Inflow Motions Associated with High-mass Protostellar Objects

High-mass stars (mass > 8 M_⊙, luminosity > 10³ L_⊙) have great physical and chemical importance in interstellar environments. They affect the energetics of galaxies via jets/outflows, strong radiation, and supernova explosions, and play a role in triggering next-generation star formation with the associated shocks. Furthermore, they enrich the surrounding systems and change chemical abundances. In spite of the importance of high-mass stars, there still remain questions about their formation process, due to difficulties arising from observational and evolutionary limitations. In order to investigate the formation of high-mass stars, it is necessary to identify sources in different evolutionary phases, especially the protostellar stage, and to understand their environments.

Gravitational collapse is the most important and fundamental key process in the early stages of star formation. Unfortunately, collapsing motion is relatively harder to observe than other motions (e.g., rotation, outflow). According to the "inside-out" collapse model and observations of low-mass protostellar cores (Shu 1977; Zhou et al. 1993; Myers et al. 1996; Evans 1999, 2003), an asymmetric double-peaked velocity profile with a higher peak at the blueshifted part (hereafter, blue profile) can be a tool for detecting inflow signatures. The blue profile depends on the optical depth of the observed line and the velocity of the inflowing material. Therefore, finding adequate inflow tracers for target sources is necessary to enhance our understanding. In this work, we study inflow motions toward high-mass star-forming regions using several molecular transitions and try to identify suitable inflow tracers.

Although inflow motion is difficult to observe, several surveys detected statistically significant evidence of inflow motions via observations of blue profiles toward low-mass star-forming regions. The molecular line surveys with various transitions indicate that active inflow motions exist regardless of the evolutionary stages of low-mass star formation (Gregersen et al. 1997, 2000; Mardones et al. 1997; Evans 2003). Therefore, gravitational collapse is a generally accepted phenomenon for low-mass star formation both theoretically and observationally.

On the other hand, inflow studies of high-mass star-forming regions toward different samples in different inflow-tracing molecular lines show inconsistent fractions of blue asymmetries (Wu & Evans 2003; Fuller et al. 2005; Purcell et al. 2006; Wyrowski et al. 2006; Wu et al. 2007; Reiter et al. 2011; He et al. 2015; Jin et al. 2016, see Section 3.1 for detailed results). Such studies are expected to give us clues for understanding the influence and importance of gravitational collapse on the formation and evolution of high-mass stars. Furthermore, they may enable us to discuss similarities between high-mass star-forming process and its low-mass counterpart. However, it is difficult not only to characterize the evolutionary stages of high-mass star-forming regions, but also to find appropriate inflow tracers. Accordingly, to understand the formation of high-mass stars there should be more comprehensive research of adequate targets, using advanced facilities.

In this study, we surveyed 82 high-mass protostellar object (HMPO) candidates in multiple molecular lines using single-dish telescopes to investigate the inflow motions via statistical analysis of the observed line spectra. We present the source selection criteria in Section 2.1 and the observational details in Section 2.2. Statistical analyses with line profiles are in Section 3.1 and identifications of inflow candidates and examinations of their characteristics are in Section 3.2. We discuss the appropriateness of determining profiles and statistics depending on sub-groups in Section 4. Finally, we conclude with a summary of the main results in Section 5.

2.1. Source Selection

2.2. Observations

We made single-point observations toward the 82 sources in up to 5 transitions, such as the HCO⁺ (1−0), HCO⁺ (3−2), HCN (3−2), H₂CO (2₁₂–1₁₁) and H¹³CO⁺ (1−0) lines. The used telescopes were the Caltech Submillimeter Observatory (CSO) 10.4 m, the Arizona Radio Observatory (ARO) 12 m, the Submillimeter Telescope (SMT) 10 m, and the Korean VLBI Network (KVN) 21 m. Table 2 summarizes the observational details, including the observed transition, frequency, telescope, main-beam size of the telescope, main-beam efficiency of the telescope, velocity resolution, and number of observed sources.

Table 2.  Summary of the Observations

Observed	Frequency		θmb		$\bigtriangleup v$	Number
Transition	(GHz)	Telescope	('')	ηmb	(km s−1)	of Sources
HCO+ (1−0)	89.188526	ARO 12 m	70	0.95a	0.34	60
		KVN 21 m	32	0.38	0.21	14
HCO+ (3−2)	267.557633	CSO 10.4 m	27	0.61	0.22	11
		SMT 10 m	28	0.78	0.28	32
HCN (3−2)	265.886431	CSO 10.4 m	27	0.61	0.22	48
H2CO (212–111)	140.839515	ARO 12 m	44	0.80a	0.21	52
		KVN 21 m	24	0.27	0.27	19
H13CO+ (1−0)	86.754330	ARO 12 m	72	0.95a	0.35	45
		KVN 21 m	32	0.38	0.22	30

Note.

^aCorrected main-beam efficiency ${\eta }_{\mathrm{mb}}^{* }$ defined as ${T}_{\mathrm{mb}}={T}_{{\rm{R}}}^{* }$/${\eta }_{\mathrm{mb}}^{* }$, where T_mb is the main-beam brightness temperature and ${T}_{{\rm{R}}}^{* }$ is the corrected radiation temperature (see Mangum 2000).

