1←0
J = 1 ← 0, F = 1 ← 1
J = 1 ← 0, F = 2 ← 1(†)
J = 1 ← 0, F = 0 ← 1
J=1←0
J=2←1
JKa ,Kc = 11,0 ← 10,1
N = 1 ← 0, J = 3/2 ← 1/2, F = 1 ← 1
N = 1 ← 0, J = 3/2 ← 1/2, F = 2 ← 1(†)
N = 1 ← 0, J = 3/2 ← 1/2, F = 1 ← 0
N = 1 ← 0, J = 1/2 ← 1/2, F = 1 ← 1
N = 1 ← 0, J = 1/2 ← 1/2, F = 0 ← 1
N = 1 ← 0, J = 1/2 ← 1/2, F = 1 ← 0
JKa ,Kc = 21,2 ← 10,1

89.1885
88.6304
88.6318
88.633990.6635
97.9809168.7627
87.2841
87.3168
87.328587.401987.407187.4464
85.3388

27.6
27.8
27.8
27.8
27.1
25.1
14.6
28.2
28.2
28.2
28.1
28.1
28.1
28.8

4.28
4.25
4.25
4.25
4.35
7.05
8.10
4.19
4.19
4.19
4.20
4.20
4.20
4.10

0.0
0.0
0.0
0.0
0.0
2.35
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0

4.19 × 10−5
2.41 × 10−5
2.41 × 10−5
2.41 × 10−5
2.69 × 10−5
1.68 × 10−5
2.68 × 10−5
2.60 × 10−7
1.53 × 10−6
1.27 × 10−6
1.27 × 10−6
1.54 × 10−6
2.61 × 10−7
2.32 × 10−5

HNC
CS
H2 S
C2 H

c-C3 H2

Notes. The dagger (†) marks the reference frequency corresponding to the reference velocity (3sys ) for a given sightline. The spectroscopic information on these transitions is taken from Jet Propulsion Laboratory (JPL) (https://spec.jpl.nasa.gov/) and the Cologne Database for Molecular
Spectroscopy (CDMS) (https://cdms.astro.uni-koeln.de/) catalogs. The frequencies of H2 S and c-C3 H2 transitions correspond to that of
their ortho spin state, and so the subsequently derived column densities and abundances for these species refer to ortho-H2 S and ortho-c-C3 H2 .
The upper energy levels of ortho-H2 S and ortho-c-C3 H2 listed in the table are relative to the ground state of the orhto species; without that, forortho-H2 S, Eu /k = 27.88 K and El /k = 19.78 K, and for ortho-c-C3 H2 , Eu /k = 6.45 K and El /k = 2.35 K.

Ta* (K)

1.0

WSw HCO + spectrum
PSw HCO + spectrum

0.5

Ta* /Tc

0.0
50 Residual 0
50
0.25
0.00
2 50 Combined 0HCO + spectrum50

100
100

1
0 50

0

50
LSR (km s 1)

100

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 (AT a∗ (PSw) + B, where A and B are the slope and yintercept of a linear least-squares regression fit, respectively), with theindividual WSw and PSw spectra in the same colors as in the top panel.

These components are not detected in the PSw spectrum,
implying that they may be dismissed as artifacts arising fromcontamination in the reference position. To identify such
A111, page 4 of 41

artifacts, we rescaled the PSw spectrum to the WSw spectrum,
allowing for both multiplicative and additive offsets, by using
the relationship of AT a∗ (PSw) + 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 becaused 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 inTable 3. We have examined if any excessive residual spectralfeatures remain after subtracting a rescaled PSw spectrum froma 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 isreplaced by the PSw value at the same velocity because the highresidual components are regarded not to be real but due to thereference position contamination. The continuum levels and rms
noise of the spectra for the seven species toward each source arelisted 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 persource) 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 theirmeasured 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.

W.-J. Kim et al.: HyGAL: Characterizing the Galactic ISM with observations of hydrides and other small molecules. II.
Table 3. Coefficients from linear regression fits.
HCO+

SourceW3 IRS5
W3(OH)NGC 6334 I
HGAL0.55−0.85
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
G45.07+0.13
DR21
NGC 7538 IRS1

HCN

HNC

CS

A

B

A

B

A

B

0.977
1.163
0.605
···
0.987
1.013
1.049
0.976
0.626
1.018
1.075
0.946
0.847
0.761

−0.225−0.441−2.148···−1.133−0.0470.867−0.681−0.1850.098−0.0150.193−0.322
0.224

0.963
0.960
0.716
···
1.033
1.037
1.050
0.969
0.749
1.042
1.072
0.906
0.851
0.932

−0.199−0.281−2.538···−1.188−0.0430.862−0.663−0.2290.089−0.005
0.184
0.293
0.238

0.942
0.856
0.670
···
1.015
0.896
1.024
0.942
0.628
0.902
1.100
0.260
0.919
0.536

−0.218−0.280−2.438···−1.145−0.0140.887−0.644−0.1850.099−0.3230.199−0.505
0.283

H2 S

C2 H

c-C3 H2

A

B

A

B

A

B

A

B

···
···
···
···
···
0.580
0.763
0.977
0.931
···
···
···

···
···
···
···
···
···
···
−0.235−0.038−0.117
0.212
···
···
···

···
···
···
···
···
···
···
0.112
0.700
0.942
0.592
···
···
···

···
···
···
···
···
···
···
−0.0280.184−0.228
0.421
···
···
···

0.944
0.869
0.454
···
0.486
0.907
0.889
0.922
0.809
1.029
1.080
0.930
0.906
0.761

−0.217−0.168−1.577···−0.539−0.0330.836−0.633−0.2640.080−0.287
0.212
0.220
0.225

0.800
0.620
0.520
···
0.156
0.907
0.819
0.928
0.891
1.074
1.031
0.625
1.010
0.278

−0.1280.005−1.904···−0.126−0.0210.807−0.655−0.2880.073−0.2380.220−0.306
0.342

Notes. The coefficients A and B refer to the slope and y-intercept of a linear least-square regression fit. The molecular transitions with blank A
and B values correspond to WSw mode-only observations with noncontaminated WSw off positions.
Table 4. Continuum levels and rms noise of the spectra.
SourceW3 IRS5
W3(OH)NGC 6334 I
HGAL0.55−0.85
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
G45.07+0.13
DR21
NGC 7538 IRS1

HCO+

HCN

HNC

CS

H2 S

C2 H

c-C3 H2

Tc
(K)

T rms
(K)

Tc
(K)

T rms
(K)

Tc
(K)

T rms
(K)

Tc
(K)

T rms
(K)

Tc
(K)

T rms
(K)

Tc
(K)

T rms
(K)

Tc
(K)

T rms
(K)

0.525
0.626
0.427
0.116
0.075
0.117
0.353
0.439
0.059
0.155
0.497
0.194
1.500
0.408

0.007
0.006
0.010
0.008
0.008
0.006
0.004
0.004
0.004
0.006
0.004
0.004
0.005
0.005

0.514
0.626
0.531
0.111
0.073
0.122
0.353
0.439
0.059
0.155
0.486
0.194
1.490
0.401

0.008
0.009
0.013
0.008
0.008
0.009
0.007
0.008
0.009
0.009
0.007
0.005
0.009
0.008

0.509
0.647
0.464
0.116
0.077
0.121
0.366
0.458
0.069
0.158
0.506
0.201
1.496
0.415

0.007
0.008
0.014
0.009
0.009
0.008
0.006
0.007
0.005
0.006
0.008
0.006
0.009
0.008

0.418
0.589
0.677
0.141
0.075
0.159
0.384
0.390
0.116
0.167
0.480
0.191
1.540
0.387

0.005
0.005
0.017
0.006
0.005
0.005
0.005
0.008
0.010
0.006
0.003
0.004
0.006
0.005

0.181
0.551
1.031
0.257
0.098
0.367
0.325
0.182
0.256
0.271
0.330
0.183
0.751
0.369

0.012
0.011
0.048
0.014
0.013
0.015
0.011
0.024
0.024
0.013
0.008
0.011
0.012
0.011

0.566
0.638
0.455
0.112
0.076
0.115
0.370
0.456
0.065
0.167
0.516
0.199
1.563
0.406

0.010
0.009
0.014
0.009
0.009
0.011
0.006
0.007
0.006
0.008
0.008
0.005
0.008
0.009

0.606
0.629
0.438
0.109
0.076
0.115
0.379
0.472
0.060
0.161
0.523
0.198
1.590
0.402

0.008
0.009
0.013
0.009
0.009
0.007
0.006
0.007
0.005
0.007
0.007
0.005
0.008
0.008

Notes. The continuum and rms noise levels are on the T a∗ scale, with a spectral resolution (∆3) of 0.8 km s−1 for all species except for H2 S for
which ∆3 = 0.36 km s−1 .

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 H2 S at their 3sys , 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 3sys . It is not clear if
the absorption lines arise from physically unrelated foregroundclouds or if they are associated with the molecular gas of thestar 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 andthese components unambiguously trace foreground diffuse ortranslucent clouds.
The continuum sources observed here are HII regions andmassive 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, H2 S, and c-C3 H2spectra are severely contaminated molecular lines emitted by
the background continuum source, various of them unidentified. As a result, the detection rates of absorption features forthese transitions are lower than those of the other species. Moreover, the c-C3 H2 transition we targeted lies close to the HCS+
A111, page 5 of 41

A&A 670, A111 (2023)
Table 5. Summary of detected species in absorption.

SourceW3 IRS5
W3(OH)NGC 6334 I
HGAL0.55−0.85
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
G45.07+0.13
DR21
NGC 7538 IRS1

HCO+

HCN

HNC

CS

H2 S

C2 H

c-C3 H2

Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y

Y
Y
Y
N
Y
Y
Y
Y
Y
Y
Y
Y
Y
N

N
Y
Y
N
Y
Y
Y
Y
Y
Y
Y
Y
Y
N

N
Y
N
N
N
Y
Y
Y
C
Y
Y
Y
Y
N

N
Y
N
N
Y
C
Y
C
C
C
Y
Y
Y
N

Y
Y
Y
N
Y
Y
Y
Y
Y
Y
Y
Y
Y
N

Y
Y
Y
N
N
C
Y
Y
N
Y
Y
Y
Y
N

Notes. Clear detection of absorption features, which are either widely separated from the emission lines associated with background continuum
sources or superposed on emission features, are marked with “Y”. Less secure detections, due to either poor S/N or severe contamination fromunidentified or identified transitions, are marked with “C” and nondetections with “N”.

(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 H2 S
transition is relatively close to the 34SO (J = 44 → 33 ) transition at 168.8151 GHz. At negative velocities with respect to thesource systemic velocity, some c-C3 H2 and H2 S 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 thesecases, we simultaneously fit the HCS+ and 34SO emission lines
with the c-C3 H2 and H2 S 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),
C2 H (12 sightlines), and c-C3 H2 (nine sightlines) transitions. CS
and H2 S are only detected toward eight and six sources, respectively, because of the poorer S/N at the higher H2 S transition
frequency or significant emission line contamination.
Figures 3–9 present the observed spectra, normalized withrespect to the continuum flux and displayed as a function of
3LSR . 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 intervalsof 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. C2 H
(J = 1 ← 0) is another molecular transition with multiple hyperfine components. This line has six hfs components, with the two
A111, page 6 of 41

weakest components being well separated and each of the twobrightest 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 C2 H as the rest
frequency for purposes of computing the 3LSR . C2 H is found tobe ubiquitous in the Milky Way, and thus it often traces multiple velocity components. HCO+ (µA = 3.90), HCN (µA = 2.984)
and HNC (µA = 3.04) have much larger dipole moments thanCO (µA = 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 indifferent evolutionary stages that belong to the W3 molecular
clouds and HII region complex, while NGC 7538 IRS1 is themost 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, C2 H, andc-C3 H2 . 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 otherspecies except for the −20 km s−1 feature, which is not observedin the HNC and H2 S 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

W.-J. Kim et al.: HyGAL: Characterizing the Galactic ISM with observations of hydrides and other small molecules. II.

