11institutetext: Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69,
53121 Bonn, Germany
11email<EMAIL_ADDRESS>22institutetext: Max Planck Institute for
Astronomy, Königstuhl 17, 69117 Heidelberg, Germany 33institutetext: Shanghai
Astronomical Observatory, Chinese Academy of Sciences, 80 Nandan Road,
Shanghai 200030, Peoples Republic of China 44institutetext: Department of
Physics, P.O.Box 64, FI-00014, University of Helsinki, Finland
55institutetext: Kavli Institute for Astronomy and Astrophysics, Peking
University, Haidian District, Beijing 100871, People’s Republic of China
66institutetext: Department of Astronomy, School of Physics, Peking
University, Beijing 100871, People’s Republic of China 77institutetext:
Department of Astronomy, Yunnan University, Kunming, 650091, PR China
88institutetext: Department of Physics, Faculty of Science, Kunming University
of Science and Technology, Kunming 650500, People’s Republic of China
99institutetext: National Astronomical Observatory of Japan, National
Institutes of Natural Sciences, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan
1010institutetext: Departamento de Astronomía, Universidad de Chile, Casilla
36-D, Santiago, Chile 1111institutetext: Satyendra Nath Bose National Centre
for Basic Sciences, BlockJD, Sector-III, Salt Lake, Kolkata-700 106
1212institutetext: Korea Astronomy and Space Science Institute, 776
Daedeokdaero, Yuseonggu, Daejeon 34055, Republic of Korea 1313institutetext:
University of Science and Technology, Korea (UST), 217 Gajeong-ro, Yuseong-gu,
Daejeon 34113, Republic of Korea 1414institutetext: Astronomical Science
Program, The Graduate University for Advanced Studies, SOKENDAI, 2-21-1 Osawa,
Mitaka, Tokyo 181-8588, Japan

# Feedback from protoclusters does not significantly change the kinematic
properties of the embedded dense gas structures

J. W. Zhou Feedback from protoclusters does not significantly change the
kinematic properties of the embedded dense gas structuresFeedback from
protoclusters does not significantly change the kinematic properties of the
embedded dense gas structures S. Dib Feedback from protoclusters does not
significantly change the kinematic properties of the embedded dense gas
structuresFeedback from protoclusters does not significantly change the
kinematic properties of the embedded dense gas structures F. Wyrowski Feedback
from protoclusters does not significantly change the kinematic properties of
the embedded dense gas structuresFeedback from protoclusters does not
significantly change the kinematic properties of the embedded dense gas
structures T. Liu Feedback from protoclusters does not significantly change
the kinematic properties of the embedded dense gas structuresFeedback from
protoclusters does not significantly change the kinematic properties of the
embedded dense gas structures S. H. Li Feedback from protoclusters does not
significantly change the kinematic properties of the embedded dense gas
structuresFeedback from protoclusters does not significantly change the
kinematic properties of the embedded dense gas structures P. Sanhueza Feedback
from protoclusters does not significantly change the kinematic properties of
the embedded dense gas structuresFeedback from protoclusters does not
significantly change the kinematic properties of the embedded dense gas
structuresFeedback from protoclusters does not significantly change the
kinematic properties of the embedded dense gas structuresFeedback from
protoclusters does not significantly change the kinematic properties of the
embedded dense gas structures M. Juvela Feedback from protoclusters does not
significantly change the kinematic properties of the embedded dense gas
structuresFeedback from protoclusters does not significantly change the
kinematic properties of the embedded dense gas structures F. W. Xu Feedback
from protoclusters does not significantly change the kinematic properties of
the embedded dense gas structuresFeedback from protoclusters does not
significantly change the kinematic properties of the embedded dense gas
structuresFeedback from protoclusters does not significantly change the
kinematic properties of the embedded dense gas structuresFeedback from
protoclusters does not significantly change the kinematic properties of the
embedded dense gas structures H. L. Liu Feedback from protoclusters does not
significantly change the kinematic properties of the embedded dense gas
structuresFeedback from protoclusters does not significantly change the
kinematic properties of the embedded dense gas structures T. Baug Feedback
from protoclusters does not significantly change the kinematic properties of
the embedded dense gas structuresFeedback from protoclusters does not
significantly change the kinematic properties of the embedded dense gas
structures Y. P. Peng Feedback from protoclusters does not significantly
change the kinematic properties of the embedded dense gas structuresFeedback
from protoclusters does not significantly change the kinematic properties of
the embedded dense gas structures K. M. Menten Feedback from protoclusters
does not significantly change the kinematic properties of the embedded dense
gas structuresFeedback from protoclusters does not significantly change the
kinematic properties of the embedded dense gas structures L. Bronfman Feedback
from protoclusters does not significantly change the kinematic properties of
the embedded dense gas structuresFeedback from protoclusters does not
significantly change the kinematic properties of the embedded dense gas
structures C. W. Lee Feedback from protoclusters does not significantly change
the kinematic properties of the embedded dense gas structuresFeedback from
protoclusters does not significantly change the kinematic properties of the
embedded dense gas structuresFeedback from protoclusters does not
significantly change the kinematic properties of the embedded dense gas
structuresFeedback from protoclusters does not significantly change the
kinematic properties of the embedded dense gas structures

(Accepted XXX. Received YYY; in original form ZZZ)

A total of 64 ATOMS sources at different evolutionary stages were selected to
investigate the kinematics and dynamics of gas structures under feedback. We
identified dense gas structures based on the integrated intensity map of
H13CO+ J=1-0 emission, and then extracted the average spectra of all
structures to investigate their velocity components and gas kinematics. For
the scaling relations between velocity dispersion $\sigma$, effective radius
$R$ and column density $N$ of all structures, $\sigma-N*R$ always has a
stronger correlation compared to $\sigma-N$ and $\sigma-R$. There are
significant correlations between velocity dispersion and column density, which
may imply that the velocity dispersion originates from gravitational collapse,
also revealed by the velocity gradients. The measured velocity gradients for
dense gas structures in early-stage sources and late-stage sources are
comparable, indicating gravitational collapse through all evolutionary stages.
Late-stage sources do not have large-scale hub-filament structures, but the
embedded dense gas structures in late-stage sources show similar kinematic
modes to those in early- and middle-stage sources. These results may be
explained by the multi-scale hub-filament structures in the clouds. We
quantitatively estimated the velocity dispersion generated by the outflows,
inflows, ionized gas pressure and radiation pressure, and found that the
ionized gas feedback is stronger than other feedback mechanisms. However,
although feedback from Hii regions is the strongest, it does not significantly
affect the physical properties of the embedded dense gas structures. Combining
with the conclusions in Zhou et al. (2023a) on cloud-clump scales, we suggest
that although feedback from cloud to core scales will break up the original
cloud complex, the substructures of the original complex can be reorganized
into new gravitationally governed configurations around new gravitational
centers. This process is accompanied by structural destruction and generation,
and changes in gravitational centers, but gravitational collapse is always
ongoing.