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2.2.1. CSO 10.4 m Observations

We used the CSO telescope to survey 48 sources in the HCN (3−2) line and 11 sources in the HCO⁺ (3−2) line. The observations were undertaken in 2005 October. The system temperatures ranged between 350 and 500 K. We employed the 50 MHz bandwidth acousto-optical spectrometer (AOS) with 1024 channels as the backend and obtained typical rms noise levels (${T}_{{\rm{A}}}^{* }$) of 0.17 K and 0.27 K at a velocity resolution of 0.22 km s⁻¹ after smoothing for HCN (3−2) and HCO⁺ (3−2), respectively.

2.2.2. ARO 12 m and SMT Observations

We surveyed 60, 52, and 45 sources in the HCO⁺ (1−0), H₂CO (2₁₂–1₁₁), and H¹³CO⁺ (1−0) lines, respectively, using the older-generation 12 m telescope. The backends were filterbanks with 256 channels and a bandwidth of 25.6 MHz (100 kHz resolution). The system temperatures were around 350 K at ∼89 GHz and 400 K at 140 GHz. The receivers were dual polarization, single-sideband SIS systems where the image rejection was typically 20 dB, obtained by tuning the mixer backshort. The observed temperatures were obtained on the ${T}_{{\rm{R}}}^{* }$ scale (Mangnum 2000). The rms noise levels were 0.07 K at ∼0.34 km s⁻¹ resolution and 0.08 K at 0.21 km s⁻¹ resolution for ∼89 and 140 GHz, respectively.

We also surveyed 32 sources in the HCO⁺ (3−2) line using the SMT. The 64 MHz filterbanks with 256 channels were used with a spectral resolution of 250 kHz. The system temperatures were around 900 K. The single polarization receiver in this case utilized the ALMA Band 6 sideband-separating SIS mixers. The observed temperatures were obtained on the ${T}_{{\rm{A}}}^{* }$ scale. The rms noise level was 0.12 K at a resolution of 0.28 km s⁻¹. These observations were all conducted in 2006 June.

2.2.3. KVN 21 m Observations

We observed 14, 19, and 30 sources in the HCO⁺ (1−0), H₂CO (2₁₂–1₁₁), and H¹³CO⁺ (1−0) lines, respectively, using the KVN 21 m telescopes at the Yonsei and Tamna stations (Kim et al. 2011). The observations were performed in 2014 May and June, 2015 February, and 2016 June. The system temperatures usually ranged between 200 and 300 K. The backends were the digital spectrometers with 4096 channels and a bandwidth of 64 MHz each. The noise levels (${T}_{{\rm{A}}}^{* }$) were typically 0.04, 0.06, and 0.02 K at velocity resolutions of 0.21, 0.27, and 0.22 km s⁻¹ after smoothing for the HCO⁺ (1−0), H₂CO (2₁₂–1₁₁), and H¹³CO⁺ (1−0) transitions, respectively, with two exceptions. The velocity resolution was 0.43 km s⁻¹ for IRAS 05137+3919 and IRAS 05345+3157 in the H¹³CO⁺ (1−0).

3.1. Line Asymmetries

Mardones et al. (1997) proposed a dimensionless parameter δv to quantify the asymmetry of the observed optically thick line profiles: $\delta v=({v}_{\mathrm{thick}}-{v}_{\mathrm{thin}})/\bigtriangleup {v}_{\mathrm{thin}}$. Here, v_thin and v_thick are the peak velocities of the optically thin and thick lines, respectively, and $\bigtriangleup {v}_{\mathrm{thin}}$ is the full width at half maximum (FWHM) of the optically thin line. This parameter has been generally used in previous inflow studies of low- and high-mass star-forming regions. The v_thick is directly obtained from the observed profile, while v_thin and $\bigtriangleup {v}_{\mathrm{thin}}$ are measured by Gaussian fitting to the observed profile. The optically thin line used in this study is the H¹³CO⁺ (1−0) line. Table 3 presents the determined parameters for the optically thin and thick lines. In order to confirm that H¹³CO⁺ (1−0) line emission is optically thin, we derived the peak optical depth, τ_thin, using the following equations:

$$\begin{eqnarray}&&{\tau }_{\mathrm{thin}}=-\mathrm{ln}\left[1-\displaystyle \frac{{T}_{\mathrm{thin}}}{({T}_{\mathrm{ex}}-{J}_{\nu }({T}_{\mathrm{bg}}))}\right],\end{eqnarray} \tag{ 1 }$$

and

$$\begin{eqnarray}&&{J}_{\nu }(T)=\displaystyle \frac{h\nu }{k}\displaystyle \frac{1}{({e}^{h\nu /{kT}}-1)}.\end{eqnarray} \tag{ 2 }$$

