# Formation of Massive Protostellar Clusters
– Observations of Massive 70 $\mu$m Dark Molecular Clouds

Shanghuo Li Shanghai Astronomical Observatory, Chinese Academy of Sciences, 80
Nandan Road, Shanghai 200030, China  Center for Astrophysics $|$ Harvard &
Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA  University of Chinese
Academy of Sciences, 19A Yuquanlu, Beijing 100049, China  Qizhou Zhang  Center
for Astrophysics $|$ Harvard & Smithsonian, 60 Garden Street, Cambridge, MA
02138, USA  Thushara Pillai  Institute for Astrophysical Research, Boston
University, 725 Commonwealth Ave, Boston, MA 02215, USA  Ian W. Stephens
Center for Astrophysics $|$ Harvard & Smithsonian, 60 Garden Street,
Cambridge, MA 02138, USA  Junzhi Wang  Shanghai Astronomical Observatory,
Chinese Academy of Sciences, 80 Nandan Road, Shanghai 200030, China  Fei Li
Shanghai Astronomical Observatory, Chinese Academy of Sciences, 80 Nandan
Road, Shanghai 200030, China  University of Chinese Academy of Sciences, 19A
Yuquanlu, Beijing 100049, China

###### Abstract

We present Submillimeter Array (SMA) observations of seven massive molecular
clumps which are dark in the far-infrared for wavelengths up to 70 $\mu\rm m$.
Our 1.3 mm continuum images reveal 44 dense cores, with gas masses ranging
from 1.4 to 77.1 $\rm M_{\odot}$. Twenty-nine dense cores have masses greater
than 8 $\rm M_{\odot}$ and the other fifteen dense cores have masses between
1.4 and 7.5 $\rm M_{\odot}$. Assuming the core density follows a power-law in
radius $\rho\propto r^{-b}$, the index $b$ is found to be between 0.6 and 2.1
with a mean value of 1.3. The virial analysis reveals that the dense cores are
not in virial equilibrium. CO outflow emission was detected toward 6 out of 7
molecular clumps and associated with 17 dense cores. For five of these cores,
CO emissions appear to have line-wings at velocities of greater than 30 km s-1
with respect to the source systemic velocity, which indicates that most of the
clumps harbor protostars and thus are not quiescent in star formation. The
estimated outflow timescale increase with core mass, which likely indicates
that massive cores have longer accretion timescale than that of the less
massive ones. The fragmentation analysis shows that the mass of low-mass and
massive cores are roughly consistent with thermal and turbulent Jeans masses,
respectively.

Protoclusters (1297), Early-type stars (430), Star formation (1569), Massive
stars (732), Protostars (1302), Stellar winds (1636), Stellar jets (1607),
Radio spectroscopy (1359), Dust continuum emission (412), Submillimeter
astronomy (1647)

††facilities: SMA, APEX, Herschel ††software: MIR, MIRIAD (Sault et al.,
1995), CASA (McMullin et al., 2007), APLpy (Robitaille & Bressert, 2012),
Astropy (Astropy Collaboration et al., 2013), LMFIT (Newville et al., 2014).

##  1 Introduction

The feedback of massive stars and clusters, such as radiation, wind, and
supernovae, accounts for most of the energy budget in galaxies. However, our
understanding of massive stars and clusters formation, especially the early
evolutionary stages is still poor (Zinnecker & Yorke, 2007; Motte et al.,
2018). The early evolutionary phases are crucial for understanding the initial
conditions of massive star and cluster formation. Massive ($>$102 $\rm
M_{\odot}$) and dense molecular clumps ($>$103 cm-3) that show no signs of on-
going star formation activities are considered to be the cradle of the massive
stars and clusters (Carey et al., 1998; Rathborne et al., 2006; Wang et al.,
2006; Henning et al., 2010; Ragan et al., 2012). Infrared dark clouds (IRDCs)
are cold and represent an early evolutionary stage of star formation molecular
clump before the star have formed, rapidly heat, ionize, and disrupt their
surrounding gas and dust (Carey et al., 1998; Rathborne et al., 2006; Ragan et
al., 2012, and references therein). Massive IRDCs that exhibit little or no
signs of on-going star formation (Rathborne et al., 2006; Wang et al., 2006),
as evidenced by the lack of powerful jets, outflows, stellar radiation and
ionization, provide an ideal laboratory to investigate the initial condition
of massive star and cluster formation since they are not significantly
affected by the stellar feedback

The cloud fragmentation is a crucially important process to form massive stars
and clusters, and it is also one of the main debate between two star formation
scenarios. The core-accretion model suggests that massive stars are formed in
near-equilibrium status with limited fragmentation within massive cores (McKee
& Tan, 2002, 2003), while the competitive accretion model suggests that
massive clump fragments into many low-mass cores that have masses of around
thermal Jean mass, and some of them have the potential to form massive stars
through competitive accretion (Bonnell et al., 2001; Bonnell & Bate, 2006).

Previous investigations of massive clumps reveal that massive cores are
responsible for forming high-mass stars are typically an order of magnitude
more massive than the global thermal Jeans mass of the clump and are more
consistent with turbulent Jeans mass when the sound speed is replaced by the
non-thermal velocity dispersion (Zhang et al., 2009; Zhang & Wang, 2011; Wang
et al., 2014; Lu et al., 2015). The properties of low-mass ($\ll$ 8 $\rm
M_{\odot}$) fragments in the clump, on the other hand, could be interpreted as
pure thermal Jeans fragmentation (e.g., Palau et al., 2014, 2015, 2018;
Beuther et al., 2018). Others find that complex structures can not be
explained by simple theoretical models (e.g., Cyganowski et al., 2017; Henshaw
et al., 2017). The fragmentation process of massive molecular clumps into
dense star-forming cores remains unclear.

In addition, the majority of these fragments show signs of star formation
activity, such as molecular outflows, H2O masers, and/or class II CH3OH masers
(Wang et al., 2006, 2012; Palau et al., 2015; Zhang et al., 2015; Cyganowski
et al., 2017; Henshaw et al., 2017; Palau et al., 2018). This is because the
majority of targets in previous studies are associated with infrared bright
sources at 4.5, 8 or 24 $\mu$m wavelengths. Therefore, they are not ideal
objects for investigating the earliest evolutionary stage of star formation.
The massive molecular clouds which are dark in the infrared for wavelengths up
to 70 $\mu$m are ideal objects for studying the extremely early phase of star
formation (Dunham et al., 2008; Ragan et al., 2012; Stutz et al., 2013; Elia
et al., 2017). Galactic wide surveys offer a unique opportunity to identify
ideal massive clouds that have the potential to form massive stars and
clusters but without signs of on-going star formation. For instance, the
ATLAGAL survey of the Galactic plane mapped over 400 square degrees of the
inner Galactic at 870 $\mu$m with Atacama Pathfinder Experiment (APEX)
telescope (Schuller et al., 2009).

To study the processes of massive star and cluster formation within massive
clumps, we used the Submillimeter Array (SMA111The Submillimeter Array is a
joint project between the Smithsonian Astrophysical Observatory and the
Academia Sinica Institute of Astronomy and Astrophysics, and is funded by the
Smithsonian Institution and the Academia Sinica., Ho et al., 2004) to observe
a sample of seven high-mass 70 $\mu$m dark clumps identified by ATLAGAL
survey. The paper is organized as follows. First we describe the sample
selection and the observations with the SMA in $\S$ 2\. Then, we present the
results and analysis in $\S$ 3\. We discuss the observational results in $\S$
4, and summarize the main findings in $\S$ 5.

##  2 Samples and Observations

###  2.1 Sample Selection

The sample of seven sources in this study, selected from the ATLASGAL survey
of the Galactic plane (Schuller et al., 2009), are among the most massive (5
$\times$ 103 to 1.5 $\times$ 104 M⊙) and the coldest 70 $\mu$m dark ($\sim$14
K) clumps within the distance of 6 kpc (3.5 to 5.9 kpc) from the Sun (Urquhart
et al., 2014). As shown in Figure 1, these sources have large reservoirs of
gas as manifested by the presence of intense dust emission at 870 $\mu$m
(Urquhart et al., 2014). These requirements are to ensure that the clumps
likely form massive stars in a cluster assuming a typical star formation
efficiency of 30%, while being infrared dark at 70 $\mu\rm m$ is to rule out
that the regions have been affected by significant stellar feedback (Dunham et
al., 2008; Stutz et al., 2013; Elia et al., 2017).

###  2.2 SMA observations

The observations were carried out with the SMA in the compact configuration
from July through August 2017. The projected baselines ranged from $\sim$8
k$\lambda$ to $\sim$60 k$\lambda$, where $\lambda$, around 1.3 mm, is the
wavelength of the observations. Four targets were observed with seven
antennas, two targets with eight antennas, and one target with six antennas.
The full width at half-maximum (FWHM) primary beam is about 55′′. The zenith
opacity at 220 GHz, $\tau_{220}$, was between 0.04 and 0.08 during the
observations. The typical system temperatures varied from 200 to 500 K
depending on the source elevations and weather conditions.

Both 230 GHz and 240 GHz receivers were used in the observations. The
simultaneous operations of two sets of receivers provide a total spectral
bandwidth of 32 GHz, with the 230 GHz receiver covering $213.4-221.4$ GHz in
the lower side band (LSB) and $229.4-237.4$ GHz in the upper side band (USB),
and the 240 GHz receiver covering $244.5-252.5$ GHz in the LSB and
$260.5-268.5$ GHz in the USB. The SMA Wideband Astronomical ROACH2 Machine
(SWARM) correlator provides a uniform channel width of 140 KHz across the
entire spectral band. An overview of observations and calibrators is
summarized in Table 1. The raw visibility data were averaged every two
channels before calibration using the IDL superset
MIR222https://www.cfa.harvard.edu/$\sim$cqi/mircook.html. Data from 230 GHz
and 240 GHz receivers were calibrated separately. The Quasars 3c279 and
3c454.3 were used for bandpass calibration. Five Quasars, 1751+096, 1743-038,
1830+063, nrao530 and 1924+292, were employed for gain calibrations. Flux
calibrations were performed using Neptune and Ganymede. We have applied the
uti-hayshft on calibrated visibility data to fix the diurnal Doppler tracking
error.