###### Key Words.:

Submillimeter: ISM – ISM:structure – ISM: evolution – Stars: formation –
methods: analytical – techniques: image processing

##  1 Introduction

Stellar feedback from high-mass stars (M$\textgreater$8 M⊙) can strongly
influence their surrounding interstellar medium and regulate star formation.
The combined effects of multiple feedback mechanisms may play an major role in
determining star formation efficiency and the initial mass function in
molecular clouds (Dib et al., 2010, 2011; Krumholz et al., 2014). In Krumholz
et al. (2014), feedback mechanisms are divided into three categories: (1)
Momentum feedback, including protostellar outflows and (probably) radiation
pressure; (2) Explosive feedback, including winds from hot main sequence
stars, photoionizing radiation, and supernovae; (3) Thermal feedback, with
non-ionizing radiation as the main form. Lopez et al. (2014) assessed the role
of stellar feedback at the scales $\sim$10–100 pc toward 32 Hii regions in the
Large and Small Magellanic Clouds, they employed multi-wavelength data to
examine several stellar feedback mechanisms, and found that the ionized gas
feedback dominates over the other mechanisms in all of the sources. Similar
methods were also used in Olivier et al. (2021), but for 106 deeply embedded
Hii regions with radii ¡ 0.5 pc. They concluded that the dust-processed
radiation dominates in 84% of the samples. In simulations, massive stellar
feedback, including ionizing radiation, stellar winds, and supernovae
(Matzner, 2002; Dale et al., 2012; Rogers & Pittard, 2013; Dale et al., 2014;
Rahner et al., 2017; Smith et al., 2018; Lewis et al., 2023), can suppress the
star formation and destroy the natal cloud. However, whether stellar feedback
promotes or suppresses star formation remains controversial. The simulations
of Dale et al. (2014) examined the effects of photoionization and momentum-
driven winds from O-stars on molecular clouds. They found that feedback has
little effect on more massive and denser clouds and it mainly destroys clouds
with lower mass and density. Dib et al. (2013) showed, using semi-analytical
models in which gas-expulsion from protocluster clouds is driven by stellar
wind feedback originating from both B and O stars that the gas expulsion
timescale depends on the clouds mass and the coupling efficiency of the wind
with the surrounding gas. The observations of Pabst et al. (2019) and Henshaw
et al. (2022) suggest that at early stages, energy-winds could dominate, even
if this is questioned by recent theoretical works (Lancaster et al., 2021a,
b). It is also possible for the feedback to be positive by triggering new star
formation. In Deharveng et al. (2005), Zavagno et al. (2006) and Liu et al.
(2017), using data at various wavelengths, they identified and studied several
objects in which star formation appears to have been triggered at the borders
of Hii regions. Thompson et al. (2012) studied a large sample of infrared
bubbles, and estimated that the fraction of massive stars in the Milky Way
formed by triggering could be between 14 and 30%. Kendrew et al. (2012) found
that approximately $\sim$22% of massive young stars may have formed as a
result of feedback from expanding Hii regions.

As presented in Watkins et al. (2019), stellar feedback from O stars clearly
modify the structure of the larger scale clouds, but without much effect on
the dynamical properties of the assembled dense gas. In the G305 GMC, feedback
has triggered star formation by the collect and collapse mechanism based on
observations using the Large APEX sub-Millimeter Array (LAsMA) 7 beam receiver
on the Atacama Pathfinder Experiment 12 meter submillimeter telescope (APEX)
(Mazumdar et al., 2021a, b). Rugel et al. (2019) showed that feedback from the
first formed cluster in W49A is not strong enough to disperse the cloud, which
likely only affect limited parts of W49A. Moreover, all feedback models used
in Rugel et al. (2019) predict recollapse of the shell after the first star
formation event.

The importance of large-scale gravitational collapse in star formation regions
has been suggested in many observational and theoretical work (Hartmann &
Burkert, 2007; Vázquez-Semadeni et al., 2009; Schneider et al., 2010; Peretto
et al., 2013, 2014; Wyrowski et al., 2016; Hacar et al., 2017; Vázquez-
Semadeni et al., 2019; Xu et al., 2023b). In a sample of 11 massive clumps,
high-resolution data reveal that protoclusters evolves to tighter by global
gravitational collapse (Xu et al., 2023a). In the LAsMA observation for the
G333 complex under feedback, on large scales, Zhou et al. (2023b, a) found
that the inflow may be driven by the larger-scale structure, consistent with
the hierarchical structure in the molecular cloud and gas inflow from large to
small scales. The large-scale gas inflow is driven by gravity, implying that
the molecular clouds in the G333 complex may be in a state of global
gravitational collapse, also refer to Dib (2023). Ubiquitous density and
velocity fluctuations also imply the widespread presence of local
gravitational collapse (Henshaw et al., 2020). For local dense gas structures,
most of them have obvious correlation between velocity dispersion and density,
which indicates the gravitational origin of velocity dispersion. For the G333
complex, although the original cloud complex is disrupted by feedback, the
substructures of the original complex can be reorganized into new
gravitationally governed configurations around new gravitational centers. This
process is accompanied by structural destruction and generation and changes in
gravitational centers, but gravitational collapse is always ongoing. The
results in Zhou et al. (2022, 2023b, 2023a) and Peretto et al. (2023) show
that the kinematic properties of parsec-scale clumps in two very different
physical environments (infrared dark and infrared bright) are comparable.
Thus, feedback in infrared bright star-forming regions, such as the G333
complex, will not change the kinematic properties of parsec-scale clumps,
which is also consistent with the survey results that most Galactic parsec-
scale massive clumps seem to be gravitationally bound regardless of their
evolutionary phases (Liu et al., 2016; Urquhart et al., 2018; Evans et al.,
2021; Dib, 2023).

In this work, we extend the cloud-clump analysis in Zhou et al. (2023a) to the
clump-core scale using high-resolution ALMA data from the ATOMS (ALMA Three-
millimeter Observations of Massive Star-forming regions) survey (Liu et al.,
2020). The ATOMS survey has observed 146 active star forming regions at ALMA
Band 3. The data can be used to systematically investigate the spatial
distribution of various dense gas tracers in a large sample of Galactic
massive clumps. The dense molecular gas structures inside the cloud serve as
star-forming sites, their physical states directly determine the star
formation capability of the molecular cloud under feedback. A more systematic
study is needed to evaluate how massive protostars influence the dense gas
distribution and star formation efficiency in their natal clumps. Using ALMA
data, we zoom in the dense gas structures close to or even connecting with
protoclusters, the effects of feedback are then inferred through the physical
properties of the surrounding dense gas structures. The sample of the ATOMS
survey includes 146 active star forming regions. In Zhou et al. (2022), we
found that hub-filament systems are very common within massive protoclusters,
and stellar feedback from HII regions gradually destroys the hub-filament
systems as protoclusters evolve. The sources at different evolutionary stages
are dominated by different feedback mechanisms. By comparing the physical
properties of dense gas structures in the clumps at different evolutionary
stages, we will be able to infer the relative importance of various feedback
mechanisms.

##  2 Observations

###  2.1 ALMA observations

We use ALMA data from the ATOMS survey (Project ID: 2019.1.00685.S; PI: Tie
Liu). The ATOMS sources were initially selected from a complete and
homogeneous CS J=2-1 molecular line survey toward IRAS sources with far-
infrared colors characteristics of UC Hii regions (Bronfman et al., 1996). As
discussed in Liu et al. (2020), the ATOMS sources are distributed in very
different environments of the Milky Way, and are an unbiased sample of the
proto-clusters with the strongest CS J=2-1 line emission (T${}_{A}>2$ K)
located in the inner Galatic plane of $-80$°$<l<40$°, $|b|<2$°(Faúndez et al.,
2004).

For the data reduction, the details of the 12 m array and 7 m array ALMA
observations were summarised in Liu et al. (2020, 2021). Calibration and
imaging were carried out using the CASA software package version 5.6 (McMullin
et al., 2007). The 7 m data and 12 m array data were calibrated separately.
Then the visibility data from the 7 m and 12 m array configurations were
combined and later imaged in CASA. For each source and each spectral window
(spw), a line-free frequency range is automatically determined using the ALMA
pipeline. This frequency range is used to (a) subtract continuum from line
emission in the visibility domain, and (b) make continuum images. Continuum
images are made from multi-frequency synthesis of data in the line-free
frequency ranges in the two 1.875 GHz wide spectral windows, spws 7 and 8,
centered on $\sim 99.4$ GHz (or 3 mm). Visibility data from the 12 m and 7 m
arrays are jointly cleaned using task tclean in CASA 5.6. We used natural
weighting and a multiscale deconvolver, for an optimized sensitivity and image
quality. All images are primary-beam corrected. The continuum image reaches a
typical 1 $\sigma$ rms noise of $\sim$0.2 mJy with a synthesized beam FWHM
size of $\sim 2.2\arcsec$. In this work, we also use H13CO+ J=1-0 (86.754288
GHz) and HCO+ J=1-0 (89.188526 GHz) molecular lines data with spectral
resolutions of 0.211 km s-1 and 0.103 km s-1. The typical beam FWHM size and
channel rms noise level for H13CO+ J=1-0 line emission are $\sim 2.5\arcsec$
and 8 mJy beam-1, respectively. For HCO+ J=1-0 line emission, the two values
are $\sim 2.4\arcsec$ and 12 mJy beam-1. The typical maximum recovered angular
scale in this survey is about 1 arcmin, which is comparable to the field of
view (FOV) in the 12 m array observations (Liu et al., 2020).