Here, T_thin is the brightness temperature of the optically thin line, H¹³CO⁺ (1−0) in this work, and T_bg is the background brightness temperature, which is assumed to be 2.73 K. We assumed that the HCO⁺ (1−0) line is optically thick (1 − e^−τ ≈ 1) and that both HCO⁺ (1−0) and H¹³CO⁺ (1−0) lines arise from the same volume with the same excitation temperature, T_ex. The excitation temperature can be calculated from the equation

$$\begin{eqnarray}&&{T}_{\mathrm{ex}}=\displaystyle \frac{h\nu }{k}{\left[\mathrm{ln}\left(1+\displaystyle \frac{(h\nu /k)}{{T}_{\mathrm{thick}}+{J}_{\nu }({T}_{\mathrm{bg}})}\right)\right]}^{-1},\end{eqnarray} \tag{ 3 }$$

where T_thick is the brightness temperature of the optically thick line, HCO⁺ (1−0). Table 3 lists the estimated optical depths of the H¹³CO⁺ (1−0) line emission in the second column. The values range from 0.04 to 0.36, with an average value of 0.13. Thus, the H¹³CO⁺ (1−0) line emission seems to be optically thin enough to measure the systemic velocity and the velocity dispersion of the target clumps. The above assumption of the same emitting volume and excitation temperature for the HCO⁺ and H¹³CO⁺ lines may be questionable because of different optical depths. That makes the two lines trace different depths of the clump and hence different volumes. However, the H¹³CO⁺ line seems to be practically the best choice because other molecular lines might trace more different volumes.

