G331.512–0.103: An Interstellar Laboratory for Molecular Synthesis. I. The Ortho-to-para Ratios for CH₃OH and CH₃CN

CH₃CN (methyl cyanide) is a symmetric top molecule. The nuclear spin state of the hydrogen atoms defines whether the molecule has an ortho (E) or para (A) symmetry. Rotational levels of CH₃CN are characterized by two quantum numbers: the total angular momentum (J) and its projection on the axis of symmetry (K). Spectral signatures are associated to K-ladder structures whose notation for the A and E configurations are $K=3n$ and $K=3n\pm 1$, respectively (Solomon et al. 1971; Boucher et al. 1980; Cummins et al. 1983).

CH₃OH (methanol) is one of the simplest asymmetric-top molecules; however, its spectrum is quite complicated because there is a strong coupling between torsional and vibrational modes. Methanol also exists in two species denoted as A and E depending on the nuclear spin alignment of the three H-atoms of the methyl group (CH₃). The energy levels of methanol can be assigned with the total angular momentum J and its component K along the symmetry axis (Lees & Baker 1968; Lovas et al. 1982).

The excellent spectral resolution of the used instrument allowed us to separately study the A and E isomers of CH₃CN and CH₃OH. Nuclear spin conversion of A and E symmetries are considered to be rare events, being affected by chemical reactions, non-reactive collisions and grain-surface mechanisms (Willacy et al. 1993; Hugo et al. 2009). However, the spin conversion has a particular relevance in molecular astrophysics. Important questions remain unsolved: for instance, how collisions stimulate conversions and, as a consequence, if that property can be used as an astronomical clock (Lee et al. 2006; Sun et al. 2015). One of our goals is to verify if the A and E pairs are equally populated at the local temperature of the source (e.g., Andersson et al. 1984; Minh et al. 1993; Wirström et al. 2011).

We organized this paper as follows. In Section 2, the observational procedure is described. In Section 3, results about the line identification are presented. In Section 4, we discuss the radiative analysis. The discussion, conclusions, and perspectives are presented in Sections 5 and 6.

We observed the transitions CH₃CN J = 16–15, J = 18–17, and J = 19–18; a set of them is displayed in Figure 1. Within those levels, the spectral resolution was high enough to separate the components K = 0, 3, 6, and 9 from K = 1, 2, 4, 5, 7 and 8, which correspond to A–CH₃CN and E–CH₃CN, respectively (see Table 2).

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Table 2.  Spectral Line Analysis of A–CH₃CN and E–CH₃CN in G331

Transition	Frequency	Eu	Aij	$\int {T}_{\mathrm{mb}}{dV}$	Vlsr	FWHM
	(MHz)	(K)	(10−3 s−1)	(K km s−1)	(km s−1)	(km s−1)
A–CH3CN
a169–159	293845.164	697.83	1.51	⋯	⋯	⋯
166–156	294098.867	377.0721	1.9	2.065 ± 0.006	−90.7 ± 0.2	10.3 ± 0.5
163–153	294251.461	184.3532	2.13	5.9 ± 0.3	−90.4 ± 0.2	8.2 ± 0.6
160–150	294302.388	120.0696	2.21	7.9 ± 0.2	−89.69 ± 0.07	8.8 ± 0.2
b189 − 179	330557.569	728.67	2.36	0.15 ± 0.04	−91.2 ± 0.1	0.9 ± 0.2
c186 − 176	330842.762	407.9468	2.8	1.53 ± 0.07	−88.2 ± 0.4	10 ± 0.1
183 − 173	331014.296	215.2437	3.07	6.6 ± 0.5	−90.3 ± 0.3	8.9 ± 0.8
180 − 170	331071.544	150.9654	3.16	9.1 ± 0.3	−89.5 ± 0.1	9.4 ± 0.3
a199 − 189	348911.401	745.42	2.87	⋯	⋯	⋯
196 − 186	349212.311	424.7065	3.34	3.01 ± 0.01	−90.4 ± 0.2	11.5 ± 0.5
d193 − 183	349393.297	232.012	3.63	3.66 ± 0.07	−91.7 ± 0.3	3.8 ± 0.6
190 − 180	349453.7	167.7368	3.72	5.5 ± 0.3	−90.5 ± 0.1	6.8 ± 0.4
E–CH3CN
e168–158	293940.916	568.69	1.65	⋯	⋯	⋯
167–157	294025.496	461.7635	1.78	0.8 ± 0.1	−88.7 ± 0.6	10 ± 2
165–155	294161.001	290.5519	1.99	2.14 ± 0.09	−89.2 ± 0.2	9.8 ± 0.5
164–154	294211.873	226.3073	2.07	2.93 ± 0.08	−90.2 ± 0.1	9.3 ± 0.3
162–152	294279.75	140.6138	2.17	4.19 ± 0.09	−90.79 ± 0.08	7.9 ± 0.2
161–151	294296.728	119.1843	2.2	7.74 ± 0.07	−91.87 ± 0.07	9.4 ± 0.1
f188 − 178	330665.206	599.54	2.52	1.21 ± 0.07	−91.4 ± 0.2	8.1 ± 0.5
187 − 177	330760.284	492.6304	2.67	0.8 ± 0.1	−90.8 ± 0.7	11 ± 2
185 − 175	330912.608	321.4329	2.91	2.9 ± 0.1	−89.4 ± 0.2	11.6 ± 0.6
184 − 174	330969.794	257.1937	3	3.3 ± 0.1	−90.5 ± 0.1	9.2 ± 0.4
182 − 172	331046.096	171.5073	3.12	6.66 ± 0.09	−90.87 ± 0.07	10.4 ± 0.2
181 − 171	331065.181	150.0797	3.15	10.252 ± 0.007	−91.62 ± 0.06	10.6 ± 0.1
a198 − 188	349024.971	616.29	3.05	⋯	⋯	⋯
g197 − 187	349125.287	509.38	3.2	0.304 ± 0.003	−90.1 ± 0.6	5.9 ± 0.7
195 − 185	349286.006	338.1962	3.45	2.106 ± 0.008	−89.6 ± 0.2	9.5 ± 0.5
h194 − 184	349346.343	273.9599	3.55	2.091 ± 0.002	−89.76 ± 0.09	6.1 ± 0.1
192 − 182	349426.85	188.2773	3.67	5.3 ± 0.1	−90.61 ± 0.9	9.8 ± 0.2
191 − 181	349446.987	166.8506	3.71	8.018 ± 0.001	−91.76 ± 0.05	9.39 ± 0.08

