A&A 634, A139 (2020)
https://doi.org/10.1051/0004-6361/201935866

Astronomy&
Astrophysics© Y. Wang et al. 2020

Cloud formation in the atomic and molecular phase: H I self
absorption (HISA) towards a giant molecular filament?
Y. Wang ()1 , S. Bihr1 , H. Beuther1 , M. R. Rugel1,2 , J. D. Soler1 , J. Ott3 , J. Kainulainen4 , N. Schneider5 ,R. S. Klessen6,7 , S. C. O. Glover6 , N. M. McClure-Griffiths8 , P. F. Goldsmith9 , K. G. Johnston10 , K. M. Menten2 ,S. Ragan11 , L. D. Anderson12,13,14 , J. S. Urquhart15 , H. Linz1 , N. Roy16 , R. J. Smith17 , F. Bigiel18 ,T. Henning1 , and S. N. Longmore19
1

Max Planck Institute for Astronomy, Königstuhl 17, 69117 Heidelberg, Germany
e-mail: wang@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
4
Chalmers University of Technology, Department of Space, Earth and Environment, SE-412 93 Gothenburg, Sweden
5
I. Physik. Institut, University of Cologne, Zülpicher Str. 77, 50937 Cologne, Germany
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
Research School of Astronomy and Astrophysics, The Australian National University, Canberra, ACT, Australia
9
Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA
10
School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, UK
11
School of Physics and Astronomy, Cardiff University, Queen’s Buildings, The Parade, Cardiff, CF24 3AA, UK
12
Department of Physics and Astronomy, West Virginia University, Morgantown, WV 26506, USA
13
Adjunct Astronomer at the Green Bank Observatory, PO Box 2, Green Bank WV 24944, USA
14
Center for Gravitational Waves and Cosmology, West Virginia University, Chestnut Ridge Research Building, Morgantown,
WV 26505, USA
15
School of Physical Sciences, University of Kent, Ingram Building, Canterbury, Kent CT2 7NH, UK
16
Department of Physics, Indian Institute of Science, Bengaluru 560012, India
17
Jodrell Bank Centre for Astrophysics, School of Physics and Astronomy, The University of Manchester, Oxford Road,
Manchester, M13 9PL, UK
18
Argelander Institut für Astronomie, Auf dem Hügel 71, 53121 Bonn, Germany
19
Astrophysics Research Institute, Liverpool John Moores University, IC2, Liverpool Science Park, 146 Brownlow Hill,
Liverpool L3 5RF, UK
Received 10 May 2019 / Accepted 10 January 2020
ABSTRACT

Molecular clouds form from the atomic phase of the interstellar medium. However, characterizing the transition between the atomic
and the molecular interstellar medium (ISM) is a complex observational task. Here we address cloud formation processes by combining
H I self absorption (HISA) with molecular line data. Column density probability density functions (N-PDFs) are a common tool for
examining molecular clouds. One scenario proposed by numerical simulations is that the N-PDF evolves from a log-normal shapeat early times to a power-law-like shape at later times. To date, investigations of N-PDFs have been mostly limited to the molecularcomponent of the cloud. In this paper, we study the cold atomic component of the giant molecular filament GMF38.1-32.4a (GMF38a,
distance = 3.4 kpc, length ∼ 230 pc), calculate its N-PDFs, and study its kinematics. We identify an extended HISA feature, which ispartly correlated with the 13 CO emission. The peak velocities of the HISA and 13 CO observations agree well on the eastern side of thefilament, whereas a velocity offset of approximately 4 km s−1 is found on the western side. The sonic Mach number we derive from thelinewidth measurements shows that a large fraction of the HISA, which is ascribed to the cold neutral medium (CNM), is at subsonicand transonic velocities. The column density of the CNM part is on the order of 1020 to 1021 cm−2 . The column density of molecularhydrogen, traced by 13 CO, is an order of magnitude higher. The N-PDFs from HISA (CNM), H I emission (the warm and cold neutral
medium), and 13 CO (molecular component) are well described by log-normal functions, which is in agreement with turbulent motions
being the main driver of cloud dynamics. The N-PDF of the molecular component also shows a power law in the high column-density
region, indicating self-gravity. We suggest that we are witnessing two different evolutionary stages within the filament. The eastern
subregion seems to be forming a molecular cloud out of the atomic gas, whereas the western subregion already shows high column
density peaks, active star formation, and evidence of related feedback processes.
Key words. ISM: atoms – ISM: clouds – ISM: molecules – radio lines: ISM – stars: formation?
Datacubes are only available at the http://www.mpia.de/thor as well as at the CDS via anonymous ftp to cdsarc.u-strasbg.fr(130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/cat/J/A+A/634/A139

A139, page 1 of 21
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 634, A139 (2020)

1. Introduction
Stars, one of the key components of our Universe, form inmolecular clouds which are composed mainly of molecularhydrogen (e.g., Larson 2003; Stahler & Palla 2005; McKee &Ostriker 2007; Dobbs et al. 2014; Tan et al. 2014), yet the formation process of molecular clouds is still under debate. Various
studies show molecular clouds form out of relatively diffuseatomic hydrogen gas (e.g., Larson 1981; Blitz et al. 2007;
Clark et al. 2012; Hennebelle & Falgarone 2012; Dobbs et al.
2014; Sternberg et al. 2014; Klessen & Glover 2016). Different processes have been proposed (e.g., Hennebelle & Falgarone
2012; Dobbs et al. 2014; Klessen & Glover 2016). Basically, theatomic gas contracts and the increased column density shield thecloud from the interstellar UV radiation and cool down to form
molecular gas. The cold neutral medium (CNM) with a typical temperature in the range of 40–100 K and volume density>10−100 cm−3 (McKee & Ostriker 1977; Wolfire et al. 1995;
Wilson et al. 2010) is the key component connecting the diffuse atomic gas with the molecular gas. Thus, observational
constraints on the physical properties of the CNM, such as density distribution and kinematics, are crucial to understanding theformation of the molecular cloud.
Although 21 cm H I line emission offers a straightforward
tool to study atomic hydrogen, it is difficult to determine theproperties of the gas from which it arises. The main challenge
is the coexistence of the warm neutral medium (WNM) and the
CNM assumed to be in pressure equilibrium (McKee & Ostriker
1977; Wolfire et al. 1995, 2003). Studies of H I self absorption(HISA) overcome this problem, as they only trace the CNM.
HISA was first detected by Heeschen (1954, 1955) towards the
Galactic center. HISA features occur if cold, dense atomic hydrogen is in front of a warmer emission background (e.g., Knapp
1974). Since then, a number of observations that have been carried out with single dish telescopes and interferometers, and
HISA features were found to be widespread in the Milky Way(e.g., Riegel & Crutcher 1972; Knapp 1974; Heiles & Gordon
1975; McCutcheon et al. 1978; Levinson & Brown 1980; Minn
1981; Shuter et al. 1987; van der Werf et al. 1988; van der Werf &Goss 1989; Montgomery et al. 1995; Gibson et al. 2000, 2005a;
Kavars et al. 2003, 2005; Dénes et al. 2018). The spin temperature of the cold H I responsible for HISA ranges from ∼10–60 K,(e.g. Gibson et al. 2000; Kavars et al. 2005; McClure-Griffiths
et al. 2006). A special case of the HISA features, so-called H I
narrow self absorption (HINSA) features, were studied towards
nearby molecular clouds, revealing small linewidths on theorder of .1 km s−1 (Li & Goldsmith 2003; Goldsmith & Li
2005; Krčo et al. 2008; Krčo & Goldsmith 2010; Zuo et al.
2018). However, studies characterizing the column density andthe kinematic distribution of the CNM in large maps are still
rare.
Recent observations have revealed a group of large (≥100 pc)
and massive (≥105 M ) filaments, known as giant molecularfilaments (GMFs), which may be linked to Galactic dynamics and trace the gravitational mid-plane in the Milky Way(MW; Jackson et al. 2010; Goodman et al. 2014; Wang et al.
2015, 2016; Zucker et al. 2015, 2018; Abreu-Vicente et al. 2016;
Li et al. 2016; Zhang et al. 2019). These observations show that
GMFs are the largest coherent gas structures in our Milky Way,and often contain different evolutionary stages of the star formation regions simultaneously in the same filament (Goodman
et al. 2014; Zucker et al. 2015), which makes them ideal targets
for studying the CNM properties in different environments thatlead to molecular cloud formation.
A139, page 2 of 21

A common tool to study molecular clouds are the probability density functions of the column density (N-PDFs; see e.g.,
Ostriker et al. 2001; Lombardi et al. 2008; Kainulainen et al.
2009; Alves de Oliveira et al. 2014; Sadavoy et al. 2014; AbreuVicente et al. 2015; Stutz & Kainulainen 2015; Schneider et al.
2015; Lin et al. 2017; Chen et al. 2018). The shape of N-PDFs
is predicted to depend on the physical processes acting within
the cloud. In the early evolution of a molecular cloud, turbulent motions within the cloud dominate and the N-PDF reveals
a log-normal shape. The width of the log-normal N-PDF is
also determined by the turbulent motions (see e.g., Federrath
et al. 2010; Ballesteros-Paredes et al. 2011; Kritsuk et al. 2011;
Federrath & Klessen 2013; Burkhart et al. 2015a; Bialy et al.
2017a). In this scenario, more evolved clouds develop a highdensity power-law tail, indicating that the cloud structure has
evolved and gravity dominates. Observations indicate that starforming clouds show such tails, lending support to this scenario(e.g., Kainulainen et al. 2009; Schneider et al. 2013). The slopeof the power-law N-PDF can be related to evolutionary stagesof the clouds with steeper slopes possibly indicating with earlier evolutionary stages (e.g., Kritsuk et al. 2011; Federrath &Klessen 2013; Ward et al. 2014).
High-mass star-forming regions reveal multiple power-laws,
having a shallower slope for the highest density regions. This
indicates a slower collapse for such regions (Schneider et al.
2015). Lombardi et al. (2015) and Alves et al. (2017) present a
contrasting argument, reporting that all N-PDFs have a powerlaw shape and the log-normal shape could be an observationalbias, a view point that has triggered considerable controversy (Ossenkopf-Okada et al. 2016; Chen et al. 2018; Körtgenet al. 2019). Theoretical work and simulations of molecular
clouds also reproduce N-PDFs in different forms (e.g., VazquezSemadeni 1994; Federrath et al. 2010; Federrath & Klessen 2012;
Burkhart et al. 2015a). Burkhart et al. (2015b) and Imara &Burkhart (2016) studied nearby molecular clouds, and report H I
N-PDFs with a log-normal shape, without any power-law tail.
Rebolledo et al. (2017) studied the Carina and Gum 31 molecularcomplex, where the H I N-PDF also shows a log-normal shape.
To investigate the transition of atomic to molecular hydrogen in more detail, we examine the hydrogen content with HISA
measurements in detail for GMF38.1-32.4a (GMF38a, Raganet al. 2014). With a velocity range between 50 and 60 km s−1(Ragan et al. 2014), GMF38a is at a median distance of 3.4 kpc
from the Sun (Galactocentric distance ∼5.9 kpc) estimated fromthe Bayesian Distance Estimator tool (Reid et al. 2016). The
top panel of Fig. 1 shows the integrated 13 CO emission fromthe GRS survey (Jackson et al. 2006). Our goal is to study thekinematics of this GMF in the molecular and atomic hydrogentraced by 13 CO emission and HISA, respectively. Furthermore,
we analyze N-PDFs for the atomic and molecular hydrogen, andcompare their properties.