H2 S

1.00

Ta*/Tcc-C3H2

1.00

Ta*/TcC2 H

0.8
1.1 c-C3H2
1.0
0.9

80

60

40

20

LSR (km s 1)

0

20

80

60

40

20

LSR (km s 1)

0

20

H2 S

1
1.5

Ta*/Tc1.0

Ta*/Tc

C2 H

CS

1.0
2

H2 S

0.75

1.0

0.75

Ta*/Tc

0.8
1.25

1

0.8
1.25

1.0

HNC

1
1.50

CS
Ta*/Tc

Ta*/Tc1.0
2

Ta*/Tc

0.5

CS

HCN

1
0
2

HNC

Ta*/Tc

Ta*/Tc

1.50

0.75
2

HCN
1.0

1.0

NGC 7538 IRS1
HCO+

1.00

Ta*/Tc

Ta*/Tc
Ta*/Tc

1

1.25

0.5

0.5

HNC

Ta*/Tc

Ta*/Tc1.0
2

Ta*/TcHCN

1.0

W3(OH)HCO+

Ta*/Tc0.5
1.2

Ta*/Tc

1.5

Ta*/Tc1.0

W3 IRS5HCO+

Ta*/Tc

Ta*/Tc

1.5

C2 H

1.0
0.5
1.5 c-C3H2
1.0
0.5

80

60

40

20

LSR (km s 1)

020

Fig. 3. Observed spectra (black) and the XCLASS modeled spectra (red) in a T a∗ /T c scale, toward W3 IRS5, W3(OH), and NGC 7538 IRS1 fromleft to right. The spectra in each panel correspond to HCO+ , HCN, HNC, CS, H2 S, C2 H, and c-C3 H2 , from top to bottom. The shaded areas indicate
velocity intervals of the local arm in cyan and the Perseus arm in gray. The 3sys of the continuum sources are indicated using vertical dashed lines.

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 theenvelope of the molecular cloud as C2 H and c-C3 H2 absorption
lines show a clear separation from the background emission. In
addition, the spectra of CH, OH, OH+ , O, C+ , and ArH+ fromthe 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) andW3 IRS5, also seen here in the millimeter spectra.
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 thelatter has a significantly broader profile (∆3 ∼ 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 tobe 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 richnessof molecular emission lines prohibits a convincing absorption

line detection in the CS and H2 S spectral windows while theother 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 (C2 H, c-C3 H2 ) show a broader line shape than the otherspecies without a red-shifted emission wing indicating an outflow as traced by HCN, CS, and H2 S. 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 andshows broad emission wings in lines from the HCO+ , HCN, andCS molecules. As seen in the upper panel of Fig. 5, only two
narrow absorption components are found in the HCO+ spectrumat −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 ScutumCentaurus 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 asshown 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 HII regions (−5–0 km s−1 ), which is
A111, page 7 of 41

A&A 670, A111 (2023)

Ta*/Tc1

Ta*/Tc2

1.25

Ta*/Tc1.00

Ta*/Tc1.0

c-C3H2

1.0
60

20

40

Ta*/Tc1

Ta*/Tc

1.0

0.5
1.50

CS

Ta*/Tc1.25
1.00

Ta*/Tc

1

1.25

C2 H

Ta*/Tc

1.00
0.75
1.25

c-C3H225025LSR (km s 1)

50

75

G09.62+0.19
HCO+
HCN

2.5

1
1.5

HNC
CS

1.0

H2 S

1
1.5

1.25

Ta*/Tc

Ta*/Tc

0.75

5.0

1.0
1.50

1.00

50

2

2

H2 S

Ta*/Tc

Ta*/Tc

2

1.0

2

HNC

1.5

0.5
1.5 c-C3H2

0
7.5

HCN

C2 H

1.0

4

HCO+

H2 S

1

0.5

60

Ta*/Tc

Ta*/Tc0

LSR (km s 1)

1
0
2

Ta*/Tc

20

DR21

2

Ta*/Tc

40

CS

1.0

1.5

Ta*/Tc

Ta*/TcC2 H

1.5

Ta*/Tc

Ta*/Tc

1
1.5

HNC

1

2

H2 S

Ta*/Tc

Ta*/Tc1.0
2

Ta*/Tc

Ta*/Tc

1.5

HCN

1

1.50

CS

HCO+

1.0

0
2

HNC

0.75
2.0

1.5

2

HCN

Ta*/Tc

Ta*/TcHCO+

0
4

Ta*/Tc

HGAL0.55 0.85

NGC 6334 I

2C2 H
c-C3H2

1.00

60

40

20

0

LSR (km s 1)

20

40

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

A111, page 8 of 41

50

0

50

LSR (km s 1)

100

Fig. 5. Same as Fig. 3 but toward HGAL0.55−0.85 and G09.62+0.19.
The brown and blue shaded areas indicate velocity intervals corresponding to the molecular cloud envelope layers or unidentified foregroundclouds, and the Scutum-Centaurus arm, respectively.

W.-J. Kim et al.: HyGAL: Characterizing the Galactic ISM with observations of hydrides and other small molecules. II.

Ta*/Tc
Ta*/Tc
Ta*/Tc

HNC

1.0

CS

1.00
0.75
1.25

Ta*/Tc

H2 S

H2 S

1.00
0.75

C2 H

Ta*/Tc

Ta*/Tc

HCN

1.0

0.8
1.25

CS

1
1.5

1.5
1.2

HNC

1.0
2

1
0
2.0

HCN

G45.07+0.13
HCO+

Ta*/Tc

Ta*/Tc
Ta*/Tc

0
1.5
1.0
0.5
1.5

Ta*/Tc1

Ta*/Tc2

1
0
2

Ta*/Tc

G10.47+0.03
HCO+

1.0
1.5 c-C3H2

Ta*/Tc

Ta*/Tc

2

1.0
0.5

0

50

100

LSR (km s 1)

150

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).

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-C3 H2 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.
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 throughits sightline and they cause HCO+ absorption features spanning a wide velocity range from −28 to +179 km s−1 , whilebackground emission ranges between +52 and +83 km s−1 , asshown in Fig. 6. Such widespread absorption line features arealso detected in the hydrides (ArH+ , o-H2 O+ , 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 crossingof the Sagittarius arm (+3.2 to +20 km s−1 ), and the ScutumCentaurus arm (+20 to +52 km s−1 ). Surprisingly, the inter-arm
HCO+ absorption feature shows a similar absorption depth,
T a∗ /T c , when compared to absorption lines arising in the spiral arms. However, the HCO+ absorption lines belonging to the

1.0

C2 H

0.8
1.1 c-C3H2
1.0
0.9

25

0

25

50

75

LSR (km s 1)

100

125

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.

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 andthe Galactic bar (3 > +80 km s−1 ), whereas the components at
velocities greater than 120 km s−1 are believed to be associatedwith the +135 km s−1 spiral arm (Sormani & Magorrian 2015)
located beyond the GC. Between these two velocity features, theHCO+ 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,
C2 H, CS, and H2 S. However, the 120 km s−1 feature is barely
seen in HCN, CS, and C2 H partly due to emission line contamination. As a well known hot core source, G10.47+0.03 is richin complex molecules (Widicus Weaver et al. 2017). For the H2 S
and c-C3 H2 spectra, we detect multiple, strong emission components that further complicates the assignment and fitting ofabsorption line features.
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
A111, page 9 of 41

A&A 670, A111 (2023)

Ta*/Tc

0.5
1.25

C2 H

1.5

c-C3H2

1.00
0.75

25

0

25

50

75

LSR (km s 1)

100

125

Ta*/Tc
Ta*/Tc
Ta*/Tc

1

C2 H

0.5
1.5 c-C3H2
1.0
0.5

25

0

25

50

75

LSR (km s 1)

100 125 150

H2 S

1
1.5

1.0

CS

1.0
2

H2 S

HNC

1
1.50

CS

1.0
2

H2 S

1
1.0

1.0

HCN

1
0
2

HNC

Ta*/Tc

Ta*/Tc0.8
2

1.5

G31.41+0.31
HCO+

1
0
2

HCN

1

1.5

CS

Ta*/Tc1.0

Ta*/Tc

HNC
1.0

Ta*/Tc

Ta*/Tc
Ta*/Tc
Ta*/Tc

Ta*/Tc

0.5

0.5
1.2

1
0
2

HCN
1.0

Ta*/Tc

Ta*/Tc

Ta*/Tc

1.50

2

Ta*/Tc1

W43 MM1
HCO+
Ta*/Tc2

Ta*/Tc

G29.96 0.02
HCO+
Ta*/Tc

Ta*/Tc

2

C2 H

1.0
0.5
1.5 c-C3H2
1.0
0.5

25

0

25

50

75

LSR (km s 1)

100 125

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 spiralarms (local arm in cyan, Sagittarius-Carina arm in magenta, Aquila-Rift in green), and the molecular cloud envelope or unidentified foregroundclouds in brown.

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 3sys (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 frominterferometric observations revealing infalling gas motion. In
addition, we also detect weak absorption lines related to the localarm (0–20 km s−1 ) at 1, 8, and 15 km s−1 in the HCO+ spectrum.
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 thesightline toward G29.96−0.02 (left panel of Fig. 8), we detectedbroad, 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 inother millimeter transitions, except those originating in the
Sagittarius arm, which are not detected in the H2 S, and c-C3 H2spectra 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 smallhydrocarbons show multiple dips within the velocity intervalof the Aquila-Rift region. Such multiple dips are also foundin HI 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
A111, page 10 of 41

transitions have counterparts of absorption components in the
spectrum of o-H2 Cl+ (Neufeld et al. 2015).
W43 MM1 and G31.41+0.31 are situated in the ScutumCentaurus 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 toforests 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 andamong 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 correspondto 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 3sys = +98 km s−1 . It is, however, not clear whether all theabsorption 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 aredetected along the sightline toward G31.41+0.31 (right panel ofFig. 8), but we have only fit components associated with the localarm (0–20 km s−1 ) because its velocity range is less affected byemission contamination. In the HCO+ spectra, both absorption
components at 7 and 13 kms have a similar depth, but for othermolecular species, the features at 7 km s−1 are much weaker thanthose 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

W.-J. Kim et al.: HyGAL: Characterizing the Galactic ISM with observations of hydrides and other small molecules. II.

Ta*/Tc

Ta*/Tc0.5
1.5

Ta*/Tc

HNC
CS
Ta*/Tc

1.0

1.0

H2 S

1

Ta*/Tc

1.00

1.0
25

0

2

0

25

50

75

LSR (km s 1)

100

125

4
0

HNC
1.0

20

0.5
1.0

1.0

1.0

CS
H2 S
C2 H

0.8
0.6

1.2 c-C3H2

Ta*/Tc

Ta*/Tc

0.75

0.8

HCN

0.5

C2 H

Ta*/Tc

1.25

1

0.5

Ta*/Tc

Ta*/Tc

2

1
0

HCN

1
1.50

Ta*/Tc

G32.80+0.19
2 HCO+

1
0
2

Ta*/Tc

G19.61 0.23
HCO+
Ta*/Tc

Ta*/Tc2

1.0

c-C3H2

0.8
20

0

20

40

60

LSR (km s 1)

80

100

120

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-Riftin 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 .
Table 6. Summary of identified spiral arms and their velocity ranges along to the observed sightlines.
SourceW3 IRS5
W3(OH)NGC 6334 I
HGAL0.55−0.85
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
G45.07+0.13
DR21
NGC 7538 IRS1

Local

Aquila-Rift

Perseus

Sagittarius-Carina

Scutum-CentaurusInter-arm(km s−1 )3-kpc(Galactic bar/center)(km s−1 )(km s−1 )Unidentified clouds
or envelope(km s−1 )(km s−1 )(km s−1 )(km s−1 )(km s−1 )−11.8, 3.6−16.0, 3.6
···
···
···
···
···
···
−5.0, 5.0
0.0, 20.0···−2.0, 20.0···
−12.2, 4.4

···
···
···
···
···
···
···
1.6, 18.4
5.0, 21.4···
5.0, 6.0
···
···
···

−35.8, −16.1−35.6, −16.0
···
···
···
···
···
···
···
···
···
···
···
···

···
···
···
···
···
3.2, 20.0
35.0, 93.0
37.0, 85.0
21.4, 50.0
30.0, 58.0
15.0, 57.0
20.0, 60.0
···
···

···
···
···
···
10.0, 40.0
20.0, 50.0
105.8, 113.9
···
···
···
58.0, 120.0
···
···
···

···
···
···
···
···
80.0, 180 (a)93.0, 127.0
···
···
···
···
···
···
···

···
···
···
···
···
−14.4, 2.4−10.0, 20.0
···
···
···
···
···
···
···

···
···
4.0, 10.0−10.0, −4.6
60.0, 75.0···
28.0, 40.0···
50.0, 100.0······
60.0, 79.0
5.0, 20.0···

Notes. In the last column, “envelope” refers to the diffuse and translucent molecular gas layers surrounding dense molecular gas regions associatedwith the background continuum sources. For the source (G32.80+0.19) marked by an asterisk, its velocity intervals of crossing spiral arms are
based on Reid et al. (2019). (a) The velocities from 120–180 km s−1 belong to the 135 km s−1 arm situated beyond the GC.

