© The Authors 2023

1 Introduction

Recent observations have shown that filaments are ubiquitous in molecular clouds (Molinari et al. 2010a; Li et al. 2016; Mattern et al. 2018; Schisano et al. 2020). Most dense clumps and cores are formed in filaments and they may play a key role in the star formation process (André et al. 2013). The filaments in molecular clouds may overlap to form a web, creating junctions of filaments and the hub-filament systems (Myers 2009). In a scenario of global hierarchical collapse of molecular clouds dominated by gravity, these filaments constitute channels for gas funneled from the extended cloud to the dense clumps (Gómez & Vázquez-Semadeni 2014; Vázquez-Semadeni et al. 2019). The clumps at the junction will accrete more materials from the surroundings and they become more massive and more likely to form high-mass star clusters. Compared to isotropic accretion, the accretion flow along the filament is a more efficient mechanism because it takes a longer time to gather mass for the high-mass star forming cores before channels are destroyed (Myers 2009). Several hub-filament systems show evidences of channeling gas feeding to the junctions with ongoing high-mass star formation (Kirk et al. 2013; Peretto et al. 2013, 2014; Yuan et al. 2018)

For clouds in gravitational collapse, the gas flows will be accelerated towards the center of the potential well because of gravitational attraction (Gómez & Vázquez-Semadeni 2014). It is expected to produce a characteristic V-shape on the gas velocity structure, which traces the accelerated gas motion around the central high mass clumps or cores. Such a feature has been detected within OMC-1 cloud (Hacar et al. 2017).

The molecular clouds in the region (323° < l < 324°, |b| < 0.5°) have been studied by Burton et al. (2013) as a sample of the Mopra Southern Galactic Plane CO Survey. Several select sub-regions have been identified and labeled A through F. Their physical parameters were derived but without studying the clouds’ structure and kinematics. However, the high angular resolution ¹³CO (J = 2−1) data from the Structure, Excitation and Dynamics of the Inner Galactic Interstellar Medium (SEDIGISM, Schuller et al. (2021)) survey reveals that molecular clouds in the region have very interesting structures and kinematics. Using this new ¹³CO (J = 2−1) survey data, we found that molecular cloud complex in sub-region F is a good cloud-cloud collision candidate (Ma et al. 2022). We also noted that molecular clouds in the sub-region A may make up a hubfilament system (G323.46-0.08), showing evidence of accretion flow in filaments and gravitationally collapse in the junction region. This provides a good target for studying of the role of filaments in the evolution of the molecular cloud and ongoing star formation. Burton et al. (2013) estimated a kinematic distance of 4.8 kpc, and a column density ($N_{{\text{H}}_2}$) of 8 × 10²¹ cm⁻² for sub-region A.

In this paper, we present a detailed study of the hub-filament system G323.46-0.08. We describe the data in Sect. 2 and present the physical parameters and kinematics of the G323.46-0.08 in Sect. 3. Section 4 discusses the evidences of convergence, accelerations, and young stellar objects (YSOs). Finally, Sect. 5 presents the conclusions of this work.

Fig. 1 Infrared and molecular spectrum line emissions of G323.46-0.08. Left: three-color map of the G323.46-0.08 region. Red, green, and blue backgrounds show the 24, 8, and 4.5 µm emission, respectively. The white contours denote the 13CO (J = 2−1) emission integrated velocity from −70 to −63 km s−1, which starts from 3 K km s−1 and with a step of 9 K km s−12. The cyan crosses and triangles are Class I and II YSOs, respectively. The red circles mark the Hπ regions identified by Anderson et al. (2014). The red cross is the central high mass clump AGAL323.459-0.079 in hub-filament system G323.46-0.08. Right: velocity map of G323.46-0.08. The color background is the velocity field of 13CO (J = 2−1). The black contours are the integrated intensity of the 13CO (J = 2−1) emission (same as in the left panel). The red contour marks the 13CO (J = 2−1) emission in the region of F-north integrated velocity from −70 to −68.25 km s−1. The red dotted line and the white interrupted dashed line represent the ridgeline of F-north, F-west, and F-south. All ridge lines are formed by connecting the peak intensity points of 13CO (J = 2−1) in the filament). The white circle denotes the high velocity component appears in F-south part 2.

2 Archival data

2.1 The ¹³CO (J = 2−1) emission data

The ¹³CO (J = 2−1) data from the SEDIGISM survey¹ has been obtained the Atacama Pathfinder Experiment (APEX) and has been used for kinematic analysis (Schuller et al. 2021). This survey mapped 84 deg² of the Galactic plane (−60° < l < 31°, |b| < 0.5°) in several molecular transitions. The angular resolution of SEDIGISM is ~30″, and the 1σ sensitivity is about 0.8–1.0 K for a 0.25 km s⁻¹ channel width.

