# Planck Galactic Cold Clumps at High Galactic Latitude-A Study with CO Lines

Fengwei Xu Department of Astronomy, School of Physics, Peking University,
Beijing, 100871, People’s Republic of China<EMAIL_ADDRESS><EMAIL_ADDRESS>Kavli Institute for Astronomy and Astrophysics, Peking
University, Haidian District, Beijing 100871, People’s Republic of China
Yuefang Wu  Department of Astronomy, School of Physics, Peking University,
Beijing, 100871, People’s Republic of China<EMAIL_ADDRESS><EMAIL_ADDRESS>Kavli Institute for Astronomy and Astrophysics, Peking
University, Haidian District, Beijing 100871, People’s Republic of China  Tie
Liu  Shanghai Astronomical Observatory, Chinese Academy of Sciences, 80 Nandan
Road, Shanghai 200030, Republic of China  Korea Astronomy and Space Science
Institute, 776 Daedeokdaero, Yuseong-gu, Daejeon 34055, Republic of Korea
Xunchuan Liu  Department of Astronomy, School of Physics, Peking University,
Beijing, 100871, People’s Republic of China<EMAIL_ADDRESS><EMAIL_ADDRESS>Kavli Institute for Astronomy and Astrophysics, Peking
University, Haidian District, Beijing 100871, People’s Republic of China  Chao
Zhang  Department of Astronomy, Yunnan University, and Key Laboratory of
Astroparticle Physics of Yunnan Province, Kunming 650091, China  Department of
Astronomy, School of Physics, Peking University, Beijing, 100871, People’s
Republic of China<EMAIL_ADDRESS><EMAIL_ADDRESS>Jarken Esimbek
Xinjiang Astronomical Observatory, Chinese Academy of Sciences, Urumqi 830011,
China  Key Laboratory of Radio Astronomy, Chinese Academy of Sciences, Urumqi
830011, China  Sheng-Li Qin  Department of Astronomy, Yunnan University, and
Key Laboratory of Astroparticle Physics of Yunnan Province, Kunming 650091,
China  Di Li  CAS Key Laboratory of FAST, National Astronomical Observatories,
CAS, Beijing 100012, China  NAOC-UKZN Computational Astrophysics Centre
(NUCAC), University of KwaZulu-Natal, Durban 4000, South Africa  Ke Wang
Kavli Institute for Astronomy and Astrophysics, Peking University, Haidian
District, Beijing 100871, People’s Republic of China  Jinghua Yuan  National
Astronomical Observatories, Chinese Academy of Sciences, 20A Datun Road,
Chaoyang District, Beijing 100012, China  Fanyi Meng  I. Physikalisches
Institut, Universität zü Köln, Zülpicher Str. 77, D-50937 Köln, Germany
Department of Astronomy, School of Physics, Peking University, Beijing,
100871, People’s Republic of China<EMAIL_ADDRESS><EMAIL_ADDRESS>Tianwei Zhang  I. Physikalisches Institut, Universität zü Köln, Zülpicher Str.
77, D-50937 Köln, Germany  Department of Astronomy, School of Physics, Peking
University, Beijing, 100871, People’s Republic of China,
<EMAIL_ADDRESS><EMAIL_ADDRESS>David Eden  Astrophysics Research
Institute, Liverpool John Moores University, IC2, Liverpool Science Park, 146
Brownlow Hill, Liverpool L3 5RF, UK  K. Tatematsu  Nobeyama Radio Observatory,
National Astronomical Observatory of Japan, National Institutes of Natural
Sciences, Nobeyama, Minamimaki, Minamisaku, Nagano 384-1305, Japan  Neal J.
Evans  Department of Astronomy The University of Texas at Austin 2515
Speedway, Stop C1400 Austin, TX 78712-1205, USA  Korea Astronomy and Space
Science Institute 776 Daedeokdae-ro, Yuseong-gu Daejeon, 34055, Republic of
Korea  Humanitas College, Global Campus, Kyung Hee University, Yongin-shi
17104, Republic of Korea  Paul. F. Goldsmith  Jet Propulsion Laboratory,
California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109,
USA  Qizhou Zhang  Center for Astrophysics — Harvard & Smithsonian, 60 Garden
Street, Cambridge, MA 02138, USA  C. Henkel  Max-Planck Institut für
Radioastronomie, Auf Dem Hügel 69, 53121 Bonn, Germanyn  Astronomy Department,
Faculty of Science, King Abdulaziz University, PO Box 80203, Jeddah, 21589,
Saudi Arabia  Hee-Weon Yi  School of Space Research, Kyung Hee University,
1732, Deogyeong-daero, Giheung-gu, Yongin-si, Gyeonggi-do 17104, Republic of
Korea  Jeong-Eun Lee  School of Space Research, Kyung Hee University, 1732,
Deogyeong-daero, Giheung-gu, Yongin-si, Gyeonggi-do 17104, Republic of Korea
Mika Saajasto  Department of Physics, P.O.Box 64, FI-00014, University of
Helsinki, Finland  Gwanjeong Kim  Nobeyama Radio Observatory, National
Astronomical Observatory of Japan, National Institutes of Natural Sciences,
462-2 Nobeyama, Minamimaki, Minamisaku, Nagano 384-1305, Japan  Mika Juvela
Department of Physics, P.O.Box 64, FI-00014, University of Helsinki, Finland
Dipen Sahu  Academia Sinica Institute of Astronomy and Astrophysics, 11F of
AS/NTU Astronomy-Mathematics Building, No.1, Sec. 4, Roosevelt Rd, Taipei
10617, Taiwan, R.O.C.  Shih-Ying Hsu  National Taiwan University (NTU),
Taiwan, R.O.C.  Sheng-yuan Liu  Academia Sinica Institute of Astronomy and
Astrophysics, 11F of AS/NTU Astronomy-Mathematics Building, No.1, Sec. 4,
Roosevelt Rd, Taipei 10617, Taiwan, R.O.C.  Somnath Dutta  Academia Sinica
Institute of Astronomy and Astrophysics, 11F of AS/NTU Astronomy-Mathematics
Building, No.1, Sec. 4, Roosevelt Rd, Taipei 10617, Taiwan, R.O.C.  Chin-Fei
Lee  Academia Sinica Institute of Astronomy and Astrophysics, 11F of AS/NTU
Astronomy-Mathematics Building, No.1, Sec. 4, Roosevelt Rd, Taipei 10617,
Taiwan, R.O.C.  Chuan-Peng Zhang  National Astronomical Observatories, Chinese
Academy of Sciences, 100101 Beijing, China  Ye Xu  Purple Mountain Observatory
and Key Laboratory of Radio Astronomy, Chinese Academy of Sciences, 8 Yuanhua
Road, Nanjing 210034, PR China  Binggang Ju  Purple Mountain Observatory and
Key Laboratory of Radio Astronomy, Chinese Academy of Sciences, 8 Yuanhua
Road, Nanjing 210034, PR China

###### Abstract

Gas at high Galactic latitude is a relatively little-noticed component of the
interstellar medium. In an effort to address this, forty-one Planck Galactic
Cold Clumps at high Galactic latitude (HGal; $|b|>25\arcdeg$) were observed in
12CO, 13CO and C18O J=1-0 lines, using the Purple Mountain Observatory 13.7-m
telescope. 12CO (1-0) and 13CO (1-0) emission was detected in all clumps while
C18O (1-0) emission was only seen in sixteen clumps. The highest and average
latitudes are $71.4\arcdeg$ and $37.8\arcdeg$, respectively. Fifty-one
velocity components were obtained and then each was identified as a single
clump. Thirty-three clumps were further mapped at 1′ resolution and 54 dense
cores were extracted. Among dense cores, the average excitation temperature
$T_{\mathrm{ex}}$ of 12CO is 10.3 K. The average line widths of thermal and
non-thermal velocity dispersions are $0.19$ km s-1and $0.46$ km
s-1respectively, suggesting that these cores are dominated by turbulence.
Distances of the HGal clumps given by Gaia dust reddening are about $120-360$
pc. The ratio of $X_{13}$/$X_{18}$ is significantly higher than that in the
solar neighbourhood, implying that HGal gas has a different star formation
history compared to the gas in the Galactic disk. HGal cores with sizes from
$0.01-0.1$ pc show no notable Larson’s relation and the turbulence remains
supersonic down to a scale of slightly below $0.1$ pc. None of the HGal cores
which bear masses from 0.01-1 $M_{\odot}$ are gravitationally bound and all
appear to be confined by outer pressure.

ISM: dark clouds - ISM: molecules - ISM: structure - stars: formation - ISM:
high Galactic latitude

††software: GILDAS/CLASS https://www.iram.fr/IRAMFR/GILDAS/, Astropy (Price-
Whelan et al., 2018), Matplotlib (Hunter, 2007), Aplpy (Robitaille & Bressert,
2012)

##  1 Introduction

Two directions in studying Galactic star formation nowadays are important: one
is to study the initial condition of star formation and the other is to cover
a more complete area. The former requires exploring the earliest stage.
Therefore, astronomers are encouraged to search for those primordial molecular
clumps which are close to the initial stage of forming stars and assumed to
harbor prestellar cores (Shu et al., 1987). The latter requires larger
surveys, especially towards the regions beyond the Galactic disk or the low
Galactic latitudes in traditional surveys (Stark, 1979; Burton & Gordon, 1978;
Blitz et al., 1982; Robinson et al., 1983; Israel et al., 1984; Sanders et
al., 1984; Dame et al., 1987). The sky coverage at high Galatic latitude
(hereafter HGal), the rest of the “iceberg”, provides an extensive view of gas
distribution and star formation in our Galaxy. The infrared cirrus (Low et
al., 1984) found by the Infra-Red Astronomical Satellite (hereafter (IRAS)) at
HGal were thought to be an environment hostile to star formation. Also,
previous works have shown that methanol masers which trace the massive star-
forming regions are rare at high latitudes (Yang et al., 2017). Besides, the
gas at HGal as a variable gas reservoir probably plays an important role in
the cycling of gas in and out of the Galactic plane (Lilly et al., 2013).
Therefore, the properties of the gas can be quite different from those in the
Galactic plane, and this inspires the idea that latitude is a sensitive
parameter for Galactic star formation and gas properties.

The molecular material at HGal had been poorly studied until the first CO
survey searched for apparent optical obscuration on the Palomar Observatory
Sky Survey (POSS) prints (Blitz et al., 1984, as well as the Whiteoak
extension to the POSS) by the 5-m Millimeter Wave Observatory in Texas (Vanden
Bout et al., 2012). 57 clouds were discovered by Magnani, Blitz, & Mundy
(1985, hereafter MBM) in 33 complexes at $|b|>20\arcdeg$ and ten complexes at
$|b|>30\arcdeg$ were mapped with a grid spacing 10′-20′ depending on the
angular extent of the source. MBM provides the first glimpse of molecular
clouds at high Galatic latitude (hereafter HGal clouds) and the number of
identified HGal clouds has increased dramatically from then on (see Magnani et
al. (1996) for a review). Subsequently, unbiased CO surveys were brought up
for more complete census of HGal clouds at northern Galactic hemisphere by
Hartmann et al. (1998) and then southern one by Magnani et al. (2000).

As soon as Blitz et al. (1984) and Magnani et al. (1985) detected CO molecular
clouds in HGal, people began to explore the physical and chemical properties
with the help of molecular lines. HGal clouds, for the most part, are thought
to be gravitationally unbound (Keto & Myers, 1986), and may be in pressure
equillibrium with the Interstellar medium (ISM). Besides, HGal clouds are
reported to have lower densities and rare isotopic CO abundances than those
encountered in dark clouds or GMCs (Polk et al., 1988). HGal clouds represent
a distinct component of molecular material and may help to provide a new
perspective of the ISM. This warrants further confirmed study.

During the flourishing age of the 8′-resolution CO sky survey (with the help
of the Columbia 1.2-m telescope twins), an important step toward discerning
the nature of HGal clouds was made by van Dishoeck & Black (1988). The HGal
clouds were considered to be translucent clouds (van Dishoeck et al., 1991,
the total extinction $A^{\text{tot}}_{V}\simeq 1-4$mag) with CO column
densities $\geq 10^{15}$ cm-2 and abundances from $10^{-6}$ to $10^{-4}$,
which represent the transitional regime between traditional diffuse and dark
clouds (Magnani et al., 1996). Those HGal clouds appear to be extraordinarily
young and may represent the earliest stages of molecular clouds condensing
from the local ISM. Besides, the CO observations with sub-parsec resolution
towards far-infrared emission in HGal clouds (Blitz et al., 1990; Reach et
al., 1994) have demonstrated that those clouds have smaller structures
(Wouterloot et al., 2000). Therefore, higher resolution and spatial sampling
rate are needed if we are to dissect and analyse the clouds on smaller scale,
which also helps understand the initial condition of star formation better.
Studies of the large-scale HGal cloud complexes with high spatial resolution
have been rare, since the spatial extent is as large as tens of square degrees
or more (Yamamoto et al., 2003). Composite CO observations were conducted
towards the Polaris Flare with 620 $\deg^{2}$ by Heithausen & Thaddeus (1990),
and towards Ursa Major clouds by de Vries et al. (1987) and Pound & Goodman
(1997). Another observation toward the Hi filament regions including MBM 53,
54, and 55 with approximately 141 $\deg^{2}$ was conducted by Yamamoto et al.
(2003).

We summarize the large CO line surveys towards HGal regions as completely as
we could in Table 1, which are listed in chronological order. However, two
main issues require further consideration. On one hand, the earliest stage of
star formation buried deep inside the cold dust at about 10 K should be
detected more sensitively at longer wavelengths, in millimeter or sub-
millimeter bands. On the other hand, it is difficult to achieve both extensive
coverage and high resolution (and also fine sampling): higher spatial accuracy
requires more integration time so that an all-sky survey with high resolution
is not feasible. Besides, signals may not be detected over a large fraction of
the sky, leading to a low efficiency in the observations. Therefore, one
possible strategy is to use a telescope with a relatively high resolution to
map specific regions that are chosen from a previous survey with a larger
coverage but lower resolution.

Fortunately, the Planck satellite provides an unprecedentedly complete spatial
distribution of the HGal sources. The all-sky nature of this sample is
particularly useful for studying the global properties of Galactic molecular
gas and clouds. The Cold Clump Catalogue of Planck Objects (C3PO), also called
Planck Galactic Cold Clumps (PGCCs), consists of 13,188 cold clumps derived
from the fluxes in the three highest frequency Planck bands (353, 545, 857
GHz) as well as the 3000 GHz IRAS band. PGCCs provides a rich catalog of
sources with the a dust temperature between $10-15$ K, probably the coldest
part of the ISM (Planck Collaboration et al., 2011a) allowing us to probe the
characteristics of the prestellar phase and the properties of starless clumps
(Wu et al., 2012). A follow-up study was conducted with the 13.7-m telescope
of the Purple Mountain Observatory (PMO) at Delingha, Qinghai Province. The
main beam size of $\sim 1^{\prime}$ and the grid spacing of 30$\arcsec$ are
the best among the surveys listed in Table 1, which satisfy the spatial
accuracy to resolve the regions of several tenths of parsec in size at
distance less than about 400 pc (Liu et al., 2012). Since Planck observations
only provide the continuum emission, it is necessary to examine molecular
lines to infer the dynamical information, which is essential for studying star
formation among these samples. PMO observations provide all 12CO(1-0),
13CO(1-0), and C18O(1-0) lines, guaranteeing fruitful information about gas
dynamics. Besides, this work uses two other emission lines, N2H+ (1-0) and C2H
(1-0), to trace dense regions and to reveal the evolutionary state of the gas
as supplementary information.

In this paper, we wish to answer the following questions: How do physical
conditions in clouds away from the Galactic plane differ from those at low
latitude? What phase are HGal gas cores in? We report an investigation of 41
PGCCs at high Galactic latitudes. We extract 54 cores condensed in these
clumps and analyze their properties further. The data descriptions are in
Section 2. The results are shown in Section 3. Further discussions follow in
Section 4 while main conclusions are summarized in Section 5.

