A&A 642, A68 (2020)
https://doi.org/10.1051/0004-6361/202038449

Astronomy&
Astrophysics© J. Syed et al. 2020

Atomic and molecular gas properties during cloud formation
J. Syed1 , Y. Wang1 , H. Beuther1 , J. D. Soler1 , M. R. Rugel2 , J. Ott3 , A. Brunthaler2 , J. Kerp4 , M. Heyer5 ,R. S. Klessen6,7 , Th. Henning1 , S. C. O. Glover6 , P. F. Goldsmith8 , H. Linz1 , J. S. Urquhart9 , S. E. Ragan10 ,K. G. Johnston11 , and F. Bigiel4
1

Max-Planck-Institut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany
e-mail: syed@mpia.de
2
Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, 53121 Bonn, Germany3
National Radio Astronomy Observatory, PO Box O, 1003 Lopezville Road, Socorro, NM 87801, USA
4Argelander-Institut für Astronomie, Auf dem Hügel 71, 53121 Bonn, Germany
5
Department of Astronomy, University of Massachusetts, Amherst, MA01003, USA
6
Universität Heidelberg, Zentrum für Astronomie, Institut für Theoretische Astrophysik, Albert-Ueberle-Str. 2, 69120 Heidelberg,
Germany
7
Universität Heidelberg, Interdisziplinäres Zentrum für Wissenschaftliches Rechnen, INF 205, 69120 Heidelberg, Germany
8
Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA
9Centre for Astrophysics and Planetary Science, University of Kent, Canterbury CT2 7NH, UK
10School of Physics and Astronomy, Cardiff University, Queen’s Buildings, The Parade, Cardiff CF24 3AA, UK
11
School of Physics and Astronomy, E.C. Stoner Building, The University of Leeds, Leeds LS2 9JT, UK
Received 19 May 2020 / Accepted 12 August 2020
ABSTRACT
Context. Molecular clouds, which harbor the birthplaces of stars, form out of the atomic phase of the interstellar medium (ISM). To

understand this transition process, it is crucial to investigate the spatial and kinematic relationships between atomic and molecular gas.
Aims. We aim to characterize the atomic and molecular phases of the ISM and set their physical properties into the context of cloudformation processes.
Methods. We studied the cold neutral medium (CNM) by means of H I self-absorption (HISA) toward the giant molecular filament
GMF20.0-17.9 (distance = 3.5 kpc, length ∼170 pc) and compared our results with molecular gas traced by 13 CO emission. We fitted
baselines of HISA features to H I emission spectra using first and second order polynomial functions.
Results. The CNM identified by this method spatially correlates with the morphology of the molecular gas toward the western region.
However, no spatial correlation between HISA and 13 CO is evident toward the eastern part of the filament. The distribution of HISA
peak velocities and line widths agrees well with 13 CO within the whole filament. The column densities of the CNM probed by HISA
are on the order of 1020 cm−2 while those of molecular hydrogen traced by 13 CO are an order of magnitude higher. The column density
probability density functions (N-PDFs) of HISA (CNM) and H I emission (tracing both the CNM and the warm neutral medium,
WNM) have a log-normal shape for all parts of the filament, indicative of turbulent motions as the main driver for these structures. The
H2 N-PDFs show a broad log-normal distribution with a power-law tail suggesting the onset of gravitational contraction. The saturationof H I column density is observed at ∼25 M pc−2 .
Conclusions. We conjecture that different evolutionary stages are evident within the filament. In the eastern region, we witness theonset of molecular cloud formation out of the atomic gas reservoir while the western part is more evolved, as it reveals pronounced H2column density peaks and signs of active star formation.
Key words. ISM: clouds – ISM: atoms – ISM: molecules – ISM: kinematics and dynamics – radio lines: ISM – stars: formation

1. Introduction
Molecular clouds play a key role in star formation processes.
Stars are born in the dense interiors of molecular clouds thatform out of the atomic phase of the highly turbulent interstellar
medium (ISM; Larson 1981; Clark et al. 2012; Dobbs et al. 2014;
Sternberg et al. 2014; Klessen & Glover 2016). Molecular clouds
consist mainly of molecular hydrogen (Larson 2003; Mac Low &Klessen 2004; McKee & Ostriker 2007; Dobbs et al. 2014). However, the cloud formation process out of the diffuse atomic phaseis still not well constrained. According to the standard photodissociation region (PDR) model, layers of cold atomic hydrogencan effectively shield the cloud from photo-dissociating UV radiation at sufficiently high densities, allowing a more complete
conversion of H I to its molecular form. The cold neutral medium(CNM) with temperatures of ≤300 K and volume densities of
10−100 cm−3 (McKee & Ostriker 1977; Heiles & Troland 2003;
Wolfire et al. 2003; Kalberla & Kerp 2009) is thought, due to
its relatively high density, to be a key component in the conversion process from diffuse atomic hydrogen to its molecularphase. Constraining the physical and dynamical properties of the
CNM is therefore crucial to understand early cloud formation
processes.
The CNM is a major constituent of the ISM (see e.g., Ferrière
2001; Heiles & Troland 2003). Even though the observation of
the H I 21cm line allows one to study the properties of atomic
hydrogen in general, it is difficult to attribute certain properties to different components of H I. In pressure equilibrium,
atomic hydrogen can exist in different phases (e.g., McKee &Ostriker 1977; Wolfire et al. 2003). Observations of H I 21cm line
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Open Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0),
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Open Access funding provided by Max Planck Society.

A&A 642, A68 (2020)

emission are generally attributed to both warm neutral medium(WNM) and CNM. To separate the WNM from the CNM, we
make use of the presence of H I self-absorption (HISA; see e.g.,
Riegel & Crutcher 1972; Knapp 1974; van der Werf et al. 1988;
Feldt 1993; Gibson et al. 2000, 2005a,b; Kavars et al. 2003;
Dénes et al. 2018; Wang et al. 2020a) to trace the cold atomic
phase. H I self-absorption is found throughout the Milky Way invarious environments. Many studies have focused on the detection of HISA, first detected in 1954 (Heeschen 1954, 1955), in
known sources, but statistical treatments of the kinematic properties and densities of the CNM in large-scale high-resolution
maps are still rare.
For HISA to be detected, sufficient background emission of
warmer gas along the line of sight is required. Since the warmcomponent of atomic hydrogen is more diffuse, it fills up alarger volume than the cold component (McKee & Ostriker 1977;
Stahler & Palla 2005; Kalberla & Kerp 2009). H I self-absorption
occurs when a cold H I cloud is located in front of a warmer H I
emitting cloud. Self-absorption can occur within the same cloud
but can also be induced by an emitting cloud in the far background that has the same velocity as the absorbing medium withrespect to the local standard of rest vLSR . Therefore, the clouds
do not have to be spatially associated for HISA to be observable. While absorption against strong continuum sources doesyield a direct measurement of the optical depth, the discreteness of the sources only delivers an incomplete grid of opticaldepth measurements (e.g., Wang et al. 2020b). The interpolation of optical depths across an entire H I cloud is challenging.
Therefore, the great advantage of HISA is that larger areas ofcold atomic hydrogen can be mapped.
Large filamentary gas structures, also known as giant molecular filaments (GMFs), are suitable to study the CNM on large
scales. These objects are the largest coherent structures foundin the Milky Way and are subject of many studies probing thephysical properties of the Galactic ISM (Jackson et al. 2010;
Goodman et al. 2014; Ragan et al. 2014; Zucker et al. 2015,2018; Abreu-Vicente et al. 2016). We study the hydrogen content by means of HISA, atomic and molecular line emission
toward the giant molecular filament GMF20.0-17.9 (Ragan et al.
2014). We address the physical processes driving the kinematics of the CNM and the properties that lead to molecular cloudformation.
GMF20.0-17.9 was already identified in part by Tackenberg
et al. (2013). Furthermore, Zucker et al. (2015, 2018) define asubsection of this filament as a “bone” of the Scutum-Centaurus(SC) spiral arm. GMF20.0-17.9 is characterized by grouping several infrared dark clouds (IRDCs) into a single structure that isvelocity-coherent as traced by 13 CO emission. Figure 1 shows
an overview of GMF20.0-17.9. Prominent IRDC features alongthe 13 CO emission are visible in the Spitzer 8 µm image, inparticular toward the western part of the filament. It furthermore shows features of stellar activity. GMF20.0-17.9 extends
from 20.2◦ to 17.6◦ in Galactic longitude and +0.3◦ to −0.7◦ in
Galactic latitude. At the computed kinematic near distance of
3.3–3.7 kpc, this corresponds to a projected length of ∼170 pc.
Ragan et al. (2014) associate the velocity range of 37−50 km s−1
with GMF20.0-17.9. The filament is near the midplane of the
Galaxy, and the velocity of the lower longitude part at ∼18◦
agrees fairly well with that of the near SC spiral arm (Vallée
2008; Reid et al. 2014, 2019). However, the sense of the velocity
gradient of GMF20.0-17.9 as defined by Ragan et al. (2014) goesagainst the trend of the spiral arm structure. Zucker et al. (2015)
argue that the bone at 19.2◦ & ` & 18.6◦ , b ≈ −0.1◦ traces thespine of the SC spiral arm well. This discrepancy is attributed
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to the different methodology for defining filaments and can bebrought into agreement if only the lower longitude section of
GMF20.0-17.9 is considered.
The ATLASGAL survey (Schuller et al. 2009) reveals several high-density clumps within GMF20.0-17.9, particularly inthe western part of the filament. Zhang et al. (2019) identified young stellar object (YSO) populations within all currently known GMFs and derive a star formation rate (SFR) of
SFR = 1.2 × 103 M Myr−1 and efficiency (SFE) of SFE = 0.01
for GMF20.0-17.9, which is consistent with SFEs of nearby
star-forming regions (see Zhang et al. 2019, and references
therein).

2. Observations and methods
2.1. H I 21 cm line and continuum

The following analysis employed the H I and 1.4 GHz continuum data from the THOR survey (The H I/OH Recombinationline survey of the inner Milky Way; Beuther et al. 2016; Wanget al. 2020b). The H I and 1.4 GHz continuum data include observations from the Karl G. Jansky Very Large Array (VLA) in bothC- and D-configuration as well as single-dish observations fromthe Green Bank Telescope (GBT) and Effelsberg, respectively,
to recover missing flux on short uv spacings. Depending on the
purpose of the analysis, different data products were utilized. For
the analysis of H I emission and the subsequent identificationof HISA features, the combined THOR H I data (VLA C+D +GBT) without continuum were used. The final data have beensmoothed to an angular resolution of ∆Θ = 4000 for better brightness sensitivity that is required especially for studying HISA.
The rms noise in emission-free channels is ∼5 K. The spectral
resolution is ∆v = 1.5 km s−1 . The final THOR 1.4 GHz continuum emission data (VLA C+D + Effelsberg) have an angularresolution of ∆Θ = 2500 .
Additionally, optical depths were derived from H I absorption against strong continuum sources. For that purpose, THORonly data that comprise H I emission with continuum wereused. THOR C-array-only data have a higher angular resolution,
making them suitable to study absorption against discrete continuum sources. Since these data consist of observations from the
VLA in C-array configuration only, large-scale H I emission iseffectively filtered out. The THOR-only data have an angular resolution of ∆Θ ∼ 2000 , depending slightly on Galactic longitude.
For more details about the THOR data, we refer to the two data
release papers by Beuther et al. (2016) and Wang et al. (2020b).
We used the Galactic Ring Survey 13 CO(1–0) data (GRS;
Jackson et al. 2006) to investigate the kinematic properties ofthe molecular gas and estimate the 13 CO and H2 column density.
The GRS 13 CO data have an angular and spectral resolution of∆Θ = 4600 and ∆v = 0.21 km s−1 , respectively.
2.2. H I self-absorption (HISA) extraction

In the following section, different methods to identify and extract
HISA spectra from the H I emission are discussed. Several
approaches have been tested as the accurate extraction of HISA
spectra poses a challenging task.
The random motion of individual H I clouds, superposed on
the Galactic rotation, contributes significantly to the broadeningof the observed 21cm emission and creates multiple emission
peaks as seen in Fig. 2. H I spectra show many features and13
CO line emission has to be inspected to search for HISA. Since
we assume that the CNM is associated with cold molecular gas,

J. Syed et al.: Atomic and molecular gas properties during cloud formation

Spitzer 8 m+00.20°Galactic Latitude+00.00°-00.20°-00.40°-00.60°-00.80°20pc @ 3.5kpc