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 backgroundcontinuum source, which drives an outflows that produces
broad red- and blue-shifted emission wings for optically thicktransitions (Furuya et al. 2011). The HCO+ absorption dip at
46 km s−1 appears at the velocity of an absorption componentof C 18O (3←2) (Furuya et al. 2011), observed with the Submillimeter Array (SMA), implying infalling gas in the low-density
A111, page 11 of 41

A&A 670, A111 (2023)

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 millimetertransitions 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 crossingsof 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 locatedon the 3 kpc arm. We also find red-shifted absorption featureswith respect to the 3sys 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, C2 H, and c-C3 H2lines show similar absorption features as the HCO+ spectrum. In
the CS and H2 S spectra fewer absorption features are identified,for H2 S 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 sevenspecies, we detect widespread absorption features spanning abroad range of velocities from 2 to 110 km s−1 with the 3sys of
15 km s−1 and emission spanning 1−28 km s−1 from the background source. Apart from the red-shifted components withrespect to 3sys , the blue-shifted absorption features in the HCO+ ,HCN, C2 H, and c-C3 H2 spectra are detected in the velocity interval between 4 and 15 km s−1 which is close to the velocity rangeof the Aquila-Rift. These absorption lines are possibly associatedwith 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 featuresthat 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 theother hand, CS and H2 S show the deepest dips at 85 km s−1 .
Absorption in the Nka ,kc = 11,0 ← 11,1 line of H2 CO 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 samebackground source at similar velocities as the CS and H2 Sline with its deepest absorption appearing at ∼85 km s−1 . The
Sagittarius arm and the Aquila Rift also cross this sightline andcorrespond to velocity ranges of 15−57 km s−1 and 5−6 km s−1 ,respectively. The red-shifted absorption features with respect tothe source’s systemic velocity at 15 km s−1 could arise from lowdensity diffuse gas associated with the molecular clouds of thecontinuum source as the H2 CO absorption features (Araya et al.
2002) correspond to the features seen in the HCO+ , C2 H, andc-C3 H2 spectra. However, as its velocities correspond to Aquila
Rift as well.

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
13
CO (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 resolutionof 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 withan 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 ofour 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) and13
CO (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 noiselevel 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.

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 thehydride molecular ions (e.g., OH+ or ArH+ , Schilke et al. 2014;
Jacob et al. 2020), whose submillimeter absorption spectra havecontinuous broad line profiles over wide velocity ranges. Suchnarrow spectral line shapes might imply that the millimeter
A111, page 12 of 41

4. Analysis
4.1. Line parameter determination with XCLASSThe spectral lines observed were modeled using the eXtended
CASA Line Analysis Software Suite (XCLASS3 , Möller et al.
3

https://xclass.astro.uni-koeln.de

W.-J. Kim et al.: HyGAL: Characterizing the Galactic ISM with observations of hydrides and other small molecules. II.

G09.62+0.19

20

0

20

40

LSR (km s 1)

60

80

50

75

100

125

100

125

G31.41+0.31

13CO (1-0) GRS X 3

10

0
2.0
1.5
1.0
0.5
0.0

HCO + (1-0) IRAM 30m

1
0

0

25

50

75

LSR (km s 1)

G32.80+0.19

15
10
5
0

12CO (1-0) FUGIN

13CO (1-0) GRS X 3

HCO + (1-0) IRAM 30m

HCO + (1-0) IRAM 30m

15
10
5
0
2.0
1.5
1.0
0.5
0.0

100

125

0

25

50

75

LSR (km s 1)

G45.07+0.13

12CO (1-0) FUGIN

13CO (1-0) GRS X 3

HCO + (1-0) IRAM 30m

Ta* /Tc

Ta* /Tc

1.5
1.0
0.5
0.0

125

50

LSR (km s 1)

Tmb

Tmb

100

25

Ta* /Tc

Ta* /Tc

Ta* /Tc

HCO + (1-0) IRAM 30m

LSR (km s 1)

0

12CO (1-0) FUGIN

13CO (1-0) GRS X 3

10
0
2

0

75

0

150

Tmb

Tmb

10

50

LSR (km s 1)

1

12CO (1-0) FUGIN

13CO (1-0) GRS X 3

25

100

HCO + (1-0) IRAM 30m

W43 MM1

G29.96 0.02

002

+ (1-0) IRAM
10015030mHCO

50

13CO (1-0) GRS X 3

5

Ta* /Tc
0

12CO (1-0) FUGIN

20

Tmb

0

1.5
1.0
0.5
0.0

Ta* /Tc

Ta* /Tc

HCO + (1-0) HyGAL

2

1.5
1.0
0.5
0.0

20

12CO (1-0) FUGIN

10

13CO FUGIN (1-0) X 3

004

G19.61 0.23

12CO FUGIN (1-0)

40

Tmb

Tmb

10

0

G10.47+0.03

13CO (2-1) SEDIGISM

Tmb

20

0

20

40

60

80

LSR (km s 1)

100

0

25

50

75

LSR (km s 1)

100

125

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.

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) andthe 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 (Ntot ), the line width(∆3), and the velocity offset (3off ) from the systemic velocity. The
column density per velocity interval, dN/d3 for each velocity
channel, i, is related to the optical depth, τi , (Paper I) by!
dN
8πν3 Q(T ex ) exp(Eu /kT ex )
(1)
= 3
τi ,
d3 i
c gu Aul exp(hν/kT ex ) − 1
where Eu is the energy of the upper state for the selected transition, gu is the upper state degeneracy, and ν is the frequency
of a molecular transition. The quantity Aul is the Einsteincoefficient for spontaneous emission, and Q(T ex ) and k are theA111, page 13 of 41

A&A 670, A111 (2023)

partition function and Boltzmann constant, respectively. For theabsorption 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 motivatedby the high dipole moments of most of the species, whichlead to critical densities for the observed transitions that lie a
few orders of magnitude above the typical number density ofhydrogen molecules (nH2 ) in translucent clouds of a few hundredcm−3 (e.g., Snow & McCall 2006; Gerin et al. 2016). Thus, theexcitation 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 χ2 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 C2 H are taken into account, andthe fitting deconvolves the hfs of these molecular transitions.
We note that we only consider the ortho transitions of H2 S
and c-C3 H2 , and thus the derived column densities of thesemolecules 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 linesand 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 theemission lines. For uncertainties of column densities derived
here, we perform the error estimation by sampling a posterior
distribution of the optical depths (∝ ln(T a∗ /T c )). The sampling
was performed using XCLASS fits to multiple realizationsof 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 thenoise-added spectra in order to take into account variability ofthe posterior distributions caused by emission components.
Figures 11 and A.1–A.5 display the column density pervelocity interval, dN(X)/d3, determined for all seven species
studied and toward all sources, with uncertainties indicated asblue shaded areas. The gray parts indicate the velocity ranges ofthe 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 ofadditional errors that may arise when emission components are
simultaneously fitted with the absorption components.
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, H2 S, C2 H, c-C3 H2 , CH,
OH, O, C+ , H2 O+ , and OH+ ) and for W3 IRS5 for 11 species(same as for W3(OH) except with the addition of ArH+ andthe omission of HNC, CS, and H2 S). 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
A111, page 14 of 41

with SOFIA toward these sightlines are all associated with thebackground continuum source; toward them foreground absorption is detected. Therefore, SH is not included in this PCA
analysis. Instead of using transmission (T a∗ /T c ) or optical depth
spectra, we used column densities, dN/d3, 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 widthof 0.8 km s−1 . As discussed further below, we also accounted
for uncertainties in the derived column densities, which cansignificantly affect the results of the PCA.
Prior to performing the PCA analysis, standardization isimperative: 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 (3)Ni (3) = ai + bikX

Ci j f j (3),

(2)

j=1

where ai and bi and Ci j are coefficients, and k is the number of
species included (13 for W3(OH) or 11 for W3 IRS5). The Ci jPobey a normalization constraint, kj=1 Ci2j = 1. To examine thereliability of the PCA results, uncertainty estimates are essential.
Therefore, we made use of 1000 realizations obtained by random sampling within the column density probability distributionfunction 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 resultspresented in the following section.
In Figs. 12 and C.1, the left panels show eigen spectra ofprinciple components with percentage of variances and uncertainties (2σ), toward W3(OH) and W3 IRS5, respectively. As
the first component ( f1 (3), labeled PC-1) accounts for more thanhalf of the variance for each source, its profile resembles thecolumn density distributions of most of the species includedin the PCA. However, there are significant differences between
the W3(OH) (Fig. 12) and W3 IRS5 (Fig. C.1) sightlines inregard 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 morethan 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, H2 S, C2 H, c-C3 H2 , CH, OH, O, C+ , H2 O+ , and
OH+ ; for W3 IRS5, HCO+ , HCN, C2 H, c-C3 H2 , CH, OH, O, C+ ,H2 O+ , 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+ , H2 O+ , OH+ , andArH+ by summing up to the first five terms : Ci1 f1 (3), Ci2 f2 (3)and Ci3 f3 (3), and additionally Ci4 f4 (3) and Ci5 f5 (3) for the mentioned species above. For both sources, the first three principal
components account for ∼90% of the total variance, and the sumof their contributions provides a reasonable approximation to thecolumn densities of the observed species.

W.-J. Kim et al.: HyGAL: Characterizing the Galactic ISM with observations of hydrides and other small molecules. II.

G29.96 0.02

G32.80+0.19

in 1012 cm 2 km 1 s

HCO+

12
2
1
5.0 in 10 cm km s2

2.5

in 1012 cm 2 km 1 s

Column density per velocity interval, dN(X)/d

0.5

HNC

0.5
2
0

in 1012 cm 2 km 1 s

CSin 1012 cm 2 km 1 s

H2 S

0.0
4 in 1013 cm 2 km 1 s

C2 H

0.5

0

HCN

in 1012 cm 2 km 1 s

HNC

in 1013 cm 2 km 1 s

CSin 1013 cm 2 km 1 s

H2 S

in 1013 cm 2 km 1 s

C2 H

0.5
0.0
1
0
1
0
2

2
02
in 1012 cm 2 km 1 s

c-C3H2

1
0

in 1013 cm 2 km 1 s

20.0
in 1012 cm 2 km 1 s
1.0
0.0

0.0

HCN

Column density per velocity interval, dN(X)/d

0

HCO+

0
in 1012 cm 2 km 1 s
1.0

c-C3H2

0.5

20

0

20

40 60
LSR (km s 1)

80

100 120

0.0

20

0

20

40 60 80
LSR (km s 1)

100 120

Fig. 11. Channel-wise column density spectra (dN/d3) as a function of velocity toward G29.96−0.02 and G32.80+0.19. The dN/d3 in each panel
shows HCO+ , HCN, HNC, CS, H2 S, C2 H, and c-C3 H2 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 Ci j 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, Ci1 and Ci2 , for the first and second components, PC-1
and PC-2, obtained for W3(OH) (left panel) and W3 IRS5 (rightpanel), while Fig. 14 shows the coefficients for the second andthird terms in the expansion. Each colored vector corresponds

to a different species as indicated, and the normalization condition for the Ci j 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 speciesof a given pair are correlated with each other. The similarity
between any two vectors may be characterized by the cosineof the angle between the vectors (known as cosine similarity);
A111, page 15 of 41

A&A 670, A111 (2023)

W3(OH)
10

W3(OH)

PC-1 (71.5±2.68%)

5 HCO +

0
2.5 PC-2 (13.4±2.02%)
0.0
2.5
5
PC-3 (5.9±1.54%)
0

0
5 HCN
0
5 HNC
0
5

2 PC-5 (2.6±0.43%)
00
5 H2 S

Scaled column density per velocity interval, dN(X)/d2 PC-4 (3.8±0.70%)
01 PC-6 (1.3±0.64%)
0
1 PC-7 (0.8±0.29%)
0
1 PC-8 (0.4±0.30%)
0
0.5 PC-9 (0.2±0.10%)
0.0
0.25 PC-10 (0.1±0.05%)
0.00
0.25 PC-11 (0.0±0.04%)
0.00

10

0
5 c-C3H2
0
5

CH

0
5

OH

05

O

0

C+

2

0.0
OH +
2

0.0
20

0
C2 H
5

0
H2 O +
2.5

0.2 PC-12 (0.0±0.01%)
0.0
0.2
0.1 PC-13 (0.0±0.0%)
30

CS

0

LSR (km s 1)

10

20

0

30

20

10

0

LSR (km s 1)

1020

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, H2 S, C2 H, c-C3 H2 , CH, OH, O, C+ , H2 O+ , and OH+ )as a function of 3LSR . Black curves represent the observational data, and red dotted curves are the spectra reproduced with only the first threeprincipal components (PC-1, PC-2, and PC-3). For C+ , H2 O+ , and OH+ , the reproduced spectra indicated by blue dotted curves include one or two
more PCs, i.e., PC-4 and PC-5.

cos θ = A · B/∥A∥ ∥B∥. Figures 15 and 16 present similarity coefficients estimated for each pair of species, with cos θ 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
A111, page 16 of 41

similarity (−100%, i.e., anticorrelation). Although the sets ofspecies detected are not exactly identical toward these sightlines,
the relative positions of the vectors appear to be similar for mostof 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, C2 H, c-C3 H2 , CH, OH, O, C+ , H2 O+ , and OH+ )W.-J. Kim et al.: HyGAL: Characterizing the Galactic ISM with observations of hydrides and other small molecules. II.