##  2 Data

###  2.1 Sample Selection

There are 41 clumps with absolute Galactic latitude higher than $25\arcdeg$
($|b|>25\arcdeg$) from the Early Cold Core (ECC; Planck Collaboration et al.
(2011b)) catalog, which were observed with the 13.7-m millimeter-wavelength
telescope of the Purple Mountain Observatory (PMO). The ECC sources have high
signal-to-noise ratios (SNR$>$15). Figure 1 shows the distribution of 41
clumps. The distribution of these 41 HGal clumps is not uniform along latitude
or along longitude. As shown in Figure 1, the clumps of belonging to the
northern sky are located only in the latitude range $25\arcdeg<b<42\arcdeg$
and those in the southern sky mainly group around $-50\arcdeg<b<-25\arcdeg$.
The longitudes of the detected clumps are mostly in the range of
$90\arcdeg<l<180\arcdeg$ and $0\arcdeg<l<45\arcdeg$. Almost half, 46.3% (19
out of 41) of these clumps are just below Taurus, Perseus, and California
Complex at $b\leq-20\arcdeg$ and $l=155-180\arcdeg$ The names of these clumps
are listed in column (1), Galactic coordinates in columns (2)–(3) and
equatorial coordinates in columns (4)–(7) of Table 2.

###  2.2 PMO Observations

The $3\times 3$ beam sideband separation Superconduction Spectroscopic Array
Receiver system was used as the front end (Shan et al., 2012). The half-power
beam width is 56$\arcsec$ in the 115 GHz band. The mean beam efficiency is
about $50\%$. The pointing accuracy is better than 5$\arcsec$. The Fast
Fourier Transform Spectrometers (FFTSs) were used as the backend. Each FFTS
with a total bandwidth of 1 GHz provides 16384 channels.

The single point mode observations of 12CO, 13CO and C18O J=1-0 towards 41
HGal clumps were conducted from April to May in 2011 and from December 2011 to
January 2012. The velocity resolutions are 0.16 km s-1 for 12CO and 0.17 km
s-1 for 13CO and C18O. The 12CO emission was observed in the upper sideband
(USB) with a system temperature (Tsys) around 210 K, while the 13CO and C18O
emissions were observed simultaneously in the lower sideband (LSB) with Tsys
around 120 K. The typical root mean square (rms) noise in T${}_{A}^{*}$ was
0.2 K for 12CO but 0.1 K for 13CO and C18O. Due to time limitations only 26 of
these 41 HGal clumps were further mapped in the on-the-fly (OTF) mode in the
three CO transitions. The antenna continuously scanned a region of
$22\arcmin\times 22\arcmin$ centered on the PGCCs with a scanning rate of
$20\arcsec$ per second. Because of the high rms noise level at the edges of
the OTF maps, only the central $14\arcmin\times 14\arcmin$ regions were used
for analyses in this work (Zhang et al., 2020). Whether the PGCC was mapped
with OTF is shown in column (10) of Table 2. If mapped, it is marked by a ‘Y’,
if no, then ‘N’.

To trace the high-density region in these 26 mapped HGal clumps, we chose the
center of cores defined in Section 3.1 to detect J=1-0 emissions of N2H+ and
C2H. We required that each candidate should have sufficient column density
with an antenna temperature of 13CO higher than 1 K. Then, 18 of these HGal
clumps with absolute latitude larger than 25°were chosen for further
observations. To compare the detection rate between high and lower latitudes,
we also observed an unbiased sample of 18 PGCCs with latitudes between 21°and
25°. Finally, 36 clumps in total were observed with N2H+ and C2H in single-
point mode from May to June in 2019. The velocity resolutions are 0.19 km s-1
for N2H+ and 0.21 km s-1 for C2H. The N2H+ emission was observed in the USB
with Tsys also around 210 K and C2H in LSB with Tsys around 210 K. The typical
noise is 0.2 K for both N2H+ and C2H.

The raw data were reduced by CLASS and GREG in the GILDAS package (Guilloteau
& Lucas, 2000; Pety, 2005).

###  2.3 Archived Data-Herschel FIR Continuum Emission

To evaluate the definition of cores (see Section 3.1) in the special clump
G004.15+35.77, the northwestern edge of LDN 134 (Lynds, 1962), the FIR
continuum emission images were taken from the project Galactic Cold Cores
(Juvela et al., 2010) which is a Herschel satellite survey (Pilbratt et al.,
2010) of the source populations revealed by Planck Cold Cores program. The
data were obtained with the Photodetector Array Camera and Spectrometer
(Poglitsch et al., 2010, PACS) at 100 and 160 $\mu m$ wavelength and the
Spectral and Photometric Imaging REceiver (Griffin et al., 2010, SPIRE) at
250, 350, and 500 $\mu m$ wavelength. The original resolution of the maps, in
order of increasing wavelengths, is $7\arcsec$, $12\arcsec$, $18\arcsec$,
$25\arcsec$ and $36\arcsec$. PACS 100 $\mu m$ image shows no detection with a
rms of 0.00144 $Jy/pixel$ and was therefore excluded from further study. We
then performed pixel-by-pixel SED fitting following Yuan et al. (2017) with
four infared bands (160, 250, 350, 500 $\mu m$) and obtained the temperature
$T_{\text{dust}}$ and column density $N_{\text{H}_{2}}$ maps, which are then
cut to the same size as our PMO’s observation ($14^{\prime}\times
14^{\prime}$). The method is described in detail in Appendix A.

###  2.4 Distance

Distance is always a puzzle in astronomy. Previous works estimated the
distances of HGal molecular clouds to be 100 pc by the velocity dispersion and
the scale height of the ensemble of clouds (Blitz et al., 1984; Magnani et
al., 1985). Follow-up star counts from POSS confirmed that HGal molecular
clouds are indeed nearby objects and the upper limit ranges from 125 to 275 pc
(Magnani & de Vries, 1986). Besides, both small $V_{lsr}$ and the lack of a
double-sine wave signature in the distribution on the $l-V_{lsr}$ plane
demonstrate that HGal molecular gas is too close to the Sun for Galactic
rotation to modulate the velocities (Magnani et al., 1996). Therefore, we
should not expect the co-rotation of HGal objects with the rotation curve,
which means that the traditional method relying on the Milky Way rotation
curve to derive distances may not be a good choice.

Recently, the Gaia satellite has provided new photometric measurement towards
galactic stars (Gaia Collaboration et al., 2016). Together with 2MASS and Pan-
STARRS 1 optical and near-infrared photometry, Gaia DR2 parallaxes can help to
infer distances and reddenings of $\sim$ 800 million stars. These stars trace
the reddening on a small patch of sky, both along the different lines of sight
and different distance intervals, allowing us to build up a map of dust
reddening in 3D (Green et al., 2014, 2019). With the help of this 3D map, we
could infer reddening as a function of distance in the given direction. We
turn to this new method to derive the distances of HGal clumps for three
reasons:

  1. 1.

Kinematic distances to nearby clouds are very unreliable due to the local
Galactic velocity dispersion.

  2. 2.

HGal clumps are less affected by Galactic rotation so it will be better if the
estimation of distances is independent from the rotation of the Milky Way.

  3. 3.

Dust and gas are proved to be well coupled in PGCCs (Wu et al., 2012), so it
is reasonable to derive the distance of molecular gas from the dust
extinction.

In the Gaia dust reddening algorithm, given Galactic longitude and latitude,
different distances of dust are assigned with probabilities and we choose the
distance with largest probability in our paper. This method is precise enough
unless the distance is larger than 1 kpc where the extinction is too strong
(Green et al., 2019). But again, HGal clumps are assumed so close that such
imprecise cases are avoided. Along with Galactic latitudes, the vertical
distance of the clumps from the Galactic midplane (elevation Z) are also
derived,

$\displaystyle Z=d\times sin(|b|)$ (1)

where Z, d, b are the elevation, distance and latitude, respectively. The
distances and elevations of all 41 PGCCs from Gaia dust extinction are listed
in columns (8) and (9) of Table 2.

##  3 Results

###  3.1 Definition of Cores

From single-point observations, we find several sources with multi-velocity
components in our sample. Eight HGal PGCCs have double-velocity components and
one has triple-velocity components. In total, 51 velocity components were
obtained in HGal. We consider each velocity component as an individual clump,
ie. 51 clumps are finally defined. Mapping observations are applied to 26
PGCCs (time is limited and the sample is unbiased) and due to multi-velocity
components, we have 33 mapped clumps. The CO integrated intensity maps of
three example clumps are shown in Figure 2 and the figures of total 33 clumps
are shown in Appendeix B. 12CO is shown as colored background and 13CO (left)
and C18O (right) are shown with blue contours from 50% to 90 % of the peak
integrated intensity. The morphologies include isolated cores, filamentary
structures and also diffuse or full-coverage features.

In this paper, we define all the local enhancements of 13CO intensity higher
than 70% of the peak intensity as individual dense cores. The reasons why we
use 70% rather than 50% are two: one is that in some detections the SNR is
limited especially on the edge of the field of view, and 70% level helps to
remove those mistaken cores by 50% level; the other is that the 13CO contours
are usually extensive and not concentrated, showing a flat density profile,
and therefore we need a more strict criterion to distinguish intensity peaks.
A typical example is the filamentary clump G101.62-28.84a, shown in the two
medium panels of Figure 2. A 70% level contour helps to distinguish four cores
while 50% level cannot do this.

As shown in Figure 2, we mark these cores with black crosses and names “C1”,
“C2”, … The 50% isolines are further fitted with ellipses, providing
measurements of the semi-major and semi-minor axes ($a$ and $b$). The ICRS
coordinate offsets of each core from the observational center are listed in
Columns (2)-(3) of Table 5. The distances of cores are assumed to be the same
as those of the host clumps and listed in Column (4) of Table 5. The sizes of
the cores are given by $R=\sqrt{ab}D$ ($D$ is the distance). Also, due to the
beam smearing effect, we only give upper limits for those cores with sizes
smaller than the beam size of our telescope. The sizes of cores are listed in
Column (5) of Table 5.

For three clumps G089.03-41.28a, G158.77-33.30b and G159.41-34.36b, no cores
are found. For only one clump G004.15+35.77, the 50% isolines significantly
overstep the boundary of the 14-arcmin box. We check the column density map
(blue background) given by pixel-by-pixel SED Fitting (detailed method in
Appendix A), shown in panel (b) of Figure 12. Two dust cores are shown with
deep blue color. The black and white contours give the 13CO and C18O
integrated intensity respectively and only one CO core appears in the map. A
shallow yellow circle gives the location of ammonia dense core (L134-A) with
kinetic temperature $T_{k}$ of 10 K and volume density of $10^{4.5}\
\text{cm}^{-3}$ (Myers et al., 1983). L134-A correlates well with the northern
dust core with a low dust temperature of 10.3 K and C18O core correlates well
with southern dust core with slightly higher dust temperature of 11.1 K. We
define the CO core “C1” traced by C18O as well as dust column density. We also
notice the reason why the northern dust core has lower CO emission. This may
be caused by a higher CO depletion due to the low temperature (Goldsmith,
2001). For consistency, we still choose 13CO emission to define the core size
and neglect the part outside the boundary. This is safe as long as the core is
nearly elliptical.

In total, 54 cores are identified among the 33 mapped clumps. Velocity
components are denoted as “a, b, c, …”, while the cores are labeled as “C1,
C2, C3, …” following Wu et al. (2012).

###  3.2 Line Parameters

We extract the 1-arcmin box towards the core center, averaging all the spectra
inside the box. Then Gaussian fitting is obtained for the three CO lines. If
the profiles arise from blended multi-velocity, multiple Gaussian components
are fitted simultaneously. If the profile originates from self-absorption,
only one Gaussian component is fitted. The centroid velocity ($V_{lsr}$), main
beam brightness temperature ($T_{b}$) and FWHM ($\Delta$V) can be obtained
from Gaussian fitting directly. For those cores without C18O detection, the
upper limit of $T_{b}$ is given by the noise of the baseline and the FWHM is
given the same value as as that for 13CO detection, which will be useful in
the calculation of the upper limits to the C18O column density. Three fitting
parameters are listed in Table 3. Cores without C18O detection have three
parameters of C18O only shown with ’…’. The centroid velocity of the 13CO
J=1-0 line of each core is adopted as the systemic velocity, because the 12CO
J=1-0 line is optically thick and the C18O J=1-0 line has only eight solid
detections in our 54 cores.

###  3.3 Line Profiles

Sometimes, the line profile cannot be fitted as a single Gaussian function and
we call them non-Gaussian. Generally, non-Gaussian profiles in optically thick
molecular lines 12CO(1-0) fall into two main categories: multi-peak and
asymmetry.

The criterion set by Mardones et al. (1997) is applied to check whether blue
or red profiles indicating cloud contraction or expansion in certain cases.
$\delta V$ = ($V_{\text{thick}}$-$V_{\text{thin}}$)/$\delta$
$V_{\text{thin}}$, where $V_{\text{thick}}$ is the peak velocity of 12CO(1-0),
$V_{\text{thin}}$ and $\delta V_{\text{thin}}$ are the systemic velocity and
the line width of 13CO(1-0). If $\delta V<$ -0.25, the line is classified as
blue asymmetric; if $\delta V>$ 0.25, then red asymmetric. Among those
asymmetric profiles, if the optically thick molecular line-12CO has double
peaks at the same time, then we have a lineshape termed blue or red profile,
depending on the blue or red asymmetric profile defined above. The rest of the
multi-peak profiles can be well described as multi-velocity components and can
be fitted by composition of two or more Gaussian functions.

In total, four non-Gaussian profiles are found by single-point observations
(see Figure 3): G089.0-41.2 (blue profile), G182.5-25.3 (red profile),
G210.6-36.7 (red profile) and G159.5-32.8 (red asymmetry). However, single-
point observations only provide one spectrum from the center (or maybe some
little offset), and thus might not represent the real line profiles from the
cores. Therefore, as mentioned before, we extract the molecular lines from the
center of the 54 cores and then carefully examine the line profiles
respectively. A more detailed discussion will be made in Section 4.2.3

###  3.4 Parameters to Be Derived

Parameters from the 54 extracted dense cores are further calculated in this
section.

The excitation temperatures ($T_{ex}$) and optical depths ($\tau$) can be
derived from the solution of the radiation transfer equation:

$\displaystyle T_{b}=$
$\displaystyle\frac{h\nu}{k}\left[\frac{1}{\exp(h\nu/kT_{ex})-1}-\frac{1}{\exp(h\nu/kT_{bg})-1}\right]$
(2) $\displaystyle\times[1-\exp(-\tau)]\ f,$

where $T_{bg}$ is the background temperature (2.73 K). Under the assumptions
that 12CO J=1-0 is optically thick ($\tau\gg$ 1), and the beam filling factor
$f$ is equal to 1, according to Equation (2) of 12CO, the excitation
temperature can be expressed as

$\displaystyle T_{ex}=$
$\displaystyle\frac{h\nu}{k}\ln^{-1}\left\\{\left[\frac{kT_{b}(^{12}\mathrm{CO})}{h\nu}+\frac{1}{\exp(h\nu/kT_{bg})-1}\right]^{-1}+1\right\\}.$
(3)

Under the condition of local thermodynamic equilibrium (LTE), 12CO and 13CO
have the same excitation temperature. We can obtain the optical depth of 13CO
($\tau_{13}$) by

$\displaystyle\tau_{13}=$
$\displaystyle-\ln\left[1-\frac{T_{b}(^{13}\mathrm{CO})}{T_{b}(^{12}\mathrm{CO})}\right].$
(4)

The $T_{\mathrm{ex}}$ of the 54 cores ranges from 6 K to 13 K with a median
value of $\sim$ 10.3 K. The values of Tex and $\tau_{13}$ are listed in
columns (2) and (3) of Table 4. The dust temperature (Tdust) of all the PGCCs
ranges from 5.8 to 20 K with a median value between 13 and 14.5 K (Planck
Collaboration et al., 2016). The similarity of two temperatures indicates that
the gas and dust are well coupled. Besides, the different median temperature
(T${}_{\mathrm{dust,median}}>$ Tex,median) implies that the gas might be
heated by the dust (Goldreich & Kwan, 1974; Wu & Evans, 1989).

The column density of 13CO (N${}_{{}^{13}\mathrm{CO}}$) and C18O
(N${}_{\mathrm{C}^{18}\mathrm{O}}$) can be derived from (Lang, 1978; Garden et
al., 1991)

$\displaystyle N=$
$\displaystyle\frac{3k}{8\pi^{3}B\mu_{d}^{2}}\frac{\exp\left({hBJ(J+1)}/{kT_{ex}}\right)}{J+1}$
(5)
$\displaystyle\times\frac{T_{ex}+hB/3k}{1-\exp(-h\nu/kT_{ex})}\int\tau_{\nu}dV,$

where $B$, $\mu_{d}$ and $J$ are the rotational constant, permanent dipole
moment of the molecule and the rotational quantum number of the lower state in
the observed transition.

