In Search of Infall Motion in Molecular Clumps. III. HCO+ (1-0) and H13CO+ (1-0) Mapping Observations toward Confirmed Infall Sources

The HCO⁺ integrated intensity maps of 17 sources show clumpy structures and the H¹³CO⁺ integrated intensity maps of 15 sources show clumpy structures (which are listed in Table 3). The HCO⁺ and H¹³CO⁺ integrated intensity maps of sources with clumpy structures superposed on the C¹⁸O (1-0) data are presented in Appendix A (Figure 1 shows an example of source G053.12+0.08). The C¹⁸O mapping data come from the MWISP project, with spatial resolutions of about 52''. In addition, the maps also show the catalog positions of SFR (Avedisova 2002), maser sources, as well as young stellar objects (YSOs), which are associated with the clumps.

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Among them, 14 sources show clear clumpy structures in both HCO⁺ (1-0) and H¹³CO⁺ (1-0) lines. For G029.06 + 4.58, G039.33-1.03, and G110.31 + 2.53, only HCO⁺ maps show clear clumps. HCO⁺ emissions have also been found in other sources, but due to insufficient angular resolution and/or sensitivity of the telescope, the integrated intensity maps do not show obvious clumps. G028.97 + 3.35 is different, i.e., its H¹³CO⁺ integrated intensity map shows a compact clump. However, the HCO⁺ map does not have sufficient signal-to-noise ratio, and no clear clump is found in this area.

Although the observation targets are selected based on the MWISP CO mapping data, the HCO⁺ spatial distributions of some sources seem to be slightly different from the CO distributions and deviate from the center position of the observation area. This may be caused by HCO⁺ and CO tracing different density regions. Similarly, although HCO⁺ and H¹³CO⁺ lines are isotopic molecular lines, the areas they traced may also be different. In most cases, the maps of HCO⁺ and H¹³CO⁺ display similar compact regions. However, there are some exceptions: the map of HCO⁺ emissions in G029.60-0.63 shows two clumps located in the north and south positions, while the H¹³CO⁺ emission map shows only one clump at the same velocity region, and the clump located slightly east of the two clumps from the HCO⁺ data. The HCO⁺ and H¹³CO⁺ maps of G109.00 + 2.73 also display some differences. The compact clump shown in the H¹³CO⁺ map is located northeast of the clumps in the HCO⁺ emission map. This may be related to the different distribution of HCO⁺ and H¹³CO⁺ in the clumps or the different optical depths of these two lines.

Another source with a relatively complicated structure is G107.50 + 4.47. Our mapping results show that both HCO⁺ and H¹³CO⁺ integrated intensity maps of this source have complex geometric shapes. We made channel maps to analyze further the structure of this source. Figure 2, panels (a) and (b) show the channel maps of HCO⁺ and H¹³CO⁺, respectively. We found that there may be four clumps in this area, which we named clump A, B, C, and D (as shown in Figure 2). Their velocity ranges are approximately [−4.7, −1.4], [−3.4, −1.4], [−2.8, −1.4], and [−1.0, 0.4] km s⁻¹, respectively. Among them, clump D is associated with two YSOs. Figure 2 (c) presents the HCO⁺ (1-0) channel maps superposed on the SCUBA-2 450 μm and 850 μm continuum contour maps ⁷ (Geach et al. 2017). The continuum data also show that there is a complex clump in this area. Some structures in the north and south of the continuum maps seem to correspond to the molecular line emissions. However, due to the limitation of the angular resolution of the telescope, the more detailed structure and properties of the clumps in this area are still unknown. We hope to use a telescope with higher resolution and sensitivity to map this target in a follow-up study.

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Using HCO⁺ and H¹³CO⁺ data, we can estimate the physical parameters of these clumps. Table 4 lists the parameters, including the radius, density, and mass of these clumps, the excitation temperatures, and the column densities of HCO⁺ and H¹³CO⁺ lines. Among them, the radius is obtained by a two-dimensional Gaussian fitting of the of HCO⁺ integrated intensity maps (for G028.97+3.35, the H¹³CO⁺ map was used). If the source is non-spherical, we adopt the average radius $r=\sqrt{a\times b}$, where a and b indicate the long and short axes of the clump. The angular sizes have been converted to linear sizes. The H₂ column densities are obtained from the previous study (Yang et al. 2020). Meanwhile, we roughly estimate the mass of these clumps by M = π R² μ m_H N(H₂), where R is the radius, μ is the mean molecular weight of the interstellar medium (i.e., 2.8), m_H is the mass of a hydrogen atom, and N(H₂) is the H₂ column density. However, because the beam size of the DLH telescope is about twice that of these observations, the H₂ density and clump mass may be underestimated due to beam dilution. In addition, due to the influence of distance and radius uncertainty, the clump mass error may also be large. What is given here is an estimate on the order of magnitude.

