Evolutions of CH₃CN abundance in molecular clumps

Our samples are taken from Hernández-Hernández et al. (2014), who searched the literature for MSFRs in the HMC phase. Most of their sample sources are associated with UC HII regions. These sources were observed at a spatial scale of ∼0.1 pc with similar observational resolution. We matched them with Atacama Pathfinder Experiment (APEX) Telescope Large Area Survey of the Galaxy (ATLASGAL; Schuller et al. 2009) dense clump catalogue based on their positions. The survey aims to provide a large and systematic list of clumps in the early embedded evolution stage. Nine massive clumps G5.89–0.39, G8.68–0.37, G10.62–0.38, G28.20–0.04N, G45.07+0.13, G45.47+0.05, IRAS 16547–4247, IRAS 18182–1433 and IRAS 18566+0408 are selected after removing some non-matched sources. The clump distances, effective radii, masses, and bolometric luminosities are taken from Urquhart et al. (2018). For our purpose, we use L_clump/M_clump – the ratio between clump luminosity and mass – as the evolutionary indicator, and the nine targets have L_clump/M_clump ranging from 10 to 154 L_⊙/M_⊙. A summary of clump properties is presented in Table 1.

The SMA observations were performed between April 2004 and January 2009. Selected targets are listed in Table 2, where observational epoch, frequency range, and spectral resolution are included. The correlator was set to the double-sideband receiver — the lower sideband (LSB) and the upper sideband (USB), each bandwidth is about 2 GHz. The rest frequencies of CH₃CN (12_K–11_K) are covered in the LSB. Spectral resolution is 0.406 MHz (∼0.53 km s⁻¹) or 0.812 MHz (∼1.1 km s⁻¹) for different sources. The system temperatures during those observations were less than 600 K.

Calibration and imaging are performed using the MIRIAD package ² (Sault et al. 1995). Calibrators of bandpass, gain, and flux for each target are listed in Table 2. Considering the SMA monitoring of quasars, we estimate the flux uncertainty of ∼20%. We combined the continuum data from LSB and USB, the synthesized beam sizes range from 1.83'' × 0.96'' to 5.37'' × 2.66''. All the line data was regrided to a uniform spectral resolution of 0.812 MHz (∼1.1 km s⁻¹).

The continuum images, as shown in Figure 1, are constructed from line-free channels of LSB and USB in the visibility domain. The 1σ noise level of continuum is lower than 20 mJy beam⁻¹. Two-dimensional Gaussian fittings are performed to obtain peak intensities, total flux densities, and deconvolved source sizes. The relevant results are listed in Table 3.

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Table 3. Derived Parameters

Source	1.3 mm Continuum Results						Derived CH3CN parameters
	${S}_{\nu }^{{\rm{Peak}}}$	${S}_{\nu }^{{\rm{Total}}}$	${S}_{\nu }^{{\rm{Dust}}\,1}$	${\theta }_{{\rm{s}}}^{2}$	rms	${N}_{{\rm{H}}2}^{3}$	${\theta }_{{\rm{m}}}^{4}$	rms	Trot	Ntot	X	${R}_{{\rm{eff}}}^{5}$
	(Jy beam−1)	(Jy)	(Jy)	(arcsec)	(mJy beam−1)	(1024 cm−2)	(arcsec)	(mJy beam−1)	(K)	(cm−2)		(pc)
G5.89–0.39	2.23±0.07	7.50±0.29	0.91±0.46	3.90×3.24	11.26	0.70	5.4	39.02	${147}_{-12}^{+17}$	${8.63}_{-1.0}^{+1.3}$(14)	1.23±0.78(-9)	0.016±0.007
G8.68–0.37	0.22±0.01	0.38±0.01	0.25±0.01	3.67×2.20	0.58	0.39	1.2	15.65	${115}_{-17}^{+27}$	${1.88}_{-0.6}^{+0.5}$(15)	4.82±3.69(-9)	0.009±0.003
G10.62–0.38	2.98±0.12	6.86±0.37	3.78±1.02	4.33×2.96	3.21	2.16	2.4	15.47	${194}_{-24}^{+49}$	${2.51}_{-0.6}^{+0.8}$(15)	1.16±0.90(-9)	0.014±0.006
G28.20–0.04N	0.87±0.01	1.15±0.01	0.62±0.21	1.73×1.12	1.50	1.88	1.4	31.50	${240}_{-53}^{+46}$	${6.23}_{-3.6}^{+2.5}$(15)	3.31±3.25(-9)	0.005±0.002
G45.07+0.13	1.13±0.03	1.63±0.07	0.73±0.42	1.31×1.18	4.09	4.73	1.3	31.14	${143}_{-38}^{+15}$	${2.89}_{-1.4}^{+0.3}$(15)	6.10±4.74(-10)	0.026±0.011
G45.47+0.05	0.42±0.01	0.60±0.02	0.35±0.09	2.02×1.55	2.18	2.15	1.5	30.12	${77}_{-6}^{+13}$	${4.34}_{-0.9}^{+1.2}$(14)	2.01±1.47(-10)	0.083±0.037
IRAS 16547–4247	0.24±0.01	0.56±0.03	0.43±0.07	1.39×1.25	19.81	1.47	1.9	93.34	${237}_{-30}^{+31}$	${2.24}_{-0.7}^{+1.3}$(15)	1.52±1.44(-9)	0.003±0.001
IRAS 18182–1433	0.28±0.01	0.47±0.01	0.46±0.01	2.37×1.17	1.09	1.64	1.4	14.22	${145}_{-22}^{+16}$	${1.12}_{-0.2}^{+0.3}$(15)	6.82±4.63(-10)	0.005±0.002
IRAS 18566+0408	0.16±0.01	0.31±0.02	0.30±0.01	2.10×1.80	2.08	0.58	1.2	28.85	${193}_{-25}^{+37}$	${7.25}_{-2.9}^{+1.4}$(15)	1.25±0.97(-8)	0.003±0.001