2.2 The infrared data

Mid-infrared emission data at 3.6, 4.5, 5.8, and 8 µm have been obtained from the Galactic Legacy Infrared Mid-Plane Survey Extraordinaire (GLIMPSE) (Benjamin et al. 2003). The 5σ sensitivities at the four bands are 0.2, 0.2, 0.4, and 0.4 mJy, respectively. The corresponding angular resolutions are between 1.5″ and 1.9″ (Fazio et al. 2004). We also used 24 and 70 µm image data from the Multiband Infrared Photometer of the Spitzer MIPS Galactic Plane Survey (MIPSGAL) (Carey et al. 2009). The 5σ sensitivity is 1.7 mJy, and the corresponding resolutions are 6″ and 18″, respectively (Rieke et al. 2004).

The Herschel Infrared Galactic Plane Survey (Hi-GAL) data has been used to derive the dust temperature and column density distribution (Molinari et al. 2010b). The angular resolutions of these Herschel maps are approximately 10.2″, 13.5″, 18.1″, 25.0″, and 36.4″ at 70, 160, 250, 350, and 500 µm, respectively.

2.3 Source catalogs

The APEX Telescope Large Area Survey of the Galaxy (ATLASGAL) dense clump catalog (Urquhart et al. 2018) and the Herschel Hi-GAL clump catalog (Elia et al. 2017) were used to trace dense clumps and the embedded pre-stellar and proto-stellar cores. The GLIMPSE Point-Source catalog (GPSC), MIPSGAL (Gutermuth & Heyer 2015) and 2MASS catalog (Skrutskie et al. 2006) are used to trace the population of Class I and II YSOs.

3 Results

3.1 Hub-filament system G323.46-0.08

Figure 1 displays the region of study centering on the high mass clump AGAL323.459-0.079 (the red cross in figure is at l = 323.459°, b = −0.079°) (Urquhart et al. 2018). The left panel presents observational results of the region at different wavelengths, where red, green, and blue background trace the 24, 8, and 4.5 µm emission, and red circles denote the HII regions identified by Anderson et al. (2014). Strong 8 µm emission is associated with the HII region. Class I (cyan crosses) and Class II (cyan triangles) YSOs are usually associated with the molecular cloud traced by integrated ¹³CO (J = 2−1) emission. The method of classification of young stars is the same as that of Gutermuth et al. (2009) and Zhou et al. (2020).

The integrated ¹³CO (J = 2−1) emission displayed by white contours in the left panel of Fig. 1 shows that there are three filamentary structures in the region, namely, F-NE, F-west, and F-south, all connecting to a single junction point. They stand out more clearly in the corresponding velocity field map in the right panel. It should be noted that we derived the velocity field with the Gaussian fitting results of ¹³CO (J = 2−1) spectra for each pixel in this work. F-west shows a velocity gradient from its eastern end to the junction region. F-NE shows obvious velocity variation from the top side to the bottom side. and F-south is made of three segments, part 1, 2, and 3. We can see clear velocity gradients in parts 1, 2, and 3, although the gradient in F-south part 3 is relatively weak.

We noted that HII region 2 appears between F-south part 1 and 2, and HII region 3 appears in the northern side of F-south part 2. The northern edge of HII region 6 overlaps with F-south part 2, and the distribution of high-velocity components well agrees with this northern edge (Fig. 1). These high-velocity components may be part of the expanding shell of HII region 6. The channel maps in Fig. A.1 shows that the molecular cloud associated with HII region 6 has a velocity range from −65.5 to −63 km s⁻¹, while F-south mainly appears in the velocity range from −68 to −66 km s⁻¹. It appears that F-south does not interact with the HII region 6 and they happen to coincide along the line of sight.

The fourth filamentary structure F-north with a velocity range of −70 to −68.25 km s⁻¹ appears in velocity map in Fig. 1 and seems to overlap with F-NE. The channel map in Fig. A.1 further confirms that this is a separate filamentary structure that seems to be associated with the central high mass clump AGAL323.459-0.079 (Fig. 1). No obvious velocity gradient is detected in F-north, possibly because F-north is perpendicular to the line of sight.

In conclusion, F-north, F-west and F-south seem to converge toward the central high-mass clump AGAL323.459-0.079 at the junction, thus constituting the hub-filament system G323.46-0.08. The source AGAL323.459-0.079, which was well traced by ¹³CO (J = 2−1) emission, is located at the center of this junction. Though another small dense clump HIGALBM323.4681-0.1011 (white cross in the right panel of Fig.1) from the catalogue of Elia et al. (2017) is located south of the junction, it is not obvious in the ¹³CO (J = 2−1) map. The AGAL323.459-0.079 is the main star-forming region that is fed by the filaments and we refer to it as the “main SF” hereafter.

