The ALMA Survey of 70 μm Dark High-mass Clumps in Early Stages (ASHES). VII. Chemistry of Embedded Dense Cores

In general, the emission from deuterated species is weak. For all the detected lines of interest, the spectra are averaged inside the dendrogram leaf (see Paper I) that defines each core, in order to increase the signal-to-noise ratio (S/N). We derive the line central velocity (v_LSR), the observed velocity dispersion (σ_obs= FWHM/$2\sqrt{2\mathrm{ln}2}$), and peak intensity (I) from Gaussian fittings to the core-averaged spectrum for each line, except for N₂D⁺, which is fitted with a hyperfine structure (hfs) model. The derived σ_obs is not corrected by the smearing effect, due to the channel width. To increase the S/N of the weak line emission, the core-averaged spectrum is spectrally smoothed over two native channels, prior to Gaussian/hfs fittings, if it shows marginal ∼3σ confidence in the native spectral resolution. The best-fit parameters, which are used to compute the column densities of molecules (see Appendix C) and the following analyses, are summarized in Appendix A.

CO emission is detected in all the identified cores. C¹⁸O is detected in 267 of the 294 cores, with a detection rate of 89%. H₂CO is the third most commonly detected line, which is detected in 156 of the 294 cores, with a detection rate of 52%. CH₃OH is detected in 51 of the 294 cores, leading to a detection rate of 17%. Among the detected deuterated species, DCO⁺ is the most commonly detected line, with a detection rate of 39% (116/294). N₂D⁺ is detected in 54 of the 294 cores, resulting in a detection rate of 18%. There are seven cores that are associated with the DCN line emission, with a detection rate of 2%. There is weak C₂D emission in three dense cores, with a detection rate of 1%. ¹³CS is detected toward four dense cores, with a detection rate of 1%. Based on the core-averaged spectra, SiO emission is detected in 27 cores.

Figure 2 shows histograms of the number distributions and detection rates of the detected lines for the prestellar cores, protostellar cores, and for each core category. N₂D⁺ is detected in 17 prestellar cores and 37 protostellar cores, resulting in a detection rate in the prestellar phase (9% = 17/197) lower than that in the protostellar phase (38% = 37/97). The high N₂D⁺ detection rate for the protostellar cores indicates that N₂D⁺ does not exclusively trace prestellar cores and that it also frequently appears in protostellar cores (Giannetti et al. 2019). Among the detected deuterated molecules, DCO⁺ has the highest detection rate in both the prestellar and protostellar cores. The DCO⁺ detection rates are 35% (69/197) and 49% (47/97) for the prestellar and protostellar cores (Figure 2), respectively. This indicates that DCO⁺ is more frequently detected than N₂D⁺ in both the prestellar and protostellar cores.

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The H₂CO detection rate in the protostellar cores (87% = 84/97) is more than twice that in the prestellar cores (37% = 72/197). On the other hand, H₂CO has a higher detection rate than N₂D⁺ in both the prestellar and protostellar cores, indicating that H₂CO is more commonly seen than the N₂D⁺ emission in these dense cores at early evolutionary phases. There are 51 (53% = 51/97) protostellar cores showing CH₃OH line emission. DCN is detected in seven protostellar cores. C₂D is detected in three prestellar cores. ¹³CS is detected in two prestellar and two protostellar cores. The detection numbers and detection rates of each line for all of the categories are summarized in Table 2.

In general, both CO and C¹⁸O show the most spatially extended emission over all clumps, followed by H₂CO and CH₃OH, and then by DCO⁺, N₂D⁺, SiO, DCN, ¹³CS, and C₂D. From Figure 1 (see also Appendix A), we note that the C¹⁸O emission is extended in the IRDC clumps. There is very weak C¹⁸O emission toward some of the dense cores, likely due to depletion (e.g., cores #28 and #30 in G14.49; see also Sabatini et al. 2022).

