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The inflow signature toward different evolutionary phases of massive star formation

We analyzed both HCN J=1-0 and HNC J=1-0 line profiles to study the inflow motions in different evolutionary stages of massive star formation: 54 infrared dark clouds (IRDCs), 69 high-mass protostellar object (HMPOs), and 54 ultra-compact HII regions (UCHIIs). The inflow asymmetry in HCN spectra seems to be prevalent throughout all the three evolutionary phases, with IRDCs showing the largest excess in blue profile. In the case of HNC spectra, the prevalence of blue sources does not appear, excepting for IRDCs. We suggest that this line is not appropriate to trace inflow motion in evolved stages of massive star formation because the abundance of HNC decreases at high temperatures. This result spotlights the importance of considering chemistry in the dynamics study of massive star-forming regions. The fact that the IRDCs show the highest blue excess in both transitions indicates that the most active inflow occurs in the early phase of star formation, i.e., the IRDC phase rather than in the later phases. However, mass is still inflowing onto some UCHIIs. We also found that the absorption dips of the HNC spectra in 6 out of 7 blue sources are red-shifted relative to their systemic velocities. These red-shifted absorption dips may indicate global collapse candidates, although mapping observations with better resolution are needed to examine this feature in more detail.


Introduction
Massive stars are considered to be decisive players in the physical and chemical evolution of galaxies, injecting energetic feedbacks into their surroundings. In recent years, there have been many studies trying to examine the formation mechanism of high-mass stars, suggesting an evolutionary sequence of massive star formation as follows. First, the formation of massive stars begins in an infrared dark cloud (IRDC) identified as dark extinction features against the bright Galactic mid-infrared background (Egan et al. 1998;Simon et al. 2006a). Their cold ( 25 K) and dense ( 10 5 cm −3 ) properties and strong (sub)millimeter emissions (e.g., Rathborne et al. 2006) suggest the regions as ideal brithplaces of massive stars. The central condensation then begins heating its environment, evolving to become a high-mass protostellar object (HMPO). They are luminous infrared point-like sources (L bol ≥ 10 3 L ⊙ ) without associated radio continuum emission (Molinari et al. 1996(Molinari et al. , 2000Sridharan et al. 2002;Beuther et al. 2002). This protostar continues to gain mass and evolves to produce UV photons, ionizing the gas, becoming an ultracompact HII region (UCHII). UCHIIs are very small (D 0.1 pc), dense (n e 10 4 cm −3 ), and bright (EM 10 7 pc cm −6 ) ionized regions (Wood & Churchwell 1989;Kurtz et al. 1994;Kim & Koo 2001). The objects are considered to represent the childhood of HII regions.
Nevertheless, the formation mechanism for the massive stars is still in debate. There are two competing theories describing the massive star formation: turbulent core accretion and competitive accretion (Mckee & Ostriker 2007;Zinnecker & Yorke 2007;Bodenheimer 2011). In the turbulent core accretion model, high-mass cloud cores form from a much larger molecular cloud clump, which is supported by quasi-virialized turbulent flows. The material that ends up as stars can be essentially determined by the process of fragmentation of the cloud clump because the cores are almost non-interacting and the remainder of the clump seldom affects the inflowing process (McKee & Tan 2003). This scenario well explains an initial mass function similar to a core mass function, which is consistent with observations (Motte et al. 1998;Beuther & Schilke 2004;Krumholz & Tan 2007).
In the competitive accretion model, star formation is regulated by the global collapse of a much larger cloud, initially containing gas of several thousand M ⊙ . The material that ends up as stars is gathered during the star-formation process from various parts of the parent cloud. The cores compete for the remaining gas and there are strong interactions among them. This scenario predicts that massive stars form at the cluster center where more massive inflow can occur than in the outer regions (Bonnell et al. 2001;Krumholz & Bonnell 2009).
Regardless of which mechanism works, gravitational inflow is a key process to initiate star formation and to control the evolution of densities in the protostellar envelope.
Therefore, characterizing this inflow process is important for a better understanding of high-mass star formation. One observational signature of inflow motion is a 'blue profile', a general prediction for a cloud collapsing model (e.g. Shu 1977). This blue profile is an asymmetric line feature that appears in an optically thick line profile with a self-absorption dip and a blue peak stronger than a red peak. The emission of an optically thin line peaks near the absorption dip of the optically thick line.
There have been many attempts to examine the inflow signature in massive starforming regions in recent years. After Wu & Evans (2003) found statistically significant blue excess (the number of blue profile minus that of red profile in units of the total number of sample) in the blue profile in the HCN J=3-2 line toward early phase of HII regions where star-forming activity still appears, the number of studies has been increasing. For example, Reiter et al. (2011a) carried out HCO + J=3-2 line observations toward similar regions of Wu & Evans (2003). They noted that every source with the blue asymmetry in the HCO + J=3-2 line also has the blue profile in the HCN J=3-2 line, and confirmed that the HCN J=3-2 line is a better inflow tracer. Rygl et al. (2013) performed the HCO + J=1-0, 4-3, and CO J=3-2 line observations toward a sample of clumps in clouds with high extinctions, and they concluded that among the three transitions, the HCO + J=1-0 line is the most sensitive to detect inflowing motions. In addition, Fuller et al. (2005) reported significant excess of blue profiles toward HMPOs in the HCO + J=1-0, 3-2, and 4-3 transitions and H 2 CO 2 12 -1 11 line.  Molinari et al. (1996) and 54 UCHIIs from the catalogs of Wood & Churchwell (1989) and Kurtz et al. (1994). The details about selection criteria are provided in Jin et al. (2015). Consequently, our sample consists of 54 IRDCs (19 qIRDCc and 35 aIRDCc), 69 HMPOs, and 54 UCHIIs.