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

The H I 21 cm line observations of GMF38.1-32.4 are partof the H I, OH, Recombination line survey of the Milky Way(THOR; Beuther et al. 2016 and Wang et al. 2020). The survey observed a part of the first quadrant of the Galactic plane(l = 14.0 − 67.4◦ and |b| ≤ 1.25◦ ) with the Karl G. Jansky Very
Large Array (VLA) in C-configuration at L band from 1 to
2 GHz, covering the H I 21 cm line, 4 OH lines, 19 Hα recombination lines, and eight continuum bands between 1 and 2 GHz

Y. Wang et al.: HISA study towards a GMF
1800

Galactic Latitude

+00.5

Off 2

◦

Off 3

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1400

Spectrum 4

Off 5

1200

Spectrum 2

1000

Spectrum 5+00.0◦

800−01.0◦

600

Spectrum 1−00.5◦

Off 1

Off 4

HI integrated intensity [K km s−1]+01.0◦

HI integrated intensity, [50, 60] km s−1
Contours: 13CO integrated intensity, [50, 60] km s−1
Spectrum 3

400
200

50 pc
0

60
+01.0◦

1.4 GHz continuumContours: 13CO integrated intensity, [50, 60] km s−1

50 pc

55
50

G34.256+0.146

4540+00.0◦

35
30−00.5◦

Continuum intensity [K]Galactic Latitude+00.5◦

25
20

SNR W44−01.0◦

15
37.0◦

36.0◦

35.0◦
Galactic Longitude

34.0◦

33.0◦

10

Fig. 1. Overview of the giant molecular filament GMF38a. Top panel: 13 CO (GRS, Jackson et al. 2006) integrated intensity contours in the range
vLSR = 50−60 km s−1 overlaid on integrated H I emission in the same velocity range. The black ellipses show the “off-positions” whose spectra
are shown in Fig. 5 and the black “×” signs mark positions whose spectra are show in Fig. 6. Bottom panel: same 13 CO integrated intensity
contours overlaid on 1.4 GHz continuum emission from the THOR survey (Wang et al. 2018). The contours in the top panel indicate integrated
13
CO emission levels of 5, 10, 20, and 30 K km s−1 . The contours in the bottom panel indicate integrated 13 CO emission levels of 5 K km s−1 forreference. The dashed box in the top panel outlines the region that is discussed in the following sections and shown in Figs. 7, 9, 11, 14, and 19.

(Beuther et al. 2016). Each pointing was observed for 4 × 2 min
to ensure a uniform uv-coverage. The spectral window for the H I
21 cm line was set to have a bandwidth of 2 MHz (∼400 km s−1 )and a spectral resolution of 3.91 kHz (∼0.82 km s−1 ). The datacalibration was done with CASA1 (McMullin et al. 2007). The
flux and bandpass were calibrated with the quasar 3C 286. J18220938 was used for the phase and gain calibration (see also
Beuther et al. 2016).
To recover the large scale structure, we combined theC-configuration data with the H I Very Large Array Galactic
Plane Survey (VGPS, Stil et al. 2006), which consists of VLA
D-configuration data combined with single-dish observations
from the Green Bank Telescope (GBT). We subtracted thecontinuum in the visibility datasets (with the CASA command
uvcontsub), and used the multiscale CLEAN in CASA2 to image
the three adjacent tiles of continuum-subtracted C-configuration
data together with D-configuration data. A pixel size of 400 , a
spectral resolution of 1.5 km s−1 , and a robust weighting value of0.45 were used. The resulting images, which have a synthesized
beam between 2000 and 4000 over the entire coverage of the THOR
survey, were all smoothed to a common resolution of 4000 . The
images were further combined with the VGPS images (D+GBT)
using the task “feather” in CASA to recover the large-scale structure. We compared the flux of the combined H I data with thesingle dish GBT data from VGPS. The flux agrees with eachother within 5.7%. Considering that the typical absolute flux

1

2

http://casa.nrao.edu; version 4.1.0.

version 5.1.1.
A139, page 3 of 21

A&A 634, A139 (2020)

120

T-on
T-off

100
TB [K]

80
60
40
Fig. 2. Schematic view of the observed H I components. The cold
absorbing cloud (HISA) with temperature T HISA is surrounded by emitting clouds with temperature T fg and T bg . Behind the H I clouds, several
continuum sources can be situated, either diffuse or discrete (marked
with a star).

calibration uncertainty for the VLA at 1.4 GHz is ∼5% (Beuther
et al. 2016), it is reasonable to conclude that our combined H I
data fully recover the extended emission. The noise level in theline-free channel is about 4 K per 1.5 km s−1 .
Additionally, the THOR C-configuration only H I line withthe continuum data (Beuther et al. 2016) are used to measure
the H I optical depth towards bright continuum sources in the
background. The THOR+VGPS 1.4 GHz continuum data (VLA
C+D+GBT, Wang et al. 2018) are employed to estimate the diffuse continuum emission in the background. By comparing theflux density of the known SNRs (Green 2014), Anderson et al.
(2017) showed that the flux retrieved from the combined continuum data is consistent with the literature. Thus, the continuum
data also recover the extended emission.
2.2. H I self absorption

The integrated H I emission over the velocity range 50–
60 km s−1 , shown in the top panel of Fig. 1, reveals diffuse
emission covering a larger area than the 13 CO emission. The
strongest H I emission does not coincide with 13 CO emission,
but an anti-correlation between the H I and 13 CO emission issuggested. Our analysis in the following section shows that thisanti-correlation is due to the HISA: the cold atomic hydrogen
absorbs the emission from an emitting atomic hydrogen cloudin the background, that is, H I self absorption. The terminology “H I self absorption” can be misleading. The emission andabsorption processes can occur in the same cloud, but it is possible that the H I emission originates from a distant backgroundcloud, which covers a similar or larger range of LSR velocities
as the absorbing foreground cloud as illustrated in Fig. 2. A
comprehensive discussion about the radiative transfer of HISA
features can be found in Gibson et al. (2000), Kavars et al.
(2003), Li & Goldsmith (2003), and Goldsmith & Li (2005). In
general, we observe an emitting foreground and background H I
cloud, which have spin temperatures, T fg and T bg , respectively.
The cold, absorbing H I cloud can be located between these two
emitting clouds, having the spin temperature, T HISA . Furthermore, we observe 1.4 GHz continuum emission, which can be adiffuse Galactic component or arise from discrete strong sources.
For simplicity, we assume that the continuum emission is situated in the background. In this, we will exclude the possibility ofstrong, discrete continuum sources and consider only the weakdiffuse continuum background when estimating the HISA properties. In Sect. 4.3, we will utilize strong continuum sources todetermine the optical depth of the atomic hydrogen, which canhelp us to constrain the spin temperature of HISA. Following theequation of radiative transfer in Rybicki & Lightman (1979), theA139, page 4 of 21

20
0
0

20

40

60
vLSR [km s−1 ]

80

100

Fig. 3. Sample spectrum showing a prominent HISA feature around
vLSR ∼ 55 km s−1 . The actual H I spectra is shown in black (T on ) andthe estimated background emission using a second order polynomial fit(see Sect. 2.3) is shown in blue (T off ).

measured on and off position brightness temperatures of the line
above the continuum at a certain velocity are:T off = T fg (1 − e−τfg ) + T bg (1 − e−τbg )e−τfg+ T cont e−(τfg +τbg ) − T cont ,T on = T fg (1 − e−τfg ) + T HISA (1 − e−τHISA )e−τfg+ T bg (1 − e−τbg )e−(τfg +τHISA ) + T cont e−(τfg +τHISA +τbg ) − T cont ,(1)

where τfg , τbg , τHISA are the corresponding optical depths ofeach component shown in Fig. 2 and T cont is the continuum
brightness temperature. During the data reduction, we subtract
the continuum emission from the H I visibility data (see also
Sect. 2), which is indicated by the last term (−T cont , see Sect. 2).
An example spectrum illustrating T on and fitted T off is shown in
Fig. 3. Assuming on and off spectra share the same T cont andcalculating the difference, we get:T on−off = T HISA (1 − e−τHISA )e−τfg − T bg (1 − e−τbg )e−τfg (1 − e−τHISA )− T cont (1 − e−τHISA )e−(τfg +τbg )= T HISA − T bg (1 − e−τbg ) − T cont e−τbg
× (1 − e−τHISA )e−τfg .

(2)

This equation can be further simplified by introducing thedimensionless parameter p (e.g., Feldt 1993; Gibson et al.
2000):p≡

T bg (1 − e−τbg )
.
T off

(3)

That means for p = 1, there is no foreground emission and for
p = 0.5, the foreground and background emission are equal.
Measuring p is difficult and it usually has to be assumed.
As a last simplification, we assume that the foreground andbackground clouds are optically thin and therefore τfg and τbg
are small (Gibson et al. 2000). This results in:T on−off = (T HISA − p T off − T cont ) × (1 − e−τHISA ).

(4)

T on and T off can be derived from our H I emission line observations, T cont is from our THOR+VGPS 1.4 GHz continuum data

Y. Wang et al.: HISA study towards a GMF
p = 0.4

10

0.5

0.7 0.9 1.0

12080
TB [K]

optical depth τ

100

1

Off 1
Off 2
Off 3
Off 4
Off 5
mean

60
40
20

0.1

1

10
Spin Temp THISA [K]100

Fig. 4. Optical depth as a function of the spin temperature (as introduced in Eq. (4)) for the region close to the strong continuum source
G34.256+0.146 with T off = 103 K, T on = 50 K, and T cont = 17 K. The
optical depth of τ = 3.5 is indicated with a black horizontal line. The
temperature of the CMB is indicated at T = 2.7 K with a black verticalline.

(see Sect. 2). With these observable quantities we can estimate
the properties of the HISA using Eq. (4). Specifically, we derive
the cloud spin temperature T HISA and the optical depth τHISA .
We cannot disentangle the spin temperature and the opticaldepth. Figure 4 shows an example of the relation between τHISA
and T HISA for the region close to the strong continuum source
G34.256+0.146 of T off = 103 K, T on = 50 K, and T cont = 17 K.
The different colors represent different values of p from 0.4
to 1. The black vertical line indicates the temperature of thecosmic microwave background radiation (Fixsen et al. 1996;
Fixsen 2009; Planck Collaboration XIII 2016) T = 2.7 K. Since
the L band continuum background emission in the Galactic
plane is larger than 0 (bottom panel Fig. 1), the spin temperaturemust be larger than 2.7 K. The general interpretation of thecurves is that a higher optical depth is necessary to produce theassumed absorption feature for higher spin temperatures. Thisdependency becomes very steep at a certain point, depending
on p. In Sect. 4 we shall discuss the relations among τ, spintemperature, and p in detail.
2.3. Background estimate to measure Toff

To extract a reliable HISA feature, it is crucial to know the background H I emission. Different methods can be found in theliterature to perform this task. The first one is to use absorptionfree H I emission spectra, located close to the absorption feature(e.g., Gibson et al. 2000), referred to as “off-positions”. Thismethod assumes that the H I background emission stays spatiallyconstant over the absorption feature, which might be true forspatially small HISA features. We tested this method by extracting H I spectra from five different regions, which are labeled as“Off 1” to “Off 5” in Fig. 1. These off-positions were chosen
to be regions without significant 1.4 GHz continuum emission
and without 13 CO emission. Furthermore, these regions did notshow significant self absorption features at the velocity range ofvLSR = 50−60 km s−1 . The corresponding spectra are presented
in Fig. 5. These spectra reveal large variations, which makes it
difficult to use them as a common off-position.
The second method utilizes a fit to the absorption free channels of the H I spectra to get T off . This method is applied

0
−100

−50

0
50
vLSR [km s−1]

100Fig. 5. Selected H I emission spectra around the GMF38a, which canbe used as “off-positions”. The regions we used for the extraction are
shown in Fig. 1. The black line shows the mean spectrum of all fiveoff-spectra and the gray shaded area indicates the velocity range of the
HISA feature (vLSR = 50–60 km s−1 ).