Adopting the typical abundance ratios, $[{\rm
H_{2}}]/[{\rm{}^{13}CO}]=89\times 10^{4}$ (McCutcheon et al., 1980) and $[{\rm
H_{2}}]/[{\rm C^{18}O}]=7\times 10^{6}$ (Frerking et al., 1982) for the solar
neighborhood, the column density of hydrogen (N${}_{\mathrm{H}_{2}}$) can be
calculated by Equation (5). Since the detection rate of C18O is low, we use
13CO to calculate H2 column densities, as listed in column (4) of Table. 4.

The one-dimensional velocity dispersion of 13CO is given by

$\sigma_{{}^{13}\mathrm{CO}}=\frac{\Delta V_{{}^{13}\mathrm{CO}}}{\sqrt{8\ln
2}}$ (6)

The thermal ($\sigma_{\text{Th}}$) and non-thermal ($\sigma_{\text{NT}}$)
velocity dispersion can be calculated from

$\sigma_{\text{Th}}=\sqrt{\frac{kT_{ex}}{m_{H}\mu}},$ (7)
$\sigma_{\text{NT}}=\left[\sigma_{{}^{13}\mathrm{CO}}^{2}-\frac{kT_{ex}}{m_{{}^{13}\mathrm{CO}}}\right]^{1/2},$
(8)

where mH is the mass of atomic hydrogen, $\mu$ is the mean weight of molecule
which equals 2.33 (Kauffmann et al., 2008), m${}_{{}^{13}\mathrm{CO}}$ is the
mass of the molecule 13CO and $k$ is the Boltzmann constant. Then the three-
dimensional velocity dispersion $\sigma_{3\mathrm{D}}$ can be calculated from

$\sigma_{3\mathrm{D}}=\sqrt{3(\sigma_{\text{Th}}^{2}+\sigma_{\text{NT}}^{2})}.$
(9)

All the derived parameters are listed in Table 4.

###  3.5 Parameters of Cores

The volume density can be derived through $n_{\mathrm{H}_{2}}$ =
$N_{\mathrm{H}_{2}}/2R$ ($N$ is the column density of hydrogen molecules and
$R$ is the size of the core) under the assumption of homogeneous spherical
material distribution. The LTE mass can be obtained directly from

$M_{\mathrm{LTE}}=\frac{4}{3}\pi R^{3}\mu n_{\mathrm{H}_{2}}m_{\mathrm{H}}.$
(10)

Assuming that the cores are isothermal spheres and supported solely by random
motions, we can calculate the virial mass $M_{\mathrm{vir}}$ as (Williams et
al., 1994)

$M_{\mathrm{vir}}=\frac{5R\ \sigma^{2}_{3D}}{3\gamma\ G},$ (11)

where G is the gravitational constant. The density profile is assumed to be
uniform (also corresponding to the isothermal distribution mentioned in
Section 4.4.2), and then $\gamma$ should be unity.

In molecular clouds, thermal pressure, turbulence and magnetic field can
support the gas against gravity collapse. Taking thermal pressure and
turbulence into account, the Jeans mass can be expressed as following
(Hennebelle & Chabrier, 2008)

$\frac{M_{\mathrm{Jeans}}}{M_{\odot}}\approx
1.0a_{\mathrm{J}}\left(\frac{T_{\mathrm{eff}}}{10K}\right)^{3/2}\left(\frac{\mu}{2.33}\right)^{-1/2}\left(\frac{n}{10^{4}cm^{-3}}\right)^{-1/2},$
(12)

where $a_{\mathrm{J}}$ is a dimensionless parameter of the order unity, $n$ is
the volume density of H2, and the effective kinematic temperature
$T_{\mathrm{eff}}$ is adopted as $\frac{\mu
m_{H}C_{\mathrm{s,eff}}^{2}}{k_{B}}$. The effective sound speed
$C_{\mathrm{s,eff}}$ is expressed by
$[(\sigma_{\mathrm{NT}})^{2}+(\sigma_{\mathrm{Th}})^{2}]^{1/2}$ to account for
combination of both thermal motion and turbulence.

According to Kauffmann et al. (2013), the virial parameter can be applied to
gauge stability against gravitational collapse:

$\alpha_{\mathrm{vir}}=\frac{M_{\mathrm{vir}}}{M_{\mathrm{LTE}}}$ (13)

The volume density, LTE mass, Jeans mass, virial mass and virial parameter are
listed in column (6) – (10) of Table 5, respectively. Also notice that some
cores only have upper limits for sizes, the size-related parameters above are
then semi-constrained and presented with upper or lower limits.

###  3.6 Dense Gas Tracers

We have observed two dense gas tracers N2H+ and C2H in eighteen clumps with
high enough 13CO antenna temperature among 26 mapped HGal PGCCs, which are
thought to be the sub-sample with embedded dense cores. For comparison
purpose, we also searched for N2H+ and C2H in eighteen clumps at the latitude
range between 21°and 25°. Only one HGal PGCC has obvious detections, of both
two dense tracers, as shown in the lower right panel of Figure 4. For another
eighteen low-latitude clumps, we find six of them having at least one kind of
dense-gas tracer. G008.5+21.8 and G158.8-21.6 have both N2H+ and C2H detection
respectively in the upper left and upper right panel of Figure 4 and clumps
like G008.6+22.1 have only C2H detection.

##  4 Discussion

###  4.1 Galactic Distribution

The distribution of HGal clumps is shown in Figure 1. The background colormap
is the CO survey of the Planck Collaboration (Planck Collaboration et al.,
2014). HGal PGCCs we observed are marked with blue crosses. Rectangles with
names were defined after Dame et al. (1987) as well as Wu et al. (2012),
marking the known CO molecular clouds or complexes. The blue rectangles mark
the published PMO 13.7-m data (Liu et al., 2012; Meng et al., 2013; Zhang et
al., 2016, 2020). Two bold rectangles at high latitude mark the regions that
have large and unbiased survey with higher resolution or spatial spacing
(Heithausen et al., 1993; Yamamoto et al., 2003). However, the survey of Dame
et al. (1987) was limited to the Galactic plane, while the surveys by
Heithausen et al. (1993) and Yamamoto et al. (2003) are limited to certain
regions (see Figure 1). Compared to prior surveys, we have detected CO
emission at higher latitude. The average latitude of 41 clumps is 36.87°. The
highest elevation is 214 pc for G153.74+35.91 and the average value is 119 pc.

To examine the consistency between PGCCs and HGal clouds with CO detections,
we cross-match the HGal PGCCs with molecular clouds that have been found and
observed in CO before, including Heithausen et al. (1993); Magnani et al.
(1996); Hartmann et al. (1998); Magnani et al. (2000). The cross-matching
result is shown in Column (11) of Table 2. Filled yellow circles in Figure 1
show 121 HGal objects summarized by Magnani et al. (1996). As we can see, most
clumps are embedded in the known molecular clouds, and tend to group in
several famous HGal cloud regions. In the Northern Hemisphere, 2 clumps come
from the Ursa Major cloud complex, 2 come from MBM 25, 6 come from the L134
complex. In the southern hemisphere, most of clumps gather at 145°$\leq
l\leq$195°, -46°$\leq b\leq$-30°, to the south of the Tarus-Aurgiae complex of
dark clouds (Magnani et al., 2000). For instance, MBM 11–12 (L1457-c) contains
7 clumps. There are also 2 clumps associated with MBM 53–55 complex surveyed
by Yamamoto et al. (2003), which has a significant extent 85°$\leq l\leq$
96°and -43°$\leq b\leq$ -32°(Blitz & Lockman, 1988; Magnani et al., 2000). We
then zoom in two clump-crowded regions of the L134 complex (6 clumps included)
and MBM 11–12 complex (7 clumps included) in the lower left and upper right
panel of Figure 1, respectively. Those clumps are mainly distributed at the
outskirts of these HGal clouds/complexes.

There are 6 clumps G101.62-28.84, G102.72-25.98, G126.65-71.43, G127.31-70.09,
G182.54-25.34 and G203.57-30.08 not associated with known HGal clouds,
contributing to 14.6% (6 in 41) of the sample. Those clumps, more diffuse in
shape and smaller in size, might escape the search with coarse sampling grid
of about 1 degree and beamwidth of $\sim 8^{\prime}$ in the surveys of
Hartmann et al. (1998) and Magnani et al. (2000). Besides, HGal PGCCs are
generally embedded in translucent molecular clouds, so the MBM clouds selected
by optical obscuration may also not include those diffuse clumps. Yet those
clumps are cold enough to be detected by Planck.

###  4.2 Emission Lines

####  4.2.1 Detection Rate

All the HGal clumps were observed in 12CO and 13CO but only 16 clumps have
C18O detections. The detection rate of 12CO is 100%, indicating that Planck
Cold Galactic Clumps (PGCCs) are well-traced by CO emission. Such a result
corresponds to similarly high detection rate of 98.4% found in a surveyed 64
Lynds Dark Clouds sample where extinction exceeds one or two magnitudes
(Dickman, 1975). However, the detection rate of C18O is only 40%, compared to
68% of the total sample-674 PGCCs (Wu et al., 2012), 77.5% in Taurus(Meng et
al., 2013), 81.5% in the First Quadrant, 79.5% in the Anti-centre Direction
(Zhang et al., 2020) and 84.4% in the Second Quadrant (Zhang et al., 2016).

Besides, two dense-gas tracers N2H+ and C2H (see in Section 3.6) show that the
detection rate of molecular lines with high critical density (molecular lines
that trace dense gas) is different between the HGal region ($|b|>25\arcdeg$)
and lower region ($25\arcdeg>|b|>21\arcdeg$). Only one clump has both N2H+
J=1-0 and C2H J=1-0 among the eighteen selected HGal clumps (see also Section
3.6), which are thought to contain dense cores. While for lower latitude
regions, four of the eighteen dense cores show significant C2H J=1-0
detections and three have N2H+ J=1-0. Such a result along with high detection
rates of 58.7% for C2H and 47.9% for N2H+ of 121 CO selected sample, mostly
around $21\arcdeg>|b|>0\arcdeg$ (Liu et al., 2019), demonstrates a significant
gradient of material density along latitude. Figure 5 shows the trend of
detection rate decreasing along latitude. There are two explanations for this:
one is that as Galactic latitude increases, gas becomes more diffuse and dense
regions become rare; the other is that the abundances of N2H+ and C2H are
lower.

####  4.2.2 CO Isotope Abundances

The Galactic gradient of isotope ratio 12C/13C is given by (Jacob et al.,
2020):

$\displaystyle\frac{{}^{12}\mathrm{C}}{{}^{13}\mathrm{C}}=5.87\frac{R_{\mathrm{gal}}}{\mathrm{kpc}}+13.25$
(14)

and 16O/18O is given by (Wilson & Rood, 1994):

$\displaystyle\frac{{}^{16}\mathrm{O}}{{}^{18}\mathrm{O}}=58.8\frac{R_{\mathrm{gal}}}{\mathrm{kpc}}+37.1$
(15)

where $R_{\mathrm{gal}}$ is the distance towards the Galactic center.

The close distances of HGal clumps (see Section 2.4) make it easier to
calculate the CO abundances, simply by adopting $R_{\mathrm{gal}}$ = 8 kpc
(solar neighbourhood). Considering CO and its isotopes 13CO and C18O, we could
derive the abundance
$\frac{X(^{13}\mathrm{CO})}{X(\mathrm{C}^{18}\mathrm{O})}$ to be about 8,
which is consistent with the single-point result (Wu et al., 2012, Fig.11) as
well as the ratio we used in Section 3.4. We then derived the column density
of hydrogen molecules $N_{\mathrm{H}_{2}}$ for all 54 HGal cores by both 13CO
and C18O. Among these cores, 8 with C18O (1-0) detections have been fitted
with Gaussian profiles and the column densities can be derived directly. For
the other 46 cores without C18O, the upper limits are given by the noise
$\sigma$ of baseline fitting (see Section 3.4). The cumulative distribution
functions of the column densities derived by 13CO (black) and C18O (blue) are
shown in Figure 6 (a). Individual uncertainties are considered and 1000 runs
of Monte Carlo simulate the data scatter. Besides, a KS test gives extremely
low $p$-value, showing that the H2 column densities derived from 13CO and C18O
are significantly different.

We also check the possibility that low column density derived from C18O is due
to low excitation temperature of the C18O molecule (Li & Goldsmith, 2003,
eq.10). Since the LTE condition is not always satisfied, especially when the
volume density (for HGal, the mean value is $10^{4}$ cm-3) is no higher than
the critical density ($\sim 10^{3}$ cm3) for pure collisional excitation by H2
(Scoville, 2013), the excitation temperature of C18O cannot be as high as that
for 12CO when the optical depth $\tau_{18}$ is low (mean value is 0.15). We
assume that the excitation temperature of C18O is as low as 5 K, then the
column density shows only 13($\pm$4)% enhancement. Such modest enhancement
cannot explain the C18O abundance we observed.

The Taurus region, reported to be close to us (Dame et al., 1987; Lada et al.,
2009; Lombardi et al., 2010), is the best place to test whether HGal gas shows
a significant deviation of CO isotopic abundances. This is because one would
expect the closeness in location (and therefore a similar distance to the
Galactic center) would produce similar abundances. We compare HGal (blue
points with error bars) to Taurus as well as non-HGal PGCCs (red contours) in
Figure 6 (b). The ratio $X_{13}/X_{18}$ in the solar neighborhood $\sim 8$ is
satisfied along grey solid line. As shown in the Figure 6 (b), PGCCs in Taurus
obey this ratio well and other regions have even lower ratios. However, HGal
cores are mostly distributed much below the solid line, showing that they have
a much higher $X_{13}$/$X_{18}$ ratio, which could be as high as 16. Above
all, the ratio $X_{13}$/$X_{18}$ in HGal cores is systematically higher than
those of previous results, which is consistent with only a 40% detection rate
of C18O by single-point observed results (see in Section 4.2.1).

High abundance ratios of 13CO to C18O (16.47$\pm 0.10$) towards photo-
dominated regions (PDR) are reported in the Orion-A giant molecular cloud and
it suggests that FUV radiation penetrates the innermost part of clouds and the
whole cloud experiences selective UV photo-dissociation (Shimajiri et al.,
2014). We examine the relation between the column density of C18O and the
abundance ratio $X_{13}$/$X_{18}$ in Figure 6 (c), shown with blue points
(deep-colored points give solid abundance values and light-colored points give
lower limits) as well as contours. The estimations of $A_{v}$ are shown at the
top x-axis of the figure using the following relation derived in the Taurus
region by Frerking et al. (1982):

$A_{v}=\frac{N_{\mathrm{C}^{18}\mathrm{O}}(\mathrm{cm}^{-2})}{2.4\times
10^{14}}+2.9$ (16)

As the column density $N_{\mathrm{C}^{18}\mathrm{O}}$ increases (extinction
$A_{v}$ increases from $\sim$3.0 to $\sim$6.0), the abundance ratio decreases.
Such decreasing trend could be interpreted as lower penetrability of external
photons into the clouds and therefore by a weaker isotopic selective photo-
dissociation effect as the extinction becomes larger. HGal clouds, reported to
be translucent (van Dishoeck & Black, 1988; van Dishoeck et al., 1991), are in
the astrochemical regime where most of the carbon becomes tied up in the form
of CO (Magnani et al., 1996). Hence, those clouds are more likely to be
influenced by UV photons in the ISM though not as strong as the Orion-A giant
molecular cloud mentioned above. Besides, the cold clumps we observed tend to
be distributed in the outskirts of those clouds (see Figure 1 and therefore
lower extinction), making the selective photo-dissociation easier.

We also notice that once column density becomes larger ($A_{v}>7$), the ratio
keeps about 14, which is still higher than the ratio of 5.5 in the solar
neighborhood. Such high ratio could not be explained solely by selective
photo-dissociation. A decreasing $X_{13}$/$X_{18}$ ratio as
$\Sigma_{\mathrm{SFR}}$ increases is reported in nearby spiral galaxies and
the possible explanation is that gas preferentially enriched by massive stars
shows low 13CO/C18O ratio (Jiménez-Donaire et al., 2017). In turn, in HGal
regions, $\sim$ 100 pc above the disk, star formation history might not be the
same as that in the disk. The scarce star formation activities (see two
zoomed-in figures in Section 4.4) indicate a low star formation rate at HGal,
which may be responsible for the high $X_{13}$/$X_{18}$ ratio.

####  4.2.3 Line Profile

Core-extracted spectra show similar results as single-point observations did,
except for the case of G159.5-32.8 (red asymmetry) which is later proved to
have double velocity components bearing totally 5 cores. G210.6-36.7 (red
profile) without mapping observation is excluded for further analyses.

