Publ. Astron. Soc. Japan (2018) 00(0), 1–27
doi: 10.1093/pasj/xxx000

CO Multi-line Imaging of Nearby Galaxies(COMING). IX. 12CO(J = 2–1)/12CO(J = 1–0) line
ratio on kiloparsec scales
Yoshiyuki YAJIMA1,* , Kazuo S ORAI1,2,3,4 , Yusuke M IYAMOTO5 ,Kazuyuki M URAOKA6 , Nario K UNO3,4,7 , Hiroyuki K ANEKO8,5 ,Tsutomu T. TAKEUCHI9,10 , Atsushi YASUDA3 , Takahiro TANAKA3 ,Kana M OROKUMA -M ATSUI11 and Masato I. N. KOBAYASHI12,13
1

Department of Cosmosciences, Graduate School of Science, Hokkaido University, N10 W8,
Kita-ku, Sapporo, Hokkaido 060-0810, Japan2
Department of Physics, Faculty of Science, Hokkaido University, N10 W8, Kita-ku, Sapporo,
Hokkaido 060-0810, Japan
3
Graduate School of Pure and Applied Sciences, University of Tsukuba, 1-1-1 Tennodai,
Tsukuba, Ibaraki 305-8571, Japan
4
Tomonaga Center for the History of the Universe, University of Tsukuba, 1-1-1 Tennodai,
Tsukuba, Ibaraki 305-8571, Japan
5
National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan
6
Department of Physical Science, Osaka Prefecture University, 1-1 Gakuen, Sakai, Osaka
599-8531, Japan
7
Department of Physics, School of Science and Technology, Kwansei Gakuin University, 2-1
Gakuen, Sanda, Hyogo 669-1337, Japan
8
Graduate School of Education, Joetsu University of Education, 1, Yamayashiki-machi,
Joetsu, Niigata 943-8512, Japan
9
Division of Particle and Astrophysical Science, Nagoya University, Furo-cho, Chikusa-ku,
Nagoya, Aichi 464-8602, Japan
10
The Research Center for Statistical Machine Learning, The Institute of Statistical
Mathematics, 10-3 Midori-cho, Tachikawa, Tokyo 190-8562, Japan
11
Institute of Astronomy, The University of Tokyo, 2-21-1 Osawa, Mitaka, Tokyo 181-8588,
Japan
12
Department of Earth and Space Science, Graduate School of Science, Osaka University,
1-1 Machikaneyama-cho, Toyonaka, Osaka 560-0043, Japan
13
Astronomical Institute, Graduate School of Science, Tohoku University, Aoba-ku, Sendai,
Miyagi 980-8578, Japan∗ E-mail: yajima@astro1.sci.hokudai.ac.jp

Received 2020 May 29; Accepted 2020 December 15

Abstract
While molecular gas mass is usually derived from 12 CO(J = 1–0) — the most fundamentalline to explore molecular gas — it is often derived from 12 CO(J = 2–1) assuming a constant
12
CO(J = 2–1)/12 CO(J = 1–0) line ratio (R2/1 ). We present variations of R2/1 and effects of
the assumption that R2/1 is a constant in 24 nearby galaxies using 12 CO data obtained with
the Nobeyama 45-m radio telescope and IRAM 30-m telescope. The median of R2/1 for all
c 2018. Astronomical Society of Japan.
⃝

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Publications of the Astronomical Society of Japan, (2018), Vol. 00, No. 0

galaxies is 0.61, and the weighted mean of R2/1 by 12 CO(J = 1–0) integrated-intensity is 0.66
with a standard deviation of 0.19. The radial variation of R2/1 shows that it is high (∼0.8)
in the inner ∼1 kpc while its median in disks is nearly constant at 0.60 when all galaxies arecompiled. In the case that the constant R2/1 of 0.7 is adopted, we found that the total molecular
gas mass derived from 12 CO(J = 2–1) is underestimated/overestimated by ∼20%, and at mostby 35%. The scatter of a molecular gas surface density within each galaxy becomes larger by∼30%, and at most by 120%. Indices of the spatially resolved Kennicutt–Schmidt relation by
12
CO(J = 2–1) are underestimated by 10–20%, at most 39% in 17 out of 24 galaxies. R2/1 has
good positive correlations with star-formation rate and infrared color, and a negative correlation
with molecular gas depletion time. There is a clear tendency of increasing R2/1 with increasing
kinetic temperature (Tkin ). Further, we found that not only Tkin but also pressure of molecular
gas is important to understand variations of R2/1 . Special considerations should be madewhen discussing molecular gas mass and molecular gas properties inferred from 12 CO(J = 2–
1) instead of 12 CO(J = 1–0).
Key words: galaxies: ISM — galaxies: star formation — ISM: molecules — radio lines: galaxies — radiolines: ISM

1 Introduction
Molecular gas is a crucial component in the interstellar
medium (ISM) because star formation is the main physicalprocess in the universe, and stars form from cold molecular gas. Therefore, it is essential to understand the properties of molecular gas to investigate galaxies and theirevolution. 12 CO(J = 1–0) line has been used as a tracer
for cold molecular gas (e.g., Solomon et al. 1987; Young& Scoville 1991) because H2 molecule cannot be directly
observed in cold environments due to no electric dipole
moment. Since the J = 1 energy level of a 12 CO molecule
is low (∆E/kB ∼ 5.5 K, where ∆E is energy gap and kB
is the Boltzmann constant), 12 CO is easily excited to theJ = 1 level and emit 12 CO(J = 1–0) line even in cold conditions. In addition, the critical density of 12 CO(J = 1–0) is
a few hundred cubic centimeters in an optical thick region.
This value is quite lower than that of other molecular gas
tracers. Furthermore, 12 CO is an abundant molecule in
the ISM except hydrogen and helium, has large dissociation energy, and its abundance ratio is nearly uniform inmolecular clouds. Thus, 12 CO(J = 1–0) is the most usefulline to study the bulk of cold molecular gas. Molecular gas
surface density (Σmol ) in galactic disks is usually derived
from the following equation with the integrated intensityof 12 CO(J = 1–0), I12 CO(1−0) ,(ΣmolM⊙ pc−2)[

I12 CO(1−0)= 1.36 × 3.20 cos i
K km s−1

[

]

]

XCO
,
2.0 × 1020 cm−2 (K km s−1 )−1into column density of H2 . Helium in molecular gas contributes the factor of 1.36 and the other factor 3.20 represents the unit conversion of K km s−1 into M⊙ pc−2 .
The product of 1.36 × 3.20 = 4.35 in units of M⊙ pc−2 (Kkm s−1 )−1 corresponding to XCO = 2.0 × 1020 cm−2 (Kkm s−1 )−1 is also widely used as the CO-to-H2 conversion
factor that converts I12 CO(1−0) into Σmol [or luminosity of
12
CO(J = 1–0) into molecular gas mass] usually denoted as“αCO ” (e.g., Bolatto et al. 2013; Leroy et al. 2013; Schruba
et al. 2019).
When the atmosphere is extremely dry, which is common at sites of short-millimeter and submillimeter telescopes, the observation eﬃciency of 12 CO(J = 1–0) for the
local universe is usually lower than that with 12 CO(J = 2–
1). This is because the rest frequency of 12 CO(J = 1–0),
115 GHz, is close to the O2 absorption band at 118 GHz,and the 12 CO(J = 2–1) attenuation caused by water vapor is small at its rest frequency of 230 GHz in such sites.
Thus, 12 CO(J = 2–1) is often used to observe molecular
gas instead of 12 CO(J = 1–0) (e.g., Leroy et al. 2009, hereafter L09; Druard et al. 2014; Sun et al. 2018). In thiscase, Σmol is derived from the following equation insteadof equation 1 by assuming the integrated-intensity ratio of
12
CO(J = 2–1)/12 CO(J = 1–0) (hereafter, R2/1 ),(ΣmolM⊙ pc−2)[−1= 1.36 × 3.20 cos i R2/1[

I12 CO(2−1)
K km s−1

]

]

XCO
,
2.0 × 1020 cm−2 (K km s−1 )−1

(2)

(1)

where i is the inclination angle of the galactic disk, XCO
is the CO-to-H2 conversion factor that converts I12 CO(1−0)

where I12 CO(2−1) is the integrated intensity of 12 CO(J = 2–
1). The value of 0.7–0.8 is usually assumed to be a constantR2/1 (e.g., L09; Leroy et al. 2013).

Publications of the Astronomical Society of Japan, (2018), Vol. 00, No. 0

Although 12 CO(J = 2–1) is used as a proxy of
CO(J = 1–0), the energy of 12 CO J = 2 level (∆E/kB ∼16.5 K) is higher than that in the typical cold molecular clouds (∼ 10 K). Therefore, it is possible that 12 CO
molecules are not well excited to reach the J = 2 levelbased on molecular gas properties (e.g., Peñaloza et al.
2017). Molecular gas traced by 12 CO(J = 2–1) is warmer
and/or denser than that traced using 12 CO(J = 1–0). R2/1
is influenced by the physical conditions of molecular gas.
12

The systematic variations of R2/1 have been reported inprevious observations of molecular gas in the Milky Way.
For nearby giant molecular clouds (GMCs), while R2/1 ismedium (∼ 0.7–0.8) in the ridges of GMCs, it exceeds
unity in interfaces of H II regions and OB associations,and it is relatively low in the peripheries of GMCs (∼ 0.5)
(Sakamoto et al. 1994; Nishimura et al. 2015). GMCs withactive star formation tend to show high R2/1 while thosewith quiescent star formation show low ratios. In large
scales of the Milky Way, R2/1 decreases from 0.75 at 4 kpc
to 0.5 at 8 kpc as a function of the Galactocentric radius(Sakamoto et al. 1995; Sakamoto et al. 1997). Further, aR2/1 gradient appears across spiral arms; it gradually increases toward the downstream of arms. In addition, R2/1
shows higher values that are close to unity in the Galactic
center compared with the Galactic disk (Oka et al. 1998;
Sawada et al. 2001).
For external galaxies, a pioneering study by Braine &Combes (1992) reported that there is a moderate positive correlation between R2/1 and infrared (IR) color, andthey attempted to infer molecular gas properties from R2/1
around the center of nearby galaxies. High R2/1 (0.9 withthe scatter of ∼ 0.3) was reported in the Large Magellanic
Cloud (LMC), and positions where R2/1 is high do not always coincide with massive star-formation regions (Sorai
et al. 2001). It was argued that it reflects dense molecular gas, which is ready to form stars and is not due towarmed gas by radiations from massive stars, whereas thelow metallicity environment in LMC may also influence
R2/1 . In several nearby galaxies, the median of R2/1 indisks is approximately constant (∼ 0.8) and R2/1 increases(> 1) in the center similar to that in the Milky Way (L09),
while some galaxies show a nearly constant R2/1 in theentire galaxy including the center (e.g., M 33; Druard etal. 2014). Leroy et al. (2013) reported the median of 0.66
with standard deviations of ∼ 0.3 for approximately 30
nearby galaxies. Based on this result, some studies using
12
CO(J = 2–1) data assumed the constant R2/1 = 0.7 andconverted the intensity of the line into that of 12 CO(J = 1–0) to derive molecular gas mass and its surface density.
A detailed study to understand R2/1 as a probe ofmolecular gas properties in the extragalactic field reported

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that while typical R2/1 is ∼ 0.7, it is relatively high (0.8–0.9) in the leading side (the downstream) of the spiral arms
and low (0.4–0.6) in the inter-arms for M 51 as well as theMilky Way (Koda et al. 2012). In addition, they foundthat R2/1 increases as surface density of star-formation
rate (ΣSFR ) and star-formation eﬃciency (SFE) in thisgalaxy. They also suggested that high R2/1 is relevant
to warm molecular gas by active star formation and compressed molecular gas before star formation. With regard
to R2/1 and star formation activity, it was found that thecorrelation of R2/1 with IR color is better than that of R2/1
with far-ultraviolet (FUV), and far IR intensities in M 83
(Koda et al. 2020). It was argued that these are attributed
to warm molecular gas heated by dust, UV photons, andcosmic ray from supernovae, considering high R2/1 in thedownstream of arms where many massive stars are seen.
As described above, R2/1 has systematic variations
within and among galaxies, and it reflects molecular gas
conditions such as temperature. Hence, it would be possible that molecular gas mass, its related quantities and relations derived from 12 CO(J = 2–1) with assumed constantR2/1 are misled (e.g., Momose et al. 2013) although there
remains the uncertainty of the CO-to-H2 conversion factor. It is better to test the validity of the assumption thatR2/1 is constant, and its eﬀect on derived quantities andrelations which are relevant to molecular gas, especially formany types of galaxies. Furthermore, the causes of R2/1
variations should be investigated with physical propertiesof molecular gas.
The largest CO-mapping survey for nearby galaxies
in the world, CO Multi-line Imaging of Nearby Galaxies(COMING; Sorai et al. 20191 , hereafter S19) was carriedout using the receiver FOur-beam REceiver System on
the 45-m Telescope (FOREST; Minamidani et al. 2016)
installed on the Nobeyama 45-m telescope. COMING
mapped 147 nearby galaxies in 12 CO, 13 CO, and C18 O
J = 1–0 lines. The addition of other CO-mapping surveys
such as Kuno et al. (2007) (hereafter, K07) and L09 enable
us to investigate spatial R2/1 variations in many types ofnearby galaxies and the eﬀects of the assumption for a constant R2/1 in a large area of galaxies. With those CO data,
we verify the assumption of fixed R2/1 . The key questionsin this paper are as follows: (i) How does the assumptionof a constant R2/1 aﬀect molecular gas mass itself and its
relevant relations? Is the assumption that R2/1 is a constant reasonable?; (ii) What changes R2/1 ? How does R2/1
vary depending on molecular gas properties?
The remainder of the paper is organized as follows.
In section 2, the samples of this study, analysis of CO
1

See also ⟨https://astro3.sci.hokudai.ac.jp/~radio/coming/⟩

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Publications of the Astronomical Society of Japan, (2018), Vol. 00, No. 0

cubes, intensity accuracy of CO considering calibrationand pointing, and ancillary data sets are explained. The
spatial distribution, statistics, and radial distribution of
R2/1 are described in the first half of section 3. In thelatter half of the section, we report eﬀects of the constant R2/1 on molecular gas mass, its scatter within agalaxy, and the ΣSFR –Σmol relation (i.e., the moleculargas Kennicutt–Schmidt relation). To investigate the relation of R2/1 and molecular gas properties, the correlationsof representative quantities and R2/1 are examined in thefirst half of section 4. We attempted to derive the intrinsic properties of molecular gas, number density, andkinetic temperature from 12 CO(J = 1–0), 12 CO(J = 2–1),
and 13 CO(J = 1–0) for COMING galaxies and comparedthem with R2/1 . These discussions and implications aredescribed in the latter half of section 4. Finally, the conclusions of this paper are provided in section 5.