HI Moment 0
500

Galactic Latitude+00.00°-00.20°4
1

2

HI emission moment 0 [K kms 1]-01.00°+00.20°5

3

400-00.40°6-00.60°300-00.80°20pc @ 3.5kpc-01.00° 20.50°

20.00°

19.50°
19.00°
Galactic Longitude

18.50°

18.00°

200

Fig. 1. GMF20.0-17.9 overview. Top panel: Spitzer GLIMPSE 8 µm image of GMF20.0-17.9 (Churchwell et al. 2009). The color scale is chosen
to bring IRDC features to prominence. Bottom panel: H I integrated emission for a small velocity interval from 44.5–47.5 km s−1 . The yellow andblack contours show the integrated 13 CO emission from 42 to 57 km s−1 at the levels of 10.5 and 15 K km s−1 , respectively. The yellow circles in thebottom panel mark the regions of the spectra shown in Fig. 4.

we take local 13 CO emission peaks as a reference point. We
thus identify HISA by constraining these features kinematically.
The 13 CO emission peaks at different velocities are not associated with GMF20.0-17.9 as their velocities are attributed toneighboring spiral arm structures (e.g., Vallée 2008; Reid et al.
2014, 2019). For the analysis of the physical properties of HISA,
we followed the derivation by Gibson et al. (2000) and Wanget al. (2020a). A comprehensive discussion of the radiative transfer of HISA clouds is given in Gibson et al. (2000), Kavars
et al. (2003), and Li & Goldsmith (2003). Adopting the geometric model from Gibson et al. (2000), we identify four different
cloud components when looking toward a HISA cloud, which
we describe below.
According to this model (see Fig. 2 in Wang et al. 2020a), we
observe emitting foreground and background clouds that havespin temperatures of T fg and T bg , respectively. Between theseclouds a cold absorbing HISA cloud can be located, with aspin temperature of T HISA . Diffuse continuum emission, T cont ,is assumed to be in the background. Strong continuum point

sources will be neglected as they contaminate the absorption
features that are caused by HISA.
By comparing an “on” spectrum, where a HISA cloud islocated along the line of sight, with the “off” spectrum that wewould observe in the absence of the HISA cloud, we can derive
the optical depth of the HISA component (see e.g., Eq. (6) inGibson et al. 2000), defined as!
T on − T off
τHISA = −ln 1 −,(1)
T HISA − pT off − T contwith the dimensionless parameter p ≡ T bg (1 − e−τbg ) /T off
describing the fraction of background emission in the opticallythin limit (Feldt 1993). Assuming a HISA spin temperature T s( = T HISA ), we can then calculate the H I column density of thecold H I gas using the general form (Wilson et al. 2013)
!
Z
NH
dv
18 T s= 1.8224 × 10
τ (T s , v)
,
(2)
K
cm−2
km s−1
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A&A 642, A68 (2020)
120
100
80

125
100

60

TB [K]

TB [K]

150

HI
HISA
13
CO × 10

40
20

75
50
25

0
−75

−50

−25

0

25

50

vLSR [km s−1]

75

100

125

Fig. 2. H I, HISA, and 13 CO spectra. The black curve shows an example spectrum of H I emission (T on ) from −80 to 160 km s−1 averaged
over an area of 18000 × 18000 centered in ` = 19.9◦ , b = −0.5◦ . The dashed
red curve is a second-order polynomial fit (T off ) to the absorption-freechannels of the H I spectrum at 33.5–43.0 and 56.0–65.5 km s−1 (seeSect. 2.2). We estimated the HISA spectrum by then subtracting the H I
spectra from the fitted background emission. The GRS 13 CO spectrum(Jackson et al. 2006) covering velocities from −5 to 135 km s−1 is shownin blue and has been multiplied by a factor of ten for better visibility.

where T s is the spin temperature of atomic hydrogen and τ (T s , v)
describes the optical depth.
To reliably identify HISA features, it is crucial to know theemission in the absence of a HISA cloud. Many methods havebeen tested to estimate T off in Eq. (1) (e.g., Gibson et al. 2000;
Kavars et al. 2003; Li & Goldsmith 2003; Krčo et al. 2008;
Wang et al. 2020a). Wang et al. (2020a) tested estimating thebackground spectrum T off by measuring several off positions
offset from apparent absorption features at slightly shifted linesof sight. Their spectra partly show large variations dependingon the line of sight, so the assumption that the H I backgroundemission stays spatially constant does not really hold. Therefore, we refrain from selecting actual off positions to estimate
T off . Instead, we estimate T off for each line of sight by fitting thebaselines of absorption features with polynomial functions. The
fits reconstruct an off spectrum as if there was no absorption
present. Different studies have been conducted successfully byapplying polynomial fitting procedures (Kavars et al. 2003; Li &Goldsmith 2003; Wang et al. 2020a).
We extensively tested various methods to find an independent and systematic fitting procedure. Fitting the baselines with
first and second order polynomial functions yielded the mostrobust results as these functions are not sensitive to small-scale
fluctuations along the spectral axis. We therefore rebinned thespectral axis of H I emission by a factor of two, which gave thebest results for reconstructing T off , independent of the chosen
velocities at which the baselines were fitted. Higher-order polynomial functions are prone to either over- or underestimating thebackground spectrum. As outlined below, we utilized a combination of first and second order polynomials in order to fit thebaselines of HISA spectra. For the baseline fitting, we furthermore smoothed the H I emission maps spatially to an angularresolution of ∆Θ = 8000 to enhance the brightness sensitivity.
Irrespective of the actual presence of 13 CO emission at individual positions, every pixel spectrum is searched for HISA andfitted at the velocities 33.5−43.0 km s−1 and 56.0−65.5 km s−1 ,omitting the velocity range associated with GMF20.0-17.9. In
the first cycle of the fitting procedure, all spectra are fitted withsecond order polynomial functions ( f (x) = ax2 + bx + c). Spectra
A68, page 4 of 21HIpoly-1poly-2

150

0
20

40

60

80

−1

vLSR [km s ]Fig. 3. Comparison of baseline fits toward continuum emission. The
black curve shows an example spectrum of H I emission centered in` = 18.95◦ , b = − 0.03◦ that is contaminated by continuum emission. The
dashed magenta and green curve show a second and first order polynomial fit to the velocity channels of the H I spectrum at 33.5–43.0 and
56.0–65.5 km s−1 , respectively. Due to the continuum contamination,
the second order polynomial yields a bad fit to the HISA baseline.

that are contaminated by continuum emission produce bad second order polynomial fits, with a > 0. For those spectra, weused first order fits instead. Figure 3 presents a comparison
between first and second order polynomial fits toward a position
that is contaminated by diffuse continuum emission, which cancontribute to the broadening of the absorption profile.
Figure 4 shows our baseline fitting procedure and extracted
HISA spectra from example regions of GMF20.0-17.9. The
example regions have been selected based on the visual inspection of the H I and 13 CO emission maps. The spectra show thecase of HISA with strong, weak, and no molecular counterparts
as well as no HISA at all. The final HISA maps were inferredby subtracting the native THOR H I emission with a spatial andspectral resolution of 4000 and 1.5 km s−1 , respectively, from thefitted baselines. The rms noise of the extracted HISA spectra is∼8 K and arises from the noise of the observations and the uncertainty of the fitting procedure. We discuss these uncertainties inAppendix A.
Using this approach, we are biased in the search of HISA
since we utilize 13 CO velocities to constrain the velocities ofextracted HISA features. We lack a systematic approach to find
HISA independent of molecular line emission. At the spectral
resolution of 1.5 km s−1 , we are not able to detect narrow selfabsorption features (HINSA; Li & Goldsmith 2003; Krčo et al.
2008) that can be identified through line profile characteristics,
such as the line width and the second derivative of the absorption
feature. H I self-absorption features with line widths ≥1 km s−1
are difficult to differentiate from emission troughs. The kinematic information of molecular line emission is therefore crucial
in our analysis.

3. Results
3.1. H I self-absorption

In order to compare the kinematics in a statistical sense, we
regridded the HISA data to the same pixel scale as the 13 CO

J. Syed et al.: Atomic and molecular gas properties during cloud formation
150

Spectrum 1

regime (Sect. 3.3.3). This underlines the robustness of the extraction method. We examined the two subregions separately in thefollowing analysis.

Spectrum 2

TB [K]

100

3.2. Kinematics
50

0
150

Spectrum 3

Spectrum 4

Spectrum 5

Spectrum 6

TB [K]

100

50

0
150

TB [K]

100

50

0
20

40

60

vLSR [km s−1 ]

80

20

40

60

80

vLSR [km s−1 ]Fig. 4. H I (T on ) and extracted HISA spectra (T off − T on ) toward theregions marked by the yellow circles in the bottom panel of Fig. 1. The
colors are the same as described in Fig. 2.

GRS data. The properties and kinematics of the CNM were analyzed by fitting single Gaussian components to the HISA spectra.
Due to the limited velocity resolution, it is not feasible to resolve
multiple HISA components between 43 and 56 km s−1 . Fits thathave a peak intensity of >25 K (∼3σ) and a line width between
1.5 and 20 km s−1 (FWHM) are considered good.
The fitted peak values of the extracted HISA spectra areshown in Fig. 5. The derived HISA peaks have intensities
between ∼30 and ∼70 K. By comparing the inferred HISA features with the molecular gas emission, the filament can beseparated into two subregions (see Fig. 5). The western partof the filament (19.3◦ & ` & 17.9◦ ) shows good spatial correlation between HISA and 13 CO as the cold atomic gas is
expected to be closely associated with its molecular counterpart.
We assess the spatial correlation quantitatively in Sect. 4.4 toconfirm this finding. However, the eastern part of the filament(20.5◦ & ` & 19.5◦ ) shows significant HISA that does not spatially overlap with the 13 CO emission at the velocities around∼45 km s−1 . On the eastern side of the cloud, the CNM as traced
by HISA appears to envelop the denser molecular filament. The
extracted features indicate the presence of a cold H I cloud as
the velocities generally agree with the molecular gas (Fig. 6).
Furthermore, optical depth measurements against bright continuum sources reveal high optical depths in the same velocity

We smoothed the 13 CO spectra to a spectral resolution of
1.5 km s−1 and applied single-component Gaussian fitting to
be consistent in our analysis. Emission features with a peakintensity of >1.25 K (∼5σ) and a line width 1.5 km s−1 <FWHM < 20 km s−1 are considered to be good fits. The peakvelocity maps of HISA and 13 CO are presented in Fig. 6. The
peak velocities of HISA in the eastern part of the filament show
a velocity of ∼44−46 km s−1 . The western part reveals slightly
higher peak velocities from ∼45 to ∼49 km s−1 . The peak velocities of 13 CO show a coherent distribution along the filament(Ragan et al. 2014).
Although there are slight systematic differences in peakvelocity at some positions, the median of the histograms ofpeak velocities reveal good agreement between H I and 13 CO
emission in both the eastern and western regions (Fig. 7). The
similar velocities are a confirmation that the extracted HISA
structures are trustworthy, even though HISA and 13 CO show
a lower degree of line-of-sight correlation in the eastern part of
the filament. The HISA structures in the northern part of the eastern region reveal large line widths of ∼8–10 km s−1 (Fig. 8). The
bulk of HISA south of the 13 CO contours shows line widths of
3–6 km s−1 . Possible implications of this line width enhancement
are discussed in Sect. 4.1.
The 13 CO line widths are ∼2–3 km s−1 in the western partand show line widths that are slightly higher in the easternpart (Fig. 9). Assuming a kinetic temperature, we can estimate
the expected thermal line width. In local thermodynamic equilibriump(LTE), the thermal line width (FWHM) is given by∆vth = 8 ln2 kB T k /(µmH ), where kB , T k , and µ are the Boltzmann constant, kinetic temperature, and the mean molecularweight of H I and the CO molecule in terms of the mass ofa hydrogen atom mH , respectively. If different line broadening
effects are uncorrelated, the total observed line width will beq∆vobs = ∆v2th + ∆v2nth + ∆v2res ,(3)
where ∆vnth is the line width due to nonthermal effects and ∆vresis the line width introduced by our spectral resolution and isequal to 1.5 km s−1 .
The observed 13 CO line widths even at the lower end of the
distribution at 2–3 km s−1 cannot be explained by thermal line
broadening. Effects such as turbulent motions are most likely thedominant driver for the broadening of the 13 CO line. More than
70% of the observed HISA line widths are ≥3 km s−1 .
We can investigate the three-dimensional Mach √number ofthe filament by assuming isotropic turbulence M = 3 σnth /c s ,where σnth is the nonthermal one-dimensional velocity dispersion √that is related to the nonthermal line width via∆vnth = 8 ln2 σnth . The sound speed cs is estimated using amean molecular weight µ = 2.34 for the molecular gas andµ = 1.27 for the cold H I phase (Allen 1973; Cox 2000). To calculate the thermal component of the velocity dispersion, we
assumed the spin temperature of the cold atomic hydrogen to
be close to the kinetic temperature and set T k = T HISA = 40 K. As
we find 13 CO excitation temperatures as high as ∼25 K where theline is becoming optically thick (see Sect. 3.3.2), we assumed
that the actual kinetic temperature of 13 CO is close to the excitation temperature in those regions, meaning these regions are
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A&A 642, A68 (2020)