###  2.2 Spitzer infrared data

We also use images at 8 $\mu$m, obtained by the Spitzer Infrared Array Camera
(IRAC), as part of the GLIMPSE project (Benjamin et al., 2003). The images of
IRAC were retrieved from the Spitzer Archive and the angular resolution of the
images are about $2\arcsec$.

##  3 Results

###  3.1 Evolutionary stages

Figure 1: The Moment 0 maps of H13CO+ J=1-0 for 3 ATOMS sources at three
evolutionary stages. Yellow contours show 3 mm continuum emission with its
minimum contour level of 5$\sigma$. Orange eclipses represent the retained
Dendrogram structures. The maps for all 64 ATOMS sources studied in this work
are presented in Appendix.B. Figure 2: Physical parameters of 64 ATOMS sources
at different evolutionary stages. Panels (a), (b), (c) and (d) show the
distributions of the radius $R$, distance $D$, luminosity-to-mass ratios $L/M$
and dust temperature $T$, respectively.

Generally, the infrared properties and the presence of H40α emission can be
used to assess the evolutionary stages of the sources (Chambers et al., 2009;
Sanhueza et al., 2012). As discussed in Zhou et al. (2022), stellar feedback
from Hii regions will gradually destroy the hub-filament systems as
protoclusters evolve. Thus, the morphology of the hub-filament structure can
also characterize the evolutionary stages. In Fig.2 and Fig.3 of Zhou et al.
(2022), for hub-filament systems, the overlaid contours of 3 mm continuum
should be located in the center of filamentary network with the strongest
H13CO+ J=1-0 emission, where the center of the gravitational potential well is
located and is the potential site for high-mass star formation. In the late
stage of evolution, the 3 mm continuum emission is almost completely separated
from H13CO+ J=1-0 emission, indicating that the relatively evolved Hii regions
have dispersed their natal gas, also refer to Liu et al. (2023). Thus the
separation between 3mm continuum emission and H13CO+ (1-0) emission can also
be used for the classification. Finally, we divided ATOMS sources into three
evolutionary stages using the following criteria:

1\. The sources in the early stage (early-sources): (1) Infrared dark and
without H40α emission; (2) Well-defined hub-filament structures; (3) Their 3mm
continuum emissions concentrate on the centers of filamentary networks with
the strongest H13CO+ (1-0) emission.

2\. The sources in the middle stage (middle-sources) have the same features
like early-sources except for having compact H40α emission.

3\. The sources in the late stage (late-sources): (1) Obvious triggering
signs, such as the bent dense gas structures traced by H13CO+ (1-0) emission;
(2) Their 3mm emission is extended, and all of them have strong H40α and 8
$\mu$m emission, indicating that 3mm continuum emission is dominant by
free–free emission (Keto et al., 2008; Zhang et al., 2023). The two conditions
mean that hubs in the late stage have developed into protoclusters. Then
powerful Hii regions driven by protoclusters will destroy the hub-filament
systems eventually. We can see the expansion of Hii regions are tearing up the
surrounding gas structures in Fig. 1(c).

The number of early-sources, middle-sources and late-sources are 30, 11, and
23. We have applied stringent criteria for the selection, and retained only
sources that can be clearly catergorized in one out of the three stages. The
values of radius, distance, bolometric luminosity, mass, and dust temperature
for ATOMS sources have been listed in the Table.A1 of Liu et al. (2020). The
luminosity-to-mass ratios $L/M$ and dust temperature $T$ of the clumps can be
used to trace the evolutionary process of star formation (Saraceno et al.,
1996; Krumholz & Tan, 2007; Molinari et al., 2008; Liu et al., 2016; Stephens
et al., 2016; Urquhart et al., 2018). As shown in Fig.2(c) and (d), from early
to middle to late stages, $L/M$ and $T$ of the sources are indeed increasing
gradually, confirming that our classification is reasonable.

###  3.2 Dendrogram structures

Figure 3: Scale distribution of all identified structures. The probability
density is estimated by the kernel density estimation (KDE) method.

The issues of identifying the structures in PPV cube by the Dendrogram
algorithm have been described in Sec.3.1 and Sec.3.2 of Zhou et al. (2023a).
Thus, we adopt the same method in Zhou et al. (2023a) to identify dense gas
structures. We directly identify hierarchical (sub-)structures based on the 2D
integrated intensity (Moment 0) map of H13CO+ (1$-$0) emission, and then
extract the average spectrum of each structure to investigate their velocity
components and gas kinematics.

For the Moment 0 map, a 5$\sigma$ threshold has been set, we therefore only
require the smallest area of the structure to be larger than 0.5 beam and do
not set other parameters to reduce the dependence of the identification on the
algorithm parameters. In Fig.1, the structures identified by Dendrogram
correspond well to the background integrated intensity maps.

The algorithm will approximate the morphology of each structure as an ellipse.
In Dendrogram, the long and short axes of an ellipse, $a$ and $b$, are the rms
sizes (second moments) of the intensity distribution along the two spatial
dimensions. As described in Zhou et al. (2023a), $a$ and $b$ will give a
smaller ellipse, compared to the size of the identified structure, thus
multiplying a factor of 2 to enlarge the ellipse is necessary. Then the
effective physical radius of an ellipse is $R\rm_{eff}$ =$\sqrt{2a\times
2b}*D$, where $D$ is the distance of the source.

As discussed in Zhou et al. (2023a), two screening criteria were used to
filter the structures: (1) Eliminating the repetitive branch structures; (2)
Excluding branch structures with complex morphology. Then for 2477 retained
structures, according to their averaged spectra, 57 structures with absorption
features are eliminated. Then following the procedure in Zhou et al. (2023a),
we fitted the averaged spectra of 2420 structures individually using the fully
automated Gaussian decomposer GAUSSPY+ (Lindner et al., 2015; Riener et al.,
2019) algorithm. The parameter settings of the decomposition are the same as
that in Zhou et al. (2023b). According to the line profiles, all averaged
spectra are divided into three categories: type1 (single velocity component,
2038), type2 (separated velocity components, 42) and type3 (blended velocity
components, 340), also refer to the Fig.6 of Zhou et al. (2023a) for the
examples of the typical line profiles. In the subsequent analysis, we discard
type2 structures because they are few (1.7%) to simplify the discussion.
Furthermore these structures are likely the product of overlapping of
unrelated gas components.

In this work, we do not classify the structures by the nomenclatures used in
astrodendro111https://dendrograms.readthedocs.io/en/stable/index.html, such as
leaf, branch or trunk, because there is always a considerable overlap of the
scales between leaf and branch structures, as described in Zhou et al.
(2023a). Moreover, in Fig.3, the scales of all structures are presented as a
continuous unimodal distribution.

###  3.3 Column density

To derive the column densities from H13CO+ (1-0) emission, we assume
conditions of local thermodynamic equilibrium (LTE) and a beam filling factor
of 1. The LTE analysis is described in detail in Appendix.A. In Shimajiri et
al. (2017), for the Aquila, Ophiuchus, and Orion B clouds, the H13CO+
abundances relative to H2, $X_{\rm H^{13}CO^{+}}\equiv N_{\rm
H^{13}CO^{+}}/N_{\rm H_{2}}$, have mean values in the range
(1.5-5.8)$\times$10-11. These abundance estimates are consistent within a
factor of a few with the findings in other regions, such as
1.1$\pm$0.1$\times$10-11 in OMC 2-FIR 4 (Shimajiri et al., 2015) and
1.8$\pm$0.4$\times$10-11 in Sagittarius A (Tsuboi et al., 2011). Peretto et
al. (2013) derived a H13CO+ abundance of $5\times 10^{-11}$ from Mopra
observations towards SDC335 using the 1D non-LTE RADEX radiative transfer code
(van der Tak et al., 2007). Here we take the mean value $X_{\rm
H^{13}CO^{+}}\sim 4.2\times 10^{-11}$ shown in Table 2 of Shimajiri et al.
(2017).