frequently, using different functions to fit the H I emission,for example, linear fits (e.g., Minn 1981; Montgomery et al.
1995; McClure-Griffiths et al. 2006) or polynomials with different order (e.g. Myers et al. 1978; Bowers et al. 1980; Shuter
et al. 1987; Kavars et al. 2003; Li & Goldsmith 2003). Figure 6
presents five different spectra from different positions indicatedin Fig. 1. We used second and fourth order polynomials to fit the
spectra for the velocity range around the HISA (vLSR = 40−50
and 60−70 km s−1 ). A polynomial function of the third ordergave very similar results as the polynomial of the second order,
thus, for clarity, we do not show it here.
It is difficult to estimate which function is more suitable tofit the H I spectra. For regions without absorption, we expectthat the fitted spectra represents the actual spectra. Spectrum 3
in Fig. 6 shows such a region and both functions represent the
H I spectra well. Spectra 2 and 4 in Fig. 6 represents H I absorption features and the difference between the second and forthorder polynomial is small. In contrast to this, Spectra 1 and 5
in Fig. 6 reveal a large difference between the fit functions. The
fourth order polynomial fit is much higher (∼50 K) than the second order polynomial for Spectrum 1, but much lower than thesecond order polynomial for Spectrum 5. It is not obvious whichfunction describes the H I spectra more accurately. However, thefourth order polynomial might overestimate the actual spectra
as steep slopes within the fitted velocity range would result inhigh values for the fitted spectra. In contrast to this, the second
order polynomial might underestimate the H I emission for thisspectra. Hence, the fourth order polynomial might be an upper
limit and the second order polynomial might be a lower limit.
We will use both functions in the following analysis to estimate
the uncertainty of T off and to extract HISA.
Another method was to utilize the second derivative representation of the spectrum as described in Krčo et al. (2008). Krčoet al. (2008) demonstrated that HINSA feature would become
dominant in the second derivative representation. We also tested
this method. For narrow HISA spectra (such as Spectrum 2 inFig. 6) the second derivative technique can recover the HISA
spectra relatively well. However, for broad spectra (e.g., Spectrum 1 and Spectrum 5), the HISA spectra were filtered out by
the method. Therefore, we do not use this method in our analysis.
McCutcheon et al. (1978), Winnberg et al. (1980), andAndersson et al. (1991) used one or several Gaussian profiles to
A139, page 5 of 21

A&A 634, A139 (2020)
200

Spectrum 1

pol. 2pol. 4
mean off

TB [K]

150
100
50
0
50

60
vLSR [km s−1 ]

70

80

50

200

Spectrum 3

pol. 2pol. 4
mean off

100

40

50
60
vLSR [km s−1 ]Spectrum 4

150

50

100

70

80

pol. 2pol. 4
mean off

50
0

0
30

30

TB [K]

40

150
TB [K]

100

1.5 km s−1 for the second order polynomial fit, ∼5 K for the forthorder fit. Since a forth order polynomial function can always fit
the small bumps in the spectra better than the second order polynomial function, it is no surprise the HISA spectra extracted withthe forth order fit have smaller noise.

pol. 2pol. 4
mean off

0

30

200

Spectrum 2

150
TB [K]

200

40

50

60
vLSR [km s−1 ]

200

70

80

30

Spectrum 5

TB [K]

150
100

40

50
60
vLSR [km s−1 ]7080pol. 2pol. 4
mean off

50
0
30

40

50
60
vLSR [km s−1 ]7080

Fig. 6. Selected H I emission spectra corresponding the positions indicated in Fig. 1. The black lines represent the H I spectra, the colors
correspond to the HISA. The gray spectra indicate the mean of thefive off-positions presented in Fig. 5. The blue and red dashed lines
represent the fits of the background to the HISA spectrum for a polynomial of second and fourth order, respectively, using the velocity rangeof vLSR = 40−50 and 60−70 km s−1 for the baseline of the fit. The blue
and red solid lines show the difference between fitted H I spectra and themeasured H I spectra (T on−off in Eq. (4)) for a polynomial of second andfourth order, respectively. We fitted Spectra 1, 2, and 5 using a Gaussianfunction, shown by the black solid curve on top of the HISA spectra.

fit the spectra and to derive the off spectra. However, as pointed
out by McCutcheon et al. (1978), this method only works if theabsorption feature is very narrow, the shape of the total spectrum
is simple, and can be represented by a few Gaussians. On theother hand Dénes et al. (2018) used a machine learning method,
the Autonomous Gaussian Decomposition algorithm (AGD;GAUSSPY) developed by Lindner et al. (2015), to decompose
the emission spectra while masking out the HISA features toderive the off spectra. However, they only need to deal with 47
spectra and it is not clear how well this method would work forour region with ∼2 million spectra. It is definitely worthwhile totest the machine learning method in the future, but it is beyond
the scope of this paper.
The mean spectrum of the five off-positions shown in Fig. 5
is shown in gray in Fig. 6 as well. While the mean off-position
represents the H I spectra of T off well in some cases (e.g., Spectrum 2 in Fig. 6), but in general it does not (e.g., Spectrum 1 or
5 in Fig. 6). There are apparent variations in the H I spectrum atvelocities outside of the HISA feature, such the assumption of a
uniform H I emission background does not seem to be adequate.
The mean spectrum method was also discussed by Myers et al.
(1978) and McCutcheon et al. (1978), and they concluded that it
is not suitable for HISA studies for the same reason. Hence, wewill use the polynomial fit method to extract the HISA feature
rather than using a mean off-spectrum.
The noise of the extracted HISA spectra measured at thevelocity ranges in vLSR = 40−50 and 60−70 km s−1 is ∼8 K per
A139, page 6 of 21

2.4. HISA extraction

With the methods described in Sect. 2.3 we can estimate T off
in Eq. (4). Using this information, we can measure the depth of
the absorption feature (T off − T on ). To analyze the absorption features, we use a Gaussian curve to fit them. This allows us to study
the exact depth of the absorption features and their kinematics.
Fits that result in a peak intensity higher than 25 K (∼3 and5 times the noise level of the HISA spectra extracted with second and forth oder fit, respectively), 1.5 km s−1 < full width half
maximum (FWHM) linewidth (= channel width) <20 km s−1 areconsidered as good fit. The peak values of the fitted Gaussian
curves are shown in Fig. 7 for different ways of estimating T off .
The absorption depth of the HISA shows values between ∼30
and ∼80 K.
As discussed in Sect. 2.3, different methods to estimate T off
resulted in differences for the peak value. Those based on thespatially averaged off-positions (bottom panel in Fig. 7) show
unrealistically large values at the edges as well as in the presenceof continuum sources. In the first case, as the Galactic H I emission drops at the edge, this method falsely identifies the edge
regions as absorption features. In the second case, the method
picks up the strong H I absorption towards the bright continuum
emission in the background, as the structure of the continuum
emission is clearly visible (bottom panel in Fig. 7).
Fitting T off of each H I spectra with a polynomial function circumvents these problems. Hence, the polynomial fitting
method is more appropriate for our analysis and in the following
we focus on the determination of T off from HISA-free channels
in the T on spectrum.
We found large differences in T off estimates made with polynomials of second and forth order, in particular towards regions
around l = 35◦ and l = 33.8◦ (Fig. 7). Using a forth order polynomial for the background estimate, we found significantly moreabsorption due to a possible overestimate of the backgroundemission (Sect. 2.3). Other regions are not affected significantly
by the choice of the fit function, for instance, the regions around
spectrum 1 or 2. The uncertainties of the HISA properties introduced by different polynomial function fittings will be discussed
in Sect. 4.7.

3. Results
3.1. Kinematics

In this section, we discuss the kinematic properties of the HISA
features. In contrast to the absorption depth, the peak velocity is
not significantly affected by the choice of the fit function. Therefore we present here only the velocity structure using the second
order polynomial for the determination of T off . The velocity
structure revealed by the fourth order polynomial is similar.
To compare the kinematics of the HISA feature with those of
the 13 CO data, we resampled both the 13 CO and H I data to thesame spatial and velocity resolution (pixel size of 2200 and spectral channel width of 1.5 km s−1 ) and applied Gaussian fitting to
the data sets pixel by pixel to determine the peak velocity and
FWHM linewidth. Due to limited sensitivity and spectral resolution of our H I data, we cannot disentangle multiple velocity

Y. Wang et al.: HISA study towards a GMF
80+00.8◦HISA Gaussian Peak+00.6◦

50 pc
70polynom-2

60+00.2◦+00.0◦

50−00.2◦40

HISA Gaussian peak [K]Galactic Latitude+00.4◦−00.4◦
30−00.6◦−00.8◦
+00.8

20
80

◦

polynom-4+00.6◦

70

60+00.2◦+00.0◦

50−00.2◦40

HISA Gaussian peak [K]Galactic Latitude+00.4◦−00.4◦
30−00.6◦−00.8◦

20
80+00.8◦
mean off+00.6◦

70

60+00.2◦+00.0◦

50−00.2◦40

HISA Gaussian peak [K]Galactic Latitude+00.4◦−00.4◦
30−00.6◦−00.8◦

37.0◦

36.0◦

35.0◦
Galactic Longitude

34.0◦

20

Fig. 7. Peak value of a Gaussian fit for the absorption depth T off −T on for different methods of estimating T off . Top and middle panels: method usinga polynomial fits with second and forth order, respectively. Bottom panel: method using a spatially averaged off spectrum shown in Fig. 5. The
white contours represent the integrated 13 CO emission at levels of 5 K km s−1 for reference. The circles from left to right marked the same positions
as in Fig. 1 where Spectra 1 to 5 shown in Fig. 6 are extracted, respectively.

components. Therefore, we chose to fit both the 13 CO and HISA
data with a single Gaussian component for simplicity and consistency. The Gaussian fitting to the HISA spectra is describedin Sect. 2.4. For the 13 CO data, fits that result in a peak intensity higher than 2 K (∼10 times noise level of the 13 CO datacube
at 1.5 km s−1 channel width), 1.5 km s−1 < FWHM linewidth<20 km s−1 are considered good fits for the 13 CO data. A few
examples of 13 CO spectra are shown in Fig. 8 to demonstrate thefitting results.
The peak velocity maps are presented in Fig. 9. The 13 CO
peak velocity shows that the majority of the filament is at ∼54–
58 km s−1 . The western part of the 13 CO filament around l = 34◦
is slightly red-shifted compared to rest of the filament, and hasa velocity of ∼57–58 km s−1 . For this region, the peak velocities revealed by the HISA feature are at ∼54–55 km s−1 , which isabout 3–4 km s−1 lower than the 13 CO velocity. This can also beseen in the right panel of Fig. 10, where we present a histogramof the HISA and 13 CO peak velocities for the eastern and westernside of the GMF, respectively. In contrast to this, the eastern sideof the filament around l = 36.5◦ shows a close correlation of thepeak velocities as shown in the left panel of Fig. 10. We will discuss this effect in Sect. 4.1. The western and eastern region werefer to here are both under the Galactic coordinate framework.
The linewidths of both 13 CO and HISA are shown in Fig. 11.
The linewidth for the 13 CO emission shows extremely high values of more than 10 km s−1 for the central region of the filament
A139, page 7 of 21

A&A 634, A139 (2020)
Spectrum 1

3

2.5 Spectrum 2

13

CO
1
HISA pol. 2 × 25

2.0
1.5

TB [K]

TB [K]

4

2

0.5
0.0

0
40

50

60
vLSR [km s−1 ]

70

80

−0.5
30

0.8 Spectrum 3 13
CO
1
0.6
HISA pol. 2 × 100
0.4
0.2
0.0
−0.2
−0.4
30
40
50
60
70
80
vLSR [km s−1 ]5 Spectrum 5
TB [K]

4

40

50
60
vLSR [km s−1 ]5 Spectrum 4
4
TB [K]

TB [K]CO
1
HISA pol. 2 × 25

1.0

1
30

13

3

70

80

13

CO
1
HISA pol. 2 × 25

2
1
0
30

40

50
60
vLSR [km s−1 ]