W3(OH)

W3 IRS5
H2 S

HNC
HCN
HCO +
CS
C2 H
OH
CH
c-C3H2
O

0.5
0.0
0.5

c-C3H2C2 H

1.0

PC-2 (22.6±2.0%)

PC-2 (13.4±2.0%)

1.0

0.5

HCO +

0.0

OH
CH

0.5

O

C+
1.0
1.0

0.5

0.0

OH +

H2 O +

0.5

1.0

PC-1 (71.5±2.6%)

HCN

C+
1.0

OH +
1.0

0.5

0.0

H2O + ArH +
0.5

1.0

PC-1 (56.9±2.2%)

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 thedifferent species analyzed. Each colored ellipse is a 2σ confidence interval for the uncertainty of the PCA results for the corresponding species.

W3(OH)
C2 H

1.0

H2 S

0.5 O
H2 O +
OH +
0.0
C+

HCN
HNC
HCO +

0.5

CS

1.0

OH
1.0

c-C3H2
0.5
0.0

CH
0.5

PC-2 (13.4±2.0%)

c-C3H2

1.0

1.0

PC-3 (7.9±1.7%)

PC-3 (5.9±1.5%)

W3 IRS5

C2 H

ArH +
0.5 OH +
0.0
0.5

HCN

H2 O +

HCO +

C+
O

1.0

CH OH
1.0

0.5

0.0

0.5

PC-2 (22.6±2.0%)

1.0

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.

for both sightlines, the relative positions stay almost the similar
as shown as in Figs. 13 and 14, and the PCA h-plots for therecomputed 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+ , H2 O+ , and ArH+ and C+ lie
away from neutral molecular species HCN, HNC, CS, H2 S, C2 H,
and c-C3 H2 and HCO+ in the h-plots. The first three mentioned
molecular ions and C+ are considered to be tracers of gas withsmall 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 heatmaps. 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 H2 S, lie close to
the neutral molecular species rather than to the molecular ionsin the h-plots, and exhibit significant similarities as shown in
Figs. 15 and 16. Such a pattern is also found for other sightlines, W31C and W49N (Neufeld et al. 2015). In agreement with
Neufeld et al. (2015), we find the abundances of these two sulfurbearing species to peak in regions of larger molecular fraction
A111, page 17 of 41

A&A 670, A111 (2023)

W3(OH), PC-1 vs. PC-2

100%

HCN
HNC

±0.5% ±0.3%

CS

99.9
100.0
99.3
±0.4% ±0.2% ±0.7%

H2 S±1.3% ±1.0% ±0.1% ±1.1%

CH c-C3H2 C2H±0.7% ±0.4% ±1.1% ±0.7% ±0.7%±3.6% ±4.1% ±5.7% ±3.3% ±7.3% ±6.6% ±0.4%OH±2.4% ±2.9% ±4.5% ±2.7% ±5.8% ±4.7% ±1.1% ±1.2%

O

82.0
79.6
72.3
79.7
72.5
80.7
94.0
92.3
91.0
±21.4% ±22.5% ±25.8% ±23.6% ±26.4% ±22.1% ±13.2% ±14.7% ±17.7%

C+±5.7% ±5.7% ±5.5% ±6.1% ±6.9% ±9.1% ±4.3% ±8.2% ±9.5% ±10.7%

OH + H2O +

90%
±0.1%

±22.7% ±23.2% ±24.9% ±24.1% ±26.0% ±24.9% ±18.5% ±20.6% ±22.3% ±16.2% ±3.2%

99.9

80%
98.8

99.4

70%
60%
98.9

99.4

100.0

99.4

100.0

100.0

99.1

100.0

50%
99.2

40%
96.6
95.5
91.5
95.5
91.7
96.0
±1.7% ±1.9% ±2.5% ±1.6% ±3.8% ±3.8%

30%
97.7

96.8

93.3

96.8

93.4

97.2

99.9

98.4

97.5

94.4

97.6

94.5

97.9

99.7

20%
99.9

10%
0
59.5

56.0

46.4

56.2

46.7

57.6

78.2

75.1

73.0

94.8

56.8

53.3

43.5

53.5

43.8

54.9

76.1

73.0

70.7

93.7

99.9

48.7

45.0

34.7

45.2

35.0

46.7

69.5

66.1

63.6

89.9

99.2

99.5

HCO + HCN

HNC

CS

H2 S

C2H c-C3H2 CH

OH

O

C+

H2 O +-10%-20%±13.3% ±13.4% ±13.9% ±13.6% ±14.8% ±15.8% ±11.2% ±14.0% ±15.2% ±17.7% ±2.8% ±4.9%

W3 IRS5, PC-1 vs. PC-2

-30%

100%

HCN

±3.6%

C2 H

±3.8%

94.5

±0.2%

c-C3H2

±4.5%

91.7

±0.6%

99.5

±0.6%

CH

±7.7%

98.8

±15.7% ±16.1% ±17.8%

89.2

88.4

84.5

OH

±1.6%

99.4

±4.7%

91.1

±5.4%

90.3

±5.9%

86.8

±4.4%

O

88.4
±4.8%

69.5
±6.1%

68.1
±7.1%

62.4
±6.8%

94.5
±4.8%

93.0
±1.8%

C+

±10.7% ±13.6% ±13.9% ±13.8% ±10.3%

80.4

58.0

56.5

50.0

88.5

±8.5%

86.4

±2.3%

H2 O +

±9.2%

15.6

±5.2%

-15.8

±5.9%

-17.7

±5.5%

-25.1

±22.2%

30.5

±7.8%

26.3

±4.9%

60.0

±11.4%

OH +±10.0%

10.3

±6.1%

-21.1

±6.9%

-22.9

±6.3%

-30.3

±22.9%

25.3

±8.3%

21.0

±5.9%

55.6

±12.1%

67.4

±0.4%

ArH +

90%

±37.5% ±40.9% ±41.0% ±41.0% ±35.8% ±35.2% ±24.2% ±20.4% ±14.9% ±16.7%

43.8

13.7

11.8

4.2

57.0

53.3

80.7

88.6

95.6

93.9

HCO +

HCN

C2 H

c-C3H2

CH

OH

O

C+

H2 O +

OH +

95.1

80%
100.0

70%
60%

99.7

50%
40%
99.9

30%
20%
98.9

10%
71.3

0
-10%

99.9

-20%
-30%

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) andW3 IRS5 (bottom).

A111, page 18 of 41

W.-J. Kim et al.: HyGAL: Characterizing the Galactic ISM with observations of hydrides and other small molecules. II.

W3(OH), PC-2 vs. PC-3

100%
90%

HCN
HNC

98.0
99.7
±10.8% ±3.1%

CS±31.0% ±29.1% ±19.2%

H2 S

74.8
82.2
86.5
41.3
±37.7% ±23.4% ±12.7% ±24.7%

CH c-C3H2 C2H±48.3% ±32.6% ±17.2% ±31.4% ±6.3%±51.2% ±35.2% ±18.3% ±29.2% ±17.8% ±8.2% ±10.7%

OH

13.9
1.9
-6.2
53.0
-55.4
-83.7
95.0
99.6
±56.0% ±44.9% ±35.6% ±34.2% ±39.3% ±28.1% ±27.2% ±17.3%

O±45.6% ±49.1% ±49.3% ±16.6% ±73.5% ±79.2% ±75.2% ±67.7% ±57.2%

C+±7.8% ±5.2% ±5.3% ±22.1% ±26.0% ±33.0% ±36.5% ±33.4% ±38.2% ±43.7%

OH + H2O +

80%

±9.0%

±35.5% ±37.1% ±29.5% ±18.8% ±41.7% ±55.9% ±67.7% ±63.7% ±65.3% ±43.7% ±32.9%

99.3

70%

91.3

42.6

85.8

53.1

60%
50%

81.4

40%

59.9

2.1

30%
20%

91.9

10%

-17.7
-29.3
-37.0
24.0
-78.6
-96.6
±51.4% ±36.5% ±23.5% ±36.9% ±19.6% ±9.5%
4.9

-84.9

-7.0

-78.0

-15.1

-72.7

45.2

-99.1

-62.6

-28.4

-88.2

11.5

0
-10%

97.4

-37.0

-20%

-56.9

-30%
-40%

-64.1

-50%

-100.0

-99.6

-98.5

-90.2

-76.5

-45.0

20.2

-2.3

-11.3

83.5

-97.5

-94.2

-91.1

-98.1

-58.2

-21.6

-4.6

-26.9

-35.4

94.5

-100.0

14.9

-60%
-70%

96.9

-80%

-98.9

-97.4

-92.4

-72.9

-40.1

-7.7

-16.6

86.4

99.9

98.1

HCO + HCN

HNC

CS

H2 S

C2H c-C3H2 CH

OH

O

C+

H2 O +±9.0% ±9.5% ±6.7% ±16.6% ±22.5% ±26.4% ±35.1% ±27.7% ±35.9% ±40.6% ±4.9% ±21.6%

W3 IRS5, PC-2 vs. PC-3

-90%
-100%

100%
90%

HCN
C2 H

±44.6%

c-C3H2±57.7%

CH-40.1±91.3%

OH-29.7±95.4%

O±61.5% ±11.9% ±10.2%

C+±35.0%

H2 O +±47.4% ±20.3% ±23.2% ±33.1% ±69.3% ±62.2% ±40.1% ±15.5%

OH +±46.9% ±19.0% ±21.1% ±26.6% ±65.1% ±41.5% ±33.1% ±11.9% ±18.6%

-78.0

-77.8

-70.6

-48.9

-26.1

-36.6

37.1

91.5

98.5

ArH +

80%
±43.0%-60.4±77.8%-60.2±38.8%-51.3±41.0%-26.2±48.2%-48.8±75.1%-58.2±66.7%

13.4±51.8%

78.9±37.4%

91.3±63.9%

97.0±30.9%

HCO +

HCN

C2 H

c-C3H2

CH

OH

O

C+

H2 O +

OH +

100.0

99.4

70%
60%

99.4

±3.6%

92.8

±8.3%

92.8

±6.0%

-40.3
±45.8%-49.9±41.8%-71.4±30.0%-29.9±39.0%-40.0±39.5%-63.2±35.9%

99.4±50.3%

-87.1

-87.2

-92.0

±3.3%

-99.1

±29.6% ±32.9%

80.0

72.8

-96.6

±9.9%

-96.6

±12.1% ±20.2% ±59.8% ±43.0% ±22.7%

-93.2

-80.0

15.2

4.1

-87.7

-87.6

-81.9

50%
40%

96.3

30%
20%
10%
0
-10%

-63.4

-8.9

-19.9

-20%
-30%

71.5

52.7

-40%
-50%

97.1

-60%
-70%
-80%
-90%
-100%

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) andW3 IRS5 (bottom).