2 Data sets
2.1 CO data and their analysis
12

CO(J = 1–0) data used in this paper were taken from
COMING firstly. Refer to sections 3 and 4 in S19 for details about the settings of observations, calibration, anddata reduction for COMING. In addition, Nobeyama CO
Atlas of Nearby Spiral Galaxies (K07) is used as the second reference of 12 CO(J = 1–0) data. Since the samplesof K07 includes galaxies with large appearances, it makes
it possible to discuss variations of R2/1 in large area ofgalaxies. For the 12 CO(J = 2–1) reference, we use HERA
CO-Line Extragalactic Survey (HERACLES; L09) carriedout with the IRAM 30-m telescope.
The 12 CO(J = 1–0) data obtained by K07 andCO(J = 2–1) data obtained by L09 were convolved tomatch the angular resolution of 17′′ , which is the original
resolution of COMING. Before measurements of R2/1 , thecoordinates for all CO cubes were matched and regridded
so that the grid size becomes 8′′ . Then, velocity channels
were binned so that the velocity resolution is 20 km s−1 .
These processes were performed to improve signal-to-noise
ratio (S/N ). After that, the baseline was subtracted.
12

The method of baseline subtraction is the same as
COMING Auto-Reduction Tool (COMING ART; see section 4.2 in S19 for detail), however, signal channels aredefined by 12 CO(J = 2–1), not by 12 CO(J = 1–0) because
12
CO(J = 2–1) data achieves a much better sensitivity
than that of 12 CO(J = 1–0). That is, the result thatwhether the channel is a ‘signal’ or ‘noise’ for each channel of 12 CO(J = 2–1) in a position was applied to thatof 12 CO(J = 1–0) at the channel of the same velocity in

Table 1. Samples in this study.
galaxy
D
i
P.A.
[Mpc]
[deg]
[deg]
(1)
(2)
(3)
NGC 337
18.9
44.5
119.6
NGC 6289.02
7
20
NGC 2146
27.7
62
−43.5
NGC 2798
29.6
60.7
158.7
NGC 2841
14.60
73.7
152.6
NGC 2903
9.46
67
−155
NGC 2976
3.63
64.5
−25.5
NGC 3034
3.53
81
68
NGC 3077
3.81
38.9
63.8
NGC 3184
8.7
21
−174
NGC 3198
13.40
71.5−145.0NGC 3351
10.7
41
−168
NGC 3521
14.20
63
−19
NGC 3627
9.04
52
176
NGC 3938
17.9
20.9−154.0
NGC 42142.93
30
65
NGC 4254
16.5
42
66
NGC 4321
16.5
27
138
NGC 4536
16.5
64.2
−54.5
NGC 4559
7.31
63.1
−36.8
NGC 4569
16.5
64
22
NGC 4579
16.5
41.7
92.1
NGC 4736
4.3
40−61
NGC 5055
9.04
61
98
NGC 5194
7.7
20
176
NGC 5457
7.2
18
42
NGC 5713
19.5
33
−157
NGC 6946
5.5
40
−118
NGC 7331
13.90
75.8
167.7

Res.
[kpc]
(4)
1.6
0.74
2.3
2.4
1.2
0.78
0.30
0.34
0.31
0.72
1.1
0.88
1.2
0.75
1.5
0.24
1.4
1.4
1.4
0.60
1.4
1.4
0.4
0.75
0.63
0.59
1.6
0.5
1.1

12 CO(1–0) ref.

(5)
S19
S19
S19
S19
S19
S19
S19
S19
S19
K07
S19
K07
S19
S19
S19
S19
K07
K07
S19
S19
K07
S19
K07
S19
K07
K07
S19
K07
S19

(1) Adopted distance. (2) Inclination angle of the disk. (3)Position angle of the major axis of the disk for the redshifted side(against the north direction, the positive values correspond to thecounterclockwise direction). (4) The linear scale corresponded tothe angular resolution of 17′′ along the major axis of the disk. (5)References of 12 CO(J = 1–0) data. References of D, i, P.A. are thesame as in S19 or K07.

the position. This methodology does not induce any
biases for 12 CO(J = 1–0) and 12 CO(J = 2–1) integratedintensities because the sensitivities of the 12 CO(J = 2–1)
data are much better than those of 12 CO(J = 1–0). The
threshold to evaluate each channel as a ‘signal’ or a ‘noise’is set as 3 σ, where σ is the root mean square (R.M.S.)
measured in the defined emission-free velocity range beforehand.
The samples in this study consist of 29 galaxies thatare overlapped between S19 + K07, and L09. They arelisted in table 1. For the overlapped galaxies between S19
and K07 (NGC 2903, NGC 3351, NGC 3521, NGC 3627,
NGC 5055), we used S19 data except for NGC 3351 because the baseline of the S19 data for this galaxy is heavily

Publications of the Astronomical Society of Japan, (2018), Vol. 00, No. 0

undulated.

2.2 Intensity accuracy of CO data regarding
calibration and pointing error
Intensity accuracy of CO data is important to study R2/1
because its contrast is relatively small (usually R2/1 = 0.4–
1.0) as argued in Koda et al. (2012, 2020). Therefore, calibration and pointing error is an issue in this paper. We
demonstrated how intensity of 12 CO(J = 1–0) data is accurate with overlapped 4 galaxies (NGC 2903, NGC 3521,
NGC 3627, NGC 5055) between S19 and K07. Although
NGC 3351 is an overlapped galaxy, the baseline of thisgalaxy is heavily undulated and thus, we excluded thisgalaxy to test intensity consistency. Both S19 and K07
data was regridded and the baseline was subtracted in thesame way described in the last subsection.
We firstly tested consistency of total integratedintensity within the whole disk (i.e., total flux) for S19 andK07 data and integrated intensity at position-to-positionin the original resolution (17′′ ) and grid size (8′′ ). The
left and center panel of figure 1 shows correlations of total integrated-intensities and integrated intensities at eachpixel, respectively. The threshold was set to be 5 σ in thecentral panel. The diﬀerence of total integrated-intensity
is at most ∼ 10%. The scatter of intensity at position-toposition is ∼ 25% in the R.M.S. level within each galaxy.
Hence, calibration error of 12 CO(J = 1–0) used in this paper is up to 10% and intensity accuracy including pointing
error and calibration error is 25% at the original resolution.
In section 3.3 and 4.1, we use convolved CO data sothat the spatial resolution and grid size are fixed to 1.5 kpc
and 650 pc, respectively. In addition, we stacked spectra
within concentric annuli in disks and galactic structures inanalyses of section 4.2. Thus, we next tested consistencyof convolved S19 and K07 data to match the resolution of
1.5 kpc and grid size of 650 pc. The right panel of figure 1
shows consistency of integrated intensity between S19 andK07 for convolved data. The scatter at position-to-positionin this case is ∼ 15% in each galaxy. Therefore, intensity
error combining calibration and pointing error in section
3.3 and 4.1 is 15%. Since in stacking analysis, spectra arestacked in a large area (galactic components and concentric
annuli whose width is r25 /8 where r25 is B-band isophotal
radius at 25 mag arcsec−2 ), intensity error due to pointing
error will be negligible.
We would like to note that intensity accuracy of
CO(J = 1–0) against 12 CO(J = 1–0) is relatively good
because 13 CO(J = 1–0) data was taken simultaneouslywith 12 CO(J = 1–0) in COMING observations. In addition, since COMING applied the On-The-Fly (OTF) mode
13

5

in their observation, while observation in K07 applied the
Position-Switch, calibration and pointing accuracy of S19
would be better than that of K07.
We could not test how calibration/pointing error of
CO(J = 2–1) data is in the same way of S19 andK07 because there is no available archival data of theline. However, L09 mentioned that daily variations of
12
CO(J = 2–1) intensity at high S/N regions is 20%.
Therefore, intensity error of 12 CO(J = 2–1) combining calibration and pointing error is 20%, which is quite better than that of 12 CO(J = 1–0). Assuming the fraction of contribution by pointing error is the same as the
12
CO(J = 1–0) case, calibration error of 12 CO(J = 2–1)
will be ∼ 8%. Hence, there will be also calibration error of ∼ 10% in 12 CO(J = 2–1) data, which is common
in short millimeter-wave observations. Similarly, intensity error due to calibration/pointing error in convolved
12
CO(J = 2–1) data will be ∼ 12%. To summarize above
descriptions, R2/1 error due to calibration error is 13%,due to calibration+pointing error at original angular resolution is 32%, and at fixed spatial resolution and grid sizeis 19%, respectively.
12

2.3 Data in other wavelengths
Star-formation rate (SFR) was derived from FUV and 22µm band intensity based on the following equation by
Casasola et al. (2017) and Leroy et al. (2008) that adopted
the Kroupa initial mass function (IMF; Kroupa 2001) aswith the method in other COMING papers (e.g., Muraoka
et al. 2019; Takeuchi et al. 2020 in prep.):(

ΣSFR
M⊙ yr−1 kpc−2

)

(

[
−3

=1.59 cos i 3.2 × 10(−2

+ 8.1 × 10

I22µm
MJy sr−1

IFUV
MJy sr−1

)

)]

,

(3)

where I22µm and IFUV are intensities of the 22-µm andFUV band. The FUV maps were obtained with the
GALEX Ultraviolet Atlas of Nearby Galaxies (Gil de Paz
et al. 2007) and were retrieved from the NASA/IPAC
Extragalactic Database (NED). The 22-µm maps obtained with the WISE band 4 were retrieved from theNASA/IPAC Infrared Science Archive.
In addition, the IR color that represents dust temperature is used as an indicator of ISM conditions. To measure
the IR color in many galaxies as much as possible, we used
the intensity ratio of the 70-µm to 160-µm band obtainedwith Herschel/PACS. This filter selection reduces the sample number of galaxies because of a lack of samples in the
far-infrared range.

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Publications of the Astronomical Society of Japan, (2018), Vol. 00, No. 0

Fig. 1. Consistency of integrated intensity for NGC 2903, NGC 3521, NGC 3627, and NGC 5055 between S19 and K07 summing up within the whole disk,
which corresponds to total flux (left), at the original resolution and grid size (center) and convolved data so that the resolution and grid size are fixed to 1.5
kpc and 650 pc (right), respectively. Pixels below 5 σ are masked in the center and right panel. The solid, dashed, and dotted lines in each panel indicateinconsistency of 0%, ±20%, and ±50%, respectively.

3 Results

by diﬃculties in the calibration method at that time.

3.1 Maps, histograms, statistics, and radial
distribution of R2/1

Figure 3 shows the histogram of R2/1 and the cumulative distribution function for all pixels in all galaxies inthe samples. As shown in the figure, the constant valueof 0.7 assumed in many cases so far is rather large. The
peak of the histogram is in the range of 0.55–0.60; themost frequently appearing value of R2/1 is lower than
0.7. Cumulative fraction also indicates R2/1 = 0.7 is quite
higher in our samples (cumulative fraction at R2/1 = 0.7
is ∼ 70%). This is significant even considering R2/1 errorof 13% due to calibration error of CO data. The median,mean weighted by 12 CO(J = 1–0) integrated-intensity, andstandard deviation of R2/1 combined for all galaxies are
0.61, 0.66, and 0.19, respectively.