70

80

13

CO
1
HISA pol. 2 × 25

3
2
1
0
30

40

50
60
vLSR [km s−1 ]7080

Fig. 8. Examples of 13 CO spectra extracted from the same positions as inFig. 6 and the Gaussian fitting results if available. The 13 CO spectra areshown in thick black lines. The HISA spectra from the same locations
are scaled to 1/25 of its original intensity and shown in thin blue lines.
The positions corresponding to each spectrum are shown in Fig. 1. For
Spectra 1, 4, and 5, we can fit the spectrum with a Gaussian component
to the 13 CO spectrum successfully, we show the Gaussian fitting resultwith a black solid curve in each panel. For Spectra 2 and 3, the Gaussian
fitting results did not meet the criteria we described in Sect. 3.1 and wereignored.

around l = 35◦ . However, these values have to be treated cautiously as the 13 CO emission exhibits multiple lines in this region
and we only use a single Gaussian function to fit them. On
the eastern side of the filament around l = 36.5◦ we find mostly
single components for the 13 CO emission and the linewidth is∆v ∼ 2 to 4 km s−1 . The linewidth of the HISA feature shows
values ∆v ∼ 3−6 km s−1 for the whole filament. This can also
be seen in the left panel of Fig. 12, where a histogram of thelinewidths is shown. The linewidth distribution of the 13 CO
emission is systematically higher in the western region of thefilament, whereas the linewidth of the HISA feature is similar to
the eastern region. This result has to be treated cautiously as wesee multiple components for the 13 CO line within the westernregion, which increases the linewidth.
To estimate the contribution of the non-thermal component in the HISA features qand the molecular emission, we
assume the relation σnth = σ2obs − σ2th − σ2res , where σobs isthe measured velocity dispersion, σth is the radial component of the thermal velocity dispersion, and σres is the velocity dispersion introduced by the channel width of our data
(1.5 km s−1 ). Assuming a Gaussian line profile with the FWHM
linewidth ∆v
fittings we get√ obtained from the aforementioned√. Assuming a
σobs = ∆v/ 8ln2, and σres = 1.5/ 8ln2 km s−1p
Maxwell-Boltzmann velocity distribution, σth = kB T k /(µmH ),where kB is the Boltzmann constant, µ is the molecular weight,
mH is the mass of the hydrogen atom, and T k is the kinetic temperature. For HISA, we assume T k = T HISA = 40 K. The peak
excitation temperature of 13 CO we derived for the filament is∼25 K (see Sect. 3.2.1) which agrees to what Roman-Duval et al.
(2010) found for the GRS molecular clouds. If we assume that theA139, page 8 of 21

brightest 13 CO emission is coming from regions where the line is
optically thick and thermalized, then this excitation temperature
will be comparable to the actual gas kinetic temperature, whichmust therefore have a value close to 20 K. Furthermore, simulations of molecular clouds in a variety of different radiation fields
show that the CO mass-weighted temperature of the gas is typically in the range 10–30 K, with very little dependence on thelocal environment (Peñaloza et al. 2018). Therefore, we assume
a uniform T k of 20 K for 13 CO.√Assuming spatial isotropy, theMach number is estimated to be 3σnth /cs , where cs is the soundspeed estimated using a mean molecular weight µ = 2.34 for themolecular cloud and µ = 1.27 for the H I cloud (Allen 1973; Cox
2000). The distribution of the Mach number for HISA and 13 CO
across the whole filament (Fig. 13) shows that the 13 CO emission is dominated by supersonic motions, whereas HISA features
have a much smaller Mach number in general with a significant
fraction of the HISA features, that is, a significant fraction of the
CNM being at subsonic and transonic velocities. If the HISA and13
CO lack spatial isotropy, we could√ be overestimating the Mach
number by a maximum factor of 3.
3.2. Column density
3.2.1. H2 column density

We use the 13 CO(1–0) data from the Galactic Ring Survey (GRS,
Jackson et al. 2006) to derive the column density and kinematic properties of the molecular gas of the filament. The data
have an angular resolution Θ = 4600 and a velocity resolution of∆v = 0.21 km s−1 . We can estimate the column density of the13
CO molecule including opacity correction with the equation(Wilson et al. 2010):
R
T MB (v) dv
τ
13
,
(5)
N(13 CO) = 3.0 × 1014
1 − e−τ13 1 − e−5.3/Tex
where N(13 CO) is the column density of the 13 CO in units of
cm−2 , dv is the velocity in km s−1 , τ13 is the 13 CO opacity, T MB
is the main beam brightness temperature, and T ex is the excitation temperature. We do not have a direct measurement for theexcitation temperature, and we assume that the excitation temperatures of the 12 CO and 13 CO are the same. Assuming that the12
CO line is optically thick, we used the 12 CO(1–0) data fromthe FOREST unbiased Galactic plane imaging survey with theNobeyama 45 m telescope (FUGIN; Umemoto et al. 2017) toestimate T ex following the formula (Wilson et al. 2010):
T ex =

5.5

,
5.5
ln 1 + Tmb (12 CO)+0.82(6)where T mb (12 CO) is the peak main-beam brightness temperature of 12 CO(1–0) line. We calculated T ex for regions where
T mb (12 CO) is above the 5σ level (2 K), which results in a T ex
between ∼5 and 25 K. For regions where T mb (12 CO) is below the5σ level (2 K), an upper limit of 5 K for T ex is applied. Following
Eq. (B.6) in Schneider et al. (2016), we can derive τ13 from T ex
and T mb (13 CO). For regions where T mb (13 CO) is above 5σ level(1.05 K), τ13 is estimated to be between ∼0.1 and 3. For regions
where T mb (13 CO) is below 5σ level (1.05 K), an upper limit of
0.1 for τ13 is applied. The majority of the region along the filament has a τ13 . 1.0, only the region around (l = 34.30, b = 0.18)
and a few pixels around (l = 35.55, b = 0.0) have a τ13 > 2.0.
For the Galactocentric distance of 5.9 kpc of GMF38a,
the fractional abundance of 13 CO relative to H2 is estimatedY. Wang et al.: HISA study towards a GMF
60+00.8◦GRS 13CO Gaussian peak velocity

58

Galactic Latitude+00.4◦+00.2◦

56+00.0◦
54−00.2◦−00.4◦

52

13+00.6◦CO Gaussian peak velocity [km s−1]

50 pc

−00.6◦−00.8◦

50◦

60
HISA Gaussian peak velocity, polynom-2

50 pc+00.6◦

58

Galactic Latitude+00.4◦+00.2◦
+00.0

56

◦

54

−00.2◦−00.4◦

52

HISA Gaussian peak velocity [km s−1]

+00.8

−00.6◦−00.8◦

37.0◦

36.0◦

35.0◦
Galactic Longitude

50

34.0◦

Fig. 9. Peak velocity of the Gaussian fit of the 13 CO data (top panel) and the HISA data (bottom panel), respectively. The HISA are extracted
by using a second order polynomial to estimate the background emission. The black contours indicate the integrated 13 CO emission at levels of
5 K km s−1 . The polygons mark the eastern (around l = 36.5◦ ) and western (around l = 34◦ ) subregions, for which we present the histograms of thepeak velocities in Fig. 10.
Eastern region

0.5

Western region

0.4
0.3
0.2
0.1
0.0
50

52

54

56
vLSR [km s−1 ]

58

0.30

13

CO
HI

Probability Density

Probability Density

13

60

0.4

CO
HI

0.3
0.2
0.1
0.0
50

52

Whole filament
13

Probability Density

0.5

54

56
vLSR [km s−1 ]

58

60

CO
HI

0.25
0.20
0.15
0.10
0.05
0.00
50

52

54
56
vLSR [km s−1 ]58

60

Fig. 10. Histograms of the HISA and 13 CO peak velocity, shown in black (thin) and red (thick) respectively. Left and middle panels: all extracted
pixels within the marked eastern (around l = 36.5◦ ) and western (around l = 34◦ ) polygon in Fig. 14. Right panel: all extracted pixels for the whole
filament (red polygon in Fig. 14).

to be 2.9 × 10−6 following the relations reported by Giannetti
et al. (2014). With this abundance, we converted the N(13 CO)
to N(H2 ). Zhang et al. (2019) employed a similar method(uniform CO abundance, T mb (12 CO) → T ex ) to estimate thecolumn density and mass of a sample of GMFs (they estimated the mass of GMF38a to be ∼3.8−11.0 × 105 M ),and discussed in detail the uncertainties brought in by T ex

and the 13 CO abundance. According to their results, the 1σ
uncertainty of the column density estimated from 13 CO is∼50%. Simulations show that the abundance of 13 CO could
vary and we could underestimate the column density forthe low column density part by ∼40% (N(13 CO) < 1016 ,or N(H2 ) < 3.4 × 1021 in this paper, Szűcs et al. 2014,2016).
A139, page 9 of 21

A&A 634, A139 (2020)
10+00.8◦GRS 13CO Gaussian FWHM

50 pc

+00.6◦

8

+00.0

6

◦

4

−00.2◦

CO FWHM [km s−1]

+00.2◦

13

Galactic Latitude+00.4◦−00.4◦

2−00.6◦−00.8◦
+00.8

0
10

◦

HISA Gaussian FWHM, polynom-2

50 pc+00.6◦

8+00.2◦
+00.0

6

◦

4

−00.2◦−00.4◦HI FWHM [km s−1]

Galactic Latitude+00.4◦

2−00.6◦−00.8◦

37.0◦

36.0◦

35.0◦
Galactic Longitude

0

34.0◦

Eastern region

0.30

Western region

0.35

13

13

CO
HI

0

2

4

6

8

10

CO
HI

0.25

Probability Density

0.45
0.40
0.35
0.30
0.25
0.20
0.15
0.10
0.05
0.00

Probability Density

Probability Density

Fig. 11. Full width at half maximum (FWHM) of the 13 CO emission (top panel) and the HISA feature (bottom panel), respectively. The linewidthis determined by using a single Gaussian fit. The contours indicate the integrated 13 CO emission at levels of 5 K km s−1 for reference. The polygons
mark the eastern (around l = 36.5◦ ) and western (around l = 34◦ ) subregions, for which we present the histograms of the FWHM linewidths in
Fig. 12.

0.20
0.15
0.10
0.05
0.00

0

FWHM [km s−1 ]

2

4

6

FWHM [km s−1 ]810Whole filament
13

CO
HI

0.30
0.25
0.20
0.15
0.10
0.05
0.00

0

2

4

6

8

10

FWHM [km s−1 ]Fig. 12. Histograms of the FWHM linewidth of the HISA and 13 CO emission in black (thin) and red (thick), respectively. Left and middle panels:
all extracted pixels within the marked eastern (around l = 36.5◦ ) and western (around l = 34◦ ) polygon in Fig. 14. Right panel: all extracted pixels
for the whole filament (red polygon in Fig. 14).