A111, page 19 of 41

(b) HNC

1012
1011
r = 0.66

1010

1010 1011 1012 1013
dN(HCO+)/d(cm 2 km 1 s)

r = 0.78

dN(X)/d (cm 2 km 1 s)

r = 0.81

1014 (c) C2H

r = 0.71

dN(X)/d (cm 2 km 1 s)

1013

Scutum-Centaurus
3-kpc(GC)Inter-armdN(X)/d (cm 2 km 1 s)

Local
1015
Aquila-Rift
Perseus14
Sagittarius-Carina
10(a) HCN
1013
1012
1011
1010

dN(X)/d (cm 2 km 1 s)

dN(X)/d (cm 2 km 1 s)

dN(X)/d (cm 2 km 1 s)

A&A 670, A111 (2023)

1013
1012
(d)c-C3H2

1012
1011

1010 1011 1012 1013
dN(HCO+)/d(cm 2 km 1 s)

1013 (e) CS
1012
1011
r = 0.45(f) H2S

1013
1012
1011

r = 0.62

1011

dN(HCO+)/d

1012

1013

(cm 2 km 1 s)

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) C2 H versus HCO+ , (d) c-C3 H2 versus HCO+ , (e) CS versus HCO+ , and (f) H2 S versus HCO+ . The color codes correspond to specificspiral 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.

rather than in regions traced by C+ and the hydride ions OH+ ,H2 O+ , and ArH+ .
Third, the vectors for CH and OH lie very close to each otherin all the h-plots shown in Figs. 13 and 14. Their correlation
coefficients exceed 99.9% (Figs. 15 and 16). In addition, thesemolecules 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 andthe vector for O located closer to those for the ionized species.
CH is considered a good tracer for H2 because it is present ingas 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 ionsthat are found in gas with small molecular fractions.
5.2. Column densities and abundances

In Fig. 17, we compare channel-wise column densities for allsightlines – except for NGC 7538 IRS1 and HGAL0.55−0.85,
toward which only HCO+ is detected – to investigate whether thecolumn densities show a linear relationship and whether there
is any noticeable variation associated with specific spiral- orinter-arm regions. Due to high noise levels and contaminationby emission lines, we have fewer detections for H2 S and CS.
To obtain a reasonable number of data points required for reliable statistical results, we constrain the detection thresholds oftheir column densities to the 1.5 rms and 2 rms levels for H2 S
and CS, respectively, while for the remaining five molecules,
we adopt a 2.5 rms threshold to mitigate uncertainties caused bypoor sensitivity.
A111, page 20 of 41

The comparison of dN(HCN)/d3 and dN(HCO+ )/d3 in
Fig. 17a shows the best correlation, with a Pearson correlation
coefficient (r) of 0.81. dN(C2 H)/d3 in Fig. 17c has the secondbest correlation with dN(HCO+ )/d3, 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 andC2 H 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)/d3 anddN(c-C3 H2 )/d3 show moderate correlations (r = 0.66–0.71) withdN(HCO+ )/d3. In contrast, the two sulfur-bearing molecules
appear to be less correlated (r = 0.45–0.62) with dN(HCO+ )/d3,
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)/d3 versus dN(HNC)/d3, 0.79
for (b) dN(C2 H)/d3 versus dN(c-C3 H2 )/d3, and 0.77 for (c)dN(CS)/d3 versus dN(H2 S)/d3. Such strong correlations between
the same chemical families (HCN and HNC, C2 H and c-C3 H2 ,as well as CS and H2 S, in Fig. 18) have also been foundin 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 slopethat 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 intervalof the best-fit uncertainties. These uncertainties are obtained by

W.-J. Kim et al.: HyGAL: Characterizing the Galactic ISM with observations of hydrides and other small molecules. II.

Fig. 18. Same as Fig. 17 but for (a) HCN versus HNC, (b) C2 H versus c-C3 H2 , and (c) CS versus H2 S.
(a1)MedianMean
Godard et al. 2010

0.02
2

4
6
N(HCN)/N(HCO + )
(a2)

2

8

0.00
0

10

Density

4

1.0
1.5
2.0
N(HNC)/N(HCO + )
(a3)

2.5

MedianMean
Godard et al. 2010

2
00.0

0.5

1.0
1.5
N(HNC)/N(HCN)

00

3.0

2.0

(b2)

(c1)

0.4

MedianMean
Lucas & Liszt et al. 2002

0.2

80

MedianMean
Godard et al. 2010

0.0
0

2

4
6
N(CS)/N(HCO + )

8

(c2)

0.2

10
Median
Mean

0.1

1

2
3
N(c-C3H2)/N(HCO + )

0.06

(b3)

0.04
0.02
0.000

MedianMean
Lucas & Liszt 2000
Godard et al. 2010

40
60
N(C2H)/N(HCO + )1

Density

0.5

20

2

MedianMean
Godard et al. 2010

1
00.0

(b1)

0.04

20

40
N(C2H)/N(c-C3H2)

4MedianMean
Lucas & Liszt 2000
Gerin et al. 2011

60

Density

0.6
0.4
0.2
0.00

0.0
0.0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0
N(H2S)/N(HCO + )
1.5
1.0
0.5
0.00.0

(c3)

0.5

1.0

MedianMean
Neufeld et al. 2015

1.5 2.0 2.5
N(CS)/N(H2S)

3.0

3.5

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).

resampling the data points and then iteratively fitting the resampled data sets. Comparing dN(HCO+ )/d3 versus dN(HCN)/d3,
we find that the median value and the best-fit agree fairly well.
For the other cases, comparing different chemical groups, thebest fit lines are not as steep as the lines representing the median.
Such discrepancies become significant when comparing sulfurcontaining molecules (CS and H2 S) with HCO+ , shown in plotse and f of Fig. 17 since their relationships are weakly correlated. In addition, each color represents a different spiral-arm orintermediate arm region, or an unassigned foreground clouds,
as tabulated in Table 6. For HCN, HNC, and the two smallhydrocarbons, 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)/d3 compared to the other spiral arms thathave dN(HCO+ )/d3 ≈ 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(C2 H)/d3 <1 × 1013 cm−2 km−1 s, which plateaus as dN(c-C3 H2 )/d3
increases (≈1−4 × 1011 cm−2 km−1 s). As dN(C2 H)/d3 increases
beyond the inflection point from ≈1 × 1013 cm−2 km−1 s tohigher C2 H column densities, the column densities of thesesmall 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 ofN(C2 H) 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 ofsample 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 dashedvertical lines are median and mean values, respectively, of the
distributions. The values for the median and mean as well as thestandard deviations (SDs) are listed in Table 7. We compare thevalues 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
A111, page 21 of 41

A&A 670, A111 (2023)
Table 7. Median, mean and standard deviation of the column density
ratios for the seven species studied in this work.

Ratio

Median

Mean

SD(†)

N(HCN)/N(HCO+ )N(HNC)/N(HCO+ )N(HNC)/N(HCN)

1.37
0.33
0.21

1.78
0.49
0.27

1.68
0.89
0.20

N(C2 H)/N(HCO+ )N(c-C3 H2 )/N(HCO+ )N(C2 H)/N(c-C3 H2 )

14.06
0.33
29.99

19.81
0.57
30.26

18.28
0.53
13.57

N(CS)/N(HCO+ )N(H2 S)/N(HCO+ )N(CS)/N(H2 S)

0.95
1.22
0.56

1.99
2.07
0.73

3.33
2.13
0.58

Notes. (†) SD is the standard deviation. For H2 S and CS, the detection threshold lowers to 1.5× rms, and 2× rms levels, respectively,
while ratios of the other species are obtained from data restricted by>2.5× rms level.

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) ratioof 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
Av 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 C2 H and c-C3 H2
to N(HCO+ ) (Figs. 19b1,b2) and N(C2 H)/N(c-C3 H2 ) (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(H2 S) versus N(HCO+ ) and N(CS) versus
N(H2 S), the mean ratios are 1.99, 2.07, and 0.73, respectively.
Like other species, these two sulfur-containing molecules havemean 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 themeasurements obtained here.
The detected absorption features of simple molecular species
studied in this work have different velocity components, andsome 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 cloudcomponents and list the average column densities for all 14 lineof-sight sources in Tables 8 and B.1. Figure 20 shows the column
densities (upper and middle image) of HCN, HNC, C2 H, c-C3 H2 ,CS, and H2 S 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 )A111, page 22 of 41= 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 Av (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 ) (Av ) 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 relationshipsof the column densities of CN-bearing molecules. They show arapid 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 abundanceof 3 × 10−9 relative to H2 , against extra-galactic continuum
sources. The lower-left panel shows the column density ratiosof 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 (C2 H and c-C3 H2 ) show
tight linear correlations with N(H2 ), and their abundance varies
only a little across different environments from diffuse (Av < 1)
gas to dense molecular gas (Av > 5), through translucent molecular gas regions in between. The C2 H abundance measured here
lies in an approximate range from 10−8 to 10−7 , while that ofc-C3 H2 is pretty much within 10−9 −10−8 . These abundances relative to H2 agree well with the X(C2 H) ∼ 4−7 × 10−8 (Lucas& Liszt 2000; Gerin et al. 2011) and X(c-C3 H2 ) ∼ 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(C2 H)/N(c-C3 H2 )ratios in individual cloud components of our targets are constantover the values of N(H2 ) probed, with an average column density
ratio of N(C2 H)/N(c-C3 H2 ) ∼ 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(H2 S) also showpoor correlations with N(H2 ) in Fig. 20, in contrast to the column
densities of HCN, HNC, C2 H and c-C3 H2 , although N(CS) has
some degree of correlation with N(H2 ). The abundances of CS
and H2 S derived in diffuse clouds are higher >10−8 than thosein translucent clouds (10−9 < abundance <10−8 ). However, apartfrom the fitting uncertainties, the derived column densities of CS
and H2 S probably contain higher uncertainties than the lines ofthe other species, for example, due to poor sensitivities, as seenin Fig. 8. Therefore, it is difficult to conclude that the abundanceof 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 H2 S). The CS abundances toward the Galactictranslucent clouds are in good agreement with X(CS) ∼ 4 × 10−9

W.-J. Kim et al.: HyGAL: Characterizing the Galactic ISM with observations of hydrides and other small molecules. II.
Table 8. Derived column densities over specific velocity intervals.
Source3LSR range(km s−1 )N(H2 )(1021 cm−2 )N(HCO+ )(1012 cm−2 )N(HCN)(1012 cm−2 )N(HNC)(1012 cm−2 )N(CS)(1012 cm−2 )N(H2 S)(1013 cm−2 )N(C2 H)(1013 cm−2 )N(c-C3 H2 )(1012 cm−2 )W3 IRS5−24, −18−6, −1−1, 5

0.37+0.10−0.10
0.08+0.01−0.01
0.27+0.06−0.06

1.11+0.31−0.30
0.24+0.03−0.03
0.82+0.18−0.18

1.67+0.50
−0.49
···
···

···
···
···

···
···
···

···
···
···

2.17+0.80
−0.69
···
···

0.79+0.08
−0.08
···
···

W3(OH)−23, −15−14, −7−7, 30.07+0.03−0.03
0.60+0.05−0.05
0.87+0.10−0.10

0.22+0.09−0.08
2.24+0.20−0.20
3.44+0.48−0.47

0.08+0.06−0.08
2.71+0.22−0.22
3.72+0.41
−0.36

···
0.36+0.03−0.03
0.78+0.04
−0.04

···
···
2.67+0.15
−0.15

···
···
0.34+0.02−0.02

0.30+0.01−0.01
1.01+0.02−0.02
4.57+0.41−0.41

0.13+0.01−0.13
0.52+0.03−0.03
1.36+0.10−0.10

NGC 6334 I

0, 12 (a)4.79+2.32−2.56

25.84+15.39−15.399.17+0.53−0.53

1.35+0.15
−0.14

···

···

1.98+0.43−0.40

0.72+0.25−0.23

HGAL0.55−0.85−14, −4 (a)0.56+0.28−0.29

2.04+1.26
−1.18

···

···

···

···

···

···

9, 20
20, 2962, 7346.14+45.78−32.942.29+0.65−0.69
0.82+0.62−0.59

922.76+915.66−658.84
10.82+3.72−3.72
3.23+3.06−2.50

13.4+0.56−0.56
24.80+3.93−3.93

4.20+0.64−0.64
14.46+23.68−13.18

···

···

···
···
···

5.66+17.06−4.99
2.25+0.66
−0.66
···

···
13.34+7.83
−7.83
···

···
···
···

−18, −9
−9, 3
3, 7
7, 14
14, 1919, 2828, 3232, 4444, 5182, 94114, 133
137, 151
151, 159
159, 164
164, 175