G089.03-41.28 and G182.54-25.34a (see Figure 3) are classified by single-point
observations as blue and red line profiles, respectively. They both have
mapping observations and further analyses find that the non-Gaussian line
profiles are probable the result of double or complicated velocity components.
These cases are discussed in the following.

G089.03-41.28 is the only blue profile detected in HGal region by single-point
observations. We then check the central 3$\times$3 mapping grids in Figure 7.
It is obvious that the source is dynamically complicated. Although single-
point observation may display a potential blue profile, the line profiles from
3$\times$3 map grids (Figure 7) show local differences at the size of 0.05-0.1
pc (0.5 arcmin per pixel at the distance of 0.183 kpc). Such a complex
velocity structure has been studied in the molecular cloud MBM 55 containing
the clump G089.03-41.28. The intrinsic velocity dispersion of MBM 55 is
reported to be 2.09 km s-1 (Magnani et al., 1985), corresponding to the
separation of our double peak 13CO emission lines.

G182.54-25.34 exhibits the only red profile observed with both single-point
and mapping observations in HGal region. To better understand the dynamical
information, a position-velocity (PV) map is applied to the central area of
G182.54-25.34. We extract the molecular lines along the strip with the same RA
offset of -0.343 arcmin in Figure 8. Two velocity components are shown: one is
located in the center of the map (marked red “1”) and the other with uniform
velocity dispersion extends to the south (marked red “2”). Therefore, the
central line profile of G182.54-25.34a.C1 is considered to result from two
velocity components with 1.3 km s-1shift rather than from an expanding motion.

###  4.3 Non-thermal Motion

PGCCs are relatively cold and quiescent on the whole compared to other typical
star forming regions (Wu et al., 2012) and the non-thermal motions in these
clumps are therefore mainly contributed by turbulence (Zhang et al., 2020). In
most of the PGCC cores we observed, non-thermal velocity dispersion is larger
than thermal one ($\sigma_{NT}\geq\sigma_{Th}$). In other words, the
turbulence is super-sonic (above blue-shaded region in Figure 9) in most of
the samples (Wu et al., 2012, Table.2). These cores might be still at an early
stage along the time sequence of condensations: confined by outer Hi gas
pressure (Heithausen, 1996) or even just in a transient phase (Magnani et al.,
1993).

First suggested by Larson (1981), a cascade in an incompressible fluid should
be responsible for observed $\sigma\sim R^{0.38}$ relation. Further
refinements have changed this simple picture and the power law index differs
depending on environment (Shore et al., 2007). The grey dash-dotted line (in
Figure 9) from the First Quadrant (IQuad) gives a correlation similar to
Larson’s relation (Zhang et al., 2020). For HGal cores (purple points with
error bars, also purple filled contours), the relation is also checked as:

$\displaystyle\sigma_{3D}=(0.57\pm 0.14)\times R^{0.50\pm 0.11}$ (17)

with a poor correlation coefficient of $R^{2}=0.36$. We exclude the cores with
only upper limits of sizes in this linear regression and mark them as light
purple with semi-errorbars. Blue contours represent other PGCC cores
(hereafter non-HGal) also observed with 13.7-m PMO telescope (Liu et al.,
2012; Meng et al., 2013; Zhang et al., 2016, 2020). These non-HGal cores also
obey the Larson’s relation derived from grey dash-dotted line on the whole.

HGal clumps are closer in distance and enable us to observe at smaller scale,
and on the other hand we tend to observe a farther clump at larger scale. Such
observational differences in size enable us to study the turbulent property at
the different scales. The conceptual foundation of turbulence is a monotonic
cascade from large injection scales to small scales where it is dissipated
(Tennekes & Lumley, 1972; McComb & Watt, 1992). As shown in Figure 9, along
the blue dash-dotted line from upper right to lower left, $\sigma_{3D}$
decreases with core size R. However, a large-scale (0.1-3 pc) Larson’s
relation cannot be extended to the small-scale (0.01-0.1 pc) continuously,
which is dramatically shown by the bimodal distribution with purple and blue
filled contours. HGal cores (purple), with the smallest size, have
significantly higher $\sigma$ than a continuous cascade from the large scale
expected, even if the error bars are taken into account.

Since energy can be injected on many scales ranging from Galactic dynamics to
individual stellar processes, the turbulent mechanism in ISM can vary due to
local differences. Many of the HGal clouds are reported to be part of large Hi
shells or fragments of shells in the local ISM (Gir et al., 1994; Bhatt, 2000)
where the shock compression at the cloud boundary plays the dominant role.
However, HGal clouds like MBM 3, MBM 16 and MBM 40 are thought to be immersed
in strong shear flows from the Hi medium, powering the turbulence inside the
clouds (Shore et al., 2003, 2006). We notice that whichever mechanism is
operating, HGal cores with extra energy injections will restart a new cascade
“path” along the purple dash-dotted line (see Figure 9). We then plot the grey
point as MBM 3, showing the typical size $\sim$ 1 pc where turbulent energy is
injected by shear flow (Shore et al., 2006).

However, the scatter in the data is large and the light purple points can’t be
simply explained by a monotonic turbulent cascade along the new “path”.
Instead, once the self-similar turbulence scales down to a typical size
$R_{0}$, velocity dispersion $\sigma$ doesn’t obey the decreasing trend but
seems to be independent of size. Such a turning-point scale $R_{\text{coh}}$
corresponds to the transition to “coherence” (Goodman et al., 1998), which can
be the case of HGal clouds MBM 16 (Magnani et al., 1993). One of the accepted
efxplanations for “coherence” is Alfvén wave cutoff (Goodman et al., 1998). If
the Alfvén waves support the turbulent cascade, then $R_{\text{coh}}$ may be
very close to the scale $R_{\text{cut}}$ below which no Alfvén wave can
propagate in the medium. $R_{\text{cut}}$ can be simply calculated from (McKee
& Zweibel, 1995):

$\displaystyle R_{\text{cut}}=\frac{\lambda_{\text{cut}}}{2}=\frac{\pi
B}{4\pi^{\frac{1}{2}}\rho^{\frac{3}{2}}x_{i}\gamma}$ (18)

where $B$, $\rho$, $x_{i}$ and $\gamma$ are magnetic field, density,
ionization fraction and drag coefficient, respectively. If we take the typical
value of number density $n=5\times 10^{3}$ cm-3, $B=20\mu G$, $x_{i}=10^{-7}$
and $\gamma=3.5\times 10^{13}$ cm3g-1s-1, then $R_{\text{cut}}\simeq 0.05$ pc.
As shown with grey-shaded area in Figure 9, the turbulent dissipation is
suppressed below 0.05 pc.

###  4.4 Core Status

####  4.4.1 Starless Cores

Matching these HGal cores with stellar objects is very useful for
understanding the environment and evolutionary status of the cloud cores.
Based on the Wide field Infrared Survey Explorer (WISE) mission, a catalog of
133,980 identified Class I/II YSO candidates (CIs) as well as Class III YSO
candidates (CIIIs) have been presented by Marton et al. (2016). The CIs and
CIIIs sources are believed to be associated with cores inside the clumps if
they are located in the mapped area of 14’$\times$14’ as well as offset to the
core center less than a beam size ($\sim 1^{\prime}$, corresponding to 0.05 pc
with the typical distance of 200 pc). As a result, none of HGal cores have
associated sources mentioned above and they are all starless cores. The non-
detection of YSO candidates indicates that the HGal gas traced by PGCCs
remains to be at early stage with barely active star formation. We also notice
that the advantage of studying associated objects of HGal PGCCs is to avoid
most of the contamination at line of sight for those distant sources in the
direction of the Galactic plane. Therefore, no associated YSO candidates
detected in HGal cores reflects the starless status.

However, we note that this result does not mean HGal regions bear no active
star formation activities. Considering PGCCs are cold and early (Planck
Collaboration et al., 2011a; Wu et al., 2012), we unfortunately miss the gas
or dust with higher temperature which traces but also is heated by young
stellar objects. Actually, although rare, HGal regions still have a handful of
ongoing star formation. A typical example is the famous HGal cloud L1642
showing definitely active star-formation (Malinen et al., 2014), The HGal
cloud consists of dense regions A1, A2, B, and C (Lehtinen et al., 2004), in
which L1642-B ($\alpha_{2000}=4^{\mathrm{h}}35^{\mathrm{m}}13^{\mathrm{s}}.1$,
$\delta_{2000}=-14\arcdeg 15\arcmin 43\arcsec$) contains two well-known binary
T Tauri stars (Sandell et al., 1987; Malinen et al., 2014), while L1642-A1
($\alpha_{2000}=4^{\mathrm{h}}34^{\mathrm{m}}00^{\mathrm{s}}.3$,
$\delta_{2000}=-14\arcdeg 10\arcmin 12\arcsec$) corresponds to the PGCC
G210.67-36.77 that we observed. These two dense regions are
$18\mbox{$.\\!\\!^{\prime}$}5$ away from each other and therefore would not be
identified to be associated by the YSO matching. The other example is the
MBM12 cloud (also known as L1453, L1454, L1457 and L1458), which is identified
to contain the young association MBM 12A (Luhman, 2001). Towards MBM12, PGCCs
have 6 detections of G158.77-33.30, G158.88-34.18, G158.97-33.01,
G159.23-34.49, G159.41-34.36 and G159.67-34.31, and we all adopted mapping
observations. Nevertheless, dense cores inside these clumps are all starless.

####  4.4.2 Gravitational Stability

Based on the criterion of virial parameters derived in Section 3.4, we can
determine the gravitational stability in each core. More specifically, if the
virial mass $M_{vir}$ (eq.11) is smaller than the $M_{\mathrm{LTE}}$ (eq.10),
the system has enough gravitational potential to restrain the material inside
and would probably collapse in the future. In turn, if $M_{vir}$ is much
larger than $M_{\mathrm{LTE}}$, the core is probably confined by external
pressure or is in a transient phase. Whichever the status is, the core would
not currently go into gravitational collapse.

The $M_{\text{LTE}}$-$\alpha_{\mathrm{vir}}$ relation is checked in all
observed cores as shown in Figure 10. Grey and light grey-shaded area gives
$M_{\mathrm{LTE}}>M_{\mathrm{vir}}$ and $3M_{\mathrm{LTE}}>M_{\mathrm{vir}}$
(Liu et al., 2012) regime as criteria for gravitational bound and marginally
gravitational bound, respectively. The results of four previous studies
(Orion, Taurus, IIQuad and IQuad&ACent) as well as this work are shown with
blue, orange, red, green and purple filled contours. Most cores in Orion,
IQuad, ACent and part of cores in IIQuad satisfy
$3M_{\mathrm{LTE}}>M_{\mathrm{vir}}$, let alone some satisfy
$M_{\mathrm{LTE}}>M_{\mathrm{vir}}$. However, none of HGal cores are
gravitational bound and 11% of the cores are close to a highly unbound phase
with $\alpha\geq 100$. Only 21% of the Taurus cores are marginally
gravitational bound and 13% of the cores are in a highly unbound phase as HGal
cores are. The similar position in $M_{\mathrm{LTE}}$-$\alpha_{\mathrm{vir}}$
plane is assumed to be related to spatial proximity: almost half of HGal cores
are the spatial extension of Taurus region (see in Section 4.1).

A broken power-law is fitted to the total sample (including this work and
Taurus, Orion, IQuad, Acent and IIQuad) with the ankle point (4.6$M_{\odot}$,
4.5) and two power-law indices of $k_{1}=-0.61$ and $k_{2}=-0.30$ (see red
dotted line in Figure 10). In the lower LTE mass regime, HGal as well as part
of Taurus cores dominate and produce a steep power-law index which is
consistent with -2/3 for pressure-confined cores (Bertoldi & McKee, 1992). But
in the high mass regime, IQuad, ACent, Orion and IIQuad cores dominate and
produce a much flatter slope of -0.3. Those grey dotted lines shown with
different $M_{\mathrm{Jeans}}$ of 1, 10, 100, 1000 $M_{\odot}$ give the
$M_{LTE}$-$\alpha_{\mathrm{vir}}$ relation under the assumption of pressure-
confined cores. For these cores (along grey dotted lines), self-gravity is
unimportant and there is barely a gradient of density or temperature
(isothermal). Therefore the Jeans mass does not change with LTE mass. As
indicated by the left end of red dotted line, HGal and a part of the Taurus
cores are dominated by external pressure with Jeans mass of 1-100 $M_{\odot}$.
As $M_{\mathrm{LTE}}$ increases, self-gravity cannot be ignored. Jeans mass
gets larger as velocity dispersion (effective temperature $T_{\mathrm{eff}}$;
see (a) in Figure 11) increases and volume density decreases (see (b) in
Figure 11), when the LTE mass becomes larger (from the ankle to the right end
of the red dotted line).

###  4.5 Unusual Characteristics of HGal Gas

The idea that HGal gas is different from that in the Galactic disk has been
reported already (Blitz et al., 1984; Magnani et al., 1985) and our follow-up
work gives further evidence and makes the idea much clearer. Section 4.2.1
shows a significant gradient of the dense-molecule detection rate along
latitude. According to the result of 54 HGal cores, the abundance of CO
isotopes bears a large deviation from that of Galactic disk (see Section
4.2.1). And no blue or red profiles are found (see Section 4.2.3). Besides,
there are no associated YSO candidates found in the host clumps (see Section
4.4.1). As shown in Section 4.4.2, none of the cores are gravitational bound
even with a looser criterion. These results demonstrate that at that high
latitude, gas is totally different from that of Galactic disk, although they
are part of the local interstellar medium within 200 pc or so. Above all, HGal
gas traced by PGCCs is at an extremely early stage and transient phase still
confined with pressure, without clear indications of star formation at the
current time.

##  5 Summary

We have performed a single-point survey in the J=1-0 transition of 12CO, 13CO
and C18O with the PMO 13.7-m telescope toward 41 Planck Galactic cold clumps
(PGCCs) at high Galactic latitude ($|b|>25\arcdeg$; HGal). In total 51
velocity components are identified and 33 of them have CO mapping
observations. 12CO and 13CO lines were detected in all of them, while C18O has
been detected in only 16 of HGal clumps. We identified 54 dense cores from the
13CO velocity integrated intensity maps. The parameters of detected lines and
identified cores were derived. Further single-point observations towards 18
HGal cores and 18 cores with lower latitude $25\arcdeg>|b|>21\arcdeg$ were
adopted. We also include other previously observed PGCCs from Orion, Taurus,
the Second Quadrant (IIQuad), the First Quadrant (IQuad) and Anti-center
(ACent) regions (Liu et al., 2012; Meng et al., 2013; Zhang et al., 2016,
2020). We call these previous observed PGCCs as ‘non-HGal PGCCs’ and some
related detailed statistic analyses are done. The main findings are summarized
as follows.

  1. 1.

The highest latitude clump we detected by single point observation is
G126.65-71.43 with $b=-71.43\arcdeg$, and the highest one we mapped is
G089.03-41.28 with $b=-41.28\arcdeg$. 14.6% of the observed clumps are not
included in previous CO surveys. All the clumps in our work are now mapped
with the high angular resolution of 1′. The one with the highest elevation is
located 214 pc above the Galactic plane. The sample from PGCCs is unbiased and
facilitates an overall knowledge of gas in our Galaxy.

  2. 2.

The ratio $X_{13}$/$X_{18}(>\sim 14)$ in HGal cores is systematically higher
than that found in the solar neighborhood or the Galactic disk, which is
consistent with our low C18O detection rate (40%) by single-point observed
results. Such a high ratio suggests that the HGal ISM is unique and might be
explained by a different star forming history compared to that in the Galactic
disk. Extremely low detection rates of two dense core tracers illustrates the
decreasing gradient of N2H+ and C2H along latitude. Such a low detection rate
shows that HGal gas is relatively diffuse and has not yet form dense regions.

  3. 3.

The 12CO excitation temperature ($T_{\rm ex}$) of HGal cores ranges from 6 to
13 K respectively. The excitation temperatures are similar to the dust
temperatures (Tdust) (Planck Collaboration et al., 2016), which might suggest
that gas and dust are well coupled in these cores. We improve the calculation
of clump distances by adopting Gaia dust extinction maps. The typical distance
is about 200 pc.

  4. 4.

No blue or red profiles are detected in HGal cores. There seem to be no signs
of star forming activities. Besides, no cores have associated YSO candidates.
The environment of these cores is proved to be quiescent and inactive.

  5. 5.

HGal cores are distinctly separated from other observed PGCCs (non-HGal) cores
on the $\sigma-R$ plane. This could indicate another turbulence energy
injection mechanism, like shear flows at the scale of clouds $\sim 1$ pc.
Besides, the monotonic turbulent cascade seems to be suppressed below 0.05 pc
where the transition to coherence takes place.