Figure 2 shows the R2/1 maps for our sample galaxies in theoriginal resolution of COMING (17′′ ). Here, error of R2/1
is derived from that of I12 CO(1−0) and I12 CO(2−1) basedon propagation of their error. Each galaxy shows various
R2/1 . For example, NGC 2798 and NGC 4736 show higher(> 0.9) R2/1 in large area. R2/1 is low (< 0.6) in mostpositions of NGC 2841 and NGC 3627. Some galaxies havesignificant variations within each galaxy. NGC 2146 andNGC 5713 show an R2/1 gradient from ∼ 1.2 to 0.4. In
NGC 4321, R2/1 is clearly high (>∼ 1.0) in the center andbar ends, low (<0.6)
ininter-arms,
and intermediate (0.7–∼0.8) in arms. In NGC 3351 and NGC 4579, R2/1 is low inthe ring-like structure, whereas R2/1 is high in the center.
Some galaxies show gradation of R2/1 from a side to theother (e.g., NGC 2146, NGC 2798, NGC 5713, NGC 7331).
We tested these gradations are due to the systematic
pointing oﬀset between 12 CO(J = 1–0) and 12 CO(J = 2–
1) observations with spectra at some doubtful positions
and residual maps of the first moment maps derived fromthe lines. According to the test, there is no indicationof systematic pointing oﬀset. Gradations of R2/1 may
be caused by interactions (e.g., NGC 2146, NGC 2798,
NGC 5713) or appearance of disk due to three-dimensional
warp (NGC 7331).
Note that the result for NGC 5194 is not consistent
with Koda et al. (2012). They reported that intensitiesof 12 CO(J = 1–0) data obtained in K07 (the original map
is from Nakai et al. 1994) for this galaxy is ∼ 2 times higher
than that of Koda et al. (2011). They argued that a calibration error in the data of Nakai et al. (1994) was caused

The median we obtained (R2/1 = 0.61) is slightly lower
than the value (R2/1 = 0.67) reported in Leroy et al. (2013),
while this diﬀerence would not be significant considering R2/1 error due to calibration error is 13% (section
2.2). If this diﬀerence is significant, this discrepancy may
have originated from diﬀerences in observed areas. Most
12
CO(J = 1–0) data Leroy et al. (2013) used are from Useroet al. (2015), which observed specific positions in a galaxy
where 12 CO(J = 2–1) is strong. Their observed areas ineach galaxy usually include the center of the galaxy whereR2/1 tends to be high as mentioned in the next paragraph. These results and statistics of R2/1 such as median, Q2 (R2/1 ), and weighted mean, R2/1 , for each galaxy
are summarized in table 2 with some properties of galaxies related to star formation. The relations between R2/1
and these properties of galaxies are discussed in section
4.1. The histograms of R2/1 for each galaxy are shown inAppendix 1.
Figure 4 shows R2/1 as a function of the galactocentric radius for all galaxies. Both the median and weighted

Publications of the Astronomical Society of Japan, (2018), Vol. 00, No. 0

7

Fig. 2. R2/1 maps (left) and near-infrared images in gray scale (right) of all galaxies in the samples. In R2/1 maps, pixels are masked when either integrated
intensities of 12 CO(J = 1–0) or 12 CO(J = 2–1) at the pixel do not reach 4.5 σ. The middle of the color bar corresponds to R2/1 = 0.7, which is the usuallyassumed value for a constant R2/1 . Open circles in the bottom left corner in each panel indicate the angular resolution of 17′′ . Black contours indicate theintegrated intensity of 12 CO(J = 2–1) at levels 2, 5, 10, 20, 50, 100, and 200 K km s−1 . The reference of near-infrared data is Spitzer/IRAC 3.6-µm images
obtained by the S4 G survey (Sheth et al. 2010) except for NGC 2146. For NGC 2146, the WISE 3.4-µm image is used alternatively.

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Publications of the Astronomical Society of Japan, (2018), Vol. 00, No. 0

Fig. 2. (Continued.)mean of R2/1 in the disk region (r > 2 kpc) are nearly constant at 0.60. Although R2/1 in the disk is lower than 0.7,
it tends to exceed 0.7 in central regions. Both the medianand weighted mean is 0.83 in the inner 0.75 kpc (the innermost bin of the bottom panel of figure 4). The usuallyassumed constant value of 0.7 for R2/1 is common only forPublications of the Astronomical Society of Japan, (2018), Vol. 00, No. 0

9

Fig. 2. (Continued.)

the transition region of the galactic center and the disk (1<kpc <∼ r ∼ 2 kpc).

3.2 Effects of R2/1 on molecular gas mass derived
from 12 CO(J = 2–1)
As eﬀects originated from the assumption that R2/1 is aconstant, we report that how molecular gas mass is under-

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Publications of the Astronomical Society of Japan, (2018), Vol. 00, No. 0

Table 2. Statistics of R2/1 and properties of the samples.
galaxyall
NGC 337
NGC 628
NGC 2146
NGC 2798
NGC 2841
NGC 2903
NGC 2976
NGC 3034
NGC 3077
NGC 3184
NGC 3198
NGC 3351
NGC 3521
NGC 3627
NGC 3938
NGC 4214
NGC 4254
NGC 4321
NGC 4536
NGC 4559
NGC 4569
NGC 4579
NGC 4736
NGC 5055
NGC 5194
NGC 5457
NGC 5713
NGC 6946
NGC 7331

Q2 (R2/1 )R2/1

σ(R2/1 )

(1)
0.61
—∗
0.54
0.66
0.99
0.51
0.59
0.67
0.56
—∗
0.55
0.46
0.48
0.61
0.46
0.56
—∗
0.70
0.76
0.79
—∗
0.76
0.50
0.84
0.54
0.40‡
0.62
0.72
0.67
0.53

(2)
0.66
—∗
0.54
0.73
1.0
0.50
0.62
0.67
0.67
—∗
0.56
0.47
0.73
0.63
0.46
0.56
—∗
0.72
0.83
0.84
—∗
0.89
0.63
0.88
0.56
0.41‡
0.64
0.80
0.71
0.55

(3)
0.19
—∗
0.14
0.23
0.33
0.12
0.11
0.20
0.15
—∗
0.14
0.10
0.21
0.12
0.10
0.11
—∗
0.17
0.18
0.24
—∗
0.25
0.20
0.24
0.11
0.16‡
0.18
0.24
0.17
0.17

Σmol
[M⊙ pc−2 ]
(4)
—
—∗
17.5
113
44.0
4.34
21.8
3.13
23.2
—∗
14.5
6.37
19.4
31.2
39.0
20.5
—∗
39.8
26.7
54.7
—∗
27.5
20.1
20.8
18.2
—§
15.3
61.3
29.6
18.3

ΣSFR
[10−2 M⊙ yr−1 kpc−2 ]
(5)
—
—∗
0.962
27.9
17.8
0.287
1.93
0.527
3.75
—∗
0.756
0.915
3.20
2.17
2.96
1.43
—∗
3.27
2.00
11.5
—∗
1.63
0.890
2.90
0.87
2.98
0.89
9.35
1.85
1.11

τdep
[Gyr]
(6)
—
—∗
1.82
0.406
0.248
1.51
1.13
0.594
0.617
—∗
1.91
0.697
0.608
1.43
1.32
1.44
—∗
1.21
1.33
0.474
—∗
1.69
2.25
0.718
2.11
—§
1.72
0.656
1.60
1.65

I70µm /I160µm
(7)
—
—∗
0.363
1.22
1.45
0.210
—†
0.483
1.43
—∗
0.307
0.493
0.765
0.423
0.543
0.409
—∗
0.483
0.421
1.18
—∗
0.420
0.396
0.870
0.330
0.436
0.336
0.804
0.491
0.426

(1) Median of R2/1 . (2) Mean of R2/1 weighted by integrated intensity of 12 CO(J = 1–0) averaged over the pixels
where R2/1 is significantly measured (cf. figure 2). (3) Standard deviation of R2/1 . (4)–(5) Mean surface density ofmolecular gas and SFR. The area used to derive these means are the same as column (2). (6) Mean depletion time
derived as total molecular gas mass over total SFR within the area used in column (2). (7) Mean IR color derived as
total luminosity of 70 µm over that of 160 µm within the area used in column (2). ∗ There are few or no pixels tomeasure R2/1 . † Archival data is not available. ‡ There may be calibration error of CO data. § Not derived due tothe possibility of calibration error.

estimated or overestimated and how the scatter of molecular gas surface density within a galaxy changes. We
adopted the standard CO-to-H2 conversion factor XCO of
2.0 × 1020 cm−2 (K km s−1 )−1 (Bolatto et al. 2013) for theentire area of all galaxies based on the widely used method.
The top panel of figure 5 shows how the total molecular gas mass within a galaxy changes (rate of change
tot
in total molecular gas mass; ∆Mmol) when the molecular12
gas mass is derived from CO(J = 2–1) with the R2/1 oftot
0.7 compared with the case wherein Mmol
is derived fromtot
CO(J = 1–0). For instance, ∆Mmol = −20% indicates thatthe total molecular gas mass derived from 12 CO(J = 2–1) isunderestimated by 20%. NGC 337, NGC 3077, NGC 4214,

and NGC 4559 are omitted because R2/1 cannot be significantly measured in most positions in these galaxies (figure2) and NGC 5194 is omitted due to the possibility of thecalibration problem as mentioned in section 3.1.
As R2/1 deviates from 0.7 (table 2), the total molecular gas mass within a galaxy is underestimated or overestimated when the molecular gas mass is derived from
12
CO(J = 2–1) assuming the constant R2/1 of 0.7. For
instance, the total molecular gas mass is underestimatedby ∼ 30% for galaxies that show low R2/1 (<∼ 0.50; e.g.,
NGC 2841, NGC 3198). Further, it is overestimated by ∼30% when R2/1 is high (>∼ 0.9; e.g., NGC 2798, NGC 4569,
NGC 4736). For the most deviated galaxy, the molecularPublications of the Astronomical Society of Japan, (2018), Vol. 00, No. 0

11

Fig. 3. Histogram of R2/1 for all pixels of all galaxies. The solid line shows
the cumulative distribution function and the dashed line indicates R2/1 =0.7.

gas mass is underestimated by ∼ 35% in NGC 3627.
The middle panel of figure 5 shows the change rateof standard deviation for log Σmol , ∆[σ(log Σmol )], ineach galaxy when R2/1 is assumed to be the constant.
∆[σ(log Σmol )] is positive for all galaxies and exceeds
30% in some galaxies (NGC 628, NGC 2798, NGC 2976,
NGC 3351, NGC 5713, and NGC 7331), and the highest
one reaches 120% (NGC 2798). When the scatter of R2/1 ,σ(R2/1 ), is relatively large (>∼ 0.2) or when R2/1 deviatesfrom 0.7, ∆[σ(log Σmol )] tends to be large. In contrast,
when σ(R2/1 ) is small, ∆[σ(log Σmol )] is also small (e.g.,
NGC 3627). These results indicate that not only the total
molecular gas mass but also molecular gas surface density
and its relevant quantities in positions-to-position are misled by the assumption of the constant R2/1 . This becomes
an issue when spatially resolved data are used, which has
been the standard recently.

3.3 Effects of R2/1 on the Kennicutt–Schmidt
relation derived from 12 CO(J = 2–1)
Next, we investigate how the Kennicutt–Schmidt (K–S)
relation (Schmidt 1959; Kennicutt 1989) changes when themolecular gas surface density is derived from 12 CO(J = 2–
1) and the fixed R2/1 compared with that derived from
12
CO(J = 1–0). The molecular K–S relation is described
as

(

log

ΣSFR
M⊙ yr−1 kpc−2)(= N logΣmolM⊙ pc−2

)

+ A,

(4)

where N is the index and A is the intercept on the doublelogarithmic plot. Several studies suggested that this relation, in particular N , reflects the processes of star for-

Fig. 4. Radial distribution of R2/1 for all galaxies. The dashed line in theboth panels indicates R2/1 = 0.7. (Top) Scatter plot of R2/1 against thegalactocentric radius. The colors indicate the cumulative fraction of data.
The typical error of R2/1 is shown on the top right with the open circle marker. (Bottom) Box plot for the top panel. Each bin is 0.75 kpc inwidth. Cross markers show mean R2/1 in a bin weighted by 12 CO(J = 1–0)
integrated-intensity. The upper whisker extends up to the maximum value
and the lower whisker extends down to the minimum value in each bin unless the maximum value is less than Q3 + 1.5IQR and the minimum value islarger than Q1 − 1.5IQR, where Q1 is the 25th percentile, Q3 is 75th percentile, and IQR is the interquartile range defined as Q3 − Q1 . Otherwise,
the upper whisker extends up to Q3 + 1.5IQR and the lower whisker extends down to Q1 − 1.5IQR without outliers for simplicity.

mation in galaxies (e.g., Elmegreen 2002; Krumholz, &McKee 2005; Komugi et al. 2006; Tan 2010; Takeuchi, T.,
T. et al. 2020 in preparation). Therefore, we focused on
how N changes in this study.
When the spatial resolution is changed, the result of the
K–S relation also changes (Onodera et al. 2010). Thus, wesmoothed 12 CO cubes and ΣSFR maps so that the spatial
resolution is the same value of 1.5 kpc for all galaxies ex-

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Publications of the Astronomical Society of Japan, (2018), Vol. 00, No. 0

tot
Fig. 5. Rate of change in the total molecular gas mass ∆Mmol(top), standard deviation of molecular gas surface density ∆[σ(log Σmol )] (middle), and index
of the K–S relation ∆N (bottom) in each galaxy.

cept for NGC 337, NGC 2146, and NGC 5713. Since theoriginal spatial resolution of these three galaxies is larger
than 1.5 kpc (table 1), we did not smooth them. We also
regridded 12 CO cubes and ΣSFR maps to fix spatial sampling (i.e., pixel size) for all galaxies. The pixel size is set
to 650 pc which is slightly smaller than the Nyquist sampling. For convolved and regridded data, pixels whose S/Nof integrated-intensities does not reach 4.5 σ were masked.
We made K–S plots from 12 CO(J = 1–0) by adopting thestandard XCO of 2.0 × 1020 cm−2 (K km s−1 )−1 for theentire area of all galaxies according to the widely usedmethod. The K–S plots from 12 CO(J = 2–1) are obtained by converting 12 CO(J = 2–1) intensity into that of
12
CO(J = 1–0) with the constant R2/1 of 0.7, which is thesame method employed in previous studies about the K–S
relation with 12 CO(J = 2–1) (e.g., Bigiel et al. 2008).
We fitted the K–S relation with the ordinary leastsquares (OLS) bisector method (Isobe et al. 1990) and
derived N and A of the relation made with 12 CO(J = 1–0) and 12 CO(J = 2–1), respectively. Indices derived from
12
CO(J = 1–0) and 12 CO(J = 2–1) (hereafter, N1−0 andN2−1 , respectively), intercepts from the two 12 CO lines(similarly, A1−0 and A2−1 , respectively), and their rates
of change (∆N and ∆A) are listed in table 3. The bottom
panel of figure 5 indicates the change rate of indices; figure
6 shows the correlation plot of N2−1 against N1−0 . The K–
S plots of each galaxy are shown in figure 7. We could not
fit the K–S relation for NGC 337, NGC 3077, NGC 4214,