The continuum emission was generated by averaging line-free channels over the
observed spectral windows. The typical root mean square (rms) noise level is
about 0.5 mJy beam-1 in continuum images, where the typical synthesized beam
size is about $\theta_{maj}\times\theta_{min}$ = 3.4′′$\times$ 2.5′′. Only
12CO 2-1, C18O 2-1 and SiO 5-4 lines were used for study in this paper. The
typical spectral line sensitivity is about 65 mJy beam-1 per 0.23 km s-1. The
calibrated visibility data were exported to Common Astronomical Software
Applications (CASA McMullin et al., 2007) for imaging. The Briggs Robust=0.5
weighting was used to construct the continuum and molecular line images.
Further analyses of data were performed using python (Robitaille & Bressert,
2012; Astropy Collaboration et al., 2013).

##  3 Results and Analysis

###  3.1 Dense structure identification

To identify the compact structures in the 1.3 mm continuum image, we employed
the astrodendro333http://dendrograms.org/ algorithm to pre-select the compact
components from the continuum image (Astropy Collaboration et al., 2013).
There were compact structures detected at $>$5$\sigma$ significance, but were
missed by astrodendro. We used the CASA-imfit task to extract dense cores from
the compact components identified from the astrodendro analysis and also to
recover the missed structures from the image. A detailed discussion about
astrodendro extraction method can be found in Rosolowsky et al. (2008). The
input parameters of astrodendro algorithm are described below. The minimum
pixel value, $\mathbf{min_{-}value}$, for which any pixel below this value is
not considered, was set to 3$\sigma$, where $\sigma$ is the rms noise level of
the continuum image. A value of 1$\sigma$ is chosen for
$\mathbf{min_{-}delta}$, the minimum difference in the peak flux between
neighboring compact structures for them to be considered as separate
structures. We set the $\mathbf{min_{-}npix}$, which is the minimum number of
pixels needed for structures to be considered as an independent entity, to the
number of pixels within the FWHM of the synthesized beam.
$\mathbf{min_{-}npix}$ ranges from 17 to 31 depending on the beam size of
sources. Using the 1.3 mm continuum image, we have identified 4 to 10 cores in
each of the 7 clumps, and a total of 44 cores. The physical parameters of
dense cores from CASA-imfit are summarized in Table 2, including coordinates,
beam-convolved major axis ($\sigma_{maj}$), beam-convolved minor axis
($\sigma_{min}$), position angle (PA), total integrated flux, beam-convolved
($R_{\rm eff}$) and beam-deconvolved effective radius ($R_{\rm eff}^{\rm
dec}$).

###  3.2 Mass determination

The gas mass ($M_{\rm gas}$) of dense cores are estimated using 1.3 mm
continuum emission following the formula:

$M_{\rm gas}=\eta\frac{F_{\nu}\;d^{2}}{B_{\nu}(T_{\rm dust})\;\kappa_{\nu}},$
(1)

where $\eta$ ($\eta$ = 100) is the gas-to-dust mass ratio, $d$ is the source
distance, $F_{\nu}$ is the continuum integrated flux which has been corrected
for primary attenuation, $B_{\nu}(T)$ is the Planck function at a dust
temperature of $T_{\rm dust}$, and $\kappa_{\nu}$ is the dust opacity at a
frequency of $\nu$. We adopt $\kappa_{\nu}$ = 0.84 cm2g-1 by assuming
$\kappa_{\nu}$ = 10(${\nu}$/1.2 THz)β cm2g-1 and $\beta$ = 1.5 (Hildebrand,
1983). The densities of clumps are higher than 104 cm-3, which implies that
gas and dust are likely well coupled toward these clumps (Goldsmith, 2001). We
assumed $T_{\rm dust}=T_{\rm K}$, where $T_{\rm K}$ is kinetic temperature
estimated from NH3 data were retrieved from Wienen et al. (2012) who performed
observations of the NH3 (J,K) = (1, 1) to (3, 3) inversion transitions with
the Effelsberg 100m Telescope. The $T_{\rm K}$ is in between 13 and 16 K, with
typical uncertainty of about 10%. For sources, AGAL024.314+00.086 and
AGAL030.844+00.177, without NH3 measurements, we adopt a temperature of
$T_{\rm K}=$ 14 K. The derived gas masses of dense cores range from 1.4 to
77.1 $\rm M_{\odot}$. Massive cores ($\gtrsim$ 8 $\rm M_{\odot}$) are detected
in all of the clumps, except for AGAL022.376+000.447 where the embedded dense
cores have a maximum gas mass of 4.8 $\rm M_{\odot}$.

The column density ($N_{\rm H_{2}}$) of dense cores are computed with:

$N_{\rm H_{2}}=\eta\frac{S_{\nu}^{\rm beam}}{B_{\nu}(T_{\rm
dust})\;\kappa_{\nu}\;\Omega\;\mu\;m_{\rm H}},$ (2)

where $S_{\nu}^{\rm beam}$ is the peak flux density, $\Omega$ is the beam
solid angle, $m_{\rm H}$ is the mass of an hydrogen atom, and $\mu$
($\mu$=2.8) is the mean molecular weight of the interstellar medium (Kauffmann
et al., 2008). The estimated $N_{\rm H_{2}}$ are between 1.1$\times 10^{22}$
and 2.0$\times 10^{23}$ cm-2, with a mean value of 5.7$\times 10^{22}$ cm-2.

The uncertainty in continuum flux is adopted to be a typical value of 10% in
the interferometer observations. The typical uncertainty in the kinematic
distances is about 10%, while in some cases it can be significantly larger due
to the near-far kinematic distance ambiguity (Reid et al., 2009). However,
since all theses clumps appear as extinction images in the near-IR (i.e., they
are infrared dark clouds), the near distance is likely the accurate distance.
The $\eta$ is adopted to be 100 in this study, while its standard deviation is
23 (corresponding to a 1$\sigma$ uncertainty of 23%) if we assume that it is
uniformly distributed between 70 and 150 (Devereux & Young, 1990; Vuong et
al., 2003; Sanhueza et al., 2017). We adopted a conservative uncertainty of
28% in $\kappa_{\nu}$ (e.g., Sanhueza et al., 2017). Taking into account these
uncertainties, we estimate an uncertainty of 44% and 32% for gas mass and
column density, respectively. However, one has to bear in mind that the
uncertainties could be larger in cases that distances are significantly
higher.

###  3.3 Dense cores and associated star formation

Below, we summarize the general morphology of each of the 7 clumps, and also
comment on their CO outflow morphology. For each clump, dense cores are
labeled in order of maximum flux to minimum flux (Table 2), e.g., MM1 to MM10,
based the flux prior to the primary beam correction.

AGAL008.691-00.401 (hereafter AGAL008) is a part of the clumpy structure that
displays elongated emission running along the southwest-northeast direction as
seen in the 250 $\mu$m and 870 $\mu$m images (Figure 1). AGAL008 breaks up
into 4 dense cores in the SMA 1.3 mm continuum image, which are labeled as MM1
to MM4. The estimated gas masses of dense cores are between 8.1 and 55.8 $\rm
M_{\odot}$. All of dense cores are within the 20% of the primary beam of the
SMA antenna, except for MM3 that is just outside the primary beam. CO outflows
are detected toward MM1, MM2 and MM3. MM1 is associated with a high-velocity
CO outflow with line-wing emission at velocities of $\geqslant$ 30 km s-1 with
respect to the source systemic velocity ($|v-v_{\rm lsr}|\geqslant$ 30 km s-1)
(Figure 2).

AGAL014.492+00.262 (hereafter AGAL014) shows an elongated feature oriented
southeast-northwest (SE-NW) in APEX 870 $\mu$m image, which breaks up into
small clumpy structures in the SMA 1.3 mm continuum image (Figure 1). Eight
dense cores reside in the central clumpy structure. Gas masses of dense cores
are between 10.8 and 47.3 $\rm M_{\odot}$, four of which, MM1/2/6/7, are
associated with CO outflows (Figure 2). Both MM2 and MM6 are associated with
high-velocity CO outflows, which suggests that there are on-going star
formation activities within these dense cores.

Figure 1 shows that the parent cloud of AGAL016.418-00.634 (hereafter AGAL016)
appears as an elongated clumpy features oriented in the southwest-northeast
direction. The 1.3 mm continuum image revealed five embedded dense cores
within AGAL016, which has masses of 3.4 to 11.0 $\rm M_{\odot}$. MM1 and MM2
are associated with outflows based on CO emission (Figure 2).

For AGAL022.376+00.447 (hereafter AGAL022), there is an elongated emission
running from east to west, as seen in the 250 $\mu$m and 870 $\mu$m images
(Figure 1). Using 1.3 mm continuum emission, we identified 6 dense cores that
contain masses between 1.4 and 4.9 $\rm M_{\odot}$. The CO outflow signature
is found toward MM1 (Figure 2).

The 250 $\mu$m and 870 $\mu$m images reveal that the AGAL024.314+00.086
(hereafter AGAL024) is a part of a clumpy structure, which shows bright dust
emission roughly running from southwest to northeast with a plateau around
AGAL024. Using the 1.3 mm dust continuum image, we have identified 6 dense
cores that contain gas masses between 7.5 and 77.1 $\rm M_{\odot}$ (Figure 1).
There are three dense cores, MM1/2/4, appearing to have clear CO outflow
emission (Figure 2).

AGAL031.024+00.262 (hereafter AGAL031) is a part of circular clumpy structure
that is clearly seen in the 250 $\mu$m and 870 $\mu$m images (Figure 1).
AGAL031 breaks up into 10 dense cores in the SMA 1.3 mm continuum image. Their
masses range from 4.0 to 34.6 $\rm M_{\odot}$. CO outflows are detected in 5
out of 10 dense cores, including two cores, MM1 and MM5, with high-velocity CO
outflows (Figure 2).

The parent cloud of AGAL030.844+00.177 (hereafter AGAL030) presents an
elongated structure along the southeast-northwest direction (Figure 1).
AGAL030 breaks up into five dense cores in the 1.3 mm image, with masses of
6.8 to 20.2 $\rm M_{\odot}$. There are no evidences of molecular outflow
toward these dense cores according to CO and SiO lines.