Notes: ¹ ${S}_{\nu }^{{\rm{Dust}}}={S}_{\nu }^{{\rm{Total}}}$ – ${S}_{\nu }^{{\rm{free}}-{\rm{free}}}$. The free-free emission was obtained from Hernández-Hernández et al. (2014), who assumed the free-free emission is optically thin from 10 to 100 GHz and estimated the free-free emission by S_ν ∝ ν^−0.1. ² Deconvolved continuum sizes from 2D Gaussian fit. ³ H₂ column density derived from the estimated 1.3 mm dust continuum emission (${S}_{\nu }^{{\rm{dust}}}$) assuming T_dust = T_CH3CN. ⁴ Deconvolved molecular distribution sizes from 2D Gaussian fit. ⁵ Effective distance of the CH₃CN-emitting region is calculated using L = 4πR² σT⁴. T is the temperature of the CH₃CN gas and L is clump bolometric luminosity.

The 1.3 mm continuum emission may be contributed by free-free radiation and dust thermal radiation, because most HMCs harbor embedded UC H II regions. The free-free emission was obtained from Hernández-Hernández et al. (2014), who assumed the free-free emission is optically thin from 10 to 100 GHz and estimated the free-free emission by S_ν ∝ ν^−0.1. The estimated dust continuum flux of each source is listed in Table 3.

To derive CH₃CN fractional abundance, we first calculate H₂ column densities for all observed regions. Assuming that the dust emission is optically thin, H₂ column density can be obtained by (Hildebrand 1983; Lis et al. 1991):

$$\begin{eqnarray}&&{N}_{{{\rm{H}}}_{2}}=8.1\times {10}^{17}\displaystyle \frac{{e}^{h\nu /kT}-1}{Q(\nu)\Omega }\left(\displaystyle \frac{{S}_{\nu }}{{\rm{Jy}}}\right){\left(\displaystyle \frac{\nu }{{\rm{GHz}}}\right)}^{-3}({{\rm{cm}}}^{-2}),\end{eqnarray} \tag{ 1 }$$

where k and h are the Boltzmann constant and Planck constant, respectively, T is the dust temperature, Q(ν) is the grain emissivity at frequency ν, Ω is the solid angle of source, S_ν is the total integrated flux of the dust continuum. We adopt Q(ν) = 2.2 × 10⁻⁵ at 1.3 mm (β = 1.5; Lis & Goldsmith 1990; Lis et al. 1991), and the gas-to-dust ratio of 100 is used. The dust temperature can be estimated from CH₃CN rotational temperature, which will be derived in Section 3.2, assuming that dust and gas are in thermal equilibrium (Kaufman et al. 1998). The derived H₂ column densities range from 0.39 × 10²⁴ to 4.73 × 10²⁴ cm⁻², the values are listed in Table 3.