###  3.4 Velocity components

In Zhou et al. (2023a), type3 structures were discarded because of the complex
line profiles. In this work, in order to increase the sample of each type of
sources, we need to consider type3 structures. The possible reasons for the
complex profiles are : (1) the optical depth effect; (2) the overlapping of
uncorrelated gas components; (3) the complex gas kinematics inside the
structures. Generally, H13CO+ J=1-0 line emission is optically thin, thus we
do not consider the first factor. The second factor has been discussed in
detail in Zhou et al. (2022), it is not an issue in the ATOMS survey, thus our
analysis in previous work can be done based on the Moment maps. The
significant overlap for the line profile of a type3 structure may indicate the
correlation between different velocity components in the structure. The more
severe the overlap between different velocity components, the more likely they
belong to the same structure. In the extreme case, they merge into a single-
peak line profile. If the velocity differences between different velocity
components are small, these velocity components are likely to be different
parts of the same structure rather than unrelated overlapping structures, thus
the velocity decomposition is not necessary. For example, in a hub-filament
structure, the velocity of gas flow in each filament is different, leading to
different velocity components in the same structure. Considering the multi-
scale hub-filament scenario described in Zhou et al. (2022), type3 structures
may be hub-filament structures at different scales.

In the subsequent analysis, we treat type3 structures as independent
structures like type1 structures, but with more complex gas motions. We will
constantly provide evidence to justify this assumption. If different velocity
components in a type3 structure are different parts of the same structure, the
velocity dispersion of the type3 structure can be obtained by an intensity-
weighted average for the velocity dispersion of all velocity components within
this structure.

###  3.5 Statistics of the basic physical quantities

Figure 4: Physical properties of different structure types at different
evolutionary stages. The first row is the comparison between type1 and type3
structures. The second row is the comparison between early-, middle- and late-
sources. Dashed lines in panels (c) and (g) mark the positions of
$\alpha_{vir}$=2. ”p” is the p-value of Kolmogorov-Smirnov (KS) test. ”p12” ,
”p13” and ”p23” are the p-values of KS tests between the structures inside
early- and middle-sources, early- and late-sources, middle- and late-sources,
respectively. The median values also show in the legends.

Below, we discuss the differences in the physical properties of different
structure types at different evolutionary stages. For two data sets, the
magnitude comparison is based on their median values. Generally, the p-value
of their Kolmogorov-Smirnov (KS) test is far less than 0.05, if their median
values are significantly different, as shown in Fig.4.

From the first line of Fig.4, type3 structures have larger velocity
dispersion, higher column density and lower virial ratios than type1
structures at different evolutionary stages, indicating that type3 structures
mainly concentrate on the hub regions, thus have higher column density and
present multiple velocity components. In Zhou et al. (2022), from the grid
maps of H13CO (1$-$0) emission, the hub regions always show multiple velocity
components which should be attributed to the complex gas motions, not the
superposition of uncorrelated foreground or background velocity components.

From the second line of Fig.4, although late-sources have powerful Hii
regions, their inner gas structures do not have significantly larger velocity
dispersion and virial ratios, compared to that in early- and middle-sources.
In Fig.4(e), the embedded dense structures inside middle-sources even have
slightly larger velocity dispersion than those inside late-sources. These
statistical results are unusual and we need to reconsider the effects of
feedback from expanding Hii regions, see Sec.3.8 for more discussion.
Moreover, the higher column density of the embedded dense structures inside
middle-sources in Fig.4(f) keeps in line with the gravitational collapse of
hub-filament systems.

###  3.6 Scaling relations

Figure 5: Scaling relations of type1 and type3 structures. (a) $\sigma-N*R$
(b) $\sigma-N$; (c) $\sigma-R$. $\sigma$, $R$ and $N$ are the velocity
dispersion, effective radius and column density of each structure,
respectively. ’r’ represents the Pearson correlation coefficient. The values
in the legends are the exponents of the power laws. The second, third and
fourth rows are the same as the first row, but for early-, middle- and late-
sources, respectively.

The scaling relations between different quantities contain information on the
physical conditions of the structures. The scaling relations between velocity
dispersion $\sigma$, effective radius $R$ and column density $N$ shown in
Fig.5 are similar to those in Zhou et al. (2023a). $\sigma-N*R$ always has
stronger correlation compared to $\sigma-N$ and $\sigma-R$. 222For a more
convenient comparison with $\sigma-R$ and $\sigma-N$ relations, we convert the
Heyer relation $\sigma/R^{0.5}\propto N^{0.5}$ to the form
$\sigma\propto(R*N)^{0.5}$ (Eq. 3 in Ballesteros-Paredes et al., 2011), both
should have a slope of 0.5. However, the slopes of $\sigma-N*R$ relations are
$\sim$0.27, which may indicate the slowing down of pure free-fall
gravitational collapse. There are significant correlations between velocity
dispersion and column density, which may imply that the velocity dispersion
originates from the gravitational collapse, also revealed by the measured
velocity gradients in Sec.3.7. $\sigma-R$ has a poor correlation, that is, a
significant deviation from the Larson-relation (Larson, 1981).

Additionally, it is noteworthy that both type1 and type3 structures present
similar scaling relations, which further confirm that type3 structures are
independent like type1 structures. The structures generated by random overlap
should not show good scaling relations.

###  3.7 Velocity gradient

Figure 6: Velocity gradient versus the length over which the gradient has been
fitted. Blue ”+” and red ”+” represent the velocity gradients fitted in early-
sources and late-sources. The dashed lines show free-fall velocity gradients
for comparison. For the free-fall model, black and cyan lines denote masses of
50M⊙ and 500M⊙, respectively.

In Zhou et al. (2022), we used the Moment 0 maps (integrated intensity maps)
of H13CO+ J=1-0 to identify filaments in ATOMS sources, and extracted the
velocity and intensity along the filament skeletons from the Moment 1 and
Moment 0 maps. Clear velocity and density fluctuations are seen along the
filaments, allowing us to fit velocity gradients around the intensity peaks.
The filaments like the streamlines, which can trace how do gas inflows
converge to local dense structures. Local dense structures as gravitational
centers will accrete the surrounding diffuse gas and then form local hub-
filament structures. A hub-filament structure can be translated into a funnel
structure in PPV space as described in Zhou et al. (2023b). As illustrated in
Fig.9 of Zhou et al. (2023b), the gradient of the funnel profile can reflect
the strength of the gravitational field. In Zhou et al. (2022) and Zhou et al.
(2023b), the filaments will pass through multiple local hub-filament
structures presented as velocity and density fluctuations. Therefore, the
local velocity gradients along the filaments can reveal the strength of local
gravitational fields. By comparing local velocity gradients, we can assess the
differences in gravitational states of the embedded dense gas structures among
different feedback environments.

For all ATOMS sources, the identified filaments, and corresponding extracted
velocity and density along the filaments have been shown in Zhou et al.
(2022). We first estimated two overall velocity gradients between the velocity
peaks and valleys at the two sides of the center of the gravitational
potential well and ignored local velocity fluctuations. Then, we also derived
local velocity gradients around local intensity peaks of the H13CO+ emission
(see Fig. 6 in Zhou et al. 2022). In Fig.4(g), the virial ratios of the
embedded dense gas structures in late-sources and early-sources are
comparable. In Fig.6, the measured velocity gradients for the structures in
early-sources and late-sources are also comparable, once again demonstrating
that feedback rarely affects the physical properties of the embedded dense gas
structures.