Overall, 44 dense cores have been identified using the 1.3 mm continuum
images. The identified dense cores have gas masses in the range of 1.4 to 77.1
$\rm M_{\odot}$ with effective radius between 0.02 and 0.11 pc. Of the 44
cores, 29 cores have gas masses greater than 8 $\rm M_{\odot}$, while the
other 15 cores are between 1.4 and 7.5 $\rm M_{\odot}$. The physical
parameters of the identified dense cores are summarized in Table 2.

###  3.4 Dense cores structures

To study the physical structure of identified cores, we estimated core density
distributions using the 1.3 mm continuum data. The detailed analysis of
density structures of cores is described below.

The SMA compact configuration gave projected baselines between $\sim$8 and
$\sim$60 k$\lambda$ at the observing frequency ($\sim$230 GHz), which
corresponds to angular physical size of 26′′ and 3.4′′, respectively. If the
dense core is internally heated, the dust temperature ($T_{\rm dust}$) and
radius ($r$) can be expressed in the form of $T_{\rm dust}\propto r^{-a}$,
where $a$ = 0.33 (Scoville & Kwan, 1976). The observed flux density ($F$) of
the dust continuum emission along the line of slight can be written as
$F\propto\int\rho\;T_{\rm dust}\;ds$ by assuming that the dust emission is
optically thin and the density ($\rho$) follows a power-law in radius
$\rho\propto r^{-b}$. A power-law density profile has been proposed by
theoretical studies (Shu et al., 1987; McKee & Tan, 2003), and confirmed by
observational investigations (van der Tak et al., 2000; Motte & André, 2001;
Beuther et al., 2005). For ($a+b$) $>$ 1, the observed flux density can be
rewritten as $F\propto r^{-(a+b-1)}$. In the $u-v$ domain, following a Fourier
transform, the observed flux density can be rewritten as $A_{uv}\propto
S_{uv}^{(a+b-3)}$ (Looney et al., 2000; Zhang et al., 2009), where $A_{uv}$ is
the visibility amplitude and $S_{uv}$ = $\sqrt{u^{2}+v^{2}}$ is the UV
distance.

We restrict our study to dense cores that have SNR higher than 9 and a roughly
circular morphology in order to avoid contamination from unresolved nearby
sources. The visibility data of dense cores is extracted from the map after
removing the bright sources using clean components. We bin the extracted
visibility data in step of 3.1 k$\lambda$ before we apply a non-linear least-
squares minimization fitting (LMFIT, Newville et al., 2014) to the visibility
data in order to determine the density profile.

The visibility amplitude versus the UV distance with the fitting results are
shown in Figure 3. The amplitude is vector averaged over concentric annulus
around the source in the $u-v$ plane. The large scatter at long UV distances
are mostly due to the limited signal-to-noise, while it can not be ruled out
the possibility that the cores host multiple unresolved compact structures. In
some cases, the fitting is not as robust due to large scatters, especially for
3 cores, i.e., AGAL008-MM2, AGAL014-MM7 and AGAL031-MM7. Assuming $a$ = 0.33,
the best fitted density power-law indexes ($b$) of dense cores are between 0.6
and 2.1, with a mean value of 1.3. Figure 4 shows the density power-law
indexes distribution for dense cores.

In previous studies, van der Tak et al. (2000) found that the power-law
density distribution has a slope of $b$ = 1.0 $-$ 1.5 through measured of a
sample of 14 ultracompact HII regions and hot cores on 102 $-$ 105 AU scales.
On the other hand, Mueller et al. (2002) via observations of 51 massive dense
cores ($\sim$3.3$\times$104 AU scale) found that b ranges from 0.75 to 2.5
with a mean value of $\langle b\rangle$ = 1.8 $\pm$ 0.4. This is similar to
the value of $\langle b\rangle$ = 1.6 reported in Beuther et al. (2005), who
studied 69 massive cores on scale of $\sim$104 AU. In a more recent study,
(Butler & Tan, 2012) found that for a sample of 42 IRDC cores
($\sim$2$\times$104 AU scale), b was about 1.6. As a comparison, low-mass
protostellar cores (103-105 AU scale) have $b$ = 1.5 $-$ 2.0 (Motte & André,
2001), $b$ = 1.5 $-$ 2.5 (Tobin et al., 2015) and $\langle b\rangle$ = 1.6
$\pm$ 0.3 (Shirley et al., 2002). Our results are in agreement with these
investigations, as we find no significant differences between power-law
indexes of our 70 $\mu$m dark dense cores and the above mentioned high- and
low-mass objects.

###  3.5 Outflow properties

Outflow signatures, as revealed by CO emission, are detected toward 17
identified dense cores. The CO outflow emission is detected in all of the
clumps, except for AGAL030. The maximum detected velocities ($|v-v_{\rm
lsr}|$) for the CO outflow emission range from 5 up to 56 km s-1 with respect
to the source systemic velocity. There are five dense cores associated with
high velocity CO outflow emission ($|v-v_{\rm lsr}|\geqslant$ 30 km s-1)
within a small spatial scale of $\leqslant$ 0.22 pc, while the rest of the
dense cores are associated with low-velocity CO outflows ($|v-v_{\rm lsr}|<$
30 km s-1). The velocity-integrated intensities of CO emission are shown in
Figure 2, while the blue and red color contours represent the red-shifted and
blue-shifted emission components, respectively. From the maps, we note that
some of the cores show well collimated CO outflows with a bipolar morphology,
while others are dominated by either the blue- or red-shifted lobes. The SiO
emission has been detected toward 5 massive and 1 intermediate-mass dense
cores that are associated with CO outflows (Figure 2). The SiO emission is
much fainter and with a narrower velocity range than that of the CO emission.

To study outflow properties, we estimated the physical parameters for each
outflow, including mass, momentum, energy, dynamical timescale, outflow rate,
as well as accretion rate. Assuming local thermodynamic equilibrium, we first
estimate the CO column density following Mangum & Shirley (2015):

$N_{\rm CO}({\rm cm^{-2}})=1.08\times 10^{13}(T_{\rm
ex}+0.92)\;exp\left(\frac{16.59}{T_{\rm ex}}\right)\\\
\int\frac{\tau_{12}}{1-e^{\tau_{12}}}T_{\rm B}dv,$ (3)

where $N_{\rm CO}$ is the CO column density, $dv$ is the velocity interval in
km s-1, $T_{\rm ex}$ is the line excitation temperature, $\tau_{12}$ is the
optical depth, and $T_{\rm B}$ is brightness temperature in K. The outflow
mass ($M_{\rm out}$), momentum ($P_{\rm out}$), energy ($E_{\rm out}$),
dynamical age ($t_{\rm dyn}$), and outflow rate ($\dot{M}_{\rm out}$) can be
estimated with (Bally & Lada, 1983; Cabrit & Bertout, 1992)

$M_{\rm out}={d^{2}}\left[\frac{\rm H_{2}}{\rm CO}\right]\overline{m}_{\rm
H_{2}}\int_{\Omega}N_{\rm CO}(\Omega)d\Omega,$ (4) $P_{\rm out}=M_{\rm
r}v_{r}+M_{b}v_{\rm b},$ (5) $E_{\rm out}=\frac{1}{2}M_{\rm r}v_{\rm
r}^{2}+\frac{1}{2}M_{\rm b}v_{\rm b}^{2},$ (6) $t_{\rm dyn}=\frac{l_{\rm
out}}{(v_{\rm max(b)}+v_{\rm max(r)})/2},$ (7) $\dot{M}_{\rm out}=\frac{M_{\rm
out}}{t_{\rm dyn}},$ (8)

where $\Omega$ is the total solid angle that the flow subtends, $d$ is the
source distance, $l_{\rm out}$ is the CO outflow physical length, $v_{\rm
max(b)}$ and $v_{\rm max(r)}$ are the maximum velocities of CO blue-shifted
and red-shifted emission, respectively. $M_{\rm r}$ and $M_{\rm b}$ are the
gas masse of CO outflows at blue-shifted ($v_{\rm b}$) and red-shifted
($v_{\rm r}$) velocities, respectively. Here, we adopt the CO-to-H2 abundance
of 10-4, $\left[\frac{\rm H_{\rm 2}}{\rm C\rm O}\right]$ = 104 (Blake et al.,
1987), mean mass per hydrogen atom $\overline{m}_{\rm H_{2}}$ = 2.33, and
assume that CO emission is optically thin in the line wing and that the
excitation temperature of outflow gas equals to the temperature ($T_{\rm K}$)
estimated from the NH3 emission (Wienen et al., 2012). As mentioned in Section
3.2, a temperature of $T_{\rm K}=$14 K was assumed for the sources without NH3
observations (AGAL024 and AGAL030). The primary beam correction have been
applied to the CO velocity integrated intensity for estimating the outflow
masses, while the inclination of the outflow axis with respect to the line of
sight have not been corrected in the derivation of the outflow parameters (see
Section 4.3 for the discussion of inclination).

The derived outflow masses range from 0.008 to 0.17 M⊙ with a mean value of
0.06 M⊙. The outflow momenta are between 0.04 and 2.7 M⊙ km s-1, while the
outflow energies are in the range of 0.1 to 34.8 M⊙ km2 s-2. Using the outflow
mass and dynamical time, we find the outflow ejection rates are between 0.6
$\times$ 10-6 and 2.1 $\times$ 10-5 M⊙ yr-1, with a mean value of 0.5 $\times$
10-5 M⊙ yr-1. In general, the most massive cores tend to have high outflow
mass, momentum, energy, outflow ejection rate and accretion rate within the
same clump. The ratios of $M_{\rm out}$/$M_{\rm core}$ are around 0.003, which
is lower than the value of 0.04 reported by Beuther et al. (2002), who studied
a sample of much massive (102 – 105 $M_{\odot}$) and evolved objects with
relatively low spatial resolution ($\sim$11′′). It should be noted that the
outflow mass estimated here is only a lower limited since the CO emission
suffers from missing flux and is likely to be optically thick (see, e.g.,
Dunham et al., 2014), as well as outflow parameters. The derived outflow
parameters are summarized in Table 3.