N₂D⁺ shows extended emission toward dense cores. The peaks of the N₂D⁺ emission are offset from the continuum peaks in some cores, with a significant decrease in intensity toward the continuum emission peaks (e.g., cores #8 and #2 in G14.49; see Figure 1). Both N₂ depletion and CO evaporation toward the centers of the cores can lead to a decrease in N₂D⁺ abundance. We are unable to distinguish between these two possibilities with the current data. DCO⁺ also shows extended emission toward the dense cores. However, the spatial distribution of DCO⁺ does not always coincide with that of N₂D⁺ (see, for example, Sakai et al. 2022). For instance, DCO⁺ shows a significantly different spatial distribution from what is observed for N₂D⁺ around cores #7, #10, and #21 in G14.49 (see Figure 1).

The peaks of the H₂CO and CH₃OH emission appear either to coincide with the continuum peaks or to be located in the direction of the outflows in the majority of cases (Figure 1 and Appendix A). The CH₃OH emission shows a behavior similar to what is observed for H₂CO, but with less extended emission. This is most likely due to the fact that the excitation conditions of H₂CO (3_0,3 − 2_0,2) are different from those of CH₃OH (e.g., lower upper-level energies and critical densities; see Table 1).

There are some pairs of molecules that show similar spatial distributions in some clumps, e.g., H₂CO and CH₃OH. To compare the spatial trends of different species, we performed a half-beam sampling for the 0th moment of each molecular line. Each data point (or pixel) is about half the beamwidth, to ensure that data points are not oversampled. The similarity of the 0th-moment maps of different molecules can be evaluated quantitatively by the cross correlation between each pair of maps, according to Guzmán et al. (2018):

$$\begin{eqnarray}&&{\rho }_{12}=\displaystyle \frac{\sum _{i,j}{I}_{1,{ij}}\,{I}_{2,{ij}}\,{w}_{{ij}}}{{\left(\sum _{i,j}{I}_{1,{ij}}^{2}\,{w}_{{ij}}\,\sum _{i,j}{I}_{2,{ij}}^{2}\,{w}_{{ij}}\right)}^{1/2}},\end{eqnarray} \tag{ 1 }$$

where the sums are taken over all positions. I_1,ij and I_2,ij are the integrated intensities at the position i, j for two arbitrary species, 1 and 2, respectively, and the weight w_ij is equal to 0 or 1, depending on whether or not the line emission was detected at that position. ρ₁₂ is equal to 1 if the 0th-moment maps of two molecules have the same spatial distribution. Although some pairs of molecules that show weak emission do not have statistically significant numbers of independent data points, they are still worth examining. To alleviate the effect of insufficient numbers of independent data points for comparison, we avoid deriving the correlation coefficients of pairs of molecules whose overlapping emitting areas are smaller than one synthesized beam.

Figure 3 presents cross-correlation coefficients for the 0th-moment maps for each pair of molecules. The correlation between N₂D⁺ and DCO⁺ is better than those for the other detected deuterated molecules (i.e., DCN and C₂D) in all the clumps. This is because the emitting regions of the DCN and C₂D lines are smaller than those for either N₂D⁺ or DCO⁺ (Figure 1). The DCO⁺ line emission coincides better with H₂CO and CH₃OH than N₂D⁺ in terms of spatial distribution. This may be because DCO⁺, H₂CO, and CH₃OH have a common precursor molecule of CO that tends to destroy N₂D⁺ (see Sections 4.2 and 4.3).

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In general, the CH₃OH and H₂CO emissions have the most similar spatial distributions in integrated intensities, with the highest correlation coefficients among the detected lines. Most of the CH₃OH and H₂CO emissions appear to be around either outflows or dense cores (Figure 1). In addition, both the CH₃OH and H₂CO emissions show good spatial correlation with the SiO emission in most of the clumps (Figure 3). These results suggest that both the CH₃OH and H₂CO line emissions are closely related to the outflow activity toward protostellar cores in the ASHES clumps.