Table 4. Physical Parameters of the Clumps

Source	Radius	Tkin	log($\tfrac{N({{\rm{H}}}_{2})}{{\mathrm{cm}}^{-2}}$)	log($\tfrac{\rho }{{\mathrm{cm}}^{-3}}$)	log($\tfrac{M}{{M}_{\odot }}$)	Tex(HCO+)	Tex(H13CO+)	log($\tfrac{N({\mathrm{HCO}}^{+})}{{\mathrm{cm}}^{-2}}$)	log($\tfrac{N({{{\rm{H}}}^{13}\mathrm{CO}}^{+})}{{\mathrm{cm}}^{-2}}$)	[HCO+]/	[H13CO+]/
Name	(pc)	(K)				(K)	(K)			[H2]	[HCO+]
G028.97 + 3.35	0.03(0.01)	12.4(0.4)	22.4(0.3)	4.8(0.7)	1	${9.1}_{-1.0}^{+2.1}$	${9.8}_{-1.1}^{+2.3}$	${11.6}_{-0.1}^{+0.2}$	${11.7}_{-0.1}^{+0.2}$	1.5 × 10−11	1.3 × 100
G029.06 + 4.58	0.05	8.7(0.3)	21.6(0.1)	4.3	1	${4.0}_{-0.01}^{+0.01}$	${3.6}_{-0.01}^{+0.03}$	${12.6}_{-0.1}^{+0.1}$	${12.1}_{-0.1}^{+0.1}$	9.7 × 10−10	5.6 × 10−1
G029.60-0.63	0.56	13.9(0.4)	22.6(0.5)	4.2	3	${6.1}_{-0.02}^{+0.6}$	${3.6}_{-0.5}^{+1.7}$	${13.8}_{-0.5}^{+0.5}$	${12.5}_{-0.3}^{+0.5}$	1.9 × 10−9	3.9 × 10−2
G030.17 + 3.68	⋯	10.4(0.4)	21.8(0.2)	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯
G031.41 + 5.25	⋯	13.8(0.6)	22.0(0.3)	⋯	⋯	⋯	Nd	⋯	Nd	⋯	Nd
G033.42 + 0.00	⋯	8.8(0.4)	21.6(0.1)	⋯	⋯	⋯	Nd	⋯	Nd	⋯	Nd
G039.33-1.03	0.06	8.8(0.3)	21.8(0.1)	4.4	1	${4.1}_{-0.01}^{+0.01}$	Nd	${12.4}_{-0.1}^{+0.1}$	Nd	4.0 × 10−10	Nd
G053.13 + 0.09	0.20	16.4(0.4)	22.0(0.2)	4.1	2	${16.3}_{-0.3}^{+0.1}$	${4.4}_{-0.01}^{+0.1}$	${15.2}_{-0.9}^{+1.1}$	${13.3}_{-0.2}^{+0.2}$	1.6 × 10−7	1.3 × 10−2
G077.91-1.16	0.01	14.3(0.3)	22.0(0.2)	5.6	1	${15.8}_{-3.8}^{+6.0}$	${17.1}_{-4.3}^{+6.5}$	${12.2}_{-0.01}^{+0.1}$	${11.8}_{-0.01}^{+0.1}$	1.0 × 10−10	4.2 × 10−1
G079.24 + 0.53	0.03	10.4(0.3)	22.4(0.4)	5.3	1	${7.6}_{-2.5}^{+3.3}$	${8.0}_{-2.7}^{+3.3}$	${12.0}_{-0.01}^{+0.1}$	${11.8}_{-0.01}^{+0.1}$	3.6 × 10−11	6.6 × 10−1
G079.71 + 0.14	0.07	9.1(0.3)	21.7(0.1)	4.2	1	${4.0}_{-0.1}^{+0.1}$	${3.5}_{-0.1}^{+0.1}$	${12.8}_{-0.1}^{+0.1}$	${12.2}_{-0.1}^{+0.1}$	1.4 × 10−9	2.3 × 10−1
G081.72 + 0.57	0.22(0.02)	38.0(0.4)	23.2(1.3)	5.0(0.2)	3	${29.6}_{-6.1}^{+5.1}$	${23.8}_{-1.9}^{+3.9}$	${13.9}_{-0.1}^{+1.4}$	${13.0}_{-0.01}^{+0.1}$	5.2 × 10−10	1.1 × 10−1
G082.21-1.53	0.23	12.7(0.3)	22.0(0.2)	4.0	2	${6.8}_{-0.02}^{+0.01}$	${3.9}_{-0.1}^{+0.03}$	${13.4}_{-0.2}^{+0.2}$	${12.8}_{-0.2}^{+0.2}$	2.4 × 10−9	2.6 × 10−1
G107.50 + 4.47	0.03	18.8(0.4)	22.4(0.4)	5.3	1	${16.3}_{-5.7}^{+9.4}$	${18.5}_{-0.1}^{+0.1}$	${13.0}_{-0.01}^{+0.2}$	${12.0}_{-0.01}^{+0.1}$	4.3 × 10−10	1.0 × 10−1
G109.00 + 2.73	0.06	17.4(0.3)	22.4(0.3)	5.0	1	${8.3}_{-2.7}^{+6.2}$	${8.7}_{-3.1}^{+7.7}$	${12.1}_{-0.1}^{+0.1}$	${11.7}_{-0.03}^{+0.1}$	5.2 × 10−11	4.0 × 10−1
G110.31 + 2.53	⋯	22.8(0.4)	22.2(0.3)	⋯	⋯	⋯	Nd	⋯	Nd	⋯	Nd
G110.40 + 1.67	⋯	12.6(0.6)	21.8(0.1)	⋯	⋯	⋯	Nd	⋯	Nd	⋯	Nd
G121.31 + 0.64	0.12(0.01)	16.6(0.4)	22.2(0.2)	4.4(0.1)	2	${15.9}_{-0.4}^{+0.4}$	${5.4}_{-0.4}^{+0.9}$	${15.4}_{-1.4}^{+1.4}$	${13.1}_{-0.2}^{+0.2}$	1.5 × 10−7	7.9 × 10−3
G121.34 + 3.42	⋯	7.2(0.3)	22.0(0.2)	⋯	⋯	⋯	⋯	⋯	⋯	5.5 × 10−10	5.9 × 10−1
G126.53-1.17	0.05	11.9(0.4)	22.0(0.3)	4.7	1	${5.1}_{-0.6}^{+1.5}$	${4.8}_{-0.9}^{+1.8}$	${12.3}_{-0.2}^{+0.3}$	${11.8}_{-0.1}^{+0.2}$	2.2 × 10−10	2.8 × 10−1
G143.04 + 1.74	0.05	14.6(0.4)	22.0(0.2)	4.7	1	${5.5}_{-0.7}^{+1.2}$	${5.1}_{-0.8}^{+1.4}$	${12.6}_{-0.1}^{+0.2}$	${11.9}_{-0.1}^{+0.1}$	3.9 × 10−10	2.2 × 10−1
G154.05 + 5.07	⋯	10.3(0.4)	21.5(0.1)	⋯	⋯	⋯	Nd	⋯	Nd	⋯	Nd
G193.01 + 0.14	0.31	20.4(0.4)	22.2(0.4)	4.1	2	${12.4}_{-0.01}^{+0.01}$	${3.8}_{-0.3}^{+1.1}$	${14.4}_{-0.4}^{+0.4}$	${12.7}_{-0.3}^{+0.4}$	1.5 × 10−8	2.2 × 10−2
G217.30-0.05	0.33	22.1(0.4)	22.4(0.5)	4.3	2	${6.6}_{-0.03}^{+1.6}$	${4.0}_{-0.8}^{+2.9}$	${13.4}_{-0.5}^{+0.5}$	${11.8}_{-0.3}^{+0.4}$	9.7 × 10−10	2.9 × 10−2