The systemic velocity of the hub junction is −67 km s⁻¹ as obtained from the averaged ¹³CO (J = 2−1) spectrum, which suggests the estimated kinematic distance of the hub-filament system G323.46-0.08 to be 3.83 ± 0.75 kpc using the kinematic distance estimator² developed by Reid et al. (2019). This new distance is smaller than that obtained by Burton et al. (2013). Because the latest distance estimator is based on the much improved rotation curve of the Galaxy, we use the newer distance of G323.46-0.08 in this work.

F-NE shows a clear velocity variation from its top side to its bottom side (Fig. 1). This region is the subject for a detailed study in a forthcoming paper. This paper will focus on the hub-filament system G323.46-0.08, namely, the region within the circled area in the right panel of Fig. 1.

3.2 Physical parameters

Based on a modified blackbody model (Kauffmann et al. 2008), we made a spectral energy distribution (SED) fitting using the Herschel data. First, using the method of constrained-diffusion-decomposition (Li 2022), we removed the background emission from the image data at different bands separately. Then we performed a spectral energy distribution fitting with the PYTHON package HIGAL-sed-fitter³. The code convolve all images at 70, 160, 250, and 350 µm to the angular resolution 36.4″ at 500 µm and regrid five bands images to the same pixel size 11.5″. Finally, the SED fitting is completed based on a modified blackbody model, $$I_v=B_v\left(1-e^{-{\tau }_v}\right),$$(1)

where the Planck function B_ν is modified by the optical depth (Kauffmann et al. 2008), $${\tau }_v={\text{μ}}_{{\text{H}}_2}{m}_{\text{H}}{K}_v{N}_{{\text{H}}_2}/R_{\text{gd}},$$(2)

where ${\text{μ}}_{{\text{H}}_2}=2.8$ is the mean molecular weight, m_H is the mass of a hydrogen atom, the gas to-dust ratio R_gd = 100, and $N_{{\text{H}}_2}$ is the H₂ column density. The dust opacity (Ossenkopf & Henning 1994) is $$K_v=4.0{\left(v/505\text{\hspace{0.17em}GHz}\right)}^{\beta }{\text{cm}}^2{\text{g}}^{-1},$$(3)

and the dust emissivity index β was fixed to 1.75 in the fitting (Wang et al. 2015).

The derived dust temperature and H₂ column density ($N_{{\text{H}}_2}$) distributions of G323.46-0.08 are shown in Fig. 2. The dust temperature varies from 18 to 32 K, and it is usually very low in filaments except for the regions where HII regions appear. The column density $N_{{\text{H}}_2}$ varies from 4 × 10²¹ to 3.7 × 10²² cm⁻². The total gas masses of filaments are calculated using the equation $$M_{{\text{H}}_2}=\text{μ}{m}_{\text{H}}{\displaystyle \sum _{\text{i}}{S}_{\text{i}}N{\left({\text{H}}_2\right)}_{\text{i}}},$$(4)

where S_i is one pixel’s area, and N(H₂)_i is obtained from SED fitting. We get gas mass of F-north, F-west, F-south, and Hub junction is 1616’ 2053’ 3682, and 3072 M_⊙, respectively. Table. 1 lists the correlated parameters of sub filaments. Because F-north overlaps with F-NE, we cannot separate it from F-NE clearly and its true mass should be less than the value listed in Table1.

A total of 35 clumps from the Herschel Hi-GAL clump catalog (Elia et al. 2017) and 3 clumps from the ATLASGAL dense clump catalog (Urquhart et al. 2018) are located in the hub filament G323.46-0.08 (see left panel of Fig. 2). These clumps represent sites of ongoing star formation and contain pre-stellar and proto-stellar cores. The sources HIGALBM323.4594-0.0789 and AGAL323.459-00.079, as well as HIGALBM323.4927-0.1781 and AGAL323.494-00.179, and HIGALBM323.5076+0.0455 and AGAL323.506+00.046 are identical sources. All 35 clumps and their parameters were recalculated using the new distance are listed in Table B.1. The mass of the central high-mass clump AGAL323.459-0.079 (main SF) from Elia et al. (2017) is much lower than the result from Urquhart et al. (2018), because the former used a smaller radius (see Table B.1). We recalculated the mass with the same radius of Urquhart et al. (2018) and obtained a mass of 1100 M_⊙, which is comparable to 1170 M_⊙ obtained by Urquhart et al. (2018).

Fig.2 H2 column density (left) and dust temperature (right) distributions within the G323.46-0.08. The black contours indicate the 13CO (J = 2−1) integrated intensity in areas, where Tmb is higher than 3σ (3 K), The contour levels start from 3 K km s−1 and with a step of 9 K km s−1. The velocity interval of the integration is from −70 to −63 km s−1. The white, rose, and black diamonds are Herschel clumps, and represent different evolution stages of starless cores, prestellar, and protostellar, respectively (Elia et al. 2017). The white crosses are ATLASGAL 870 µm clumps (Urquhart et al. 2018). The red circles show the HII regions identified by Anderson et al. (2014).