Notes. Columns 1–4 list the spectroscopic parameters collected from databases such as CDMS and JPL. Columns 5–7 contain the resulting parameters and uncertainties derived from Gaussian fits; they are line flux ($\int {T}_{\mathrm{mb}}{dV}$), local standard of rest velocity (V_lsr), and the line width (FWHM). Likely blended lines with:

^bHCOOCH₂CH₃ (330557 MHz) and/or c-C₃HD (330558 MHz). ^cHNCO (330848 MHz). ^dC₂H (349400 MHz). ^eCS (293912 MHz). ^f34SO₂ (330667 MHz). ^gCH₃OCHO (349124 MHz). ^hC₂H (349339 MHz).

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The line identification was performed overlapping the laboratory values on the observed spectral bands at the rest velocity of the source. A high coincidence was obtained, as the K-ladder structures appeared separately and well centered, at the source's rest frequency (with V_lsr = −90 km s⁻¹), as predicted by the spectroscopic databases (Figure 1). This inspection revealed that most of the lines have a Gaussian profile, but only a few of them presented broad blue and red wings due to the outflow activity. We applied Gaussian functions to fit and model the emission. For that, the spectral line processing was carried out using the CLASS package, by means of which we fitted baselines and Gaussian functions for each processed line. As a result, in Table 2 we listed the Gaussian fit parameters and uncertainties of each analyzed line; those parameters are the integrated line flux ($\int {T}_{\mathrm{mb}}{dV}$ in K km s⁻¹), local standard of rest (LSR) velocity (V_lsr in km s⁻¹), and the line width given by the FWHM (FWHM in km s⁻¹).

From a simple comparison of the A–CH₃CN fluxes, we observed a stiff increase of them as the lines go from the K = 6 to K = 0 transitions. This behavior is in agreement with the probabilities predicted by the Einstein coefficients (A_ij). For the transitions with J_up = 16, 18, and 19, the obtained patterns are 16₆:16₃:${16}_{0}\,\approx$ 1:3:4, 18₆:18₃:${18}_{0}\approx 1$:4:6, and 19₆:19₃:${19}_{0}\,\approx$ 1:1:2, respectively. Only few transitions diverged from this pattern, namely, A–CH₃CN J = 18₆ − 17_6, and J = 19₃ − 18₃, whose emission appeared blended with HNCO (15_1,14 − 14_1,13) and C₂H (${4}_{\mathrm{4,4}}-{3}_{\mathrm{3,2}}$) at 330848 MHz and 349400 MHz, respectively. Those contaminant transitions were previously detected by Jewell et al. (1989) and Sutton et al. (1991) in Orion A and OMC-1.

For E–CH₃CN lines, the derived fluxes also increase when the K-ladders vary from seven to one. This is in agreement with the spontaneous decay rates predicted by Aij. For the transitions with J_up = 16, 18, and 19, the complete patterns are 16₇:16₅:16₄:16₂:${16}_{1}\,\approx$ 1:2:3:5:10, 18₇:18₅:18₄:18₂:${18}_{1}\,\approx$ 1:3:4:8:12, and 19₇:19₅:19₄:19₂:19₁ ≈1:7:7:12:26, respectively. Here, the transition E–CH₃CN J = 19₄ − 18₄ at 349346 MHz appeared blended with C₂H (${4}_{\mathrm{5,4}}-{3}_{\mathrm{4,3}}$) at 349339 MHz. We also found that the transition E–CH₃CN J = ${19}_{7}-{18}_{7}$ at 349125 MHz might be blended with CH₃OCHO at 349124 MHz.

The search for the high levels K = 8 and K = 9 yielded negative results; we did not detect lines of these K-ladder numbers above the detection limit of the APEX data. For the cases A–CH₃CN (16₉ − 15₉) and (19₉ − 18₉), we did not observe emission at all. In the case of the 18₉ − 17₉ line, we obtained a marginal flux from the Gaussian fits. This line also might be blended with c-C₃HD and/or weeds,¹³ see Table 2. For the cases E–CH₃CN (16₈ − 15₈) and (18₈ − 17₈), the emission appeared fully and partially blended with CS (6–5) and ³⁴SO₂ (21₂ − 21₁), respectively. For the 19₈ − 18₈ transition, we did not detect emission. The results are listed in Table 2. In addition, a search for emission of CH₃CN (${v}_{8}=1$) was performed with the current data set; however, we did not observe clear evidences to conclude about its presence in G331.