HISA Gaussian peak

Galactic Latitude+00.00°-00.20°

4
1

2

60

5

3

50

-00.40°-00.60°HISA Gaussian peak [K]+00.20°640Eastern
region30

Western
region-00.80°20pc @ 3.5kpc-01.00° 20.50°

20.00°

70

19.50°
19.00°
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18.50°

18.00°

20

Fig. 5. Peak values of a Gaussian fit applied to the estimated HISA spectra. This panel presents the fitted peak values of the extracted HISA
spectra. The spectra have been fitted with a single-component Gaussian curve. The black contours represent the integrated 13 CO emission from 42
to 57 km s−1 at levels of 10.5 and 15 K km s−1 . The red dashed polygons define the eastern and western part of the filament. The yellow circles markthe regions of the spectra shown in Fig. 4.

dense and in LTE. We therefore set a uniform kinetic temperatureof T k = 20 K for the Mach number estimates of 13 CO.
Figure 10 shows that the Mach number of the CNM traced
by HISA peaks at ∼3, indicating that a significant fraction of
the CNM has transonic and supersonic velocities. Furthermore,
there is an indication of a shoulder at M ∼ 6. The Mach numbers of 13 CO show a broad distribution and are dominated bysupersonic motions. The distribution is slightly skewed towardhigher Mach numbers as we observe multiple 13 CO components
between 43 and 56 km s−1 in some regions. Consequently, fitting
single Gaussian components results in overly broad line widths
where we observe multiple velocity components. Hence, thenonthermal velocity dispersion and therefore the Mach number
is systematically overestimated. If we utilize a single Gaussiancomponent fit on the GRS spectra at the full spectral resolution of 0.21 km s−1 , the 13 CO Mach number distribution does
not significantly change. Therefore, the spectral smoothing has
a negligible effect on the derivation of the Mach numbers if
we fit single components. To address the uncertainty of possible
component blending, we assumed that the 13 CO line width is on
average systematically overestimated by 30% due to the singlecomponent fitting. The Mach number distribution is then shiftedto lower values with a more pronounced peak (see Fig. 10).
Furthermore, if the filament lacks spatial isotropy, we could√beoverestimating the Mach number by a factor as high as 3,
which would lead to a distribution with a median of M ∼ 6(Fig. 10).
3.3. Column density and masscalculate the column density. This is a typical spin temperatureof cold self-absorbing H I clouds (e.g., Knapp 1974; Gibson et al.
2000; Heiles & Troland 2003). We emphasize that a constantspin temperature is an approximation that might not hold forevery region of the cloud. However, the maximum spin temperature is constrained in Appendix A.2 and the actual temperature
variation should be moderate. Different spin temperatures (ifconstant over the whole cloud) will not change the structure of
the column density distribution in the cloud but only change thenormalization factor.
Furthermore, we have to assume the fraction of backgroundemission parameterized by the factor p (Eq. (1)). Although wecannot measure this parameter directly, we can constrain p by
its effect on the spin temperature and the location of the cloud.
Because of the cloud’s location toward the inner Galactic plane(` ∼ 19◦ ) and its distance of ∼3.5 kpc (Ragan et al. 2014), it isunlikely that most of the H I emission originates in the foreground. The fraction of background emission should therefore
be at least p & 0.5. Since self-absorption can also be induced by
H I emission from the far side of the Galaxy due to the kinematic
distance ambiguity, the background fraction p should be systematically higher than the foreground emission fraction. Therefore,
we assumed a background fraction of p = 0.9 and discuss its
uncertainties in Appendix A.1. Wang et al. (2020a) assumed thesame background fraction for their HISA analysis of the giant
molecular filament GMF38.1-32.4a (Ragan et al. 2014). Furthermore, Gibson et al. (2000) argue that the HISA detection isbiased toward higher p values since a high background fraction
is more efficient in producing prominent HISA features.

3.3.1. CNM column density traced by HISA

3.3.2. Molecular gas column density traced by 13 CO

We calculated the column density of the CNM traced by HISA
following Eqs. (1) and (2). We therefore have to assume either
an optical depth or a spin temperature. As we know that HISA
traces the coldest component of atomic hydrogen, we assumed
a constant spin temperature of T S = 40 K for the whole cloud toIn the optically thin limit, the 13 CO column density is computedby (Wilson et al. 2013)
R
T B (v) dv,(4)
N(13 CO) = 3.0 × 1014
1 − exp(−5.3/T ex )A68, page 6 of 21

J. Syed et al.: Atomic and molecular gas properties during cloud formation50
HISA Gaussian peak velocity [km s 1]

HISA Gaussian peak velocity+00.20°48-00.20°46-00.40°44-00.60°Eastern
region42

Western
region-00.80°20pc @ 3.5kpc-01.00° 20.50°

20.00°

19.50°

19.00°

18.50°

40

18.00°

50

GRS 13CO Gaussian peak velocity+00.20°

GRS 13CO Gaussian peak velocity [km s 1]

Galactic Latitude+00.00°48

Galactic Latitude+00.00°-00.20°46-00.40°44-00.60°42-00.80°20pc @ 3.5kpc-01.00° 20.50°

20.00°

19.50°
19.00°
Galactic Longitude

18.50°

40

18.00°

Fig. 6. Peak velocity maps. Upper panel: HISA peak velocities inferred from Gaussian fits. Lower panel: fitted 13 CO peak velocities. The black
contours indicate the integrated 13 CO emission at levels of 10.5 and 15 K km s−1 for reference. The red dashed polygons mark the eastern andwestern part of the filament that were used for a separate analysis.

HISA
13
CO

Probability density

Whole filament

0.25 Eastern region

HISA
13
CO

0.100

0.15

0.10

0.075
0.10

0.05

0.00

HISA
13
CO

Western region

0.125

0.20

0.15

0.150

0.050

0.05
40.0

42.5

45.0

47.5

vLSR [km s−1]

50.0

52.5

0.00

0.025
40.0

42.5

45.0

47.5

vLSR [km s−1]

50.0

52.5

0.000

40.0

42.5

45.0

47.5

vLSR [km s−1]

50.0

52.5

Fig. 7. Histogram of peak velocities. The histograms show the peak velocities of HISA and 13 CO in black and blue, respectively. Middle and rightpanels: velocity distribution in the regions marked by the left and right polygon in Fig. 6, respectively.

A68, page 7 of 21

A&A 642, A68 (2020)

12

HISA Gaussian line width+00.20°8-00.20°6-00.40°-00.60°4

Eastern
region2Western
region-00.80°20pc @ 3.5kpc-01.00° 20.50°

20.00°

19.50°

19.00°

18.50°

0

18.00°

12

GRS 13CO Gaussian line width+00.20°10+00.00°Galactic Latitude

GRS 13CO Gaussian FWHM [km s 1]

Galactic Latitude+00.00°HISA Gaussian FWHM [km s 1]

108-00.20°6-00.40°-00.60°4-00.80°2

20pc @ 3.5kpc-01.00° 20.50°

20.00°

19.50°
19.00°
Galactic Longitude

18.50°

0

18.00°

Fig. 8. Line width maps. Upper panel: HISA line widths inferred from Gaussian fits. Lower panel: fitted 13 CO line widths. The black contours
indicate the integrated 13 CO emission at levels of 10.5 and 15 K km s−1 for reference. The red dashed polygons mark the eastern and western partof the filament that were used for a separate analysis.

Probability density

0.20

0.25

HISA
13
CO

0.20

Whole filament

0.20

HISA
13
CO

Eastern region

HISA
13
CO

Western region

0.15

0.15
0.15

0.10

0.10
0.10
0.05
0.00
0

0.05

0.05
2

4

6

8
−1

FWHM [km s ]

10

12

0.00
0

2

4

6

8
−1

FWHM [km s ]

10

12

0.00
0

2

4

6

8

10

12

FWHM [km s−1]

Fig. 9. Histogram of line widths. The histograms show the line widths of HISA and 13 CO in black and blue, respectively. Middle and right panels:
line width distribution in the regions marked by the left and right polygon in Fig. 8, respectively.

A68, page 8 of 21

J. Syed et al.: Atomic and molecular gas properties during cloud formation
HISA
13
CO
13
CO /1.3√
13
CO / 3

Probability density

0.14
0.12
0.10
0.08
0.06
0.04
0.02
0.00
0.0

2.5

5.0

7.5

10.0

12.5

15.0

17.5

20.0

Mach number M
Fig. 10. Distribution of the turbulent Mach number across the whole
filament. The cold atomic hydrogen traced by HISA is shown in black.
The Mach numbers of the molecular gas seen in 13 CO emission are
shown in blue. The green and gray dashed distribution shows the 13 CO
Mach numbers
if the 13 CO line width is on average overestimated by√
30% and 3, respectively.

where N(13 CO) is the column density of 13 CO molecules in
cm−2 , dv is in units of km s−1 , T B and T ex are the brightness
temperature and excitation temperature of the 13 CO line in unitsof Kelvin, respectively. By assuming that the excitation temperatures of 12 CO and 13 CO are the same in LTE, we derived
the excitation temperature from 12 CO(1-0) emission data of
the FOREST Unbiased Galactic plane Imaging survey with theNobeyama 45m telescope (FUGIN; Umemoto et al. 2017), using(Wilson et al. 2013)
 
 
T ex = 5.5 · ln 1 +−1
5.5 ,T B12 + 0.82

(5)where T B12 is the brightness temperature of the 12 CO line in unitsof Kelvin. The FUGIN 12 CO data have an angular and spectral
resolution of ∆Θ = 2000 and ∆v = 1.3 km s−1 , respectively. To calculate the excitation temperature, we reprojected the data cubeon the same spatial and spectral grid as the GRS 13 CO data of
GMF20.0-17.9.
We find a lower limit to the excitation temperature of 5 K forregions where the 12 CO brightness temperature reaches the 5σ
level (2 K). We can then derive the optical depth of the 13 CO linefrom the excitation and brightness temperature, using (see e.g.,
Wilson et al. 2013; Schneider et al. 2016)

"
−1 
!
#−1


 
5.3
TB·  exp
− 1 − 0.16  .
τ = −ln 1 −
(6)
5.3
T ex
We estimate a lower limit of the optical depth of τ ∼ 0.06 forCO brightness temperatures above 1.25 K (∼5σ) and the highest excitation temperatures we find (∼25 K). Hence, we set the
optical depth to τ = 0.06 in regions where τ < 0.06. Only few
positions show optical depths as high as τ ∼ 2. We employ acorrection factor to compensate for high optical depth effects
by replacing the integral in Eq. (4) with (Frerking et al. 1982;
Goldsmith & Langer 1999)
ZZτ
T B (v) dv .
(7)
T B (v) dv →1 − e−τ13This correction factor is accurate to 15% for τ < 2.