Observation
The J=1-0 transitions of HCN and HNC and their isotopic lines (Table 1)  The focus and pointing were adjusted by observing strong SiO maser sources every one to two hours. The system temperature ranged from 170 K to 280 K. The rest frequencies, dipole moments, and relative weights of the hyperfine components of the observed lines are summarized in Table 1. All spectra were reduced using CLASS in the GILDAS software package, and the reduced line spectra have velocity resolution of 0.21 km s −1 .

Analysis & Results
To select sources for analysis of inflow signatures, first, we used a 3σ-detection criterion According to Wu & Evans (2003), the inflow proceeds at a relatively low velocity so that its observational signature can be easily masked by other mechanism or a beam dilution effect. However, all our samples that are listed in the SCUBA legacy catalogue have larger effective radii than half of our beam size in the 850µm continuum (Di Francesco et al. 2008;Jin et al. 2015), indicating that the emission is not likely beam-diluted. The HCN and HNC line emissions are known to be well correlated with the dust emission (Wu et al. 2010; Reiter et al. 2011b).
The general signature of inflow is the so called 'blue profile'. This is an asymmetric line feature with a self-absorption dip where the blue peak is stronger than the red peak, while an optically thin line must peak near the dip of the optically thick line. In this case, the ratio of the blue peak to the red peak (T (B)/T (R)) can be one measure for the line asymmetry. However, depending on the opacity of the line, the blue profiles can show other features, for example, a single blue peak with red shoulder or a blue-skewed single peak. respectively, ranging from a clearly self-absorbed blue profile to a blue-skewed profile.
In low-mass star forming regions, Mardones et al. (1997) have suggested δv as an alternative measure of the blue profile for these blue skewed lines, which is defined as a difference between the line central velocity of an optically thick line (v thick ) and that of an optically thin line (v thin ), in units of the line width of the optically thin line (∆v thin ) A line can be identified as blue/red profile if the difference between v thick and v thin is greater than a quarter of ∆v thin . That is, a blue profile would have δv < -0.25 while a red profile would have δv > 0.25 (Mardones et al. 1997). However, it is important to note that adopting the same boundaries on δv for these high-mass objects actually demands a larger velocity shift than for the low-mass sources because the molecular lines towards these high-mass samples are significantly broader (Fuller et al. 2005).
We measured the line asymmetries of all the detected sources using the δv analysis under the assumption that both H 13 CN and HN 13 C lines are optically thin. The optical depth for each line was obtained by adopting the values of Jin et al. (2015) or by following the same analysis described therein. The resulting mean value for each line was less than An asymmetric profile may also be induced by other mechanism (e.g., rotation and outflow). If this is the case, a large sample with a random distribution of angles between the axis and the line of sight will not produce an excess of one type of profile (Wu & Evans 2003). So the concept of the "blue excess" was introduced by Mardones et al. (1997) to quantify the statistics of the line asymmetry in a survey: where N blue and N red are the numbers of blue and red profiles in the total samples (N total ).
These statistical results are summarized in Table 5.