Table 3.  Line Velocities and Asymmetry Parameters

IRAS	H13CO+ (1–0)			vthicka				δv				Profile
Name	τthinb	v $({v}_{\mathrm{err}})$ a	$\bigtriangleup v(\bigtriangleup {v}_{\mathrm{err}}$)a	L1c	L2c	L3c	L4c	L1	L2	L3	L4	L1	L2	L3	L4	${v}_{\mathrm{in}}$ a
00117+6412	0.09	−36.21 (0.11)	2.32 (0.30)	−35.46	−36.44	−35.63	−36.20	0.32	−0.10	0.25	0.00	R	N	N	N	⋯
$00420+{5530}^{* }$	0.05	−51.44 (0.21)	1.41 (0.55)	−52.04	−51.34	−51.71	−51.80	−0.43	0.07	−0.20	−0.26	B	N	N	B	0.50
04579+4703*	0.18	−16.70 (0.08)	1.43 (0.20)	−16.67	−16.55	−17.32	⋯	0.02	0.11	−0.44	⋯	N	N	B	⋯	⋯
05137+3919*	0.05	−25.32 (0.16)	1.46 (0.31)	−26.58	−25.20	−25.28	−25.27	−0.86	0.08	0.03	0.04	B	N	N	N	0.35
05168+3634	0.24	−15.15 (0.06)	1.18 (0.18)	−15.68	⋯	⋯	−14.73	−0.45	⋯	⋯	0.36	B	⋯	⋯	R	⋯
05274+3345*	0.21	−3.36 (0.04)	2.49 (0.08)	−4.47	−3.77	−3.63	−4.00	−0.45	−0.16	−0.11	−0.26	B	N	N	B	0.48
05345+3157*	⋯	−18.16 (0.17)	1.99 (0.33)	⋯	⋯	⋯	−18.80	⋯	⋯	⋯	−0.32	⋯	⋯	⋯	B	⋯
05358+3543	0.07	−17.31 (0.04)	2.38 (0.10)	−17.84	−14.96	−14.21	−18.00	−0.22	0.99	1.30	−0.29	N	R	R	B	⋯
05373+2349	0.32	2.23 (0.03)	1.66 (0.08)	1.95	⋯	2.79	2.00	−0.17	⋯	0.34	−0.14	N	⋯	R	N	⋯
05391−0152	0.16	9.91 (0.04)	1.21 (0.10)	9.16	10.89	11.03	10.53	−0.62	0.81	0.93	0.52	B	R	R	R	⋯
05393−0156	0.09	10.13 (0.07)	2.06 (0.16)	9.16	11.10	11.03	10.96	−0.47	0.47	0.44	0.40	B	R	R	R	⋯
05490+2658*	0.13	0.55 (0.07)	1.24 (0.19)	0.11	⋯	0.33	0.73	−0.36	⋯	−0.18	0.15	B	⋯	N	N	0.50
05553+1631	0.12	5.65 (0.05)	1.90 (0.12)	6.37	⋯	5.29	5.47	0.38	⋯	−0.19	−0.10	R	⋯	N	N	⋯
06053−0622	0.07	10.49 (0.08)	2.64 (0.22)	9.83	10.45	10.59	9.89	−0.25	−0.01	0.04	−0.23	N	N	N	N	⋯
06056+2131	0.10	2.54 (0.03)	2.22 (0.06)	2.53	2.81	⋯	2.73	0.00	0.12	⋯	0.09	N	N	⋯	N	⋯
06061+2151	0.13	−0.88 (0.08)	2.02 (0.19)	−1.05	⋯	−0.02	−1.00	−0.08	⋯	0.43	−0.06	N	⋯	R	N	⋯
06084−0611	0.13	11.59 (0.06)	1.98 (0.14)	11.85	11.10	11.25	11.60	0.13	−0.25	−0.17	0.00	N	N	N	N	⋯
06103+1523	0.09	15.57 (0.05)	1.87 (0.11)	16.37	⋯	16.76	16.27	0.43	⋯	0.64	0.37	R	⋯	R	R	⋯
06105+1756*	0.04	7.78 (0.14)	1.32 (0.36)	7.24	⋯	7.46	⋯	−0.41	⋯	−0.24	⋯	B	⋯	N	⋯	0.28
06382+0939	0.33	5.22 (0.02)	2.13 (0.06)	4.70	⋯	4.94	5.31	−0.24	⋯	−0.13	0.04	N	⋯	N	N	⋯
06584−0852	⋯	⋯(⋯)	⋯(⋯)	41.13	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯
07299−1651	0.08	17.18 (0.11)	1.78 (0.30)	17.48	17.22	17.77	17.34	0.17	0.02	0.34	0.09	N	N	R	N	⋯
07427−2400*	0.12	67.82 (0.25)	4.88 (0.58)	66.13	67.22	69.06	68.67	−0.35	−0.12	0.25	0.17	B	N	N	N	0.42
17417−2851*	0.08	−5.33 (0.17)	2.77 (0.42)	−6.44	−5.46	−6.30	−6.13	−0.40	−0.05	−0.35	−0.29	B	N	B	B	0.68
17450−2742	⋯	⋯(⋯)	⋯(⋯)	−16.06	−15.64	⋯	−15.73	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯
17504−2519*	0.18	12.65 (0.06)	1.38 (0.13)	11.56	11.70	12.97	12.08	−0.79	−0.69	0.23	−0.42	B	B	N	B	1.26
17527−2439	0.17	13.52 (0.13)	2.21 (0.35)	14.04	⋯	⋯	13.95	0.24	⋯	⋯	0.19	N	⋯	⋯	N	⋯
18014−2428	⋯	⋯(⋯)	⋯(⋯)	12.67	12.64	⋯	12.39	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯
18018−2426	0.07	10.92 (0.08)	1.92 (0.19)	10.67	11.48	⋯	10.82	−0.13	0.29	⋯	−0.05	N	R	⋯	N	⋯
18024−2119	⋯	0.39 (0.05)	2.14 (0.11)	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯
18089−1732	0.21	33.41 (0.13)	3.40 (0.30)	35.43	⋯	29.75	34.35	0.59	⋯	−1.08	0.28	R	⋯	B	R	⋯
18134−1942	0.19	10.38 (0.05)	1.70 (0.11)	11.00	10.92	11.10	10.61	0.37	0.32	0.43	0.14	R	R	R	N	⋯
18144−1723	0.08	48.23 (0.16)	3.00 (0.37)	48.81	48.84	50.57	48.47	0.19	0.20	0.78	0.08	N	N	R	N	⋯
18151−1208	0.06	32.96 (0.16)	2.96 (0.42)	32.63	32.94	⋯	32.69	−0.11	−0.01	⋯	−0.09	N	N	N	⋯
18159−1550	0.14	59.21 (0.12)	2.86 (0.31)	60.88	59.56	60.58	60.23	0.58	0.12	0.48	0.36	R	N	R	R	⋯
18159−1648	0.24	22.38 (0.07)	3.43 (0.15)	24.62	21.68	25.39	23.06	0.65	−0.20	0.88	0.20	R	N	R	N	⋯
18162−1612	0.06	61.85 (0.14)	1.73 (0.31)	61.63	⋯	⋯	61.69	−0.12	⋯	⋯	−0.09	N	⋯	⋯	N	⋯
18236−1205*	0.24	26.90 (0.12)	3.20 (0.26)	25.02	⋯	⋯	25.67	−0.59	⋯	⋯	−0.38	B	⋯	⋯	B	1.65
18256−0742*	0.15	36.82 (0.10)	1.27 (0.21)	36.20	⋯	⋯	35.96	−0.49	⋯	⋯	−0.68	B	⋯	⋯	B	0.40
18258−0737	0.05	37.27 (0.40)	2.93 (1.03)	38.40	⋯	38.78	38.43	0.39	⋯	0.52	0.40	R	⋯	R	R	⋯