To translate the 13 CO column density into a column densityof molecular hydrogen, we first estimated the relative abundanceof 12 CO with respect to 13 CO. Milam et al. (2005) and Giannetti
et al. (2014) derived relative abundance relations based on different CO isotopologs and metallicities. At the Galactocentric
radius of DGC = 5.0 kpc (Ragan et al. 2014), these relations give
[12 CO]/[13 CO] abundances between 40 and 56. Given the large
uncertainty of these numbers, we chose a canonical conversion
factor of 45. The relative abundance of the main isotopolog
12
CO compared to molecular hydrogen is given in Fontani
et al. (2012) who derive an H2 abundance with respect to 12 CO
of X12−1CO = 7500. Therefore, we adopted a conversion factor of[H2 ]/[13 CO] = 3.4 × 105 . The derived H2 column densities have
uncertainties of at least a factor of two due to the large uncertainties in these relations. Furthermore, CO might not always bea good tracer of H2 as “CO-dark H2 ” could account for a significant fraction of the total H2 (Pineda et al. 2008, 2013; Goodman
et al. 2009; Smith et al. 2014).
For the derivation of the column densities we integrated over
the whole velocity range between 43 and 56 km s−1 where wefind HISA. The H I (CNM) and H2 column densities derived
from HISA, and 13 CO, respectively, are presented in the lower
panels of Fig. 11. The column densities are partly correlated
in the western part of the filament but the strongest cold H I
column density peaks in the eastern part (` ∼ 20◦ , b ∼ +0.2◦ )do not show an H2 column density counterpart. The strongest
H2 column density peak in the western part (` ∼ 18.1◦ , b ∼−0.3◦ ) reveals little H I column density but coincides with
continuum emission. Continuum emission contaminates selfabsorption features and hence makes it difficult to measure
HISA. Most locations that are associated with continuum emission do not show HISA counterparts. However, we can measure
the optical depth toward strong continuum emission sources andthus constrain the spin temperature of the HISA cloud. This isaddressed in the following subsection.
3.3.3. Atomic gas column density seen in H I emission

In addition to HISA, we investigated the properties of atomic
hydrogen (WNM+CNM) by measuring the column density from
H I emission and correcting for optical depth effects and diffuse
continuum. We can utilize the measurement of the optical depth
to constrain the spin temperature of the cold atomic hydrogen(see Appendix A.2). Further details of optical depth and column
density corrections are given in Bihr et al. (2015) and Wang et al.
(2020a).
As the optically thin assumption might not hold for someregions, we can utilize strong continuum emission sources todirectly measure the optical depth. H I continuum absorption(HICA) is a classical method to derive the properties of theCNM (e.g., Strasser & Taylor 2004; Heiles & Troland 2003).
This method employs strong continuum sources, such as Galactic H II regions or active galactic nuclei (AGNs), to measure theoptical depth of H I. As these sources have brightness temperatures that are larger than typical spin temperatures of cold H I
clouds (T s ∼ 100 K), we observe the H I cloud in absorption. The
absorption feature is furthermore dominated by the CNM since
the absorption is proportional to T s−1 . By measuring on and off
positions, we can directly compute the optical depth of H I. The
optical depth is given by (see Bihr et al. 2015; Wang et al. 2020a)
τ = −ln!
T on − T off,
T cont(8)
A68, page 9 of 21

A&A 642, A68 (2020)

3.6 × 1021

-00.20°-00.40°

2.8 × 1021

-00.80°20pc @ 3.5kpc-01.00° 20.50°

20.00°

19.50°

19.00°

Galactic Latitude

18.00°

N(HI) THISA = 40 K

+00.20°+00.00°-00.40°6.0 × 1020

3.2 × 1020

-00.60°20pc @ 3.5kpc-01.00° 20.50°

20.00°

19.50°

19.00°

18.50°

18.00°

N(H2) from 13CO

+00.20°+00.00°

1.8 × 1020
3.0 × 1022
2.0 × 1022

-00.20°-00.40°

1.0 × 1022

-00.60°-00.80°

2.0 × 1021

4.6 × 1020

-00.20°-00.80°Galactic Latitude

18.50°HI Column density [cm 2]-00.60°H2 Column density [cm 2]

Galactic Latitude+00.00°HI Column density [cm 2]

N(HI) - corrected+00.20°

4.4 × 1021

20pc @ 3.5kpc-01.00° 20.50°

20.00°

19.50°
19.00°
Galactic Longitude

18.50°

18.00°

4.0 × 1020

Fig. 11. Top panel: H I column densities of the combined WNM and CNM seen in H I emission. The column densities were corrected for optical depth, weak diffuse continuum emission, and the kinematic distance ambiguity. The optical depth is measured toward the continuum source
G19.075-0.287 and is applied to correct the column densities throughout the whole cloud (see Sect. 3.3.3). The position of G19.075-0.287 is indicated by the green cross. Middle panel: H I column densities of the CNM inferred from HISA features assuming a spin temperature of T HISA = 40 K
and a background fraction of p = 0.9. Bottom panel: H2 column densities inferred from 13 CO as a tracer. We assumed an H2 /13 CO ratio of 3.4 × 105 .
The red dashed polygons in each panel indicate the eastern and western part of the filament that are analyzed separately. The white and black
contours indicate the column density thresholds that were used for the derivation of the column density probability density functions (see Sect. 4.2).
A68, page 10 of 21

where T on and T off is the H I brightness temperature toward astrong continuum background source and offset from the source,
respectively. The brightness temperature T cont describes the continuum level of the background source that is not affected by H I
absorption. The advantage of this method is the direct measurement of the optical depth. However, the HICA method requires
strong continuum emission sources. As most strong continuum
sources are discrete point sources, this method results in an
incomplete census of optical depth measurements (see Wanget al. 2020b, for a compilation of all optical depth measurementsin the THOR survey). Consequently, the intrinsic structure ofindividual H I clouds cannot be determined. Some continuum
emission sources also show extended structures. Therefore, finding reliable off positions could pose difficulties. As we exploited
THOR-only (VLA C-configuration) data for this measurement,
we filter out most large-scale H I emission. The THOR-only data
reveal H I emission of less than 30 K, often just within the noise.
Therefore, we can neglect the emission of the H I cloud in Eq. (8)and set T off = 0. We can then calculate the optical depth without
measuring an off position by!
T on
τsimplified = −ln.
(9)
T contDepending on the brightness of the continuum source and the H I
optical depth, the absorption spectrum can approach zero. Dueto the noise in the spectra, the spectra can exhibit brightness temperatures smaller than zero, which is not physically meaningful.
We therefore report a lower limit for the optical depth where theabsorption T on becomes smaller than 5σ.
Besides strong continuum sources we observe weak continuum emission throughout the Galactic plane. This component
has brightness temperatures between 10 and 50 K. For thederivation of the H I column densities, we employed the combined THOR data as in the case of HISA. The continuum
emission has been subtracted during data reduction as describedin Sect. 2.1. However, even weak continuum emission can stillinfluence the observed brightness temperature. If we neglect
weak continuum emission, the measured H I emission will be
underestimated as weak continuum emission can suppress asignificant fraction of H I emission (e.g., Bihr et al. 2015). Consequently, the derived H I column densities will be underestimated.
We took this effect into account when computing the H I column
density (see Bihr et al. 2015, Eq. (9)).
In contrast to Wang et al. (2020b), where they used a 6σ
threshold to select continuum sources, we measured the optical depth of atomic hydrogen toward the brightest continuum
sources with brightness temperatures T cont > 200 K to not sufferfrom low saturation limits since we expect the optical depth to behigh. Four sources have been identified with this threshold. The
measured optical depths of these sources vary between 0.5 and2.5 (lower limit). We selected the continuum source G19.0750.287 (Wang et al. 2018) as a representative source for the opticaldepth as it is not in the 5σ saturation at most velocities between
43 and 56 km s−1 , which gives a mean optical depth of τ ∼ 0.9(Fig. 12). This is a reasonable approximation as the optical depth
map derived by Wang et al. (2020b) gives a mean optical depthof ∼1.0 when averaged over the whole filament.
However, this optical depth measurement is a lower limit asG19.075-0.287 is a Galactic H II region located in the Galactic
plane. As no strong extragalactic continuum sources are identified toward the position of GMF20.0-17.9, the optical depth
measurement has drawbacks in the current investigation. For
the emission data, we have to take into account an opacity

Optical depth τ

J. Syed et al.: Atomic and molecular gas properties during cloud formation2

G19.075-0.287

1

0
0

20

40
vLSR [km s−1 ]60

80

Fig. 12. Optical depth measurement toward the H II region
G19.075-0.287 (Wang et al. 2018). The plot shows the optical depth asa function of LSR velocity and was computed using Eq. (9). For somechannels, the absorption spectrum saturates and the measured opticaldepth is a lower limit of τ = 1.6, which is indicated by the horizontal
dotted line. The gray shaded area indicates the velocity range between
43 and 56 km s−1 , where HISA features have been extracted.

contribution from the far side H I beyond the location of the
H II region. To first approximation, we assumed that the optical depth from the background is similar to that of the measured
foreground. We therefore adopted 2 × τ(vLSR ) for the whole map
and corrected the H I column density for the optical depth pervelocity channel. Given the corrected mean optical depth of
2 × τ ∼ 1.8, the opacity correction factor τ/(1 − e−τ ) increases
the mean column density by a factor of ∼2.
The derived column densities are a result of the H I emission stemming from both the kinematic far (12.0 kpc) and near
(3.5 kpc) side of the Milky Way. The kinematic distances havebeen obtained using the Kinematic Distance Utilities1 (Wenger
et al. 2018) and employing the Galactic rotation model from
Reid et al. (2019). Since the distribution of the atomic gas in the
Galactic plane is approximately axisymmetric with respect to the
Galactic center (Kalberla & Dedes 2008), we can assume that theatomic gas density distribution in the vertical direction is similar for a given Galactocentric radius. Using the average verticaldensity profile from Dickey & Lockman (1990), we can estimate
the gas fraction at the kinematic near and far side for each lineof sight. Since most H I emission is observed close to the Galactic midplane, the foreground gas fraction is ∼50%. Therefore,
due to the kinematic distance ambiguity half of the H I emission is attributed to the background, which is not associated with
GMF20.0-17.9. We derived the H I column density map shownin the top panel of Fig. 11 taking into account only the near side
gas at 3.5 kpc.
3.3.4. Masses

As we have determined the column densities and know the distance of GMF20.0-17.9 (∼3.5 kpc, Ragan et al. 2014), we candirectly estimate the atomic and molecular mass of each part of
the filament (see Table 1). All masses were calculated from thecolumn densities integrated over 43–56 km s−1 .
The molecular hydrogen mass of the whole filament as
marked by both the red polygons in Fig. 11 is 3.5 × 105 M .
Inside the polygon regions, the mass of the total atomic hydrogen, accounting for WNM and CNM measured from H I emission, corresponds to ∼75% of the H2 mass (2.6 × 105 M ) for
the whole filament after correcting for optical depth effects,
1

https://github.com/tvwenger/kd
A68, page 11 of 21

A&A 642, A68 (2020)
Table 1. Derived masses of the giant molecular filament GMF20.0-17.9.

RegionM(H2 )M(H I)M(HISA)(T s = 40 K)
[M ]

fHISA
(T s = 20 K)

fHISA(T s = 40 K)

fH I

[M ]

M(HISA)(T s = 20 K)[M ]2.6 × 10 (4.6 × 105 ) (a)1.2 × 105
1.5 × 105

4.6 × 103
1.9 × 103
2.6 × 103

1.3 × 104
5.7 × 103
7.5 × 103

1%
2%
1%

4%
5%
3%

75% (130%) (a)
110%
65%

[M ]
Total
East
West

5

3.5 × 10
1.1 × 105
2.3 × 105

5

Notes. The masses were calculated for each part of the filament as well as the whole filament marked by the red polygons in Fig. 11. The second
column gives the molecular hydrogen mass as traced by 13 CO emission. The third column shows the total atomic hydrogen mass inferred from theoptical depth and continuum corrected H I emission. The fourth and fifth column present the mass of the cold atomic hydrogen traced by HISA
with an assumed spin temperature of 20 and 40 K, respectively. The last three columns give the corresponding mass fractions with respect to theH2 mass. (a) This mass was calculated using the corrected H I emission between 43 and 56 km s−1 , 20.6 > ` > 17.6◦ and −1.25 < b < +0.5◦ .

weak continuum emission, and the kinematic distance ambiguity. However, if we take into account all diffuse H I emission
beyond the polygon regions, arising from the region between
20.6 > ` > 17.6◦ and −1.25 < b < +0.5◦ , the mass of the total
H I component rises by 75% to ∼4.6 × 105 M . The molecularfilament is therefore embedded in a large gas reservoir of atomic
hydrogen.
The CNM mass traced by HISA corresponds to 1–5% of
the molecular mass, depending on the region and assumed spintemperature. The uncertainty of the column density directlytranslates to an uncertainty of mass. If we assume a spin temperature of 20 K, instead of our canonical value of 40 K, the mass
traced by HISA decreases by a factor of ∼3. Hence, the largest
uncertainty arises from the assumption of a spin temperature.
We are able to constrain an upper limit of the spin temperature
for the column density derivation by assuming an optically thick(τ → ∞) cloud, as we show in Appendix A.2.
The atomic mass fraction generally increases toward the eastern part of the filament, agreeing with our findings in the column
density distributions (see Sect. 4.2 for details). As discussed
in Appendix A, we estimated a column density uncertainty of∼40% to account for systematic differences and noise in ourbaseline extraction method. Depending on the background fraction p, the column density further varies by a factor of ∼2
between p = 0.9−0.7 (see Appendix A.1). It is difficult to exactly
quantify the uncertainty of the cold H I column density and mass
traced by HISA. Considering the estimated uncertainties dueto the extraction method, background fraction, and spin temperature, the HISA-traced column density and mass have an
uncertainty of a factor of 2–4.
As we study the CNM through HISA, we might miss a significant fraction of it. Since we can only trace gas that is coldenough to be observed in absorption against a warmer background, we are limited in our HISA detection by the requirementof sufficient background emission. The CNM has temperatures.300 K (McKee & Ostriker 1977; Wolfire et al. 2003). For future
investigations, simulations could help to quantify the fraction of
CNM that is invisible to our HISA method. The computed H2column density and mass has an uncertainty of at least a factorof two due to the uncertainties in the value for the CO-to-H2
conversion (Milam et al. 2005; Giannetti et al. 2014; Fontani
et al. 2012). Furthermore, we could miss a significant fraction of
CO-dark H2 column density (Pineda et al. 2008, 2013; Goodman
et al. 2009). Simulations suggest that the fraction of CO-dark H2
could even be as high as ∼50% at conditions typical of the Milky
Way disk (Smith et al. 2014; Duarte-Cabral & Dobbs 2016).
However, this fraction should be moderate in low-temperatureenvironments (Glover & Smith 2016).
A68, page 12 of 21