Publications of the Astronomical Society of Japan, (2018), Vol. 00, No. 0

Table 3. Fitted parameters of the K–S relation.
galaxy
N1−0
N2−1

all
NGC 337
NGC 628
NGC 2146∗
NGC 2798
NGC 2841
NGC 2903
NGC 2976
NGC 3034
NGC 3077
NGC 3184
NGC 3198
NGC 3351
NGC 3521
NGC 3627
NGC 3938
NGC 4214
NGC 4254
NGC 4321
NGC 4536
NGC 4559
NGC 4569
NGC 4579
NGC 4736
NGC 5055
NGC 5457
NGC 5713∗
NGC 6946
NGC 7331(1)
1.299 ± 0.005—
1.08 ± 0.03
1.29 ± 0.02
0.95 ± 0.05
0.5 ± 0.1
0.95 ± 0.02
0.99 ± 0.09
1.13 ± 0.03—
1.04 ± 0.04
1.26 ± 0.06
1.81 ± 0.05
0.89 ± 0.02
1.07 ± 0.02
0.78 ± 0.03—
0.98 ± 0.01
0.90 ± 0.01
0.81 ± 0.04—
1.15 ± 0.02
1.31 ± 0.04
1.13 ± 0.05
0.969 ± 0.009
1.21 ± 0.04
1.25 ± 0.03
1.24 ± 0.02
1.07 ± 0.02

(2)
1.132 ± 0.004—
0.96 ± 0.02
1.07 ± 0.02
0.58 ± 0.04
0.5 ± 0.2
0.87 ± 0.02
0.8 ± 0.1
1.01 ± 0.02—
0.93 ± 0.03
1.28 ± 0.06
1.35 ± 0.03
0.82 ± 0.01
1.05 ± 0.02
0.67 ± 0.02—
0.872 ± 0.008
0.79 ± 0.01
0.65 ± 0.03—
0.91 ± 0.02
0.86 ± 0.03
0.96 ± 0.03
0.866 ± 0.007
1.35 ± 0.03
0.99 ± 0.01
1.19 ± 0.02
0.90 ± 0.01

∆N
[%]
(3)
−12.8
—
−11.5
−17.2
−38.8
−0.24
−8.18
−22.7
−10.9
—
−10.2
1.48
−25.7
−7.77
−1.73
−13.6
—
−10.8
−12.5
−19.7
—
−20.6
−34.2
−15.7
−10.6
10.9
−20.2
−3.56
−15.8

13

A1−0

A2−1

(4)
−3.537 ± 0.008—−3.37 ± 0.05
−3.24 ± 0.03
−2.37 ± 0.06
−2.9 ± 0.4−2.99 ± 0.03
−2.8 ± 0.2−2.99 ± 0.04—
−3.33 ± 0.07
−3.06 ± 0.08
−4.02 ± 0.07
−2.98 ± 0.03
−3.23 ± 0.04
−2.86 ± 0.05—
−3.08 ± 0.02
−2.98 ± 0.02
−2.33 ± 0.06—
−3.46 ± 0.04
−3.78 ± 0.06
−3.04 ± 0.07
−3.28 ± 0.02
−3.55 ± 0.06
−3.28 ± 0.05
−3.58 ± 0.03
−3.31 ± 0.03

(5)
−3.253 ± 0.007—−3.10 ± 0.04
−2.77 ± 0.03
−1.81 ± 0.04
−2.8 ± 0.4−2.82 ± 0.03
−2.7 ± 0.2−2.77 ± 0.04—
−3.12 ± 0.05
−2.90 ± 0.08
−3.34 ± 0.04
−2.83 ± 0.02
−3.01 ± 0.03
−2.65 ± 0.04—
−2.93 ± 0.01
−2.87 ± 0.02
−2.10 ± 0.03—
−3.19 ± 0.04
−3.12 ± 0.05
−2.82 ± 0.05
−3.04 ± 0.01
−3.58 ± 0.04
−2.87 ± 0.02
−3.49 ± 0.03
−2.99 ± 0.02

∆A
[%]
(6)
−8.02
—
−8.05
−14.3
−23.5
−2.87
−5.64
−1.54
−7.27
—
−6.21
−5.22
−16.9
−4.98
−6.89
−7.19
—
−4.94
−3.92
−9.81
—
−7.89
−17.5
−7.16
−7.36
1.07
−12.5
−2.52
−9.7

(1) Index of the K–S relation derived from 12 CO(J = 1–0). (2) Index of the K–S relation derived from
12
CO(J = 2–1) and the constant R2/1 of 0.7. (3) Change rate of index. (4) Intercept of the K–S relation
derived from 12 CO(J = 1–0). (5) Intercept of the K–S relation derived from 12 CO(J = 2–1) and the constantR2/1 of 0.7. (6) Change rate of intercept. ∗ The spatial resolution is diﬀerent from 1.5 kpc (cf. table 1).

and NGC 4559 because the number of pixels at which R2/1
is significantly measured is not enough. Therefore, thesefour galaxies were excluded from the K–S relation of allcompiled galaxies in the samples (the last panel in figure
7).
We find that indices decrease typically by 10–20%, up
to 39%, when the relation is derived from 12 CO(J = 2–
1) with the constant R2/1 = 0.7 in 17 galaxies. The K–
S relation using molecular gas surface density derived bythis method produces a lower index than that derived by
12
CO(J = 1–0) for most galaxies. This tendency is thesame as Momose et al. (2013) that discussed the discrepancy between their super-linear slope of the K–S relation
derived by 12 CO(J = 1–0) and the linear slope derived by
12
CO(J = 2–1) reported in Bigiel et al. (2008). The significant change (∆N < −20%) of the index is shown in

NGC 2798, NGC 2976, and NGC 3351. In these galaxies, σ(R2/1 ) within a galaxy tends to be relatively larger
than others (table 2). When the variation of R2/1 in agalaxy is small (e.g., NGC 3198, NGC 3627), ∆N is small(|∆N | <∼ 2%). The diﬀerences of the K–S relation for all
sample galaxies also shows a lower index (∆N = −13%).
We interpret these underestimated indices of the K–S
relation derived from 12 CO(J = 2–1) as follows. R2/1 isoften higher than 0.7 when ΣSFR and Σmol are high (thetop right on the K–S plot), while R2/1 is prone to be lower
than 0.7 when ΣSFR and Σmol are low (the bottom left
on the K–S plot). Here, we mean that “Σmol ” is derived
from 12 CO(J = 1–0). As a result, molecular gas surface
density derived from 12 CO(J = 2–1) with the fixed R2/1 of
0.7 is overestimated (data points move to right in the plot)
where ΣSFR and Σmol are high, and it is underestimated14

Publications of the Astronomical Society of Japan, (2018), Vol. 00, No. 0

4 Discussion
4.1 Correlations of R2/1 with basic properties ofgalaxies
To investigate how R2/1 changes depending on basic properties of galaxies such as ΣSFR , correlations of R2/1 withrepresentative quantities are examined in this section. The
spatial resolution and grid spacing are fixed to be 1.5 kpc
and 650 pc except for NGC 337, NGC 2146, and NGC 5713,
similar to the K–S relation case (these three galaxies wereanalyzed with their original resolution as shown in table
1).

Fig. 6. Indices of the K–S relation derived from 12 CO(J = 2–1) with the constant R2/1 of 0.7 (N2−1 ) against that from 12 CO(J = 1–0) (N1−0 ). The
diagonal dashed line indicates N2−1 = N1−0 . Dotted lines indicate that
N2−1 is higher and lower by 20% than N1−0 .

(data points move to left in the plot) where ΣSFR and Σmol
are low (we examine correlations of R2/1 , ΣSFR , and Σmolin section 4.1; figures 8 and 9). This becomes prominent
in galaxies whose σ(R2/1 ) is large, as seen in the plot of
NGC 2798, NGC 3351, and NGC 4579 of figure 7. We notethat indices are underestimated even if R2/1 is assumed as
the mean or median of R2/1 in a galaxy.
When the K–S relation is derived from higher-J 12 COlines such as 12 CO(J = 3–2), the same tendency of lower
indices is seen (Morokuma-Matsui & Muraoka 2017).
Dense gas tracers also produce nearly linear K–S relations, whereas 12 CO(J = 1–0) produces super-linear relations (e.g., Gao et al. 2007; Kennicutt 1989). According
to these results, it seems that indices of the K–S relation
become low when the relation is derived from the molecular gas, that is more related to star-formation activity.
We conclude that the K–S relation, the basic relation ofmolecular gas with star formation, will be misinterpreted,in addition to total molecular gas within a galaxy and surface density of molecular gas when 12 CO(J = 2–1) is used
as a molecular gas tracer with a fixed R2/1 . Previous studies of the K–S relation using molecular gas surface density
derived from this method would underestimate their indices.

First, we describe the correlation of R2/1 with ΣSFR .
The top panel of figure 8 shows the correlation plot of R2/1
against ΣSFR for spatially resolved data and integrated
data over the pixels where R2/1 is significantly measured(table 2, figure 2). The bottom panel of the figure shows
the box plot for the top panel binned with 0.2 dex and themean R2/1 weighted by 12 CO(J = 1–0) integrated-intensity
in each bin. The Spearman’s rank correlation coeﬃcient(ρs ) for the spatially resolved case and the integrated one
are 0.47 and 0.51, respectively. Although the scatter israther large, Q2 (R2/1 ) and R2/1 in each bin clearly increase from ∼ 0.4 to ∼ 0.9 as ΣSFR increases. This result is consistent with Koda et al. (2012) and Koda etal. (2020), whereas the spatial resolution of the former
is approximately twice higher than ours. From this result, possibilities are as follows: one main physical factor
to change R2/1 can be star-formation feedback (i.e., highR2/1 is a result and high ΣSFR is a cause) or R2/1 becomeshigh because the molecular gas is dense and as a result,the star-formation rate is high (i.e., high-density condition is a cause and high R2/1 and high ΣSFR are results).
Otherwise, this correlation might be just mere coincidence.
Second, we investigate the dependence of R2/1 on Σmolas shown in figure 9. Mean Σmol is derived by the same
method of that for mean ΣSFR case. R2/1 loosely increases
from ∼ 0.55 to ∼ 0.8 as Σmol increases according to the bottom panel, while there seems to be no clear tendency according to the scatter plot in the top panel. The ρs for the
spatially resolved and global result is 0.28 and 0.51, respectively. Since the tendency of R2/1 against ΣSFR is clearer
than that against Σmol , the lower indices of the K–S relation using molecular gas mass derived from 12 CO(J = 2–1)
(discussed in section 3.3) are mainly due to fluctuated R2/1
by ΣSFR rather than Σmol .
Third, the correlation between R2/1 and the depletiontime of molecular gas (τdep ) is examined. The τdep is derived as the following equation:

(

τdep
yr

)

(

=

Σmol
M⊙ pc−2)/(

ΣSFRM⊙ yr−1 pc−2

)

.

(5)

Publications of the Astronomical Society of Japan, (2018), Vol. 00, No. 0

15

Fig. 7. The K–S relation of the sample galaxies derived from 12 CO(J = 2–1) assuming R2/1 = 0.7 (top panels, blue plots) and from 12 CO(J = 1–0) (bottom
panels, black plots). The index of each panel is provided on the top left. Solid lines and dashed lines indicate regression lines of the panel and the other panel,
respectively. Dotted lines indicate that the depletion time of molecular gas is 10−1 Gyr, 100 Gyr, and 101 Gyr from bottom to top. The K–S plot of all galaxies(excluding NGC 337, NGC 3077, NGC 4214, NGC 4559, and NGC 5194) is shown in the panel at the bottom right corner.

16

Publications of the Astronomical Society of Japan, (2018), Vol. 00, No. 0

Fig. 8. (Top) Correlation of spatially resolved data (circles) and integrated
data over the whole galaxy (open orange diamonds) of R2/1 and ΣSFR .
The colors indicate the cumulative fraction of data points. The typical errorof R2/1 is shown on the top right in the panel. Errors of ΣSFR is negligible.
(Bottom) Box plot and R2/1 in each bin (cross markers) for the top panel.
The bin width is 0.2 dex. Settings of the box plot are the same as figure 4.