Assuming that the outflows are powered by winds that driven by accretion disks
(e.g., Keto, 2003; McKee & Tan, 2003) and that there is efficient mixing at
the wind/molecular gas interface (Richer et al., 2000), the conservation of
momentum can be used to approximate the relation between outflows and winds.
In this case, the mass-loss rate of the wind can be estimated by $\dot{M}_{\rm
w}v_{\rm w}=P_{\rm out}/t_{\rm dyn}$, where $\dot{M}_{\rm w}$ and $v_{\rm w}$
are mass-loss rate and the velocity of the wind, respectively. We assume a
wind velocity of 500 km s-1 and a ratio of 3 for the mass-loss rate of wind to
accretion rate (Tomisaka, 1998; Shu et al., 2000). The derived accretion rates
are between 1.8 $\times$ 10-8 and 2.3 $\times$ 10-6 $\rm M_{\odot}$ yr-1, with
a mean value of 4.4 $\times$ 10-7 $\rm M_{\odot}$ yr-1. The derived accretion
rates are similar to that of 24 $\mu\rm m$ dark sources (Lu et al., 2015),
while they are two or three order magnitude lower than that of more evolved
sources; the typical value is several 10-4 $\rm M_{\odot}$ yr-1 for HMPOs
(Beuther et al., 2002; Zhang et al., 2005; Qiu et al., 2009) and $\sim$10-5
$\rm M_{\odot}$ yr-1 for 24 $\mu\rm m$ bright sources (Wang et al., 2011;
Zhang et al., 2015).

To compare the free-fall timescale and the outflow dynamical timescale, we
have computed the average volume density in dense cores, $n_{\rm
H_{2}}=3M_{\rm gas}/(4\pi R^{3})$, and the free-fall time, $t_{\rm
ff}=\sqrt{3\pi/(32\,G\,n_{\rm H_{2}})}$. Here, $n_{\rm H_{2}}$ is dense core
averaged-volume density, $R$ is the effective radius, $t_{\rm ff}$ is the
free-fall timescale and $G$ is the gravitational constant. The outflow
dynamical timescales show a correlation with the free-fall timescales (Figure
5). The Spearman-rank correlation test, which assesses monotonic
relationships, returns a coefficient of 0.59. This indicates a moderate
correlation between the two timescales. They are in same order of magnitude
($\sim$ few 104 yr) and is relatively smaller than the typical outflow
dynamical timescale of $\sim$105 yr in more evolved objects, such as HMPOs
(Beuther et al., 2002; Zhang et al., 2005). The shorter timescale is
consistent with the fact that our sample is at a very early evolutionary stage
of star formation.

We find a positive correlation between outflow dynamical timescale and gas
mass of dense cores, with a correlation coefficient of 0.62 estimated from
Spearman-rank correlation test. The massive cores tend to have a longer
outflow dynamical timescale than that of less massive cores. This trend
suggests that the more massive cores had longer accretion history that allows
it to assemble more mass. This also implies that the most massive cores may
form earlier than the less massive cores. A confirmation of this trend from a
more sensitive and larger sample is still needed.

##  4 Discussion

###  4.1 Dense cores dynamical state

We computed the virial mass for both clumps and dense cores following:

$M_{\rm vir}=3k\frac{\sigma_{v}^{2}R}{G},$ (9)

where $M_{\rm vir}$ is the virial mass, $\sigma_{v}$ is the velocity
dispersion, $R$ is the effective radius, $G$ is the gravitational constant,
and the correction factor $k$ = (5-2$b$)/(3-$b$) depends on the density
profile $\rho\propto r^{-b}$ (MacLaren et al., 1988). Here, we use the derived
density profile $b$ for dense cores, and a mean value of $\langle b\rangle$ =
1.3 for dense cores without $b$ measurements (see Section 3.4). The virial
parameter is computed using $\alpha=M_{\rm vir}/M_{\rm gas}$, where $M_{\rm
gas}$ is the gas mass.

We used the C18O line width to estimate the velocity dispersion for dense
cores, as was done for condensations in IRDC G28.34+0.06 (Zhang et al., 2015).
This line was chosen over other lines observed in the SMA SWARM bandwidth
because it is bright and less confused by outflow motions and/or severe
depletion than H2CO, CH3OH, HCN and HCO+. We extracted the average spectrum of
C18O within dense cores and fitted the Gaussian profile to measure the
observed line width (full width half maximum, FWHM), $\bigtriangleup v_{\rm
obs}$. The derived C18O line widths are systemically narrower than the 13CO
line, with a mean $\bigtriangleup v_{\rm obs}$ of 1.7 km s-1 and 2 km s-1 for
C18O and 13CO, respectively. This could be due to the fact that the optical
depth of 13CO is larger than that of C18O (e.g., Hacar et al., 2016), or the
13CO line widths are affected by outflows (Stephens et al., 2018). Therefore,
the line width from C18O is better suited for estimating of the virial
parameters of the identified dense cores.

The velocity dispersion $\sigma_{v}$ contains both non-thermal and thermal
motions from particles of mean mass contributions. To estimate the velocity
dispersion, we first subtract the C18O thermal motions from the observed line
width using $\sigma_{\rm nt}^{2}$ = $\sqrt{\sigma_{\rm obs}^{2}-\sigma_{\rm
th}^{2}}$, where $\sigma_{\rm obs}$ is the channel-deconvolved line width,
$\sigma_{\rm obs}$ = $\left(\bigtriangleup v_{\rm obs}^{2}-\bigtriangleup
v_{\rm ch}^{2}\right)^{0.5}\left(2\sqrt{2ln(2)}\right)^{-0.5}$, and
$\bigtriangleup v_{\rm ch}$ is the spectral resolution. The molecular thermal
motion $\sigma_{\rm th}$ = 9.08 $\times$ 10-2 km s${}^{-1}\left(\frac{T}{\rm
K}\right)^{0.5}\left(\frac{m}{m_{\rm H}}\right)^{-0.5}$ (Myers, 1983), where
$m$ is the molecule weight, $m_{\rm H}$ is the hydrogen mass, and $T=T_{\rm
K}$ is the gas temperature. We used this equation to calculate the thermal
motion (sound speed $c_{s}$) of the free particle of mean mass assuming a mean
mass of gas of 2.37 $m_{\rm H}$ (Kauffmann et al., 2008). Finally we estimated
the velocity dispersion using $\sigma_{v}$ = $\sqrt{\sigma_{\rm
nt}^{2}+c_{s}^{2}}$.

We restrict the virial analysis to 15 dense cores whose C18O spectra have
fitted SNR higher than 5. Figure 6 shows the $\sigma_{\rm obs}$ versus gas
mass for the dense cores, while the red and black circles represent the high-
and low-velocity CO outflows, respectively. Although number of data points is
limited, we find no significant relation between $\sigma_{\rm obs}$ and dense
cores with and without associated CO outflows. Therefore, the line width
derived by C18O is a reliable parameter for estimating the virial parameter,
$\alpha$. The derived virial parameters of dense cores range from 0.2 to 4.1
with a mean value of 1.1. After propagating uncertainties from gas mass and
virial mass, we find the uncertainties for the virial parameters are
$\sim$54%.

Non-magnetized cores with $\alpha<$ 2, $\alpha\sim$ 1 and $\alpha<$ 1 are
considered to be gravitationally bound, in hydrostatic equilibrium and
gravitationally unstable, respectively. Considering the uncertainty of virial
parameters, we find that the virial parameters of 8 cores are smaller than 1,
of 5 cores are between 1 and 2, and of 2 cores range from 2 to 4.1. This
indicates that most of the dense cores are gravitationally bound. The virial
parameters are not significantly different for dense cores associated with and
without CO outflows. Figure 6 shows the virial parameters versus the gas mass
of dense cores. We noted that the most massive cores tend to have lower virial
parameters. Previous investigations of parsec scale massive clumps and low-
mass star formation regions have found similar trend between virial parameter
and mass (Lada et al., 2008; Foster et al., 2009; Urquhart et al., 2015).
Several recent studies find that the observation anti-correlation between the
virial parameter and the mass is subject to a few observational biases
(Kauffmann et al., 2013; Ballesteros-Paredes et al., 2018; Traficante et al.,
2018).

To study the virial state of the dense clumps, we use the NH3 (1, 1) line
widths (Wienen et al., 2012). Both AGAL024 and AGAL030 are not been considered
in the analysis of clump virial state since they are no observations of NH3
nor N2H+ in the low-J transitions. The NH3 (1, 1) velocity dispersion range
from 0.6 to 1.2 km s-1 for these clumps. The derived virial parameters of the
clumps are between 0.44 and 0.61, which indicates that these clumps are
gravitationally unstable.

Our analysis does not include magnetic fields and external pressure. The
magnetic fields supply additional support to counteract gravity (Hull & Zhang,
2019). Since these cores are embedded in dense clumps, the external pressure
with the cloud provides additional force against the internal support, which
could decreases the virial parameters. Therefore, these effects may play an
important role in the balance between the external pressure, gravitational
potential energy and internal kinetic energy (Pattle et al., 2015; Zhang et
al., 2015; Kirk et al., 2017).

###  4.2 Fragmentation

Fragmentation exists on various spatial scales from giant molecular clouds
down to dense cores. In this study we investigate how the pc-scale massive 70
$\mu$m dark molecular clumps fragment into 0.1 pc-scale dense cores that might
form massive stars.

With the high spatial resolution and mass sensitivity, we can directly compare
the detected dense cores with predictions of Jeans fragmentation (Kippenhahn
et al., 2012). The APEX 870 $\mu$m continuum and NH3 (1, 1) emission are used
to compute the Jean length and Jeans mass under pure thermal support, and both
thermal and non-thermal support (turbulent support).