4. Discussion
4.1. Kinematics

The histograms of line-of-sight peak velocities derived fromHISA and 13 CO generally agree for both parts of the filament.
The results of the Gaussian fits to the spectra might not always
reflect the actual kinematic structure as 13 CO emission exhibits
multiple velocity components in some regions between 37 and
50 km s−1 . However, the 13 CO velocities generally agree with the
HISA features in a statistical sense, even in the eastern part of thefilament where we do not observe a spatial correlation along theline of sight. We take this as a confirmation that our extracted
HISA features are in fact due to self-absorption.
The line widths of HISA show a broad distribution of 2–
10 km s−1 . The eastern part reveals enhanced HISA line widths,
which are 3–4 km s−1 higher toward the north of the molecularfilament. Although speculative, this could be a signature of thecompression of H I gas passing through the spiral arm potential and triggering H2 formation (Bergin et al. 2004). As thegas is leaving the spiral arm structure, this could inject turbulence on the downstream side that enhances the line widths.
Although observationally difficult to distinguish, simulations of
the galactic dynamics of the ISM suggest that there are systematic differences in velocity dispersion between molecular clouds
within the spiral arm potential and inter-arm clouds (Dobbs
2015; Duarte-Cabral & Dobbs 2016, 2017). The morphologicaland kinematic differences in each part of the filament could
therefore be related to its position with respect to the spiralarm potential. However, in order to differentiate between different scenarios, we need to investigate synthetic H I observations,which is beyond the scope of our current analysis. We note thatthe broadened HISA lines toward some positions of the cloudmight be subject to resolution effects and could be the superposition of multiple lines. Spectrum 5 in Fig. 4 clearly shows
multiple 13 CO components where we detect an enhanced HISA
line width. The lack of spatial correlation between HISA and
13
CO, particularly in the eastern region, makes it difficult toassess if multiple 13 CO components are preferentially associatedwith enhanced HISA line widths. Since the velocity dispersion
is mostly due to turbulence in both tracers, we conclude that theagreement in velocities is robust.
4.2. Column density probability density functions (N-PDFs)

The column density maps derived in Fig. 11 can be further evaluated by determining their probability density function (PDF).
Column or volume density PDFs are commonly used as a

J. Syed et al.: Atomic and molecular gas properties during cloud formation

measure of the density structure and physical processes acting
within the cloud (e.g., Kainulainen et al. 2014). A log-normal
shape of the N-PDF is usually attributed to turbulent motions
dominating the early diffuse phase of a cloud’s evolution. Furthermore, the width of the log-normal distribution reflects theamplitude of turbulence and can be associated with the Mach
number (e.g., Padoan et al. 1997; Passot & Vázquez-Semadeni
1998; Kritsuk et al. 2007; Federrath et al. 2008). In later evolutionary stages, molecular clouds can develop high-density
regions due to the increasing effect of self gravity, producing
a power-law tail in their N-PDF. Molecular cloud complexes thatshow star-forming activity favor this scenario as they reveal such
power-law tails (Kainulainen et al. 2009; Schneider et al. 2013,2016).
The shape of the resulting N-PDF is also sensitive to theregions where column densities are taken into account, especially in the low column density regime (Lombardi et al. 2015),
and it is sensitive to the treatment of zero spacing information ininterferometric data (Ossenkopf-Okada et al. 2016). We derived
each N-PDF from the regions marked by the red polygons in
Fig. 11, respectively. However, if we take into account low column densities that extend beyond the region enclosed by thepolygons, we will miss a significant fraction of low column densities and hence the shape of the N-PDF will not recover the
structure at the lower end well. We therefore chose to derive
the N-PDFs from column densities approximately within thelast closed contours that are still within the selected polygon
regions. In order to compare the H I column densities with thoseof molecular hydrogen, we converted N(H2 ) to N(H) to construct
the H2 N-PDFs. For the N-PDFs, we chose closed contours of
1.9 × 1020 and 3.2 × 1021 cm−2 for HISA and H2 , respectively.
The selected closed contours that go beyond the polygon regions
do not significantly change the shape of the N-PDFs. We set thecolumn density threshold for H I emission to 2.7 × 1021 cm−2 .
It is difficult to define a last closed contour for H I emission.
However, this boundary bias has a negligible impact on the
shape of the H I N-PDF as we observe a small range of column densities due to the diffuse nature of H I emission. For
turbulence-dominated gas, last closed contours are not essential
to sample the N-PDF properly (Körtgen et al. 2019). We furthermore normalized each N-PDF by the mean column density.
Figure 13 presents the N-PDFs of H I emission, HISA, and H2column densities for each part of the filament (east/west) as wellas the whole filament (east+west), respectively.
As expected from the column density maps in Fig. 11, the
N-PDF of the CNM as traced by HISA peaks at lower column
densities than molecular hydrogen. The HISA N-PDFs are well
represented by a log-normal function. The results of log-normal
fits are shown in Table 2. The log-normal shape implies that
turbulent motions might be dominant and gravitational collapse
leading to high column density peaks is not visible in HISA
within the whole filament. There is no significant difference
between the subregions defined in the eastern and western partof the filament. The widths of the HISA N-PDFs are the samefor both regions. The mean column density derived from HISA
is ∼3 × 1020 cm−2 .
The mean column densities and widths of the N-PDFs
agree well with those found by Wang et al. (2020a) for
GMF38.1-32.4a. To investigate how observational uncertainties
affect the width of the N-PDF, Wang et al. (2020a) created model
images of H I and continuum emission with similar properties
and noise as the real THOR data. They introduced artificial H I
absorption features from known column density distributions
and added them to the model data. They extracted the HISA

Table 2. Results of the fits to the N-PDFs.

Component
H I (WNM+CNM)
Whole filament
East
West
HISA (CNM)
Whole filament
East
West
H2
Whole filament
East
West
All gasWhole filamenthNH i [cm−2 ]Width σPL index α

3.2 × 1021
3.3 × 1021
3.2 × 1021

0.11
0.12
0.09

–
–
–

3.0 × 1020
3.0 × 1020
3.0 × 1020

0.29
0.30
0.28

–
–
–

7.6 × 1021
7.3 × 1021
7.7 × 1021

0.57
0.54
0.58

2.99
4.34
2.81

8.3 × 1021

–

3.53

Notes. The second column shows the mean column density of eachcomponent designated in the first column. The third column presents
the widths of the log-normal function fitted to the N-PDFs. The lastcolumn shows the index of the power-law (PL) function fitted to the tailof the H2 and All gas N-PDFs.

features using a similar method and derived column density distributions showing that the widths of the N-PDFs they find do
not significantly increase due to observational uncertainties orthe HISA extraction method. They conclude that the widths ofthe derived N-PDFs are robust and not subject to broadening
introduced by observational noise and the fitting approach.
The mean column densities of molecular hydrogen are about
an order of magnitude higher than the column densities of HISA.
In contrast to the HISA N-PDFs, the N-PDFs of molecularhydrogen are poorly represented by a log-normal function. Even
though the eastern region does not show similarly high column
density peaks as the western region, a power-law behavior isevident in both column density distributions. Therefore, powerlaw functions (p(x) ∝ x−α ) were additionally fitted to the highcolumn density tail of the H2 N-PDFs. The best minimal column density for the power-law fit is obtained from the minimal
Kolmogorov-Smirnov distance between the fit and the N-PDF.
The fits were performed using the python package Powerlaw(Alstott et al. 2014). The fitted parameters of the power-law
functions are also listed in Table 2.
Power-law tails can be a sign of gravitational collapse, which
creates high column density peaks (Klessen 2000; Federrath
et al. 2008; Kainulainen et al. 2009; Schneider et al. 2016). In
agreement with observations, simulations of self-gravitating, turbulent molecular clouds show that star-forming activity reveals
strong deviations from the log-normal shape in the form of
power-law tails toward high column densities (Kritsuk et al.
2011). The slope of the power-law tails can then be associatedwith the evolutionary stage of the cloud, with shallower slopes
indicative of an increasing degree of star formation efficiency(Federrath & Klessen 2013). In general, theoretical studies andsimulations of molecular clouds can reproduce N-PDFs of different forms, depending on the degree of turbulence, star-forming
activity, and magnetic field support (Vazquez-Semadeni 1994;
A68, page 13 of 21

A&A 642, A68 (2020)
Column density NH [cm−2]
1021

1022

Probability density

101

1022

Column density NH [cm−2]

1023

101

1021

σ = 0.11

σ = 0.09
100

10−1

10−1

10−1

10−2

10−2

10−2

10

101

20

10

21

102
10

10−3 −1
10

22

100
10

101

20

10

101

whole filament Ts = 40 K

21

102
10

22

10

10−1

10−1

10−1

10−2

10−2

10−2

1021
10

1022

1023

1

102

10−3 −1101021
10whole filament H2

σ = 0.57
α = 2.99

100

100

101

1022

1023

1

100

102

10−3 −1101021

eastern H210

σ = 0.54
α = 4.34

100

10−1

10−1

10−2

10−2

10−2

100

101

NH/hNHi10

western HISA Ts = 40 K

102

10−3 −1
10

100

101

NH/hNHi

102

100

101

1022

1023

1

10−1

10−3 −1
10

10

102
22

σ = 0.28
100

101

101
21

σ = 0.30
100

100

100
20

101

eastern HISA Ts = 40 K

σ = 0.29

10−3 −1
10100

10−3 −1
101023
western HI

σ = 0.12
100

100

1022

101

eastern HI

100

101

Probability density

1021

whole filament HI

10−3 −1
10

Probability density

Column density NH [cm−2]

1023

10−3 −1
10102

western H2

σ = 0.58
α = 2.81

100

101

102

NH/hNHi

Fig. 13. Top panels: N-PDFs traced by H I emission. The distributions are derived from the H I column densities that have been corrected for
optical depth and continuum emission (top panel of Fig. 11). Middle panels: N-PDFs of the gas traced by HISA. Bottom panels: H2 N-PDFs traced
by 13 CO. Left panels: derived N-PDF of the whole filament (east+west), respectively. Middle and right panel: N-PDFs of the eastern and westernpart of the filament, respectively. The blue curves indicate the log-normal fits to the distribution. The red vertical dashed and solid lines mark thecolumn density threshold (last closed contour) and mean column density, respectively. The red solid lines in the lower panels indicate the fit to thepower-law tail.

Federrath et al. 2010; Burkhart et al. 2015a). Both subregions
miss a small fraction of low column densities above the closed
contour threshold. However, the shape of the H2 N-PDFs does
not change significantly if we take into account all closed
contours beyond the polygon regions.
The N-PDFs derived from the H I emission that traces a combination of CNM and WNM show a narrow log-normal shapewith widths of σ = 0.09−0.12. Observations toward well-known
molecular cloud complexes also show N-PDFs of H I emission
with narrow log-normal shapes (Burkhart et al. 2015b; Imara &Burkhart 2016; Rebolledo et al. 2017). We might overestimate
the column densities as the optical depth derived from absorption (see Sect. 3.3.3) is mostly due to cold atomic gas acting as
the absorbing medium. However, we used this optical depth measurement to correct for H I emission that might also be attributed
to warm and optically thin gas. Bihr et al. (2015) assess thiseffect and investigate the overestimation by comparing the corrected total H I column densities with actual column densities
of known spin temperatures and optical depths. They show that
A68, page 14 of 21

this overestimate is <10% for measured CNM optical depths
τ < 1.5. This effect is therefore negligible compared to the uncertainty of the optical depth measurement itself. Furthermore, thissystematic effect does not significantly affect the shape of the
N-PDF.
The mean column densities inferred from H I emission are
hNHI i ∼ 3 × 1021 cm−2 . The H I column densities show a narrowlog-normal distribution driven by turbulent motions whereas the
N-PDFs of molecular hydrogen show a broad distribution with apower-law behavior toward high column densities that might besubject to gravitational collapse. The column densities traced by
H I emission are an order of magnitude higher than those traced
by self-absorption. The narrow width of the N-PDF represents
the diffuse nature of H I emission while the broader column density distribution traced by HISA indicates a clumpier structure of
the CNM.
We examined the column density distribution of the entire
hydrogen content of the filament, that is, both the atomic andmolecular phase of GMF20.0-17.9. We derived an “All gas”

J. Syed et al.: Atomic and molecular gas properties during cloud formation
50

101

All gas0whole filament

α = 3.53

10
10

−1

30

2

20
1

pixel counts [log]40ΣHI [M pc−2]

Probability density

1021

Column density NH [cm−2]
1022
1023

10

10−2

101

102

−2

103

0

ΣHI + ΣH2 [M pc ]10−3 −1
10

100

101

102

NH/hNHi

Fig. 14. All gas N-PDF of GMF20.0-17.9. The PDF is derived byadding the column densities of H I, HISA, and H2 . The plot shows thederived N-PDF of the whole filament marked by both the red polygons
in Fig. 11. The red vertical dashed and solid line marks the column density threshold (last closed contour) at 4.5 × 1021 cm−2 and mean column
density, respectively. The red solid line indicates the power-law fit to thehigh column density tail of the distribution.