Figure 10 shows the relation between R2/1 and τdep in thesame way as figure 8. Mean τdep is derived by dividing
total molecular gas mass by total SFR within the pixels
where R2/1 is significantly measured. Both the top andbottom panels show significantly decreased R2/1 as τdep
increases. This relation is also consistent with Koda et al.
(2012) (note that their horizontal axis is proportional to
SFE that is equivalent to the reciprocal number of τdep ).
The ρs for the spatially resolved and integrated case is−0.47 and −0.50, respectively. Q2 (R2/1 ) and R2/1 de-Fig. 9. The same as figure 8 but for Σmol .

crease from ∼ 1.2 to ∼ 0.45 when τdep increases from ∼ 0.1
Gyr to ∼ 5 Gyr. Therefore, R2/1 may be related to aneﬃcient conversion from molecular gas into stars becauseof the dense condition (e.g., Muraoka et al. 2016; Yajima
et al. 2019). As another possibility, molecular gas is easily warmed by active star formation (heat source) withpoor molecular gas (low heat capacity) when τdep is short.
These possibilities are relevant to the dense or warm conditions of molecular gas likely mentioned in the ΣSFR case.
Finally, the correlation of R2/1 with IR color is examined. The IR color is derived from Herschel/PACS 70-µm
and 160-µm intensity ratios. Usually, the peak of spectralenergy distribution (SED) for cool dust, which is dominant
in ISM, is around the 160-µm band. Therefore, this band

Publications of the Astronomical Society of Japan, (2018), Vol. 00, No. 0

Fig. 10. The same as figure 8 but for τdep .

selection well reflects dust temperature, especially in thepresent case of lacking data of the long-wavelength side formost of the sample galaxies. Cool dust temperature may
also be a good probe of ISM conditions. Since there is
no archival data of PACS for NGC 2903, we do not derive
IR color for this galaxy. Figure 11 shows the correlation
between R2/1 and IR color and the box plot in the samemanner as figure 8. The mean IR color is derived from theratio of total intensity of I70µm to that of I160µm within
the pixels where R2/1 is significantly measured. The ρs ofthe spatially resolved and integrated case is 0.39 and 0.49.
Both Q2 (R2/1 ) and R2/1 increase from ∼ 0.4 to ∼ 0.85 as
IR color increases (corresponding dust temperature is from∼ 15 K to ∼ 35 K) similarly to the ΣSFR case. The ten-

17

Fig. 11. The same as figure 8 but for IR color (I70µm /I160µm ). Errors of IR
color is negligible.

dency is consistent with Koda et al. (2020). However, thecorrelation coeﬃcient between R2/1 and IR color is higher
than that for R2/1 and ΣSFR in their paper, whereas it is
not higher (0.47 and 0.39) in our results. This diﬀerence
may be originated from far IR band selection and sample
selection because their resolution is comparable to ours
(their resolution is 1.2 kpc and ours is 1.5 kpc).

4.2 R2/1 and physical properties of molecular gas
4.2.1 R2/1 and 12 CO(J = 1–0)/13 CO(J = 1–0) ratio
In this section, we investigate how properties of molecular gas themselves (such as density and temperature)

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Publications of the Astronomical Society of Japan, (2018), Vol. 00, No. 0

Fig. 12. Regions for spectra stacking in NGC 628: center (red), inner arm
1 (magenta), inner arm 2 (cyan), outer arm 1 (yellow), outer arm 2 (yellow
green), inter-arm 1 (orange), inter-arm 2 (blue), and outer disk (gray). Gray
scale is the integrated-intensity map of 12 CO(J = 2–1) obtained by L09.

Fig. 14. The same as figure 12 but for NGC 3627: center (red), bar (purple), northern bar end (yellow), southern bar end (yellow green), westernarm (cyan), eastern arm (orange), southern stream (blue), northern offset
stream (mint), arm-bar end interacting region (magenta), inter-arm (green),
and outer disk (gray). The reference of 12 CO(J = 2–1) data is the same as
figure 12.

& Solomon 1974; Goldreich & Kwan 1974).
Since 13 CO(J = 1–0) emission is weak compared with
CO lines, we measured the integrated intensity with thevelocity-alignment stacking analysis (Schruba et al. 2011;
Morokuma-Matsui et al. 2015) within concentric annuli
or galactic structures such as arms and the bar. We determined galactic structures for NGC 628, NGC 2903, andNGC 3627 because the structures of these three galaxies
can be clearly seen in the integrated-intensity maps of the12
CO lines. The determined structures are shown in figures
12–14. For other galaxies, the regions for spectra stacking
are determined as concentric annuli whose width is r25 /8.
To align spectra along the velocity axis, we used the firstmoment maps of H I obtained by The H I Nearby Galaxy
Survey (THINGS; Walter et al. 2008) if a galaxy was observed in the survey. The H I first-moment maps enable
us to stack spectra even in outer disks. When H I data is
not available, the first-moment maps of 12 CO(J = 2–1) are
used.
12

Fig. 13. The same as figure 12 but for NGC 2903: center (red), northern bar(purple), southern bar (cyan), northern bar end (yellow green), southern bar
end (yellow), northern arm (orange), southern arm (mint), inter-arm (blue),and outer disk (gray). The reference of 12 CO(J = 2–1) data is the same as
figure 12.

change R2/1 . We obtained 13 CO(J = 1–0) maps of the
COMING galaxies in our samples. Therefore, the number density of molecular gas, n(H2 ), and the kinetic temperature of molecular gas, Tkin , can be derived with a
non-local thermodynamic equilibrium (non-LTE) analysis
with integrated-intensity ratios of the three lines (Scoville

Integrated intensities, integrated-intensity ratios, andfull width at half maximum (FWHM) of stacked spectra are summarized in Appendix 2. The 3 σ lower limitof 12 CO(J = 1–0)/13 CO(J = 1–0) integrated-intensity ratio (hereafter, denoted as R12/13 ) is adopted when S/N of

Publications of the Astronomical Society of Japan, (2018), Vol. 00, No. 0

19tematic diﬀerences of molecular gas properties between thecentral region and the disk influencing R2/1 and R12/13
are seen in the figure. Among galactic structures in disks(arms, inter-arms, and bars etc.), R2/1 tends to be relatively low in bars and inter-arms, and high in arms andbar ends, although the contrast of R2/1 is low (see results ofstacked spectra for NGC 628, NGC 2903, and NGC 3627 in
Appendix 2). In addition, the tendency of R2/1 and R12/13
among these structures roughly follow the disk-phase feature (i.e., R2/1 decreases as R12/13 increases). Previous
studies about R12/13 suggested that high R12/13 indicates
low n(H2 ) (Meier & Turner 2004), high Tkin (Paglione etal. 2001), or low abundance of 13 CO due to selective photodissociation (e.g., Davis 2014). Since R2/1 is also highin galactic centers with active star formation, both highn(H2 ) and high Tkin conditions are possible.
4.2.2 Non-LTE analysis using R2/1
Fig. 15. Correlation of R2/1 with R12/13 measured from stacked spectra.
Black circle markers represent results in disks, blue triangles indicate galactic centers with active star formation (mean ΣSFR in inner r25 /8 or the region defined as “center” is > 0.1 M⊙ yr−1 kpc−2 ; NGC 2146, NGC 2903,
NGC 3034, NGC 3351, NGC 4536, and NGC 5713), and blue squares indicate galactic centers with quiescent star formation (mean ΣSFR in the region
is lower than the value). Black histograms are results of disk regions (blackplots) and blue histograms are results of galactic centers (blue plots). Colorsof tick labels correspond to those of histograms.

To compare R2/1 with intrinsic molecular gas properties,n(H2 ) and Tkin are derived with the non-LTE analysis.
In this study, we made use of the 1D non-LTE radiativetransfer code RADEX (van der Tak et al. 2007). Settings
for RADEX are based on those in Yajima et al. (2019).

Regions where S/N of 13 CO(J = 1–0) is poor (derived
as only the upper limit of integrated intensity) even withstacking are mainly inter-arms and outer disks. Since thearea where 13 CO(J = 1–0) is emitted is much smaller thanthat of 12 CO lines in such regions, a diﬀerent beam-filling
factor may be eﬀective, i.e., the line ratio is no longer aprobe of molecular gas properties.

Input parameters for calculations are R2/1 , R12/13 , column density of 12 CO of all energy levels (N12 CO ), thatof 13 CO (N13 CO ), and FWHM of a GMC’s spectrum(dv). To derive N12 CO and N13 CO from column density of H2 with observed I12 CO(1−0) , abundance ratiosof [12 CO]/[H2 ], [12 CO]/[13 CO], and XCO were basicallyadopted as 8.5 × 10−5 (Pineda et al. 2008), 70 (the solar neighborhood value; Milam et al. 2005), and 2.0 × 1020
cm−2 (K km s−1 )−1 (Bolatto et al. 2013), respectively.
For the central region of galaxies, [12 CO]/[13 CO] and XCO
were also adopted as 40 and 1.0×1020 cm−2 (K km s−1 )−1 ,respectively, to reflect the environment of galactic centers(e.g., Meier & Turner 2001; Oka et al. 2001). The escapeprobability of photon was calculated based on the Sobolev
approximation (Sobolev 1960).

In figure 15, it appears that there are two components(or groups): one is that both R2/1 and R12/13 are highand the other is not so high R2/1 (<∼ 0.7) with various
R12/13 (∼ 7–20). The former largely includes central regions of galaxies with active star formation (mean ΣSFR
within inner r25 /8 or within the region defined as “center”
is higher than 0.1 M⊙ yr−1 kpc−2 ; NGC 2146, NGC 2903,
NGC 3034, NGC 3351, NGC 4536, and NGC 5713). The
latter corresponds to galactic disks and centers with quiescent star formation (mean ΣSFR in the region is lower
than the value above). The same tendency of decreasing R2/1 with increasing R12/13 can be seen in results ofanother survey (Cormier et al. 2018). It is likely that sys-

The FWHM of GMCs dv was estimated by assumingthat dv in a region is proportional to the FWHM of thestacked spectrum in the region as described below. This isbecause molecular gas is a continuous medium and GMCs
do not have a rigid boundary. Thus, internal kinematics of
GMCs is likely to be influenced by dynamics of surrounding gas (i.e., large-scale dynamics), especially in bar ends
and bars where large velocity dispersion can be seen. In
addition, since our velocity resolution is 20 km s−1 andour spatial resolution is a kpc order, which are much wider
than the typical velocity width of GMCs and much larger
than the typical size of them, FWHM of a stacked spectrum, ∆V , reflects velocity dispersion among molecular

13

CO(J = 1–0) integrated-intensity is lower than 3 σ. Prior
to the non-LTE analysis, we discuss the relation of R2/1
and R12/13 as a bare observed quantity. Figure 15 shows
the correlation plot of R2/1 against R12/13 .

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Publications of the Astronomical Society of Japan, (2018), Vol. 00, No. 0

Fig. 16. Correlation of R2/1 with n(H2 ) (left) and Tkin (right) and their histograms. Black circle markers represent results in disks and those of blue filled
triangle and square are galactic centers with active and quiescent star formation as with figure 15. Blue open markers correspond to central regions in which
different [12 CO]/[13 CO] and XCO are adopted. As with the plots, black histograms are results of disk regions and blue histograms are results of galactic
centers. Colors of tick labels correspond to those of histograms. Blue histograms exclude the results for which different [12 CO]/[13 CO] and XCO are adopted(open blue markers).

Way (e.g., Heyer et al. 2009). Next, the dv of 20 km s−1
was adopted corresponding to ∆V of the galaxy center(hereafter, denoted as ∆Vcenter ). This 20 km s−1 is basedon FWHM of GMCs found in the central region of galaxies
and the Milky Way (e.g., Oka et al. 2001; Leroy et al.
2015). Then, the dv for each region (i.e., each annulus or
galactic structure) was calculated by linearly interpolating
or extrapolating with its ∆V , ∆Vdisk , and ∆Vcenter . Thatis, the dv for region i (dvi ) is determined by the following
equation:(dvi
km s−1
where

(

)

=a

∆Vi
km s−1()

a ≡ 20 km s−1 − 5 km s−1
Fig. 17. R2/1 distribution on the Tkin –n(H2 ) plot. Dashed lines indicatethat pressure divided by kB is 103 K cm−3 , 3 × 103 K cm−3 , and 104 K
cm−3 from bottom to top.

clouds within the beam. This is a good indicator of largescale dynamics of molecular gas.
At first, ∆V of a stacked spectrum within the entire
disk in each galaxy was measured (hereafter, this ∆V isdenoted as ∆Vdisk ) and the dv of 5.0 km s−1 was adopted
corresponding to ∆Vdisk . This velocity of 5.0 km s−1 asthe standard of dv in the entire disk was determined basedon the typical FWHM of GMCs in the disk of the Milky

(

(6)

+ b,

/
) [( ∆Vcenter ) ( ∆Vdisk )])km s−1−km s−1, (7)∆Vcenter,(8)
km s−1and ∆Vi is the FWHM of the stacked spectrum in the region. The reason why the dv for the innermost region isfixed to be 20 km s−1 is ∆Vcenter mainly reflects not velocity dispersion in a large scale but the velocity gradient due
to the rigid rotation of the galactic disk. High-resolution
observations support increasing dv as close to the galactic
center in inner disks (e.g., Sun et al. 2020). Note that dv
is not monotonically increases towards the center in outerdisks. Since ∆V in outer disks is almost constant, dv isalso constant (see the result of NGC 5055 in Appendix 2).
b ≡ 20 km s−1 − aPublications of the Astronomical Society of Japan, (2018), Vol. 00, No. 0