Note. Nd denotes non-detection with H¹³CO⁺ (1-0) emissions. The values in parentheses are the uncertainty of parameters.

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The excitation temperatures and column densities of HCO⁺ and H¹³CO⁺ are estimated from the 1D non-LTE RADEX radiative transfer code (van der Tak et al. 2007). The input parameters of this program are the spectral range for the output, the cosmic microwave background temperature (i.e., 2.73 K), the kinetic temperature (estimated from the T_ex of ¹²CO, while the T_ex is calculated from ¹²CO data given by the MWISP project Yang et al. 2020), and the H₂ volume density (assuming that the source is a uniform sphere, it is estimated from the H₂ column density) of the cloud and the molecular line width.

We iterate through the molecular column density in a loop to match the model line intensities with the observed line intensities' peak values. The obtained results show that the excitation temperatures of HCO⁺ and H¹³CO⁺ are about a few to 20 Kelvin. The HCO⁺ column densities are about 10¹¹ to 10¹⁵ cm⁻², while the H¹³CO⁺ densities are about 10¹¹ to 10¹³ cm⁻². Combining the H₂ column density, we can estimate the abundance ratios of H₂, HCO⁺, and H¹³CO⁺ in these clumps: [HCO⁺]/[H₂] is about 10⁻¹¹ to 10⁻⁷, and [H¹³CO⁺]/[HCO⁺] is about 10⁻³ to 1.3. Except for the H¹³CO⁺ density of G028.97 + 3.35, which is slightly higher than for HCO⁺, the HCO⁺ abundances of the remaining clumps are all greater than H¹³CO⁺. In most clumps, the abundances of HCO⁺ are 10–100 times those of H¹³CO⁺. We changed the input parameters and performed many calculations to estimate the uncertainty values of the results caused by the input parameter errors. However, due to the radius uncertainty caused by the kinematic distance error and the local thermal equilibrium assumption and the uncertainty of H₂ abundance ratio we used when estimated the H₂ density, the uncertainty values of the results may be greater than the values we give.