  6. 6.

All the HGal cores are not gravitationally bound but instead appear to be
pressure-confined, while for massive non-HGal cores, the gravity dominates.
These two different behaviours are shown by a broken power law in the
$M_{\mathrm{LTE}}-\alpha_{\mathrm{vir}}$ plane with an ankle
(MLTE,$\alpha_{\mathrm{vir}}$) = (4.6$M_{\odot}$,4.5)

This project was supported by NSFC No.11433008 and the China Ministry of
Science and Technology under State Key Development Program for Basic Research
(No. 2012CB821800), and the National Key R&D Program of China
No.2017YFA0402600, and the NSFC No.12033005, 11988101, 11373009, 11503035 and
11573036. Natalia Inostroza acknowledges CONICYT/PCI/REDI170243. We thank
Lianghao Lin’s helpful reminder of GAIA DRii and related reference, which
contributes a lot to our distance calculator. We thank the staff at PMO 13.7-m
for their support during the observations. This research was performed in part
at the Jet Propulsion Laboratory, California Institute of Technology, under a
contract with the National Aeronautics and Space Administration
(80NM0018D0004). This research made use of Montage which is funded by the
National Science Foundation under Grant Number ACI-1440620.

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Table 1: CO Line Survey at High Galactic Latitude

Sample Selectiona. | Telescope | Resolution | Sampling | Covering Range
---|---|---|---|---
POSS platesb. | Texas 5-mc. | 2$.\\!\\!^{\prime}$3 | 10′ | $|b|\geq 20\arcdeg$
ESO platesd. | South CU 1.2-me. | 8$.\\!\\!^{\prime}$6 | 7$.\\!\\!^{\prime}$5 | R.A.: 3-15h, Decl.$<-20^{\circ}$
Infrared cirrusf. | North CU 1.2-mg. | 8$.\\!\\!^{\prime}$6 | 8$.\\!\\!^{\prime}$6 | $l:141\sim 149\arcdeg,b:34\sim 42\arcdeg$
2nd quadrant HGalh. | North CU 1.2-m | 8$.\\!\\!^{\prime}$7 | 7$.\\!\\!^{\prime}$5 | $l:117\sim 160\arcdeg,b:16\sim 44\arcdeg$
Catalog1996i. |  |  |  | $|b|\geq 25\arcdeg$
Northj. | North CU 1.2-m | 8$.\\!\\!^{\prime}$4 | 0.3-1° k. | $b\geq 30\arcdeg$
Southl. | North CU 1.2-m | 8$.\\!\\!^{\prime}$4 | 0.3-1° | $b\leq-30\arcdeg$
Hi Filamentm. | NANTEN 4-mn. | 2$.\\!\\!^{\prime}$6 | 4${}^{\prime}(\times\cos b)$ o. | $l:82\sim 98\arcdeg,b:-45\sim-29\arcdeg$
PGCC at HGalp. | PMO 13.7-mq. |  $\sim$56′′ | 30′′ | $|b|\geq 25\arcdeg$

${}^{\textbf{{a.}}}$The criterion of the source selection in the survey.
${}^{\textbf{{b.}}}$Optical obscuration selected from POSS southern sky survey
plates (Magnani et al., 1985). ${}^{\textbf{{c.}}}$5-m Millimeter Wave
Observatory in Texas. ${}^{\textbf{{d.}}}$European Southern Observatory (ESO)
southern sky survey plates were examined for regions of faint obscuration or
reflection. 135 in 151 prints were searched for CO emission (Keto & Myers,
1986). ${}^{\textbf{{e.}}}$The Columbia University 1.2-m Millimeter-Wave
Telescope in Cerro Tololo, Chile. The telescope was constructed at Columbia
and shipped to Chile in 1982. ${}^{\textbf{{f.}}}$The patchy far-infrared
emission (“cirrus”) in Ursa Major, discovered by IRAS (Low et al., 1984; de
Vries et al., 1987). ${}^{\textbf{{g.}}}$The Columbia University 1.2-m
Millimeter-Wave Telescope which was removed to the Center for Astrophysics
(CfA) in 1986. One of the twin instruments was located in the Northern
hemisphere, the other one is in Chiled. ${}^{\textbf{{h.}}}$Composite large-
scale CO survey at high Galactic latitude in the second quadrant (Heithausen
et al., 1993). ${}^{\textbf{{i.}}}$The catalog of molecular gas at high
Galactic latitude by 1996. Related references are included in Magnani et al.
(1996). ${}^{\textbf{{j.}}}$the northern Galactic hemisphere.
${}^{\textbf{{k.}}}$The sampling interval is $\Delta l\times\cos b$.
${}^{\textbf{{l.}}}$the sorthern Galactic hemisphere. ${}^{\textbf{{m.}}}$The
Hi filament that contains the HGal clouds complex of MBM 53, 54, and 55
complex which is one of the largest and most massive complexes at HGal
(Yamamoto et al., 2003). ${}^{\textbf{{n.}}}$NANTEN 4-m (sub)millimeter-wave
telescope of Nagoya University at Las Campanas Observatory in Chile.
${}^{\textbf{{o.}}}$To begin with, 12CO has been measured with 8′ in latitude
$b$ and 8${}^{\prime}\times\cos b$ in longitued $l$; next observe 13CO with 4′
in $b$ and 4${}^{\prime}\times\cos b$ in $l$; finanly observe 13CO and C18O
with 2′ in $b$ and 2${}^{\prime}\times\cos b$ in $l$. ${}^{\textbf{{p.}}}$This
work: Planck Galactic Cold Clumps (PGCCs) at high Galactic latitude.
${}^{\textbf{{q.}}}$Purple Mountain Observatory 13.7-m Millimeter Radio
Telescope.

Table 2: Catalogue of PGCCs at High Galactic Latitude

Name | Glon. | Glat. | R.A.(J2000) | Decl.(J2000) | R.A.(B1950) | Decl.(B1950) | Distance | Elevation | OTF Map | Comment
---|---|---|---|---|---|---|---|---|---|---
| deg | deg | h:m:s | d:m:s | h:m:s | d:m:s | pc | pc |  |
G004.15+35.77 | 4.1528 | 35.7772 | 15 53 29.82 | -04 38 52.39 | 15 50 51.56 | -04 40 30.16 | 145.0 | 85.0 | Y | L134a, MBM 36b
G004.17+36.67 | 4.1748 | 36.6789 | 15 50 42.66 | -04 04 20.84 | 15 48 05.00 | -03 55 20.10 | 130.0 | 77.0 | Y | CB 63c, LBNd
G004.54+36.74 | 4.5483 | 36.7487 | 15 51 14.27 | -03 47 40.14 | 15 48 36.88 | -03 38 41.35 | 130.0 | 78.0 | Y | L169, MBM 37
G004.81+37.02 | 4.8120 | 37.0285 | 15 50 52.79 | -03 27 20.38 | 15 48 15.74 | -03 18 20.28 | 130.0 | 78.0 | Y | L169, MBM 37
G005.69+36.84 | 5.6909 | 36.8419 | 15 53 11.88 | -03 00 56.50 | 15 50 35.24 | -02 52 04.98 | 122.0 | 73.0 | N | MBM 37
G006.04+36.74 | 6.0424 | 36.7487 | 15 54 10.81 | -02 50 56.32 | 15 51 34.33 | -02 42 08.46 | 122.0 | 73.0 | Y | L183
G008.43+36.35 | 8.4375 | 36.3540 | 16 00 02.55 | -01 32 25.18 | 15 57 27.34 | -01 23 59.32 | 130.0 | 77.0 | Y | MBM 38, CB 64
G011.40+36.19 | 11.4038 | 36.1921 | 16 06 03.58 | +00 19 32.84 | 16 03 30.26 | +00 27 35.75 | 130.0 | 77.0 | Y | MBM 39, LBN
G037.51+44.57 | 37.5193 | 44.5732 | 16 10 54.35 | +21 45 37.26 | 16 08 44.35 | +21 53 20.74 | 122.0 | 86.0 | N | MBM 40, LBN
G089.03-41.28 | 89.0331 | -41.2869 | 23 08 43.43 | +14 43 35.71 | 23 06 13.66 | +14 27 19.66 | 183.0 | 121.0 | Y | MBM 55
G091.29-38.15 | 91.2963 | -38.1584 | 23 08 26.74 | +18 18 20.84 | 23 05 58.02 | +18 02 05.05 | 218.0 | 134.0 | N | MBM 54, LBN
G101.62-28.84 | 101.6235 | -28.8436 | 23 24 47.63 | +30 25 04.98 | 23 22 20.08 | +30 08 35.36 | 244.0 | 118.0 | Y | Newe
G102.72-25.98 | 102.7221 | -25.9859 | 23 24 03.29 | +33 26 00.51 | 23 21 36.65 | +33 09 31.40 | 259.0 | 113.0 | Y | New
G118.25-52.70 | 118.2512 | -52.7054 | 00 39 55.42 | +10 03 41.94 | 00 37 19.73 | +09 47 13.89 | 194.0 | 154.0 | N | MBM 02
G126.65-71.43 | 126.6563 | -71.4392 | 00 56 13.82 | -08 36 07.67 | 00 53 42.53 | -08 52 21.24 | 183.0 | 174.0 | N | New
G127.31-70.09 | 127.3183 | -70.0954 | 00 57 27.24 | -07 16 29.84 | 00 54 55.63 | -07 32 42.13 | 145.0 | 137.0 | N | New
G131.35-45.73 | 131.3571 | -45.7346 | 01 15 57.51 | +16 44 08.07 | 01 13 17.42 | +16 28 18.47 | 259.0 | 185.0 | N | MBM 03, LBN
G133.72-45.31 | 133.7257 | -45.3151 | 01 23 04.84 | +16 53 32.68 | 01 20 24.08 | +16 37 53.49 | 231.0 | 164.0 | N | MBM 04, LBN
G145.08-39.30 | 145.0854 | -39.3061 | 02 04 00.04 | +20 25 25.62 | 02 01 13.71 | +20 11 03.42 | 163.0 | 103.0 | Y | MBM 06, LBN
G150.35-38.06 | 150.3588 | -38.0636 | 02 22 11.93 | +19 55 36.57 | 02 19 24.33 | +19 41 57.58 | 173.0 | 107.0 | N | MBM 07, LBN
G151.58-38.58 | 151.5893 | -38.5866 | 02 24 53.06 | +19 01 47.06 | 02 22 05.92 | +18 48 14.91 | 154.0 | 96.0 | Y | MBM 08, LBN
G153.74+35.91 | 153.7426 | 35.9152 | 08 36 34.59 | +62 26 27.09 | 08 32 20.45 | +62 36 52.58 | 365.0 | 214.0 | Y | HSVMT 27f
G156.42+32.53 | 156.4233 | 32.5313 | 08 06 27.98 | +60 34 20.05 | 08 02 12.51 | +60 42 57.52 | 290.0 | 156.0 | Y | MBM 26, HSVMT 29
G158.77-33.30 | 158.7744 | -33.3089 | 02 57 33.29 | +20 38 31.01 | 02 54 42.16 | +20 26 30.43 | 205.0 | 113.0 | Y | MBM 11–12, L1457-cg
G158.88-34.18 | 158.8842 | -34.1837 | 02 55 48.23 | +19 51 50.97 | 02 52 57.95 | +19 39 45.12 | 231.0 | 129.0 | Y | MBM 11–12, L1457-c
G158.97-33.01 | 158.9721 | -33.0193 | 02 58 50.03 | +20 47 23.13 | 02 55 58.66 | +20 35 26.45 | 274.0 | 149.0 | Y | MBM 11–12, L1457-c
G159.23-34.49 | 159.2358 | -34.4999 | 02 56 04.75 | +19 26 23.35 | 02 53 14.84 | +19 14 18.34 | 244.0 | 138.0 | Y | MBM 11–12, L1457-c
G159.41-34.36 | 159.4116 | -34.3643 | 02 56 54.67 | +19 28 15.70 | 02 54 04.66 | +19 16 13.20 | 205.0 | 116.0 | Y | MBM 11–12, L1457-c
G159.58-32.84 | 159.5873 | -32.8415 | 03 01 05.17 | +20 38 43.23 | 02 58 13.76 | +20 26 53.47 | 290.0 | 157.0 | Y | MBM 11–12, L1457-c
G159.67-34.31 | 159.6752 | -34.3191 | 02 57 46.94 | +19 23 09.02 | 02 54 56.94 | +19 11 09.16 | 194.0 | 109.0 | Y | MBM 11–12, L1457-c
G160.64-35.04 | 160.6420 | -35.0449 | 02 58 48.02 | +18 20 11.95 | 02 55 58.90 | +18 08 15.22 | 173.0 | 99.0 | Y | MBM 11–12, L1457-c
G161.43-35.59 | 161.4330 | -35.5935 | 02 59 41.08 | +17 30 58.04 | 02 56 52.65 | +17 19 04.04 | 183.0 | 107.0 | Y | MBM 13, LBN
G161.85-35.75 | 161.8505 | -35.7542 | 03 00 26.79 | +17 11 16.08 | 02 57 38.60 | +16 59 24.43 | 163.0 | 95.0 | Y | MBM 13, LBN
G162.64-31.67 | 162.6415 | -31.6726 | 03 12 56.11 | +20 04 33.85 | 03 10 04.36 | +19 53 21.59 | 231.0 | 121.0 | Y | MBM 14, LBN
G165.91-44.02 | 165.9188 | -44.0278 | 02 50 21.82 | +08 41 43.64 | 02 47 41.31 | +08 29 21.83 | 173.0 | 120.0 | N | DIR 164-44h
G173.32+31.27 | 173.3203 | 31.2789 | 08 03 20.34 | +46 11 45.20 | 07 59 46.38 | +46 20 12.22 | 274.0 | 142.0 | N | MBM 25, LBN
G173.91+31.16 | 173.9135 | 31.1699 | 08 03 07.66 | +45 40 41.82 | 07 59 34.74 | +45 49 08.07 | 290.0 | 150.0 | N | MBM 25, LBN
G182.54-25.34 | 182.5488 | -25.3444 | 04 23 04.85 | +12 13 03.09 | 04 20 18.04 | +12 06 06.23 | 365.0 | 156.0 | Y | New
G203.57-30.08 | 203.5766 | -30.0861 | 04 47 58.28 | -05 56 06.84 | 04 45 31.19 | -06 01 21.77 | 218.0 | 109.0 | N | New
G210.67-36.77 | 210.6738 | -36.7720 | 04 34 00.52 | -14 10 28.57 | 04 31 42.53 | -14 16 40.54 | 145.0 | 87.0 | N | MBM 20
G210.89-36.53 | 210.8935 | -36.5395 | 04 35 10.69 | -14 14 37.73 | 04 32 52.81 | -14 20 44.94 | 145.0 | 87.0 | N | MBM 20

${}^{\textbf{a}}$Identifications with LDN prefix refers to optical dark nebula
identified by Lynds (1962) ${}^{\textbf{b}}$Identifications with MBM prefix
refer to optically selected molecular clouds observed with CO by Magnani,
Blitz, & Mundy (1985) ${}^{\textbf{c}}$Identifications with CB prefix refer to
optically selected molecular clouds (Clemens & Barvainis, 1988).
${}^{\textbf{d}}$Identifications with LBN prefix refer to bright nebula given
in column[8] in Lynds (1965). ${}^{\textbf{e}}$New CO observation.
${}^{\textbf{f}}$Identifications with HSVMT prefix refers to Heithausen et al.
(1993). ${}^{\textbf{g}}$L1457 complex (Moriarty-Schieven et al., 1997)
${}^{\textbf{h}}$Identifications with DIR prefix refers to the diffuse
infrared clouds noted by Reach et al. (1998).

Note. — Column(10) indicates, which observational modes are adopted. N for no
OTF mapping, only single-point observation. Y for both OTF mapping and single-
point observations.