3.3 The velocity dispersion

Figure 3 displays the distribution of the ¹³CO (J = 2−1) velocity dispersion of the region. The main SF has the largest velocity dispersion of 3.2 km s⁻¹, which may be attributed to ongoing star formation activity but also to a possible outflow in the source (Yang et al. 2022). The source F-west has a very small and uniform velocity dispersion, even at the regions where HII regions 1 and 4 appear. On the other hand, F-south also has a similar small velocity dispersion, but it is large in the HII regions 2, 3, and 6. The source F-north has a relative large velocity dispersion at its eastern edge, which may be attributed to the gas mixing of F-north and F-NE or interaction between them.

The contributions of thermal and non-thermal motions to the velocity dispersion may be determined following Myers & Benson (1983) and Tang et al. (2017, 2018a,b, 2021): $${\sigma }_{\text{NT}}^2={\sigma }_{\text{obs}}^2-{\sigma }_{\text{T}}^2,$$(5)

and $${\sigma }_{\text{NT}}=\sqrt{\frac{\text{Δ}{\upsilon }_{\text{obs}}^2}{8\ln 2}-\frac{k_B{T}_{\text{kin}}}{m_{\text{obs}}}},$$(6)

where σ_NT, σ_obs, and σ_T are the non-thermal, observed, and thermal velocity dispersions, respectively. In addition, ∆ υ_obs represents the observed full width at half maximum (FWHM) line width of ¹³CO (J = 2−1), k_B is the Boltzmann constant, T_kin is the kinematic temperature of the gas, and m_obs is the mass of the observed molecule for ¹³CO (J = 2−1). Assuming the kinematic temperature of gas is equal to the dust temperature (Fig. 2), the average thermal dispersion is about 0.076, 0.079, and 0.083 km s⁻¹ for F-north, F-west, and F-south, respectively. The corresponding non-thermal velocity dispersion are about 0.46 (F-north), 0.25 (F-west) and 0.53 km s⁻¹ (F-south), which are greater than the thermal dispersion. Therefore, the velocity dispersion of these filaments is dominated by non-thermal motions.

Fig. 3 Moment 2 map of G323.46-0.08. The colour backgrounds represents the velocity dispersion of 13CO (J = 2−1). The white contours denote the 13CO (J = 2−1) emission integrated velocity from −70 to −63 km s−1, which starts from a 3σ level of 3 K km s−1 and with a step of 11.5 K km s−1.

Fig. 4 13CO (J = 2−1) line velocity along F-north. The x-axis is taken along the red dotted line in the right panel of Fig. 1, with the zero position starting from its intersection at the junction.

4 Discussion

4.1 Global velocity gradient

To clearly show the kinematics along the filament and the relation between F-north, F-west, F-south, and the main SF, two position-velocity diagrams have been created using the V_LSR at all pixels with S/N > 5 in ¹³CO (J = 2−1) emission as a function of their corresponding offset along the filaments (Figs. 4 and 5). For F-north in Fig. 4, the x-axis is taken along the red dotted line in the right panel of Fig. 1, with the zero position starting from its intersection at the junction. For F-south and F-west in Fig. 5, the x-axis starts at the end of F-south part 2 and along the white interrupted dashed line across the main SF to the end of F-west. These lines are determined by connecting the peak intensity points of ¹³CO (J = 2−1) along the filaments. In Fig. 5, F-west shows a continuous velocity gradient from its end to the main SF. By least-squares fitting, we obtained a large scale velocity gradient of 0.28 ± 0.06 km s⁻¹ pc⁻¹ along F-west.

The velocity variation along F-south is more complex. F-south part 1 as a whole shows a velocity gradient approaching the junction region, while F-south part 2 shows an opposite velocity variation that may result from different projection angles. The northern part of the HII region 6 seems to overlap with F-south part 2 along the line of sight, but these components cannot be separated clearly. The high-velocity components in the red circle marked as HVC in the bottom panel of Fig. 5 appear as an arc structure and may include part of HII region 6’s expanding shell (also see Fig. 1).

