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

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 H$^{13}$CO$^+$ 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. 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+2023 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.


Introduction
Stellar feedback from high-mass stars (M > 8 M ⊙ ) can strongly influence their surrounding interstellar medium and regulate star formation.The combined effects of multiple feedback mechanisms may play a major role in determining star formation efficiency and the initial mass function in molecular clouds (Dib et al. 2010;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; and (3) thermal feedback, with non-ionizing radiation as the main form.Lopez et al. (2014) assessed the role of stellar feedback at scales ∼10-100 pc toward 32 HII regions in the Large and Small Magellanic Clouds.They employed multiwavelength 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 dustprocessed radiation dominates in 84% of the samples.In simulations, massive stellar feedback, including ionizing radiation, stellar winds, and supernovae (Matzner 2002;Dale et al. 2012Dale et al. , 2014;;Rogers & Pittard 2013;Rahner et al. 2017;Smith et al. 2018;Lewis et al. 2023), can suppress 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, and found that feedback has little effect on denser and more massive clouds, which mainly destroy clouds with a lower density and mass.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), 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 ∼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 modifies 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) seven-beam receiver on the 12-meter Atacama Pathfinder Experiment submillimeter telescope (APEX; Mazumdar et al. 2021a,b).In Rugel et al. (2019), feedback from the first formed cluster in W49A is not strong enough to disperse the cloud, which likely only affects 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 works (Hartmann & Burkert 2007;Vázquez-Semadeni et al. 2009, 2019;Schneider et al. 2010;Peretto et al. 2013Peretto et al. , 2014;;Wyrowski et al. 2016;Hacar et al. 2017).In a sample of 11 massive clumps, high-resolution data reveal that protoclusters evolves to tighter by global gravitational collapse (Xu et al. 2024).In the LAsMA observation for the G333 complex under feedback, on large scales, Zhou et al. (2023Zhou et al. ( , 2024) ) 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 (see also Dib 2023).Ubiquitous density and velocity fluctuations also imply the widespread presence of local gravitational collapse (Henshaw et al. 2020).As for local dense gas structures, most of them exhibit an 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 by changes in gravitational centers, but gravitational collapse is always ongoing.The results in Zhou et al. (2022Zhou et al. ( , 2023Zhou et al. ( , 2024) ) 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).
In this work, we extend the cloud-clump analysis in Zhou et al. (2024) 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 zoomed into the dense gas structures close to or even connecting with protoclusters.The effects of feedback were 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 find that hub-filament systems are very common within massive protoclusters, and that 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.

ALMA observations
We used 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 protoclusters with the strongest CS J = 2-1 line emission (T A > 2 K) located in the inner Galactic plane of Faúndez et al. 2004).
For the data reduction, the details of the 12 m array and 7 m array ALMA observations were summarized in Liu et al. (2020Liu et al. ( , 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 was automatically determined using the ALMA pipeline.This frequency range was used to (a) subtract continuum from line emission in the visibility domain, and (b) make continuum images.Continuum images were made from multifrequency synthesis of data in the line-free frequency ranges in the two 1.875 GHz wide spectral windows, spws 7 and 8, centered on ∼99.4 GHz (or 3 mm).Visibility data from the 12 m and 7 m arrays were jointly cleaned using the task tclean in CASA 5.6.We used natural weighting and a multiscale deconvolver for an optimized sensitivity and image quality.All images were primary beam-corrected.The A173, page 2 of 15 continuum image reaches a typical 1 σ rms noise of ∼0.2 mJy with a synthesized beam FWHM size of ∼2.2 ′′ .In this work, we also used H 13 CO + J = 1-0 (86.754288GHz) and HCO + J = 1-0 (89.188526GHz) 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 H 13 CO + J = 1-0 line emission are ∼2.5 ′′ and 8 mJy beam −1 , respectively.For HCO + J = 1-0 line emission, the two values are ∼2.4 ′′ 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).

Spitzer infrared data
We also used images at 8.0 µm, 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 is about 2 ′′ .