3.2.2. CNM column density from HISA measurements

Besides the kinematics, the column density of H I is also a critical cloud parameter. To estimate the column density of the HISA
feature we use the equation given by Wilson et al. (2010):
Z
NH = 1.8224 × 1018 T S τ(v) dv,(7)
A139, page 10 of 21

where T S and τ are the spin temperature and optical depth,
respectively. For the CNM traced by HISA, T S = T HISA andτ = τHISA (Eq. (4)). However, as mentioned in Sect. 2.2 we measure the spin temperature and the optical depth together anddisentangling them is difficult. Hence, we assume a constantspin temperature over the cloud and calculate the optical depth
using Eq. (4). As we have no measurement for p, this value is

Y. Wang et al.: HISA study towards a GMF

depth map from the strong continuum sources in the background(G33.498+0.194, G33.810-0.189, G33.915+0.110, G34.133+
0.471, G35.053–0.518, G35.574+0.068, G35.947+0.379,
G36.056+0.357, and G36.551+0.002; Wang et al. 2018). Following the method described in Bihr et al. (2015), the optical depth
measured towards the continuum source is:!
T on, cont − T off, cont
τ = −ln,(8)
T cont0.25
Probability Density

13

CO
HI

0.20
0.15
0.10
0.05
0.00

0

5

10
15
20
Mach Number

25

30

Fig. 13. Histograms of the Mach number of the HISA and 13 CO
emission, shown in black and red, respectively.

difficult to estimate. Considering GMF38a is at the near side of
the Milky way, we assume a value of p = 0.9 in the following anddiscuss the corresponding uncertainties in Sects. 4.2 and 4.7. We
will discuss the uncertainty of column density brought in by themethod we choose to estimate the background temperature T off
in Sect. 4.7
We integrate between 50 and 60 km−1 and derive the column
density map shown in Fig. 14, assuming for the HISA featurea spin temperature T S = 40 K, p = 0.9 and using a second orderpolynomial to estimate the background temperature T off . Larger
spin temperatures do not change the structure of the column
density map significantly, but will increase its value everywhere.
The column density peaks in the 13 CO map do not coincide
well with the column density peaks of the atomic hydrogen. As
shown in Fig. 1, the highest peak in the 13 CO (around l = 34◦ )coincides with a strong continuum source and hence makes thedetermination of the HISA feature at this position impossible.
However, we use this continuum source to constrain the opticaldepth, which we present in Sect. 4.3. The highest column density
peak for the atomic hydrogen can be found in the eastern area ofthe filament (l = 36.5◦ ). In this region, the H2 is diffuse and its
column density is low. Another CNM column density peak can
be found in the center of the filament around l = 35.4◦ , b = + 0.3◦ .
This CNM feature has almost a round shape and only a very weak
counterpart in the 13 CO emission.
Assuming a typical CNM thermal pressure of PCNM /k ∼ 4000 K cm−3 (Heiles 1997; Jenkins & Tripp 2011; Goldsmith2013), and T K = T HISA = 40 K, we can estimate the size of the
CNM along the line of sight by dividing the column density by
PCNM /k/T K . Depending on the column density, the line of sight
size is estimated to be ∼0.5–3 pc, which is much smaller than
the width and length of the filament (∼25 and ∼230 pc, respectively). Arguing the other way round, if the line of sight sizeof the CNM is similar to the width of the filament (∼25 pc),
the thermal pressure would be significantly lower, and the CNM
could be under-pressured or the pressure may be dominated bysome other (magnetic or turbulent) component.
3.2.3. Atomic gas column density from H I emission

Since HISA traces only the CNM, it is likely that this component
is surrounded or even mixed with a warm component. We also
derive the column density traced by the H I emission (between
50 and 60 km s−1 , 32.65◦ < l < 37.27◦ and |b| ≤ 1.25◦ ),which traces both the CNM and WNM. Following the method
described in Bihr et al. (2015), we derived the mean H I optical

where T on, cont is the on-continuum-source brightness temperature, and T off, cont is the off-continuum-source temperature. Since
we use the THOR C array data to calculate τ, the smooth, largescale structure is mostly filtered out (Beuther et al. 2016). We canneglect the off emission T off, cont and simplify Eq. (8) to:!
T on,contτsimplified = −ln.
(9)
T contFor channels with a T on, cont value smaller than 3 times the rms,
we use the 3σ value to get a lower limit of τ. The mean opticaldepth varies between 1.1 and 1.9 from 50 to 60 km s−1 . The optical depth corrected spin temperature is T S = T B /(1 − e−τ ), whereT B is the brightness temperature of the H I emission. The opticaldepth corrected atomic hydrogen column density is calculatedwith Eq. (7). Since the absorption features towards these continuum sources between 50 and 60 km s−1 often saturates, theoptical depth we derived is a lower limit as shown in Fig. 18 and
we are underestimating the H I column density.
The column density we derived from H I emission is a combined result from the far (10.3 kpc) and near side (3.4 kpc) due
to the kinematic distance ambiguity. Assuming the atomic gas in
the Galactic plane is approximately axisymmetric with respect to
the Galactic center (Kalberla & Dedes 2008), the atomic gas atnear side and far side that are at the same Galactocentric distanceshare the same density distribution in the vertical direction. We
used the average vertical density profile described by Lockman(1984; see Eq. (5) and Table 1 in their paper) to estimate howmuch gas is at near distance for each line of sight and derived thecolumn density map of H I emission at 3.4 kpc shown in Fig. 14.
By comparing the column density maps of CNM and H2 , weproduce the CNM-to-H2 ratio map and show it for the Easternand Western regions in Fig. 15. We masked out regions outside
the column density threshold contours shown in Fig. 14. In bothsubregions, the CNM-to-H2 ratio varies between ∼0.5 and 25%
with a median value of ∼9%. Figure 15 shows that the outer layers of the filament have high CNM-to-H2 ratio, while the inner
regions show lower CNM-to-H2 ratio. This change from the outside to the inside of the cloud can be interpreted as signature of
the conversion of atomic to molecular gas with increasing density. Zuo et al. (2018) studied HINSA towards nearby clouds andfound a much lower ratio between 0.2 and 2%.
Figure 16 shows the surface density comparison between
the atomic hydrogen (CNM+WNM) and the total gas(CNM+WNM+H2 ). The surface density of the atomic hydrogenrises up to ∼14−23 M pc−2 (∼1.8−2.9 × 1021 cm−2 ) and thensaturates to an almost flat distribution. This turnover is at lower
values than that found by Bihr et al. (2015) towards W43 (50–80 M pc−2 ) but it is still higher than the 10 M pc−2 observed
towards nearby clouds (Lee et al. 2015) and predicted by models(e.g., Krumholz et al. 2008, 2009; Sternberg et al. 2014). Suchhigher than predicted H I column densities can be explained by
the clumpy nature of the ISM with several H I-to-H2 transitions
along the line of sight (Bialy et al. 2017b).
A139, page 11 of 21

A&A 634, A139 (2020)
×1022 3.0

+00.8◦
N (H2) from 13CO

2.7

+00.6◦

2.4+00.4◦

1.8+00.0◦

1.5−00.2◦

1.2

cm−2

Galactic Latitude

2.1+00.2◦

0.9−00.4◦

0.6−00.6◦

0.3−00.8◦
×1020 8.0

+00.8◦

7.2+00.4◦

6.4
5.6+00.2◦

4.8+00.0◦

cm−2

Galactic Latitude

N (H) THISA = 40K+00.6◦

4.0−00.2◦

3.2−00.4◦

2.4−00.6◦

1.6

50 pc−00.8◦

37.0◦

1.0◦

N (H) τ corrected

36.0◦

35.0◦

34.0◦
×1021 3.2

2.8

2.4

2.0
0.0◦

1.6

cm−2

Galactic Latitude

0.5◦

1.2
−0.5◦
0.8

0.4

50 pc

−1.0◦
37.0

◦

36.0

◦

◦

35.0
Galactic Longitude

34.0

◦

33.0

◦

Fig. 14. Top panel: column density map of the molecular cloud derived from 13 CO emission (see Sect. 3.2.1). Middle panel: column density mapof the CNM derived from HISA, assuming T S = 40 K, p = 0.9 and using a second order polynomial to estimate the background temperature T off .
Bottom panel: optical depth corrected column density map of atomic hydrogen derived from H I emission. The contours indicate column density
threshold used for the N-PDFs (see Sect. 4.5). For the H2 , HISA, and H I emission they have levels of 6 × 1020 , 1.5 × 1020 , and 1.7 × 1021 cm−2 ,respectively. The red and green polygons mark the region for the mass estimates and the column density PDF measurements shown in Figs. 20
and 22, respectively.

3.3. Mass estimate

As we know the column density and the distance to thecloud (∼3.4 kpc), we can directly estimate the mass of H I and
H2 gas. We do so for three different regions, the “full filament”(red polygon in Fig. 14), the “eastern region” (eastern green
dashed polygons in Fig. 14) and the “western region” (westerngreen dashed polygons in Fig. 14). Table 1 summarizes the mass
A139, page 12 of 21

measurements. The molecular hydrogen mass for the entire filament is ∼3.6 × 105 M and the CNM mass traced by the HISA
is significantly less, showing values of 3.4 × 103 –9.5 × 103 M ,depending on the assumed spin temperature.
Furthermore, we studied the cold atomic to the molecularhydrogen mass ratio M(CNM)/M(H2 ). For the entire filament,
this value is between 1 and 3%, again depending on the assumed

Y. Wang et al.: HISA study towards a GMF
Table 1. Mass estimates of the GMF.

RegionM(H2 )

Full filament
Eastern region
Western region

M(CNM)(40 K)[M ]M(CNM)/M(H2 )(40 K)M(H I emission)[M ]M(CNM)(20 K)[M ]3.6 × 105
7.9 × 104
1.1 × 105

3.4 × 103
1.1 × 103
1.1 × 103

9.5 × 103
3.4 × 103
2.9 × 103

3%
4%
3%

2.3 × 105 (6.1 × 105 ) (a)5.0 × 104
7.1 × 104

[M ]Notes. (a) This mass is calculated including all H I emission between 50 and 60 km s−1 , 32.65◦ < l < 37.27◦ , |b| ≤ 1.1◦ (bottom panel in Fig. 14).

−00.4◦◦+00.4◦+00.2◦+00.0◦−00.2◦−00.4◦

37.0◦ 36.8◦ 36.6◦ 36.4◦ 36.2◦ 36.0◦
Galactic Longitude

Western region

25.0
22.5
20.0
17.5
15.0
12.5
10.0
7.5
5.0
2.5

15
102
10
101

5

10

100
ΣHI + ΣH2 [M pc−2 ]1000

pixel counts [log]−00.2◦

103

20
ΣHI [M pc−2 ]+00.0◦

25

CNM − to − H2 ratio[%]+00.2◦−00.6

Galactic Latitude

Eastern region

25.0
22.5
20.0
17.5
15.0
12.5
10.0
7.5
5.0
2.5

100

Fig. 16. Surface density of the atomic hydrogen (vlsr = 50−60 km s−1 )as a function of the total gas surface density (ΣHI + ΣH2 ). The solid line
represents a one-to-one relation.

CNM − to − H2 ratio [%]Galactic Latitude

+00.4

◦

34.4◦ 34.2◦ 34.0◦ 33.8◦ 33.6◦
Galactic LongitudeFig. 15. Ratio of the CNM and H2 column densities in percentage of
the Eastern region (top panel) and Western region (bottom panel). The
contours in both panels indicate the integrated 13 CO emission at levelsof 5, 10, 20, and 30 K km s−1 .

the eastern region. Considering that 13 CO does not trace all themolecular hydrogen gas (Pineda et al. 2008; Goodman et al.
2009; Gong et al. 2018), the M(CNM)/M(H2 ) ratio we derive
could be just an upper limit.
We further estimate the mass of the atomic component traced
by H I emission. Within the same area (polygons in Fig. 14), theatomic gas traced by H I emission has lower mass as the molecular gas (Table 1). However, since there is no clear boundaryof the GMF shown in the H I column density map (see bottom panel in Fig. 14), we can assume all H I emission between
50 and 60 km s−1 within 32.65◦ < l < 37.27◦ and |b| ≤ 1.1◦
(same latitude range as the GRS coverage) is associated withthe filament to obtain the mass. The mass is estimated to be
6.1 × 105 M , which is about ∼60 times larger than the massestimated for the CNM traced by HISA (40 K). The mass of theatomic hydrogen is about 60% larger than the molecular hydrogen mass (3.6 × 105 M ), which makes sense since the molecular
cloud is surrounded by a large reservoir of atomic gas.