###  3.8 Feedback of early-sources vs. late-sources

Table 1: Velocity dispersion produced by different physical processes in early-sources. vturb,out, vin and vrad correspond to the outflows, the inflows and the radiation pressure, respectively. early-sources | vturb,out (km s-1) | vin (km s-1) | vrad (km s-1)
---|---|---|---
G261.65-2.09 | 0.07 | 0.49 $\pm$ 0.16 | 0.28
G294.51-1.62 | 0.11 | 0.59 $\pm$ 0.19 | 0.33
G305.8-0.24 | 0.10 | 0.86 $\pm$ 0.32 | 0.6
G305.89+0.02 | 0.12 | 0.92 $\pm$ 0.33 | 0.28
G307.76+0.35 | 0.03 | 0.81 $\pm$ 0.28 | 0.17
G310.14+0.76 | 0.15 | 1.26 $\pm$ 0.47 | 0.91
G313.58+0.32 | 0.03 | 0.64 $\pm$ 0.21 | 0.33
G313.77-0.86 | 0.10 | 0.95 $\pm$ 0.34 | 0.34
G318.05+0.09 | 0.13 | 1.23 $\pm$ 0.45 | 0.61
G326.47+0.7 | 0.24 | 0.85 $\pm$ 0.3 | 0.24
G327.12+0.51 | 0.00 | 1.28 $\pm$ 0.47 | 0.78
G329.47+0.5 | 0.26 | 1.11 $\pm$ 0.42 | 0.29
G329.41-0.46 | 0.04 | 1.19 $\pm$ 0.5 | 1.19
G335.59-0.29 | 0.11 | 1.14 $\pm$ 0.42 | 0.46
G339.62-0.12 | 0.09 | 1.22 $\pm$ 0.42 | 0.41
G339.88-1.26 | 0.06 | 0.92 $\pm$ 0.33 | 1.04
G341.13-0.35 | 0.01 | 1.31 $\pm$ 0.47 | 0.33
G343.13-0.06 | 0.32 | 0.94 $\pm$ 0.35 | 0.74
G352.63-1.07 | 0.11 | 0.86 $\pm$ 0.28 | 0.35
G6.8-0.26 | 0.04 | 1.08 $\pm$ 0.39 | 0.36
G12.42+0.51 | 0.06 | 1.11 $\pm$ 0.38 | 0.42
G12.91-0.26 | 0.20 | 1.01 $\pm$ 0.4 | 0.5
G14.33-0.64 | 0.09 | 0.98 $\pm$ 0.34 | 0.31
G16.59-0.05 | 0.04 | 1.07 $\pm$ 0.4 | 0.47
G19.36-0.03 | 0.11 | 1.14 $\pm$ 0.41 | 0.22
G19.88-0.53 | 0.14 | 1.1 $\pm$ 0.41 | 0.28
G25.65+1.05 | 0.13 | 1.03 $\pm$ 0.36 | 0.37
G28.86+0.07 | 0.04 | 1.6 $\pm$ 0.65 | 0.99
G31.58+0.08 | 0.04 | 0.98 $\pm$ 0.36 | 0.51
G37.43+1.52 | 0.05 | 0.42 $\pm$ 0.15 | 0.48
median | 0.10 | 1.02 $\pm$ 0.37 | 0.39
mean | 0.10 | 1 $\pm$ 0.37 | 0.49
Table 2: Velocity dispersion produced by different physical processes in late-sources. vHII and vrad correspond to the ionized gas pressure and the radiation pressure, respectively. late-sources | vHII (km s-1) | vrad (km s-1)
---|---|---
G268.42-0.85 | 1.8 $\pm$ 0.14 | 0.61
G305.2+0.03 | 6 $\pm$ 0.5 | 1.27
G312.11+0.31 | 4.85 $\pm$ 0.43 | 1.02
G316.14-0.51 | 4.44 $\pm$ 0.36 | 1.15
G324.2+0.12 | 8.98 $\pm$ 0.71 | 1.68
G326.45+0.91 | 5.75 $\pm$ 0.54 | 1.16
G326.72+0.61 | 6.14 $\pm$ 0.52 | 0.84
G329.47+0.22 | 6.78 $\pm$ 0.44 | 0.91
G332.65-0.61 | 5.88 $\pm$ 0.42 | 1.16
G333.31-0.37 | 7.23 $\pm$ 0.61 | 1.4
G337.12-0.17 | 13.79 $\pm$ 1.12 | 2.77
G340.78-1.02 | 4.08 $\pm$ 0.26 | 1.16
G344.22-0.59 | 4.41 $\pm$ 0.35 | 0.63
G350.51+0.96 | 8.9 $\pm$ 0.65 | 1.06
G350.1+0.08 | 2.98 $\pm$ 0.21 | 1.63
G1.13-0.11 | 1.44 $\pm$ 0.15 | 1.17
G8.14+0.22 | 8.32 $\pm$ 0.67 | 1.2
G9.62+0.19 | 9.5 $\pm$ 0.64 | 1.41
G11.94-0.62 | 6.68 $\pm$ 0.52 | 0.83
G13.87+0.28 | 5.09 $\pm$ 0.38 | 1.4
G18.3-0.39 | 6.8 $\pm$ 0.48 | 0.9
G23.95+0.15 | 10.33 $\pm$ 0.71 | 1.55
G32.8+0.19 | 16.13 $\pm$ 1.35 | 1.96
median | 6.14 $\pm$ 0.5 | 1.16
mean | 6.8 $\pm$ 0.53 | 1.26

In the analysis of the kinematics in early-sources, we mainly focus on the
outflows and inflows. When investigating the gas kinematics in late-sources,
we primarily consider the ionized gas pressure. Moreover, the radiation
pressure exists in all sources at different evolutionary stages. But late-
sources must have stronger radiation pressure than early-sources, because they
embed luminous ionizing (young) stellar objects. We note that inflow is not a
feedback mechanism. However, as a line broadening mechanism, it is comparable
to other feedback mechanisms. Below, we quantitatively estimate the velocity
dispersion generated by the four physical processes, and then compare them
with the statistical results in Sec.3.5.

####  3.8.1 Outflow

We assume that the line emission of H13CO+ J=1-0 and high velocity emission of
HCO+ J=1-0 are optically thin, and the excitation temperature of H13CO+ J=1-0
and HCO+ J=1-0 lines are the same and constant in both low-velocity gas and
high-velocity outflow gas. Then according to equations (4) and (5) in Zhou et
al. (2021), the mass of the outflows can be estimated by:

$\frac{M_{\rm out}}{M_{\rm gas}}\approx\left[\frac{\rm H^{13}CO^{+}}{\rm
HCO^{+}}\right]\frac{F_{\rm out,HCO^{+}}}{F_{\rm gas,H^{13}CO^{+}}}$ (1)

The expression in bracket is the abundance ratio of the molecules, here we
take $\left[\rm H^{13}CO^{+}/\rm HCO^{+}\right]\sim 1/60$ (Milam et al.,
2005). $F_{\rm out,HCO^{+}}$ and $F_{\rm gas,H^{13}CO^{+}}$ are the
corresponding total velocity-integrated flux (the sum of all pixels on Moment
0 maps) of the outflows and the dense gas of the clump traced by HCO+ (1-0)
and H13CO+ (1-0) emission. $M_{\rm gas}$ is calculated using the column
density map derived by LTE analysis in Sec.3.6. After obtaining the value of
$M_{\rm out}$, according to the total velocity-integrated flux of the
redshifted and blueshifted lobes of the outflows $F_{\rm out,HCO^{+},r}$ and
$F_{\rm out,HCO^{+},b}$, the masses of two lobes are

$M_{\rm out,r}=\frac{F_{\rm out,HCO^{+},r}}{F_{\rm out,HCO^{+}}}\times M_{\rm
out},$ (2) $M_{\rm out,b}=\frac{F_{\rm out,HCO^{+},b}}{F_{\rm
out,HCO^{+}}}\times M_{\rm out}.$ (3)

Assuming that the momentum of the outflows completely transfers to the
surrounding dense gas (i.e. this is an upper limit), then the corresponding
turbulent velocity $v_{\rm turb,out}$ inside the dense gas caused by the
outflows can be estimated from the equation

$M_{\rm gas}v_{\rm turb,out}=M_{\rm out,r}v_{\rm r}+M_{\rm out,b}v_{\rm b}.$
(4)

According to the Moment 1 maps of the two lobes, their average velocities are
$v_{\rm r0}$ and $v_{\rm b0}$, the systematic velocity of the clump is $v_{\rm
0}$, then the velocities of the two lobes are $v_{\rm r}=v_{\rm r0}-v_{\rm 0}$
and $v_{\rm b}=v_{\rm 0}-v_{\rm b0}$.