Figure 4 shows the distribution of the derived I and σ_obs of each line for the prestellar and protostellar cores (see also Table 3). Overall, σ_obs shows no significant difference between the prestellar and protostellar cores for the C¹⁸O and DCO⁺ emissions. This indicates that the protostellar cores are still at a very early evolutionary phase, in which the line widths of C¹⁸O (a low-density gas tracer) and DCO⁺ (a high-density tracer) have not been significantly affected by protostellar activity. In general, the N₂D⁺ line has a comparable I in both the prestellar and protostellar cores, except for four protostellar cores that present a relatively higher I than for the prestellar cores. On the other hand, the N₂D⁺ line emission shows a relatively larger σ_obs in the protostellar cores compared with the prestellar cores. This might be because the N₂D⁺ line emission toward the protostellar cores is influenced by the injection of turbulence, as a result of protostellar activity.

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Table 3. Median and Mean Values of the Derived Line Parameters for Each Category

Name	Prestellar		Protostellar								All
			Outflow Core		Warm Core		Outflow + Warm Core		Sum
	Median	Mean	Median	Mean	Median	Mean	Median	Mean	Median	Mean	Median	Mean
${I}_{{{\rm{C}}}^{18}{\rm{O}}}$	0.98	1.12	0.81	0.88	0.86	0.96	1.22	1.30	0.90	1.09	0.93	1.11
${\sigma }_{{{\rm{C}}}^{18}{\rm{O}}}$	0.75	0.89	0.88	0.95	0.92	1.02	0.85	0.97	0.88	0.99	0.79	0.92
${I}_{\ {{\rm{N}}}_{2}{{\rm{D}}}^{+}}$	0.41	0.42	0.29	0.31	0.52	0.47	0.44	0.53	0.40	0.47	0.41	0.45
${\sigma }_{\ {{\rm{N}}}_{2}{{\rm{D}}}^{+}}$	0.22	0.21	0.21	0.25	0.19	0.21	0.24	0.26	0.23	0.25	0.22	0.23
${I}_{{\mathrm{DCO}}^{+}}$	0.32	0.37	0.37	0.46	0.33	0.37	0.36	0.37	0.35	0.39	0.33	0.38
${\sigma }_{{\mathrm{DCO}}^{+}}$	0.29	0.30	0.29	0.29	0.38	0.39	0.32	0.35	0.32	0.35	0.30	0.32
${\sigma }_{{\mathrm{CH}}_{3}\mathrm{OH}}$	⋯	⋯	⋯	⋯	1.23	1.59	1.46	1.98	1.35	1.82	1.35	1.82
${I}_{{{\rm{H}}}_{2}\mathrm{CO}}$	0.18	0.19	0.28	0.28	0.33	0.42	0.61	0.88	0.38	0.60	0.26	0.41
${\sigma }_{{{\rm{H}}}_{2}\mathrm{CO}}$	0.72	0.84	0.96	1.06	1.19	1.36	1.85	2.21	1.33	1.68	1.00	1.29
${I}_{{}^{13}\mathrm{CS}}$	0.38	0.38	0.27	0.27	⋯	⋯	0.18	0.18	0.22	0.22	0.28	0.30
${\sigma }_{{}^{13}\mathrm{CS}}$	0.34	0.34	0.46	0.46	⋯	⋯	1.30	1.30	0.88	0.88	0.42	0.61
${I}_{\mathrm{DCN}}$	⋯	⋯	⋯	⋯	⋯	⋯	0.26	0.22	0.26	0.22	0.26	0.22
${\sigma }_{\mathrm{DCN}}$	⋯	⋯	⋯	⋯	⋯	⋯	1.21	1.04	1.21	1.04	1.21	1.04
${I}_{{{\rm{C}}}_{2}{\rm{D}}}$	0.22	0.24	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	0.22	0.24
${\sigma }_{{{\rm{C}}}_{2}{\rm{D}}}$	0.13	0.17	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	0.13	0.17

Note. The units are K and km s⁻¹ for peak intensity and observed line width, respectively.