0.54+0.14−0.14
2.00+0.82−0.89
0.65+0.15−0.16
2.64+0.95−1.01
0.95+0.20−0.21
1.52+0.38−0.40
1.71+0.75−0.82
2.53+0.74−0.78
0.06+0.03−0.06(b)0.23+0.07−0.05(b)1.26+0.27−0.28
0.85+0.15−0.16
4.02+1.47
−1.57
+0.06
0.24−0.06
0.22+0.04−0.04

1.61+0.42−0.42
9.21+4.63−4.63
2.45+0.69−0.69
12.83+5.58−5.58
3.83+0.96−0.96
6.70+2.01−2.01
7.67+4.11−4.11
12.20+4.31−4.31
0.18+0.08−0.18
0.70+0.20−0.14
5.36+1.38−1.38
3.37+0.73−0.73
21.02+9.33−9.33
0.71+0.18−0.18
0.65+0.13−0.13

3.59+1.13−1.13
15.95+7.50−7.50
7.18+7.31−5.63
20.99+12.26−12.26
3.62+4.78−2.53
9.57+7.96−7.81
7.92+3.76−3.76
36.84+22.83−22.79···22.05+2.23−2.23
9.75+3.56−3.56
7.05+2.11−2.11
19.50+13.7−13.7
1.81+0.47−0.47
1.15+0.81
−0.54

···
···
1.17+0.32−0.32
3.38+0.82−0.82
1.54+0.39
−0.39
···
···
4.87+1.38
−1.38
···
···
···
···
3.08+0.92
−0.92
···
···

···
2.65+0.32−0.32
4.46+0.82−0.82
5.44+0.81
−0.81
···
···
···
···
···
···
9.58+0.96−0.96
13.44+2.94−2.93
13.78+2.30−2.30
4.49+0.54−0.54
7.44+1.02
−1.02

···
···
···
···
···
···
···
···
···
···
···
···
···
···
···

···
···
1.85+0.27−0.27
12.51+4.56−4.47
2.49+1.45−1.24
17.59+2.06−1.82
11.05+1.20−1.20
22.93+8.24
−5.39
···
···
···
···
4.23+1.43
−1.41
···
···

···
···
···
···
···
···
···
···
···
···
···
···
···
···
···

G09.62+0.19

G10.47+0.03

Notes. N(H2 ) is derived using N(HCO+ ); N(H2 ) = N(HCO+ )/ 3 × 10−9 for a case with N(HCO+ ) < 2.8 × 1012 cm−2 , N(H2 ) = N(HCO+ )/2 × 10−8
for a case with 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.
The column densities derived for each species toward the remaining sources is tabulated in Appendix B. The velocity intervals are defined, basedon HCO+ absorption line profiles. (a) Refers to the velocity intervals corresponding to molecular gas components associated with the backgroundcontinuum sources, and thus the derived column densities of these velocity intervals indicate lower limits. (b) Indicates the N(H2 ) for the velocity
intervals belonging to the GC region where likely have higher X(HCO+ ) (>3.9 × 10−9 for the central molecular zone Riquelme et al. 2018) than the
Galactic disk regions.

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 abundancesof H2 S are similar with X(H2 S) determined from diffuse clouds
in different parts of the Galactic plane (Neufeld et al. 2015). In
the plot of N(CS)/N(H2 S), 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(Av ∼ 1−3 mag). In addition, the column density ratios do notshow any correlation with the total hydrogen column density inthe sightlines studied here.
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 abundanceof 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 dottedlines separating the three types of molecular gas clouds; diffuse
clouds below Av < 1.0, translucent clouds in 1.0 < Av < 5.0,
while regions with Av > 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 areshown 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 H2 S, cyan cross for C2 H, and grayhexagons for c-C3 H2 .
Overall, some variations in abundance along the selectedsightlines 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 C2 H and c-C3 H2 change little andare instead consistent in both velocity ranges or between diffuse
A111, page 23 of 41

A&A 670, A111 (2023)

1012 10 81011 10 9

10 81011 10 9

N(X)/N(X)

N(X)/N(X)
Av=1 Av=5
21
10
1022
2
N(H2) (cm )1020

1011 10 91010 10 10
20
1021
C210
H/c-C
3 H2

1012 10 8101
Av=1 Av=5
21
10
1022
2
N(H2) (cm )1013 10 71012 10 810111 10 91010202S 1021
CS/H

1022

102

1020

1013 10 7

10 9
1011
14
10
H2S N(H2) (cm 2)1012 10 8

109

1022

101
100

1012 10 8

N(X) (cm 2)

HNC N(H2) (cm 2)

10102 10 10101020 1021
HCN/HNC

1013 10 7

N(X)/N(X)

1012

CS

1011 10 921013 c-C3H2 N(H2) (cm )N(X) (cm 2)

N(X) (cm 2)

1013

C2 H
6
10
14
10

N(X) (cm 2)1013 10 7

N(X) (cm 2)

N(X) (cm 2)1014 HCN

1022

100

10 1

Av=1 Av=5
21
10
1022
2
N(H2) (cm )1020

Fig. 20. Comparison of the column density of the presented molecular species and N(H2 ). Each colored symbol represents different individualclouds in the sightline toward the observed background continuum sources (DR21: red X, G09.62+0.19: blue circle, G10.47+0.03: green uptriangle, 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 ofgiven 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(C2 H)/N(c-C3 H2 ), the gray horizontal dashed line indicates a mean value of 30.26 in the column
density ratio.

and translucent clouds. In Table 9 the mean abundances of thesesmall hydrocarbons are surprisingly similar, while N(H2 ) of diffuse clouds is smaller than that of translucent clouds by a factorof 4. We note that all calculations for the median values do notinclude the absorption features associated with background continuum sources. The median abundances of HCN and HNC donot show significant changes from diffuse to translucent clouds.
In contrast, we note that X(H2 S) (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 ofX(H2 S) and X(CS) are 2.8 × 10−9 and 6.6 × 10−9 , respectively.
These species’ higher abundances in diffuse clouds are alreadynoticeable in Figs. 20, 21, E.1, and E.2. Overall, the mean ormedian abundances of the discussed species fit well within
the ranges of values derived for high-altitude clouds or otherclouds 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
A111, page 24 of 41

et al. 2021), the high UV fields (∼5 × 105 in Habing units, Rizzo
et al. 2003) from embedded massive star-forming regions, oroutflows, or the feedback from young high mass stars at thelate stage of molecular clouds (e.g., influence of turbulenceand shocks caused by expanding HII regions and stellar winds).
All these effects could, to different degrees, mix gas from starforming regions with diffuse or/and translucent gas, and resultin 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-positionvelocity images of two selected sightlines (G19.61−0.23 andG32.80+0.19). Compared with other sightlines, these twosightlines have absorption features well separated from thebackground emission lines. As a result, absorption lines of allseven 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 theoriginal spectral resolution (0.2 km s−1 ). Toward both sightlines,
we notice complex structures of dense molecular gas rather thanW.-J. Kim et al.: HyGAL: Characterizing the Galactic ISM with observations of hydrides and other small molecules. II.

N(H2) (cm 2)

W3(OH)

Translucent cloud

1021

Diffuse cloud

1020

HCN
HNC
CS
H2S
C2 H
c-C3H2

N(X)/N(H2)

10 6
10 8
10 10
25

20

15

10

5
1
(km
s
)
LSR

N(H2) (cm 2)
N(X)/N(H2)10Translucent cloud

1021

Diffuse cloud

1020
10 6
10 8

10 10

12CO

0

12CO

20

40

LSR (km s 1)

12CO

60

80

100

G19.61-0.23

1022
N(H2) (cm 2)5

G29.96-0.02

1022

N(X)/N(H2)0Translucent cloud

1021

Diffuse cloud

1020
10 7
10 9

12CO

20

0

12CO

20

40

12CO

60

LSR (km s 1)

80

100

120

140

N(X)/N(H2)

N(H2) (cm 2)

G32.80+0.19
Translucent cloud
1021

Diffuse cloud

10 6
10 8

10 10

12CO

0

12CO

20

40

60

LSR (km s 1)

12CO

80

100

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 detectedfrom archival data at its given sensitivity. All the other sources are displayed in Figs. E.1 and E.2.

A111, page 25 of 41

A&A 670, A111 (2023)
Table 9. Median value of abundances relative to H2 and N(H2 ) of each targeted species X observed toward different cloud components.

All clouds (a)Species

Diffuse cloudTranslucent cloud#

N(X)/N(H2 )N(H2 ) (cm−2 )#N(X)/N(H2 )N(H2 ) (cm−2 )#N(X)/N(H2 )N(H2 ) (cm−2 )

HCN
HNC

64
42

4.80 × 10−9
1.17 × 10−99.69 × 1020
1.11 × 1021

31
164.49 × 10−9
1.02 × 10−9

5.26 × 1020
5.77 × 1020

30
236.13 × 10−9
1.40 × 10−9

1.72 × 1021
1.80 × 1021

C2 H
c-C3 H246
33

3.84 × 10−8
1.36 × 10−9

1.09 × 1021
8.68 × 1020

20
17

4.11 × 10−8
1.93 × 10−95.40 × 1020
5.26 × 1020

24
143.82 × 10−8
1.23 × 10−9

1.72 × 1021
1.72 × 1021

CS
H2 S

28
16

3.26 × 10−9
7.67 × 10−9

1.20 × 1021
1.50 × 1021

1049.28 × 10−92.53 × 10−8

5.40 × 1020
4.02 × 1020

18
112.77 × 10−9
6.62 × 10−9

1.74 × 1021
1.69 × 1021

Notes. (a) Includes all cloud types (dense, translucent, and diffuse). The # columns indicate the number of foreground components used for thestatistics. All features associated with background sources are excluded in these calculations because the column densities of these features only
represent lower limits.

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).

simple shapes like spheres or cylinders. We can clearly see dense
and clumpy molecular gas structures at the systemic velocitiesof these sightlines (for G19.61−0.23, 3sys = 41.8 km s−1 , andfor G32.80+0.19, 3sys = 15 km s−1 ). Some foreground clouds(velocity ranges of 28–40 km s−1 and 58.5–70.8 km s−1 forG19.61−0.23 and 90–110 km s−1 for 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.
A111, page 26 of 41

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) tostudy 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 cloudis in a static state. Throughout the model cloud, the thermaland chemical profiles are computed by assuming thermal and4https://ism.obspm.fr/pdr.html

W.-J. Kim et al.: HyGAL: Characterizing the Galactic ISM with observations of hydrides and other small molecules. II.
Table 10. Input parameters of the Meudon PDR isobaric models.