Evolutionary stages
Generally, the infrared properties and the presence of H40 α 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 Figs. 2 and 3 of Zhou et al. (2022), for hub-filament systems, the overlaid contours of the 3 mm continuum should be located at the center of filamentary network with the strongest H 13 CO + J = 1-0 emission, where is the center of the gravitational potential well and the potential site for high-mass star formation.In the late stage of evolution, the 3 mm continuum emission is almost completely separated from H 13 CO + J = 1-0 emission, indicating that the relatively evolved HII regions have dispersed their natal gas (see also Liu et al. 2023).Thus, the separation between 3 mm continuum emission and H 13 CO + (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 at an early stage (early sources): (1) infrared dark and without H40 α emission; (2) well-defined hub-filament structures; and (3) their 3mm continuum emissions concentrate on the centers of filamentary networks with the strongest H 13 CO + (1-0) emission.
2. The sources at a middle stage (middle sources) have the same features as the early sources apart from having compact H40 α emission.
3. The sources at a late stage (late sources): (1) obvious triggering signs, such as the bent dense gas structures traced by H 13 CO + (1-0) emission; (2) their 3mm emission is extended, and all of them have strong H40 α and 8 µm emission, indicating that 3mm continuum emission is dominated 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.Powerful HII regions driven by protoclusters will destroy the hub-filament systems eventually.We can see the expansion of HII regions is tearing up the surrounding gas structures in Fig. 1c.
The number of early sources, middle sources, and late sources is 30, 11, and 23, respectively.We applied stringent criteria for the selection, and retained only sources that can be  clearly categorized in one out of the three stages.The values of the radius, distance, bolometric luminosity, mass, and dust temperature of ATOMS sources are listed in 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 Figs.2c and d, from the early stage through to the middle and late stages, L/M and T of the sources are indeed increasing gradually, confirming that our classification is reasonable.

Dendrogram structures
The issues of identifying the structures in a PPV cube by the dendrogram algorithm are described in Sects.3.1 and 3.2 of Zhou et al. (2024), and thus we adopted the same method as in Zhou et al. (2024) to identify dense gas structures.We directly identified hierarchical (sub-)structures based on the 2D integrated intensity (moment 0) map of H 13 CO + (1-0) emission, and then extracted the average spectrum of each structure to investigate its velocity components and gas kinematics.
For the moment 0 map, a 5σ threshold was set, and we therefore only required the smallest area of the structure to be larger than 0.5 beam and did not set other parameters to reduce the dependence of the identification on the algorithm parameters.In Fig. 1, the structures identified by the dendrogram correspond well to the integrated intensity maps.
The algorithm approximates the morphology of each structure as an ellipse.In the 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. (2024), a and b will give a smaller ellipse compared to the size of the identified structure, and thus multiplying by a factor of two to enlarge the ellipse is necessary.Then the effective physical radius of an ellipse is where D is the distance of the source.
As discussed in Zhou et al. (2024), two screening criteria were used to filter the structures: (1) eliminating the repetitive branch structures; and (2) excluding branch structures with complex morphology.Then for 2477 retained structures, according to their averaged spectra, 57 structures with absorption features were eliminated.Then, following the procedure in Zhou et al. (2024), 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 were the same as that in Zhou et al. (2023).According to the line profiles, all the averaged spectra were divided into three categories: type1 (single velocity component, 2038), type2 (separated velocity components, 42), and type3 (blended velocity components, 340).We also refer to Fig. 6 of Zhou et al. (2024) for examples of typical line profiles.In the subsequent analysis, we discarded type2 structures because there are too few of them (1.7%) to simplify the discussion.Furthermore, these structures are likely the product of the overlapping of unrelated gas components.
In this work, we do not classify the structures by the nomenclatures used in astrodendro1 , such as leaf, branch, or trunk, because there is always a considerable overlap in the scales between leaf and branch structures, as described in Zhou et al. (2024).Moreover, in Fig. 3, the scales of all structures are presented as a continuous unimodal distribution.

Column density
To derive the column densities from H 13 CO + (1-0) emission, we assumed conditions of local thermodynamic equilibrium (LTE) and a beam filling factor of one.The LTE analysis is described in detail in Appendix A. In Shimajiri et al. (2017), for the Aquila, Ophiuchus, and Orion B clouds, the H 13 CO + abundances relative to H 2 , X H 13 CO + ≡ N H 13 CO + /N H 2 , have mean values in the range (1.5-5.8)× 10 −11 .These abundance estimates are consistent within a factor of a few with the findings in other regions, Here, we take the mean value X H 13 CO + ∼ 4.2 × 10 −11 shown in Table 2 of Shimajiri et al. (2017).

