Context. Hub-filament systems are suggested to be the birth cradles of high-mass stars and clusters. Aims. We investigate the gas kinematics of hub-filament structures in the G333 giant molecular cloud complex using ¹³CO (3–2) observed with the APEX/LAsMA heterodyne camera. Methods. We applied the FILFINDER algorithm to the integrated intensity maps of the ¹³CO J = 3–2 line to identify filaments in the G333 complex, and we extracted the velocity and intensity along the filament skeleton from moment maps. Clear velocity and density fluctuations are seen along the filaments, allowing us to fit velocity gradients around the intensity peaks. Results. The velocity gradients we fit to the LAsMA and ALMA data agree with each other over the scales covered by ALMA observations in the ATOMS survey (<5 pc). Changes in velocity gradient with scale indicate a funnel structure of the velocity field in position-position-velocity (PPV) space. This is indicative of a smooth, continuously increasing velocity gradient from large to small scales, and thus is consistent with gravitational acceleration. The typical velocity gradient corresponding to a 1 pc scale is ~1.6 km s⁻¹ pc⁻¹. Assuming freefall, we estimate a kinematic mass within 1 pc of ~1190 M_⊙, which is consistent with typical masses of clumps in the ATLASGAL survey of massive clumps in the inner Galaxy. We find direct evidence for gravitational acceleration from a comparison of the observed accelerations to those predicted by freefall onto dense hubs with masses from millimeter continuum observations. On large scales, we find 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 hub-filament structures at different scales may be organized into a hierarchical system extending up to the largest scales probed through the coupling of gravitational centers at different scales. Conclusions. We argue that the funnel structure in PPV space can be an effective probe for the gravitational collapse motions in molecular clouds. 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.

The massive star-forming region G332.83-0.55 contains at least two levels of hub-filament structures. The hub-filament structures may form through the “gravitational focusing” process. High-resolution LAsMA and ALMA observations can directly trace the gas inflows from cloud to core scales. We investigated the effects of shear and tides from the protocluster on the surrounding local dense gas structures. Our results seem to deny the importance of shear and tides from the protocluster. However, for a gas structure, it bears the tidal interactions from all external material, not only the protocluster. To fully consider the tidal interactions, we derived the tide field according to the surface density distribution. Then, we used the average strength of the external tidal field of a structure to measure the total tidal interactions that are exerted on it. For comparison, we also adopted an original pixel-by-pixel computation to estimate the average tidal strength for each structure. Both methods give comparable results. After considering the total tidal interactions, for the scaling relation between the velocity dispersion σ, the effective radius R, and the column density N of all the structures, the slope of the σ − N _* R relation changes from 0.20 ± 0.04 to 0.52 ± 0.03, close to 0.5 of the pure free-fall gravitational collapse, and the correlation also becomes stronger. Thus, the deformation due to the external tides can effectively slow down the pure free-fall gravitational collapse of gas structures. The external tide tries to tear up the structure, but the external pressure on the structure prevents this process. The counterbalance between the external tide and external pressure hinders the free-fall gravitational collapse of the structure, which can also cause the pure free-fall gravitational collapse to be slowed down. These mechanisms can be called “tide-regulated gravitational collapse”.

Using the optimal sampling model, we synthesized the embedded clusters of ATLASGAL clumps with H ii regions (H ii-clumps). The 0.1 Myr isochrone was used to estimate the bolometric luminosity of each star in an embedded cluster, we also added the accretion luminosity of each star in the embedded cluster. The total bolometric luminosity of synthetic embedded clusters can well fit the observed bolometric luminosity of H ii-clumps. More realistically, we considered the age spread in the young star and protostar populations in embedded clusters of H ii-clumps by modeling both constant and time-varying star formation histories (SFHs). According to the age distribution of the stellar population, we distributed the appropriate isochrones to each star, and sorted out the fraction of stellar objects that are still protostars (Class 0 and Class I phases) to properly add their accretion luminosities. Compared to a constant SFH, burst-like and time-dependent SFHs can better fit the observational data. We found that as long as 20% of the stars within the embedded cluster are still accreting, the contribution of accretion luminosity will be significant to the total bolometric luminosity of low-mass H ii-clumps with mass log₁₀(M _cl/M _⊙) < 2.8. Variations in the accretion rate, the SFE and the initial mass function and more physical processes like the external heating from H ii regions and the flaring from pre-main sequence stars and protostars need to be investigated to further explain the excess luminosity of low-mass H ii-clumps.

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 the structures to investigate their velocity components and gas kinematics. For the scaling relations between the velocity dispersion, σ, the effective radius, R, and the column density, N, of all the structures, σ − N * R always has a stronger correlation compared to σ − N and σ − R. There are significant correlations between velocity dispersion and column density, which may imply that the velocity dispersion originates in 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. Combined with the conclusions in our previous work 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.

Context. Feedback from young massive stars has an important impact on the star formation potential of their parental molecular clouds. Aims. We investigate the physical properties of gas structures under feedback in the G333 complex using data of the ¹³CO J = 3–2 line observed with the LAsMA heterodyne camera on the APEX telescope. Methods. We used the Dendrogram algorithm to identify molecular gas structures based on the integrated intensity map of the ¹³CO (3–2) emission, and extracted the average spectra of all structures to investigate their velocity components and gas kinematics. Results. We derive the column density ratios between different transitions of the ¹³CO emission pixel by pixel, and find the peak values N₂₋₁/N₁₋₀ ≈ 0.5, N₃₋₂/N₁₋₀ ≈ 0.3, and N₃₋₂/N₂₋₁ ≈ 0.5. These ratios can also be roughly predicted by the nonlocal thermodynamic equilibrium (NLTE) molecular radiative transfer code RADEX for an average H₂ volume density of ~4.2 × 10³ cm⁻³. A classical virial analysis does not reflect the true physical state of the identified structures, and we find that external pressure from the ambient cloud plays an important role in confining the observed gas structures. For high-column-density structures, velocity dispersion and density show a clear correlation that is not seen for low-column-density structures, indicating the contribution of gravitational collapse to the velocity dispersion. Branch structures show a more significant correlation between 8 μm surface brightness and velocity dispersion than leaf structures, implying that feedback has a greater impact on large-scale structures. For both leaf and branch structures, σ − N * R always has a stronger correlation compared to σ − N and σ − R. The scaling relations are stronger, and have steeper slopes when considering only self-gravitating structures, which are the structures most closely associated with the Heyer relation. Conclusions. 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.

We used the dendrogram algorithm to decompose the surface density distributions of stars into hierarchical structures. These structures were tied to the multiscale structures of star clusters. A similar power-law for the mass-size relation of star clusters measured at different scales suggests a self-similar structure of star clusters. We used the minimum spanning tree method to measure the separations between clusters and gas clumps in each massive star-forming region. The separations between clusters, between clumps, and between clusters and clumps were comparable, which indicates that the evolution from clump to embedded cluster proceeds in isolation and locally, and does not affect the surrounding objects significantly. By comparing the mass functions of the ATLASGAL clumps and the identified embedded clusters, we confirm that a constant star formation efficiency of ≈0.33 can be a typical value for the ATLASGAL clumps.