$\lambda_{\rm J}=\sigma\left(\frac{\pi}{G\rho}\right)^{1/2}\\\ =0.06\,\rm
pc\left[\frac{\sigma}{0.188\;\rm km\;\rm s^{-1}}\right]\left[\frac{n_{\rm
H_{2}}}{10^{5}\;\rm cm^{-3}}\right]^{-1/2},$ (10)

Assuming a spherical symmetry with a radius of $\lambda_{\rm J}$/2 the Jeans
mass can be estimated by:

$M_{\rm J}=\rho\lambda_{\rm J}^{3}=0.8\,\rm
M_{\odot}\left[\frac{\sigma}{0.188\;\rm km\;\rm
s^{-1}}\right]^{3}\left[\frac{n_{\rm H_{2}}}{10^{5}\;\rm
cm^{-3}}\right]^{-1/2},$ (11)

Where $\lambda_{\rm J}$ is the Jeans length, $M_{\rm J}$ is the Jean mass,
$n_{\rm H_{2}}$ is the dense core averaged-volume density, and $\sigma$ is the
velocity dispersion. If the dense cores are supported by pure thermal motions,
the $\sigma$ equals to the sound speed. If the dense cores are supported by
turbulent motions, then $\sigma$ equal to $\sigma_{v}$ = $\sqrt{\sigma_{\rm
nt}^{2}+c_{s}^{2}}$. We also calculated the Jeans number $N_{\rm J}$, which is
given as

$N_{\rm J}=\frac{M_{\rm clump}}{M_{\rm J}}$ (12)

Where $M_{\rm clump}$ is the total mass of compact clumps toward the region of
our observations. The larger Jeans number means the more possibility of
fragmentation. The estimated Jeans mass, Jeans length, and Jeans number are
summarized in Table 4. The gas masses of dense cores are estimated from the
1.3 mm dust emission (see section 3.2). The separations of dense cores are the
projected distance on the sky of the nearest neighbor cores.

In the case of pure thermal fragmentation (Figure 7), the Jeans masses are
much smaller than the observed massive cores and more consistent with the low-
mass cores. In AGAL022 that only detected intermediate- and low-mass cores,
the Jeans mass and length are roughly consistent with the observed values.
This is in agreement with the studies of Palau et al. (2013, 2015) and Pokhrel
et al. (2018), who investigated a sample of intermediate- and low-mass cores.
The pure thermal Jeans fragmentation fails to explain the massive cores that
contain masses much greater than the thermal Jeans mass. The Jean numbers of
pure thermal fragmentation are significantly larger than the observed numbers
of dense cores, and leads to the ratios of Jean number to observed number of
0.01-0.03. These ratios are similar to what Pokhrel et al. (2018) found in
Perseus (0.06), which suggests that pure thermal motions do not support large
clumps. Additional support, such as turbulence and/or magnetic fields, may be
needed to counteract gravitational collapse and further fragmentation. On the
other hand, we cannot rule out that these massive cores have a higher
multiplicity that is not resolved due to limited spatial resolution (e.g.,
Zhang et al., 2015; Palau et al., 2018).

We also study the Jeans fragmentation with regards to the non-thermal motion
together with the thermal support (also known as turbulent Jeans
fragmentation). Since both AGAL024 and AGAL030 have no reliable line width
information, they are not considered in this analysis. The predicted turbulent
Jean masses are approximately consistent with the observed massive cores (see
Figure 7). This indicates that the turbulent support may be needed for these
massive cores, which is consistent with the results of investigations of
massive dense cores (e.g., Zhang et al., 2009; Pillai et al., 2011; Zhang &
Wang, 2011; Wang et al., 2014; Lu et al., 2015; Zhang et al., 2015). The Jean
number of turbulent Jeans fragmentation are slightly larger than or similar to
the observed numbers of dense cores, which implies that the turbulent motions
might play a role in supporting larger clumps.

The velocity dispersion in the dense cores ($R_{\rm eff}^{\rm dec}\sim$ 0.05
pc) is smaller than their natal clumps ($R_{\rm eff}^{\rm dec}\sim$ 0.65 pc).
The former is dominated by transonic motions (i.e., as derived by C18O
emission), while the latter is dominated by supersonic motions (as derived by
NH3). Such variations in the line width from the clump scale down to the dense
core scale toward massive star formation regions have been reported in
previous studies (Wang et al., 2008; Zhang et al., 2015). The observed
supersonic line widths at clump scales could be due to the effect of a poor
linear resolution; spatially unresolved motions within the telescope beam
broaden the observed line widths. The line widths decrease from clump to dense
core scales also could be due to the dissipation of turbulences. Since C18O (a
critical density $c_{\rm cr}\sim$ 104 cm-3) is more easily depleted via
freezing onto dust grains than that of NH3 1-1 ($c_{\rm cr}\sim$ 103 cm-3), it
is possible that NH3 and C18O are tracing different gas components.

The gas masses of the majority (90%) of the identified dense cores are greater
than 4 $\rm M_{\odot}$, which is higher than the gas mass in the predictions
of competitive accretion model (Bonnell & Bate, 2002, 2006). We did not find a
population of low-mass dense cores within these massive clumps, which
certainly could be due to the lack of mass sensitivity and the spatial
resolution of the observations. In addition, the dense cores are not in a
virial equilibrium (see Figure 6), which is not consistent with the turbulent
core model which hypothesizes that the dense cores are in a virial equilibrium
due to turbulent support that counteracts gravity (McKee & Tan, 2002; Krumholz
et al., 2005, 2007). However, we caution that the identified massive cores
might fragment into less massive cores in higher spatial resolution
observations (e.g., Zhang et al., 2015). In addition, the presence of strong
magnetic fields provides additional internal support and helps to virialize
the core.

To study the relationship of the number of cores fragmented from the clump
with the clumps properties, we have computed the clump parameters using APEX
870 $\mu\rm m$ emission, including column and volume densities, Mach number,
gas mass, virial parameter and density distribution. Comparisons of fragments
with the clump properties show no apparent correlation. This could be due to
either the small sample size, or the fact that the fragmentation is dominated
by a combination of multiple physical processes (e.g., turbulence, magnetic
fields, protostar feedback, and density distributions).

###  4.3 Inclination corrections

Since we can not derive the inclination of the outflow axes, the parameters in
Table 3 have not been corrected for their inclination. Assuming a outflow
inclination angles $\theta$ ($\theta$ = 0∘ correspond to outflow along the
line of sight, $\theta$ = 90∘ correspond to the outflow perpendicular the line
of sight), we can estimate the correction factors for the outflow parameters.
Table 5 presents the correction factors for a mean inclination angle
$\langle\theta\rangle\approx 57.3^{\circ}$ assuming all orientations have the
equally probability (Bontemps et al., 1996), nearly pole-on ($5^{\circ}$) and
nearly edge-on ($85^{\circ}$) inclination angles (e.g., Dunham et al., 2014).

For the mean inclination angle the $t_{\rm dyn}$ decreases by a factor of 0.6,
while the $P_{\rm out}$, $E_{\rm out}$ and $\dot{M}_{\rm out}$ increase by
factors of 1.9, 3.4 and 1.7, respectively. The correction factors for $t_{\rm
dyn}$ are greater and smaller than 1 for $\theta<$ 45∘ and $\theta>$ 45∘,
respectively. The correction factors for $P_{\rm out}$ and $E_{\rm out}$ are
always larger than or equal to 1 for all of possible inclination angle. For
$\dot{M}_{\rm out}$, its correction factors are greater and smaller than 1 for
$\theta>$ 45∘ and $\theta<$ 45∘, respectively. The possibility of inclination
angles $\theta>$ 45∘, $\int_{45}^{90}{\rm sin\,\theta\,}d\theta$, is 71%,
which is higher than that of $\theta<$ 45∘, $\int_{0}^{45}{\rm
sin\,\theta\,}d\theta\sim 29\%$. This indicates that the inclination
correction factors for $t_{\rm dyn}$ and $\dot{M}_{\rm out}$, are typically
smaller and greater than 1, respectively. The correlation between $t_{\rm
dyn}$ and gas mass of dense cores could be affected by the outflow
inclination, while this correlation can persist if the outflow inclinations
are not in the most extreme cases (Figure 5).

###  4.4 Evolutionary stage

Infrared emission can be an indicator of star formation activities in
molecular clouds since thermal radiation from embedded protostars heats the
surrounding dust and gas. The clumps in this study are dark in the infrared
wavelengths up to 70 $\mu\rm m$, and are believed to be at an extreme early
phase of star formation, possibly encompassing starless and prestellar
candidates (Figure 1). In total, we have uncovered 44 dense cores in seven 70
$\mu\rm m$ dark clumps using 1.3 mm continuum image. Seventeen of these dense
cores are associated with CO outflows and 5 of these 17 were identified as
having high velocity CO components. This indicates that these 70 $\mu\rm m$
dark clumps have already begun forming stars, and not all of embedded dense
cores are starless and/or prestellar (see also Pillai et al., 2019). There are
some dense cores associated with very weak or no line emission (e.g.,
CO/13CO/C18O, CH3OH, H2CO, HCN and HCO+), which could be starless or
prestellar candidates. With the molecular line emission we found that there
are chemical differentiation between different dense cores within the same
parent clumps, which suggests that they maybe at different evolutionary
stages. A detailed analysis of spectral lines is beyond the scope of this
paper, which will be presented in a forthcoming publication (Li et al., in
preparation).

For each clump, the most massive cores are associated with CO outflows, with
the exception of AGAL030, which shows no outflow signatures toward its
embedded dense cores. All CO outflows are associated with massive cores ($>$ 8
$\rm M_{\odot}$), with the exception of AGAL022-MM1 that contains gas mass of
4.1 $\rm M_{\odot}$. We cannot fully rule out that the lack of CO outflow
detections toward the intermediate- and low-mass cores due to the limited
sensitivity of our observations.

In addition, we find that the outflow dynamical timescale in the massive cores
tend to be longer than that of less massive cores. In a protocluster, if
massive protostars are formed at an earlier stage than their low-mass
counterparts (e.g., Zhang et al., 2015), we expect to see outflow activities
in the massive cores earlier than the less massive ones. On the other hand,
the outflow dynamical timescale might be affected by sensitivity of
observations arising from mostly missing flux since without single dish data
to recover missing short spacing fluxes in the SMA data. Apart from that, the
outflow dynamical timescale is also biased by the outflow inclination (see
Section 4.3).

AGAL030 is one exception that its five embedded dense cores are not associated
with molecular outflow. There are no CO, 13CO, C18O, SiO and HCN emission
toward these dense cores, while faint HCO+ emission is detected toward MM1 and
MM2. In addition, faint H2CO and CH3OH emission are detected toward MM1. We
also found CO emission on the west of MM2 and north-east of MM1, while these
emission are produced by the ambient gas rather than outflow motions. The
observed lines emission imply that there are no star-forming signatures in
these five embedded cores. This indicates that these cores could be starless
or prestellar candidates. The averaged-volume and surface densities,
$\Sigma=M/(\pi r^{2}$), of AGAL030 are similar to the AGAL022 that only
detected one outflow motion, while is relatively lower than other five clumps
that detected significant outflow motions (see Table 4). The dense cores
embedded in higher densities clumps are most likely associated with outflow
motions for this 70 $\mu$m dark cloud sample. This speculation can be tested
by studying a large sample of 70 $\mu$m dark cloud.