4. Discussion
spin temperature. However, this ratio has to be treated cautiously.
The HISA extraction method does not work reliably in the center of the filament due to strong continuum emission and wemight miss some H I mass. The mass ratio for the smaller regions
show slightly higher values (3 to 4%). The H2 column density
shows significantly higher values for the western region in comparison to the eastern region. In contrast to this, the H I column
density reveals a prominent peak on the eastern side and hence
the M(CNM)/M(H2 ) ratio is lower for the western than that for4.1. Kinematics

For nearby galaxies, the ratios of the CO to H I linewidth isaround σHI /σCO = 1−1.4 (Caldú-Primo et al. 2013; Mogotsi
et al. 2016). The linewidth values found in these studies areapproximately σ ∼ 6−12 km s−1 , which corresponds to ∆vFWHM ∼14−28 km s−1 for both the H I and CO lines. These measurements are done for the CO and H I emission over large
regions (∼0.5 kpc), which can increase the linewidth due toA139, page 13 of 21

0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.0

3.5
3.0
2.5
τ

Probability Density

A&A 634, A139 (2020)

2.0
1.5
1.0
0.5
0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

13

∆v(HISA)/∆v( CO)
Fig. 17. Ratio of HISA and 13 CO linewidths in the eastern region
indicated in Fig. 11.

superposition of different velocity components in the supersonically turbulent ISM (e.g., Klessen & Glover 2016). Our Galactic
HISA measurements of GMF38a show significantly smaller values for the linewidth of ∆vFWHM ∼ 2−8 km s−1 for CNM. The
reason is that we observe a much smaller region and we areable to separate multiple components. Furthermore, they observe
H I emission and the linewidth is dominated by WNM, whereas
we observe cold H I absorption features produced by CNM.
To study the linewidth ratio in detail, we determine thisratio for the eastern region, which is indicated in Fig. 11. We
focus on this region as it is not significantly affected by multiple component line spectra. A histogram of the H I/13 CO ratio
is shown in Fig. 17. The mean values for the linewidths are∆vFWHM (13 CO) = 3.6 km s−1 and ∆vFWHM (H I) = 4.5 km s−1 .
4.2. The percentage of background emission – p

The percentage of background emission, parameterized with p,
is difficult to estimate. Different assumptions can be found in
the literature. For example, McClure-Griffiths et al. (2006) andDénes et al. (2018) assume that p = 1 and 0.9 for the observed
Riegel-Crutcher cloud, respectively, as the corresponding distance is small (∼125 pc). Rebolledo et al. (2017) studied the
HISA features in the Gum 31 molecular complex with a simple two component assumption (p = 1). Li & Goldsmith (2003)
studied the H I narrow self-absorption towards dark clouds in the
Taurus and Perseus region. Since these clouds are located at highGalactic latitude away from the Galactic mid-plane, they canassume a simple Gaussian Galactic H I disk model (Lockman1984) and estimate the factor p with the complementary error
function.
Since the background and foreground H I emission occurs
from warm and diffuse H I clouds, we do not expect fluctuationsof this emission on small scales. Hence, the assumption of a constant p for the entire filament is reasonable. Furthermore, we canobtain a lower limit for p. As shown in Fig. 4, low values of
p . 0.4 are not feasible as the spin temperature would become
smaller than the temperature of the CMB. As we further discussed in Sect. 4.4, low values of p . 0.7 would also result an
unrealistic low spin temperature.
For Galactocentric radius 7 . R . 35 kpc, Kalberla & Dedes(2008) reported the average mid-plane volume density distribution of the atomic gas follows n(R) ∼ n0 e−(R−R )/Rn with
A139, page 14 of 21

0

20
40
vLSR [km s−1 ]60

80

Fig. 18. Spectrum of the H I optical depth towards the UCH II region
G34.256+0.146 using the THOR data. For some channels, the absorption spectra saturates and the measured optical depth is a lower limitof τ = 3.5, which is indicated by the dotted line. The gray shaded area
indicates the velocity range of the HISA feature (vLSR = 50−60 km s−1 ).

n0 = 0.9 cm−3 , and Rn = 3.15 kpc, R = 8.5 kpc (IAU recommendations). Assuming n(R < 7 kpc) = n(7 kpc), we integrate thedensity along the line of sight of GMF38a (l = 35.5◦ , b = 0◦ ) andobtain the amount of gas in the foreground and background of
GMF38a. Assuming optically thin emission, p is estimated to be
0.91, which agrees with our adopted value of 0.9.
4.3. Optical depth measurement toward a strong continuum
sourceWe can use strong continuum sources to estimate the opticaldepth of the CNM. The UCH II region G34.256+0.146 (seeFig. 1) is an ideal candidate to perform this task as it is very
bright (T cont (max) ∼ 1300 K) and slightly extended (d ∼ 7000 ).
We use the THOR data to extract the absorption spectrum
towards the continuum peak and determine the optical depth
and the lower-limit of the optical depth using Eq. (9). The optical depth spectrum is shown in Fig. 18. In the velocity rangeof the HISA feature, the absorption spectrum saturates and thedetermined optical depth τ = 3.5 is a lower limit. Furthermore,since the UCH II region is at the same distance as the filament(Anderson et al. 2014) and associated with the filament, there
could be CNM that are behind the UCH II region and are nottraced by the absorption spectrum. Therefore, the determined
optical depth represents a lower limit.
As explained in Sect. 2.2, the general HISA extraction
method measures the optical depth together with the spin temperature and we are not able to disentangle them. However, theadditional information from the absorption spectra towards thestrong continuum source and the corresponding optical depth
measurement allows us to overcome this problem. Figure 4
presents the optical depth as a function of the spin temperaturefor different values of p. The lower limit of the optical depth
measurement is shown at τ = 3.5 using a black horizontal line.
Assuming p = 0.9 reveals a spin temperature of T HISA ∼ 55 K.
This is a bit higher than the assumed spin temperature for thecolumn density determination presented in Fig. 14 (40 K). Since
we measure the spin temperature close to an UCH II region, we
expect rather high values.
A problem for HISA studies is that low level of backgroundemission can be interpreted as an absorption feature. Studying

4.4. Maximum spin temperature

As explained in Sect. 4.3, we can use strong continuum sources
to measure the optical depth and therefore disentangle the spintemperature and the optical depth. However, this is only possible in a selected number of locations, that is, in the vicinity ofa strong continuum source. In general we can only give the spintemperature as a function of the optical depth. Figure 4 showsthat the function becomes very steep for certain spin temperatures. Hence, this shows that the maximum spin temperature will
be reached for the case of large optical depth. This can also beseen by solving Eq. (4) for T HISA :T on−off+ p T off + T cont .
1 − e−τ(10)

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

(11)

T HISA =Since T on−off is always negative, T HISA reaches an upper limit for
on−offa given T off and T cont when T1−e−τ has its minimum value, which
occurs for τ → ∞. This means the maximal T HISA is:
This equation depends on the assumption of the ratio of foreground and background emission, which is described by thefactor p. For p = 1, the upper limit of the spin temperaturereaches a maximum. We can use this information to calculate
the upper limit of the spin temperature for each pixel in ourmap. However, we do not assume p = 1, but rather a more realistic value of p = 0.9. The result is given in Fig. 19. We focus
the discussion on regions offset from strong continuum sources,
since for strong continuum sources the attenuation of the continuum exceeds by far the contribution of self-absorption to the H I
absorption spectrum. As expected, we see a clear anti-correlationof the upper limit for the spin temperature and the column density of the HISA feature. A weaker absorption feature (T on−offis always negative) will result in a higher T HISA , and a lower
column density. The lowest values are found for the compact
HISA feature in the center around l = 35.5◦ with values around
T HISA (max.) ∼ 25 K. Similar values can be found for the easternregion of the filament, whereas the western side of the filamentshows in general higher values around T HISA (max.) ∼ 75 K. As
this is only an upper limit for the spin temperature, we cannot
directly infer the actual temperature. However, it is plausible thatthe H I spin temperature is higher on the western side of the cloud
due to star formation activity and feedback processes, such as theprominent UCH II region. We will discuss this aspect further in
Sect. 4.6.
For the H I column density determination in Sect. 3.2, we
assumed a spin temperature of T HISA = 40 K. As seen in Fig. 19,
this is higher than the upper limit of the spin temperature for+00.8◦+00.6◦+00.4◦+00.2◦+00.0◦−00.2◦−00.4◦−00.6◦−00.8◦

G34.256+0.146

37.0◦

36.0◦

50 pc

SNR W44

35.0◦
Galactic Longitude

34.0◦

110
100
90
80
70
60
50
40
30
20

(
THISA(max.) [K]very narrow absorption features, HINSA (e.g., Li & Goldsmith
2003; Goldsmith & Li 2005; Goldsmith et al. 2007; Krčo &Goldsmith 2010), can avoid this problem, since the steep absorption profiles of these HINSA features cannot be induced by two
broad emission profiles on each side of the absorption feature.
The broad HISA features we identified could be caused by twoemission components. Fortunately, the optical depth informationfrom the spectrum toward the strong continuum source helps tosolve this problem. Since the optical depth is high (τ > 3.5) for
the velocity range of the HISA feature (Fig. 18), we are confident that we actually indeed observe a HISA feature rather
than missing H I emission. Furthermore, the correlation of the
HISA feature with the 13 CO emission is another indicator ofcold, dense H I.

Galactic Latitude

Y. Wang et al.: HISA study towards a GMF

Fig. 19. Maximum spin temperature (Eq. (11)) of the absorption features assuming p = 0.9. The black contours show the HISA column
density map assuming T HISA = 40 K, p = 0.9, and the contour levels are
1.5, 3.5, and 5.5 × 1020 cm−2 with a smoothing of 3 pixels. Regionswith strong continuum emission are not reliable, such as SNR W44 andG34.256+0.146 (see Fig. 1).

certain cold regions. Hence for a few channels we cannot determine a column density for these regions, we exclude thesepixels in these channels from our column density calculation.
Since we observe only small regions with T HISA (max.) < 40 K
in only a few velocity channels, the column density calculation
is not affected significantly. However, assuming a larger value
for the spin temperature increases this effect and larger regions
are affected, which would make the determined column density
unreliable.
Furthermore, as indicated in Eq. (11), the factor p also affects
the value of T HISA (max.). If we take p = 0.7, the T HISA (max.)
for the whole filament would drop ∼20 K. Regions aroundl = 35.5◦ and in the eastern part of the filament would have a
T HISA (max.) < 10 K, which is highly unlikely, since simulations
find very little H I has a temperature .20 K (Glover & Smith
2016). Furthermore, previous HISA study towards nearby molecular clouds reveals a T S of 20–80 K (Gibson et al. 2000, 2005b;
Dénes et al. 2018). Therefore, our assumption of T HISA = 40 K
and p = 0.9 in the previous sections is reasonable.
4.5. Column density probability density functions (N-PDFs)

The column density maps derived in Sect. 3.2 can be utilized
to determine the probability density functions of column densities (N-PDFs). We resampled all the column density maps
into the same spatial resolution and constructed the N-PDFs.
Figure 20 presents the N-PDFs in units of hydrogen atoms per
square cm for the entire filament traced by HISA, H I emission
and 13 CO. For the HISA feature, we assumed a spin temperatureof T HISA = 40 K, p = 0.9, and used a second order polynomial toestimate the background emission, which are the same assumptions used to produce Fig. 14. We derived the H2 column densityfrom 13 CO (see Sect. 3.2.1), and converted it into the unit ofhydrogen atoms per square centimeter for easy comparison withHISA and H I emission. We calculated the column density traced
by H I emission with optical depth correction (see Sect. 3.3).
In the following, we first consider the quantification of the
shapes of the observed N-PDFs and then the interpretation of
the observed shapes. It has been argued that it may be necessary to consider “completeness” of the N-PDFs when defining
the column density range that can be studied (Kainulainen &Tan 2013, see also Brunt 2015; Lombardi et al. 2015; Alves et al.
2017), although, it is unclear if such a requirement is meaningfulwhen studying possibly turbulence-dominated gas (Körtgen et al.
2019). In our analysis, we define the completeness for the HISA
and 13 CO data, but do not apply such requirement for the H I
emission data that we expect to be clearly turbulence-dominated.
A139, page 15 of 21

A&A 634, A139 (2020)
log10N (H) [cm−2]
21.0
21.5
22.0

22.5

23.0

HI
σ = 0.12

100
10−1
10−2
10−3
10−4

0.1

1
N (H)/hN (H)i

10

10

1

20.5

log10N (H) [cm−2]
21.0
21.5
22.0

22.5

CNM THISA= 40K
σ = 0.31

100
10−1
10−2
10−3
10−4

23.0

1

10
N (H)/hN (H)i100

10Probability Density

20.5

Probability Density

Probability Density

10

1

1

20.5

log10N (H) [cm−2]
21.0
21.5
22.0

22.5

23.0

H2
σ = 0.71
α = 3.40

100
10−1
10−2
10−3
10−4

0.1

1
N (H)/hN (H)i

10

Fig. 20. N-PDFs of the gas traced by H I (left panel) emission, HISA (middle panel), and 13 CO (right panel) in units of hydrogen atoms per square
cm. The light green lines show the log-normal fit in each panel. σ is the width of the log-normal distribution. The dashed vertical lines in eachpanel mark the column density threshold, and the solid vertical lines mark the mean column densities. The red line in the 13 CO panel shows thepower-law fit with an index −α to the high column density tail.
Table 2. Results of the fits to the N-PDFs.