As a forest of spectral lines (Figure 1), the main part of the CH₃OH emission has appeared only in an interval of 3 GHz along the whole survey. The lines were identified by a simple comparison of their frequencies, corrected by the source V_lsr = −90 km s⁻¹, with the rest frequencies reported in molecular databases. The methanol lines exhibit a symmetrical distribution which were fitted by simple Gaussian functions. The spectroscopic and fit parameters estimated for these lines are listed in Table 3. We find a FWHM of around 5.5 km s⁻¹ and a V_lsr = −90 km s⁻¹ with a dispersion of ±2km s⁻¹, mainly due to lines which exhibited a low signal-to-noise ratio (S/N). In Figure 1, we show a set of A and E–CH₃OH lines with J = 7–6.

Table 3.  The Table 2 Caption Applies Here for A–CH₃OH and E–CH₃OH

Transition	Frequency	Eu	Aij	$\int {T}_{\mathrm{mb}}{dV}$	Vlsr	FWHM
Jk	(MHz)	(K)	(10−5 s−1)	(K km s−1)	(km s−1)	(km s−1)
A–CH3OH
61–51	292672.889	63.707	10.6	6.95 ± 0.06	−90.67 ± 0.02	5.24 ± 0.05
32–41	293464.055	51.6381	2.89	3.39 ± 0.09	−90.35 ± 0.09	6.8 ± 0.2
122–113	329632.881	218.8033	6	0.59 ± 0.07	−89.8 ± 0.3	4.1 ± 0.6
111–110	331502.319	169.0101	19.6	3.394 ± 0.001	−90.17 ± 0.02	2.82 ± 0.03
a73–81	332920.822	114.794	1.15 × 10−5	⋯	⋯	⋯
121–120	336865.149	197.0765	20.3	6.9 ± 0.5	−91.9 ± 0.2	6.9 ± 0.3
70–60	338408.698	64.9817	17	10.83 ± 0.07	−90.51 ± 0.02	5.31 ± 0.04
76–66	338442.367	258.6994	4.53	1.09 ± 0.06	−91.3 ± 0.1	5.7 ± 0.4
75–65	338486.322	202.8864	8.38	2.11 ± 0.08	−90.98 ± 0.09	4.9 ± 0.2
72–62	338512.853	102.7032	15.7	7.3 ± 0.4	−90.5 ± 0.1	5.5 ± 0.4
73–63	338543.152	114.7948	13.9	9.21 ± 0.08	−89.77 ± 0.02	5.62 ± 0.05
72–62	338639.802	102.7179	15.7	7.4 ± 0.7	−90.6 ± 0.2	5.6 ± 0.6
22–31	340141.143	44.6729	2.79	2.14 ± 0.06	−90.71 ± 0.08	5.5 ± 0.2
a161–152	345903.916	332.6545	9.02	⋯	⋯	⋯
54–63	346204.271	115.1625	2.17	2.31 ± 0.07	−90.74 ± 0.09	5.9 ± 0.2
141 − 140	349106.997	260.2068	22	4.25 ± 0.06	−90.77 ± 0.04	5.41 ± 0.09
11–00	350905.1	16.841	33.1	12.19 ± 0.05	−90.58 ± 0.01	5.13 ± 0.03
a82–90	351685.48	121.2915	16.2	⋯	⋯	⋯
a104–112	355279.539	207.9929	1.22 × 10−3	⋯	⋯	⋯
130–121	355602.945	211.0285	12.6	4.02 ± 0.04	−91.01 ± 0.02	4.76 ± 0.06
151–150	356007.235	295.2675	23	2.68 ± 0.05	−90.46 ± 0.05	5.8 ± 0.1
E–CH3OH
8−3–9−2	330793.887	138.3774	5.38	1.96 ± 0.06	−91.03 ± 0.07	4.6 ± 0.1
16−1–15−2	331220.371	312.7333	5.23	0.55 ± 0.06	−91.4 ± 0.3	5.3 ± 0.6
33–42	337135.853	53.7412	1.58	1.09 ± 0.06	−91.1 ± 0.1	4.7 ± 0.3
a72–62	337671.238	456.8285	15.5	⋯	⋯	⋯
a75–65	337685.248	486.0568	8.28	⋯	⋯	⋯
a7−1–6−1	337707.568	470.3161	16.5	⋯	⋯	⋯
70–60	338124.488	70.1794	16.9	9.09 ± 0.06	−90.74 ± 0.01	5.01 ± 0.04
7−1–6−1	338344.588	62.6521	16.6	9.61 ± 0.08	−90.63 ± 0.02	4.87 ± 0.05
a76–66	338404.61	235.8941	4.51	⋯	⋯	⋯
a7−6–6−6	338430.975	246.0504	4.54	⋯	⋯	⋯
7−5–6−5	338456.536	181.1017	8.34	1.3 ± 0.4	−90.9 ± 0.7	5 ± 2
75–65	338475.226	193.1625	8.34	1.5 ± 0.6	−91 ± 0.1	5 ± 3
7−4–6−4	338504.065	144.9961	11.5	4 ± 2	−91.3 ± 0.04	6 ± 1
74–64	338530.257	153.0934	11.5	3.1 ± 0.6	−91.1 ± 0.4	5 ± 1
7−3–6−3	338559.963	119.8084	14	4.5 ± 0.1	−90.93 ± 0.6	5.2 ± 0.1
73–63	338583.216	104.8115	13.9	6.9 ± 0.2	−90.99 ± 0.08	6.6 ± 0.2
71–61	338614.936	78.1537	17.1	21.4 ± 0.8	−89.5 ± 0.2	9.9 ± 0.5
7−2–6−2	338722.898	83.0148	15.7	12.53 ± 0.07	−90.04 ± 0.01	5.61 ± 0.03
a182−173	344109.039	411.5062	6.79	⋯	⋯	⋯

Note.