##  5 Summary

We studied a sample of seven massive 70 $\mu\rm m$ dark clumps in both dust
continuum and the CO 2-1 emission through high angular resolution observations
using the SMA. The main findings are as follows.

  * •

In total, 44 cores are identified based on the 1.3 mm dust continuum emission.
They have masses ranging from 1.4 up to 77.1 $\rm M_{\odot}$ with effective
radius of 0.02 – 0.11 pc. Among the 44 cores, 29 dense cores have masses in
the range 8.1 to 77.1 $\rm M_{\odot}$ and the other 15 cores with masses
between 1.4 and 7.5 $\rm M_{\odot}$. Assuming the core density follows a
power-law distribution in radius $\rho\propto r^{-b}$, the power-law index $b$
is between 0.6 and 2.1, while majority of dense cores (70%) have an index
between 1 and 2.

  * •

The outflow activities revealed by CO emission are detected toward 17 dense
cores that are embedded in 6 clumps. The CO outflows are only detected toward
the massive cores ($>$ 8 $\rm M_{\odot}$), except for AGAL022-MM1 (4.1 $\rm
M_{\odot}$). Five out of seventeen dense cores are associated with high-
velocity CO outflows. These results suggest that these 70 $\mu\rm m$ dark
clumps host protostars, and therefore they are not quiescent in star
formation.

  * •

There appears to be a positive correlation between outflow dynamical timescale
and gas mass of dense cores. The outflows from massive cores have longer
dynamical timescale than that of less massive cores, which indicates that the
massive cores have a longer accretion history than the less massive ones. In
addition, the outflow dynamical timescales are comparable to the free-fall
timescales with a same order of magnitude of $\sim$104 yr.

  * •

We find that the gas masses of identified low-mass dense cores are roughly
consistent with the pure thermal Jeans fragmentation, while massive cores are
approximately consistent with the turbulent Jean fragmentation. The identified
cores are not in a state of virial equilibrium when magnetic fields and
external cloud pressure are not considered.

This work is supported by the National Key R&D Program of China (No.
2017YFA0402604). SL acknowledges support from the CfA pre-doctoral fellowship,
the Chinese Scholarship Council and National Natural Science Foundation of
China grant 11629302 and U1731237.

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Figure 1: Left: the APEX 870 $\mu$m emission (white contours) overlaid on
three-color Herschel composite image (blue/green/red = 70/160/250 $\mu$m). The
white contours are $\pm$(4, 8, 12 ….)$\times$ $\sigma$, where the $\sigma$ is
the rms level for each source. Right: the 1.3 mm dust continuum overlaid on
Herschel 70 $\mu$m. The white contours are $\pm$(3, 5, 7, 9 ….)$\times$
$\sigma$. The dash circle is the SMA primary beam FWHM size. The synthesized
beam are shown in the bottom left corner of the image. The dash green circle
is the SMA primary beam FWHM size. Figure 1: Continuation Figure 1:
Continuation Figure 2:  (a) the redshifted (red contours) and blueshifted
(blue contours) emission of CO outflows, and SiO velocity integrated intensity
(green contours) overlaid on the 1.3 mm continuum emission. The blue and red
contours are $\pm$(5, 7, 9 …)$\times\,\sigma$, while the green contours are
$\pm$(3, 5, 7 …)$\times\,\sigma$, where the $\sigma$ is the rms level. The
dash black lines indicate the direction of outflows and the labelled
corresponding to the dense cores numbers (e.g., 1 belongs to MM1). The
integrated velocity range is shown in the upper right corner of image. The
green stars represent the identified dense cores. The dash gray circle marks
the FWHM of the SMA primary beam. The synthesized beam is shown in the bottom
left corner of the image. (b)–(f) same as (a), but for AGAL014, AGAL016,
AGAL022, AGAL024 and AGAL031, respectively.  Figure 3: Vector averaged
amplitude distribution versus UV distance in the dense cores. The red solid
line is the least-squared fitting result for the dense cores. Figure 4: The
histogram is the power-law index of density distribution.  Figure 5: Left: the
free-fall time versus outflow dynamical time. The Spearman-rank correlation
test returns a correlation coefficient of 0.59, while the best Least-squares
fitting result is $y=10x^{0.7}$ (black solid line). Right: the dense core mass
versus outflow dynamical time. The correlation coefficient is about 0.62 from
the Spearman-rank correlation test. The black solid line is the best least-
squares fitting result $y=3570x^{0.5}$. The errorbars values of tdyn
correspond to the mean inclination angle ($\langle\theta\rangle\approx
57.3^{\circ}$) correction. The errorbars of $t_{\rm ff}$ and $M_{\rm gas}$
correspond to their uncertainties.  Figure 6: Left: the C18O line width, after
deconvolution with the channel width, versus gas mass of dense cores. The grey
shadow is the sound speed. Right: the virial parameter, $\alpha$, against gas
mass of dense cores. The red and black circles represent the cores associated
with high- (velocity $\geqslant$ 30 km s-1 with respect to the source systemic
velocity) and low-velocity (velocity $<$ 30 km s-1) CO outflow, respectively.
Figure 7: Fragment mass versus projected separation on the sky of the nearest
neighbor fragments. The black symbols are the fragments identified by SMA
observations. The black cross is the typical uncertainly of the observed
fragments. The red symbols represent the prediction of thermal Jeans
fragmentation. The orange symbols represent the prediction of turbulent Jeans
fragmentation, where the turbulent component is from the clump non-thermal NH3
line width. The green shaded regions show the mass sensitivity and spatial
resolution limit of the observations.

Table 1: Observations.

Date | Sources | R.A. | Decl. | $D$ | Calibrator | Calibrator | Calibrator | $N_{\rm ant}$
---|---|---|---|---|---|---|---|---
|  | (J2000) | (J2000) | (kpc) | (Gain) | (Flux) | (Bandpass) |
08/Jul/2017 | AGAL030.844+00.177 | 18:46:59.88 | -01:46:38.6 | 5.4 | 1751+096, 1830+063 | Ganymede | 3c279 | 7
AGAL024.314+00.086 | 18:35:19.01 | -07:37:27.2 | 5.9 | 1751+096, 1830+063 | Ganymede | 3c279 | 7
25/Jul/2017 | AGAL014.492-00.139 | 18:17:22.16 | -16:24:58.4 | 3.6 | nrao530, 1924-292 | Neptune | 3c279 | 8
AGAL016.418-00.634 | 18:22:57.37 | -14:57:08.6 | 3.5 | nrao530, 1924-292 | Neptune | 3c279 | 8
01/Aug/2017 | AGAL031.024+00.262 | 18:47:01.36 | -01:34:41.0 | 4.5 | 1743-038, 1830+063 | Neptune | 3c454.3 | 7
AGAL008.691-00.401 | 18:06:31.80 | -21:37:43.6 | 4.5 | 1743-038, 1830+063 | Neptune | 3c454.3 | 7
06/Aug/2017 | AGAL022.376+00.447 | 18:30:37.40 | -09:12:47.2 | 3.8 | 1743-038, 1830+063 | Neptune | 3c454.3 | 6

††footnotetext: Notes. Columns are (1)observational day, (2) source name, (3)
right ascension, (4) declination, (5)target distance, (6)gain calibrator,
(7)flux calibrator, (8) bandpass calibrator, (9) number of antenna.

Table 2: Dense core physical parameters.