N-PDF in Fig. 14 by adding together the column densities of all
three tracers. We fitted the high column density tail of the distribution with a power-law function. The N-PDF can be very welldescribed by a single power-law function.
The western part shows higher H2 column density peaks anda shallower power-law tail in the N-PDF. The H2 column densities are generally lower in the eastern part of the filament.
The ATLASGAL survey (Schuller et al. 2009) reveals several
high-density clumps in the western part of the filament and few
clumps in the eastern part within the 13 CO velocity range. The
N-PDFs traced by HISA do not show significant differences
between each part of the filament. However, the mass of HISA
compared to its molecular counterpart does therefore increase
toward the eastern part of the filament. The maximum spin temperature of our extracted HISA features is also lower in theeastern subregion (Fig. A.3). This might be an indication that theeastern subfilament is a young, cold H I cloud while the westernregion exhibits a more evolved structure and star-forming activity. To furthermore test the validity of this hypothesis, we would
need to extend our analysis to a larger sample of GMFs to deduce
statistical evidence. This will be addressed in a future analysis. Simulations of cloud formation could also give constraints
on signatures of kinematics and column densities in atomic andmolecular line tracers. However, this is beyond the scope of thiscurrent investigation.
4.3. Signatures of phase transition

The conversion of atomic to molecular gas (H I-to-H2 ) is fundamental for molecular cloud formation processes. Theoreticalmodels predict for a single H I-to-H2 transition a mass surface
density threshold of ΣHI ∼ 5–10 M pc−2 for solar metallicity(Krumholz et al. 2008, 2009; Sternberg et al. 2014). In such models, the H I-to-H2 transitions are computed assuming a balance
between far-UV photodissociation and molecular formation, andaccounting for the rapid attenuation of the radiation field due
to H2 self-shielding and dust absorption (see also Klessen &Fig. 15. H I-to-H2 transition. The plot shows the H I mass surface density traced by H I emission as a function of the total hydrogen mass
surface density. The black solid line indicates a 1-to-1 relation. The
dashed blue line shows a fit to the mean of the distribution.

Glover 2016). Figure 15 presents the atomic hydrogen as afunction of the total hydrogen mass surface density. We take
into account all H I column densities traced by the corrected
H I emission between 20.6 > ` > 17.6◦ and −1.25 < b < +0.5◦ .
The figure reveals a saturation of atomic hydrogen at a mass
surface density of ∼20–30 M pc−2 . A least squares fit to themean of the distribution yields a mass surface density thresholdof ∼25 M pc−2 ( = 3 × 1021 cm−2 ). When examined individually, both the eastern and western subregion show the same
H I saturation level within the uncertainties (24 and 26 M pc−2 ,respectively). This transition exceeds the column density threshold predicted by theoretical models (Krumholz et al. 2008,2009; Sternberg et al. 2014). Bihr et al. (2015) report a column density threshold of 50–80 M pc−2 toward the star-forming
region W43, which is significantly higher than predicted transitions at ∼5–10 M pc−2 . Bialy et al. (2017) argue that such highmass surface density thresholds cannot be explained by typicalphysical properties of the CNM as it would require an unrealistically high UV radiation field or low dust-to-gas ratio. As theclumpiness of a molecular cloud might regulate how far UV radiation penetrates the medium (e.g., Stutzki et al. 1988; Shibai
et al. 1991), Bialy et al. (2017) suggest that the high thresholds can naturally be explained by a superposition of multiple
transition layers observed along the line of sight. These authors
predict a mass surface density threshold of ∼13 M pc−2 forthe more active star-forming region W43. Wang et al. (2020a)
find similar values of 14 – 23 M pc−2 toward GMF38.1-32.4a,
where the atomic gas surface density saturates to an almost flat
distribution.
While the derived atomic mass surface densities are a resultof the combined column densities of WNM and CNM, theshielding from dissociating Lyman-Werner (LW) photons provided by a transition layer between atomic and molecular gas
should be dominated by the CNM (Krumholz et al. 2009).
The H2 formation rate per atom scales as the number density n, so the CNM, due to its higher density, is far more
effective at shielding than the WNM. The observed transition should therefore be an upper limit and the actual critical surface density is ≤25 M pc−2 , depending to the first
approximation on the ratio ΣCNM /ΣWNM . Taking these considerations into account, we conclude that we observe at most 3–5transition layers of atomic to molecular gas between 43 and
56 km s−1 .
A68, page 15 of 21

A&A 642, A68 (2020)

4.4. Spatial correlation between atomic and molecular gas

2

https://github.com/solerjuan/astroHOG

A68, page 16 of 21

V
450

55

400

whole filament

350vHI [km s−1 ]

50

300
250

45

200
150

40

100
50

35
35

40

45

50

55

55
eastern region

0
300
250

vHI [km s−1 ]

50
200
45

150
100

40

50
35
35

40

45

50

55

55
western region

0
300
250

50
vHI [km s−1 ]The Histogram of Oriented Gradients2 (HOG) is a method basedon machine vision to study the spatial correlation in the emission
by two or more spectral line tracers across velocity channels in an
unbiased and systematic way. In Appendix B we briefly outline
the basic principles involved in this method. A comprehensive
description is given by Soler et al. (2019).
We applied the HOG on each part of the filament to investigate the spatial correlation between H I and 13 CO. The output of
the HOG analysis is a matrix where the rows and columns correspond to the different velocity channels in each tracer, as shownin Fig. 16. The number in each matrix position corresponds to theprojected Rayleigh statistic (V), which is an optimal estimatorof the morphological correlation between the velocity channel
maps as evaluated by the orientation of its intensity gradients.
High values of V correspond to high spatial correlation and values of V ≈ 0 correspond to very low spatial correlation. The
intensity gradients are calculated using a Gaussian derivative
kernel whose width determines the spatial scales under consideration. To exploit the available spatial resolution, we selected aderivative kernel size that matches the synthesized beam size of
the GRS 13 CO data, that is, 4600 . The projected Rayleigh statistic√
is a measure of the significance of the spatial correlation, V ≈ 2is roughly the equivalent of a 1σ deviation from complete lack ofcorrelation, which corresponds to a flat distribution in the angles
between the intensity gradients. However, the significance of theresult also has to be evaluated with respect to the chance correlation that may be present between the velocity channel maps.
We use the standard deviation of V in the velocity range between
10 and 90 km s−1 as an estimate of the amplitude of the chancecorrelation against which we can evaluate the significance of
the V values. This assumes that there are enough independent
velocity-channel maps in the selected velocity range.
Figure 16 presents the correlation distribution between H I
and 13 CO for all parts of the filament as a function of velocity. We observe a significant spatial correlation in the velocity
channels around vHI ≈ v13 CO ∼ 43 and ∼47 km s−1 toward thewest. However, the eastern part of the filament shows no significant correlation between H I and 13 CO emission at the velocitiesof GMF20.0-17.9. The observed correlation within the whole
filament is therefore dominated by the western region.
While we computed the spatial correlation between H I and
13
CO emission, we test the validity of the correlation by applying the HOG analysis to the inferred HISA and 13 CO emission
maps. The HOG yields similar findings for HISA and 13 CO. As
the absence of spatial correlation within the eastern part of thefilament is reproduced in both analyses, we are confident that
we do not observe any significant spatial correlation between H I
and 13 CO within the eastern part of the filament.
Small kernel sizes close or equal to the angular resolutionof the telescope makes features produced by noise and nonideal telescope beams more evident. Since spatial correlation
is expected across multiple scales (Green 1993; Lazarian &Pogosyan 2000; Lazarian et al. 2001), we also examine the correlation in each analysis by setting the kernel size to 9000 , which
is approximately twice the angular resolution of the THOR andGRS data (4000 and 4600 , respectively). The differences we findbetween the eastern and western region with our HISA method
are reproduced by the HOG analysis, irrespective of the spatial
scale we use. Thus, we consider these findings robust and not an
artifact of our HISA extraction method.

200
45

150
100

40

50
35
35

40
45
50
vCO [km s−1 ]55

0Fig. 16. HOG correlation plane of the filament as marked by thered polygons in Fig. 11. This figure presents the computed correlation between H I and 13 CO across velocities defined by the projected
Rayleigh statistic. The white line shows a 1-to-1 correlation acrossvelocities. The blue contours show the 5σ level on V. Large values of V
indicate a high spatial correlation. Values of V close to zero indicate anegligible spatial correlation.

We conclude that the CNM appears to be associated withmolecular gas in the western part whereas the molecular gas
seems to be decoupled from its atomic counterpart in the more

J. Syed et al.: Atomic and molecular gas properties during cloud formation

diffuse cloud envelope toward the east. The systematic differences in spatial correlation between east and west can beinterpreted as an indication of different evolutionary stages.

5. Conclusions
We have studied the atomic and molecular gas within the giant
molecular filament GMF20.0-17.9. The molecular component
is traced by GRS 13 CO observations whereas the atomic gas
is observed via H I emission from the THOR survey. We isolated HISA features to disentangle the CNM from the atomic
gas traced by H I emission. We aimed to study the propertiesof the CNM as traced by HISA and compare our findings withthe molecular counterpart. The results are summarized in thefollowing:
1. We extracted HISA features by estimating the H I emission
spectrum in the absence of HISA. We employed a combination of first and second order polynomial functions to fit thebaselines of HISA spectra at velocities adjacent to HISA features. This method gave the most reliable and robust results
among the procedures we tested.
2. The extracted HISA features reveal a spatial correlation with
13
CO emission toward the western region of the filament
while the eastern part shows no evidence that HISA traces
the molecular gas. This finding is supported by the HOG
analysis reporting significant spatial correlation toward thewestern part and no correlation toward the eastern part of
the filament. However, the peak velocities of HISA and 13 CO
are in good agreement in both parts of the filament. The
observed line widths of 13 CO and HISA suggest that nonthermal effects like turbulent motions are the dominant driver for
most regions within the filament.
3. We derived H2 column densities from 13 CO emission andcompared the molecular column density distribution with its
atomic counterpart. The HISA column densities show a morediffuse structure compared to those of molecular hydrogen.
The H2 column densities reveal high-density peaks, particularly in the western part of the filament. The mass ratio of
H I (traced by HISA) and H2 is 0.01−0.05, depending on
the assumed spin temperature and region. This mass ratio
increases toward the eastern part of the filament. The total
H I mass traced by H I emission is similar to the molecularmass within the defined regions. The mass surface density threshold from the total H I to H2 is observed to be∼25 M pc−2 , in excess of predictions by theoretical models.
However, this result can naturally be explained by a superposition of multiple transition layers or an additional WNM
fraction that is less effective at shielding.
4. The HISA N-PDFs can be well described by log-normal
functions in both parts of the filament, indicative of turbulent motions as the main driver for these structures. While
the magnitude of the column densities are dependent on
the assumed parameters of spin temperature and backgroundfraction, the shape and width of the N-PDFs are robust.
The N-PDFs of H I emission tracing both the WNM and
CNM of the atomic gas represent the diffuse structure andshow a narrow log-normal shape. The H2 column densities
show a broad log-normal distribution with an indication of apower-law tail, more pronounced in the western part of thefilament.
5. We speculate that the two parts of the filament reflect different evolutionary stages. Interestingly, the derived HISA features in the eastern part of the cloud show lower maximum

spin temperatures. This favors the scenario of a younger, lessevolved cloud that is forming molecular gas out of the atomicgas reservoir. The western region harbors signs of active
star formation and shows more pronounced column density
peaks of H2 . Moreover, the mass fraction of H2 compared
to cold atomic hydrogen traced by HISA is larger toward
the western part of the filament. While the HISA features
correlate well with the molecular gas in the western part of
the filament, they lack spatial correlation with the molecularcomponent in the eastern region. Furthermore, we speculate that signatures of spiral arm interaction with atomic gas
are visible toward the eastern part of the filament, due to an
enhancement of line widths. The spatial structure and kinematics provide useful observables for theoretical models andsimulations.
A statistical treatment of the HISA properties in the Galactic
plane is still missing. However, this case study toward a known
large-scale filament, which is complementary to the analysis by
Wang et al. (2020a), serves as a good laboratory to study theproperties of the CNM.
Acknowledgements. J.S., H.B., R.S.K., and S.C.O.G. acknowledge support fromthe Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) –Project-ID 138713538 – SFB 881 (“The Milky Way System”, subprojects A01,
B01, B02, and B08). Y.W., H.B., and J.D.S. additionally acknowledge support
from the European Research Council under the Horizon 2020 Framework Program via the ERC Consolidator Grant CSF-648505. R.S.K. and S.C.O.G. also
thank for funding from the Heidelberg Cluster of Excellence STRUCTURES
in the framework of Germany’s Excellence Strategy (grant EXC-2181/1 –390900 948). R.S.K. also thanks for funding from the European ResearchCouncil via the ERC Synergy Grant ECOGAL (grant 855130). F.B. acknowledges funding from the European Research Council (ERC) under the European
Union’s Horizon 2020 research and innovation programme (grant agreement
No.726384/Empire). This work was carried out in part at the Jet Propulsion Laboratory which is operated for NASA by the California Institute of Technology.
This research made use of Astropy and affiliated packages, a communitydeveloped core Python package for Astronomy (Astropy Collaboration 2018),
Python package SciPy (https://www.scipy.org), and APLpy, an open-source
plotting package for Python (Robitaille & Bressert 2012). The authors thank theanonymous referee for the detailed comments and constructive suggestions that
improved the paper.