The velocity gradient along F-south part 1 is 0.44 ± 0.1 km s⁻¹ pc⁻¹, which obtained by least-squares fitting. The velocity gradients detected in F-west and F-south part 1 are comparable to those detected in other hub-filament systems, for instance, 0.8 ± 0.1 km s⁻¹ pc⁻¹ in the DR 21 South Filament (Hu et al. 2021) and 0.15−0.6 km s⁻¹ pc⁻¹ in SDC13 (Peretto et al. 2014). Above results suggest that F-west and F-south may be channeling materials into the main SF at the junction region. Furthermore, a characteristic V-shaped structure (see hub junction in Fig. 5) appears around the main SF. This feature is in good agreement with the simulation results of Kuznetsova et al. (2018) and Gómez & Vázquez-Semadeni (2014), and is similar to what is detected in Orion by Hacar et al. (2017). The V-shaped structure indicates that accelerated collapse is taking place around the main SF.

The velocity gradients of the two sides of the V-shaped structure are 1.85 and 2.2 km s⁻¹ pc⁻¹, respectively (Fig. 5). They are much less than the simulation result 4–7 km s⁻¹ pc⁻¹ of Kuznetsova et al. (2018) and the observation result 5–7 km s⁻¹ pc⁻¹ in Orion (Hacar et al. 2017). Considering that ¹³CO (J = 2−1) is optically thick in the dense regions at the core, the infall motion of dense gas with a large velocity gradient cannot be detected and only the outer parts of the clump with a small gradient that are detected as gravitationally collapsing. It is evident more observations with dense molecular tracers and high angular resolution are needed for further validation. In addition, the projection effect may also make the velocity gradient relatively low.

F-north has no obvious velocity gradient (Fig. 4), perhaps because it is close to perpendicular to the direction of the line of sight. However, there are velocity fluctuations along F-north.

4.2 Gravitational collapse of the junction region

Accelerated collapse is taking place close to the main SF as seen in Fig. 5. If this characteristic feature is caused by gravity, we can use a simple model to plot the gas velocity structure as a function of the distance. All points in the junction with ¹³CO (J = 2−1) emission greater than 5σ were selected. Assuming the position of high mass clump AGAL323.459-0.079, that is, l₀ = 323.459° and b₀ = −0.079°, is the offset (0,0), the gas velocity structure of the whole junction as a function of distance to the offset (0,0) is plotted in the top panel of Fig. 6. The distance R of the x-axis is obtained through $R=\sqrt{{\left(l-l_0\right)}^2+{\left(b-b_0\right)}^2}$. There is a clear velocity gradient in Fig. 6.

Assuming the model of a point-like mass in free-fall, the observed velocity V_LSR at a given impact parameter p can be described by the following relation (Hacar et al. 2017): $$V_{\text{LSR}}\left(p\right)=V_{\text{sys,0}}+V_{\text{infall}}\left(p\right)\cdot \cos \left(\alpha \right),$$(7)

where V_sys,0 is the initial system velocity, and $$V_{\text{infall}}\left(p\right)=-\sqrt{2GM/R}=-\sqrt{2GM/\left(p/\sin \alpha \right),}$$(8)

is the infall velocity in a potential of a mass M as a function of the distance R to its center with α as the orientation angle between the direction of infall motion and the direction of the line of sight. In Fig. 6 the expected velocity profiles are displayed for particles in free-fall in different potential wells and with different orientation angles. The model results show masses between 1000 and 1500 M_⊙ and an orientation angle of about 55° are well consistent with observations, which are showed as color solid lines in Fig. 6. This agrees with the fact that the main SF has a mass of 1100 M_⊙. The result shows that the gradient is very small for the points with distances larger than ~2 pc, but increases rapidly as the points approach the center of the main SF. Namely, motions of the points from the main SF or the region close to it is dominated by the gravity, and is in gravitational collapse. The corresponding density plot (blue contours in Fig. 6) also shows the same trend. This is consistent with the theoretical results that filamentary collapse is a lot slower than spherical collapse (Pon et al. 2012; Clarke et al. 2017).

Because F-west and F-south transfer materials into the junction region from two directions, the materials from both sides of the junction may fall into the main SF at different orientation angles respectively. To test this idea, we used the same method to plot the velocity structure for the left and right half of the junction separately. The results are shown in middle and bottom panel of Fig. 6. Indeed, the orientation angles α for the left and right half of junction are different, specifically, they are about 35° and 55°, respectively. However, model fitting for the left and right half of junction both obtain a mass of 1000–1500 M_⊙ for the main SF. Model fitting for the whole junction or for the two sides both present a systemic velocity V_sys,₀ = −65.8 km s⁻¹, which is similar to the observed gas velocities at the beginning of gas acceleration zones in the V-shaped structure (see Fig. 5). Above results indicate that although F-west and F-south part 1 may transfer materials into the junction at different angles, they are both attracted by the same gravitational source at the junction. As pointed out by Hacar et al. (2017), the above results suggest that the accelerated motions identified toward the main SF could actually correspond to the kinematic signature generated by its gravitational collapse.