####  3.8.2 Inflow

Figure 7: The relation between the inflow rate and the mass of the clump. Data
points are from the tables of He et al. (2015, 2016). ”r” is the Pearson
coefficient.

Assuming spherical symmetry, the clump has a mass inflow rate of

$\dot{M}\approx 4\pi r_{\rm in}^{2}\rho v_{\rm in},$ (5) $\rho=\frac{M_{\rm
c}}{4/3\pi R_{\rm c}^{3}}.$ (6)

$R_{\rm c}$ and $M_{\rm c}$ are the radius and mass of the clump, $r_{\rm in}$
and $v_{\rm in}$ are the infall radius and velocity. We note that the distance
$D$, radius $R_{\rm c}$, dust temperature $T_{\rm d}$, mass $M_{\rm c}$ and
bolometric luminosity $L_{\rm bol}$ of the clumps are taken the values listed
in the Table A1 of Liu et al. (2020). For the clumps as hub-filament systems,
they should be in the state of global gravitational collapse, thus we assume
$R_{\rm c}$=$r_{\rm in}$.

For the inflow rate $\dot{M}$ of the clump, the tables in He et al. (2015,
2016) listed mass infall rates of 231 clumps. Based on the tables, we fitted
the quantitative relation between the inflow rate and the mass of the clump,
as shown in Fig.7. Then, the infall rates of early-sources can be estimated
using this relation according to their masses. Finally, the infall velocity
can be estimated by

$v_{\rm in}=\frac{\dot{M}\times R_{\rm c}}{3M_{\rm c}}.$ (7)

####  3.8.3 Radiation pressure

Following Lopez et al. (2014), the volume-averaged radiation pressure $P_{\rm
rad}$ is

$P_{\rm rad}=\frac{3L_{\rm bol}}{4\pi R_{\rm c}^{2}c}.$ (8)

$L_{\rm bol}$ is the bolometric luminosity of the clump.

####  3.8.4 Ionized gas pressure

Following Lopez et al. (2014), the ionized gas pressure is given by the ideal
gas law, $P_{\rm HII}=(n_{\rm e}+n_{\rm H}+n_{\rm He})kT_{\rm HII}$, where
$n_{{\rm e}}$, $n_{\rm H}$, and $n_{\rm He}$ are the electron, hydrogen, and
helium number densities, respectively, and $T_{\rm HII}$ is the temperature of
the Hii gas, which is assumed to be the same for electrons and ions. If helium
is singly ionized, then $n_{{\rm e}}+n_{\rm H}+n_{\rm He}\approx 2n_{\rm e}$.
The electron temperature and density of resolved UC Hii regions identified in
the ATOMS survey have been derived from radio recombination lines H${}_{\rm
40}\alpha$ and 3 mm continuum emission in Zhang et al. (2023). The
corresponding velocities contributed by $P_{\rm rad}$ and $P_{\rm HII}$ are
estimated by $P_{\rm rad}=\rho v_{\rm rad}^{2}$ and $P_{\rm HII}=\rho v_{\rm
HII}^{2}$.

####  3.8.5 Relative importance of feedback processes

From Table.1 and Table.2, $v_{\rm HII}$ is significantly larger than other
velocities, consistent with the conclusions in Lopez et al. (2014) that the
ionized gas feedback dominates over the other considered feedback mechanisms.
In this work, we do not intend to study which feedback mechanism is the
strongest, thus we ignored some feedback mechanisms, such as dust reprocessed
radiation and stellar wind, which may also play important roles (Pabst et al.,
2019; Olivier et al., 2021; Henshaw et al., 2022). Here we note that the
estimated $v_{\rm HII}$ is obviously larger than the observed line-widths in
H13CO+ J=1-0, this is not surprising because the energy is deposited into the
ionized gas and photodissociation regions. As expected, late-sources present
significantly stronger radiation pressure than early-sources. For early-
sources, the velocity dispersion caused by the outflows is significantly
smaller than that from the infalls and the radiation pressure.

##  4 Discussion

###  4.1 Gravitational collapse under feedback

Figure 8: Schematic diagram of the scenario argued in this work. Evolution of
a cloud with multi-scale hub-filament structures with increasing effects of
feedback. Here we borrowed three pictures from Fig.1 as the background, for
demo only. Yellow lines are the filament skeletons identified in Zhou et al.
(2022). Considering the competitive accretion scenario, the precursor of the
protocluster is located in the central position of the hub. With the evolution
of the protocluster, feedback from HII regions destroys the hub by mechanical
force, i.e. the expanding HII regions push away and reshape the hub region,
accompanied by the redistribution of small-scale dense structures which may be
local hub-filament structures. We note that small-scale hub-filament
structures were not directly identified in this work due to the limitation of
the resolution.

As discussed in Sec.3.7, even under strong feedback, the embedded dense
structures in late-sources can still retain gravitational collapse. Feedback
may redistribute local dense gas structures, as illustrated in Fig.8, because
feedback does not seem to affect the internal dynamics of the embedded dense
gas structures. The results are consistent with the conclusion in Zhou et al.
(2023a): Although the feedback disrupting the molecular clouds will break up
the original cloud complex, the substructures of the original complex can be
reorganized into new gravitationally governed configurations around new
gravitational centers. This process is accompanied by structural destruction
and generation, and changes in gravitational centers, but gravitational
collapse is always ongoing.

Moreover, in Fig.6, we can find the same gas kinematic mode presented in Zhou
et al. (2023b). The variations of velocity gradients at small and large scales
($\sim$ 0.2 pc as the boundary) are consistent with gravitational free-fall
with central masses of $\sim$ 50 M⊙, $\sim$ 500 M⊙. It means that the velocity
gradients on larger scales require larger mass to maintain, larger masses
imply larger scales, that is to say, the larger scale inflow is driven by the
larger scale structure which may be the gravitational clustering of smaller
scale structures, consistent with the hierarchical/multi-scale hub-filament
structures in the clouds and the gas inflow from large to small scales. In
Zhou et al. (2023b), we studied the gas motions of the G333 molecular cloud
complex, the longest filament is $\sim$50 pc. However, the largest scale in
Fig.6 is only $\sim$1 pc. The similar gas kinematic modes may indicate the
self-similar kinematic structures on cloud-clump and clump-core scales, as
illustrated in Fig.9 of Zhou et al. (2023b).

###  4.2 The role of feedback

In Sec.3.8, the significantly larger vHII will make us naturally think that
late-sources should have the strongest feedback effects. However, that is not
the case, as shown in Sec.3.5. In Sec.3.5, overall, the velocity dispersion
and virial ratios of the structures inside early- and late-sources are
comparable. As shown in Sec.3.7, the gas structures in late-sources are also
in gravitational collapse like that in early-sources. Gravitational collapse
may also have a significant contribution to the velocity dispersion of the gas
structures in late-sources. Thus, the proportion of the velocity dispersion of
the gas structures contributed by expanding Hii regions in late-sources
decreases further. The clouds exist as gas reservoirs, which contain dense gas
structures as local gravitational centers. Feedback from Hii regions destroys
the clouds by mechanical force, i.e. the expanding Hii regions push away and
reshape the loose cloud complex, some examples can refer to McLeod et al.
(2015); Beuther et al. (2022); Bonne et al. (2023). But the processes do not
significantly affect the physical properties of the embedded dense gas
structures in the clouds, suggesting that Hii regions may not effectively
inject momentum into the embedded dense gas structures as star-forming sites.
However, the triggering does not necessarily result from momentum being
transferred inside the gas structures but by compressing them, so they become
gravitationally unstable.

Although feedback from Hii regions is very strong, it is acting from the
outside on the embedded dense gas structures. By comparison, the outflows and
inflows can go deep inside of the embedded dense gas structures, and thus,
their effect on the physical properties of the gas structures is not
necessarily weaker than feedback from Hii regions. We should not only focus on
the strength of a feedback mechanism itself, but also assess the extent to
which it can affect the embedded dense gas structures.