References
Abreu-Vicente, J., Ragan, S., Kainulainen, J., et al. 2016, A&A, 590, A131
Allen, C. W. 1973, Astrophysical quantities (New York: Springer)
Alstott, J., Bullmore, E., & Plenz, D. 2014, PLoS One, 9, 1
Astropy Collaboration (Price-Whelan, A. M., et al.) 2018, AJ, 156, 123
Bergin, E. A., Hartmann, L. W., Raymond, J. C., & Ballesteros-Paredes, J. 2004,
ApJ, 612, 921
Beuther, H., Bihr, S., Rugel, M., et al. 2016, A&A, 595, A32
Bialy, S., Bihr, S., Beuther, H., Henning, T., & Sternberg, A. 2017, ApJ, 835, 126
Bihr, S., Beuther, H., Ott, J., et al. 2015, A&A, 580, A112
Burkhart, B., Collins, D. C., & Lazarian, A. 2015a, ApJ, 808, 48
Burkhart, B., Lee, M.-Y., Murray, C. E., & Stanimirović, S. 2015b, ApJ, 811, L28
Churchwell, E., Babler, B. L., Meade, M. R., et al. 2009, PASP, 121, 213
Clark, P. C., Glover, S. C. O., Klessen, R. S., & Bonnell, I. A. 2012, MNRAS,
424, 2599
Cox, A. N. 2000, Allen’s astrophysical quantities (New York: Springer)
Dénes, H., McClure-Griffiths, N. M., Dickey, J. M., Dawson, J. R., & Murray,
C. E. 2018, MNRAS, 479, 1465
Dickey, J. M., & Lockman, F. J. 1990, ARA&A, 28, 215
Dobbs, C. L. 2015, MNRAS, 447, 3390
Dobbs, C. L., Krumholz, M. R., Ballesteros-Paredes, J., et al. 2014, Protostars andPlanets VI, eds. H. Beuther, R. S. Klessen, C. P. Dullemond, & T. Henning(Tucson, AZ: University of Arizona Press), 3
Duarte-Cabral, A., & Dobbs, C. L. 2016, MNRAS, 458, 3667
Duarte-Cabral, A., & Dobbs, C. L. 2017, MNRAS, 470, 4261
Federrath, C., & Klessen, R. S. 2013, ApJ, 763, 51
Federrath, C., Glover, S. C. O., Klessen, R. S., & Schmidt, W. 2008, Phys. Scr.,
132, 014025
Federrath, C., Roman-Duval, J., Klessen, R. S., Schmidt, W., & Mac Low, M. M.
2010, A&A, 512, A81

A68, page 17 of 21

A&A 642, A68 (2020)
Feldt, C. 1993, A&A, 276, 531
Ferrière, K. M. 2001, Rev. Mod. Phys., 73, 1031
Fissel, L. M., Ade, P. A. R., Angilè, F. E., et al. 2019, ApJ, 878, 110
Fontani, F., Giannetti, A., Beltrán, M. T., et al. 2012, MNRAS, 423, 2342
Frerking, M. A., Langer, W. D., & Wilson, R. W. 1982, ApJ, 262, 590
Giannetti, A., Wyrowski, F., Brand, J., et al. 2014, A&A, 570, A65
Gibson, S. J., Taylor, A. R., Higgs, L. A., & Dewdney, P. E. 2000, ApJ, 540, 851
Gibson, S. J., Taylor, A. R., Higgs, L. A., Brunt, C. M., & Dewdney, P. E. 2005a,
ApJ, 626, 195
Gibson, S. J., Taylor, A. R., Higgs, L. A., Brunt, C. M., & Dewdney, P. E. 2005b,
ApJ, 626, 214
Glover, S. C. O., & Smith, R. J. 2016, MNRAS, 462, 3011
Goldsmith, P. F., & Langer, W. D. 1999, ApJ, 517, 209
Goodman, A. A., Pineda, J. E., & Schnee, S. L. 2009, ApJ, 692, 91
Goodman, A. A., Alves, J., Beaumont, C. N., et al. 2014, ApJ, 797, 53
Green, D. A. 1993, MNRAS, 262, 327
Heeschen, D. S. 1954, AJ, 59, 324
Heeschen, D. S. 1955, ApJ, 121, 569
Heiles, C., & Troland, T. H. 2003, ApJ, 586, 1067
Imara, N., & Burkhart, B. 2016, ApJ, 829, 102
Jackson, J. M., Rathborne, J. M., Shah, R. Y., et al. 2006, ApJS, 163, 145
Jackson, J. M., Finn, S. C., Chambers, E. T., Rathborne, J. M., & Simon, R. 2010,
ApJ, 719, L185
Jow, D. L., Hill, R., Scott, D., et al. 2018, MNRAS, 474, 1018
Kainulainen, J., Beuther, H., Henning, T., & Plume, R. 2009, A&A, 508, L35
Kainulainen, J., Federrath, C., & Henning, T. 2014, Science, 344, 183
Kalberla, P. M. W., & Dedes, L. 2008, A&A, 487, 951
Kalberla, P. M. W., & Kerp, J. 2009, ARA&A, 47, 27
Kavars, D. W., Dickey, J. M., McClure-Griffiths, N. M., Gaensler, B. M., &Green, A. J. 2003, ApJ, 598, 1048
Klessen, R. S. 2000, ApJ, 535, 869
Klessen, R. S., & Glover, S. C. O. 2016, Saas-Fee Advanced Course, 43, 85
Knapp, G. R. 1974, AJ, 79, 527
Körtgen, B., Federrath, C., & Banerjee, R. 2019, MNRAS, 482, 5233
Kritsuk, A. G., Norman, M. L., Padoan, P., & Wagner, R. 2007, ApJ, 665, 416
Kritsuk, A. G., Norman, M. L., & Wagner, R. 2011, ApJ, 727, L20
Krumholz, M. R., McKee, C. F., & Tumlinson, J. 2008, ApJ, 689, 865
Krumholz, M. R., McKee, C. F., & Tumlinson, J. 2009, ApJ, 693, 216
Krčo, M., Goldsmith, P. F., Brown, R. L., & Li, D. 2008, ApJ, 689, 276
Larson, R. B. 1981, MNRAS, 194, 809
Larson, R. B. 2003, Rep. Prog. Phys., 66, 1651
Lazarian, A., & Pogosyan, D. 2000, ApJ, 537, 720
Lazarian, A., Pogosyan, D., Vázquez-Semadeni, E., & Pichardo, B. 2001, ApJ,
555, 130
Li, D., & Goldsmith, P. F. 2003, ApJ, 585, 823
Lombardi, M., Alves, J., & Lada, C. J. 2015, A&A, 576, L1
McKee, C. F., & Ostriker, J. P. 1977, ApJ, 218, 148
McKee, C. F., & Ostriker, E. C. 2007, ARA&A, 45, 565

A68, page 18 of 21

Mac Low, M.-M., & Klessen, R. S. 2004, Rev. Mod. Phys., 76, 125
Milam, S. N., Savage, C., Brewster, M. A., Ziurys, L. M., & Wyckoff, S. 2005,
ApJ, 634, 1126
Ossenkopf-Okada, V., Csengeri, T., Schneider, N., Federrath, C., & Klessen,
R. S. 2016, A&A, 590, A104
Padoan, P., Nordlund, A., & Jones, B. J. T. 1997, MNRAS, 288, 145
Passot, T., & Vázquez-Semadeni, E. 1998, Phys. Rev. E, 58, 4501
Pineda, J. E., Caselli, P., & Goodman, A. A. 2008, ApJ, 679, 481
Pineda, J. L., Langer, W. D., Velusamy, T., & Goldsmith, P. F. 2013, A&A, 554,
A103
Ragan, S. E., Henning, T., Tackenberg, J., et al. 2014, A&A, 568, A73
Rebolledo, D., Green, A. J., Burton, M., et al. 2017, MNRAS, 472, 1685
Reid, M. J., Menten, K. M., Brunthaler, A., et al. 2014, ApJ, 783, 130
Reid, M. J., Dame, T. M., Menten, K. M., & Brunthaler, A. 2016, ApJ, 823, 77
Reid, M. J., Menten, K. M., Brunthaler, A., et al. 2019, ApJ, 885, 131
Riegel, K. W., & Crutcher, R. M. 1972, A&A, 18, 55
Robitaille, T., & Bressert, E. 2012, Astrophysics Source Code Library[ascl:1208.017]
Schneider, N., André, P., Könyves, V., et al. 2013, ApJ, 766, L17
Schneider, N., Bontemps, S., Motte, F., et al. 2016, A&A, 587, A74
Schuller, F., Menten, K. M., Contreras, Y., et al. 2009, A&A, 504, 415
Shibai, H., Okuda, H., Nakagawa, T., et al. 1991, ApJ, 374, 522
Smith, R. J., Glover, S. C. O., Clark, P. C., Klessen, R. S., & Springel, V. 2014,
MNRAS, 441, 1628
Soler, J. D., Beuther, H., Rugel, M., et al. 2019, A&A, 622, A166
Stahler, S. W., & Palla, F. 2005, The Formation of Stars (New York: John Wiley& Sons)Sternberg, A., Le Petit, F., Roueff, E., & Le Bourlot, J. 2014, ApJ, 790, 10
Strasser, S., & Taylor, A. R. 2004, ApJ, 603, 560
Stutzki, J., Stacey, G. J., Genzel, R., et al. 1988, ApJ, 332, 379
Tackenberg, J., Beuther, H., Plume, R., et al. 2013, A&A, 550, A116
Umemoto, T., Minamidani, T., Kuno, N., et al. 2017, PASJ, 69, 78
Vallée, J. P. 2008, AJ, 135, 1301
van der Werf, P. P., Goss, W. M., & Vanden Bout, P. A. 1988, A&A, 201, 311
Vazquez-Semadeni, E. 1994, ApJ, 423, 681
Wang, Y., Bihr, S., Beuther, H., et al. 2020a, A&A, 634, A139
Wang, Y., Beuther, H., Rugel, M. R., et al. 2020b, A&A, 634, A83
Wang, Y., Bihr, S., Rugel, M., et al. 2018, A&A, 619, A124
Wenger, T. V., Balser, D. S., Anderson, L. D., & Bania, T. M. 2018, ApJ, 856,
52
Wilson, T. L., Rohlfs, K., & Hüttemeister, S. 2013, Tools of Radio Astronomy(Berlin Heidelberg: Springer Science & Business Media)
Wolfire, M. G., McKee, C. F., Hollenbach, D., & Tielens, A. G. G. M. 2003, ApJ,
587, 278
Zhang, M., Kainulainen, J., Mattern, M., Fang, M., & Henning, T. 2019, A&A,
622, A52
Zucker, C., Battersby, C., & Goodman, A. 2015, ApJ, 815, 23
Zucker, C., Battersby, C., & Goodman, A. 2018, ApJ, 864, 153

J. Syed et al.: Atomic and molecular gas properties during cloud formation

Appendix A: H I self-absorption uncertainties

A.1. Background fraction

The HISA column density computation relies on assumptionsof the spin temperature T HISA and background fraction p. We
assumed a background fraction of p = 0.9 for the whole filament
since we expect large contributions to the H I emission originating in the background due to the distance and location of thefilament as well as the kinematic distance ambiguity. Figure A.1
shows the optical depth as a function of the spin temperaturefor different background fractions (Eq. (1)). Mean temperaturesof T on = 40 K, T off = 70 K, and T cont = 20 K were adopted fromour results. For a constant spin temperature the optical depth
increases with decreasing background fraction p. Consequently,
the column density increases with lower background fraction.
To investigate the variation of the column density as a function of p, we calculated the HISA N-PDFs assuming backgroundfractions of p = 0.7, 0.8, and 0.9, respectively. Furthermore, we
assumed a constant spin temperature of T HISA = 40 K. Figure A.2
shows the HISA N-PDFs for the whole filament. The shape andwidth of the N-PDF does not change with varying backgroundfraction p. However, the mean column density increases by a

Optical depth HISA

p=0.3 0.4 0.5 0.6 0.8 1.0

1

0.1
2.7

10
Spin temperature THISA [K]100

Fig. A.1. Optical depth τHISA as a function of spin temperature
T HISA at the derived mean temperatures of T on = 40 K, T off = 70 K, andT cont = 20 K (Eq. (1)). The different colors represent varying backgroundfractions p, with values from 0.3 to 1.0. The horizontal black line marks
an optical depth of 0.9 that was determined from H I absorption against
strong continuum emission.