To obtain the spatial details of the line profiles of these sources, we use the mapping data to form the HCO⁺ (1-0) map grids of these sources, which are gridded to one beam size (28${}^{{\prime} ^{\prime} }$). The map grids of all 24 sources are shown in Appendix B. Five sources, G029.60-0.63, G053.13 + 0.09, G081.72 + 0.57, G121.31 + 0.64, and G193.01 + 0.14, show significant blue asymmetric double-peaked profiles over the entire clump areas, which may indicate that these sources are global infall sources. Among them, G081.72 + 0.57 is located in the famous SFR DR21, which has been detected to have gas infall motion in previous studies (e.g., Schneider et al. 2010). G053.13 + 0.09 and G121.31 + 0.64 also have been confirmed to have a trend of global gas collapse (e.g., Zhang et al. 2017; Pirogov et al. 2016). Other sources, i.e., G082.21-1.53, G107.50 + 4.47, G109.00 + 2.73, and G217.30-0.05, show both blue and red line profiles in the observed areas, showing that these sources have more complex local motions. For the remaining sources, the optically thick line does not show clear double-peaked profiles. Therefore, we need to quantify the asymmetry of HCO⁺ lines through a dimensionless parameter, to confirm further the line profiles of other sources.

We selected some single-point spectra from the mapping data, and then gave their line parameters. In most cases, the positions of the single-point spectra we selected are the positions where the HCO⁺ lines have the strongest emissions and the most significant asymmetric profiles (excluding strong emissions from other sources at the edge of the mapping area). For G028.97 + 3.35, its HCO⁺ emission of this source is weak, the single-point spectrum we selected is located at the position where the emission of the H¹³CO⁺ line is strongest. For the sources with complex line components in optically thick lines, we also select the lines at the strongest emission positions of optically thin lines. The position coordinates of these single-point spectra are listed in Table 5 columns 2 and 3, and the line profiles of all 24 sources are presented in Figure 3.

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According to the asymmetric profiles of the optically thick lines, we can divide these sources into three kinds: sources with blue profiles, red profiles, and neither (including multi-peaked profiles). Mardones et al. (1997) proposed that a dimensionless parameter, δ V can be used to quantify the asymmetry of the line profile:

$$\begin{eqnarray}&&\delta V=\displaystyle \frac{{V}_{\mathrm{thick}}-{V}_{\mathrm{thin}}}{{\rm{\Delta }}{V}_{\mathrm{thin}}}\end{eqnarray} \tag{ 1 }$$

where V_thick and V_thin are the peak velocities of optically thick and thin lines, respectively, and ΔV_thin is the FWHM of the optically thin line. The V_thick values are taken from the brightest emission peak positions of HCO⁺ (1-0) lines and the V_thin and ΔV_thin are taken from the Gaussian fitting of H¹³CO⁺ (1-0). If no H¹³CO⁺ emissions were detected in the sources, the C¹⁸O (1-0) lines from Yang et al. (2020) were used as optically thin lines (these sources are marked in Table 5). For G109.00 + 2.73 and G126.53-1.17, because no H¹³CO⁺ emissions are detected at their positions, we used H¹³CO⁺ line data at approximately 32'' and 54'' offsets to determine the central radial velocities. The dimensionless parameter δ V less than 0 indicates that the HCO⁺ line shows a blue asymmetric profile; δ V greater than 0 indicates that the HCO⁺ line shows a red profile. If δ V is approximately equal to 0, it indicates that the HCO⁺ line does not show obvious asymmetry profiles.

In addition to the nine sources mentioned above that show significant blue profiles, there are sources without typical infall line characteristics that may still be infall sources. Because in some cases, the self-absorption of the optically thick lines is weak, this makes the double-peaked profile not so obvious. In such a situation, the optically thick line may show a peak-shoulder profile or a single-peaked one with the peak skewed to the blue. In general, we also categorize this profile as a blue profile. Four sources show a peak-shoulder profile, while another six show a single-peaked profile with the peak positions skewed to the blue. All these sources are marked as P-S and S in Table 5.