^aMarginal emission ($\lt 5\sigma$).

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Although most of the methanol emission corresponds to the torsional ground state, we also identified lines corresponding to the first excited state (${\nu }_{t}=1$). Such is the case for the lines displayed in Figure 2 (upper panel), where it is observed a broad line of ³⁴SO at ∼337580 MHz blended with the transition E–CH₃OH (${\nu }_{t}=1$) ${7}_{4}-{6}_{4}$ at a frequency, corrected by the source V_lsr, of 337581.663 MHz. Around the ³⁴SO peak, minor satellite emission also was identified as corresponding to (A/E)-CH₃OH ${\nu }_{t}=1;$ the spectroscopic parameters are summarized in Table 4. In the bottom panel of Figure 2, we display the only excited line without contaminant emission, which corresponds to A–CH₃OH (${\nu }_{t}=1$) ${7}_{1}-{6}_{1}$ at a frequency, corrected by the source V_lsr, of 337969.414 MHz.

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Table 4.  The Table 2 Caption Applies Here for A–CH₃OH $({\nu }_{t}=1)$ and E–CH₃OH $({\nu }_{t}=1)$

Transition	Frequency	Eu	Aij	$\int {T}_{\mathrm{mb}}{dV}$	Vlsr	FWHM
Jk	(MHz)	(K)	(10−5 s−1)	(K km s−1)	(km s−1)	(km s−1)
A–CH3OH $({\nu }_{t}=1)$
a75–65	337546.048	485.4	8.13	1.047 ± 0.004	−92.8 ± 0.3	9.1 ± 0.5
a72–62	337625.679	363.5	15.5	10.2 ± 0.9	−90.5 ± 0.3	8 ± 1
a72–62	337635.655	363.5	15.5	1.2 ± 0.2	−92.6 ± 0.6	9 ± 2
71–61	337969.414	390.1	16.6	0.39 ± 0.05	−90.8 ± 0.3	5.2 ± 0.7
E–CH3OH $({\nu }_{t}=1)$
a74–64	337581.663	428.2	11.3	⋯	⋯	⋯
a7−2–6−2	337605.255	429.4	15.6	1.513 ± 0.003	−89.8 ± 0.3	11.7 ± 0.5
a70–60	337643.864	365.4	16.9	1.1 ± 0.8	−90.2 ± 0.2	5.9 ± 0.5
b10−2–11−3	344312.267	491.91	17.7	⋯	⋯	⋯

Note. Transitions and quantum numbers from Xu & Lovas (1997) and references therein. Likely blended lines with:

^a34SO 8₈–7₇ (337580 MHz). ^bSO 8₈–7₇ (344310 MHz).

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Emission of excited methanol is typically observed toward hot molecular cores. For instance, Menten et al. (1986), Sutton et al. (1995) and Schilke et al. (2001) have reported its emission in OMC-1, W3(OH), and W51.

The observed lines of excited methanol constitute an evidence for its presence in G331. However, to solve questions as whether the excited emission is populated at the same conditions of the ground state, it is necessary to carry out complementary observations; for instance, at frequencies between 600–720 GHz. These observations could reveal a larger number of CH₃OH ${\nu }_{t}=1,2$ lines favoring a better estimation on the physical conditions. In the bottom panel of Figure 2, we displayed a broad line close to 337900 MHz, which is associated to SO₂; however, that line could be also blended with CH₃OH (${\nu }_{t}=2$) J = 7–6 at 337877 MHz.

We searched for lines of the D, ¹³C, ¹⁵N and ¹⁸O isotopologues of CH₃CN and CH₃OH. As predicted by the spectroscopic databases, several frequencies of those isotopologues fall across the bands; however we only confirm the presence of ¹³CH₃OH. Emission related to ¹³CH₃CN J = 19–18 was also identified; however, the lines are blended with SO J = 3–2 at 339341 MHz. Those lines were also reported by Jewell et al. (1989) in Orion A.

We detected a couple of transitions of A–¹³CH₃OH. The associated spectroscopic parameters are presented in Table 5. The lines were identified at the rest frequencies 330252.798 MHz and 350103.118 MHz with S/N of ${\rm{S}}/{\rm{N}}\geqslant 5$. Such detections have been fundamental to analyze the opacity of the detected emission. For instance, we estimated flux ratios using lines of A–¹³CH₃OH and A–CH₃OH with comparable spectroscopy, namely using those transitions that have exhibited similar frequencies, A_ij and E_u values. Then, by selecting the ${7}_{0}$–${6}_{0}$ and ${1}_{1}$–${0}_{0}$ transitions both of A–CH₃OH and A–¹³CH₃OH (Tables 3 and 5), whose A_ij values are in agreement almost by a factor 1, we obtained the flux ratios C/¹³C = 18.1 ± 0.7 and C/¹³C = 17.7 ± 0.1, respectively. Such flux ratios are similar to the values reported in sources toward the Galactic center, where C/¹³C = 20 (Wilson & Rood 1994; Requena-Torres et al. 2006). These ratios imply finite values of opacities, therefore in the subsequent sections we will take into account optical depth corrections to estimate the physical conditions derived from the CH₃OH and CH₃CN emission.