Considering an absolute flux uncertainty of ∼20% for SMA observations, dust temperature uncertainty of ∼20%, we estimate H₂ column density uncertainties of ∼50% (Sanhueza et al. 2019). The H₂ column density that we derived is comparable to the result of Hernández-Hernández et al. (2014). The difference may be caused by the fact that they used the CH₃CN temperature of hot dense component to assume the dust temperature, while we derived a relatively low CH₃CN temperature using single component fitting. The H₂ column density is sensitive to dust temperature.

The spectral lines are extracted from the continuum peak position. Their continuum-subtracted spectra are plotted with intensity in units of Kelvin in Figure 2. The CH₃CN (12_K–11_K) lines are identified following Hernández-Hernández et al. (2014).

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Spectral lines are modelled using the XCLASS package ³ (Möller et al. 2017) to derive molecular temperature and column density. The modeling parameters are source size, rotational temperature, column density, line width, and velocity offset. The source sizes are obtained by two-dimension Gaussian fits to CH₃CN (12₂–11₂) line images. The 1σ noise level in line images is lower than 100 mJy beam⁻¹. The line width and velocity offsets are obtained by Gaussian fitting. Those parameters are used as initial parameters. The optimization algorithm in MAGIX is used to explore the parameter space and minimize the χ² distribution space. The detailed fitting functions and modelling procedures are described in Möller et al. (2017), where local thermodynamical equilibrium (LTE) is assumed. The derived molecular temperature and column density are presented in Table 3.

We derive molecular fractional abundances relative to H₂ using X = N_tot/N_H2 , where N_H2 is the H₂ column density. CH₃CN rotational temperatures, column densities, and abundances are listed in Table 3. Both temperature and column density of CH₃CN obtained by our single component fitting are lower than yet comparable to that of the hot dense component and higher than that of the warm extended component obtained by Hernández-Hernández et al. (2014).

The distribution of ATLASGAL sources in the luminosity-mass (L_clump-M_clump) plane are presented in Figure 3. This type of diagram has been used in the studies of low-mass and high-mass star-forming regions (e.g., Saraceno et al. 1996; Molinari et al. 2008; Giannetti et al. 2017), and can be used as a tool for separating different evolutionary stages. Evolutionary tracks were derived by Molinari et al. (2008), vertical and horizontal arrow refer to as the accretion and the envelope dispersion phases. Three lines of constant L_clump/M_clump ratios (i.e., 1, 10 and 100 L_⊙/M_⊙) are shown in figure. Our sources at different evolutionary stages are marked in Figure 3.

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Based on previous studies, G8.68–0.37, IRAS 18182–1433, and IRAS 18566+0408 have no or weak continuum emission at centimeter observations (Longmore et al. 2011; Beuther et al. 2006; Araya et al. 2005b), and they are massive star-forming regions at an early evolutionary stage before forming a significant UC H II region. Clumps reaching L_clump/M_clump ∼ 10 L_⊙/M_⊙ are likely to stay in the transition phase between the main accretion phase and the dispersion phase (Giannetti et al. 2017). Most sources with L_clump/M_clump ≳ 30 L_⊙/M_⊙ are harboring UC H II regions (Su et al. 2009; Hunter et al. 1997; Afflerbach et al. 1994; Wood & Churchwell 1989a), especially G5.89–0.39 and G45.07+0.13 have a L_clump/M_clump in excess of 100 L_⊙/M_⊙. G5.89–0.39 is an expanding shell-like UC H II region (Wood & Churchwell 1989b). Recently, Zapata et al. (2019) have presented sensitive CO(J = 32) observations that revealed the possible presence of an explosive outflow in G5.89–0.39. G45.07+0.13 is a pair of spherical UC H II regions, these regions are interpreted as a shell generated by stellar wind (Turner & Matthews 1984). A detailed description of each source is given in Hernández-Hernández et al. (2014).

Our sources have similar masses yet different luminosity-to-mass ratios. Taking advantage of this, we propose that our sources G8.68–0.37, IRAS 18566+0408, IRAS 18182–1433, G28.200.04N, IRAS 16547–4247, G45.47+0.05, G10.62–0.38, G5.89–0.39, and G45.07+0.13 form a sequence with L_clump/M_clump ranging from 10 to 154 L_⊙/M_⊙.