18316−0602	0.26	42.46 (0.07)	3.38 (0.20)	41.36	42.06	44.71	41.88	−0.32	−0.12	0.67	−0.17	B	N	R	N	⋯
18317−0513	0.08	42.27 (0.08)	1.33 (0.22)	42.03	42.06	⋯	42.09	−0.18	−0.16	⋯	−0.13	N	N	N	⋯
18360−0537*	0.10	101.71 (0.71)	4.16 (0.37)	100.45	101.04	99.71	101.13	−0.30	−0.16	−0.48	−0.14	B	N	B	N	2.00
18372−0541	⋯	22.93 (0.11)	2.70 (0.25)	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯
18396−0431	0.14	97.22 (0.08)	1.80 (0.18)	98.48	⋯	⋯	⋯	0.70	⋯	⋯	⋯	R	⋯	⋯	⋯	⋯
18488+0000	0.33	83.15 (0.06)	2.56 (0.16)	81.48	82.78	84.84	81.67	−0.65	−0.15	0.66	−0.58	B	N	R	B	⋯
18507+0121	0.36	57.46 (0.07)	4.06 (0.17)	59.96	58.64	⋯	56.99	0.62	0.29	⋯	−0.11	R	R	⋯	N	⋯
18511+0146	0.18	57.70 (0.13)	2.97 (0.30)	59.99	⋯	⋯	57.55	0.77	⋯	⋯	−0.05	R	⋯	⋯	N	⋯
18527+0301*	0.16	76.05 (0.10)	1.88 (0.26)	75.50	⋯	⋯	75.47	−0.30	⋯	⋯	−0.31	B	⋯	⋯	B	0.80
18532+0047	0.24	58.77 (0.07)	2.50 (0.16)	58.95	⋯	⋯	59.27	0.07	⋯	⋯	0.20	N	⋯	⋯	N	⋯
18565+0349*	0.10	91.42 (0.13)	2.26 (0.29)	90.76	91.18	⋯	91.49	−0.29	−0.11	⋯	0.03	B	N	⋯	N	1.40
18566+0408	0.13	85.52 (0.21)	3.72 (0.52)	82.58	⋯	⋯	87.34	−0.79	⋯	⋯	0.49	B	⋯	⋯	R	⋯
18567+0700	0.20	29.52 (0.05)	1.20 (0.14)	29.57	⋯	⋯	29.29	0.04	⋯	⋯	−0.18	N	⋯	⋯	N	⋯
19045+0518	0.10	53.72 (0.10)	1.88 (0.41)	53.43	⋯	53.26	53.49	−0.16	⋯	−0.24	−0.12	N	⋯	N	N	⋯
19088+0902	0.17	59.92 (0.19)	2.00 (0.46)	61.45	⋯	57.73	59.28	0.77	⋯	−1.10	−0.32	R	⋯	B	B	⋯
19282+1814*	0.11	24.18 (0.09)	0.95 (0.24)	23.60	⋯	⋯	23.78	−0.61	⋯	⋯	−0.42	B	⋯	⋯	B	0.23
19368+2239*	0.10	36.51 (0.12)	2.29 (0.28)	36.23	35.70	35.68	36.29	−0.12	−0.36	−0.36	−0.10	N	B	B	N	⋯
20050+2720	0.24	6.10 (0.07)	1.98 (0.18)	4.22	5.42	7.20	5.23	−0.95	−0.34	0.56	−0.44	B	B	R	B	⋯
20056+3350*	0.09	9.33 (0.17)	2.05 (0.46)	9.57	8.42	8.12	8.87	0.12	−0.44	−0.59	−0.22	N	B	B	N	⋯
20062+3550*	0.11	0.81 (0.14)	1.31 (0.33)	0.77	1.02	0.88	0.28	−0.03	0.16	0.06	−0.40	N	N	N	B	⋯
20106+3545*	0.08	8.08 (0.09)	1.64 (0.23)	7.63	⋯	⋯	7.91	−0.27	⋯	⋯	−0.11	B	⋯	⋯	N	0.25
20126+4104	0.10	−3.36 (0.07)	2.29 (0.18)	−3.40	−3.20	−3.01	−3.58	−0.01	0.07	0.16	−0.09	N	N	N	N	⋯
20188+3928	0.18	1.77 (0.09)	2.08 (0.19)	2.68	2.20	2.76	2.46	0.43	0.21	0.48	0.33	R	N	R	R	⋯
20220+3728*	0.04	−1.89 (0.23)	3.40 (0.56)	−2.87	−3.68	−4.20	−2.81	−0.29	−0.53	−0.68	−0.27	B	B	B	B	0.47
20227+4154	0.21	5.84 (0.07)	1.43 (0.15)	6.40	⋯	⋯	5.58	0.39	⋯	⋯	−0.18	R	⋯	⋯	N	⋯
20278+3521	0.05	−3.99 (0.18)	2.71 (0.44)	−4.67	⋯	⋯	−4.61	−0.25	⋯	⋯	−0.23	N	⋯	⋯	N	⋯
20286+4105*	0.06	−3.70 (0.12)	3.89 (0.31)	−4.30	−4.78	−4.73	−4.97	−0.16	−0.28	−0.27	−0.33	N	B	B	B	⋯
20333+4102*	0.07	8.64 (0.05)	1.25 (0.12)	8.57	8.26	8.57	8.51	−0.05	−0.30	−0.05	−0.10	N	B	N	N	⋯
21078+5211	⋯	⋯(⋯)	⋯(⋯)	−6.60	−6.80	−6.88	−6.42	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯
21391+5802*	0.27	0.65 (0.04)	1.97 (0.11)	−0.44	−0.30	−0.16	0.08	−0.55	−0.48	−0.41	−0.29	B	B	B	B	1.10
21519+5613	⋯	⋯(⋯)	⋯(⋯)	−62.70	−63.06	−62.68	−62.88	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯
22172+5549	0.09	−43.56 (0.10)	2.78 (0.28)	−43.63	−43.38	−43.15	−43.48	−0.03	0.06	0.15	0.03	N	N	N	N	⋯
22198+6336	0.11	−11.00 (0.13)	1.48 (0.25)	−11.60	−11.52	−9.93	−11.42	−0.41	−0.35	0.72	−0.28	B	B	R	B	⋯
22267+6244	0.16	−1.32 (0.07)	1.51 (0.15)	−2.00	−1.92	0.07	−1.39	−0.45	−0.40	0.92	−0.05	B	B	R	N	⋯
22272+6358*	0.14	−9.95 (0.06)	1.11 (0.13)	−10.40	−10.88	−10.54	−10.01	−0.41	−0.84	−0.53	−0.05	B	B	B	N	0.47
22308+5812	0.04	−52.29 (0.23)	5.08 (0.66)	−53.41	⋯	⋯	−52.93	−0.22	⋯	⋯	−0.13	N	⋯	⋯	N	⋯
22506+5944	0.19	−51.46 (0.05)	2.08 (0.14)	−51.33	−50.52	−49.51	⋯	0.06	0.45	0.94	⋯	N	R	R	⋯	⋯
23026+5948	0.04	−51.10 (0.12)	1.77 (0.29)	−51.27	⋯	⋯	−51.42	−0.10	⋯	⋯	−0.18	N	⋯	⋯	N	⋯
23133+6050	0.04	−56.55 (0.08)	2.61 (0.23)	−56.48	⋯	⋯	−56.27	0.03	⋯	⋯	0.11	N	⋯	⋯	N	⋯
23140+6121*	0.15	−51.27 (0.08)	1.77 (0.17)	−52.00	⋯	⋯	−51.61	−0.41	⋯	⋯	−0.19	B	⋯	⋯	N	1.47
23314+6033	0.06	−45.24 (0.14)	2.41 (0.40)	−45.23	⋯	⋯	−45.53	0.00	⋯	⋯	−0.12	N	⋯	⋯	N	⋯
23545+6508*	0.14	−18.47 (0.06)	1.15 (0.16)	−19.58	−18.54	−18.76	−18.72	−0.96	−0.06	−0.26	−0.22	B	N	B	N	0.23