Fig. 5 13CO (J = 2−1) line velocity along F-south to F-west. The blue lines indicate the velocity gradient in the F-west and F-south part 1. The vertical black dotted lines indicate the position of HII region along the filament, and red arrows indicate the location of the numbered pre-stellar and proto-stellar clumps located along the filament. The data points circled by the red ellipse is the HVC high-velocity component defined in the right panel of Fig. 1.

4.3 Accretion from the filament

Following Kirk et al. (2013), the accretion rate from the filament could be estimated from the velocity gradient using a simple cylindrical model, $\dot{M}=\left(\nabla VM\right)/\tan \left(\beta \right)$. Here, M is the cylinder’s mass and β is an inclination angle of the cylinder relative to the plane of the sky and assumed to be 45°. The accretion rates of F-west, and F-south part 1 are 575 and 641 M_⊙ Myr⁻¹, respectively. Since F-north has no velocity gradient, its accretion rate cannot be calculated in this way. Therefore, at least ~1216 M_⊙ of gas will be channeled into the junction region of hub-filament G323.46-0.08 in 1 Myr if the current accretion rates are sustained. Such a accretion rate is higher than that of Kirk et al. (2013) 30 M_⊙ and Yuan et al. (2018) 440 M_⊙, and is comparable to 1100 M_⊙ Myr⁻¹ in DR21SF (Hu et al. 2021). Therefore, filamentary accretion flows may play an important role for supplying the material to spur high-mass clump and star formation therein.

4.4 Other possibilities

Except the inflows along the filament, the rotation and outflow may also lead to a radial velocity gradient along the filamentary molecular cloud. To take into account the effect of rotation, F-west may be taken as a homogeneous rigidly rotating cylinder with a total rotation energy to be calculated using the following equation (Kirk et al. 2013; Wu et al. 2018): $$E_{\text{rot}}=\frac{1}{6}\left(M{L}^2\right){\left(\nabla V\right)}^2,$$(9)

where the second term is the moment of inertia for a cylinder rotating longways along its axis, and the final term represents the angular velocity squared. The E_rot obtained for F-west is about 4889 M_⊙ km² s⁻². The gravitational binding energy is calculated by the equation: $$E_{\text{grav}}=GM{M}_{\text{clust}}/L,$$(10)

where M_clust is the mass of whole junction of 3072 M_⊙. The gravitational binding energy, E_grav ≃ 2077 M_⊙ km² s⁻², is less than the rotation energy. Therefore, we cannot rule out the possibility that F-west may be rotating. However, even if F-west is rotating around the junction, the rotation energy of F-west close to the junction will be much smaller than the gravitational binding energy. F-west would be dominated by the gravity quickly as the matter approaches the junction.

We checked the distributions of red and blue line wings of ¹³CO (J = 2−1), and proved that F-west could not be a red- or blue-shifted lobe of the outflow detected in main SF. We thus suggest the velocity gradient in F-west indicates an accretion flow along the filament, which is induced by the gravitational field of the entire junction region of the hub-filament system G323.46-0.08. This is also true for F-south part 1.

Fig. 6 Gas velocity structure as a function of the distance to the center clump (l = 323.459°, b = −0.079°). The data points from the top to the bottom panels of the diagram are from the whole junction, the left half of the junction (l > 323.46°) and the right half of the junction (l < 323.46°), respectively. For all panels different fitted lines describe the expected velocity profile for a free-falling particle in a series of potential wells with different masses M observed at different angles α following Eq. (4). The parameters are showed at the lower right corner of each panel, the masses are in M⊙ and angles are in degrees. The blue contours are the density-plot of the cross points.

4.5 Star formation

Assuming cylindrical hydrostatic equilibrium, André et al. (2014) presented the thermal critical mass per unit length for a gas filament as: $$M_{\text{line,crit}}=2c_s^2/G=16.7\left(T/10\text{\hspace{0.17em}K}\right)M_{\odot }{\text{pc}}^{-2}.$$(11)

In this manner, the values for M_line,crit for F-north, F-west, and F-south are 31.7, 34.4, and 36.7 M_⊙ pc⁻¹ for dust temperature 19.6, 20.6’ and 22 K, respectively. The mass per unit length for the three filaments ranges from 125.2 to 242.7 M_⊙ pc⁻¹ (see Table 1). These filaments are supercritical with M_line significantly larger than the critical value.

Thermally, supercritical filaments are usually associated with dense clumps and star formation activities (André et al. 2014). At least 35 dense clumps from the Hi-GAL dense clump catalog are located along the filaments (see left panel of Fig. 2 and here we only consider clumps located in hub filament system G323.46-0.08) and most of these are pre-stellar clumps. Pre-stellar clumps are usually located in the filaments, while proto-stellar clumps often appear near HII regions (see left panel of Fig. 2). The Class I (cyan crosses) and II YSOs (cyan triangles) sources in Fig. 1 (left) are also distributed on or nearby the filaments, which suggests that their formation is also correlated with the filaments.