Table 5.  Spectroscopic and Observational Parameters of the of the $A{-}^{13}$ CH₃OH Lines Analyzed in G331

Transition	Frequency	Eu	Aij	$\int {T}_{\mathrm{mb}}{dV}$	Vlsr	FWHM	aC/13C
Jk	(MHz)	(K)	(10−5 s−1)	(K km s−1)	(km s−1)	(km s−1)
70–60	330252.798	63.4	15.8	0.60 ± 0.07	−90.7 ± 0.3	5.0 ± 0.6	18.1 ± 0.7
11–00	350103.118	16.8	32.9	0.69 ± 0.05	−91.2 ± 0.2	4.3 ± 0.3	17.7 ± 0.1

Note. Similarly, the Table 2 caption applies here.

^aFlux ratios derived by considering the integrated fluxes of A–CH₃OH (7₀–6₀) and (1₀–0₀) listed in Table 3.

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Two lines of E–¹³CH₃OH were also identified, although they exhibited contamination. Close to their rest frequencies, lines of ³⁴SO₂ J = 8–7 and CH₃OCH₃ J = 16–15 are candidates for blended emission. These contaminants were also detected toward the Hot Molecular Core G34.3+0.15 (MacDonald et al. 1996).

In this section, we present results based on statistical equilibrium models when considering collisions between the analyzed molecules and molecular hydrogen. To estimate the kinetic temperatures and column densities, we ran the RADEX code into CASSIS, whose formalism is analogous to the Large Velocity Gradient approximation (van der Tak et al. 2007). RADEX considers the probability that a photon escape in an isothermal and homogeneous medium without large-scale velocity fields. Collision rate data were collected from the LAMDA database.¹⁴

Conjointly with RADEX/CASSIS, we used the Markov Chain Monte Carlo (MCMC) method to simulate the observed lines from the resulting best solutions, which are given by the minimal ${\chi }^{2}$ value. The MCMC algorithm operates on values chosen randomly within a sample defined by a minimum and maximum limit for an N-dimensional parameter space. This characteristic is the most relevant when calculations require as inputs several free parameters. In detriment, the quality of the fit is a monotonically increasing function of the number of iterations introduced in the chain, which in turn affects the "computational time" to achieve convergence (e.g., Guan & Krone 2007; Foreman-Mackey et al. 2013; Tahani et al. 2016).

We prepared MCMC routines for each A and E species. The numerical sample explored by the algorithm was delimited by five free parameters: kinetic temperature (T_k), column density (N), source size (θ), FWHM and hydrogen density (${n}_{{{\rm{H}}}_{2}}$). To guarantee that the code has visited the sample, we tested routines with number of iterations of the order of 10⁵. Once the algorithm achieves convergence, the minimal ${\chi }^{2}$ is computed printing the statistical results for each parameter. This methodology implied large run-times. As a total, we modeled seven and 13 lines of A–CH₃CN and E–CH₃CN, respectively, and 10 and 13 lines of A–CH₃OH and E–CH₃OH, respectively. The statistical calculations are summarized in Table 6. Likewise, the best-fit model lines are exhibited in Figure 3.

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Table 6.  Parameters and Physical Conditions Derived from the Statistical Equilibrium Calculations that have Yielded Hydrogen Densities between 0.7 and 1 × 10⁷ cm⁻³

Parameters	A–CH3CN	E–CH3CN	A–CH3OH	E–CH3OH
Modeled lines	7	13	10	13
${\chi }^{2}\,\min$	5.69	7.77	6.23	4.42
FWHM (km s−1)	5.49 ± 0.01	5.49 ± 0.01	4.9 ± 0.1	4.88 ± 0.01
N (1014 cm−2)	4.77 ± 0.05	3.69 ± 0.04	85 ± 20	98 ± 0.1
Tk (K)	142.1 ± 0.9	140.5 ± 0.3	64 ± 2	84.8 ± 0.1
θ ('')	4.51 ± 0.01	4.53 ± 0.02	5.7 ± 0.3	5.01 ± 0.04

Note. The number of computed lines and the reduced ${\chi }^{2}$ values have also been included.

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There are two aspects that were common for the models of A/E–CH₃OH and A/E–CH₃CN. First, we obtained H₂ densities in the interval ${n}_{{{\rm{H}}}_{2}}=(0.7\mbox{--}1)\times {10}^{7}$ cm⁻³, which is in agreement within a factor ≳1.5 with the density derived from the dust continuum (Hervías-Caimapo et al. submitted). Also, we intended to differentiate the densities of the ortho-H₂ and para-H₂ collisional partners (o-H₂ and p-H_2, respectively). Although studies explain the differences when A and E species collide with o-H₂ and p-H₂ (e.g., Rabli & Flower 2010), for our purposes we just conclude that the o-H₂/p-H₂ ratio varied between ∼0.6 and 1.0 for the different MCMC computations. That interval is consistent with the ortho-to-para limit of 0.2, when H₂ is thermalized at the CO temperature, and ortho-to-para limit of three when H₂ first forms (Flower & Watt 1984; Lacy et al. 1994).

The second aspect is that the modeled spectral lines yielded source sizes in agreement with a compact emitter region. For CH₃CN and CH₃OH we found sizes of ∼45 and ∼53, respectively. This result is supported by previous CO (7–6) maps obtained with the Australia Telescope Compact Array (ATCA), for which Bronfman et al. (2008) determined a compact and dense region of ∼43. Merello et al. (2013a, 2013b) mapping the emission traced by SiO (8–7) found a ring-type structure of ≲5''.