Column density NH [cm−2]
1020
1021
1022
101
Probability density

To extract HISA features, we have employed a combination of
first and second order polynomial functions to fit the HISA baselines at smoothed H I spectra to estimate the H I spectra in theabsence of self-absorption (T off ). Different polynomial functions
have partly shown significant differences in the derivation of
the background spectrum. In reality we do not know what thebackground spectrum would look like in the absence of selfabsorption and it is therefore difficult to quantify the uncertainty
of T off . We can estimate the systematic uncertainty of T off due toour baseline fitting routine by the deviation of different polynomial function fits. We compare the baseline fits inferred fromfirst and second order polynomial functions and calculate thestandard deviation of the difference of the baseline fits. The difference has a mean of −2 K, indicating that the second orderbaseline fits on average overestimate the background with respect
to first order fits. The standard deviation of the difference is∼7 K. If we add the observational noise and fitting uncertainty of
8 K to the systematic error, the total uncertainty is ∆T off = 11 K.
For the mean temperatures of T on = 40 K and T off = 70 K that wemeasure with our extraction method between 43–56 km s−1 , thispropagates to a relative uncertainty of ∼40% for the optical depth
and therefore column density. While this uncertainty affects theamplitude of the HISA features, the centroid velocities should berobust and weakly dependent on the employed fitting method.
The column densities and masses are furthermore affectedby the integration over velocities. We integrated all derived column densities from 43 to 56 km s−1 as we extracted significant
HISA features in that velocity regime. Ragan et al. (2014) assign
velocities between 37 and 50 km s−1 to the giant molecular filament as they define their filaments through smooth velocity
gradients. Furthermore, velocities &50 km s−1 might not be associated with the near Scutum-Centaurus spiral arm based on themodel by Vallée (2008). If we take into account velocities of 43–
51 km −1 for the derivation of the column densities, the column
densities decrease by ∼30%. However, employing the additional
maser parallax information in the Bayesian distance calculator of
the BeSSeL survey (Reid et al. 2014, 2016, 2019) yields velocities up to ∼55 km s−1 associated with the near Scutum-Centaurus
spiral arm. We therefore included the velocities >50 km s−1 forthe column density calculation.

10

p = 0.9
p = 0.8100

p = 0.7

whole filament

10−1
10−2
10−3 −1
10

100

101

102

NH/hNHi

Fig. A.2. H I self-absorption N-PDFs for different values of backgroundfraction p. The plot shows the derived N-PDF of the whole filamentmarked by both the red polygons in Fig. 11. The blue, red, and green
distributions correspond to a background fraction of 0.9, 0.8, and 0.7,
respectively. The vertical lines show the corresponding mean column
densities.

factor of ∼2 from p = 0.9 to 0.7. We can furthermore estimate theamount of background emission from the radial H I volume density distribution in the Galactic plane. For Galactocentric radii
7 . R . 35 kpc, Kalberla & Dedes (2008) report an average
mid-plane volume density distribution of n(R) ∼ n0 e−(R−R )/Rn
with n0 = 0.9 cm−3 , R = 8.5 kpc, and Rn = 3.15 kpc. Assuming a
constant volume density of n(R < 7 kpc) = n(R = 7 kpc), we canintegrate the densities along the line of sight and estimate theamount of gas up to the distance of the filament (foreground) andbeyond (background). We thus obtained a background fraction of∼0.92 by integrating up to a Galactocentric distance of 35 kpc.
This relation gives the averaged distribution of the northern andsouthern Galactic plane and could hold systematic differences insome regions (Kalberla & Kerp 2009). Since the foreground andA68, page 19 of 21

A&A 642, A68 (2020)

110+00.20°100
90-00.20°80-00.40°70-00.60°60-00.80°50

20pc @ 3.5kpc-01.00° 20.50°

20.00°

19.50°
19.00°
Galactic Longitude

18.50°

18.00°THISA(max. ) [K]

Galactic Latitude+00.00°40

Fig. A.3. Maximum spin temperature of the HISA features assuming a background fraction of p = 0.9. The black contour indicates the HISA
column density at 3 × 1020 cm−2 .

background emission stems from the more diffuse H I component, we do not expect large fluctuations on small scales. Hence,
the assumption of a constant background fraction over the wholecloud is reasonable.

shows this relation. For high optical depths the spin temperaturereaches a maximum. Solving Eq. (1) for T HISA illustrates that

A.2. Maximum spin temperature

Since T on − T off is always negative in the case of self-absorption,
T on −T off
T HISA reaches a maximum if 1−e−τHISA becomes minimal. This is
the case for τ → ∞. The maximum spin temperature therefore is

We have measured cold H I in absorption against strong continuum sources to directly determine the optical depth. However,
we cannot map the entire filament as this method requires continuum sources strong enough to induce absorption features.
Interpolating the optical depth between locations of individual
measurements is not trivial. We have estimated the uncertaintyof the optical depth by a factor of two. The shape of the N-PDF
is not affected by different optical depths if assumed constantfor the whole filament. Within the uncertainty of the opticaldepth the mean column density varies by a factor of ∼1.5. In
the velocity range of the HISA features the absorption spectra
toward some sources are saturated and we can only report lower
limits of the optical depth. Since the optical depths are high, weare confident that we in general do observe actual HISA insteadof low H I emission. We can only measure the optical depthof HISA together with its spin temperature and disentanglingthese quantities is difficult. We therefore assumed a constant spintemperature for the whole cloud. This is a poor assumption as
the spin temperature is likely to vary within the filament. However, the optical depth measurements toward strong continuum
sources alleviates this problem. The optical depth measurement
toward G19.075-0.287 is more accurate as it is not saturated. The
optical depth of τ = 0.9 is shown in Fig. A.1 as a black horizontal
line. Assuming p = 0.9 and adopting the derived mean temperatures for T on , T off , and T cont reveals a spin temperature of ∼32 K.
This is slightly lower than our assumed spin temperature of 40 K.
This is again a poor assumption since we adopt a constant opticaldepth for the whole cloud. However, we are able to constrain an
upper limit of the spin temperature in the limit of high opticaldepths.
In general we can solely measure the optical depth of cold
H I as a function of the spin temperature (Eq. (1)). Figure A.1
A68, page 20 of 21

T HISA =T on − T off+ p T off + T cont .
1 − e−τHISA

T HISA (max.) = T on + T cont − (1 − p) T off .

(A.1)

(A.2)

The maximum spin temperature increases with increasing
background fraction p. We use this relation to compute theupper limit of the spin temperature for each pixel in the map.
We assumed a background fraction of p = 0.9. Figure A.3
presents the maximum spin temperature for the whole filament.
Regions exposing continuum emission are not reliable as they
contaminate HISA features. We see a clear correlation between
the maximum spin temperature and the HISA column densities.
As expected, we find the lowest maximum spin temperatures of∼45 K where we observe the strongest absorption features. For
the derivation of the column densities and masses, we assumed
a spin temperature of 40 K. This is lower than the upper limit
in any region of the filament. Therefore, the optical depths are
not expected to be in the optically thick limit and the column
densities we derived are reliable. Furthermore, we conclude thatthe estimated background fraction of p = 0.9 at T HISA = 40 K is
reasonable. However, as we can only report an upper limit of
the spin temperature in the optically thick limit, we are not able
to deduce the actual spin temperature of the HISA features. If
we assume p = 0.7, the maximum spin temperature drops by∼20 K and the assumed spin temperature of 40 K would exceed
the upper limit for the coldest regions. The column density
derivation of the coldest regions would therefore not be reliable
anymore. In general, the spin temperature gives an additional
constraint on the lower limit of the background fraction p as thespin temperature would drop to unrealistically low values forcertain background fractions.

J. Syed et al.: Atomic and molecular gas properties during cloud formation

Appendix B: Histogram of oriented gradients
The Histogram of Oriented Gradients (HOG; Soler et al. 2019)is based on the assumption that the appearance and shape ofan object can be characterized by the representation of its local
intensity gradients. One simple application is deriving the spatial correlation between two images. If two images are spatiallycorrelated, the relative angle Φ between their local gradients
is approximately ∆Φ ∼ 0◦ where the correlation is high. Twocompletely uncorrelated images would have a flat distribution ofrelative orientation angles Φ while two identical images would
disclose a Dirac delta distribution peaked at ∆Φ = 0◦ as all
gradients are aligned.
We used the HOG to analyze the spatial correlation between
maps of H I and 13 CO across the radial velocities vLSR . We therefore regridded the H I data cube to match the spatial grid andpixel size of the 13 CO data for comparison. The gradients arecomputed using Gaussian derivatives. The derivatives are theresult of the convolution of an image f with the spatial derivative of a two-dimensional Gaussian function ∂G(k) . The size of
the Gaussian kernel k determines the size over which the gradients are computed. Large kernel sizes compute gradients on large
scales and therefore probe the correlation of the more diffuse
structure of the cloud. Small scale correlation can be investigatedby invoking small Gaussian kernel sizes. If the kernel size is toolarge, we smear out small-scale structures as we compute theaverage gradient over a larger spatial range.
A quantity representing a measure for the spatial correlation
between H I at velocity l and 13 CO at velocity m is the projected
Rayleigh statistic (V). It is defined asVlm =Σi j wi j,lm cos(2Φi j,lm ),p
Σi j [(wi j,lm )2 /2](B.1)

where the numerator is the sum over all pixels i, j of the relative angles Φi j,lm between the gradients of H I and 13 CO at thevelocities l and m, respectively. The statistical weight wi j,lm is

introduced to account for spatial correlations of the gradients
due to the telescope beam. The factor 2 in the cosine accounts
for relative orientations between [−π/2, +π/2], thus the correlation is measured independently of the direction of the gradients.
Consequently, we are able to report both positive and negative(HISA) spatial correlation between H I and 13 CO emission. The
projected Rayleigh statistic V can be related to a random walk(see e.g., Jow et al. 2018; Fissel et al. 2019), characterizing the
distance from the origin after taking unit steps in the direction determined by each angle Φi j,lm . The expectation value ofa random walk in two dimensions is zero, so any significant
deviation from the origin would indicate preferential angles. We
are particularly interested whether intensity gradients tend to bepreferentially parallel (Φi j,lm = 0) and how strong that preference
is. The sum over a preferred orientation angle of Φi j,lm = 0 will
result in high V values, just as a preferred orientation angle ofΦi j,lm = 0 in a “random” walk would result in a large distancefrom the starting point. Spatially uncorrelated data would reveal
V values of approximately zero.
Associated physical structures probed by spectral line emission are not independent across velocities and inherently showa correlation as well. To assess the statistical significance ofeach velocity-channel map, we used the mean value hVi of the Vover the velocity range that we analyzed and estimated the standard deviation by the population variance of the distribution. We
therefore assumed that over a broad velocity range the velocity channels are independent. Another uncertainty arises fromobservational noise in the data. The HOG addresses this by
the use of Monte Carlo sampling to propagate the uncertainties in the observations. Therefore, for each velocity-channel
map n different realizations are generated within the observational uncertainty and with the same mean intensity. Using thissampling, the uncertainty of the correlation can be determinedby estimating the variance of the correlation of different Monte
Carlo realizations. Since we expect a contribution from nonuniform noise introduced by the observation, we report only ≥5σconfidence levels.

A68, page 21 of 21