Component

N Thresholdlog10 (N(H))hN(H)ilog10 (N(H))

Log-normal widthσPower-law indexαNminlog10 (N(H))

CNM
H I emission
H2
All gas
CNM West
CNM East
H2 WestH2 East

20.18
21.23
21.08
21.23
20.18
20.18
21.64
21.64

20.39
21.34
21.70
21.59
20.42
20.38
22.03
21.86

0.31
0.12
0.71
0.51
0.27
0.35
0.71
0.71

–
–
3.40
3.59
–
–
2.61
–

–
–
22.25
22.33
–
–
21.64
–

We define the completeness with the help of the lowest “closed
contours” in the column density maps. These lowest closed contours are 1.5 × 1020 cm−2 for the HISA data and 1.2 × 1021 cm−2
for the 13 CO data and lead to regions that are marked with redpolygons in Fig. 14. For H I emission, we include all the data
within 32.65◦ < l < 37.27◦ , b < 1.1◦ and use the column density level of 1.7 × 1021 cm−2 to define the range over which therange is analyzed. We normalize all N-PDFs by the mean column
density of the tracer (shown in Table 2).
We first note that the N-PDFs of all components appear
curved in log–log representation, even when only taking into
account the data above the completeness levels. Therefore, we
do not make an effort to quantify the N-PDFs with single powerlaw functions. Given the appearance of the N-PDFs, we decided
to quantify their shapes through fits of log-normal functions. The
N-PDF from H I emission shows a clear log-normal shape. We
cannot identify a clear peak in the N-PDFs of HISA and 13 CO,
but proceed with the log-normal fit nevertheless. The best fit for
HISA is not well constrained and shows some excess over the
fit at the high column density side. The best fit for 13 CO agrees
well with a log-normal function over a wide range at low column
densities, but shows an excess over it at higher columns; a powerlaw could also describe the high column densities relatively well.
We fitted the power-law tail of the 13 CO N-PDF with a powerlaw (p(x) ∝ x−α ) from the optimal column density threshold
Nmin , which results in the minimum Kolmogorov-Smirnov distance between the fit and the N-PDF. The fit was performed withthe python package Powerlaw (Alstott et al. 2014). The fitted
parameters of the log-normal functions and power-laws, whenapplicable, are listed in Table 2.
The N-PDF from the H I emission peaks at 2.2 × 1021 cm−2 ,corresponding to AV = 1 (Güver & Özel 2009). Studies towards
A139, page 16 of 21

nearby clouds have found that the N-PDFs from H I emission
there peak around ∼1−2 × 1021 cm−2 (Imara & Burkhart 2016),
slight lower than we find here for our target. The widths of thefitted log-normal models vary among the tracers; the H I emission has the smallest width, followed by HISA and the 13 COthat has the widest width (see Table 2). The narrowness of the
H I emission N-PDF indicates that H I emission is relatively
smoothly distributed without large variations and substructure(Fig. 14). The width of H I emission N-PDF is similar to thoseseen towards nearby clouds (Burkhart et al. 2015b; Imara &Burkhart 2016). We note that the width of the HISA N-PDF ismuch larger than the error introduced by our HISA extraction
method (see Appendix B); we consider it is robustly between thewidths of H I emission and 13 CO.
We also examine the N-PDF of “all gas” (Fig. A.1), derived
by adding together the column density maps from all three tracers (Fig. 21). We note that “all gas” does not, in fact, trace all
the gas, since there is some amount of H2 that 13 CO does nottrace (Pineda et al. 2008; Goodman et al. 2009), a.k.a. CO-darkgas. This fraction could be as high as 26 to 79% of the total H2gas (Gong et al. 2018). The N-PDF of “all gas” (Fig. 21) can
not be fitted with single log-normal or power-law function. Similar to what we applied to the 13 CO, we fitted the N-PDF witha log-normal function and the high-column density side with apower-law, but obviously, a single power law cannot account forthe peak in the observed distribution.
Next, we discuss the N-PDFs of the two subregions of thefilament. The N-PDFs for the eastern and western regions, indicated with dashed polygons in Fig. 14, are shown in Fig. 22. The
N-PDFs of the cold dense H I traced by HISA for both subregions
still can be described by a single log-normal function with a similar width as that found over the whole filament. The N-PDFs of

Y. Wang et al.: HISA study towards a GMF

Probability Density

10

1

20.5

log10N (H) [cm−2]
21.0 21.5 22.0 22.5

23.0

23.5

All Gasσ = 0.51
α = 3.59

100
10−1
10−2
10−3
10−4

0.1

1
N (H)/hN (H)i

10

Fig. 21. N-PDF of the combination of atomic and molecular gas overthe entire region in Fig. 14. The green line shows the log-normal fit.
The dashed vertical line mark the column density threshold (the contour
levels in Fig. 14), and the vertical solid line mark the mean column
density. The red line shows the power-law fit with an index −α to thehigh column density tail.

Probability Density101

σ = 0.27
σ = 0.35

100

22.5

23.0

CNM West
CNM East

10−1
10−2
10−3

101
Probability Density

20.5

log10N (H) [cm−2]
21.0
21.5
22.0

1

10
N (H)/hN (H)i20.5

log10N (H) [cm−2]
21.0
21.5
22.0

H2 West σ = 0.44
H2 East σ = 0.20

100

22.5

23.0

α = 2.61

100
10−1

4.6. Evolutionary stages

10−2
10−3

the molecular gas show very different shapes for two subregions.
While the N-PDF for the eastern subregion can be described by alog-normal function, the N-PDF for the western subregion showsa clear power-law shape.
Recall that we pointed out in Sect. 1 that theoretical studies predicted that the shapes of the N-PDFs are depend on thephysical processes acting within the cloud, a log-normal N-PDF
indicates that turbulent dominates and a power-law indicatesthat gravity dominates (e.g., Federrath et al. 2010; BallesterosParedes et al. 2011; Kritsuk et al. 2011; Federrath & Klessen
2013; Burkhart et al. 2015a). A possible explanation for thedifferent N-PDF for different subregions is that the western subregion shows ongoing high-mass star formation activities, that is,
UCH II region, indicating that the molecular cloud is dominatedby gravitational collapse.
One possible reason we do not see a power-law tail in the
N-PDF of the molecular gas in the eastern subregion is that the13
CO could be frozen onto the dust grains in the densest andcoldest part of the molecular cloud (e.g., Giannetti et al. 2014). In
this case we could not recover the high density part, whereas in
the western subregion the feedback effects from the UCH II havereleased the 13 CO molecules from the dust grains. As the line is
not excited at very low density, altogether 13 CO only traces theintermediate density gas between the dense star forming cores,
and so these do not show up in the N-PDF (see e.g., Ossenkopf
2002 for a similar effect in the ∆-variance.)
We estimated the 13 CO depletion factor by comparing themolecular cloud column density we derived from 13 CO with
the H2 column density derived from the ATLASGAL dust
continuum. Four ATLASGAL dense clumps (AGAL036.406+
00.021, AGAL036.666-00.114, AGAL036.826-00.039, and
AGAL036.839-00.022) that have velocities within the respective 13 CO velocity range are located in the eastern subregion(Urquhart et al. 2018). We smoothed the ATLASGAL image into
the same pixel size and angular resolution calculated the column
density of molecular hydrogen following Eq. (15) in Giannetti
et al. (2014). The same dust opacity κ = 1.8 cm2 g−1 as that used
by Giannetti et al. (2014) is employed, and we assume the dust
temperature from Herschel Hi-GAL results (Marsh et al. 2017).
The 13 CO depletion factors we derived are between 2 and 4, witha mean value of 3, which agrees with the numbers (Giannetti
et al. 2014) derived for infrared dark sources. Therefore, thehigh column density part of the N-PDF in the eastern subregion
could be underestimated due to 13 CO depletion.

0.1

1
N (H)/hN (H)i

10

Fig. 22. N-PDFs for the two subregions within the filament marked withdashed polygons in Fig. 14. Top and bottom panels: N-PDF of atomic
and molecular hydrogen derived with HISA and 13 CO measurements,
respectively. The lighter lines show the log-normal (top and bottom
panels) and power-law (bottom panel) fits. The black dashed lines ineach panel mark the column density threshold, and the solid verticallines indicate the mean column densities. The bottom x-axes in bothpanels are the relative column density for the N-PDF of the western subregion, i.e., the red histogram in both panels. Other N-PDFs are shiftedto the correct absolute column density for comparison. The thick blackline in the molecular component panel shows the power-law fit with anindex −α to the column density distribution of the western region.

As mentioned in Sect. 3.2, we observe a significant differencein the distribution of the H2 column density for the eastern andwestern subregion of the filament. The eastern subregion showsa more diffuse column density distribution, whereas the western
subregion reveals several high column density peaks. Hence, thewestern subregion reveals a power-law in the N-PDFs shown in
Fig. 22 and the eastern subregion shows a log-normal shaped
PDF. Furthermore, we see a luminous UCH II region within
the western subregion, whereas the eastern subregion does notharbor significant continuum emission. The ATLASGAL survey (Schuller et al. 2009) shows strong extended submillimeteremission with a group of star forming clumps in the western
subregion, whereas only a few unresolved continuum clumps arefound with velocities within the respective 13 CO velocity range
in the eastern subregion (Ragan et al. 2014; Urquhart et al. 2018).
All these different tracers are indicative of active high mass star
A139, page 17 of 21

A&A 634, A139 (2020)

4.7. Uncertainties for the determined HISA properties

Several factors introduce uncertainties to the determined properties of the HISA features. In the following we will discuss
three contributions: the ratio of foreground to background emission – factor p, different methods to determine the backgroundemission and the assumption of the spin temperature T HISA .
Figure 4 also shows that for a fixed spin temperature T HISA ,the larger the value of p is, the lower the optical depth τ is, hence
the lower the column density is. Depending on the p value wechoose (between 0.7 and 0.9), the column density can change byat most a factor of ∼2. This is shown in Fig. 23 for N-PDFs of theentire filament assuming three different values for p. The column
density structure stays almost constant, but the actual values are
shifted for different p values.
As discussed in Sect. 2.3, the chosen method for the background estimate can influence the absorption depth of the HISA
feature and thus the column density. We showed in Sect. 2.3 thatthe best method is a polynomial fit to the H I spectra and interpolate for the HISA feature. The difference for a second or fourthorder polynomial is negligible for most regions. As we can see
in the bottom panel of Fig. 23, the column density structures ofthe second and fourth order polynomial are almost identical, themean column density of the fourth order polynomial fit is ∼3%higher than the one of second order (Table 3). Thus we chose touse a second order polynomial fit for T off .
Another important factor is the assumption of a constant spintemperature for the cloud. This is obviously a poor assumption, but using additional measurements we can constrain therange of the spin temperature. The most important one is theupper limit for the spin temperature introduced in Sect. 4.4.
A139, page 18 of 21

Probability Density

101

20.0

log10N (H) [cm−2]
20.5
21.0

21.5

22.0

p = 0.9 , σ = 0.31
p = 0.8 , σ = 0.31
p = 0.7 , σ = 0.30

100
10−1
10−2
10−3
10−4

1

10
N (H)/hN (H)i

101
Probability Density

formation with strong feedback effects on the western side of thefilament, while the eastern side shows no effects of feedback.
The kinematics of the HISA do not exhibit significant differences between the eastern and western subregion. However,comparing the HISA and 13 CO kinematics shows an interesting
difference. The eastern subregion shows similar peak velocities
for the H I and CO, whereas the western subregion reveals a
difference of ∼4 km s−1 . Using the newly developed histogramof oriented gradients (HOG) tool, Soler et al. (2019) confirmed
morphological correlation between the H I and 13 CO emissionin velocity channels separated by 3–4 km s−1 towards the western subregion. The H I at ∼54 km s−1 is spatially correlated with
13
CO emission at ∼57.5 km s−1 (Fig. 15 in Soler et al. 2019).
They further demonstrated by applying the HOG analysis on
synthetic observations from MHD simulations that this velocity offset between 13 CO and H I could arise from more generalmolecular cloud formation conditions. Another explanation forthis velocity offset could be the feedback from the expanding
UCH II region G34.256+0.146. A significant amount of the 13 CO
gas at ∼54 km s−1 has been driven away by the radiation from theforming high-mass star.
Studying the cold H I column density, we found higher column density peaks on the eastern side in comparison to a morediffuse H I column density structure on the western side. The
maximum spin temperature also shows smaller values on theeastern side. This might be an indication of a younger, colder,
and more dense H I cloud on the eastern side in comparison toa more evolved cloud on the western side. It is possible that thedense H I cloud on the eastern side of the filament is about tobecome a dense molecular cloud, forming high density peaks
and subsequently form stars. However, further observations or
simulations are needed to support this hypothesis.