Table 3: Parameters of lines at core centers

Core Name | RA. offset | Dec. offset | Vlsr(12CO) | ${\rm\Delta V_{{}^{12}CO}}$ | Tb(12CO) | Vlsr(13CO) | ${\rm\Delta V_{{}^{13}CO}}$ | Tb(13CO) | Vlsr(C18O) | ${\rm\Delta V_{C^{18}O}}$ | Tb(C18O)
---|---|---|---|---|---|---|---|---|---|---|---
| (arcsec) | (arcsec) | (km s-1) | (km s-1) | (K) | (km s-1) | (km s-1) | (K) | (km s-1) | (km s-1) | (K)
G004.15+35.77a.C1 | 156.0 | -186.0 | 2.33(0.1) | 2.7(0.26) | 7.44(0.69) | 2.57(0.04) | 1.56(0.09) | 5.69(0.3) | 2.77(0.01) | 0.65(0.02) | 1.84(0.0)
G004.17+36.67a.C1 | 42.0 | 6.0 | 2.47(0.02) | 0.97(0.05) | 10.12(0.44) | 2.36(0.01) | 0.66(0.02) | 5.95(0.14) | 2.55(0.03) | 0.52(0.06) | 0.7(0.01)
G004.54+36.74a.C1 | -12.0 | -24.0 | 2.33(0.02) | 1.1(0.04) | 9.32(0.29) | 2.43(0.01) | 0.75(0.03) | 5.71(0.18) | 2.64(0.03) | 0.56(0.07) | 0.72(0.01)
G004.81+37.02a.C1 | 234.0 | -66.0 | 3.12(0.05) | 2.38(0.13) | 9.39(0.45) | 3.28(0.02) | 1.29(0.04) | 5.67(0.16) | 3.48(0.06) | 1.08(0.13) | 0.55(0.01)
G006.04+36.74a.C1 | -120.0 | -204.0 | 2.27(0.05) | 2.41(0.11) | 7.83(0.36) | 2.59(0.01) | 1.23(0.04) | 6.42(0.16) | 2.66(0.01) | 0.59(0.03) | 2.47(0.0)
G008.43+36.35a.C1 | 54.0 | -84.0 | 1.05(0.03) | 0.84(0.07) | 8.45(0.6) | 0.99(0.01) | 0.52(0.01) | 5.33(0.13) |  $\cdots$ |  $\cdots$ |  $\cdots$
G011.40+36.19a.C1 | -90.0 | 42.0 | 2.37(0.03) | 1.19(0.06) | 8.02(0.38) | 2.42(0.03) | 0.92(0.08) | 3.68(0.28) |  $\cdots$ |  $\cdots$ |  $\cdots$
G101.62-28.84a.C1 | 60.0 | 330.0 | -5.76(0.01) | 1.32(0.03) | 8.78(0.19) | -5.8(0.02) | 0.88(0.06) | 2.8(0.16) |  $\cdots$ |  $\cdots$ |  $\cdots$
G101.62-28.84a.C2 | -78.0 | 144.0 | -5.68(0.01) | 1.33(0.03) | 6.99(0.14) | -5.87(0.01) | 0.71(0.03) | 2.43(0.08) |  $\cdots$ |  $\cdots$ |  $\cdots$
G101.62-28.84a.C3 | -18.0 | 60.0 | -5.89(0.01) | 1.15(0.02) | 8.4(0.12) | -5.86(0.01) | 0.77(0.02) | 3.21(0.08) |  $\cdots$ |  $\cdots$ |  $\cdots$
G101.62-28.84a.C4 | -48.0 | -126.0 | -5.9(0.01) | 1.38(0.03) | 6.22(0.11) | -5.98(0.02) | 0.81(0.04) | 2.28(0.09) |  $\cdots$ |  $\cdots$ |  $\cdots$
G101.62-28.84b.C1 | 150.0 | -90.0 | -4.97(0.03) | 1.88(0.07) | 5.8(0.18) | -4.9(0.03) | 0.95(0.07) | 1.31(0.08) |  $\cdots$ |  $\cdots$ |  $\cdots$
G102.72-25.98a.C1 | 126.0 | -42.0 | -7.33(0.01) | 2.41(0.03) | 8.1(0.09) | -7.32(0.03) | 1.82(0.06) | 2.42(0.07) |  $\cdots$ |  $\cdots$ |  $\cdots$
G145.08-39.30a.C1 | -90.0 | -42.0 | 6.73(0.03) | 1.56(0.07) | 10.16(0.44) | 6.86(0.02) | 1.21(0.05) | 5.47(0.19) |  $\cdots$ |  $\cdots$ |  $\cdots$
G151.58-38.58a.C1 | -114.0 | 18.0 | 4.34(0.03) | 1.01(0.07) | 7.8(0.49) | 4.35(0.02) | 0.67(0.06) | 1.99(0.14) |  $\cdots$ |  $\cdots$ |  $\cdots$
G151.58-38.58b.C1 | -12.0 | 216.0 | 5.41(0.03) | 1.41(0.06) | 7.68(0.28) | 5.41(0.01) | 0.75(0.03) | 3.54(0.12) |  $\cdots$ |  $\cdots$ |  $\cdots$
G151.58-38.58b.C2 | -366.0 | 0.0 | 4.75(0.04) | 1.6(0.09) | 7.47(0.37) | 4.88(0.12) | 1.64(0.28) | 1.49(0.23) |  $\cdots$ |  $\cdots$ |  $\cdots$
G151.58-38.58b.C3 | -60.0 | -6.0 | 5.34(0.11) | 2.46(0.38) | 6.73(0.82) | 5.53(0.03) | 1.03(0.08) | 2.26(0.13) |  $\cdots$ |  $\cdots$ |  $\cdots$
G151.58-38.58b.C4 | 240.0 | -366.0 | 5.15(0.02) | 1.2(0.04) | 8.48(0.26) | 5.05(0.04) | 0.92(0.12) | 2.16(0.21) |  $\cdots$ |  $\cdots$ |  $\cdots$
G153.74+35.91a.C1 | -24.0 | 156.0 | -2.15(0.01) | 1.18(0.04) | 7.91(0.21) | -2.15(0.02) | 0.77(0.03) | 2.81(0.12) |  $\cdots$ |  $\cdots$ |  $\cdots$
G156.42+32.53a.C1 | 18.0 | -12.0 | -0.29(0.04) | 2.19(0.1) | 3.87(0.58) | -0.3(0.06) | 1.49(0.12) | 1.02(0.23) |  $\cdots$ |  $\cdots$ |  $\cdots$
G156.42+32.53a.C2 | 138.0 | -114.0 | -0.52(0.02) | 1.8(0.05) | 3.57(0.17) | -0.51(0.03) | 0.69(0.07) | 1.78(0.19) |  $\cdots$ |  $\cdots$ |  $\cdots$
G156.42+32.53a.C3 | 228.0 | -120.0 | -0.7(0.04) | 1.58(0.09) | 4.49(0.33) | -0.78(0.03) | 0.74(0.07) | 1.49(0.14) |  $\cdots$ |  $\cdots$ |  $\cdots$
G158.77-33.30a.C1 | -144.0 | -138.0 | -2.75(0.03) | 3.87(0.08) | 6.2(0.12) | -2.7(0.02) | 2.38(0.04) | 4.26(0.07) | -2.79(0.17) | 2.36(0.43) | 0.43(0.02)
G158.88-34.18a.C1 | -90.0 | 114.0 | -4.93(0.02) | 2.71(0.06) | 6.78(0.11) | -5.28(0.01) | 1.0(0.02) | 5.65(0.12) |  $\cdots$ |  $\cdots$ |  $\cdots$
G158.88-34.18a.C2 | 120.0 | -108.0 | -5.5(0.02) | 3.74(0.07) | 8.04(0.12) | -5.5(0.01) | 1.62(0.03) | 4.5(0.07) |  $\cdots$ |  $\cdots$ |  $\cdots$
G158.97-33.01a.C1 | -192.0 | 90.0 | -2.6(0.01) | 0.78(0.02) | 6.06(0.14) | -2.58(0.01) | 0.53(0.03) | 3.73(0.2) |  $\cdots$ |  $\cdots$ |  $\cdots$
G158.97-33.01a.C2 | 30.0 | -6.0 | -2.75(0.05) | 1.24(0.1) | 5.25(0.4) | -2.76(0.05) | 1.19(0.13) | 2.39(0.22) |  $\cdots$ |  $\cdots$ |  $\cdots$
G158.97-33.01a.C3 | -366.0 | -36.0 | -2.02(0.03) | 1.27(0.09) | 6.45(0.36) | -1.92(0.08) | 1.09(0.21) | 2.15(0.35) |  $\cdots$ |  $\cdots$ |  $\cdots$
G158.97-33.01b.C1 | 114.0 | 324.0 | 0.43(0.04) | 1.44(0.12) | 6.98(0.81) | 0.28(0.02) | 0.82(0.06) | 3.64(0.37) |  $\cdots$ |  $\cdots$ |  $\cdots$
G158.97-33.01b.C2 | -132.0 | -6.0 | 1.56(0.03) | 1.64(0.07) | 6.7(0.25) | 1.57(0.03) | 0.76(0.09) | 2.31(0.22) |  $\cdots$ |  $\cdots$ |  $\cdots$
G158.97-33.01b.C3 | 336.0 | -354.0 | 1.96(0.03) | 1.87(0.06) | 7.21(0.24) | 1.96(0.03) | 1.0(0.05) | 2.7(0.14) |  $\cdots$ |  $\cdots$ |  $\cdots$
G159.23-34.49a.C1 | -294.0 | 126.0 | -4.98(0.08) | 7.01(0.3) | 7.45(0.28) | -5.37(0.07) | 3.08(0.21) | 3.96(0.21) |  $\cdots$ |  $\cdots$ |  $\cdots$
G159.23-34.49a.C2 | 108.0 | 48.0 | -4.17(0.09) | 4.51(0.22) | 8.25(0.39) | -5.01(0.14) | 2.67(0.45) | 5.1(0.53) | -4.89(0.11) | 1.46(0.23) | 0.97(0.02)
G159.23-34.49b.C1 | 6.0 | 66.0 | -3.07(0.07) | 2.5(0.17) | 7.62(0.47) | -2.83(0.05) | 1.85(0.12) | 2.24(0.13) |  $\cdots$ |  $\cdots$ |  $\cdots$
G159.41-34.36a.C1 | -66.0 | -120.0 | -5.12(0.03) | 1.66(0.08) | 10.34(0.42) | -5.05(0.03) | 1.25(0.09) | 6.14(0.34) |  $\cdots$ |  $\cdots$ |  $\cdots$
G159.58-32.84a.C1 | -324.0 | 222.0 | 3.08(0.04) | 1.0(0.08) | 2.91(0.23) | 3.1(0.1) | 0.79(0.21) | 0.8(0.2) |  $\cdots$ |  $\cdots$ |  $\cdots$
G159.58-32.84a.C2 | 18.0 | 60.0 | 3.23(0.05) | 2.01(0.08) | 3.44(0.19) | 3.38(0.17) | 1.73(0.23) | 0.98(0.21) |  $\cdots$ |  $\cdots$ |  $\cdots$
G159.58-32.84a.C3 | 60.0 | -72.0 | 4.72(0.03) | 3.99(0.07) | 4.07(2.69) | 2.03(0.08) | 0.84(0.26) | 0.18(0.04) |  $\cdots$ |  $\cdots$ |  $\cdots$
G159.58-32.84b.C1 | 138.0 | 108.0 | 3.92(0.01) | 2.15(0.03) | 3.07(0.03) | 4.4(0.04) | 1.11(0.12) | 0.66(0.06) |  $\cdots$ |  $\cdots$ |  $\cdots$
G159.58-32.84b.C2 | 6.0 | 42.0 | 3.53(0.01) | 2.29(0.03) | 3.92(0.04) | 3.66(0.02) | 1.83(0.06) | 0.96(0.03) |  $\cdots$ |  $\cdots$ |  $\cdots$
G159.67-34.31a.C1 | 6.0 | 54.0 | -1.13(0.01) | 1.95(0.02) | 7.95(0.11) | -1.15(0.01) | 1.38(0.02) | 3.77(0.06) |  $\cdots$ |  $\cdots$ |  $\cdots$
G160.64-35.04a.C1 | -66.0 | 270.0 | -5.07(0.01) | 0.91(0.02) | 7.39(0.13) | -5.07(0.01) | 0.69(0.02) | 3.5(0.11) |  $\cdots$ |  $\cdots$ |  $\cdots$
G160.64-35.04a.C2 | -384.0 | 132.0 | -5.29(0.02) | 1.23(0.05) | 6.48(0.2) | -5.26(0.02) | 0.51(0.05) | 2.9(0.24) |  $\cdots$ |  $\cdots$ |  $\cdots$
G160.64-35.04a.C3 | -246.0 | 30.0 | -4.82(0.02) | 1.38(0.06) | 5.94(0.22) | -4.86(0.03) | 0.88(0.08) | 2.51(0.17) |  $\cdots$ |  $\cdots$ |  $\cdots$
G160.64-35.04a.C4 | -78.0 | -132.0 | -4.72(0.02) | 1.27(0.06) | 7.25(0.27) | -4.68(0.04) | 1.16(0.12) | 2.4(0.19) |  $\cdots$ |  $\cdots$ |  $\cdots$
G160.64-35.04a.C5 | -312.0 | -264.0 | -4.47(0.02) | 1.05(0.04) | 7.5(0.23) | -4.31(0.04) | 0.55(0.1) | 2.22(0.36) |  $\cdots$ |  $\cdots$ |  $\cdots$
G161.43-35.59a.C1 | 78.0 | 186.0 | -5.9(0.02) | 1.37(0.05) | 6.66(0.2) | -5.86(0.01) | 0.94(0.04) | 3.53(0.11) |  $\cdots$ |  $\cdots$ |  $\cdots$
G161.43-35.59a.C2 | 36.0 | -42.0 | -5.9(0.01) | 0.74(0.02) | 10.43(0.22) | -5.85(0.0) | 0.57(0.01) | 7.19(0.13) |  $\cdots$ |  $\cdots$ |  $\cdots$
G161.85-35.75a.C1 | -60.0 | 0.0 | -6.48(0.01) | 1.05(0.03) | 6.67(0.15) | -6.6(0.02) | 0.76(0.04) | 4.3(0.18) | -6.74(0.03) | 0.58(0.07) | 0.8(0.01)
G162.64-31.67a.C1 | -30.0 | 96.0 | -1.05(0.03) | 0.84(0.06) | 6.48(0.51) | -1.02(0.05) | 0.79(0.2) | 1.3(0.21) |  $\cdots$ |  $\cdots$ |  $\cdots$
G162.64-31.67a.C2 | 18.0 | -0.0 | -1.06(0.03) | 0.9(0.06) | 8.13(0.58) | -1.02(0.02) | 0.59(0.05) | 1.71(0.12) |  $\cdots$ |  $\cdots$ |  $\cdots$
G162.64-31.67a.C3 | -66.0 | -66.0 | -0.92(0.05) | 0.99(0.11) | 5.94(0.67) | -0.94(0.02) | 0.58(0.04) | 1.99(0.13) |  $\cdots$ |  $\cdots$ |  $\cdots$
G182.54-25.34a.C1 | 24.0 | 48.0 | 0.72(0.04) | 2.54(0.09) | 7.08(0.43) | 0.67(0.05) | 1.74(0.11) | 2.33(0.2) |  $\cdots$ |  $\cdots$ |  $\cdots$

Note. — All the cores are shown in the table.