There are 20 clumps numbered from C8 to C28 (see Table B.1) in Fig. 5 and 5 HII regions numbered from 1 to 5 located in F-west and F-south as indicated in Fig. 1. These co-locations are consistent with the global hierarchical collapse model, which predicts that filaments transfer materials into the central hub and form high mass stars or star clusters (Vázquez-Semadeni et al. 2017). Simultaneously, the filaments themselves will also fragment into dense clumps or cores and form low- and intermediate-mass stars locally, which results in local accretion flows along the fragmented filaments to those dense clumps. As Hacar & Tafalla (2011) showed in their Fig. 12, the PV diagram along the filament may show obvious velocity undulation around dense clumps, which trace the red- or blue-shifted accretion flows toward the dense clumps. The PV diagram along the filaments F-south and F-west (Fig. 5) shows clear velocity undulation. The seesaw velocity patterns around clumps C8-C9’ C 10, HII2, C20-C21, and C23-C25 suggest that they are also accreting materials from the filament. However, velocities near some clumps do not show seesaw patterns due to projection effects and the complex structure of the filament itself. On the other hand, our data has a limited resolution and sensitivity, and most clumps were not clearly detected in ¹³CO (J = 2−1) emission and their kinematics. The seesaw pattern of the velocity structure on a large scale should be the result of gas flows along the filament toward the clumps or cores (Hacar & Tafalla 2011).

These results support the global hierarchical collapse model (Vázquez-Semadeni et al. 2017), where materials converge through filaments towards a gravitational potential center, while simultaneously forming stars locally on the way to the convergence center.

5 Conclusions

Using the gas kinematics derived from ¹³CO (J = 2−1) spectral lines, we found a giant hub-filament system G323.46-0.08. Our results are given below.

1. The G323.46-0.08 consists of three filaments named F-north, F-west, and F-south which have lengths of 8, 13.5, and 29.4 pc and masses 1616, 2053, and 3682 M_⊙, respectively. Here, $N_{{\text{H}}_2}$ varies from 4 × 10²¹ in the filaments to 3.7 × 10²² cm⁻² in the main SF. All three filaments are supercritical with M_line significantly larger than the critical value M_line,_crit indicating that the filaments are unstable. There are YSOs and 35 clumps with pre-stellar and proto-stellar cores lying mainly along the filaments of G323.46-0.08. The seesaw patterns near most dense clumps in the PV diagram suggests that mass accretion also occurs along the filament toward the clumps. The large velocity dispersion and a possible outflow in the main SF indicate that high-mass star formation appears to be ongoing.

2. Very clear velocity gradients of 0.28 and 0.44 km s⁻¹ pc⁻¹ are found along for F-west and F-south part1, respectively, which suggests the channeling of materials towards the junction of hub-filament system G323.46-0.08. Furthermore, the characteristic V shape structure detected in the PV diagram at the hub-junction is in good agreement with a gravitational collapse model. Our best-fitting parameters with a hub-junction mass between 1000 and 1500 M_⊙ are consistent with the observed mass 1100 M_⊙ for AGAL323.459-0.079.

3. An estimate of the minimum accretion rate onto G323.46-0.08 is 1216 M_⊙ Myr⁻¹, obtained by channeling gas from filaments feeding onto the central clump. Filamentary accretion flows therefore appear to be an important mechanism for feeding high-mass star formation in the central highmass clump AGAL323.459-0.079 and for intermediate star formation in clumps along the filaments.

In a brief, G323.46-0.08 is accreting materials through the filaments onto AGAL323.459-0.079. AGAL323.459-0.079 is under gravitational collapsing and forming high-mass stars. Many dense clumps in the filaments also show evidences of forming stars.

Acknowledgements

This work was mainly supported by the National Key R&D Program of China under grant No.2022YFA1603103 and the National Natural Science foundation of China (NSFC) under grant No.11973076. It was also partially supported by the NSFC under grant Nos. 12173075, and 12103082, the Natural Science Foundation of Xinjiang Uygur Autonomous Region under grant Nos. 2022D01E06 and 2022D01A359, the Tianshan Talent Program of Xinjiang Uygur Autonomous Region under grant No. 2022TSYCLJ0005, the Chinese Academy of Sciences (CAS) “Light of West China” Program under Grant Nos. 2020-XBQNXZ-017, 2021-XBQNXZ-028, 2022-XBJCTD-003 and xbzg-zdsys-202212, the Regional Collaborative Innovation Project of Xinjiang Uyghur Autonomous Region under grant No. 2022E01050, and the Science Committee of the Ministry of Science and Higher Education of the Republic of Kazakhstan grant No. AP13067768. W.B. has been supported by the Chinese Academy of Sciences President International Fellowship Initiative by Grant No. 2022VMA0019 and 2023VMA0030.