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For the H₂CO emission, both I and σ_obs in the protostellar cores are higher than in the prestellar cores. This is because H₂CO abundances can be significantly enhanced in warm and dense environments, and its line width can be broadened by protostellar activity (e.g., outflows; Tafalla et al. 2010; Sakai et al. 2012). In addition, H₂CO is the molecule in our sample that shows a clearly increasing trend in both I and σ_obs for categories 1 to 4 (see Figure 4), indicating that its abundance and line width are sensitive to the evolution of the dense cores. This implies that H₂CO could be used as a diagnostic tool for inferring star formation activities.

From Figure 4, one notes that the H₂CO (〈σ_obs〉 = 1.68 km s⁻¹) and CH₃OH (〈σ_obs〉 = 1.82 km s⁻¹) lines show relatively larger σ_obs than C¹⁸O (〈σ_obs〉 = 0.99 km s⁻¹), DCO⁺ (〈σ_obs〉 = 0.35 km s⁻¹), and N₂D⁺ (〈σ_obs〉 = 0.25 km s⁻¹) toward the protostellar cores (see also Table 3). This could be because H₂CO and CH₃OH are associated with more turbulent gas components that are affected by protostellar activity (e.g., outflows; Tychoniec et al. 2021). We refrain from investigating I and σ_obs for the ¹³CS, DCN, and C₂D emissions, due to the lack of a sufficient number of detections for a meaningful analysis, as well as the SiO emission, which is mainly associated with outflows.

The rotational excitation temperature (${T}_{{\mathrm{NH}}_{3}}$) is derived from NH₃ (1, 1) and (2, 2) transition lines obtained from the CACHMC survey (Complete ATCA ¹⁶ Census of High-Mass Clumps; D. Allingham et al. 2022, in preparation) at ∼5'' angular resolution (see Appendix B for the detailed procedure for the excitation temperature determination). More details of the procedure for the temperature determination and the survey results will be presented in a forthcoming paper (D. Allingham et al. 2022, in preparation). The derived ${T}_{{\mathrm{NH}}_{3}}$ is used as the excitation temperature in the calculation of all molecular parameters, except for G332.96, which has no available NH₃ data. We used the dust temperature at the clump scale of 12.6 K for G332.96 (Paper I). The averaged temperatures of the dense cores in the same category for a given clump are used for those dense cores that have no available ${T}_{{\mathrm{NH}}_{3}}$. The approximation of using ${T}_{{\mathrm{NH}}_{3}}$ as the excitation temperature is based on the local thermodynamic equilibrium (LTE) conditions in the calculation of the molecular density. The results could be highly sensitive to the choice of the excitation temperature.

Using these new temperatures, we have recalculated the ASHES cores properties. The analysis of how these new core properties affect the analysis presented in Paper I will be presented in a forthcoming paper (S. Li et al. 2022, in preparation). For the chemical analysis of the current work, we have used the updated core-averaged H₂ column densities and core volume densities (see Appendix C). The updated parameters are 4.9 × 10²¹–2.0 × 10²³ cm⁻² for the core-averaged column density and 1.4 × 10⁵–1.7 × 10⁷ cm⁻³ for the core-averaged volume density. The protostellar cores have higher column densities and volume densities than the prestellar cores (Table 4).