Rotational diagrams were constructed to estimate the excitation temperatures (T_exc) and column densities (N) of A/E–CH₃CN and A/E–CH₃OH. Assuming that the emission is optically thin and uniformly fills the antenna beam, T_exc and N can be calculated from

$$\begin{eqnarray}&&\mathrm{ln}\left(\displaystyle \frac{{N}_{u}}{{g}_{u}}\right)=\mathrm{ln}\left(\displaystyle \frac{N}{Z}\right)-\displaystyle \frac{{E}_{u}}{{{kT}}_{\mathrm{exc}}},\end{eqnarray} \tag{ 1 }$$

where ${N}_{u}/{g}_{u}$ and E_u are the column density per statistical weight and the energy of the upper level, respectively, and Z is the partition function (Goldsmith & Langer 1999). In local thermodynamic equilibrium (LTE), Equation (1) represents a Boltzmann distribution whose values $\mathrm{ln}{N}_{u}/{g}_{u}$ versus ${E}_{u}/k$ can be fitted using a straight line, whose slope is defined by the term $1/{T}_{\mathrm{exc}}$.

The rotational diagrams were constructed taking a beam dilution factor associated with a point-like emitter region. Therefore, a correction that is provided by the term $\mathrm{ln}({\rm{\Delta }}{{\rm{\Omega }}}_{a}/{\rm{\Delta }}{{\rm{\Omega }}}_{s})$ was introduced on the right-hand side of Equation (1) (Goldsmith & Langer 1999). This ratio relates the subtended angle of the source with the solid angle of the antenna beam. The beam dilution factor that we introduced is based on the results derived from the RADEX/MCMC calculations. Then, for CH₃CN and CH₃OH, we adopted averaged source sizes of 45 and 53, respectively.

Because the lines observed in this work fell in a broad band, from 290 to 350 GHz, yielding different beamwidths, the adopted sizes have been used in the comparisons between temperatures and column densities for the different lines.

Depending on the density of the region, the K-ladder structures of CH₃CN and CH₃OH can exhibit an important scattering of ($\mathrm{ln}{N}_{u}/{g}_{u},{E}_{u}$) values in their rotational diagrams. More generally, it is expected that the higher is the gas density, the lower is the K-ladder segregation (Olmi et al. 1993; Cesaroni et al. 1997; Goldsmith & Langer 1999; Remijan et al. 2004; Araya et al. 2005; Cuadrado et al. 2017). To check the amount of scatter, we compared the rotational diagrams when they were individually constructed for each J_K level and with those obtained when an unique fit was determined across all the K-levels. As a result, we did not observe considerable discrepancies between the two cases; temperatures and column densities were found within the adopted uncertainty from calibration (Section 2). For instance, in Figure 4 we display the result for E–CH₃CN.

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Optical Depth Correction

The rotational diagrams obtained from the A/E–CH₃CN and A/E–CH₃OH lines are displayed in Figure 5. They were constructed selecting only the transitions in the ground state and without contaminant emission. So far, the rotational diagrams have been scaled only considering the beam dilution factor. However, they represent a solution under the assumption of emission optically thin, $\tau \ll 1$. To revise how different the LTE solutions are from a radiative scenario with finite values of optical depths, we have applied an optical depth correction on the rotational diagrams of A/E–CH₃CN and A/E–CH₃OH. Expressed mathematically, the correction consisted in including the term $-\mathrm{ln}{C}_{\tau }$, with ${C}_{\tau }=\tau /1-{\exp }^{-\tau }$, on the right-hand side of Equation (1) (Goldsmith & Langer 1999; Gibb et al. 2000; Remijan et al. 2004; Araya et al. 2005). Thus, the ordinates of our rotational diagrams were readjusted considering a term associated with the photon escape probability.

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We have performed this adjust based on (first) the results obtained from the statistical equilibrium calculations. In the case of CH₃CN, transitions with K = 0, 1, 2 and 3 were the most affected with $\tau \approx 1$. And, (second) considering the flux ratio C/¹³C ≲ 20 as we described in Section 3.3, which suggests finite optical depths.

To perform the optical depth correction, we used CASSIS which executes iterative calculations of ${C}_{\tau }$ adjusting the level populations until achieving a consistent solution. With these corrections, slight changes are expected in the LTE solutions. For instance, Araya et al. (2005) obtained differences around 10 and 14% in the temperature and column density of CH₃CN when the optical depth correction was applied, respectively.

The A/E–CH₃CN rotational diagrams (RDs), with the optical depth correction, are displayed in the upper panels of Figure 5. For A–CH₃CN, we obtained N = (6.4 ± 2.0) × 10¹⁴ cm⁻² and T_exc = 156 ± 25 K. For E–CH₃CN, we obtained N = (8.4 ± 2.0) × 10¹⁴ cm⁻² and T_exc = 152 ± 20 K. The percentage difference of N and T_exc, with respect to the RD without the optical depth correction, are ranged between (5–14)% and (2–12)%, respectively.

The A/E–CH₃OH RDs, with the optical depth correction, are displayed in the lower panels of Figure 5. For A–CH₃OH, we obtained N = (1.9 ± 0.5) × 10¹⁶ cm⁻² and T_exc = 71 ± 10 K. For E–CH₃OH, we obtained N = (2.0 ± 0.1) × 10¹⁶ cm⁻² and T_exc = 68 ± 8 K. The percentage difference of N and T_exc, with respect to the RD without the optical depth correction, are ranged between (10–22)% and (9–17)%, respectively.