Velocity components
In Zhou et al. (2024), type3 structures were discarded because of the complex line profiles.In this work, to increase the samples of each source, we needed to consider type3 structures.Possible reasons for the complex profiles were: (1) the optical depth effect; (2) the overlapping of uncorrelated gas components; and (3) the complex gas kinematics inside the structures.Generally, H 13 CO + J = 1-0 line emission is optically thin, and thus we did not consider the first factor.The second factor has been discussed in detail in Zhou et al. (2022) and is not an issue in the ATOMS survey, and thus our analysis in the 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, and 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 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 of the velocity dispersion of all velocity components within this structure.

Statistics of the basic physical quantities
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 a larger velocity dispersion, higher column density, and lower virial ratios than type1 structures at different evolutionary stages, indicating that type3 structures are mainly concentrated in the hub regions, and thus have a higher column density and present multiple velocity components.In Zhou et al. (2022), from the grid maps of H 13 CO (1−0) emission, the hub regions always show multiple velocity components that 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 a significantly larger velocity dispersion and virial ratios, compared to that in early and middle sources.In Fig. 4e, the embedded dense structures inside middle sources even have a slightly larger velocity dispersion than those inside late sources.These statistical results are unusual.We need to reconsider the effects of feedback from expanding HII regions (see Sect. 3.8 for more discussion.)Moreover, the higher column density of the embedded dense structures inside middle sources in Fig. 4f is in line with the gravitational collapse of hub-filament systems.

Scaling relations
The scaling relations between different quantities contain information on the physical conditions of the structures.The scaling relations between the velocity dispersion, σ, effective radius, R, and column density, N, shown in Fig. 5 are similar to those in Zhou et al. (2024).σ − N * R always has a stronger correlation compared to σ − N and σ − R2 .However, the slopes of σ − N * R relations are ∼0.27,which may indicate the slowing down of a 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, something which is also revealed by the measured velocity gradients in Sect.3.7.σ − 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 confirms that type3 structures are independent like type1 structures.The structures generated by random overlap should not show good scaling relations.

Velocity gradient
In Zhou et al. (2022), we used the moment 0 maps (integrated intensity maps) of H 13 CO + 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 gas inflows converge to local dense structures.Local dense structures as gravitational centers will accrete the surrounding  diffuse gases and then form local hub-filament structures.A hub-filament structure can be translated into a funnel structure in the PPV space, as described in Zhou et al. (2023).As illustrated in Fig. 9 of Zhou et al. (2023), the gradient of the funnel profile can reflect the strength of the gravitational field.In Zhou et al. (2022Zhou et al. ( , 2023)), 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.Then, by comparing local velocity gradients, we can assess the differences in the 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 the local velocity fluctuation, then we also derived local velocity gradients around local intensity peaks of the H 13 CO + emission (see Fig. 6 in Zhou et al. 2022).In Fig. 4g, the virial ratios of the embedded dense gas structures in late and early sources are comparable.In Fig. 6, the measured velocity gradients of the structures in early and late sources are also comparable, once again demonstrating that feedback rarely affects the physical properties of the embedded dense gas structures.

Feedback of early sources versus late ones
In an analysis of the kinematics in early sources, we mainly focused on the outflows and inflows.When investigating the gas kinematics in late sources, we primarily considered 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; but 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 Sect.3.5.