Fixed parameters
Oxygen abundance
Carbon abundance
Nitrogen abundance
Sulfur abundance
Rv = Av /E(B − V)
Gas to Dust ratio
Grain size distribution index
Minimum grain radius (µm)
Maximum grain radius (µm)

3.2 × 10−4
1.3 × 10−4
7.5 × 10−5
1.9 × 10−5
3.1
100
3.5
0.003
0.3

Free parameters
Radiation field G0
Cosmic ray ionization rate ζ (s−1 )Av,max (mag)Pressure (K cm−3 )1 & 100
5 × 10−17 , 10−16 & 10−15
0.1, 1, 5 & 10
103 , 3 × 103 , 5 × 103 & 104

Notes. The carbon and sulfur atoms are in their ionized form in thechemical file. The UV interstellar radiation field is in Mathis unit; G0 =1 corresponds to a flux of 3.03 × 10−4 ergs cm−2 s−1 .

chemical equilibrium for every location. All models simulated
here are isobaric models that consider constant thermal pressure. The calculated temperature and density profiles show thatthe 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 thiswork, 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 thesimulated PDR models. We used default values for initial abundances of elements, extinction curve (Rv ), and dust properties
and considered them to be fixed parameters. However, we havechanged the values for the interstellar radiation field (G0 in
Mathis units), which for the solar neighborhood is G0 = 1 andfor FUV illuminated PDRs such as the Horsehead Nebula isG0 =100 (Pety et al. 2005). The value of G0 only changes on theobserver side and is fixed to 1 for the backside of the cloud in allmodels. Since the observed galactic sightlines pass over different
parts of the Milky Way, we assume that diffuse clouds along thesightlines 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 and1 × 10−15 s−1 in our models. In addition, we have assumed typicalvalues of interstellar pressure in diffuse and translucent cloudsof 1000, 3000, 5000, and 10 000 K cm−3 and chosen total extinctions along the plane-parallel slab of Av = 0.1, 1, 5, and 10 mag.
We note that in the Meudon PDR isobaric models, each velocityintegrated 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 andlines. 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 andζ = 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 andζ = 1 × 10−15 s−1 in purple. Initial pressures of 1000, 3000, 5000,
and 10 000 K cm−3 are indicated with dotted-, dashed-, dasheddotted-, and solid-lines, respectively. In addition, the results withdifferent visual extinctions are represented by colored triangles(Av = 1 mag), colored squares (Av = 5 mag), and colored circles(Av = 10 mag). We note that all the predicted column densities
at Av = 0.1 mag fall outside the range of column densities shownin 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 theobserved quantities, only those models with ζ = 5 × 10−17 −1 ×
10−16 s−1 and an initial pressure of 10 000 K cm−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 areat nH ∼ 1400−2000 cm−3 and decrease in gas temperature at
Av ∼ 1 mag. For HNC, all models fit reasonably within theobserved 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+ ) fromthe 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 Av ≤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, especiallyfor 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 underestimationof 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 (seeGodard 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 H2 O +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-dominatedchemistry cannot reproduce the observed column densities ofthese species in diffuse and translucent clouds. In the turbulencedominated 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+ , CH+2 , CH+3 as wellas NH. The TDR models from Godard et al. (2009, 2014) show a
A111, page 27 of 41

A&A 670, A111 (2023)

1012
1011

1013
1012

1013

HNC N(H2) (cm 2)

1012
1011
102

1014

C2 H

1011
N(X) (cm 2)

N(X) (cm 2)

N(X) (cm 2)

1013

1013

N(X)/N(X)HCN

HCN/HNC

101

c-C3H2 N(H2) (cm 2)

1012
1011
10104
10

N(X)/N(X)

N(X) (cm 2)1014

C2H/c-C3H2

103
102
101

100
1011

1011

1012
1013
N(HCO + ) (cm 2)

1014

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 andζ = 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-, andsolid-lines, respectively. Av =1, 5, and 10 mag are marked with colored
triangles, squares, and circles, respectively.

A111, page 28 of 41

1012
1013
N(HCO + ) (cm 2)

1014

Fig. 24. Column densities of C2 H and c-C3 H2 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.

considerable increase in the formation of these three species via
ion-neutral reactions, CH+ + N → CN+ + H2 → HCN+ or HNC+
+ H2 → HCNH+ ; CH+2 + N → HCN+ + H2 → HCNH+ ; CH+3 + N→ HCNH+ ; CH+3 + O → HCO+ + H2 . Additionally, the reactionof CH+ with oxygen enhances the abundance of CO+ , leading to
HCO+ .
5.4.2. C2 H and c-C3 H2Figure 24 shows comparisons between column densities predicted from isobaric PDR models and observations for C2 H

W.-J. Kim et al.: HyGAL: Characterizing the Galactic ISM with observations of hydrides and other small molecules. II.

N(X) (cm 2)

1014

CS

1013
1012
1011

N(X) (cm 2)

1014
1013
1012
10111
10
N(X)/N(X)

H2 S

CS/H2S100

10 11011

1012
1013
N(HCO + ) (cm 2)

1014

Fig. 25. Column densities of CS and H2 S 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 × 10−17 s−1 , for less shielded regions Av < 5 (colored squaresymbols). By contrast, in denser regions having N(HCO+ ) >2 × 1012 cm−2 , the low-density models (dashed lines, nH ≈100−500 cm−3 ) with lower G0 of 1 (red and blue colors) at high
Av > 5 mag seem to fit the observed column densities better. For
c-C3 H2 , 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 C2 H. The comparison between N(C2 H)/N(c-C3 H2 )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 ofthese hydrocarbons close to the observed values, unlike the casesof HCN, HNC, and HCO+ which are associated better with highdensity gas materials. Nevertheless, the predicted column densities of the small hydrocarbons are underestimated by a factor
of a few. In particular, for c-C3 H2 , toward diffuse clouds with
N(c-C3 H2 ) < 2 × 1012 cm−2 , the discrepancy is more than abouta factor of 10. In the isobaric PDR models, the predicted column
densities of c-C3 H2 are total column densities of ortho and para
species without separate spin symmetries (with a spin-weightratio of 3/1 for ortho/para). Thus, with consideration of thisfact, the discrepancies between the observations and the models
become larger.
In the PDR chemistry, C2 H is mainly produced by the recombination of C2 H+2 and C2 H+3 with electrons (e.g., Godard et al.
2009; Mookerjea et al. 2012). In addition, it is formed by thephotodissociation of C2 H2 (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-C3 H2 , once C3 H+ isformed by reactions of C2 H2 with C+ , C3 H+ produces the linear
and cyclic C3 H+3 isomers via reactions with H2 (Maluendes et al.
1993). The resulting isomers produce linear and cyclic-C3 H2 by
dissociative recombination (Fossé et al. 2001). In addition, therecombination of C3 H+ also contributes to the abundances of
C2 H (Guzmán et al. 2015).
Similar to HCN, HNC, and HCO+ , turbulence-dominatedchemistry can considerably increase the abundances of C2 H
and c-C3 H2 by enhancing abundances of their precursor, C2 H+
which is formed from CH2 via hydrogenation reactions. Not
only that, but also the endoenergetic reaction of C+2 + H2 with−∆E/k = 1260 K (Godard et al. 2009) increases the abundanceof C2 H. Aside from the contribution of turbulent dissipation,
the formation of small hydrocarbons possibly involves the topdown hydrocarbon chemistry that describes polycyclic aromatichydrocarbons (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).
5.4.3. CS and H2 S+

and c-C3 H2 . 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 nH ≈ 100−500 cm−3 up to 1000 cm−3 . The N(C2 H) toward
the diffuse clouds with N(HCO+ ) < 2 × 1012 cm−2 (corresponding to an observed Av ∼ 1) is close to the column densities
from the isobaric models with moderate pressure values (dashedand dash-dotted green lines) of 3000−5000 K cm−3 giving nH ≈500−1000 cm−3 and strong UV radiation of G0 = 100 and ζ =Figure 25 shows comparisons of the column densities of thetwo sulfur-bearing species and their column density ratios with
N(HCO+ ). The top panel shows a good agreement between thepredicted 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 K cm−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
A111, page 29 of 41

A&A 670, A111 (2023)

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 S + CH+3 → HCS+ in the TDR
route (Neufeld et al. 2015). We have found that the resultsof our PDR models are obtained in more shielded gas (nH ∼100−1000 cm−3 and Av > 1 mag) compared to the more diffuse gas (nH = 50 cm−3 and Av = 0.4 mag) considered in the
TDR and shock models presented in Neufeld et al. (2015). The
destruction of CS reacting with 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 H2 S. We
also note that, as in the case of c-C3 H2 , the H2 S 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-H2 S. In
UV-dominated chemistry, reactions of S+ + H2 → H2 S+ + e –→ H2 S is the main pathway to form H2 S. However, in low Av(<0.5 mag) regions, the endothermic reaction of SH + H2 → H2 S
+ hν (with −∆E/k = 6862 K) becomes the predominant formation pathway for H2 S (e.g., Sternberg & Dalgarno 1995; Neufeld
et al. 2015). In addition, the abundances of H2 S+ , which is the
precursor of H2 S, can be enhanced by two other endothermic
reactions: SH+ + H2 → H2 S+ + H (−∆E/k = 6380 K), and S++ H2 → H2 S+ + hν (−∆E/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 H2 S toward theobserved 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 H2 S
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) andmost dust grains are negatively charged. According to the gasgrain models of Navarro-Almaida et al. (2020), the chemicaldesorption of H2 S (via solid-H + solid-HS → H2 S) can explain
the high H2 S abundances observed in translucent clouds (cloudedges, 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 chemicaldesorption may also help explain the high H2 S abundances
derived toward the Galactic sightlines in our sample.

Using principal component analysis to investigate correlations among the species observed with the IRAM 30 m telescopeand 7 other species observed with SOFIA (Paper I), we findthat C+ and the hydride ions OH+ , H2 O+ , and ArH+ are poorly
correlated with neutral molecules and HCO+ . Sulfur-bearing
molecules, CS and H2 S, appear to be better correlated with theneutral molecules than with hydride ions, which are tracers ofgas with small molecular fractions. In addition, CH, OH, and O
tend to be partially associated with both mostly molecular andpredominantly atomic gas.
For the column densities, we find that N(HCN) and N(HNC)
increase nonlinearly with N(H2 ). While the abundances of thetwo molecules increase linearly in diffuse clouds (Av < 1),
their abundances suddenly increase in regions with N(H2 ) ≳1021 cm−2 , where gas is further shielded against ultraviolet radiation. In contrast, C2 H and c-C3 H2 do not increase as rapidly, andtheir 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 H2 S in
diffuse clouds are 5–10 times higher than in translucent clouds(Av ≈ 1). This might imply the onset of sulfur depletion ataround Av 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 othermolecular species observed here, except for H2 S, are underestimated by a factor of 2–10. Any of the models failed to reproduce
the column densities of H2 S. 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+ , C2 H, and c-C3 H2 . For H2 S, additional formation routes,
for example grain-surface production and chemical desorption of
H2 S, may play an important role in increasing the abundance of
H2 S 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 isbased on observations made with the Institut de Radioastronomie Millimétrique(IRAM) 30 m telescope and used the data from Paper I obtained with theNASA/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.

6. Summary and conclusions
Using the IRAM 30 m telescope, we have studied seven simple molecular species – HCO+ , HCN, HNC, C2 H, c-C3 H2 , CS,
and H2 S – 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), C2 H (12sightlines), and c-C3 H2 (9 sightlines), CS (8 sightlines) and H2 S
(6 sightlines). Our sensitivity to CS and H2 S is reduced by thepresence of significant emission line contamination near the CS
frequency and the poorer S/N ratios achieved at the higher H2 S
transition frequency.
A111, page 30 of 41

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A111, page 31 of 41

A&A 670, A111 (2023)

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.

W3(OH)

DR21

2 in 1012 cm 2 km 1 s

HCO+

0
12
2
1
2 in 10 cm km s

0

HCN

in 1013 cm 2 km 1 s

HCN

in 1012 cm 2 km 1 s

HNC

in 1012 cm 2 km 1 s

CSin 1013 cm 2 km 1 s

H2 S

in 1013 cm 2 km 1 s

C2 H

in 1012 cm 2 km 1 s

c-C3H2

0.5

1
0
11
2
1
5.0 in 10 cm km s

HNC

2.5
0.0
in 1012 cm 2 km 1 s
1.0

CS

0.5
0.0
12
2
1
2 in 10 cm km s

H2 S

1
in 1013 cm 2 km 1 s

0.0
Column density per velocity interval, dN(X)/dColumn density per velocity interval, dN(X)/d

HCO+

2

1

0

in 1012 cm 2 km 1 s

C2 H

2

1
0
2
0
0.5
0.0
2

0
11
2
1
4 in 10 cm km s

0

c-C3H2

1

2
0

30

20

10

0

LSR (km s 1)

10

20

0

10

5

0

5

10

15

LSR (km s 1)

20

25

30

Fig. A.1: Channel-wise column density spectra (dN/d3) as a function of velocity toward W3(OH) and DR21. The dN/d3 in eachpanel shows HCO+ , HCN, HNC, CS, H2 S, C2 H, and c-C3 H2 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).

A111, page 32 of 41

W.-J. Kim et al.: HyGAL: Characterizing the Galactic ISM with observations of hydrides and other small molecules. II.

Fig. A.2: Channel-wise column density spectra (dN/d3) as a function of velocity toward G19.61−0.23 and G31.41+0.31 The dN/d3
in each panel shows HCO+ , HCN, HNC, CS, H2 S, C2 H, and c-C3 H2 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).