Among the remaining sources, the HCO⁺ lines of G039.33-1.03 and G110.31 + 2.53 show a red profile. No H¹³CO⁺ emission is detected in G033.42 + 0.00, so its central radial velocity is based on C¹⁸O data. Compared with the center radial velocity, we found that the HCO⁺ line of this source did not show an asymmetric profile. The HCO⁺ lines of G077.91-1.16 and G079.24 + 0.53 show multiple peaks, and optically thin lines have only one velocity component. However, because of the low velocity resolution of H¹³CO⁺ and the insufficient signal-to-noise ratios at the dip of the HCO⁺ line, we cannot determine whether the multiple peaks are caused by multiple velocity components or systematic motions.

In the previous subsection, we identified 19 sources that have gas infall motions. Among them, the HCO⁺ lines of eight sources show a significant blue profile and the signal-to-noise ratios are greater than 10. We use some models to analyze further the physical properties of these sources. The RATRAN (radiative transfer and molecular excitation) 1D Monte Carlo radiative transfer code model of a collapsing cloud (Hogerheijde & van der Tak 2000) is a model usually used to fit the optically thick lines to estimate the infall velocity of sources. Using this model, we fit the HCO⁺ lines of their single-point spectra, and then estimated the infall velocities and the mass infall rates of these candidates. The input parameters of RATRAN are the shell number, the radius of the clump, the density distribution (cm⁻³) and the abundance distribution of the line, the kinetic temperature distribution, turbulent velocity dispersion, and infall velocity distribution. Among them, the size and other input parameters of these sources we used are quoted in Table 4. We use 10 concentric spherical shells with a power-law density and velocity distribution to model the envelope, with a power index of −1.5 and −0.5, respectively. Based on Section 3.2, we fixed the HCO⁺ abundance relative to H₂. Then, we ran the code varying the infall velocity and the velocity dispersion to get a series of models to fit the HCO⁺ lines. The Kolmogorov–Smirnov (K–S) test is used to verify the similarity between the HCO⁺ fitting results obtained by the model and the observation. We selected the one with the highest probability in the K–S test in a series of models as a reasonable fit of the HCO⁺ line. For H¹³CO⁺ line, we also use the RATRAN model for fitting. However, compared with HCO⁺, the variation of H¹³CO⁺ infall velocity and velocity dispersion has no significant effect on the fitting results. The model results of HCO⁺ and H¹³CO⁺ are presented in Figure 4, and the parameters are listed in Table 6.

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Table 6. Infall Velocities and Mass Infall Rates of Nine Infall Candidates with Double-peaked Profiles

Source	σ	Vin	Vin	${\dot{M}}_{\mathrm{in}}$	${\dot{M}}_{\mathrm{in}}$
	RAT	RAT a	Myers	RAT	Myers
Name	(km s−1)	(km s−1)	(km s−1)	( × 10−4 M⊙ yr−1)	( × 10−4 M⊙ yr−1)
G029.60-0.63	0.5(0.2)	1.3(0.2)	1.6(0.9)	45	55
G053.13 + 0.09	1.8(0.1)	0.9(0.1)	0.7(0.5)	2.8	2.2
G081.72 + 0.57	1.0(0.2)	0.5(0.2)	0.4(0.6)	27	22
G082.21-1.53	0.7(0.3)	0.5(0.1)	0.1(0.3)	2.9	0.57
G107.50 + 4.47	0.7(0.2)	0.6(0.1)	0.3(0.2)	0.97	0.49
G109.00 + 2.73	⋯	⋯	0.3(0.8)	⋯	1.0
G121.31 + 0.64	1.0(0.1)	0.6(0.2)	0.3(0.9)	2.4	1.2
G193.01 + 0.14	0.5(0.2)	0.7(0.2)	1.5(0.8)	5.3	11
G217.30-0.05	0.4(0.2)	0.3(0.2)	0.2(0.1)	3.8	2.6

Note.

^a V_in(RAT) is the mean velocity value (weighted by the shell's width) of the clump obtained by the RATRAN model.

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An alternative way to estimate the infall velocity is the Myers et al. (1996) model. This analytical model allows one to infer an infall velocity from the data of the optically thick and thin lines:

$$\begin{eqnarray}&&{V}_{\mathrm{in}}=\displaystyle \frac{{\sigma }^{2}}{{V}_{\mathrm{red}}-{V}_{\mathrm{blue}}}\mathrm{ln}\left(\displaystyle \frac{1+e({T}_{\mathrm{bd}}/{T}_{\mathrm{dip}})}{1+e({T}_{{rd}}/{T}_{\mathrm{dip}})}\right)\end{eqnarray} \tag{ 2 }$$