Outflow
We assumed that the line emission of H 13 CO + J = 1-0 and high velocity emission of HCO + J = 1-0 are optically thin, and that the excitation temperatures of the H 13 CO + J = 1-0 and HCO + J = 1-0 lines are the same and constant in both lowand high-velocity outflow gas.Then, according to Eqs. ( 4) and (5) in Zhou et al. (2021), the mass of the outflows can be estimated by The expression in brackets is the abundance ratio of the molecules.Here, we took H 13 CO + /HCO + ∼ 1/60 (Milam et al. 2005).F out,HCO + and F gas,H 13 CO + are the corresponding total velocity-integrated fluxes (the sum of all pixels in the moment 0 maps) of the outflows and dense gases of the clump traced by the HCO + (1-0) and H 13 CO + (1-0) emission.M gas was calculated using the column density map derived by LTE analysis in Sect.3.6.After obtaining the value of M out , according to the total velocity-integrated flux of the redshifted and blueshifted lobes of the outflows F out,HCO + ,r and F out,HCO + ,b , the masses of the two lobes were A173, page 6 of 15  (3) Assuming that the momentum of the outflows completely transfers to the surrounding dense gas (i.e., the upper limit), then the corresponding turbulent velocity, v turb,out , inside the dense gas caused by the outflows can be estimated from the equation According to the moment 1 maps of the two lobes, their average velocities are v r0 and v b0 , the systematic velocity of the clump is v 0 , and then the velocities of the two lobes are v r = v r0 − v 0 and v b = v 0 − v b0 .

Inflow
Assuming spherical symmetry, the clump has a mass inflow rate of with R c and M c are the radius and mass of the clump, respectively.r in and v in are the infall radius and velocity.We note that the distance, D, radius, R c , dust temperature, T d , mass, M c , and bolometric luminosity, L bol , of the clumps were taken as the values listed in Table A.1 of Liu et al. (2020).For clumps to be hubfilament systems, they should be in a state of global gravitational collapse, and thus we assumed that R c = r in .
A173, page 7 of 15 For the inflow rate, Ṁ, of the clump, the tables in He et al. (2015He et al. ( , 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 could be estimated using this relation according to their masses.Finally, the infall velocity could be estimated by

Radiation pressure
Following Lopez et al. (2014), the volume-averaged radiation pressure, P rad , is L bol is the bolometric luminosity of the clump.

Ionized gas pressure
Following Lopez et al. (2014), the ionized gas pressure is given by the ideal gas law, P HII = (n e + n H + n He )kT HII , where n e , n H , and n He are the electron, hydrogen, and helium number densities, respectively, and T HII is the temperature of the HII gas, which was assumed to be the same for electrons and ions.If helium is singly ionized, then n e + n H + n He ≈ 2n e .The electron temperature and density of resolved UC HII regions identified in the ATOMS survey were derived from radio recombination lines, H 40 α, and 3 mm continuum emission in Zhang et al. (2023).The corresponding velocities contributed by P rad and P HII were estimated by P rad = ρv 2 rad and P HII = ρv 2 HII .

Relative importance of feedback processes
In Tables 1 and 2, v HII is significantly larger than other velocities, consistent with the conclusions in Lopez et al. (2014) that Notes.v turb,out , v in , and v rad correspond to the outflows, the inflows, and the radiation pressure, respectively.
the ionized gas feedback dominates over the other considered feedback mechanisms.In this work, we did not intend to study which feedback mechanism is the strongest, and 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 HII is obviously larger than the observed line widths in H 13 CO + 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.

Gravitational collapse under feedback
As discussed in Sect.3.7, even under strong feedback, the embedded dense structures in late sources can still retain A173, page 8 of 15  et al. (2024): 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 by 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. (2023).The variations in the velocity gradients at small and large scales (∼0.2 pc as the boundary) are consistent with gravitational free-fall, with central masses of ∼50 M ⊙ and ∼500 M ⊙ .It means that the velocity gradients on larger scales require larger masses to be maintained, and 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 or multi-scale hub-filament structures in the clouds and the gas inflow from large to small scales.In Zhou et al. (2023), we studied the gas motions of the G333 molecular cloud complex.The longest filament is ∼50 pc; however, the largest scale in Fig. 6 is only ∼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. (2023).