Derived n(H2 ), Tkin , and ancillary results of excitation temperature for 12 CO(J = 1–0), 12 CO(J = 2–1), and12(1−0)12(2−1)13(1−0)13
CO(J = 1–0) [Tex
, Tex
, Tex
], and opticaldepth of these lines [τ12(1−0) , τ12(2−1) , τ13(1−0) ] are listed
in table 4. Errors of n(H2 ) and Tkin are derived from errorsof R2/1 and R12/13 . Namely, four pairs of [n(H2 ), Tkin ] areobtained from R2/1 ± dR2/1 and R12/13 ± dR12/13 (wheredR2/1 and dR12/13 are errors of R2/1 and R12/13 , respectively). Errors of n(H2 ), Tkin toward the positive direction
are adopted as max[Xi ,i = 1,2,3,4]−X0 , where X0 is n(H2 )and Tkin derived from R2/1 and R12/13 , and Xi is n(H2 )and Tkin derived from R2/1 ± dR2/1 and R12/13 ± dR12/13 .
Errors of n(H2 ), Tkin toward the negative direction are
adopted as X0 − min[Xi ,i = 1,2,3,4]. Errors of other ancillary quantities such as intrinsic intensities and excitation
temperature are nearly the same factor of errors for n(H2 )and Tkin . There are no solutions of RADEX calculations
in several regions. These are caused by the low S/N of
13
CO(J = 1–0) even with stacking. It is also possible thatthe one-zone model adopted for RADEX is not valid because the area seen in 13 CO(J = 1–0) is much smaller thanthose seen in 12 CO(J = 1–0) and 12 CO(J = 2–1). Based onthese RADEX results, we examined the R2/1 dependence
on n(H2 ) and Tkin as shown in figure 16.
There is a clear tendency that R2/1 increases with Tkin ,while R2/1 seems to decrease with increasing n(H2 ). The
Spearman’s rank correlation for R2/1 and Tkin is 0.67 witha p-value of O(10−9 ) and that for R2/1 and n(H2 ) is −0.36;
however, it is not statistically significant with the significance level of 5% (p-value is 0.06). In addition, the tendency of increased R2/1 with Tkin is not changed evenwhen diﬀerent [12 CO]/[13 CO] and XCO for galactic centers {[12 CO]/[13 CO] = 40 and XCO = 1.0 × 1020 cm−2 (Kkm s−1 )−1 } are adopted. The result indicates that thevariations of R2/1 in galaxies seen in kpc-scale resolutions
reflect the temperature of molecular gas. As discussed in
section 4.1, the positive correlation between R2/1 and ΣSFR
indicates that R2/1 varies depending on Tkin or n(H2 ) [highΣSFR enhances Tkin and R2/1 or high n(H2 ) induces high
ΣSFR and R2/1 ]. Based on the results of the non-LTE
analysis, the correlation implies the former case. Radiation
feedback from stars warms dust and molecular gas directly
and/or dust warms molecular gas; therefore, R2/1 becomes
high, as suggested by Koda et al. (2020).
Moreover, it seems that there are two phases of molecular gas. One is relatively dense (102 –103 cm−3 ) and cold
(5–10 K) with R2/1 <∼ 0.7. Its correlation of R2/1 with
Tkin is tight and steep but no clear correlation with n(H2 ).
The other is the diﬀuse (20–300 cm−3 ), warm (30–200K) with high R2/1 , and it is loosely correlated with Tkinand n(H2 ). The former corresponds to results for disk re-

21

gions and galactic centers with quiescent star formation(low R2/1 and low R12/13 indicated by black markers andblue squares in figure 15). The latter is the central regions of galaxies with active star formation (high R2/1
and high R12/13 ) indicated by blue triangles in the figure. Diﬀerences of molecular gas properties in disks andgalactic centers are tested with the Kolmogorov–Smirnov
test (i.e., for black and blue histograms in figure 16). It
is confirmed that the hypothesis that Tkin and R2/1 are
the same between the disks and galactic centers is rejected
at the significance level of 5%; however, that for n(H2 )cannot be rejected at the same level (p-value is 0.15). In
short, diﬀerences of molecular gas phases in disks and centers are clearly seen in R2/1 and physical properties planes,
especially for Tkin , at the kpc-scale resolutions.
The relation between R2/1 and n(H2 ) seems inconsistent with other studies for GMCs (Sakamoto et al. 1994;
Nishimura et al. 2015; Peñaloza et al. 2018), although thenegative correlation of R2/1 with n(H2 ) is not statisticallysignificant. For instance, R2/1 is high in not only warm
environments but also dense regions such as ridges andfilaments in molecular clouds in these studies. The discrepancy is because spatial scale is quite diﬀerent between
ours (kpc scale) and theirs (order of pc scale), and dynamic
range of characteristic n(H2 ) is much wider for cloud-scalestudies than galactic-scales. If observations with such highspatial resolution for galaxies is conducted, high R2/1 withhigh n(H2 ) would appear. Furthermore, observations formolecular clouds in the Milky Way do not contain highR2/1 and high R12/13 environments (common in galactic
centers with active star formation) that show warm anddiﬀuse conditions via non-LTE calculations. Thus, the discrepancy possibly originated from observed environments(represented on the R2/1 –R12/13 plane). Related to it, thisnegative correlation would be produced by data distribution of the bimodality of molecular gas properties seen in
figure 15.
Moreover, studies of molecular gas in other galactic centers support our results of high R2/1 with warm diﬀuse
molecular gas seen in central regions with active star formation. For example, Meier et al. (2000) suggested that
there are two phases of molecular gas: warm diﬀuse layers
and cold dense clumps in the starburst nucleus of IC 342.
In addition, low-J 12 CO lines, in particular 12 CO(J = 2–1), are dominantly emitted in such warm diﬀuse moleculargas. Israel & Baas (2003) modeled properties of molecular gas in the center of IC 342 and Maﬀei 2 (this galaxy
also has the modest starburst nucleus) with transitionsof 12 CO from J = 1 to J = 4; those of 13 CO from J = 1
to J = 3 and [C I]. Further, they argued the existence of
the warm diﬀuse molecular gas of Tkin ∼ 100–150 K and22

Publications of the Astronomical Society of Japan, (2018), Vol. 00, No. 0n(H2 ) ∼ 102 cm−3 associated with the photon-dominatedregion (PDR), and the cold dense clumps of Tkin ∼ 10–20
K and n(H2 ) ∼ 103 cm−3 . It was also suggested that thiswarm diﬀuse molecular gas accounts for approximately 2/3of the total molecular gas. Our results of physical properties with high R2/1 reflect such hot diﬀuse molecular gas
related to PDR.
Figure 17 shows R2/1 distribution on the Tkin –n(H2 )plot. Most of molecular gas is nearly under the pressure
equilibrium of a few 103 K cm−3 . This figure indicates thatboth Tkin and pressure of molecular gas are important forvariations of R2/1 in galaxies. That is, even when pressure3−3
is so high (>∼ 3 × 10 K cm ), R2/1 is not always high(∼ 0.5–0.6) as long as Tkin is low (<∼ 10 K). Similarly, R2/1
is not always very high (< 0.8) even when Tkin is high3(>
∼ 30 K) as long as pressure is not relatively high (∼ 10−3
K cm ).
Our results of R2/1 and molecular gas properties suggest
an issue of molecular gas mass derived from 12 CO(J = 2–1)
according to fluctuated R2/1 and XCO as follows. Somestudies reported that XCO is lower in galactic centers,(ultra-) luminous infrared galaxies, and mergers than thatin disks (i.e., hosting active star formation; e.g., Oka et al.
2001; Narayanan et al. 2011; Papadopoulos et al. 2012;
Sandstrom et al. 20132 ; Yasuda et al. 2020 in prep).
In these systems, R2/1 should be higher than in normal
disks considering our results (e.g., figure 4, 8, 11, 16,
and 17). In addition, the recent synthetic observationof 12 CO(J = 1–0) and 12 CO(J = 2–1) in a 3D magnetohydrodynamics simulation (Gong et al. 2020) shows that
XCO is low in the environments where R2/1 is high. Hence,
the molecular gas mass derived from 12 CO(J = 2–1) ismore overestimated in active star-formation environments
when the constant R2/1 and XCO are adopted because
Mmol ∝ I12 CO(2−1) × XCO /R2/1 . When R2/1 increases and
XCO decreases, the fluctuation of XCO /R2/1 is amplified.
Based on the reported variations of XCO /R2/1 so far, active star-formation environments lead to more overestimated molecular gas if 12 CO(J = 2–1), constant XCO , andfixed R2/1 are used compared with the 12 CO(J = 1–0) case.

5 Conclusions
We present the variations of 12 CO(J = 2–1)/12 CO(J = 1–0) line ratio (R2/1 ) within and among galaxies, the eﬀects
of the assumption that R2/1 is a constant on the derivationof molecular gas mass, and the properties of molecular gas
2

Sandstrom et al. (2013) assumed the constant R2/1 to derive molecular
gas mass from 12 CO(J = 2–1), however, the tendency of lower CO-to-H2
conversion factors in galactic centers can also be seen in 12 CO(J = 1–0)based studies.

reflecting variations of R2/1 in 24 nearby galaxies on kpc
scales. The main conclusions of this paper are as follows:(1) The median and mean R2/1 weighted by 12 CO(J = 1–0)
integrated-intensity for spatially resolved data of galaxies in our samples are 0.61 and 0.66, respectively, withthe standard deviation of 0.19. R2/1 varies from 0.4 to
0.9 among and within galaxies. While R2/1 in the galactic centers (inner ∼ 1 kpc) is typically higher (∼ 0.8), themedian of R2/1 in disks (exterior to ∼ 2 kpc) is nearly
constant at 0.60.
(2) The total molecular gas mass within a galaxy derived
from 12 CO(J = 2–1) is underestimated or overestimatedby ∼ 20% for most galaxies, and at most by 35%, whenR2/1 is assumed to be the constant of 0.7. In addition,
the scatter of molecular gas surface density (Σmol ) by
12
CO(J = 2–1) within a galaxy increases in all galaxies.
Its change rate exceeds ∼ 30% in some galaxies, and it
is 120% in the highest case when the constant R2/1 isadopted. This increased scatter of Σmol is serious formapping (spatially resolved) observations.
(3) The indices of the Kennicutt–Schmidt relation using
molecular gas surface density derived from 12 CO(J = 2–
1) and R2/1 = 0.7 become lower by 10–20%, up to 39%
compared with that using 12 CO(J = 1–0) for 17 galaxies out of 24. This is because R2/1 tends to be higher
than 0.7 when ΣSFR and Σmol are high while R2/1 isoften lower than 0.7 when ΣSFR and Σmol are low.
Underestimated indices are prominent when the scatter of R2/1 within a galaxy is large.
(4) R2/1 has positive correlations with ΣSFR and IR color
and the negative correlation with depletion time ofmolecular gas. These suggest that R2/1 becomes highby warmed molecular gas from stars (stars influence onmolecular gas properties and R2/1 ). Otherwise, R2/1 ishigh because molecular gas is dense; as a result, starformation is active (molecular gas properties influenceon star formation activity and R2/1 ). There is no clear
tendency between R2/1 and Σmol .
(5) Comparing R2/1 with 12 CO(J = 1–0)/13 CO(J = 1–0)line ratio (R12/13 ) measured within each galactic structure or concentric annulus, there seems to be two components; one is both R2/1 and R12/13 are high, and theother is relatively low R2/1 with various R12/13 . The
former corresponds to molecular gas in galactic centerswith active star formation (mean ΣSFR within inner
r25 /8 or the region defined as “center” is higher than
0.1 M⊙ yr−1 kpc−2 ) and the latter corresponds to thatin disk regions and centers of galaxies with quiescentstar formation (mean ΣSFR in the region is lower than
the above value).
(6) According to the non-LTE analysis, there is a clear ten-Publications of the Astronomical Society of Japan, (2018), Vol. 00, No. 0

dency that R2/1 increases with Tkin ; however, R2/1 andn(H2 ) show a rather negative correlation but it is notstatistically significant. This suggests that variations of
R2/1 on kpc scales imply the temperature of moleculargas. The dependence of R2/1 on n(H2 ) would appear
when the spatial resolution is higher. Stellar radiation
feedback influences molecular gas properties and R2/1 .
The bimodality caused by diﬀerences of properties between galactic centers and disks seen on the R2/1 –R12/13
plane can also be seen on the R2/1 –Tkin and R2/1 –n(H2 )plots. Molecular gas in the centers is warm and diﬀuse,
and its R2/1 has relatively loose correlations between
Tkin and n(H2 ). The disk phase molecular gas is cold,
relatively dense, and its R2/1 is tightly correlated with
Tkin ; however, it has no relation with n(H2 ).
(7) Not only Tkin but also pressure of molecular gas isimportant to understand R2/1 variations in galaxies.
3
Namely, even when pressure is so high (>∼ 3 × 10 K
−3cm ), R2/1 is not always high (∼ 0.5–0.6) as long asTkin is low (<∼ 10 K). Likewise, even when Tkin is high>(∼ 30 K), R2/1 is not always very high (< 0.8) as longas pressure is not relatively high (∼ 103 K cm−3 ).
(8) Considering variations of the CO-to-H2 conversion
factor XCO , molecular gas mass in active starformation environments such as galactic centers and(U)LIRGs is more overestimated when it is derived from
12
CO(J = 2–1) and the constant R2/1 of 0.7. This is because molecular gas mass is ∝ I12 CO(2−1) × XCO /R2/1 ,XCO decreases, and R2/1 increases [where I12 CO(2−1)
is integrated intensity of 12 CO(J = 2–1)]. As a result,fluctuations of XCO /R2/1 are amplified.

Acknowledgments
We are grateful to the anonymous referee for the constructive, meaningful comments and suggestions that significantly improve the manuscript. We also thank thestaﬀ of Nobeyama Radio Observatory for their help
in our observations with the 45-m radio telescope andthe continuous eﬀorts to improve the performance of
the instruments. This work has been partially supported by JSPS Grants-in-Aid for Scientific Research(17H01110, 18K13593, 19H05076). This work has also
been supported in part by the Sumitomo Foundation
Fiscal 2018 Grant for Basic Science Research Projects(180923), and the Collaboration Funding of the Instituteof Statistical Mathematics “New Development of theStudies on Galaxy Evolution with a Method of Data
Science”. The Nobeyama 45-m radio telescope is operated
by Nobeyama Radio Observatory, a branch of National
Astronomical Observatory of Japan. This work made23

use of HERACLES, ‘The HERA CO-Line Extragalactic
Survey’ (Leroy et al. 2009). This research has madeuse of the NASA/IPAC Extragalactic Database, which
is operated by the Jet Propulsion Laboratory, California
Institute of Technology, under contract with the National
Aeronautics and Space Administration. This research has
made use of the NASA/ IPAC Infrared Science Archive,
which is operated by the Jet Propulsion Laboratory,
California Institute of Technology, under contract with the
National Aeronautics and Space Administration. This research also made use of APLpy, an open-source plotting
package for Python (Robitaille, & Bressert 2012). We
would like to thank Editage (www.editage.com) for English
language editing.