Sources | Core ID | R.A. | Decl. | $\sigma_{maj}$ | $\sigma_{min}$ | PA | $F_{\nu}$ | $S_{\nu}^{\rm beam}$ | $M_{\rm gas}$ | $N_{\rm H_{2}}$ | $n_{\rm H_{2}}$ | $R_{\rm eff}$ | $R_{\rm eff(dec)}$ | $\sigma_{\rm obs}$ | $M_{\rm vir}$ | $\alpha_{\rm vir}$ | $b$ | $T_{\rm K}$ | CO | SiO
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
|  | (hh:mm:ss) | (dd:mm:ss) | (arcsec) | (arcsec) | (deg) | (mJy) | (mJy beam-1) | (M⊙) | (cm-2) | (cm-3) | (pc) | (pc) | (km s-1) | (M⊙) |  |  | (K) |  |
AGLA008 | MM1 | 18:06:32.13 | -21:37:45.00 | 8.1 | 5.6 | 25 | 7.43E-02 | 1.78E-02 | 55.78 | 1.08E+23 | 5.59E+05 | 0.09 | 0.07 | 1.00 | 69.40 | 1.24 | 1.2$\pm$0.1 | 16 | Y | Y
MM2 | 18:06:31.30 | -21:37:51.48 | 6.3 | 5.3 | 21 | 4.22E-02 | 1.38E-02 | 31.69 | 8.35E+22 | 6.46E+05 | 0.08 | 0.06 | 0.91 | 23.85 | 0.75 | 2.1$\pm$0.1 | 16 | Y | N
MM3 | 18:06:33.13 | -21:37:16.43 | 5.5 | 3.5 | 163 | 4.94E-02 | 2.77E-02 | 37.13 | 1.68E+23 | 2.78E+06 | 0.06 | 0.04 | … | … | … | … | 16 | Y | N
MM4 | 18:06:32.68 | -21:37:44.11 | 5.1 | 4.2 | 58 | 1.08E-02 | 5.49E-03 | 8.14 | 3.33E+22 | … | 0.06 | … | … | … | … | … | 16 | N | N
AGAL014 | MM1 | 18:17:22.54 | -16:24:59.70 | 5.6 | 5.5 | 77 | 1.14E-01 | 3.17E-02 | 47.29 | 1.98E+23 | 1.41E+06 | 0.058 | 0.049 | … | … | … | 1.3 $\pm$0.1 | 16 | Y | N
MM2 | 18:17:21.54 | -16:25:02.16 | 8.3 | 4.4 | 141 | 1.02E-01 | 2.39E-02 | 42.18 | 1.49E+23 | 9.00E+05 | 0.063 | 0.054 | … | … | … | 1.1 $\pm$0.1 | 16 | Y | Y
MM3 | 18:17:22.05 | -16:24:49.19 | 9.9 | 6.6 | 38 | 4.47E-02 | 5.88E-03 | 18.49 | 3.67E+22 | 1.38E+05 | 0.085 | 0.077 | 1.00 | 75.21 | 4.07 | … | 16 | N | N
MM4 | 18:17:22.26 | -16:24:54.68 | 7.0 | 4.2 | 128 | 3.31E-02 | 9.69E-03 | 13.71 | 6.04E+22 | 4.81E+05 | 0.057 | 0.046 | 0.74 | 14.89 | 1.09 | … | 16 | N | N
MM5 | 18:17:21.39 | -16:24:55.35 | 8.5 | 6.4 | 102 | 3.32E-02 | 5.29E-03 | 13.75 | 3.30E+22 | 1.41E+05 | 0.077 | 0.069 | 0.79 | 27.34 | 1.99 | … | 16 | N | N
MM6 | 18:17:22.85 | -16:24:55.00 | 4.6 | 3.7 | 133 | 3.13E-02 | 1.59E-02 | 12.97 | 9.91E+22 | 1.78E+06 | 0.043 | 0.029 | … | … | … | 1.4 $\pm$0.2 | 16 | Y | N
MM7 | 18:17:22.12 | -16:25:05.54 | 4.4 | 4.3 | 136 | 2.62E-02 | 1.17E-02 | 10.83 | 7.29E+22 | 1.04E+06 | 0.046 | 0.033 | 0.99 | 34.05 | 3.14 | 0.9 $\pm$0.3 | 16 | Y | Y
MM8 | 18:17:23.27 | -16:25:01.20 | 8.1 | 6.0 | 129 | 3.05E-02 | 5.37E-03 | 12.65 | 3.35E+22 | 1.51E+05 | 0.073 | 0.066 | … | … | … | … | 16 | N | N
AGAL016 | MM1 | 18:22:57.98 | -14:57:01.49 | 9.3 | 6.2 | 23 | 2.18E-02 | 3.21E-03 | 10.95 | 2.65E+22 | 1.11E+05 | 0.08 | 0.07 | … | … | … | … | 13 | Y | N
MM2 | 18:22:56.15 | -14:57:14.47 | 4.8 | 3.9 | 179 | 1.21E-02 | 5.48E-03 | 6.07 | 4.52E+22 | 6.52E+05 | 0.04 | 0.03 | … | … | … | … | 13 | Y | Y
MM3 | 18:22:57.35 | -14:57:10.98 | 4.8 | 3.5 | 68 | 6.66E-03 | 3.37E-03 | 3.35 | 2.78E+22 | 1.43E+06 | 0.04 | 0.02 | … | … | … | … | 13 | N | N
MM4 | 18:22:57.63 | -14:57:24.53 | 5.7 | 4.1 | 36 | 8.88E-03 | 3.20E-03 | 4.46 | 2.64E+22 | 3.16E+05 | 0.05 | 0.04 | … | … | … | … | 13 | N | N
MM5 | 18:22:55.41 | -14:57:07.47 | 4.7 | 3.5 | 150 | 1.29E-02 | 6.73E-03 | 6.49 | 5.55E+22 | 1.01E+06 | 0.04 | 0.03 | … | … | … | … | 13 | N | N
AGAL022 | MM1 | 18:30:38.38 | -9:12:44.57 | 7.9 | 3.5 | 117 | 8.91E-03 | 4.39E-03 | 4.10 | 1.75E+22 | … | 0.06 | … | … | … | … | … | 16 | Y | N
MM2 | 18:30:37.07 | -9:13:07.95 | 8.4 | 3.5 | 129 | 1.05E-02 | 4.72E-03 | 4.82 | 1.88E+22 | 2.49E+05 | 0.06 | 0.04 | … | … | … | … | 16 | N | N
MM3 | 18:30:38.93 | -9:12:44.83 | 6.4 | 2.7 | 142 | 9.26E-03 | 7.28E-03 | 4.26 | 2.90E+22 | 1.56E+06 | 0.05 | 0.02 | 0.696 | 5.45 | 1.28 | … | 16 | N | N
MM4 | 18:30:38.14 | -9:13:01.96 | 6.9 | 2.6 | 138 | 6.97E-03 | 5.14E-03 | 3.20 | 2.04E+22 | 1.06E+06 | 0.05 | 0.02 | … | … | … | … | 16 | N | N
MM5 | 18:30:37.46 | -9:12:36.64 | 6.7 | 2.4 | 151 | 3.48E-03 | 2.88E-03 | 1.60 | 1.14E+22 | … | 0.04 | … | 0.454 | … | … | … | 16 | N | N
MM6 | 18:30:37.47 | -9:12:48.32 | 4.4 | 3.0 | 143 | 3.02E-03 | 3.12E-03 | 1.39 | 1.24E+22 | … | 0.04 | … | … | … | … | … | 16 | N | N
AGAL024 | MM1 | 18:35:19.54 | -7:37:25.39 | 7.1 | 5.3 | 18 | 5.71E-02 | 1.19E-02 | 77.06 | 9.78E+22 | 3.34E+05 | 0.11 | 0.09 | 0.71 | 24.87 | 0.32 | 1.3$\pm$0.2 | 14 | Y | Y
MM2 | 18:35:18.72 | -7:37:39.74 | 8.9 | 4.1 | 164 | 2.54E-02 | 5.50E-03 | 34.28 | 4.52E+22 | 1.70E+05 | 0.10 | 0.09 | 0.62 | 15.54 | 0.45 | … | 14 | Y | N
MM3 | 18:35:19.32 | -7:37:08.54 | 11.5 | 4.2 | 97 | 2.80E-02 | 4.51E-03 | 37.81 | 3.71E+22 | 1.27E+05 | 0.12 | 0.10 | 0.57 | 13.44 | 0.36 | … | 14 | N | N
MM4 | 18:35:18.30 | -7:37:15.97 | 6.7 | 3.3 | 58 | 1.55E-02 | 5.46E-03 | 20.94 | 4.49E+22 | 7.90E+05 | 0.08 | 0.05 | … | … | … | … | 14 | Y | N
MM5 | 18:35:19.22 | -7:37:30.12 | 3.2 | 2.6 | 152 | 8.88E-03 | 8.24E-03 | 11.99 | 6.78E+22 | 2.20E+07 | 0.05 | 0.01 | 0.75 | 2.88 | 0.24 | 2$\pm$0.1 | 14 | N | N
MM6 | 18:35:19.06 | -7:37:25.04 | 4.0 | 2.3 | 127 | 5.53E-03 | 4.61E-03 | 7.47 | 3.79E+22 | … | 0.05 | … | … | … | … | … | 14 | N | N
AGAL031 | MM1 | 18:47:00.86 | -1:34:42.49 | 8.3 | 2.9 | 148 | 2.42E-02 | 1.04E-02 | 20.59 | 7.02E+22 | 9.54E+05 | 0.064 | 0.042 | … | … | … | 1.8$\pm$0.1 | 13 | Y | Y
MM2 | 18:47:01.47 | -1:34:47.55 | 5.3 | 4.3 | 56 | 2.13E-02 | 9.66E-03 | 18.18 | 6.54E+22 | 2.12E+06 | 0.063 | 0.031 | 0.76 | 11.21 | 0.62 | 1$\pm$0.1 | 13 | Y | N
MM3 | 18:47:01.76 | -1:34:25.88 | 10.2 | 4.5 | 135 | 2.34E-02 | 5.20E-03 | 19.96 | 3.52E+22 | 1.44E+05 | 0.090 | 0.078 | … | … | … | … | 13 | N | N
MM4 | 18:47:00.66 | -1:34:24.31 | 7.4 | 3.7 | 142 | 2.01E-02 | 7.57E-03 | 17.12 | 5.12E+22 | 3.79E+05 | 0.069 | 0.054 | 0.78 | 21.94 | 1.28 | 0.9$\pm$0.2 | 13 | Y | N
MM5 | 18:47:01.14 | -1:34:28.36 | 7.0 | 3.0 | 136 | 1.52E-02 | 7.33E-03 | 12.99 | 4.96E+22 | 6.47E+05 | 0.061 | 0.041 | … | … | … | 0.6$\pm$0.3 | 13 | Y | N
MM6 | 18:47:01.76 | -1:34:09.29 | 10.0 | 4.5 | 153 | 4.05E-02 | 9.22E-03 | 34.56 | 6.24E+22 | 2.62E+05 | 0.089 | 0.077 | … | … | … | … | 13 | N | N
MM7 | 18:47:02.14 | -1:34:52.55 | 4.5 | 2.6 | 143 | 1.19E-02 | 1.03E-02 | 10.14 | 6.95E+22 | 7.52E+06 | 0.045 | 0.017 | 0.84 | 7.69 | 0.76 | 1.5$\pm$0.3 | 13 | Y | N
MM8 | 18:47:01.58 | -1:34:59.55 | 4.6 | 4.1 | 7 | 1.08E-02 | 5.85E-03 | 9.17 | 3.96E+22 | 1.42E+06 | 0.057 | 0.028 | 0.60 | 4.27 | 0.46 | … | 13 | N | N
MM9 | 18:47:01.82 | -1:34:44.39 | 5.4 | 2.2 | 149 | 6.79E-03 | 5.75E-03 | 5.79 | 3.89E+22 | … | 0.046 | … | 0.61 | … | … | … | 13 | N | N
MM10 | 18:47:01.58 | -1:34:38.35 | 6.7 | 3.2 | 151 | 4.71E-03 | 2.20E-03 | 4.01 | 1.49E+22 | 1.66E+05 | 0.062 | … | … | … | … | … | 13 | N | N
AGAL030 | MM1 | 18:47:00.02 | -1:46:31.15 | 8.5 | 2.6 | 110 | 1.79E-02 | 5.98E-03 | 20.21 | 5.12E+22 | 1.22E+06 | 0.07 | 0.04 | … | … | … | … | 14 | N | N
MM2 | 18:47:00.06 | -1:46:38.71 | 4.4 | 2.6 | 60 | 6.00E-03 | 3.92E-03 | 6.76 | 3.35E+22 | … | 0.05 | … | … | … | … | … | 14 | N | N
MM3 | 18:47:01.09 | -1:46:34.88 | 5.8 | 2.6 | 162 | 8.79E-03 | 4.28E-03 | 9.90 | 3.67E+22 | 8.38E+06 | 0.06 | 0.02 | … | … | … | … | 14 | N | N
MM4 | 18:47:00.21 | -1:46:12.50 | 4.5 | 3.6 | 4 | 1.30E-02 | 6.00E-03 | 14.69 | 5.14E+22 | 5.90E+05 | 0.06 | 0.04 | … | … | … | … | 14 | N | N
MM5 | 18:46:59.27 | -1:46:27.38 | 5.5 | 4.0 | 94 | 6.61E-03 | 2.25E-03 | 7.44 | 1.93E+22 | 1.26E+05 | 0.07 | 0.06 | … | … | … | … | 14 | N | N