where σ is the velocity dispersion of the H¹³CO⁺ line. V_red and V_blue are the velocities of the HCO⁺ line. T_dip is the intensity of the self-absorption dip. T_bd and T_rd are the temperatures of the blue and red peaks above the dip, respectively. All these parameters come from a combination of an emission Gaussian peak and an absorption Gaussian peak fitting. As a comparison, we also used this approach to estimate the infall velocity of the sources with a blue profile, and the results are also listed in Table 6. Compared with the infall velocities calculated by the same method in Yang et al. (2020), the result for G121.31 + 0.64, G029.60-0.63, and G081.72 + 0.57 infall velocities reduced. This may be due to the infall line profile being quite sensitive to changes in spatial position. Therefore, the difference of V_in may be related to factors such as the coordinate position of the extracted single-point line, the pointing accuracy and the spatial resolution of the telescope. Compared with the infall velocities calculated by RATRAN, the velocities of G082.21-1.53, G107.50 + 4.47, and G121.31 + 0.64 are lower, and the infall velocity of G193.01 + 0.14 is larger than the result of the RATRAN model. This may be caused by the difference between the two models. For other sources, the results are relatively close.

Using López-Sepulcre et al.'s (2010) method, a rough estimate of the mass infall rate, ${\dot{M}}_{\mathrm{in}}$, may be determined from:

$$\begin{eqnarray}&&{\dot{M}}_{\mathrm{in}}=4\pi {R}^{2}{V}_{\mathrm{in}}\rho \end{eqnarray} \tag{ 3 }$$

where R is the clump radius estimated from the integrated intensity map, V_in is an estimate of infall velocity from the RATRAN and/or Myers model (see Section 4.2), and ρ is the average density of the clump. Table 6 also lists the obtained mass infall rates. The results show that the ${\dot{M}}_{\mathrm{in}}$ of these sources is between 10⁻³ and 10⁻⁵ M_⊙ yr⁻¹. For most sources, there is roughly no difference in the magnitude of the mass infall rate values calculated by the two models. According to some previous studies, for massive star formation, the mass infall rates onto the host clumps are about 10⁻² to 10⁻⁴ M_⊙ yr⁻¹ (e.g., Palla & Stahler 1993; Whitney et al. 1997; Kirk et al. 2005). For low-mass star formation, the mass infall rates are about 10⁻⁵ to 10⁻⁶ M_⊙ yr⁻¹ (e.g., Rygl et al. 2013; He et al. 2015). This suggests that intermediate or massive stars may be forming in some of the clumps. However, this estimation approach assumes that the clump is isotropic, which may cause the local mass infall rate to be overestimated or underestimated. To study the local mass infall rate of clumps further, higher-resolution observations are necessary.

We also checked the correlation between infrared point sources and the identified infall sources to distinguish the evolutionary stages of these sources. If the infrared point sources are located near the clump centers, or near the spectral lines' emission positions, we consider that this source is associated with the infrared point sources. The infrared source catalogs we used are the AllWISE Source Catalog (Cutri 2013) and the Spitzer catalog, GLIMPSE (Benjamin et al. 2003; Churchwell et al. 2009). After excluding the foreground sources, shock emission blobs, and resolved structure, all sources with infall signatures were associated with AllWISE and/or GLIMPSE sources, with the exception of G031.41 + 5.25 and G110.40 + 1.67.

Using the sources' classification criteria suggested by Koenig et al. (2012), we have identified that 12 of them are associated with Class 0/I YSOs, which are marked in Table 1. Most of these sources are close to the radio sources in the SFR, as well as a variety of masers, including Class I and Class II methanol, OH, and/or H₂O masers, indicating that these sources have more active star-forming activities. We will analyze and discuss each source with other star-forming activities in the next subsection.

The remaining sources, G028.97 + 3.35, G029.06 + 4.58, G030.17 + 3.68, G121.34 + 3.42, and G154.05 + 5.07 are not associated with Class 0/I YSOs, while G031.41 + 5.25 and G110.40 + 1.67 lack infrared sources associated with them. Thus, those data suggest that these sources may be at a very early stage of evolution. Unfortunately, the signal-to-noise ratios of these sources are relatively low, and the line profiles are mostly peak-shoulder profiles or single-peaked profiles with the peaks skewed to the blue. The model we currently use cannot fit these line profiles well. If there are better optically thick line data in the future, further research on these sources will help us better understand the physical process of the initial stage of star formation.

In addition to showing infall characteristics, some infall candidates also have evidence for outflow and other star-forming activities. In this paper, we only make a rough diagnosis and a more detailed analysis is beyond the scope of this work and will be given in a future paper.