We detected two lines of ¹³CH₃OH (Table 5). In the absence of collisional coefficients, those lines were modeled assuming LTE conditions applying the MCMC method leaving various inputs as free parameters: N, T_exc, FWHM, and θ. However, we put an upper limit of $N\,\lt$ 5 × 10¹⁵ cm⁻², which was derived from the column density of the main isotopologue and considering the ratio C/¹³C ≲ 20. The results were consistent with the physical conditions of the main isotopologue. The best LTE models are displayed in Figure 6, whose solution (${\chi }^{2}=2.82$) yielded N = (1.01 ± 0.06) × 10¹⁵ cm⁻² and T_exc = 89.5 ± 0.4 K for a modeled source size of 57. Additionally, the resulting FWHM values (∼4.4 km s⁻¹) are consistent with the resulting fits reported in Table 5.

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CH₃OH is more abundant and traces a region about 70 K colder than that traced by CH₃CN. From the LTE and non-LTE analysis, we found that the ratio (A + E)-CH₃OH/(A + E)-CH₃CN is about 25, indicating almost the same overabundance of A and E–CH₃OH over A–CH₃CN and E–CH₃CN.

ALMA observations of the ion H¹³CO⁺ (4–3) probed the existence of a core and various clumpy structures in G331 (Hervías-Caimapo et al. submitted). Maps of SiO (8–7) show as well an internal cavity surrounded by molecular emission confined in ≲5'', for which these authors have estimated N(H¹³CO⁺) ≈ (1.5–3) ×10¹³ cm⁻² (e.g., Bronfman et al. 2008; Merello et al. 2013a, 2013b). The column densities of CH₃OH and CH₃CN were divided by N(H₂) values to obtain their abundances. Following the works cited above, to estimate a scaled density of H₂ in G331, we applied the ratio H¹³CO⁺/H₂ = 3.3 × 10⁻¹¹ of Orion KL (e.g., Blake et al. 1987) on the H¹³CO⁺ column densities derived for G331 (Merello et al. 2013a). As an approximation for the present work, we adopted the H¹³CO⁺/H₂ ratio of the Orion KL system, as this source is an excellent template for comparative studies on abundances and molecular complexity (e.g., Schilke et al. 2001; Beuther et al. 2005). The total abundances of CH₃OH and CH₃CN are summarized in Table 7; as a total, we refer to the A+E contribution from the nuclear spin symmetries (e.g., Fuente et al. 2014 ). Thus, the CH₃CN emission is linked to a hot core with ${T}_{k}\approx 141$ K and $\theta \approx 4\buildrel{\prime\prime}\over{.} 5$, while CH₃OH traces a cold bulk medium with ${T}_{k}\approx 74$ K and $\theta \approx 5\buildrel{\prime\prime}\over{.} 3$. Also in Table 7, we included the abundance uncertainties computed from the errors obtained with the radiative models (Bevington & Robinson 2003); although we listed errors of ≲25%, the abundance uncertainties could be of up to 40% including other sources of errors, such as the calibration uncertainty, adopted here as 20%. In Table 7, the abundances of the ¹³C isotopologues are also listed. Although we obtained an inaccurate result based only on two lines of ¹³CH₃OH, we found that it could be not only 20 times lower, resulting from the ¹³C/C flux ratio, but up to 40 times under abundant than CH₃OH, as the LTE analysis suggested (see Figure 6). Thus, we determined [¹³CH₃OH] ≲ 2.1 × 10⁻⁹.

Table 7.  Abundances of CH₃OH and CH₃CN Derived from the LTE and Non-LTE Analysis

Method	Hot Component			Cold Component
	[CH3CN]	[13CH3CN]	${ \% }_{A-{\mathrm{CH}}_{3}\mathrm{CN}}$	[CH3OH]	[13CH3OH]	${ \% }_{A-{\mathrm{CH}}_{3}\mathrm{OH}}$
	10−9	10−9	$\approx$	10−9	10−9	$\approx$
non-LTE	1.8 ± 0.2	⋯	56	38 ± 10	⋯	46
LTE	3.1 ± 0.6	$\lesssim 0.08$	43	81 ± 15	$\lesssim 2.1$	49

Note. We have included the contribution of each spin isomer as a percentage of the total abundance, assumed as the sum A+E of the symmetries.

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For the undetected ¹³CH₃CN, we propose upper limits assuming that the ¹³CH₃CN/¹³CH₃OH ratio works as what we found for the main isotopologues: CH₃CN/CH₃OH $\approx \,1/25$. From that conjecture, we conclude that [¹³CH₃CN] ≲ 8 × 10⁻¹¹.

One of the goals of this work was to separately analyze the emission of the A and E spin nuclear isomers; however, the analysis indicated common physical conditions (N and T) for both spin symmetries meaning that they trace the same reservoir. The opposite case would imply spin conversion processes, induced by molecular interactions on molecular ices or collisions in gas phase, favoring an overabundance in a given spin symmetry. However, this result would be expected at earlier stages or in younger stellar sources (e.g., Minh et al. 1993; Wirström et al. 2011).

Independent of the employed analysis, we find that both the A and E isomers contribute with approximately half of the total emission of CH₃OH and CH₃CN. The percentage derived from both methods are listed in Table 7, as explained above, assuming a total abundance as A+E. As a similar result, MacDonald et al. (1996) determined the ratio [A–CH₃OH]/[E–CH₃OH] ≈ 0.9 for the hot molecular core G34.3+0.15. In the envelopes around low-mass protostars, Jørgensen et al. (2005) found ortho-to-para ratios close to unity for CH₃OH. Recently, similar results were reported for the pairs A/E–CH₃CN, A/E–CH₃OH, and A/E–CH₃CHO in the Orion Bar photodissociation region (PDR; Cuadrado et al. 2017).