††footnotetext: Notes. Sources: source name. Core ID: dense core. R.A.: right
ascension. Decl.: declination. $\sigma_{maj}$: beam-convolved major axis.
$\sigma_{min}$: beam-convolved minor axis. PA: position angle. $F_{\nu}$:
total integrated flux. $S_{\nu}^{\rm beam}$: peak flux density. $M_{\rm gas}$:
gas mass. $N_{\rm H_{2}}$: column density. $n_{\rm H_{2}}$: volumn density.
$R_{\rm eff}$: beam-convolved effective radius. $R_{\rm eff(dec)}$: beam-
deconvolved effective radius. $\sigma_{\rm obs}$: channel width deconvolved
line width of C18O. $M_{\rm vir}$: virial mass. $\alpha_{\rm vir}$: virial
parameters. $b$: best fitted density power-law index. $T_{\rm K}$: kinematical
temperature. CO: CO outflow detection. SiO: SiO detection.

Table 3: Outflow parameters.

Source | Core ID |  | $\Delta v$ | $M_{\rm out}$ | $P_{\rm out}$ | $E_{\rm out}$ | $t_{\rm dyn}$ | $\dot{M}_{\rm out}$ | $l_{\rm out}$
---|---|---|---|---|---|---|---|---|---
|  |  | (km s-1) | (M⊙) | (M⊙ km s-1) | (M⊙ km2 s-2) | (104 yr) | (10-5 M⊙ yr-1) | (pc)
AGAL008 | MM1 | Blue | [19, 35] | 0.035 | 0.281 | 1.36 | 2.61 | 0.136 | 0.51
Red | [41, 70] | 0.031 | 0.272 | 1.43 | 0.48 | 0.647 | 0.15
MM2 | Blue | [30, 38] | 0.016 | 0.080 | 0.22 | 0.81 | 0.203 | 0.07
Red | [39, 48] | 0.010 | 0.043 | 0.10 | 1.67 | 0.058 | 0.15
MM3 | Blue | [21, 35] | 0.012 | 0.096 | 0.50 | 0.95 | 0.13 | 0.17
Red | [43, 61] | 0.011 | 0.112 | 0.63 | 0.73 | 0.15 | 0.17
AGAL014 | MM1 | Red | [41, 56] | 0.061 | 0.353 | 1.49 | 2.51 | 0.24 | 0.41
MM2 | Blue | [3, 38] | 0.017 | 0.250 | 2.43 | 0.35 | 0.49 | 0.13
Red | [40, 96] | 0.148 | 2.42 | 32.36 | 0.41 | 3.59 | 0.23
MM6 | Blue | [15, 38] | 0.048 | 0.466 | 2.94 | 0.94 | 0.52 | 0.24
Red | [43, 75] | 0.036 | 0.432 | 3.45 | 0.52 | 0.70 | 0.18
MM7 | Blue | [11, 35] | 0.024 | 0.306 | 2.09 | 0.40 | 0.60 | 0.12
AGAL016 | MM1 | Red | [46, 58] | 0.006 | 0.045 | 0.19 | 0.9 | 0.06 | 0.15
MM2 | Red | [46, 59] | 0.003 | 0.032 | 0.16 | 0.7 | 0.05 | 0.11
AGAL022 | MM1 | Red | [83, 89] | 0.01 | 0.04 | 0.09 | 1.55 | 0.06 | 0.11
AGAL024 | MM1 | Blue | [96, 112] | 0.006 | 0.037 | 0.15 | 1.61 | 0.04 | 0.28
Red | [117, 133] | 0.087 | 0.827 | 4.31 | 1.62 | 0.54 | 0.33
MM2 | Red | [120, 133] | 0.050 | 0.403 | 1.74 | 2.69 | 0.19 | 0.48
MM4 | Red | [117, 134] | 0.055 | 0.279 | 0.83 | 2.52 | 0.22 | 0.41
AGAL031 | MM1 | Blue | [49, 78] | 0.036 | 0.965 | 13.82 | 0.38 | 0.55 | 0.18
Red | [97, 141] | 0.087 | 1.225 | 12.18 | 0.55 | 0.93 | 0.24
MM2 | Red | [96, 114] | 0.113 | 0.851 | 4.30 | 1.22 | 2.57 | 0.22
MM4 | Blue | [72, 78] | 0.007 | 0.15 | 1.65 | 0.42 | 0.17 | 0.11
Red | [97, 113] | 0.051 | 0.33 | 1.42 | 1.04 | 0.50 | 0.17
MM5 | Blue | [73, 78] | 0.019 | 0.387 | 3.99 | 1.02 | 0.18 | 0.25
Red | [97, 141] | 0.043 | 0.544 | 5.19 | 0.32 | 0.50 | 0.15
MM7 | Blue | [52, 77] | 0.050 | 1.171 | 14.02 | 0.47 | 1.08 | 0.21
Red | [83, 94] | 0.028 | 0.320 | 1.93 | 0.78 | 0.35 | 0.13

††footnotetext: Notes. $\Delta v$: velocity range for blue- and red-shifted
components. $M_{\rm out}$: outflow mass. $P_{\rm out}$: outflow momentum.
$E_{\rm out}$: outflow energy. $t_{\rm dyn}$: outflow dynamical time.
$\dot{M}_{\rm out}$: outflow rate. $L_{\rm out}$: outflow physical length.

Table 4: Jean analysis in the clump.

Sources | $M_{\rm clump}$ | $R_{\rm eff(dec)}$ | $M_{\rm J}^{\rm th}$ | $M_{\rm J}^{\rm tur}$ | $L_{\rm J}^{\rm th}$ | $L_{\rm J}^{\rm tur}$ | $N_{\rm J}^{\rm th}$ | $N_{\rm J}^{\rm tur}$ | $N_{\rm core}$ | $M_{\rm core}$ | $L_{\rm core}$ | $\Sigma$ | $n_{\rm H_{2}}$
---|---|---|---|---|---|---|---|---|---|---|---|---|---
| (M⊙) | (pc) | (M⊙) | (M⊙) | (pc) | (pc) |  |  |  | (M⊙) | (pc) | ($\rm cm^{-2}$) | ($\rm cm^{-3}$)
AGAL008 | 486 | 0.32 | 2.0 | 32.9 | 0.10 | 0.32 | 243 | 15 | 4 | 8.1-55.8 | 0.18-0.62 | 1.71E+22 | 5.21E+04
AGAL014 | 856 | 0.33 | 1.8 | 113.1 | 0.08 | 0.41 | 476 | 8 | 8 | 10.8-47.3 | 0.11-0.15 | 2.85E+22 | 8.48E+04
AGAL016 | 538 | 0.42 | 2.5 | 56.5 | 0.14 | 0.48 | 215 | 10 | 5 | 3.4-11.0 | 0.22-0.24 | 1.08E+22 | 2.49E+04
AGAL022 | 714 | 0.53 | 4.1 | 66.9 | 0.19 | 0.59 | 173 | 11 | 6 | 1.4-4.8 | 0.21-0.32 | 8.85E+21 | 1.61E+04
AGAL024 | 1181 | 0.54 | 2.7 | … | 0.14 | … | 437 | … | 6 | 7.5-77.1 | 0.16-0.49 | 1.44E+22 | 2.59E+04
AGAL031 | 559 | 0.35 | 1.9 | 20.4 | 0.10 | 0.29 | 294 | 27 | 10 | 4.0-34.6 | 0.14-0.37 | 1.58E+22 | 4.35E+04
AGAL030 | 484 | 0.45 | 3.2 | … | 0.17 | … | 151 | … | 5 | 5.3-20.2 | 0.20-0.50 | 8.46E+21 | 1.82E+04

††footnotetext: Notes. $M_{\rm clump}$: total mass of compact clump. $R_{\rm
eff(dec)}$: beam-deconvolved effective radius of compact clump. $M_{\rm
J}^{\rm th}$: thermal Jeans mass. $M_{\rm J}^{\rm tur}$: turbulent Jeans mass.
$L_{\rm J}^{\rm th}$: thermal Jeans length. $L_{\rm J}^{\rm tur}$: turbulent
Jeans length. $N_{\rm J}^{\rm th}$: thermal Jean number. $N_{\rm J}^{\rm
tur}$: turbulent Jean number. $N_{\rm core}$ number of detected cores. $M_{\rm
core}$: observed mass of detected cores. $L_{\rm core}$: observed separation
between nearest neighbor cores. $\Sigma$: the clump surface density. $n_{\rm
H_{2}}$: the clump averaged-volumn density.

Table 5: Inclination correction factors.  Outflow parameters | Inclination Dependence |  | Correction angles |
---|---|---|---|---
|  | $\langle\theta\rangle\approx 57.3^{\circ}$ | $\theta=5^{\circ}$ | $\theta=85^{\circ}$
$v_{\rm out}$ | 1/cos$\,\theta$ | 1.9 | 1.0 | 11.5
$l_{\rm out}$ | 1/sin$\,\theta$ | 1.2 | 11.5 | 1.0
$t_{\rm dyn}$ | cos$\,\theta$/sin$\,\theta$ | 0.6 | 11.4 | 0.09
$P_{\rm out}$ | 1/cos$\,\theta$ | 1.9 | 1.0 | 11.5
$E_{\rm out}$ | 1/cos${}^{2}\,\theta$ | 3.4 | 1.1 | 131.6
$\dot{M}_{\rm out}$ | sin$\,\theta$/cos$\,\theta$ | 1.7 | 0.09 | 11.4