G029.60-0.63 spectra map (presented in Figure B1) shows that the HCO⁺ lines of the north clump have infall signatures with a blue line wing. We made an integrated intensity map of the line wing that is presented in Figure 5, top left panel, with a velocity range of 70.0–73.5 km s⁻¹. This source may be an outflow candidate with a blue lobe. Using the ¹³CO (3-2) and C¹⁸O (3-2) data, a previous study also found outflows in this area (e.g., de Villiers et al. 2014). However, what they found is a red lobe outflow, which is different from our result. Therefore, we made a velocity channel map of the HCO⁺ with a velocity range of 72.6–82.5 km s⁻¹ to analyze the structure of this source (as shown in Figure 5 top right panel). It can be seen that the velocity range of the two clumps in the upper right corner of the map is about 72.6–76.5 km s⁻¹. However, in the range of 79.2–82.5 km s⁻¹, another clump with a slightly different location seems to exist. The red line wing found in previous CO data is likely to correspond to this velocity component. In addition, G029.60-0.63 is associated with an SFR, while several Class 0/I YSOs have been found in this region (e.g., Camarata et al. 2015). However, the clump position of HCO⁺ with infall line profile was found to deviate slightly from the positions of these YSOs. Other studies have detected a 22 GHz H₂O maser (e.g., Svoboda et al. 2016) and a variety of kinds of methanol masers (such as 6.7 GHz Class II and 95 GHz Class I methanol masers, e.g., de Villiers et al. 2014; Yang et al. 2017) near this clump. Among them, Class II methanol masers usually trace the high-mass SFRs (e.g., Billington et al. 2019), while a H₂O maser is generated in the shock wave produced by outflows and stellar winds (e.g., Torrelles et al. 2005). The evidence shows that the star-forming activity of this source is very active, and massive stars may be forming in this area.

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The HCO⁺ lines of G053.13 + 0.09 have obvious blue and red wing components, indicating that this source may have a bipolar outflow. From the lobes' integral diagram shown in Figure 5, it can be seen that the direction of outflow is roughly from southeast to northwest. The outflow center basically coincides with the radio source 53.14 + 0.07 in the massive SFR. And several YSOs at the Class I stage have been detected in this region (e.g., Avedisova 2002). This is consistent with the results obtained by Zhang et al. (2017) using SiO lines to trace the shock gas associated with molecular outflows. The Class I YSOs here are likely to be the host sources of the infall and outflow motion, but further analysis still requires higher-resolution observations to support this conclusion. On the other hand, this source is also maser-rich, with 6.7 GHz Class II CH₃OH, 95 GHz Class I CH₃OH, H₂O and OH masers reported (e.g., Szymczak et al. 2000; Hu et al. 2016; Svoboda et al. 2016; Yang et al. 2017; Beuther et al. 2019). This indicates that the star formation activity of this source is very active, and intermediate- or high-mass stars may be forming in this area.

G081.72 + 0.57 is associated with the well-known massive SFR DR21 (Downes & Rinehart 1966), which consists of a group of several compact H ii regions (e.g., Harris 1973) with energetic outflow (e.g., Garden et al. 1991; Russell et al. 1992; Davis & Smith 1996). We found significant line wings at its HCO⁺ line, which are likely to be caused by outflow gas. The integral diagram of the red and blue lobes is shown in Figure 5, which seems to show that the outflow from this source has a southeast–northwest direction, while some YSOs are close to the outflow center. However, because there are several YSOs in this area, we are not sure which sources host the molecular outflow and/or infall. A large number of previous studies have reported that there are many kinds of masers here: Genzel & Downes (1977) found 22 GHz H₂O maser, and other researchers have detected OH masers here (e.g., Norris et al. 1982; Argon et al. 2000; Szymczak & Kus 2000). A large amount of research has shown that the methanol maser here is also rich, with a variety of Class I and Class II methanol masers, including 6.7, 36, 44, 84.5, 95, 107, and 133 GHz methanol masers (e.g., Haschick & Baan 1989; Haschick et al. 1990; Menten 1991; Val'tts et al. 1995; Slysh et al. 1997; Kalenskiĭ et al. 2019). In addition, many studies have been focused on gas collapse in this area. Some of them have indicated a global gas infall motion here and tried to estimate the infall velocity of the gas. Schneider et al. (2010) used the simple Myers et al. (1996) model to infer an infall velocity from the HCO⁺ line profiles of the DR21 filament to be about 0.2–1 km s ⁻¹. Using the RATRAN and Myers model, the infall velocities we estimated are about 0.5 and 0.4 km s⁻¹, respectively, which are consistent with previous results.