Notes.

^aIn units of km s⁻¹. ^bOptical depth for the H¹³CO⁺ (1-0) line. ^cL1: HCO⁺ (1–0), L2: HCO⁺ (3–2), L3: HCN (3–2), L4: H₂CO (2₁₂–1₁₁).

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As in most previous inflow studies (e.g., Gregersen et al. 1997; Mardones et al. 1997; Fuller et al. 2005), we categorized the optically thick line profiles into three types on the basis of the measured value of δv: blue (B) for $\delta v\lt -0.25$, red (R) for $\delta v\gt 0.25$, neither (N) for −0.25 ≤ δv ≤ 0.25. Figure 1 displays sample HCO⁺ (1−0) spectra with B, N, and R profiles, along with the H¹³CO⁺ (1−0) spectra. We counted the numbers of B, R, and N profiles (N_Blue, N_Red, N_Neither, and N_Total ≡ N_Blue+N_Red+N_Neither) for each optically thick line. The detection rates of blue profiles D_Blue (=N_Blue/N_Total) are 0.39, 0.26, 0.25 and 0.25, and those of red profiles D_Red (=N_Red/N_Total) are 0.19, 0.16, 0.40, and 0.13 in the HCO⁺ (1−0), HCO⁺ (3−2), HCN (3−2), and H₂CO (2₁₂–1₁₁) lines, respectively (Table 4). Table 3 presents the estimated values of δv and identified profile types for each source in the individual optically thick lines, and Figure 2 exhibits histograms of δv for each transition.

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Table 4.  Blue Excess Statistics for the Entire Sample

Transition	NBlue	NRed	NTotal	DBlue	DRed	E	P
HCO+ (1–0)	29	14	74	0.39	0.19	0.20	0.016
HCO+ (3–2)	11	7	43	0.26	0.16	0.09	0.240
HCN (3–2)	12	19	48	0.25	0.40	−0.15	0.925
H2CO (212–111)	18	9	71	0.25	0.13	0.13	0.061

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We are able to quantify the dominance of blue profile with respect to red profile by the non-dimensional parameter, so-called blue excess (E), introduced by Mardones et al. (1997):

$$\begin{eqnarray}&&E=({N}_{\mathrm{Blue}}-{N}_{\mathrm{Red}})/{N}_{\mathrm{Total}}.\end{eqnarray} \tag{ 4 }$$

Table 4 summarizes our statistical analysis results in four optically thick molecular lines. As mentioned above, the H¹³CO⁺ (1−0) line is used as an optically thin tracer to determine v_thin and $\bigtriangleup {v}_{\mathrm{thin}}$. We found 29 blue profiles and 14 red profiles in the HCO⁺ (1−0) line for a sample of 74 sources. The blue excess E for the HCO⁺ (1−0) line is 0.20. This value is in good agreement with the estimate (E = 0.22) obtained by He et al. (2015) for 201 HMPOs in the same transition, and is slightly higher than the estimates of E = 0.15 acquired by Fuller et al. (2005) for 68 HMPOs and E = 0.17 by Wu et al. (2007) for 29 HMPOs. We found less significant blue excesses of E = 0.09 and E = 0.13 in the HCO⁺ (3−2) and H₂CO (2₁₂–1₁₁) lines, respectively. For comparison, Fuller et al. (2005) obtained E = 0.04 in the HCO⁺ (3−2) for 24 sources and E = 0.19 in the H₂CO (2₁₂–1₁₁) for 64 sources. On the other hand, we found 12 blue and 19 red profiles in the HCN (3−2) line for 48 sources. Thus, our sample shows a quite significant red excess of E = −0.15, suggesting that the HCN (3−2) line traces other dynamics rather than inflows in HMPOs, such as outflow, rotation, and turbulent motions. In contrast, Wu & Evans (2003) measured a blue excess of 0.21 in the HCN (3−2) for 28 UCH iis and compact H ii regions, which are mostly more evolved and luminous than the sources in our sample (see Section 4). The molecular tracer appears to have suitable optical depth and critical density for their sample but this is not the case for most sources in our sample.