Appendix 1 Histograms of R2/1 in eachgalaxyFigure 18 shows histograms of R2/1 in each galaxy for dataof the original resolution of 17′′ .

Appendix 2 Results of stacked spectra
Table 5 summarizes parameters of stacked spectra in eachregion of galaxies.

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24

Publications of the Astronomical Society of Japan, (2018), Vol. 00, No. 0

Table 4. Derived physical properties of molecular gas with the non-LTE analysis.
galaxyregion∗n(H2 )

Tkin[cm−3 ][K]

(1)

NGC 628

centerinner arm1
inner arm2
outer arm2
inter-arm1
center†NGC 2146

centerring1
ring2
center†NGC 2841

τ12(2−1)τ13(1−0)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

6.5+0.9
−0.7

6.3

6.1

4.4

18

22

0.41

8.2+2.5
−1.7

6.9

6.1

3.4

19

26

0.64

8.8+2.2−1.6
4.8+1.3−1.0
7.2+4.5−2.2
8.5+1.9−1.5
210+110
−80
69+71
−29
23+149
−13

7.4

6.6

3.5

20

29

0.7

4.5

4.0

3.3

13

10

0.26

5.9

5.0

3.2

17

20

0.49

7.8

7.2

4.9

9.8

15

0.45

14

14

3.5

18

40

1.6

10

9.4

3.2

20

38

1.2

7.0

6.0

3.0

19

27

0.74

—

—

—

—

4.0

17

17

0.36

5.1+0.9
−0.9

5.0

4.8

4.0

15

14

0.3

4.7

4.3

3.6

14

12

0.27

11

9.9

3.9

20

38

1.1

8.5

7.5

3.4

20

33

0.9

7.5

6.7

3.6

20

29

0.69

7.1

6.6

3.8

19

26

0.59

7.3−1.1 × 10

4.8+1.6−1.2
14+3.0−2.0
13+7.0−3.0
9.6+5.9−3.0
8.8+0.9−0.7
8.7+1.2−1.1
7.8+1.0−1.0
6.2+0.5
−0.6

5.9

5.5

3.9

18

20

0.42

—

—

—

—

—

—

—

9.5+6.8
−3.1

7.0

6.0

3.2

19

26

0.63

center†( +1.1 )1.2−0.6 × 102( +4.1)
1—

6.8−2.9 × 10

52+97
−26

12

11

4.1

10

22

1.1

center

—

—

—

—

—

—

—

—

34+17
−20

12

11

3.6

18

38

1.2

southern bar end
northern arm
southern arm
inter-armouter disk

( +0.2 )1.2−0.4 × 103( +2.3)
1.8−0.6 × 103( +1.7 )1.1−0.5 × 103( +0.3)
1.5−0.3 × 102( +0.6)
1.0−0.4 × 102( +1.2)
1.1−0.6 × 102( +0.6)
3.6−0.5 × 102( +0.7)2.3−0.4 × 102( +1.7 )4.0−0.8 × 102( +1.5
)
2

7.0

6.0

3.2

19

27

0.68

7.9

7.4

4.0

19

30

0.67

16+11
−5.0

11

10

3.9

19

39

1.1

9.6+4.0
−2.6

8.8

8.4

4.5

19

32

0.68

ring2

( +8.0 )5.3−4.1 × 101)( +0.91.3−0.5 × 102)( +2.3
4.5−1.7 × 102)( +0.42.3−0.4 × 101( +0.8 )1.9−0.5 × 101)( +1.01

center†1.8−0.6 × 10
—

ring1
ring2
ring3
centerring1

centerring1
center†centerring1
ring2
center†NGC 3521

τ12(1−0)—

southern bar

NGC 3351[K]

5.1

northern bar end

NGC 3198[K]—

northern bar

NGC 3034[K]

5.4

center—13(1−0)

Tex

—

ring4

NGC 2976

2.9−2.2 × 10

12(2−1)Tex

5.5+1.2
−0.8

ring2
ring3

NGC 2903( +0.6 )1.1−0.3 × 103( +1.0)1.9−0.6 × 102( +0.8 )2.1−0.5 × 102)( +4.7
6.6−2.2 × 102( +1.9)1.8−0.9 × 102( +3.9)8.5−2.3 × 102( +0.6)
1.7−0.4 × 101( +1.1)
2.1−0.7 × 101( +5.5 )1

12(1−0)Tex

center
ring1
ring2
ring3
center†( +2.6 )6.0−1.6 × 102( +2.6)2.2−1.1 × 102( +2.0)3.7−1.3 × 102( +3.7)
5.6−2.6 × 101( +5.5 )3.6−1.5 × 102)( +11.0
× 102
7.2)( −3.2+3.5
2.8−1.3 × 101)( +0.6
2.2−0.4 × 102)( +0.22.1−0.2 × 102)( +0.4
1.3−0.3 × 102( +0.7 )1.6−0.5 × 102( +0.6)2
1.3−0.4 × 10

95+30
−19

13

12

3.5

18

40

1.6

110+70
−40

12

11

3.4

19

40

1.4

80+66
−35

10

9.3

3.2

20

38

1.2

—

—

—

—

—

—

—

6.3+1.2
−1.0

5.9

5.5

3.7

17

19

0.42

7.6+5.3
−2.5

6.4

5.6

3.3

18

22

0.53

9.7+4.1
−2.5

7.7

6.7

4.1

9.3

14

0.51

+73
48−20

16

16

4.1

18

43

1.8

7.6+5.1−2.6
5.7+2.2−1.5
230+110−180
9.9+1.4−1.2
10+1.0−1.0
10+2.0−2.0
9.4+3.5
−2.2
22+16
−7.0

7.0

6.4

3.7

20

27

0.62

5.5

5.0

3.7

16

17

0.36

16

16

4.2

12

30

1.6

8.3

7.6

3.7

20

32

0.79

8.5

7.8

3.7

20

33

0.81

7.6

6.6

3.3

20

30

0.76

7.4

6.5

3.4

19

28

0.71

10

8.9

4.0

9.8

19

0.83

Publications of the Astronomical Society of Japan, (2018), Vol. 00, No. 0

25

Table 4. (Continued.)galaxyregion∗centerbar
northern bar end
southern bar end
western arm
eastern arm
oﬀset stream
southern arm
arm-bar end inter. region
center†NGC 3938

center
ring1
ring2
ring3
center†

NGC 4536

center

[K]

[K]

[K]

[K]

3.0−1.5 × 10

center†
NGC 4579

centerτ12(2−1)τ13(1−0)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

8.8+3.0
−1.8

6.0

5.0

3.1

18

21

0.54

6.9+2.0
−1.2

5.6

4.8

3.2

17

18

0.46

6.6+0.6−0.5
6.4+0.6−0.6
6.7+1.4−1.0
5.7+0.8−0.6
8.4+2.5−1.6
6.8+2.5−1.6
8.7+8.8
−3.1
31+98
−17
7.6+0.7−0.8
7.1+1.0−0.8
8.0+1.4−1.2
5.5+1.1−0.1
11+2.0−2.0
95+222
−54

6.0

5.3

3.5

18

20

0.55

5.8

5.2

3.5

17

19

0.45

5.9

5.1

3.3

18

20

0.48

5.4

5.0

3.6

16

17

0.37

6.8

5.9

3.3

19

26

0.64

6.0

5.2

3.4

18

20

0.49

5.4

4.5

3.0

17

17

0.45

6.1

5.1

3.2

9.1

11

0.42

7.1

6.7

4.1

18

25

0.51

6.6

6.1

3.8

19

24

0.52

7.0

6.4

3.6

19

26

0.6

5.4

5.2

4.2

16

16

0.3

9.0

8.1

4.5

9.8

17

0.6

16

15

3.8

18

42

1.8

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

8.0+5.4
−2.6

6.9

6.2

3.5

19

26

0.62
0.52

ring2

3.3−0.8 × 10

6.3

5.7

3.5

18

22

center†

—

—

—

—

—

—

—

—

11+1.0
−1.0

9.2

8.6

3.9

20

35

0.87

center
ring2
ring3
ring4
ring5
ring6
center†( +0.3 )2.2−0.3 × 102)( +1.6
7.8−1.4 × 102)( +0.5
3.8−0.4 × 102)( +1.85.8−1.1 × 102( +1.6 )4.0−0.9 × 102)( +5.03.8−1.7 × 102)( +13.0
× 102
9.1)( −4.3+0.4
2
1.2−0.2 × 10

6.3+0.5
−0.4

6.0

5.6

4.0

18

20

0.42

6.3+0.5
−0.4

5.8

5.1

3.4

17

19

0.45

6.1+0.7
−0.7

5.7

5.2

3.6

17

18

0.41

6.4+1.1
−1.0

5.9

5.2

3.5

17

19

0.45

6.3+3.2
−1.9

5.7

5.1

3.4

17

19

0.43

4.2+1.8
−1.2

4.0

3.7

3.2

11

7.1

0.19

24+13
−6.0

11

9.8

4.1

10

21

0.95
—

center

—

—

—

—

—

—

—

ring1

—

—

—

—

—

—

—

—

1
1.6+5.1−1.2 × 10

97+390
−79

9.9

9.2

3.2

19

37

1.1

ring2
center†
NGC 7331

τ12(1−0)

7.1+1.7
−1.5

ring1

NGC 5713

Tex( +3.1 )2.4−1.2 × 102( +1.8)2

ring1

NGC 5055Tex

13(1−0)[cm−3 ]

( +4.3 )9.5−3.3 × 101( +0.8)1.8−0.6 × 102( +0.4 )3.4−0.4 × 102( +0.8)3.9−0.6 × 102( +1.0)2.8−0.7 × 102( +1.6)
6.2−1.4 × 102( +0.7)
1.7−0.5 × 102( +1.9)2.7−1.0 × 102( +10.3)
7.7−4.8 × 101( +5.4 )4.3−2.9 × 101( +1.4)
5.9−0.9 × 102( +1.4)4.4−0.7 × 102( +1.0)2.9−0.7 × 102( +3.2)
1.8−0.8 × 103( +1.1)
4.0−0.8 × 102( +2.1 )1Tex

12(2−1)

Tkin(1)

NGC 362712(1−0)n(H2 )

center
ring1
ring2
ring3
center†()—( +0.6 )2.0−0.4 × 102( +1.6)8.3−1.4 × 102( +2.1 )8.7−1.8 × 102( +1.8)5.3−1.3 × 102( +5.3)1
9.8−4.1 × 10

—

—

—

—

—

—

—

9.9+2.1
−1.6

8.2

7.4

3.6

19

31

0.77

6.2+0.5
−0.3

6.0

5.6

4.0

18

21

0.42

6.0+0.5
−0.4

5.8

5.4

3.9

18

20

0.41

5.7+1.1
−0.8

5.4

4.8

3.5

16

16

0.38

24+32
−9.0

9.5

8.4

3.8

10

19

0.86

(1) Number density of molecular gas. (2) Kinetic temperature of molecular gas. (3) Excitation temperature of 12 CO(J = 1–0). (4) The
same as (3) but for 12 CO(J = 2–1). (5) The same as (3) but for 13 CO(J = 1–0). (6) Optical depth of 12 CO(J = 1–0). (7) The same as (6)but for 12 CO(J = 2–1). (8) The same as (6) but for 13 CO(J = 1–0). Results of (1)–(8) are obtained from the one-zone model of RADEX. ∗In annuli cases, regions of each annulus are named ‘ring1’, ‘ring2’... in order from the galactic center. † Adopted XCO and [12 CO]/[13 CO]
are diﬀerent to reflect environments in galactic centers.