In Fig.4(e), the structures in middle-sources display slightly larger velocity
dispersion than that in late-sources. Notably, middle-stage sources possess
larger-scale hub-filament structures compared to their late-stage
counterparts. The complex gas kinematics in these hub regions within middle-
stage sources may contribute to the observed higher velocity dispersion.
Furthermore, early-sources also exhibit large-scale hub-filament structures,
but their gas structures present smaller velocity dispersion compared to those
in middle-sources. This suggests that feedback from UC-Hii regions in middle-
sources plays a significant role. At least, we can conclude that feedback from
protocluster-driven Hii regions may not be the most powerful factor that
affects the physical properties of local dense gas structures. It is important
to note that the above discussion treats each clump in isolation, without
considering the potential effects from the surrounding gas environment on the
physical properties of the internal structures of the clumps, due to the
limited FOV of ALMA observations. Given that the protocluster-driven Hii
regions may be still bound by the abundant surrounding gas, possible quasi-
static expanding processes also indicate the limited effect of feedback from
Hii regions on the embedded dense gas structures. As shown in Kuhn et al.
(2019), star clusters and associations that are still embedded in molecular
clouds are less likely to be expanding than those that are partially or fully
revealed.

As illustrated in Fig.8, hierarchical hub-filament structures of star-forming
regions mean that star-forming regions exist as loose gravitational complexes.
Feedback will reshape the overall structures of star-forming regions. This
process is accompanied by the redistribution of the internal structures of the
clouds, while the gravitational coupling between the internal structures is
also reorganizing them into new gravitationally governed configurations around
new gravitational centers. Generally, feedback will ultimately disperse the
clouds and the reorganization is simply a resistance to the dispersal process.
The negative effects from feedback are that feedback destroys the gas
reservoir inhabited by dense gas structures, inhibiting the further growth of
dense structures by accreting the surrounding gas, thus suppressing the
formation of massive stars. But oppositely, if feedback makes the distribution
of dense gas structures more separated, and if these dense structures are
still in a rich gas environment, the more separated distribution will improve
the material accumulation efficiency of the dense structures by weakening the
competitive accretion between them, and may eventually form more massive
stars.

##  5 Summary

A total of 64 ATOMS sources at different evolutionary stages were selected to
investigate the kinematics and dynamics of gas structures under feedback.

1\. We identified dense gas structures based on the 2D integrated intensity
(Moment 0) map of H13CO+ (1$-$0) emission, and then extracted the average
spectrum of each structure to investigate their velocity components and gas
kinematics. We discussed the differences in the physical properties of
different structure types at different evolutionary stages: (1) Type3
structures with blended velocity components (refer to the Fig.6 of Zhou et al.
(2023a)) have larger velocity dispersion, higher column density and lower
virial ratios than type1 structures with single velocity component at
different evolutionary stages, which can be attributed to type3 structures
being mainly located in hub regions. (2) Overall, the velocity dispersion and
virial ratios of the structures inside early- and late-sources are comparable.
The structures inside middle-sources even have slightly larger velocity
dispersion than that inside late-sources. These unusual results led us to
question the effectiveness of feedback from Hii regions in late-sources.

2\. $\sigma-N*R$ always has stronger correlation compared to $\sigma-N$ and
$\sigma-R$. There are significant correlations between velocity dispersion and
column density, which may imply that the velocity dispersion originates from
the gravitational collapse, also revealed by the measured velocity gradients.
Type1 and type3 structures present similar scaling relations, which further
confirms that type3 structures are independent structures, not the
superposition of uncorrelated foreground or background velocity components.

3\. Dense gas structures in late-sources are in gravitational collapse like
that in early-sources. Late-sources do not have large-scale hub-filament
structures, but the embedded dense gas structures in late-sources show similar
kinematic modes to those in early- and middle-sources. These results may be
explained by the multi-scale hub-filament structures in the clouds.

4\. The differences in gravitational states of dense gas structures in
different feedback environments were investigated by comparing local velocity
gradients. The measured velocity gradients for the structures in early-sources
and late-sources are comparable, indicating that feedback has a limited impact
on the kinematic properties of local dense gas structures. The velocity
gradients on larger scales require larger mass to maintain, larger masses
imply larger scales, that is to say, the larger scale inflow is driven by the
larger scale structure which may be the gravitational clustering of smaller
scale structures, consistent with the hierarchical/multi-scale hub-filament
structures in the clouds and the gas inflow from large to small scales.

5\. We quantitatively estimated the velocity dispersion generated by the
outflows, inflows, ionized gas pressure and radiation pressure, and found that
the ionized gas feedback is stronger than other feedback mechanisms. Late-
sources present significantly stronger radiation pressure than early-sources.
For early-sources, the velocity dispersion caused by the outflows is
significantly smaller than that from the infall and the radiation pressure.
However, although feedback from Hii regions is the strongest, it does not
significantly affect the physical properties of the embedded dense gas
structures in the clumps, suggesting that Hii regions may not effectively
inject momentum into the embedded dense gas structures as star-forming sites.

6\. This work on clump-core scales reaches the same conclusion with the study
of the G333 molecular cloud complex on cloud-clump scales in Zhou et al.
(2023a). Thus, we suggest that although feedback from cloud to core scales
will break up the original cloud complex, the substructures of the original
complex can be reorganized into new gravitationally governed configuration
around new gravitational centers. This process is accompanied by structural
destruction and generation, and changes in gravitational centers, but
gravitational collapse is always ongoing.

###### Acknowledgements.

We would like to thank the referee for the detailed and constructive comments
and suggestions that significantly improve and clarify this work. We thank J.
H. He to share the tables of their studied infall samples. This paper makes
use of the following ALMA data: ADS/JAO.ALMA$\sharp$2019.1.00685.S. ALMA is a
partnership of ESO (representing its member states), NSF (USA) and NINS
(Japan), together with NRC (Canada), MOST and ASIAA (Taiwan), and KASI
(Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA
Observatory is operated by ESO, AUI/NRAO and NAOJ. This work has been
supported by the National Key R$\&$D Program of China (No. 2022YFA1603101).
Tie Liu acknowledges the supports by National Natural Science Foundation of
China (NSFC) through grants No.12073061 and No.12122307, the international
partnership program of Chinese Academy of Sciences through grant
No.114231KYSB20200009, and Shanghai Pujiang Program 20PJ1415500. PS was
partially supported by a Grant-in-Aid for Scientific Research (KAKENHI Number
JP22H01271 and JP23H01221) of JSPS. LB gratefully acknowledges support by
ANID-BASAL project FB210003. MJ acknowledges support from the Research Council
of Finland grant 348342.

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##  Appendix A LTE analysis

Following the procedures described in Garden et al. (1991); Mangum & Shirley
(2015), for a rotational transition from upper level J + 1 to lower level J,
we can derive the total column density by

$N_{tot}=\frac{3k}{8\pi^{3}{\mu}^{2}B(J+1)}\frac{(T_{\rm
ex}+hB/3k)\exp[hBJ(J+1)/kT_{\rm ex})]}{1-\exp(-h\nu/kT_{\rm ex})}\int{\tau{\rm
dv}},$ (9) $\tau={\rm-ln}[1-\frac{T_{\rm mb}}{J(T_{\rm ex})-J(T_{\rm bg})}],$
(10)

$\int{\tau{\rm
dv}}=\frac{1}{J(T_{ex})-J(T_{bg})}\frac{\tau}{1-e^{-\tau}}\int{T_{\rm mb}{\rm
dv}}$ (11)

$J(T)=\frac{h\nu/k}{e^{h\nu/kT}-1}$ (12)

where $B=\nu/[2(J+1)]$ is the rotational constant of the molecule, $\rm\mu$ is
the permanent dipole moment, and $\rm\mu=3.89$ Debye for H13CO+. $\rm
T_{bg}=2.73$ K is the background temperature, $\int{T_{\rm mb}{\rm dv}}$
represents the integrated intensity. In the above formulas, the correction for
high optical depth was applied (Frerking et al. 1982; Goldsmith et al. 2008;
Areal et al. 2019). Assuming optically-thick emission of HCO+ (1-0) emission,
we can estimate the excitation temperature $T_{\rm ex}$ following the formula
(Garden et al. 1991; Pineda et al. 2008)

$T_{\rm ex}=\frac{4.28}{{\rm ln}[1+1/(0.23T_{\rm peak}+0.26)]},$ (13)

where Tpeak is the observed HCO+ (1-0) peak brightness temperature.