In order to get rid of the statistical uncertainty coming from the use of different beam sizes of the telescopes, we also obtained statistics of line parameters separately for the ARO 12 m and the KVN 21 m. That is, we calculated blue excesses of the HCO⁺ (1−0) line using the H¹³CO⁺ (1−0) line as an optically thin line observed by the same telescope. In case of the ARO 12 m, the numbers of blue and red profiles are 19 and 9, respectively, out of 45 total sources, which leads to a blue excess of E = 0.22. On the other hand, in the case of KVN 21 m, the numbers of blue and red profiles are 5 and 2, respectively, for a total of 14 sources, which leads to a blue excess of E = 0.21. However, the blue excess of the latter case has a statistical weakness arising from the small number of sources. If we combine two observations, the numbers of blue and red profiles are 24 and 11, respectively, for a total of 59 sources and hence the blue excess is E = 0.22. Thus, our statistics for the entire sample of 74 sources (E = 0.20) obtained by the combination of the HCO⁺ (1−0) and H¹³CO⁺ (1−0) lines detected by different telescopes, seems to be acceptable.

To evaluate the probability that the measured blue excess is produced by coincidence from a random distribution with the same numbers of blue and red profiles, we performed a binomial test (Fuller et al. 2005; Wu et al. 2007; He et al. 2015; Jin et al. 2016) defined as

$$\begin{eqnarray}&&P(X\geqslant V)=\displaystyle \sum _{x=V}^{N}\displaystyle \frac{N!}{x!(N-x)!}{p}^{x}{(1-p)}^{(N-x)}.\end{eqnarray} \tag{ 5 }$$

Here, N is the number of performances, V is the the number of successes, and p is the probability of occurrence in a single independent performance. In our case, N is the total number of blue and red profiles and V is the number of blue profiles. Table 4 also lists the derived values of P. The P value for the HCO⁺(1–0) line is 0.016, which implies that the estimated blue excess (E = 0.20) is very unlikely to be generated by chance from an even distribution.

3.2. Inflow Candidates

Our sample is divided into two groups (Low and High) in the IRAS color–color diagram of [25–12] and [60–12], as discussed in Section 2.1. The sources in the High group are believed to be in a relatively more evolved stage than those of the Low group, although the two groups have similar distributions of infrared luminosities (Palla et al. 1991; Molinari et al. 1996, 1998). We derive blue excesses separately for the Low and High groups. Table 5 presents the statistical results in all the optically thick transitions (see also Figure 2) and Figure 3 shows the distributions of blue- and red-profile sources in the two groups on the color–color diagram. In comparison with the High group, the Low group shows higher blue excesses in the HCO⁺ (1−0) and H₂CO (2₁₂–1₁₁) lines but lower excesses in the HCO⁺ (3−2) and HCN (3−2) lines. In the case of the Low group, however, it should be noted that only the HCO⁺ (1−0) and H₂CO (2₁₂–1₁₁) lines have statistically sufficient numbers of sources, so the blue excess estimates of the HCO⁺ (3−2) and HCN (3−2) lines may not be meaningful. Thus, further observations for a substantially large number of sources are required for the latter transitions to obtain more significant results for evolutionary study of inflow.

There are very few previous studies investigating the evolutionary effect in the inflow statistics, the results of which are inconclusive. Wu et al. (2007) reported a higher blue excess for 12 UCH iis (E = 0.58) than 29 HMPOs (E = 0.17) in the HCO⁺ (1−0) transition. Jin et al. (2016) also found a similar increasing trend in the HCN (1-0) line for their sample consisting of 26 HMPOs (E = 0.15) and 23 UCH iis (E = 0.30), although they obtained the highest blue excess (E = 0.42) for 12 high-mass prestellar clumps. On the contrary, He et al. (2015) found a decreasing evolutionary trend of blue excess in the HCO⁺ (1−0) line for a much larger sample: E = 0.29 for 84 prestellar clumps, 0.22 for 201 HMPOs, −0.11 for 79 UCH iis. Our result is consistent with that of He et al. (2015) although the decreasing trend is less prominent. This difference may be because their sample contains many more evolved UCH iis than High sources in our sample.

Fuller et al. (2005) surveyed 77 submillimeter clumps associated with HMPOs in multiple molecular lines for an extensive inflow study toward high-mass star-forming regions. The blue excesses were derived to be E = 0.15 and E = 0.19 for the HCO⁺ (1−0) and H₂CO (2₁₂–1₁₁) lines, respectively. When they considered only sources with distances ≤6 kpc in order to avoid beam dilution effects due to large distances of the sources, the excesses considerably increased and became comparable to the values estimated for low-mass star-forming regions, E ≃ 0.3 (Evans 2003). However, we do not find such a trend in the same analysis for our sample. For instance, the blue excesses for the HCO⁺ (1−0) and H₂CO (2₁₂–1₁₁) lines are E = 0.20 and E = 0.13 for the entire sample and E = 0.12 and E = 0.16 for the 65 and 63 sources within 6 kpc, respectively. This inconsistent result may be caused by large uncertainty in the determination of the distances to the sources. The vast majority of the sources in both our sample and Fuller et al.'s (2005) are located in the inner Galaxy, but the distance ambiguity is not resolved for most of them.