Discussion
Values of the blue excess derived from the HCN J=1-0 line for IRDCs, HMPOs, and UCHIIs (0.42, 0.15, and 0.30, respectively) are larger than those derived from the HNC J=1-0 line (0.28, -0.07, and 0.00, respectively). In the HCN spectra, a prevalence of blue profiles relative to red profiles is found in every evolutionary stage, with the IRDCs showing the largest blue excess ( Figure 4). In contrast, the distribution of the δv derived from the HNC line is relatively centered on neutral profiles, excepting for IRDCs ( Figure 5).
We performed a binomial test and calculated the probability P that the one type of excess is induced by chance. The binomial distribution is described as follows where n is the total number of trials, k is the number of successes, and p is the success probability. In this case, n is the total number of sources, k is the number of the blue sources, and the success probability p=0.5 if the distribution shows no bias toward red or blue.
Then the possibility that the number of blue sources is equal to or higher than the observed number by chance can be calculated by adding all possibilities P (n, k, p) + P (n, k + 1, p) + ...
until k = n. A small value of P indicates that it is unlikely for a blue excess to arise by chance (Rygl et al. 2013). All resulting values of E and P are listed in Table 5. The E of the HCN line is statistically significant with a sufficiently low probability P throughout all evolutionary phases. In the case of the HNC line, in contrast, such a significant value of E appears only in the IRDC phases. The fact that the IRDCs show the highest blue excess in both inflow tracers indicates that the most active inflow occurs in the early phase of massive star formation, even though the characteristics of blue profile largely depend on the suitable combination of optical depth and critical density. It should be noted that the small sample size of HCN sources in IRDCs would bring about statistical instability in calculating blue excess E. Nevertheless, the probability P as low as 6 % indicates that the prevalence of blue profile is not likely to occur by chance. In addition, the HNC line also shows significant excess to blue in the IRDCs.

The astrochemical effect on inflow tracer
These results suggest that the HCN J=1-0 line is a better inflow tracer than the HNC J=1-0 line in massive star-forming regions. The δv values of the sources detected in both inflow tracers are plotted in Figure 6. The sources located outside the blue/red dashed lines are considered as the blue/red profiles, while the sources located inside those lines are regarded as neutral profiles. Many sources blue in HCN are neutral in HNC, but not vice versa, indicating the HNC is less appropriate to trace inflow motion. We attribute this to an astrochemical effect that reduces the abundance, hence, the optical depth of HNC. Jin et al. (2015) have found that HCN/HNC abundance ratio increases while the optical depth of HN 13 C decreases as sources evolve from IRDC to UCHIIs, even though both HCN and HNC are mainly formed in equal measure by dissociative recombination (Mendes et al. 2012). One suggested reason for this phenomenon is a neutral-neutral reaction where HNC is selectively consumed at high temperatures (T K ≥ 24 K; Hirota et al. (1998)). Hirota et al. (1998) showed that the HCN abundances in the high kinetic temperature regions (OMC-1 cores) are comparable to those in the dark cloud cores whereas the HNC abundances decrease as the temperature rises. By this astrochemical effect, the opacity of the HNC line would decrease as an object evolves so that the line cannot trace inflow motion well; an inflow profile appears in lines sufficiently opaque (Myers et al. 1996). In Figure 6, a significant number of HMPO and UCHII sources are bluer in HCN than HNC.
On the contrary, the HNC line is rather bluer in the IRDCs, and this opposite tendency is more obvious in qIRDCc than aIRDCc, supporting our scenario again. The qIRDCc is considered to be in the earlier phase (Chambers et al. 2009) and show the smaller value of the HCN/HNC abundance ratio than aIRDCc (Jin et al. 2015). This result spotlights the importance of regarding chemistry when studying dynamics of star-forming regions.

Comparison with previous studies
There have been many attempts to examine the inflow signature as mentioned in §1.
Some of those studies have suggested the HCO + J=1-0 line as the best inflow tracer in massive star-forming regions. We compare our results not only with the previous inflow surveys using the HCO + J=1-0 line but also with the study using a higher transition line of HCN.
In the HCO + J=1-0 line, IRDCs seem to undergo the most detectable active inflow process (Purcell et al. 2006;Rygl et al. 2013;He et al. 2015) whereas sources in more

Global collapse?
An interesting feature in double-peaked HNC spectra is that the absorption dips in 6 out of 7 blue sources are red-shifted relative to the systemic velocities. For the sources whose lines are strongly self-absorbed, the asymmetries of the spectra are determined using the Mapping observations with better resolution are needed to rule out this possibility.

Summary
To understand the gravitational inflow taking place in high-mass star formation, we surveyed 54 IRDC cores, 69 HMPOs, and 54 UCHIIs in the HCN J=1-0 and HNC J=1-0 lines.
(1) We found a statistically significant blue excess of the HCN line for every evolutionary phase (0.42, 0.15, and 0.30 for IRDCs, HMPOs, and UCHIIs, respectively).
These are comparable to the values derived using other inflow tracers, including HCO + J=1-0, known to be one of the best inflow tracer. This indicates the HCN line is a good tracer of gravitational inflow.
(2) With the HNC line, the blue profile appears significant only in IRDCs. We concluded that this line is not appropriate to trace inflow motion in evolved stages of massive star formation because of the HNC abundance (and thus, its optical depth) decreases at high temperatures. This result spotlights the importance of considering chemistry in studying dynamics of massive star-forming regions.
(3) The fact that IRDCs show the highest blue excess in both inflow tracers indicates that the IRDC phase is undergoing the most active inflow process. This result is consistent with a general prediction of inflow process where the younger sources are expected to be more actively inflowing onto the central source. However, the UCHIIs is also likely inflowing matters yet.