##  Appendix B The maps of all samples

Figure 9: Same as Fig.1. Figure 10: Same as Fig.1. Figure 11: Same as Fig.1.


Send correspondence to<EMAIL_ADDRESS>
# Noise and dose reduction in CT brain perfusion acquisition by projecting
time attenuation curves onto lower dimensional spaces

Vojtěch Kulvait  Institute for Medical Engineering and Research Campus
STIMULATE, University of Magdeburg, Magdeburg, Germany  Philip Hoelter
Department of Neuroradiology, University Hospital Erlangen, Friedrich-
Alexander-Universität (FAU) Erlangen-Nürnberg, Erlangen, Germany  Arnd
Doerfler  Department of Neuroradiology, University Hospital Erlangen,
Friedrich-Alexander-Universität (FAU) Erlangen-Nürnberg, Erlangen, Germany
Georg Rose  Institute for Medical Engineering and Research Campus STIMULATE,
University of Magdeburg, Magdeburg, Germany

###### Abstract

CT perfusion imaging (CTP) plays an important role in decision making for the
treatment of acute ischemic stroke with large vessel occlusion. Since the CT
perfusion scan time is approximately one minute, the patient is exposed to a
non-negligible dose of ionizing radiation. However, further dose reduction
increases the level of noise in the data and the resulting perfusion maps. We
present a method for reducing noise in perfusion data based on dimension
reduction of time attenuation curves. For dimension reduction, we use either
the fit of the first five terms of the trigonometric polynomial or the first
five terms of the SVD decomposition of the time attenuation profiles. CTP data
from four patients with large vessel occlusion and three control subjects were
studied. To compare the noise level in the perfusion maps, we use the wavelet
estimation of the noise standard deviation implemented in the scikit-image
package. We show that both methods significantly reduce noise in the data
while preserving important information about the perfusion deficits. These
methods can be used to further reduce the dose in CT perfusion protocols or in
perfusion studies using C-arm CT, which are burdened by high noise levels.

###### keywords:

CT perfusion imaging, dose reduction, noise reduction, dimension reduction,
SVD decomposition

##  1 INTRODUCTION

CT perfusion imaging (CTP) helps select population of patients with acute
ischemic stroke and large vessel occlusion within 6 to 24 hours from the
symptoms onset who are suitable for mechanical thrombectomy [1, 2]. A typical
perfusion scan takes approximately one minute and involves a significant dose
of radiation for the patient. Low dose protocols cause additional noise in the
data and resulting perfusion maps. Dimension reduction of the temporal
attenuation profiles is a tool that can reduce noise in the data, as has been
shown in the case of C-arm CT perfusion studies [3, 4]. In this paper, we
apply dimension reduction techniques to CT perfusion data to decrease noise
with applications to radiation dose reduction.

##  2 METHODS

CT perfusion data from 4 acute ischemic stroke patients and 3 control subjects
were used. Time attenuation curves (TACs) were obtained from individual CTP
acquisitions. For noise reduction we used two different dimension reduction
techniques. In the first approach, we fit the first 5 terms of the
trigonometric polynomial including the constant to the TACs. In the second
approach, we first perform an SVD decomposition of the TACs, see Fig. 1. We
then fit the 5 profiles corresponding to the highest singular values to the
data. A Gaussian blurr with $\sigma=$2\text{\,}\mathrm{px}$$ was added into
the original volume data and the reduced-dimension data sets and these data
were processed using a standard deconvolution-based perfusion processing
method [5]. Perfusion maps of CBF, CBV, MTT and TTP were generated. To compare
the noise levels in the perfusion maps, we use a wavelet-based estimator
skimage.restoration.estimate_sigma of the noise standard deviation implemented
in the scikit-image package.

Figure 1: Example SVD basis derived from the patient data. In the legend,
there is a singular value corresponding to each temporal vector.

##  3 RESULTS

Tables 1 and 2 summarize Pearson correlation coefficients when comparing data
with and without dimension reduction. Table 1 contains the correlation
coefficients for dimension reduction using trigonometric functions and table 2
contains the correlation coefficients for dimension reduction using SVD
decomposition. Figure 2 shows the differences between data processed with and
without dimension reduction on the example of a patient with large vessel
occlusion. Table 3 summarizes the estimates of the standard deviation of the
noise using the skimage.restoration.estimate_sigma function of the scikit-
image package. Paired T-test showed a significant reduction in noise level
with $p<0.01$ values for all perfusion parameters and for both dimension
reduction methods.

| Patient | Control
---|---|---
| 1A | 2A | 3A | 4A | C1 | C2 | C3
CBF | 0.96 | 0.92 | 0.96 | 0.97 | 0.96 | 0.97 | 0.99
CBV | 0.94 | 0.90 | 0.92 | 0.92 | 0.93 | 0.95 | 0.97
MTT | 0.81 | 0.78 | 0.79 | 0.78 | 0.76 | 0.73 | 0.74
TTP | 0.58 | 0.59 | 0.59 | 0.58 | 0.56 | 0.39 | 0.49
Table 1: Perarson correlation coefficients comparing data without dimension reduction with data of reduced dimension using first five terms of trigonometric polynomial. | Patient | Control
---|---|---
| 1A | 2A | 3A | 4A | C1 | C2 | C3
CBF | 0.97 | 0.97 | 0.95 | 0.95 | 0.96 | 0.98 | 0.98
CBV | 0.96 | 0.96 | 0.92 | 0.92 | 0.96 | 0.97 | 0.97
MTT | 0.82 | 0.79 | 0.73 | 0.75 | 0.75 | 0.82 | 0.74
TTP | 0.59 | 0.70 | 0.60 | 0.55 | 0.59 | 0.49 | 0.51
Table 2: Perarson correlation coefficients comparing data without dimension reduction with data of reduced dimension using first five terms of SVD decomposition. | No dimension reduction | Trigonometric functions | SVD decomposition
---|---|---|---
CBF | $0.21\pm 0.01$ | $0.12\pm 0.01$ | $0.14\pm 0.01$
CBV | $0.033\pm 0.001$ | $0.016\pm 0.001$ | $0.021\pm 0.001$
MTT | $0.19\pm 0.01$ | $0.13\pm 0.01$ | $0.10\pm 0.01$
TTP | $0.99\pm 0.07$ | $0.31\pm 0.01$ | $0.30\pm 0.01$
Table 3: Noise standard deviation estimates using the
skimage.restoration.estimate_sigma function of the scikit-image package for
data without dimension reduction and data with dimension reduction using
trigonometric functions and SVD decomposition. Figure 2: Comparison of the
original data (A) with the data of reduced dimension using trigonometric
functions (B) or SVD decomposition of temporal profiles (C).

##  4 CONCLUSIONS

Table 3 shows that both dimension reduction methods significantly reduce the
noise in the perfusion maps. Dimension reduction using trigonometric
polynomial and SVD decomposition had very comparable effects on the data used,
see tables 1, 2 and 3. The image data, see Figure 2, show that the noise
reduction using both dimension reduction methods is most significant for the
CBV map. The data suggest that SVD reduction can stabilize the TTP and MTT
maps better.

Both dimension reduction methods preserve well the essential patterns of
perfusion deficits in perfusion maps as seen, for example, in Figure 2. Our
proposed method of noise reduction in CT perfusion data can be used to further
reduce the dose in CT perfusion acquisitions. We will also investigate these
dimension reduction methods to process interventional perfusion data from
C-arm CT systems.

###### Acknowledgements.

The work of this paper is partly funded by the Federal Ministry of Education
and Research within the Research Campus STIMULATE under the number 13GW0473A.

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This work has not been submitted, published or presented elsewhere.