As noted in Section 3.1, Wu & Evans (2003) found that the HCN (3−2) line shows a significant blue excess (E = 0.21) for their sample, thus it is useful for tracing inflow motions toward UCH iis and compact H ii regions. However, we find that the transition is a much worse tracer of inflow motions toward HMPOs in our sample than the HCO⁺ (1−0) line. It is worthwhile to note that their sources are more massive and luminous, as well as more evolved than ours: median mass of 8.9 × 10² M_⊙ and median L_IR of 1.06 × 10⁵ L_⊙ (Wu & Evans 2003) versus median L_IR of 1.11 × 10⁴ L_⊙. In fact, the critical density of the HCN (3−2) transition is two orders of magnitude larger than that of the HCO⁺ (1−0) transition (Shirley 2015). Therefore, we interpret that the HCO⁺ (1−0) line, which has a relatively low critical density, is better suited for investigating inflow motions in our sources than the HCN (3−2) line. This seems to be consistent with the previous suggestion that the characteristic blue profile will show up only if the critical density of the molecular tracer is suitable for the optical depth of the target (Myers et al. 1996; Wu & Evans 2003).

Although the blue profile has been widely accepted as an indicator of infall motions, as noted earlier, it is sometimes tricky to interpret the signature due to other kinematics, especially for massive star-forming regions that are much more turbulent and distant than low-mass star-forming regions. Alternatively, the redshifted absorption feature can be used to study inflow motions in massive star-forming regions because they are usually bright radio and infrared sources. For example, Wyrowski et al. (2012, 2016) observed 11 massive molecular clumps in the NH₃ 3₂₊–2_2– line at 1.81 THz using the GREAT instrument on board SOFIA (beam size = 16''). They detected redshifted NH₃ absorption features with respect to the systemic velocities toward eight sources, and derived the velocity shifts to be 0.3–2.9 km s⁻¹. Their measurements are roughly in agreement with the estimated infall velocities of this study (see Section 3.2). These two kinds of studies utilizing blue profiles and redshifted absorption features would complement each other.

We performed a survey of one optically thin and up to four optically thick molecular lines toward 82 HMPO candidates to understand gravitational collapse in the early stages of high-mass star formation. To quantify the asymmetries of the optically thick line profiles, we derived δv's of the individual sources in each transition and estimated the blue excess for our sample with δv = ±0.25 as threshold values. The main results are summarized as follows:

1. We obtained a statistically significant blue excess in the HCO⁺ (1−0) line (E = 0.20), but nonsignificant excesses in the HCO⁺ (3−2) and the H₂CO (2₁₂–1₁₁) lines (E = 0.09 and E = 0.13, respectively). The HCN (3−2) line shows a negative blue excess of E = −0.15. The HCO⁺ (1−0) line thus seems to be the suitable tracer of inflow motions in high-mass star-forming regions, as some previous studies proposed (e.g., Fuller et al. 2005; Wu et al. 2007). On the contrary, the other lines do not appear to have a suitable opacity and critical density for the appearance of blue profile toward most sources in our sample, and may be affected by dynamics other than inflow, such as outflow, rotation, and turbulent motions.

2. We found 27 inflow candidates by adopting the criteria of Fuller et al. (2005), namely, one or more blue profiles and no red profile. All of them are newly identified inflow candidates except one (IRAS 05490+2658), which had been classified by Fuller et al. (2005) as an inflow candidate. We derived inflow velocities for 20 out of the 27 candidates using the two-layer radiative transfer model of Myers et al. (1996). The estimated inflow velocities range between 0.23 and 2.00 km s⁻¹, with a median value of 0.49 km s⁻¹. On the other hand, there are 18 sources that have red profile(s) but no blue profile. They might be more affected by dynamics other than inflow motion in the observed optically thick lines.

3. The sources in our sample are all HMPO candidates but they are known to be divided into two different evolutionary stages: Low and High groups. The statistical results for the Low group show that blue excesses in the HCO⁺ (1−0) and H₂CO (2₁₂–1₁₁) lines, of which the number of both groups are statistically meaningful, are slightly higher than those for High groups. We also estimated blue excesses for a subsample of sources at relatively small (≤6 kpc) distances and obtained less significant excesses than those for the entire sample. This is not consistent with the result of Fuller et al. (2005). This discrepancy may be caused by large uncertainties in determining the distances to the sources in our sample and theirs.

We are grateful to all the staff members at KVN who helped to operate the telescope. The KVN is a facility operated by the Korea Astronomy and Space Science Institute. H.Y. and J.C.'s work is supported by the National R & D Program through the National Research Foundation of Korea (NRF), funded by the Ministry of Education (NRF-2016R1D1A1B02015014).

In this appendix, we present all the detected molecular line spectra of the individual sources. Table 3 lists detailed information on the inflow statistics of these spectra.

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