In the upper left panel of Figure 4, we show the rotational temperature traced by CH₃CN gas as a function of the L_clump/M_clump. It seems that the temperature increases with L_clump/M_clump when the ratio between 10 to 40 L_⊙/M_⊙, and decreases when L_clump/M_clump is greater than 40 L_⊙/M_⊙. It is puzzling that rotational temperatures do not demonstrate a monotonic increase over the increase of L_⊙/M_⊙ ratios. One would expect, in an idealized situation, that as a massive protostar gains masses and luminosity, the protostellar heating raises temperatures of the surrounding gas. Therefore, rotational temperatures are expected to increase with L_⊙/M_⊙ ratios. This trend was observed by single dish observations (e.g., Molinari et al. 2016; Giannetti et al. 2017; Urquhart et al. 2018). In these literatures, all molecular temperatures are considered to be continuously heated up when L_clump/M_clump ≳ 10 L_⊙/M_⊙.

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Several factors may bias the data. The most direct influence on the observation results is the spatial resolution. The spatial resolution range of our nine sources is from ∼10000 to ∼20000 AU, except for IRAS 16547–4247 with ∼3000 AU. The L_clump/M_clump of IRAS 16547–4247 is 35 L_⊙/M_⊙, and it cannot result the decreasing trend of molecular temperature when L_clump/M_clump > 40 L_⊙/M_⊙. Thus the spatial dilution effect is not significant. Therefore, when L_clump/M_clump > 40 L_⊙/M_⊙, the decreasing trend of temperature is not caused by spatial resolution. The expansion of embedded UC H II regions might also affect the gas temperature. The L_clump/M_clump ∼ 10 L_⊙/M_⊙ is considered a threshold that the birth of the zero age main sequence (Urquhart et al. 2014; Molinari et al. 2016; Giannetti et al. 2017), where hydrogen burning begins, then UC H II regions start to form and disperse the parent clumps (Hoare et al. 2007). Those processes may push ISM into the outer warm envelope, resulting a cavity located in the molecular clouds (e.g., G5.89, see Fig. 1). Such an expansion of UC H II region may cause molecular temperature decrease when L_clump/M_clump ≥ 40 L_⊙/M_⊙, where dissipation may dominate in this phase (Giannetti et al. 2017).

In Figure 1, the CH₃CN emission coincides with the 1.3 mm continuum emission, viewed at our current resolution. At the same time, we noticed that CH₃CN has a relatively complicated morphology in G5.89, where multiple dust continuum regions were found (Hunter et al. 2008).

Assuming that the gas is heated by the central star, molecular temperature is determined by radiative heating, molecular effective distance relative to the central heating source can be estimated by:

$$\begin{eqnarray}&&L=4\pi {R}^{2}\sigma {T}^{4},\end{eqnarray} \tag{ 2 }$$

where R is the distance of the region with temperature T, the central source has bolometric luminosity L. We use this formula to estimate molecular effective distance R_eff, based on the bolometric luminosity of source, and on the molecular temperature derived in Section 3.2. Keto et al. (1987) studied the temperature scales of NH₃ gas in the vicinity of UC H II region G10.6–0.4, where the NH₃ gas temperature scales outward with a radius as R^−1/2.

The molecular effective distances were estimated using Equation (2) ranging from ∼ 0.003 to ∼ 0.083 pc, shown in Table 3. It is likely that CH₃CN originated from circum-stellar instead of interstellar. We also plot the relation between R_eff and L_clump/M_clump in the lower left panel of Figure 4. According to our estimation, CH₃CN radiation should originate from ∼ 1/100 to ∼ 1/1000 of the ATLASGAL clump size and there is evidence for a correlation between the R_eff and L_clump/M_clump where R_eff ∼ (L_clump/M_clump)^{0.5 ± 0.2}. As the star evolves, the molecule is located relatively farther away from the central star.

In the upper right panel of Figure 4, we plot the relation between the molecular abundance and the L_clump/M_clump. It seems that the abundance decreases as L_clump/M_clump increases, where a correlation of X_CH3CN ∼ (L_clump/M_clump)^{−1.0 ± 0.7} can be found. CH₃CN is abundant in the early stage of HMC, and then the abundance decreases with the formation and evolution of UC H II region.

As stars evolve, they release more and more energy through UV radiation. Chemical model revealed that molecules have high column density at lower UV fields, while many species are photodissociated away for high UV fields (Stäuber et al. 2004). CH₃CN is subject to such photodissociation by UV radiation. The species whose abundances are enhanced are simple molecules including radicals and ions in photodissociated region (PDR), there are strong lines of simple species containing 2–4 atoms in W3 IRS4 (Helmich & van Dishoeck 1997), supporting the photodissociation hypothesis. As shown in the bottom right of Figure 4, molecular abundance decreases with the increase of ionization flux (X_CH3CN ∼ Ionization flux^−0.3±0.2). It can also support the explanation of the decrease of molecular abundance caused by ionization.