A111, page 33 of 41

A&A 670, A111 (2023)

Fig. A.3: Channel-wise column density spectra (dN/d3) as a function of velocity toward G45.07+0.13 and G09.62+0.19. The dN/d3
in each panel shows HCO+ , HCN, HNC, CS, H2 S, and C2 H from top to bottom, but no C2 H 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).

A111, page 34 of 41

W.-J. Kim et al.: HyGAL: Characterizing the Galactic ISM with observations of hydrides and other small molecules. II.

Fig. A.4: Channel-wise column density spectra (dN/d3) as a function of velocity toward W43 MM1 and NGC 6334 I. The dN/d3 ineach panel shows HCO+ , HCN, HNC, CS, and H2 S 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 (pervelocity interval).

A111, page 35 of 41

A&A 670, A111 (2023)

Fig. A.5: Channel-wise column density spectra (dN/d3) 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/d3 in each panel shows HCO+ ,HCN, C2 H, and c-C3 H2 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).

A111, page 36 of 41

W.-J. Kim et al.: HyGAL: Characterizing the Galactic ISM with observations of hydrides and other small molecules. II.

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.
Table B.1: Continuation of Table 8.
Source3LSR range(km s−1 )N(H2 )(1021 cm−2 )N(HCO+ )(1012 cm−2 )N(HCN)(1012 cm−2 )N(HNC)(1012 cm−2 )N(CS)(1012 cm−2 )N(H2 S)(1013 cm−2 )N(C2 H)(1013 cm−2 )N(c-C3 H2 )(1012 cm−2 )G19.61−0.23−10, 44, 12
14, 1927, 32a48, 5858, 6767, 7575, 8287, 9393, 106
106, 114
114, 122
122, 127

0.30+0.04−0.04
0.55+0.05
−0.05
+0.03
0.21−0.03
0.28+0.06−0.06
2.62+0.29
−0.30
+0.07
1.14−0.07
3.46+0.46−0.47
0.65+0.08−0.08
0.10+0.02−0.02
b1.80+0.22−0.22
0.25+0.02−0.02
b0.67+0.05−0.05
b0.11+0.01−0.01

0.90+0.13−0.13
1.66+0.15−0.15
0.62+0.08−0.08
0.83+0.18−0.18
12.69+1.68
−1.68
+0.34
4.76−0.34
17.59+2.81−2.81
1.95+0.24−0.24
0.30+0.07−0.07
8.12+1.16
−1.16
+0.07
0.74−0.07
2.52+0.21−0.21
0.33+0.02−0.02

0.48+0.01−0.01
0.55+0.01
−0.01
···
···
15.68+1.56−1.56
2.95+0.07−0.07
20.36+1.62−1.62
1.28+0.05−0.05
0.47+0.01−0.01
15.85+1.55
−1.55
+0.03
1.95−0.03
4.07+0.24−0.24
1.03+0.03
−0.03

···
···
···
···
3.23+0.29−0.29
0.89+0.07−0.07
4.82+0.41
−0.41
+0.02
0.34−0.02
0.19+0.01−0.01
3.13+0.25−0.25
0.63+0.04−0.04
0.98+0.06−0.06
0.3+0.02−0.02···
1.36+0.07
−0.07
···
···
16.89+0.88−0.88
0.80+0.05−0.05
5.43+0.51
−0.51
···
···
2.87+0.19
−0.19
···
···
···

···
···
···
···
3.23+0.51
−0.51
···
···
···
···
···
···
···
···

3.62+1.22−1.22
2.73+1.08−1.08···
0.92+0.08−0.08
10.03+1.75
−1.58
+4.43
9.51−4.37
10.20+1.03−1.03
1.18+0.38−0.26···
3.80+0.19−0.19
1.69+0.11−0.11
1.00+0.09−0.09
0.45+0.05
−0.05

···
···
···
0.81+0.07−0.07
3.47+0.25−0.25
0.99+0.07−0.07
2.75+0.19−0.19
0.23+0.01−0.01
0.30+0.01−0.01
2.29+0.14
−0.14
+0.06
1.16−0.06
0.70+0.03
−0.03
···

G29.96−0.02−1, 1010, 1414, 2150, 5656, 6464, 7474, 791.81+0.25−0.25
0.53+0.04−0.04
0.15+0.02
−0.02
+0.05
0.18−0.05
0.42+0.10−0.10
1.08+0.14−0.14
0.12+0.04−0.04

8.22+1.34−1.34
1.58+0.11−0.11
0.44+0.06−0.06
0.53+0.14−0.14
1.25+0.29−0.29
4.47+0.68−0.68
0.37+0.13−0.12

13.34+3.13−3.13
2.14+0.21−0.21
0.52+0.12−0.08
0.71+0.07−0.07
1.54+0.17−0.17
7.47+0.64
−0.64
···

2.63+0.22−0.22
0.43+0.05
−0.05
···
···
0.17+0.02−0.02
1.01+0.07
−0.07
···

4.67+0.44−0.44
1.52+0.13
−0.13
···
···
···
···
···

1.58+0.48
−0.48
···
···
···
···
···
···

9.82+0.89−0.89
3.71+0.43−0.43
1.12+0.22
−0.22
···
···
3.50+0.54
−0.54
···

3.71+0.23−0.23
1.37+0.04−0.04
0.61+0.01
−0.01
···
···
···
···

W43 MM1

1, 9
9, 13
13, 21
21, 2727, 3939, 4747, 61a61, 69a69, 75a75, 87a2.40+1.72−1.74
6.02+7.27−6.02
2.81+1.84−2.03
0.73+0.21−0.22
1.16+0.30−0.31
0.64+0.16−0.17
0.99+0.33
−0.35
+0.33
0.5−0.33
0.55+0.20−0.22
3.09+4.86−1.68

11.46+10.23−8.95
33.88+52.39−33.8813.79+11.17−10.73
2.81+0.98−0.98
4.85+1.51−1.51
2.42+0.74−0.74
4.01+1.64
−1.64
+0.99
1.50−0.99
2.01+0.90−0.90
15.40+31.62−9.30

13.81+35.52−13.8110.65+8.42−8.01
8.66+3.81−3.81
3.47+1.7−1.7
2.65+1.18−1.17
0.66+0.46−0.66
10.24+4.82
−4.82
+2.89
6.27−2.82
1.53+0.65−0.58
13.64+0.89−0.89

0.92+0.80−0.53
1.18+0.91
−0.90
···
···
···
0.30+0.44−0.30
3.34+1.93
−1.84
+0.59
1.39−0.58
0.62+0.26−0.26
2.23+1.30
−1.30

···
···
···
···
···
···
···
···
···
···

···
···
···
···
···
···
···
···
···
···

5.89+1.10−1.10
23.22+7.49−7.49
8.66+2.66
−2.66
···
···
···
···
···
···
···

···
6.57+2.53−2.53
4.03+1.43
−1.43
···
···
···
···
···
···
···

G31.41+0.31

3, 10
10, 180.69+0.12−0.12
0.99+0.18−0.19

2.63+0.55−0.55
4.03+0.88−0.88

3.97+0.83−0.83
3.68+0.92
−0.92

···
1.09+0.11−0.11

3.85+0.76−0.76
5.98+1.25
−1.25

···
0.16+0.02−0.02

4.36+0.79−0.79
11.83+2.30−2.30

0.47+0.15−0.47
2.42+0.49−0.49

G32.80+0.19

4, 7
7, 15
28, 4343, 5959, 7777, 8383, 8787, 9292, 101
101, 109

0.57+0.01−0.01
1.74+0.05−0.05
0.41+0.01−0.01
0.82+0.02−0.02
1.63+0.03−0.03
1.36+0.03−0.03
1.69+0.16−0.16
3.14+0.10−0.10
1.10+0.03−0.03
0.16+0.01−0.01

1.72+0.03−0.03
7.81+0.25−0.25
1.22+0.01−0.01
3.23+0.10
−0.10
+0.15
7.23−0.15
5.86+0.15−0.15
7.58+0.85−0.8515.69+0.59−0.59
4.57+0.14
−0.14
+0.01
0.49−0.01

3.00+0.04−0.04
8.15+0.13−0.13
1.33+0.0−0.0
3.04+0.01−0.01
11.47+0.04−0.04
16.3+0.16−0.16
31.1+0.30−0.30
29.97+0.22−0.22
3.46+0.01
−0.01
+0.01
0.44−0.01······
0.49+0.07−0.07
0.06+0.04−0.06
2.28+0.23−0.23
4.51+0.71−0.71
6.62+1.90−1.90
5.22+0.59−0.59
0.36+0.03
−0.03
···

···
···
···
···
3.55+0.04−0.04
4.06+0.04−0.04
17.8+0.34−0.34
9.57+0.12−0.12
0.58+0.04
−0.04
···

···
···
···
···
0.63+0.02−0.02
0.35+0.01−0.01
1.73+0.19−0.19
1.19+0.10
−0.10
···
···

2.08+0.12−0.12
0.93+0.06−0.06
4.62+0.65−0.65
0.90+0.19−0.19
6.19+0.31−0.31
3.86+0.24−0.24
5.66+0.53−0.53
10.99+0.8−0.8
5.41+0.29
−0.29
+0.13
0.41−0.12

0.70+0.04−0.04
0.86+0.06−0.06
0.90+0.03−0.03
1.67+0.08−0.08
3.35+0.23−0.23
1.35+0.23−0.23
1.51+0.22−0.22
3.70+0.30−0.30
1.25+0.06
−0.06
+0.02
0.31−0.02

G45.07+0.13

−1, 3
3, 11
12, 1921, 3030, 3863, 71a71, 80a

0.21+0.05−0.05
0.12+0.03
−0.03
+0.03
0.15−0.03
1.12+0.16−0.17
0.12+0.05−0.05
3.64+0.48−0.49
0.34+0.24−0.20

0.62+0.15−0.15
0.35+0.08−0.08
0.45+0.09−0.09
4.66+0.81−0.81
0.36+0.15−0.15
18.71+2.91−2.91
1.02+0.73
−0.59

···
···
···
2.29+0.60−0.57···
18.88+1.11
−1.11
···

···
···
···
0.45+0.06
−0.06
···
+0.47
1.30−0.42······
2.62+0.77−0.75···
4.41+0.85−0.85
1.42+1.04
−1.04
+0.93
7.37−0.93
···

···
···
0.29+0.03−0.03
0.74+0.12−0.12
0.40+0.12−0.11
1.77+0.18
−0.18
···

···
···
···
8.33+0.96
−0.96
···
···
···

···
···
···
···
···
···
···

DR21

0, 10a10, 17a1.38+0.10−0.10
0.65+0.09−0.09

5.93+0.53−0.53
1.96+0.27−0.27

10.08+0.36−0.36
1.52+0.18−0.18

3.68+0.17−0.17
0.52+0.17−0.16

5.38+0.21
−0.21
···

2.38+0.20−0.20
2.06+0.21−0.21

9.29+1.71−1.54
1.86+0.81−0.78

3.83+0.33−0.32
0.89+0.22−0.22

NGC 7538 IRS1

−13, −5

0.13+0.07−0.05

0.39+0.22
−0.16

···

···

···

···

···

···

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A&A 670, A111 (2023)

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, C2 H, c-C3 H2 , CH, OH, O, C+ ,H2 O+ , OH+ , and ArH+ ) as a function of 3LSR . 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+ , H2 O+ , OH+ , and ArH+ , the reproduced
spectra indicated by blue dotted curves include one or two more PCs, i.e., PC-4 and PC-5.
A111, page 38 of 41

W.-J. Kim et al.: HyGAL: Characterizing the Galactic ISM with observations of hydrides and other small molecules. II.

Appendix D: H-plots for the ten considered species (HCO+ , HCN, C2 H, c-C3 H2 , CH, OH, O, C+ , H2 O+ , andOH+ ) 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 theright 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 uncertaintyof 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.

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A&A 670, A111 (2023)

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 afunction 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 6334 I,
DR21, and G09.62+0.19. Different species are labeled with different symbols and colors as shown in the legend displayed in the rightcorner of the W3(OH) diagram. The gray areas indicate the velocity ranges of the emission lines. In the upper panels, the dottedhorizontal 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.

A111, page 40 of 41

W.-J. Kim et al.: HyGAL: Characterizing the Galactic ISM with observations of hydrides and other small molecules. II.

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.

A111, page 41 of 41