Table 4: Parameters derived at the core center

Core Name | Tex | $\tau_{13}$ | N${}_{\mathrm{H}_{2}}$ | $\sigma_{\mathrm{Therm}}$ | $\sigma_{\mathrm{NT}}$ | $\sigma_{3\mathrm{D}}$
---|---|---|---|---|---|---
| (K) |  | (1021 cm-2) | (km s-1) | (km s-1) | (km s-1)
G004.15+35.77a.C1 | 10.8(0.7) | 1.45(0.35) | 15.9(2.48) | 0.2(0.01) | 0.66(0.04) | 1.19(0.06)
G004.17+36.67a.C1 | 13.5(0.4) | 0.89(0.07) | 6.11(0.31) | 0.22(0.0) | 0.27(0.01) | 0.61(0.01)
G004.54+36.74a.C1 | 12.7(0.3) | 0.95(0.07) | 6.66(0.4) | 0.21(0.0) | 0.31(0.01) | 0.66(0.02)
G004.81+37.02a.C1 | 12.8(0.5) | 0.93(0.08) | 11.3(0.65) | 0.21(0.0) | 0.54(0.02) | 1.01(0.03)
G006.04+36.74a.C1 | 11.2(0.4) | 1.71(0.24) | 15.8(1.53) | 0.2(0.0) | 0.52(0.02) | 0.96(0.03)
G008.43+36.35a.C1 | 11.8(0.6) | 1.0(0.13) | 4.28(0.28) | 0.2(0.01) | 0.21(0.0) | 0.51(0.01)
G011.40+36.19a.C1 | 11.4(0.4) | 0.61(0.08) | 4.37(0.53) | 0.2(0.0) | 0.39(0.03) | 0.76(0.05)
G101.62-28.84a.C1 | 12.2(0.2) | 0.38(0.03) | 2.93(0.26) | 0.21(0.0) | 0.37(0.03) | 0.73(0.04)
G101.62-28.84a.C2 | 10.4(0.1) | 0.43(0.02) | 1.99(0.11) | 0.19(0.0) | 0.3(0.01) | 0.61(0.02)
G101.62-28.84a.C3 | 11.8(0.1) | 0.48(0.02) | 3.04(0.11) | 0.2(0.0) | 0.32(0.01) | 0.66(0.01)
G101.62-28.84a.C4 | 9.6(0.1) | 0.46(0.02) | 2.12(0.14) | 0.18(0.0) | 0.34(0.02) | 0.67(0.03)
G101.62-28.84b.C1 | 9.1(0.2) | 0.26(0.02) | 1.29(0.12) | 0.18(0.0) | 0.4(0.03) | 0.76(0.05)
G102.72-25.98a.C1 | 11.5(0.1) | 0.36(0.01) | 5.06(0.23) | 0.2(0.0) | 0.77(0.03) | 1.38(0.04)
G145.08-39.30a.C1 | 13.6(0.4) | 0.77(0.06) | 9.81(0.61) | 0.22(0.0) | 0.51(0.02) | 0.96(0.03)
G151.58-38.58a.C1 | 11.2(0.5) | 0.3(0.03) | 1.48(0.17) | 0.2(0.0) | 0.28(0.03) | 0.59(0.04)
G151.58-38.58b.C1 | 11.1(0.3) | 0.62(0.04) | 3.4(0.19) | 0.2(0.0) | 0.31(0.01) | 0.64(0.02)
G151.58-38.58b.C2 | 10.8(0.4) | 0.22(0.04) | 2.59(0.6) | 0.2(0.0) | 0.69(0.12) | 1.25(0.2)
G151.58-38.58b.C3 | 10.1(0.8) | 0.41(0.07) | 2.65(0.27) | 0.19(0.01) | 0.43(0.03) | 0.82(0.05)
G151.58-38.58b.C4 | 11.9(0.3) | 0.29(0.03) | 2.24(0.37) | 0.2(0.0) | 0.39(0.05) | 0.76(0.08)
G153.74+35.91a.C1 | 11.3(0.2) | 0.44(0.03) | 2.57(0.15) | 0.2(0.0) | 0.32(0.01) | 0.66(0.02)
G156.42+32.53a.C1 | 7.1(0.6) | 0.31(0.1) | 1.62(0.4) | 0.16(0.01) | 0.63(0.05) | 1.13(0.09)
G156.42+32.53a.C2 | 6.8(0.2) | 0.69(0.12) | 1.58(0.25) | 0.16(0.0) | 0.29(0.03) | 0.57(0.05)
G156.42+32.53a.C3 | 7.8(0.3) | 0.4(0.06) | 1.22(0.17) | 0.17(0.0) | 0.31(0.03) | 0.61(0.05)
G158.77-33.30a.C1 | 9.5(0.1) | 1.16(0.06) | 15.8(0.52) | 0.18(0.0) | 1.01(0.02) | 1.78(0.03)
G158.88-34.18a.C1 | 10.1(0.1) | 1.79(0.13) | 11.3(0.64) | 0.19(0.0) | 0.42(0.01) | 0.8(0.01)
G158.88-34.18a.C2 | 11.4(0.1) | 0.82(0.03) | 10.3(0.28) | 0.2(0.0) | 0.69(0.01) | 1.24(0.02)
G158.97-33.01a.C1 | 9.4(0.1) | 0.96(0.09) | 2.82(0.25) | 0.18(0.0) | 0.22(0.01) | 0.49(0.02)
G158.97-33.01a.C2 | 8.6(0.4) | 0.61(0.1) | 3.45(0.52) | 0.17(0.0) | 0.5(0.06) | 0.92(0.09)
G158.97-33.01a.C3 | 9.8(0.4) | 0.4(0.09) | 2.64(0.68) | 0.19(0.0) | 0.46(0.09) | 0.86(0.14)
G158.97-33.01b.C1 | 10.3(0.8) | 0.74(0.17) | 3.96(0.58) | 0.19(0.01) | 0.34(0.03) | 0.68(0.04)
G158.97-33.01b.C2 | 10.1(0.3) | 0.42(0.05) | 2.01(0.31) | 0.19(0.0) | 0.32(0.04) | 0.64(0.06)
G158.97-33.01b.C3 | 10.6(0.2) | 0.47(0.04) | 3.19(0.24) | 0.19(0.0) | 0.42(0.02) | 0.8(0.03)
G159.23-34.49a.C1 | 10.8(0.3) | 0.76(0.07) | 16.5(1.53) | 0.2(0.0) | 1.31(0.09) | 2.29(0.15)
G159.23-34.49a.C2 | 11.6(0.4) | 0.96(0.18) | 20.6(4.39) | 0.2(0.0) | 1.13(0.19) | 1.99(0.33)
G159.23-34.49b.C1 | 11.0(0.5) | 0.35(0.04) | 4.68(0.42) | 0.2(0.0) | 0.78(0.05) | 1.4(0.09)
G159.41-34.36a.C1 | 13.8(0.4) | 0.9(0.1) | 12.1(1.23) | 0.22(0.0) | 0.53(0.04) | 0.99(0.06)
G159.58-32.84a.C1 | 6.1(0.2) | 0.32(0.1) | 0.71(0.26) | 0.15(0.0) | 0.33(0.09) | 0.63(0.14)
G159.58-32.84a.C2 | 6.7(0.2) | 0.34(0.09) | 1.86(0.48) | 0.15(0.0) | 0.73(0.1) | 1.3(0.17)
G159.58-32.84a.C3 | 7.3(2.8) | 0.05(0.03) | 0.14(0.05) | 0.16(0.03) | 0.35(0.11) | 0.67(0.18)
G159.58-32.84b.C1 | 6.3(0.0) | 0.24(0.02) | 0.79(0.11) | 0.15(0.0) | 0.47(0.05) | 0.85(0.08)
G159.58-32.84b.C2 | 7.2(0.0) | 0.28(0.01) | 1.85(0.08) | 0.16(0.0) | 0.78(0.03) | 1.37(0.04)
G159.67-34.31a.C1 | 11.3(0.1) | 0.64(0.02) | 6.79(0.16) | 0.2(0.0) | 0.58(0.01) | 1.07(0.01)
G160.64-35.04a.C1 | 10.8(0.1) | 0.64(0.03) | 3.1(0.14) | 0.2(0.0) | 0.29(0.01) | 0.6(0.01)
G160.64-35.04a.C2 | 9.8(0.2) | 0.59(0.07) | 1.82(0.24) | 0.19(0.0) | 0.21(0.02) | 0.49(0.03)
G160.64-35.04a.C3 | 9.3(0.2) | 0.55(0.06) | 2.63(0.31) | 0.18(0.0) | 0.37(0.03) | 0.71(0.05)
G160.64-35.04a.C4 | 10.6(0.3) | 0.4(0.04) | 3.19(0.42) | 0.19(0.0) | 0.49(0.05) | 0.91(0.08)
G160.64-35.04a.C5 | 10.9(0.2) | 0.35(0.07) | 1.38(0.34) | 0.2(0.0) | 0.23(0.04) | 0.52(0.06)
G161.43-35.59a.C1 | 10.0(0.2) | 0.76(0.05) | 4.4(0.25) | 0.19(0.0) | 0.4(0.02) | 0.76(0.03)
G161.43-35.59a.C2 | 13.9(0.2) | 1.17(0.06) | 7.24(0.26) | 0.22(0.0) | 0.23(0.0) | 0.56(0.01)
G161.85-35.75a.C1 | 10.0(0.2) | 1.03(0.09) | 4.88(0.37) | 0.19(0.0) | 0.32(0.02) | 0.64(0.03)
G162.64-31.67a.C1 | 9.8(0.5) | 0.22(0.05) | 1.06(0.32) | 0.19(0.0) | 0.33(0.09) | 0.66(0.13)
G162.64-31.67a.C2 | 11.5(0.6) | 0.24(0.03) | 1.1(0.12) | 0.2(0.01) | 0.24(0.02) | 0.55(0.03)
G162.64-31.67a.C3 | 9.3(0.7) | 0.41(0.07) | 1.29(0.13) | 0.18(0.01) | 0.24(0.02) | 0.52(0.03)
G182.54-25.34a.C1 | 10.4(0.4) | 0.4(0.05) | 4.62(0.51) | 0.19(0.0) | 0.74(0.05) | 1.32(0.08)

Note. — All of the cores are shown in the table.

Table 5: Emission Region Parameters

Core Name | RA offset | Dec offset | Distance | R | nvol | $M_{\mathrm{LTE}}$ | $M_{\mathrm{Jeans}}$ | $M_{\mathrm{vir}}$ | $\alpha_{\mathrm{vir}}$
---|---|---|---|---|---|---|---|---|---
| (arcsec) | (arcsec) | (kpc) | (pc) | (103 cm-3) | (M⊙) | (M⊙) | (M⊙) |
G004.15+35.77a.C1 | 156.0 | -186.0 | 0.145(0.02) | 0.12(0.02) | 21.7(4.55) | 8.85(2.86) | 11.8(2.25) | 65.7(65.7) | 7.42(1.75)
G004.17+36.67a.C1 | 42.0 | 6.0 | 0.13(0.022) | 0.04(0.01) | 24.5(4.42) | 0.39(0.14) | 1.46(0.16) | 5.76(5.76) | 14.8(2.74)
G004.54+36.74a.C1 | -12.0 | -24.0 | 0.13(0.019) | 0.05(0.01) | 23.8(3.76) | 0.53(0.16) | 1.86(0.22) | 7.52(7.52) | 14.1(2.37)
G004.81+37.02a.C1 | 234.0 | -66.0 | 0.13(0.019) | 0.09(0.01) | 20.3(3.19) | 3.58(1.07) | 7.43(0.84) | 35.8(35.8) | 10.0(1.66)
G006.04+36.74a.C1 | -120.0 | -204.0 | 0.122(0.018) | 0.1(0.01) | 26.2(4.61) | 5.95(1.85) | 5.64(0.7) | 35.3(35.3) | 5.92(1.1)
G008.43+36.35a.C1 | 54.0 | -84.0 | 0.13(0.022) | 0.07(0.01) | 9.64(1.78) | 0.86(0.3) | 1.39(0.15) | 7.3(7.3) | 8.44(1.58)
G011.40+36.19a.C1 | -90.0 | 42.0 | 0.13(0.019) | 0.04(0.01) | 19.2(3.65) | 0.23(0.07) | 3.16(0.73) | 8.12(8.12) | 35.1(8.27)
G101.62-28.84a.C1 | 60.0 | 330.0 | 0.244(0.064) | 0.04(0.01) | 11.3(3.12) | 0.2(0.11) | 3.78(0.8) | 8.74(8.74) | 43.4(12.8)
G101.62-28.84a.C2 | -78.0 | 144.0 | 0.244(0.064) |  $<$0.03(0.01) |  $>$11.8(3.13) |  $<$0.06(0.03) |  $<$2.15(0.35) |  $<$3.97(3.97) |  $>$68.0(18.6)
G101.62-28.84a.C3 | -18.0 | 60.0 | 0.244(0.064) | 0.04(0.01) | 13.8(3.62) | 0.15(0.08) | 2.5(0.36) | 6.04(6.04) | 39.8(10.6)
G101.62-28.84a.C4 | -48.0 | -126.0 | 0.244(0.064) | 0.03(0.01) | 10.3(2.77) | 0.09(0.05) | 3.02(0.54) | 5.79(5.79) | 62.9(17.6)
G101.62-28.84b.C1 | 150.0 | -90.0 | 0.244(0.064) | 0.04(0.01) | 5.61(1.56) | 0.07(0.04) | 5.98(1.39) | 8.36(8.36) | 119.0(36.1)
G102.72-25.98a.C1 | 126.0 | -42.0 | 0.259(0.045) | 0.11(0.02) | 7.49(1.34) | 2.37(0.83) | 31.0(4.0) | 80.8(80.8) | 34.1(6.47)
G145.08-39.30a.C1 | -90.0 | -42.0 | 0.163(0.034) | 0.05(0.01) | 35.3(7.69) | 0.78(0.33) | 4.83(0.74) | 16.1(16.1) | 20.7(4.75)
G151.58-38.58a.C1 | -114.0 | 18.0 | 0.154(0.054) | 0.02(0.01) | 9.93(3.64) | 0.03(0.02) | 2.14(0.56) | 3.29(3.29) | 98.2(38.0)
G151.58-38.58b.C1 | -12.0 | 216.0 | 0.154(0.054) | 0.02(0.01) | 27.5(9.68) | 0.05(0.04) | 1.63(0.32) | 3.2(3.2) | 60.0(21.4)
G151.58-38.58b.C2 | -366.0 | 0.0 | 0.154(0.054) |  $<$0.02(0.01) |  $>$25.3(10.6) |  $<$0.03(0.02) |  $<$12.5(6.52) |  $<$10.0(10.0) |  $>$360.0(189.0)
G151.58-38.58b.C3 | -60.0 | -6.0 | 0.154(0.054) | 0.04(0.01) | 11.3(4.1) | 0.15(0.1) | 5.29(1.43) | 9.88(9.88) | 66.5(25.7)
G151.58-38.58b.C4 | 240.0 | -366.0 | 0.154(0.054) | 0.02(0.01) | 16.1(6.2) | 0.04(0.03) | 3.49(1.28) | 5.01(5.01) | 113.0(49.2)
G153.74+35.91a.C1 | -24.0 | 156.0 | 0.365(0.032) | 0.1(0.01) | 4.25(0.46) | 0.96(0.18) | 4.43(0.45) | 16.4(16.4) | 17.0(2.07)
G156.42+32.53a.C1 | 18.0 | -12.0 | 0.29(0.044) |  $<$0.02(0.0) |  $>$10.6(3.05) |  $<$0.04(0.01) |  $<$14.2(3.82) |  $<$12.2(12.2) |  $>$315.0(102.0)
G156.42+32.53a.C2 | 138.0 | -114.0 | 0.29(0.044) |  $<$0.03(0.0) |  $>$10.1(2.18) |  $<$0.04(0.01) |  $<$1.88(0.5) |  $<$3.19(3.19) |  $>$80.1(21.6)
G156.42+32.53a.C3 | 228.0 | -120.0 | 0.29(0.044) |  $<$0.02(0.0) |  $>$8.66(1.75) |  $<$0.02(0.01) |  $<$2.49(0.62) |  $<$3.29(3.29) |  $>$133.0(33.5)
G158.77-33.30a.C1 | -144.0 | -138.0 | 0.205(0.051) | 0.11(0.03) | 23.4(5.87) | 7.42(3.7) | 37.4(5.04) | 134.0(134.0) | 18.1(4.57)
G158.88-34.18a.C1 | -90.0 | 114.0 | 0.231(0.048) | 0.06(0.01) | 28.6(6.21) | 1.84(0.78) | 3.09(0.37) | 16.0(16.0) | 8.7(1.91)
G158.88-34.18a.C2 | 120.0 | -108.0 | 0.231(0.048) | 0.09(0.02) | 18.1(3.84) | 3.43(1.44) | 14.4(1.69) | 54.7(54.7) | 16.0(3.42)
G158.97-33.01a.C1 | -192.0 | 90.0 | 0.274(0.076) | 0.04(0.01) | 13.0(3.81) | 0.14(0.08) | 1.08(0.2) | 3.32(3.32) | 24.3(7.33)
G158.97-33.01a.C2 | 30.0 | -6.0 | 0.274(0.076) | 0.06(0.02) | 9.98(3.16) | 0.42(0.24) | 8.0(2.68) | 18.5(18.5) | 43.5(16.2)
G158.97-33.01a.C3 | -366.0 | -36.0 | 0.274(0.076) |  $<$0.03(0.01) |  $>$15.2(5.77) |  $<$0.08(0.05) |  $<$5.25(2.82) |  $<$8.04(8.04) |  $>$98.6(49.9)
G158.97-33.01b.C1 | 114.0 | 324.0 | 0.274(0.076) | 0.05(0.01) | 13.1(4.14) | 0.37(0.21) | 2.82(0.66) | 8.79(8.79) | 23.9(8.02)
G158.97-33.01b.C2 | -132.0 | -6.0 | 0.274(0.076) |  $<$0.03(0.01) |  $>$10.0(3.2) |  $<$0.08(0.05) |  $<$2.68(0.84) |  $<$5.16(5.16) |  $>$62.7(23.0)
G158.97-33.01b.C3 | 336.0 | -354.0 | 0.274(0.076) | 0.05(0.01) | 10.8(3.11) | 0.29(0.16) | 5.09(0.98) | 12.0(12.0) | 41.7(12.5)
G159.23-34.49a.C1 | -294.0 | 126.0 | 0.244(0.064) | 0.07(0.02) | 37.8(10.4) | 3.24(1.71) | 62.9(15.3) | 144.0(144.0) | 44.4(13.6)
G159.23-34.49a.C2 | 108.0 | 48.0 | 0.244(0.064) | 0.11(0.03) | 30.0(10.1) | 9.96(5.6) | 46.6(24.2) | 171.0(171.0) | 17.2(8.06)
G159.23-34.49b.C1 | 6.0 | 66.0 | 0.244(0.064) | 0.08(0.02) | 10.1(2.77) | 1.04(0.55) | 27.9(6.41) | 57.3(57.3) | 55.0(16.6)
G159.41-34.36a.C1 | -66.0 | -120.0 | 0.205(0.068) | 0.08(0.03) | 23.1(7.97) | 3.39(2.26) | 6.51(1.65) | 32.2(32.2) | 9.48(3.47)
G159.58-32.84a.C1 | -324.0 | 222.0 | 0.29(0.091) | 0.06(0.02) | 2.09(1.01) | 0.08(0.06) | 5.58(4.02) | 8.47(8.47) | 101.0(66.6)
G159.58-32.84a.C2 | 18.0 | 60.0 | 0.29(0.091) | 0.05(0.02) | 6.15(2.49) | 0.18(0.12) | 28.4(12.3) | 32.0(32.0) | 183.0(87.7)
G159.58-32.84a.C3 | 60.0 | -72.0 | 0.29(0.091) |  $<$0.03(0.01) |  $>$0.67(0.34) |  $<$0.01(0.0) |  $<$12.0(9.91) |  $<$5.97(5.97) |  $>$935.0(676.0)
G159.58-32.84b.C1 | 138.0 | 108.0 | 0.29(0.091) |  $<$0.02(0.01) |  $>$5.14(1.77) |  $<$0.02(0.01) |  $<$8.84(3.03) |  $<$6.98(6.98) |  $>$372.0(148.0)
G159.58-32.84b.C2 | 6.0 | 42.0 | 0.29(0.091) | 0.06(0.02) | 4.64(1.47) | 0.3(0.19) | 38.7(7.14) | 47.1(47.1) | 156.0(50.5)
G159.67-34.31a.C1 | 6.0 | 54.0 | 0.194(0.056) | 0.07(0.02) | 15.2(4.38) | 1.38(0.79) | 10.1(1.5) | 31.9(31.9) | 23.1(6.65)
G160.64-35.04a.C1 | -66.0 | 270.0 | 0.173(0.032) | 0.03(0.01) | 14.6(2.78) | 0.14(0.05) | 1.85(0.21) | 4.84(4.84) | 33.6(6.55)
G160.64-35.04a.C2 | -384.0 | 132.0 | 0.173(0.032) |  $<$0.02(0.0) |  $>$15.3(3.49) |  $<$0.03(0.01) |  $<$0.95(0.2) |  $<$1.76(1.76) |  $>$67.2(17.2)
G160.64-35.04a.C3 | -246.0 | 30.0 | 0.173(0.032) | 0.04(0.01) | 12.1(2.65) | 0.13(0.05) | 3.37(0.84) | 6.94(6.94) | 54.5(14.4)
G160.64-35.04a.C4 | -78.0 | -132.0 | 0.173(0.032) | 0.04(0.01) | 12.3(2.8) | 0.22(0.09) | 6.98(2.06) | 13.6(13.6) | 61.4(17.8)
G160.64-35.04a.C5 | -312.0 | -264.0 | 0.173(0.032) |  $<$0.01(0.0) |  $>$16.8(5.18) |  $<$0.01(0.0) |  $<$1.1(0.4) |  $<$1.39(1.39) |  $>$147.0(55.5)
G161.43-35.59a.C1 | 78.0 | 186.0 | 0.183(0.042) | 0.04(0.01) | 18.5(4.42) | 0.26(0.12) | 3.28(0.52) | 8.61(8.61) | 33.6(8.39)
G161.43-35.59a.C2 | 36.0 | -42.0 | 0.183(0.042) | 0.06(0.01) | 19.0(4.47) | 1.08(0.5) | 1.28(0.16) | 7.44(7.44) | 6.9(1.63)
G161.85-35.75a.C1 | -60.0 | 0.0 | 0.163(0.036) | 0.04(0.01) | 20.2(4.73) | 0.29(0.13) | 1.89(0.32) | 6.22(6.22) | 21.3(5.26)
G162.64-31.67a.C1 | -30.0 | 96.0 | 0.231(0.048) |  $<$0.02(0.0) |  $>$9.08(3.31) |  $<$0.01(0.01) |  $<$3.06(1.89) |  $<$3.19(3.19) |  $>$213.0(115.0)
G162.64-31.67a.C2 | 18.0 | -0.0 | 0.231(0.048) |  $<$0.02(0.0) |  $>$9.21(2.16) |  $<$0.02(0.01) |  $<$1.76(0.35) |  $<$2.25(2.25) |  $>$141.0(36.4)
G162.64-31.67a.C3 | -66.0 | -66.0 | 0.231(0.048) |  $<$0.02(0.0) |  $>$9.35(2.14) |  $<$0.03(0.01) |  $<$1.5(0.28) |  $<$2.36(2.36) |  $>$93.7(23.2)
G182.54-25.34a.C1 | 24.0 | 48.0 | 0.365(0.106) | 0.05(0.01) | 15.5(4.84) | 0.42(0.25) | 18.8(4.45) | 32.5(32.5) | 77.4(25.8)