Appendix A ¹³CO (J = 2−1) velocity channel maps

Fig. A.1 Channel maps of the 13CO (J = 2−1) emission for G323.46-0.08 with black contour levels at 3, 6, 9, 12, and 15 and 18 K km s−1. The background is the H2 column density distribution.

Appendix B Table B.1

Appendix C A selection of typical ¹³CO (J = 2−1)spectra of G323.46-0.08

Fig. C.1 Black contours are 13CO (J = 2−1) integrated intensity from velocity −69 to −63 km s−1 and the red contour is 13CO (J = 2−1) integrated intensity from velocity −69 to −68.75 km s−1. The spectral lines at the corresponding positions of the numbers are shown, the red lines are the Gaussian fitting results.

References

All Tables

All Figures

Fig. 1 Infrared and molecular spectrum line emissions of G323.46-0.08. Left: three-color map of the G323.46-0.08 region. Red, green, and blue backgrounds show the 24, 8, and 4.5 µm emission, respectively. The white contours denote the 13CO (J = 2−1) emission integrated velocity from −70 to −63 km s−1, which starts from 3 K km s−1 and with a step of 9 K km s−12. The cyan crosses and triangles are Class I and II YSOs, respectively. The red circles mark the Hπ regions identified by Anderson et al. (2014). The red cross is the central high mass clump AGAL323.459-0.079 in hub-filament system G323.46-0.08. Right: velocity map of G323.46-0.08. The color background is the velocity field of 13CO (J = 2−1). The black contours are the integrated intensity of the 13CO (J = 2−1) emission (same as in the left panel). The red contour marks the 13CO (J = 2−1) emission in the region of F-north integrated velocity from −70 to −68.25 km s−1. The red dotted line and the white interrupted dashed line represent the ridgeline of F-north, F-west, and F-south. All ridge lines are formed by connecting the peak intensity points of 13CO (J = 2−1) in the filament). The white circle denotes the high velocity component appears in F-south part 2.

In the text

Fig.2 H2 column density (left) and dust temperature (right) distributions within the G323.46-0.08. The black contours indicate the 13CO (J = 2−1) integrated intensity in areas, where Tmb is higher than 3σ (3 K), The contour levels start from 3 K km s−1 and with a step of 9 K km s−1. The velocity interval of the integration is from −70 to −63 km s−1. The white, rose, and black diamonds are Herschel clumps, and represent different evolution stages of starless cores, prestellar, and protostellar, respectively (Elia et al. 2017). The white crosses are ATLASGAL 870 µm clumps (Urquhart et al. 2018). The red circles show the HII regions identified by Anderson et al. (2014).

In the text

	Fig. 3 Moment 2 map of G323.46-0.08. The colour backgrounds represents the velocity dispersion of 13CO (J = 2−1). The white contours denote the 13CO (J = 2−1) emission integrated velocity from −70 to −63 km s−1, which starts from a 3σ level of 3 K km s−1 and with a step of 11.5 K km s−1.
In the text

	Fig. 4 13CO (J = 2−1) line velocity along F-north. The x-axis is taken along the red dotted line in the right panel of Fig. 1, with the zero position starting from its intersection at the junction.
In the text

Fig. 5 13CO (J = 2−1) line velocity along F-south to F-west. The blue lines indicate the velocity gradient in the F-west and F-south part 1. The vertical black dotted lines indicate the position of HII region along the filament, and red arrows indicate the location of the numbered pre-stellar and proto-stellar clumps located along the filament. The data points circled by the red ellipse is the HVC high-velocity component defined in the right panel of Fig. 1.

In the text

Fig. 6 Gas velocity structure as a function of the distance to the center clump (l = 323.459°, b = −0.079°). The data points from the top to the bottom panels of the diagram are from the whole junction, the left half of the junction (l > 323.46°) and the right half of the junction (l < 323.46°), respectively. For all panels different fitted lines describe the expected velocity profile for a free-falling particle in a series of potential wells with different masses M observed at different angles α following Eq. (4). The parameters are showed at the lower right corner of each panel, the masses are in M⊙ and angles are in degrees. The blue contours are the density-plot of the cross points.

In the text

	Fig. A.1 Channel maps of the 13CO (J = 2−1) emission for G323.46-0.08 with black contour levels at 3, 6, 9, 12, and 15 and 18 K km s−1. The background is the H2 column density distribution.
In the text

	Fig. C.1 Black contours are 13CO (J = 2−1) integrated intensity from velocity −69 to −63 km s−1 and the red contour is 13CO (J = 2−1) integrated intensity from velocity −69 to −68.75 km s−1. The spectral lines at the corresponding positions of the numbers are shown, the red lines are the Gaussian fitting results.
In the text