The role of feedback
In Sect.3.8, the significantly larger v HII will naturally make us think that late sources should have the strongest feedback effects.However, that is not the case, as shown in Sect.3.5.In Sect.3.5, overall, the velocity dispersion and virial ratios of the structures inside early and late sources are comparable.As shown in Sect.3.7, the gas structures in late sources are also in gravitational collapse like those in early sources.Gravitational collapse may also contribute significantly 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 that contain dense gas structures as local gravitational centers.Feedback from HII regions destroys the clouds by mechanical force; in other words, the expanding HII regions push away and reshape the loose cloud complex (see e.g., 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 the gas structures being compressed, and so becoming gravitationally unstable.
Although the 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 the effect of them on the physical properties of the gas structures is not necessarily weaker than the 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. 4e, the structures in middle sources display a slightly larger velocity dispersion than those in late sources.Notably, middle-stage sources possess larger-scale hub-filament structures than their late-stage counterparts.The complex gas kinematics in these hub regions within middle-stage sources may contribute to the higher velocity dispersion observed.Furthermore, early sources also exhibit large-scale hub-filament structures, but their gas structures present a 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 affecting 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 of 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 still be 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 A173, page 9 of 15  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 that 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.
by the redistribution of the internal structures of the clouds, while the gravitational coupling between the internal structures also reorganizes them into new gravitationally governed configurations around new gravitational centers.Generally, feedback will disperse the clouds.Finally, to some extent, the reorganization is a resistance to the dispersing process, although the resistance will in the end fail.The negative effects of the feedback are that it destroys the gas reservoir inhabited by dense gas structures, inhibiting the further growth of dense structures by accreting the surrounding gas, and thus suppressing the formation of massive stars.On the other hand, if feedback makes the dense gas structures more spread out, and if these dense structures are still in a gas-rich environment, the looser 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.

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 directly identified dense gas structures based on the 2D integrated intensity (moment 0) map of H 13 CO + (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 (see Fig. 6 of Zhou et al. 2024) have a larger velocity dispersion, higher column density, and lower virial ratios than type1 structures with a 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 a slightly larger velocity dispersion than those inside late sources.These unusual results led us to question the effectiveness of feedback from HII regions in late sources.
2. σ − N * R always has a stronger correlation than σ − N and σ − R.There are significant correlations between velocity dispersion and column density, which may imply that the velocity dispersion originates in the gravitational collapse, something 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 those 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 the gravitational states of dense gas structures in different feedback environments were investigated by comparing local velocity gradients.The measured velocity gradients of the structures in early 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 a larger mass to be maintained, and larger masses imply larger scales; that is to say, the largerscale inflow is driven by the larger-scale structure, which may be the gravitational clustering of smaller-scale structures, consistent with the hierarchical or 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 infalls 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 as the study of the G333 molecular cloud complex on cloud-clump scales in Zhou et al. (2024), and thus we suggest that although feedback from cloud to core scales will A173, page 10 of 15 break up the original cloud complex, the substructures of the original complex can be reorganized into a new gravitationally governed configuration around new gravitational centers.This process is accompanied by structural destruction and generation, and by changes in gravitational centers, but gravitational collapse is always ongoing.

Fig. 1 .
Fig. 1.Moment 0 maps of H 13 CO + J = 1-0 for three ATOMS sources at three evolutionary stages.Yellow contours show 3 mm continuum emission with its minimum contour level of 5σ.Orange eclipses represent the retained Dendrogram structures.The maps of all 64 ATOMS sources studied in this work are presented in Appendix B.

Fig. 2 .
Fig. 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.

Fig. 4 .
Fig. 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.The dashed lines in panels c and g mark the positions of α vir = 2. "p" is the p value of the 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, and middle and late sources, respectively.The median values also show in the legends.

Fig. 5 .
Fig. 5. Scaling relations of type1 and type3 structures.(a) σ − N * R, (b) σ − N, and (c) σ − R. σ, 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.

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

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

Fig. 8 .
Fig. 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 demonstration only.The 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 that 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.

Table 1 .
Velocity dispersion produced by different physical processes in early sources.Early-sources v turb,out (km s −1 ) v in (km s −1 ) v rad (km s −1 )

Table 2 .
Velocity dispersion produced by different physical processes in late sources.Notes.vHIIand v rad correspond to the ionized gas pressure and the radiation pressure, respectively.gravitationalcollapse.Feedback may redistribute local dense gas structures, as illustrated in Fig.becausefeedback does not seem to affect the internal dynamics of the embedded dense gas structures.The results are consistent with the conclusion in Zhou