20.0

log10N (H) [cm−2]
20.5
21.0

21.5

22.0

Pol 2, 40K , σ = 0.31
Pol 2, 20K , σ = 0.30
Pol 4, 40K , σ = 0.32

100
10−1
10−2
10−3
10−4

1

10
N (H)/hN (H)i

Fig. 23. Top panel: N-PDFs for the atomic hydrogen for different p. The
PDF is measured over the entire filament indicated with a red polygon in
Fig. 14, assuming a constant spin temperature of T HISA = 40 K. Bottom
panel: N-PDFs for the atomic hydrogen for different spin temperatureand different polynomial functions fit to get T off . The dashed verticallines in each panel indicate the column density threshold, and the solid
vertical lines indicate the mean column densities. The bottom x-axes inboth panels are the relative column densities for the N-PDF of “Pol 2,
p = 0.9, 40 K”, i.e., the black histogram in both panels. Other N-PDFs
are shifted to the correct absolute column density for comparison.

Using this information, we can constrain the spin temperature
to values of T HISA < 70 K for the majority of the HISA features. For the CNM mass estimation given in Sect. 3.3, we
assumed a spin temperature of T HISA = 20 and 40 K. As seenin Fig. 23, the N-PDF does not change significantly, but higher
spin temperatures result in larger column densities and masses(Table 3). In Sect. 3.3, we showed that the mass is about a factor of three larger for T HISA = 40 K with respect to that assuming
T HISA = 20 K.
Furthermore, we performed our HISA extraction method
on model images (see Appendix B) to estimate the uncertainty brought in by the T off fitting method to the width of the
N-PDF. The test results show that the “instrument broadening”
introduced by the fitting method to the N-PDF is not very large
and the log-normal width of the CNM we derive in the paper isrobust.
In summary, it is difficult to quantify exactly the uncertaintyof the CNM column density and mass. Considering all assumptions, the CNM mass has an uncertainty of a factor of 2–3(dominated by the uncertainty of T S ), which is similar to the H2mass uncertainty based on 13 CO. However, we showed that theshape of the column density PDF is robust.

Y. Wang et al.: HISA study towards a GMF

6. We hypothesize that the eastern and western sides of the filament represent different evolutionary stages. The easternside represents an earlier stage, which is currently forminga dense molecular cloud out of the atomic reservoir. As we
do not observe high molecular column density peaks, theH I shows low spin temperatures and high column densities. In contrast, the western side of the filament shows highH2 column density peaks, signs of active star formation,such as UCH II regions, and, in general, a warmer and lessdense atomic counterpart. These differences provide interesting constraints for theoretical models and simulations of
the formation of molecular clouds.

Table 3. Results of the fits to the N-PDFs of CNM for different
parameters (Fig. 23).

Pol.

p

T HISA[K]

N Thresholdlog10 (N(H))hN(H)ilog10 (N(H))

Width
σ

Pol 2
Pol 2
Pol 2
Pol 2
Pol 4

0.9
0.8
0.7
0.9
0.9

40
40
40
20
40

20.18
20.28
20.43
19.71
20.18

20.39
20.49
20.63
19.92
20.40

0.31
0.31
0.30
0.30
0.32

5. Conclusions
We studied atomic and molecular gas components of the giant
molecular filament GMF38a. The molecular component is traced
via observations of 13 CO, whereas the cold atomic gas isobserved via HISA features and H I 21 cm emission. The main
results can be summarized as:
1. We extracted HISA by estimating the background emission
with different methods. For the observed giant filament, apolynomial fit of second order to the neighboring channelsof each HISA is the most reliable method from the different
options we tested to estimate the background emission.
2. The HISA features and the 13 CO emission are spatially correlated. While in the eastern subregion they correlate well,
the peak velocities of the two tracers show an offset of∼4 km s−1 for the western subregion of the filament.
3. Although the linewidth ratio between HISA and 13 CO
is around unity, the Mach number estimation shows thatthe 13 CO emission is dominated by supersonic turbulent
motions, whereas a large fraction of the CNM is at subsonicor transonic velocities.
4. Assuming a spin temperature of T HISA = 40 K for the H I,
we determined the column densities of the cold dense H I
and compared them to the H2 column density distribution
derived from the 13 CO emission. The column density peaks
do not coincide and the H I column density shows in general a diffuse structure. The H2 column density reveals
prominent peaks in the western subregion of the filament
whereas the eastern subregion appears more diffuse. The
CNM-to-H2 column density ratio varies between 0.5 and
25% with a median value of ∼9%. The outer layer of thefilament exhibits a higher ratio than that toward the cloudcenters. The surface density of atomic hydrogen peaks at∼14−23 M pc−2 (corresponding to ∼1.8−2.9 × 1021 cm−2 ).
Furthermore, the mass traced by HISA is only ∼3% of themolecular mass, and ∼1.6% of the mass traced by atomic
H I emission.
5. Studying the N-PDFs, we are able to provide constraints on
the physical processes within the cloud. The location of the
HISA N-PDF is strongly dependent on the assumed parameters, but the width is not. The N-PDFs of CNM, H I emission,and H2 can be described by a log-normal function, whichindicates turbulent motions as the main physical driver. Only
the H2 column density of the western subregion within thefilament is characterized by a high column density powerlaw structure, consistent with the observed star formation
activity. Adding the column density maps of all three tracers (CNM, H I emission, and H2 ) up, we generated a column
density map of “all gas.”Acknowledgements. The National Radio Astronomy Observatory is a facility of
the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. Y.W., H.B., S.B., and J.D.S. acknowledge support fromthe European Research Council under the Horizon 2020 Framework Program via
the ERC Consolidator Grant CSF-648505, and R.S.K. via the ERC AdvancedGrant 339177 (STARLIGHT). H.B., S.C.O.G., and M.R. acknowledge support
from the Deutsche Forschungsgemeinschaft in the Collaborative Research Center (SFB 881) “The Milky Way System” (subproject B1, B2, B8). R.S.K. andS.C.O.G. also acknowledge support from the DFG via Germany’s Excellence
Strategy EXC-2181/1 - 390900948 (the Heidelberg STRUCTURES Cluster of
Excellence). This work was carried out in part at the Jet Propulsion Laboratory which is operated for NASA by the California Institute of Technology.
N.S. acknowledges support by the french ANR and the german DFG throughthe project “GENESIS” (ANR-16-CE92-0035-01/DFG1591/2-1). F.B. acknowledges funding from the European Union’s Horizon 2020 research and innovation
program (grant agreement No 726384). This research made use of Astropy andaffiliated packages, a community-developed core Python package for Astronomy(Astropy Collaboration 2018), Python package SciPy3 , APLpy, an open-source
plotting package for Python (Robitaille & Bressert 2012), and software TOPCAT(Taylor 2005). The authors thank the anonymous referee for the constructive
comments that improve the paper.

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Y. Wang et al.: HISA study towards a GMF

Appendix A: All gas
×1022 5.0

1.0◦

4.5
All gas column density N (H)
4.0
3.5
3.0
0.0◦

2.5

cm−2

Galactic Latitude

0.5

◦

2.0
1.5

−0.5◦

1.0
0.5
50 pc

−1.0◦
37.0◦

36.0◦

35.0◦
Galactic Longitude

34.0◦

33.0◦

Fig. A.1. The column density map of the gas combined molecular component (from 13 CO), CNM (from HISA), and WNM+CNM (from H I
emission) (see Sect. 3.2.1). The red and green polygons mark the region for the mass estimates and the column density PDF measurements (onlymolecular component and CNM) shown in Figs. 20 and 22, respectively.

101
Probability Density

To test how much our HISA identification and fitting method
broadens the N-PDF of the CNM, we tested our HISA extraction
method on artificial H I emission maps with absorption features.
We made a model H I map with a relative uniform peak T B ∼85 K with a noise of ∼4 K, which is similar to the real data wehave. The H I spectra in the model map have a random linewidthvarying between ∼30 and 45 km s−1 , and a random peak velocity
between 47.5 and 52.5 km s−1 . We also made a model continuum
map with a relative uniform T B ∼ 13 K with a noise of 0.7 K,
and both values are similar to the diffuse continuum emission
flux and the noise level of the real data. Both model images havethe same pixel size (1000 ) and beam size (4000 ) as the real data.
For the first test, we generate artificial absorption featuresfrom a single column density value with T HISA = 40 K and
p = 0.9, and added them into the model H I image. This column
density value equals to the mean CNM column density of the
GMF38a in Table 2 (log10 (N(H)) = 20.39 cm−2 ). The artificial absorption features peak at 50 km−1 and have a linewidthof 5 km s−1 . Following the method described in Sects. 2 and3, we extracted the HISA spectra, estimated the column density
and construct the N-PDF shown in the top panel of Fig. B.1. The
absorption features we put in the model image all have the same
column density, so the modeled N-PDF is a delta function. Due
to noise and the uncertainty we brought in through our HISA
extraction method, the N-PDF we derived has a width of 0.19,
and about 10% lower mean column density than the input one.
For the second test, instead of a single column density value,
we generate artificial absorption features from a log-normal distribution column density with T HISA = 40 K and p = 0.9, andadded them into the model H I image. The input log-normal
distribution has a width of 0.15, and a peak at the mean CNM
column density of the GMF38a in Table 2 (log10 (N(H)) =20.39 cm−2 ). Similarly, we ran our procedure on the model image
and the N-PDF is shown in the bottom panel of Fig. B.1. The

input width of 0.15 is broadened to 0.22, and the mean column
density is also about 10% lower than the input one.
Both tests demonstrate that the “instrument broadening” contribution to the N-PDF of our method is not very large and thelog-normal width of the CNM we derive in the paper is robust.
20.5

log10N (H) [cm−2]
21.0
21.5
22.0

22.5

23.0

Recovered HISA THISA= 40K
log10(hN (H)i) = 20.35
σ = 0.19
log10(hN (H)inputi) = 20.39

100
10−1
10−2
10−3

10
Probability Density

Appendix B: CNM N-PDF width test

1

1

20.5

10
N (H)/hN (H)ilog10N (H) [cm−2]
21.0
21.5
22.0

100

22.5

23.0

Recovered HISA THISA= 40K
log10(hN (H)i) = 20.36
σ = 0.22
log10(hN (H)inputi) = 20.39
σinput = 0.15

100
10−1
10−2
10−3

1

10
N (H)/hN (H)i

100

Fig. B.1. The N-PDFs of the CNM recovered from the tests.
A139, page 21 of 21