This tendency is similar to another aspect aimed to examine in this study: whether o- and p-H₂ collisional partners may affect the population of the A and E nuclear spin isomers of CH₃OH and CH₃CN. However, the MCMC/RADEX computations yielded H₂ ortho-to-para ratios close to unity.

Laboratory studies have offered new measurements about spin conversion, generally assumed as improbable processes. In gas phase, Sun et al. (2015) found that molecular collisions induce the interconversion of spin in molecules of methanol exhibiting a rate that decreases as the pressure increases with the number of collisions. A quantum relaxation mechanism explains the interconversion. In condensed phase, Lee et al. (2006) observed that methanol can suffer a slow conversion from the E to the A symmetry when it is trapped in a solid matrix of p-H₂ prepared at low temperatures (∼ 5 K). In theoretical works, Rabli & Flower (2010) studied the implications of methanol colliding with o-H₂ and p-H₂, finding qualitative and quantitative differences for those cases.

As we summarized in Table 4, emission of torsionally excited methanol was also evidenced; however, only one line appeared without blended emission: A–CH₃OH (${\nu }_{t}=1$) at ∼337969 MHz. In some studies, it has been analyzed whether excited transitions may be populated at the same LTE conditions of the ground torsional levels (e.g., Lovas et al. 1982; Menten et al. 1986; Sutton et al. 1995; Ren et al. 2011; Sánchez-Monge et al. 2014). We made a minor examination based on the unique line without contamination; however, we found that, to account for the flux, different regimes are needed with ${T}_{\mathrm{exc}}\gtrsim 90$ K. Complementary observations with APEX will be carried out to determine with a better precision the physical conditions of excited methanol in G331.

In this study, we identified two different components that could candidate G331 as a Hot Molecular Core (HMC). Other characteristics also support this hypothesis. For instance, the source is compact, harbors a massive and energetic molecular outflow, and is embedded in a H ii region where masers of OH and CH₃OH reveal a high star formation activity. Besides, the temperatures of the gas components are above and below the limits where evaporation of icy mantles plays an important role; for instance, to explain abundances of Complex Organic Molecules and aspects related to the age of the source. The gas densities also support such classification, since we determined H₂ densities typical of a dense medium (0.7–1) $\times {10}^{7}$ cm⁻³.

N- and O-bearing molecules help to diagnose the presence of different gas components in HMCs (e.g., Beuther & Sridharan 2007; Fontani et al. 2007). In this first work, it is proposed that A/E–CH₃CN and A/E–CH₃OH trace a hot (${T}_{k}\simeq 141$ K) and cold (${T}_{k}\simeq 75$ K) component with sizes around 45 and 53, respectively. Such results are in agreement with ALMA observations of CO (7–6), SiO (8–7) and H¹³CO⁺ (4–3). The emission of these species was found to be compacted in ∼5'' (Bronfman et al. 2008; Merello et al. 2013a; Hervías et al. 2015).

In Figure 7, we compare the abundances derived in this work with other sources. Our results are similar with the abundances reported in G34.3+0.15. More generally, our results suggest different abundances, physical components, and a chemical differentiation for CH₃OH and CH₃CN in G331. The high sensitivity and spectral resolution of our single-dish spectra have been useful to realize subtle differences in the line profiles of CH₃OH and CH₃CN, inspected via the V_lsr and FWHM parameters listed in Tables 2 and 3. In agreement with the radiative models, these spectral signatures reveal clues on the origin and size of the emitter regions. In spite of that, and as a perspective, further observations at higher spatial resolution are needed to study the spatial distribution of different tracers in G331. Also, these observations may reveal density gradients toward the core and the outflow, allowing more accurate determinations of molecular abundances.

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The fact of CH₃OH being more abundant than CH₃CN is in agreement with the chemistry that has been modeled in HMCs, where these molecules are usually referred as parent and daughter species, respectively, since CH₃OH is expected to be formed at early stages in grain surfaces, via successive hydrogenation of CO, while CH₃CN appears later via reaction between HCN and ${\mathrm{CH}}_{3}^{+}$ (Millar et al. 1997; Nomura & Millar 2004; Guzmán et al. 2013; Loison et al. 2014). Other alternatives to produce methanol are ${\mathrm{CH}}_{3}^{+}$ + OH $\to$ CH₃OH and CH₂ + H₂O $\to$ CH₃OH. They can occur when frozen mixtures of CH₄ and H₂O are bombarded with electrons (Hiraoka et al. 2006). In addition, we have found that the physical conditions traced by those molecules might explain the regimes where prebiotic and complex organic molecules have been detected, such as CH₃OCH₃, CH₃CHO, NH₂CHO, and the C₂H₄O₂ isomers.

Nomura & Millar (2004) performed time-dependent chemical models considering observational aspects of the hot molecular core G34.3+0.15; for instance, that CH₃CN is associated to an inner and hot core region, while CH₃OH traces the gas present in clumps (e.g., Hatchell et al. 1998; Millar & Hatchell 1998; van der Tak et al. 2000). Comparing our column densities with the temporal values calculated by those authors, an age of 10⁴ years may represent the epoch for G331, when substantial quantities of daughters molecules (e.g., CH₃CN) are produced without substantially decimate their parents (e.g., CH₃OH). Preliminary results derived by us, obtained with the gas-grain chemical code Nautilus (Ruaud et al. 2016),¹⁵ show a CH₃OH/CH₃CN ratio similar to those derived from the observations. However, these results will be presented in a subsequent work depicting the chemistry of O-bearing molecules detected in the source.