G107.50 + 4.47 is also an outflow candidate. Its HCO⁺ lines have some components that exceed the Gaussian profiles and the lobes' integral diagram of this source is shown in Figure 5. In this source, we detected some HCO⁺ lines with blue profiles at the positions of clumps A, B, and C (marked with white letters in the figure; the velocity ranges are slightly different; see Section 3.1), while in the southwest of the mapping area, some red profile lines are detected. A part of the mapping area shows a blue line profile, and the other shows a red line profile. The distribution of the two kinds of line profiles is almost symmetric, which may also be evidence of gas outflow (He et al. 2015). Using the CO (2-1) data, Kim & Kurtz (2006) previously confirmed that there is gas outflow in this area. In the ensuing research, they observed HCO⁺ (1-0) and SiO (2-1) on 18 YSOs, including a source in this area, and confirmed that there may be intermediate- or high-mass counterparts of Class 0 objects, and it is experiencing active accretion (Kim et al. 2015). Moreover, there is an SFR 107.43+4.54 nearby, with a velocity range close to these clumps. Clumps A, B, and C all show some infall line profiles, but clump C is the most obvious one with global infall characteristics. Valdettaro et al. (2001) detected H₂O maser emissions near clump C, while the clumps associated with the H₂O maser usually have other indicators of star formation activity. Using the RATRAN and Myers model, we estimated the infall velocities of clump C to be about 0.6 and 0.3 km s⁻¹, respectively. The mass infall rates are about 10⁻⁴–10⁻⁵ M_⊙ yr⁻¹. This indicates that there may be intermediate-mass stars forming in this clump, which is similar to previous observation results.

G121.31 + 0.64 is associated with SFR 121.20+0.62 (IRAS 00338+6312). Some previous studies have already detected signs of outflow and infall here: CO observation results indicate a bipolar outflow of CO gas (e.g., Snell et al. 1990; Yang et al. 1991), and the HCO⁺ and H¹³CO⁺ data taken by the 20 m radio telescope of the Onsala Space Observatory (Sweden) indicates infall motion in this source (Pirogov et al. 2016). Our observations also confirmed these results. The spectra map grids of this source show that the HCO⁺ lines have a blue profile in the entire area, which indicates that this source may be a global collapse source, while the mass infall rate we estimated is about 10⁻⁴ M_⊙ yr⁻¹. This means that G121.31 + 0.64 is likely to be gestating intermediate-mass stars. We also found some outflow evidence here. HCO⁺ lines show both blue and red wings and the integrated intensity map of the line wings shows a northeast–southwest outflow direction (as shown in Figure 5), which is consistent with the results of previous studies (e.g., Juárez et al. 2019). In addition, rich maser sources have been found in this source, including OH, H₂O, and a variety of methanol masers (6.7 GHz Class II, 44 GHz and 95 GHz Class I methanol masers; e.g., Wouterloot et al. 1993; Valdettaro et al. 2001; MacLeod et al. 1998; Gan et al. 2013; Yang et al. 2017). OH and H₂O masers can be used to trace SFRs, while Class II methanol masers are usually found close to strong radiation sources, and are associated with high-mass SFRs. This is also strong evidence that massive stars are forming in this source.

The HCO⁺ line profiles of G193.01 + 0.14 also have line wing components. Figure 5 shows the integrated intensity map of the line wings of this source. From the figure, it can be seen that the outflow direction of G193.01 + 0.14 seems to be toward the line of sight. Some infrared point sources have been found in the center of the bipolar outflow. These infrared sources may be the host source of the gas outflow and infall.

G217.30-0.05 is associated with IRAS 06567-0350. We have also found some WISE sources in the early stages of evolution, which are located around this SFR. In addition, there is an H ii region BFS56 (Gl = 21731 & Gb = −005) associated with the molecular cloud complex in this area (e.g., Blitz et al. 1982). Some previous studies have detected H₂O masers (e.g., Han et al. 1998; Valdettaro et al. 2001), but not the 95 GHz Class I methanol maser here (e.g., Gan et al. 2013). Volp et al. (2000) confirmed that IRAS 06567-0350 has very similar characteristics to other transitional YSOs. From the spectra map grids of G217.30-0.05 (Figure B1), we found that optically thick line HCO⁺ shows blue asymmetrical profiles in the northeast of the clump, while it shows red profiles in the southwest. Its HCO⁺ profile also shows blue and red wings at the HCO⁺ lines, which may indicate that this source has outflow motion. The integrated intensity map of the line wings is shown in Figure 5, with the integration range being 22.0–24.7 km s⁻¹ and 28.0–30.0 km s⁻¹. It can be seen that the direction of outflow in G217.30-0.05 is roughly northeast–southwest. There are some class 0/I YSOs in the outflow center, which may be related to outflow and infall activities in this source.

It can be seen that out of the nine confirmed infall sources with a blue asymmetric double-peaked profile, seven have outflow characteristics. The percentage of double-peaked infall sources with outflow motion relative to the total candidates is higher than expected. Moreover, six of them are associated with one or more kinds of masers. All six sources are associated with SFRs. On the other hand, no confirmed infall sources with a peak-shoulder profile or single-peaked profile have been found with outflow evidence. It cannot be ruled out whether it is caused by the weak HCO⁺ signals of these sources. Even if the effects of insufficient signal-to-noise ratios are excluded, there are still some confirmed sources that do not have outflow characteristics. These sources should be in the early stages of evolution, probably earlier than the Class 0 stage. At this time, the central object has not yet experienced molecular outflow.