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Publications of the Astronomical Society of Japan, (2018), Vol. 00, No. 0

Table 5. Results of the stacking analysis.
galaxyregion
I12 CO(1−0)[K km s−1 ](1)
NGC 628
center6.8 ± 0.3
inner arm1
5.3 ± 0.2
inner arm2
5.1 ± 0.2
outer arm1
3.0 ± 0.2
outer arm2
3.8 ± 0.3
inter-arm1
3.1 ± 0.2
inter-arm2
1.6 ± 0.1
NGC 2146
center148 ± 1
ring1
52.3 ± 0.6
ring2
16.4 ± 0.6
ring3
6.5 ± 0.5
NGC 2841
ring1
5.1 ± 0.2
ring2
3.7 ± 0.2
ring3
2.4 ± 0.1
ring4
1.6 ± 0.1
NGC 2903
center46 ± 1northern bar
21.7 ± 0.8
southern bar
28.0 ± 0.7
northern bar end
41.7 ± 0.7
southern bar end
36.5 ± 0.7
northern arm
19.7 ± 0.4
southern arm
18.8 ± 0.5inter-arm
13.8 ± 0.4
outer disk
3.9 ± 0.2
NGC 2976
center
3.1 ± 0.3
ring1
2.6 ± 0.2
ring2
3.3 ± 0.1
ring3
2.0 ± 0.1
ring4
0.6 ± 0.1
NGC 3034
center462 ± 2
ring1
204 ± 1
ring2
115.0 ± 0.8
ring3
60.8 ± 0.8
ring4
33 ± 1ring5
33.9 ± 0.9
ring6
27.9 ± 0.8
ring7
23.1 ± 0.9
ring8
17.0 ± 0.7
ring9
13.5 ± 0.7
ring1011.6 ± 0.5
ring11
11.2 ± 0.6
NGC 3198
center
8.0 ± 0.3
ring1
4.0 ± 0.3
ring2
1.9 ± 0.2
NGC 3351
center
17.5 ± 0.4
ring1
3.1 ± 0.4
ring2
3.6 ± 0.2
ring3
2.7 ± 0.3
ring4
1.5 ± 0.2
NGC 3521
center
32.3 ± 0.6
ring1
27.7 ± 0.4
ring2
16.8 ± 0.3
ring3
5.7 ± 0.3
ring4
2.1 ± 0.2
ring5
1.2 ± 0.1

I12 CO(2−1)[K km s−1 ](2)
4.23 ± 0.09
2.80 ± 0.05
2.93 ± 0.05
1.92 ± 0.06
1.47 ± 0.06
1.37 ± 0.03
0.69 ± 0.04
123.9 ± 0.3
36.0 ± 0.2
8.2 ± 0.1
3.7 ± 0.2
2.2 ± 0.1
2.01 ± 0.09
1.29 ± 0.06
0.74 ± 0.06
33.5 ± 0.2
13.0 ± 0.3
14.1 ± 0.2
27.0 ± 0.2
21.4 ± 0.2
11.9 ± 0.1
10.4 ± 0.1
7.0 ± 0.1
1.98 ± 0.06
2.61 ± 0.09
1.98 ± 0.08
2.41 ± 0.05
1.44 ± 0.07
0.41 ± 0.04
365.5 ± 0.4
155.4 ± 0.2
78.9 ± 0.2
38.5 ± 0.1
24.56 ± 0.1
19.33 ± 0.07
15.6 ± 0.1
12.83 ± 0.07
9.9 ± 0.1
8.23 ± 0.08
7.15 ± 0.09
7.25 ± 0.09
4.3 ± 0.1
1.98 ± 0.06
1.26 ± 0.04
15.4 ± 0.1
1.8 ± 0.1
1.79 ± 0.06
1.08 ± 0.05
0.64 ± 0.04
20.5 ± 0.2
17.8 ± 0.1
9.28 ± 0.08
3.15 ± 0.06
0.96 ± 0.05
0.59 ± 0.04

I13 CO(1−0)[K km s−1 ](3)
1.0 ± 0.1
0.35 ± 0.07
0.38 ± 0.06
< 0.070.27 ± 0.06
< 0.07< 0.047.2 ± 0.4
2.0 ± 0.2
< 0.18< 0.2
0.55 ± 0.1
0.49 ± 0.07
0.35 ± 0.06
< 0.053.9 ± 0.4
1.3 ± 0.2
< 0.354.4 ± 0.4
2.9 ± 0.3
2.1 ± 0.3
2.1 ± 0.2
< 0.160.19 ± 0.05
< 0.12< 0.050.27 ± 0.06
0.26 ± 0.07
< 0.0523.6 ± 0.7
8.8 ± 0.6
4.2 ± 0.4
1.5 ± 0.2
1.1 ± 0.2
< 0.26< 0.26< 0.21< 0.19< 0.22< 0.21< 0.250.8 ± 0.1
< 0.1
< 0.051.3 ± 0.2
< 0.13< 0.13< 0.09< 0.072.8 ± 0.3
2.3 ± 0.1
1.0 ± 0.1
0.36 ± 0.07
< 0.09< 0.06

R2/1

R12/13(4)
0.62 ± 0.03
0.53 ± 0.02
0.57 ± 0.03
0.65 ± 0.06
0.39 ± 0.03
0.43 ± 0.03
0.44 ± 0.04
0.839 ± 0.006
0.689 ± 0.009
0.50 ± 0.02
0.57 ± 0.05
0.42 ± 0.03
0.54 ± 0.04
0.53 ± 0.04
0.46 ± 0.05
0.72 ± 0.02
0.60 ± 0.03
0.50 ± 0.02
0.65 ± 0.01
0.59 ± 0.01
0.61 ± 0.01
0.56 ± 0.02
0.51 ± 0.02
0.51 ± 0.03
0.84 ± 0.08
0.76 ± 0.05
0.74 ± 0.04
0.71 ± 0.05
0.7 ± 0.2
0.792 ± 0.003
0.762 ± 0.004
0.686 ± 0.005
0.633 ± 0.008
0.74 ± 0.03
0.57 ± 0.01
0.56 ± 0.02
0.56 ± 0.02
0.58 ± 0.03
0.61 ± 0.03
0.62 ± 0.03
0.65 ± 0.04
0.54 ± 0.03
0.49 ± 0.04
0.68 ± 0.07
0.88 ± 0.02
0.59 ± 0.08
0.50 ± 0.03
0.41 ± 0.05
0.42 ± 0.07
0.64 ± 0.01
0.64 ± 0.01
0.55 ± 0.01
0.55 ± 0.03
0.46 ± 0.05
0.51 ± 0.07

(5)6.8 ± 0.9
15.1 ± 3.1
13.5 ± 2.1> 41.1
14.3 ± 3.3> 42.9> 37.320.4 ± 1.0
26.4 ± 2.3> 92.8> 31.89.2 ± 1.7
7.5 ± 1.2
6.9 ± 1.3
> 30.8
11.8 ± 1.1
17.3 ± 3.4> 79.29.5 ± 0.8
12.5 ± 1.5
9.6 ± 1.4
8.8 ± 0.8
> 85.520.8 ± 6.0> 24.9> 49.012.0 ± 2.7
7.7 ± 2.0
> 11.019.5 ± 0.6
23.2 ± 1.5
27.4 ± 2.3
41.7 ± 7.0
29.5 ± 6.3
> 128
> 108
> 107
> 88.5> 60.9> 56.0> 44.110.0 ± 1.7> 41.9> 34.5
13.5 ± 2.1> 23.2> 28.1> 29.8> 21.5
11.7 ± 1.3
11.9 ± 0.8
17.1 ± 2.1
16.0 ± 3.2> 24.1> 19.3∆V[km s−1 ](6)30 ± 228 ± 237 ± 228 ± 427 ± 332 ± 430 ± 5202 ± 3150 ± 4160 ± 2171 ± 1288 ± 858 ± 659 ± 567 ± 10157 ± 1394 ± 7151 ± 4101 ± 3119 ± 465 ± 265 ± 482 ± 553 ± 533 ± 531 ± 430 ± 231 ± 428 ± 9147 ± 1137 ± 2126 ± 2112 ± 3106 ± 13105 ± 6102 ± 791 ± 982 ± 882 ± 1287 ± 1591 ± 1892 ± 763 ± 842 ± 9194 ± 896 ± 29
41 ± 540 ± 933 ± 13165 ± 13118 ± 392 ± 388 ± 949 ± 956 ± 13

Publications of the Astronomical Society of Japan, (2018), Vol. 00, No. 0

Table 5. (Continued.)galaxyregionNGC 3627

NGC 3938

NGC 4536

NGC 4579

NGC 5055

NGC 5713

NGC 7331

centerbar
northern bar end
southern bar end
western arm
eastern arm
oﬀset stream
southern arm
arm-bar end inter. region
inter-armouter disk
center
ring1
ring2
ring3
ring4
centerring1
ring2
center
ring1
ring2
ring3
center
ring1
ring2
ring3
ring4
ring5
ring6
ring7
center
ring1
ring2
ring3
center
ring1
ring2
ring3
ring4
ring5
ring6

I12 CO(1−0)[K km s−1 ](1)50.4 ± 0.7
24.7 ± 0.8
31.9 ± 0.6
41 ± 113.7 ± 0.4
18.4 ± 0.4
19.1 ± 0.5
11.1 ± 0.6
12.3 ± 0.4
10.0 ± 0.5
2.6 ± 0.2
9.5 ± 0.2
6.4 ± 0.2
4.3 ± 0.1
2.4 ± 0.2
1.02 ± 0.09
34 ± 16.5 ± 0.4
2.2 ± 0.2
13.0 ± 0.7
5.5 ± 0.4
5.1 ± 0.2
2.8 ± 0.3
40.0 ± 0.6
20.1 ± 0.3
14.0 ± 0.2
8.5 ± 0.2
5.5 ± 0.2
2.7 ± 0.2
1.8 ± 0.2
1.1 ± 0.2
36.3 ± 0.7
20.7 ± 0.4
10.4 ± 0.4
5.7 ± 0.3
28.6 ± 0.935.2 ± 0.7
23.0 ± 0.4
11.6 ± 0.6
5.8 ± 0.4
3.1 ± 0.3
1.9 ± 0.2

I12 CO(2−1)[K km s−1 ](2)
21.1 ± 0.6
10.2 ± 0.2
15.7 ± 0.2
20.3 ± 0.2
6.4 ± 0.1
9.0 ± 0.2
9.7 ± 0.2
5.3 ± 0.1
4.4 ± 0.1
4.7 ± 0.1
1.03 ± 0.07
5.98 ± 0.09
3.68 ± 0.05
2.46 ± 0.04
1.36 ± 0.04
0.55 ± 0.03
29.7 ± 0.2
4.9 ± 0.1
1.34 ± 0.07
10.1 ± 0.2
3.05 ± 0.09
2.68 ± 0.07
1.30 ± 0.08
27.3 ± 0.3
11.4 ± 0.1
6.79 ± 0.08
4.38 ± 0.07
2.74 ± 0.07
1.28 ± 0.05
0.65 ± 0.04
0.54 ± 0.06
34.4 ± 0.2
16.6 ± 0.1
7.1 ± 0.1
3.4 ± 0.1
17.6 ± 0.2
20.1 ± 0.1
12.8 ± 0.1
5.46 ± 0.1
2.60 ± 0.07
1.18 ± 0.07
0.66 ± 0.05

29

I13 CO(1−0)[K km s−1 ](3)
2.0 ± 0.3
1.2 ± 0.2
2.8 ± 0.2
3.3 ± 0.3
0.9 ± 0.1
1.7 ± 0.2
1.1 ± 0.2
0.7 ± 0.2
< 0.19< 0.14< 0.091.2 ± 0.1
0.63 ± 0.07
0.36 ± 0.05
0.35 ± 0.06
< 0.032.0 ± 0.3
< 0.14< 0.1< 0.35< 0.2
0.41 ± 0.08
< 0.133.7 ± 0.3
2.4 ± 0.2
1.08 ± 0.09
0.82 ± 0.1
0.44 ± 0.07
< 0.06< 0.06< 0.061.3 ± 0.2
0.8 ± 0.1
< 0.12< 0.112.2 ± 0.3
4.3 ± 0.3
2.8 ± 0.3
1.0 ± 0.2
< 0.14< 0.11< 0.08R2/1

R12/13(4)
0.42 ± 0.01
0.41 ± 0.01
0.49 ± 0.01
0.49 ± 0.01
0.47 ± 0.02
0.49 ± 0.02
0.51 ± 0.02
0.48 ± 0.03
0.36 ± 0.02
0.47 ± 0.03
0.39 ± 0.05
0.63 ± 0.02
0.57 ± 0.02
0.57 ± 0.02
0.56 ± 0.05
0.54 ± 0.06
0.86 ± 0.02
0.74 ± 0.05
0.61 ± 0.07
0.78 ± 0.05
0.55 ± 0.04
0.52 ± 0.03
0.47 ± 0.06
0.68 ± 0.01
0.569 ± 0.01
0.484 ± 0.01
0.51 ± 0.02
0.5 ± 0.02
0.48 ± 0.04
0.35 ± 0.04
0.51 ± 0.09
0.95 ± 0.02
0.80 ± 0.02
0.68 ± 0.03
0.59 ± 0.03
0.61 ± 0.02
0.57 ± 0.01
0.56 ± 0.01
0.47 ± 0.02
0.45 ± 0.04
0.38 ± 0.04
0.34 ± 0.05

(5)25.3 ± 3.9
20.3 ± 3.8
11.5 ± 0.8
12.5 ± 1.2
15.1 ± 2.5
11.0 ± 1.4
16.9 ± 3.2
15.0 ± 4.1> 65.4> 70.5> 30.48.2 ± 0.8
10.1 ± 1.2
12.1 ± 1.9
6.9 ± 1.3
> 29.717.0 ± 2.2> 45.1> 22.8> 37.0> 28.012.3 ± 2.5> 21.010.9 ± 0.8
8.4 ± 0.6
12.9 ± 1.0
10.4 ± 1.3
12.4 ± 2.1> 42.4> 30.5> 18.128.8 ± 5.7
24.5 ± 4.2> 86.2> 50.212.9 ± 1.6
8.1 ± 0.6
8.2 ± 0.8
12.0 ± 2.0> 40.6> 29.1> 23.5∆V[km s−1 ](6)
164 ± 9108 ± 1168 ± 396 ± 1148 ± 268 ± 360 ± 345 ± 351 ± 386 ± 958 ± 1243 ± 229 ± 128 ± 127 ± 324 ± 3161 ± 17136 ± 2380 ± 16154 ± 3650 ± 650 ± 446 ± 11120 ± 471 ± 253 ± 147 ± 244 ± 243 ± 449 ± 849 ± 12112 ± 580 ± 461 ± 654 ± 5143 ± 21119 ± 9114 ± 486 ± 1093 ± 2374 ± 2067 ± 14(1) Integrated intensity of stacked 12 CO(J = 1–0) spectra. (2) The same as (1) but for 12 CO(J = 2–1). (3) The same as (1) but for
13
CO(J = 1–0). (4) Integrated-intensity ratio of stacked 12 CO(J = 2–1) to that for 12 CO(J = 1–0). (5) The same as (4) but for
stacked 12 CO(J = 1–0)/13 CO(J = 1–0). (6) FWHM of stacked 12 CO(J = 1–0) spectra.