Note. — All of the cores are shown in the table.

Figure 1: CO surveys are shown in this figure, including previous ones and our
work. The all-sky map is projected onto a rectangle (cylinder projection by
the package Montage). The background is CO J=1-0 integrated intensity (Planck
Collaboration et al., 2014). The horizontal distortion at high latitude ($\geq
60\arcdeg$) is due to the effect of projection. Follow-up observations towards
41 PGCCs at HGal with the PMO 13.7-m telescope (PMO) are shown with blue
crosses. The white point line marks a declination of -20°, above which the PMO
can observe efficiently. Unequal spacing of the points is due the effect of
projection. Rectangles with names were either defined by Dame et al. (1987) or
Wu et al. (2012). Those blue rectangles mark the published PMO data (Liu et
al., 2012; Meng et al., 2013; Zhang et al., 2016, 2020). Bold white rectangles
mark the regions measured by large CO surveys (Heithausen et al., 1993;
Yamamoto et al., 2003). The filled yellow inverted-triangles show 121 HGal
objects summarized by Magnani et al. (1996). We zoom in two HGal cloud
complexes, the L134 complex and the MBM 11–12 complex, where PGCCs are grouped
in the northern and southern hemisphere, respectively. In the two zoomed-in
figures, white contours give the CO integrated intensity and all the mentioned
HGal objects inside the boxes are included. The concentric filled blue circles
show the field of view (14′) in our observation. Figure 2: Three examples of
CO integrated intensity maps. Figures for the total sample are shown in
Appendix B. The background grey color maps show 12CO(1-0) emission and the
colorbars show the value of W(12CO) in units of [K km s-1]. The blue contours
of 13CO(1-0) or C18O(1-0) step from 50% to 90% by 10% of the peak value.
Defined cores are marked by red crosses and named ‘C1’, ‘C2’, and so on in the
order of left-to-right and up-to-down. The specific line is labeled on the top
of each panel. Source names are labeled above each pair of panels. Figure 3:
Non-Gaussian profiles defined by single-point observations. Upper left, right,
lower left and right are respectively G089.0-41.2 (blue profile), G182.5-25.3
(red profile), G210.6-36.7 (red profile) and G159.5-32.8 (red asymmetry).

Figure 4: Solid detection of N2H+ J=1-0 and C2H J=1-0 at HGal and at lower
latitude ($21\arcdeg<|b|<25\arcdeg$). Source names are labeled on the upper
right of the panels. Three detections from lower latitude (upper left, upper
right and lower left) and only one detection of both two molecules at HGal
region (lower right). Figure 5: The detection rate of both C2H J=1-0 and N2H+
J=1-0 for three regions along the Galactic latitude: $0^{\circ}\sim
21\arcdeg$, $21\arcdeg\sim 25\arcdeg$ and $>25\arcdeg$. The negative gradient
of detection rate along latitude is shown.

Figure 6: (a) Cumulative distribution function of column density derived by
two ways-13CO (black) and C18O (blue). Individual uncertainties are considered
and 1000 runs of Monte Carlo simulates the data scatterings. The column
density derived from two ways show significant difference. KS test also gives
extremely low p value. (b) Assuming the abundance of isotope in the solar
neighborhood, the column density of hydrogen molecules are derived. Along the
black solid line, the column densities derived from 13CO and C18O are
consistent. Grey points are from Taurus (Meng et al., 2013). Orange contours
show the distribution of all non-HGal PGCCs in previous work (Liu et al.,
2012; Meng et al., 2013; Zhang et al., 2016, 2020). Blue points are from HGal
(this work). Deep blue points are 8 cores with solid C18O detection while
light blue points only give upper limits. Grey dotted line gives a much better
estimation of abundance $X_{13}/X_{18}$ of 16. (c) Abundance ratio
$X_{{}^{13}\mathrm{CO}}/X_{\mathrm{C}^{18}\mathrm{O}}$ versus the C18O column
density $N_{\mathrm{C}^{18}\mathrm{O}}$ Figure 7: 3$\times$3 map grids of
G089.03-41.28a are shown. The x and y coordinates are the offsets of two
equatorial direction in unit of arcmin. Two CO molecular lines 12CO and 13CO
are marked with black and blue, respectively. Figure 8: The position-velocity
map along RA offset of -0.3 arcmin in the clump G182.54-25.34a. Red numbers
’1’ and ’2’ mark the velocity components we defined. Figure 9: The
relationship between of core size and internal velocity dispersion is shown.
HGal cores (purple points with error bars, also filled contours) gives a
power-law index 0.50. Cores with only upper limits of sizes are shown with
lighter purple errorbars. The linear fitting is shown with purple dash-dotted
line. The scattering is large with $R^{2}$=0.36. Grey dash-dotted line from
IQuad (Zhang et al., 2020) gives a better Larson’s relation with index of 0.33
at large scale (0.1-3 pc). Blue contours represent other PGCCs cores observed
in previous works (Liu et al., 2012; Meng et al., 2013; Zhang et al., 2016,
2020). There is a valley (0.1 pc) for bimodal distribution of total observed
PGCCs sample, shown with black vertical dotted line. Different turbulence
regime is separated by grey solid horizontal line and sub-sonic turbulence
regime is filled with royal blue color, assuming the temperature is 10 K and
sound speed is 0.17 km s-1. Figure 10: IQuad, ACent (green), IIQuad (red),
Orion (blue), Taurus (orange) and HGal (purple) cores are shown in
$M_{\mathrm{LTE}}-\alpha_{\mathrm{vir}}$ plane. Grey and light grey-shaded
region are the gravitational bound and marginally gravitational bound,
respectively. Pressure-confined cores obey paralleled dashed grey lines with
different Jeans mass. The dashed red line is the fitted broken power-law with
two slopes -0.61 and -0.3 as well as the ’ankle’ (4.6$M_{\odot}$, 4.5).

Figure 11: (a) $M_{\mathrm{LTE}}-\alpha$ relation with color coding for the
effective temperature $T_{\mathrm{eff}}$ ($=\frac{\mu
m_{H}\left(\sigma_{\mathrm{NT}}^{2}+\sigma_{\mathrm{Th}}^{2}\right)}{k_{B}}$)
in log scale. (b) $M_{\mathrm{LTE}}-\alpha$ relation with color coding for the
volume density $n_{\mathrm{H}_{2}}$ in log scale.

##  Appendix A Spectral Energy Distribution Fitting

In order to be able to estimate physical properties from Herschel
multiwavelength observations (160, 250, 350 and 500 $\mu m$) with different
angular resolutions (12, 18, 25 and 36 arcsec), we convolved the images to a
common angular resolution of $40\arcsec$ which is slightly larger than the
poorest resolution among the four bands. The convolution package of Astropy
(Robitaille et al., 2013) was used with a Gaussian kernel of
$\sqrt{\theta_{0}^{2}-\theta_{\lambda}^{2}}$ where $\theta_{0}=40\arcsec$ and
$\theta_{\lambda}$ is the HPBW beam size for a given band. The convolved data
were then regridded to be aligned pixel by pixel with a common pixel size of
$10\arcsec$.

A modified blackbody model is applied to these data:

$\displaystyle I_{\nu}=B_{\nu}(T)(1-e^{-\tau_{\nu}})$ (A1)

where optical depth is given by:

$\displaystyle\tau_{\nu}=\mu_{\text{H}_{2}}m_{\text{H}}\kappa_{\nu}N_{\text{H}_{2}}/R_{\text{gd}}$
(A2)

Here $\mu_{\text{H}_{2}}=2.33$ is the mean molecular weight adopted from
Kauffmann et al. (2008), $m_{\text{H}}$ is the mass of a hydrogen atom,
$N_{\text{H}_{2}}$ is the $\text{H}_{2}$ column density, and
$R_{\text{gd}}=100$ is the gas-to-dust ratio. The dust opacity $\kappa_{\nu}$
can be expressed as a power law in frequency (Ossenkopf & Henning, 1994),

$\displaystyle\kappa_{\nu}=3.33\left(\frac{\nu}{600\ (GHz)}\right)^{\beta}\
\text{cm}^{2}\text{g}^{-1}$ (A3)

where the power law index $\beta$ is assumed to be 2.0 in agreement with the
standard value for cold dust emission (Hildebrand, 1983). We filtrate out the
pixel as long as any one of its four bands have non-positive value. Then the
temperature and column density will be set null.

The column density and dust temperature of G004.15+35.77 are presented in
Figure 12. A clear anti-correlation between the distributions of column
density and temperature: the regions with lower temperature have higher column
density. Along NE-SW direction, there is a low-temperature ($\leq$ 11 K )
valley where the column density reach its ridge ($\geq 10^{22}$ cm-2). From
Planck 857 GHz dust map (Planck Collaboration et al., 2011c), the clump
G004.15+35.77 is at the tip of L134 and both the Northeast and Northwest part
of the clump are on the edge of L134. The clump are exposed to Galactic
starlight and the grains are heated not by local sources but by background
emission instead (de Vries et al., 1987, also found in Ursa Major complex),
which might explain the temperature gradient along West-East direction.

Figure 12: (a) The dust temperature map of G004.15+35.77a is shown as
background Reds colormap with linear scale between 9.5 and 12.5 K. The median
value is 11.3 K. Part of null-value pixels are filled with pure white. (b) The
column density map is shown as background blue colormap with linear scale
between $1.3\times 10^{21}$ and $2.0\times 10^{22}\ \text{cm}^{-2}$. Both two
maps contain the same group of contours and markers: 1) black contours:
smoothed integrated 13CO intensity between velocity range of 0.22-0.40 km s-1
with levels of 1.5, 3.1, 4.6, 6.2, 7.8 K km s-1. 2) white contours: smoothed
integrated C18O intensity between velocity range of 0.22-0.40 km s-1 with
levels of 1.0, 1.3, 1.7, 2.0, 2.3, 2.6 K km s-1. 3) Filled yellow circle: the
center of the ammonia dense core (L134-A) identified by Myers et al. (1983)
and the size of the circle gives the beamwidth $1\fdg 2$ of NRAO 37-m Haystack
Observatory. 4) White cross: the peak of C18O emission, defined as the center
of dense core G004.15+35.77a.C1 hereafter. 5) White filled circle: the
beamwidth $40\arcsec$ of background dust map after the convolution of Herschel
data. 6) black circle: the beamwidth $55\arcsec$ of PMO 13.7-m 13CO and C18O
observations.

##  Appendix B Three CO-lines integrated intensity maps

Figure 13: CO integrated intensity maps for total 33 velocity-defined clumps.
The background grey color maps show 12CO(1-0) emission and the colorbars show
the value of W(12CO) in units of [K km s-1]. The blue contours of 13CO(1-0) or
C18O(1-0) step from 50% to 90% by 10% of the peak value. Defined cores are
marked by red crosses and named ‘C1’, ‘C2’, and so on in the order of left-to-
right and up-to-down. The names of CO emission lines are labeled on the top of
each panel. Source names are labeled above each two panels. Figure 13:
continued Figure 13: continued Figure 13: continued