Table 4. Median and Mean values of the Derived Core Properties for Each Category

Name	Prestellar		Protostellar								All
			Outflow Core		Warm Core		Outflow + Warm Core		Sum
	Median	Mean	Median	Mean	Median	Mean	Median	Mean	Median	Mean	Median	Mean
${T}_{{\mathrm{NH}}_{3}}$(K)	14.1	14.2	12.8	13.8	14.8	14.3	15.3	14.9	14.8	14.4	14.4	14.3
		Core-averaged volume densities (cm−3) and averaged column densities (cm−2)
${n}_{{{\rm{H}}}_{2}}$	1.06E+06	1.51E+06	1.52E+06	2.50E+06	1.20E+06	2.69E+06	3.42E+06	5.28E+06	2.30E+06	3.69E+06	1.25E+06	2.23E+06
${N}_{{{\rm{H}}}_{2}}$	2.10E+22	2.56E+22	3.25E+22	3.83E+22	2.57E+22	4.15E+22	5.64E+22	7.91E+22	4.36E+22	5.59E+22	2.56E+22	3.56E+22
				Column Densities (cm−2)
${N}_{{{\rm{C}}}^{18}{\rm{O}}}$	1.10E+15	1.42E+15	8.35E+14	1.30E+15	1.18E+15	1.54E+15	1.79E+15	2.20E+15	1.29E+15	1.77E+15	1.16E+15	1.54E+15
${N}_{{{\rm{N}}}_{2}{{\rm{D}}}^{+}}$	2.63E+11	3.30E+11	2.28E+11	2.61E+11	3.55E+11	4.06E+11	2.96E+11	4.39E+11	2.74E+11	3.94E+11	2.72E+11	3.74E+11
${N}_{{\mathrm{DCO}}^{+}}$	1.47E+11	1.89E+11	1.71E+11	2.12E+11	2.22E+11	2.37E+11	1.92E+11	2.05E+11	1.92E+11	2.18E+11	1.67E+11	2.01E+11
${N}_{{\mathrm{CH}}_{3}\mathrm{OH}}$	⋯	⋯	⋯	⋯	8.36E+12	2.09E+13	1.86E+13	3.61E+13	1.74E+13	2.98E+13	1.74E+13	2.98E+13
${N}_{{{\rm{H}}}_{2}\mathrm{CO}}$	1.39E+12	1.61E+12	2.84E+12	3.00E+12	4.29E+12	5.83E+12	1.20E+13	2.04E+13	6.11E+12	1.18E+13	2.43E+12	7.09E+12
${N}_{{}^{13}\mathrm{CS}}$	1.14E+12	1.14E+12	1.06E+12	1.06E+12	⋯	⋯	1.89E+12	1.89E+12	1.47E+12	1.47E+12	1.29E+12	1.31E+12
${N}_{\mathrm{DCN}}$	⋯	⋯	⋯	⋯	⋯	⋯	7.73E+11	1.05E+12	7.73E+11	1.05E+12	7.73E+11	1.05E+12
${N}_{{{\rm{C}}}_{2}{\rm{D}}}$	8.91E+12	8.33E+12	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	8.91E+12	8.33E+12
NSiO	⋯	⋯	1.74E+12	1.46E+12	⋯	⋯	1.70E+12	5.59E+12	1.74E+12	5.13E+12	1.74E+12	5.13E+12
					Molecular Abundances
${X}_{{{\rm{C}}}^{18}{\rm{O}}}$	4.95E-08	6.74E-08	3.53E-08	3.68E-08	3.85E-08	6.37E-08	2.33E-08	2.95E-08	2.99E-08	4.43E-08	4.23E-08	5.96E-08
${X}_{{{\rm{N}}}_{2}{{\rm{D}}}^{+}}$	7.57E-12	8.07E-12	5.94E-12	5.99E-12	7.78E-12	7.91E-12	4.90E-12	5.07E-12	5.23E-12	5.81E-12	6.12E-12	6.52E-12
${X}_{{\mathrm{DCO}}^{+}}$	5.23E-12	5.95E-12	4.79E-12	4.71E-12	6.58E-12	7.60E-12	2.46E-12	2.84E-12	4.02E-12	4.98E-12	4.78E-12	5.56E-12
${X}_{{\mathrm{CH}}_{3}\mathrm{OH}}$	⋯	⋯	⋯	⋯	2.75E-10	4.44E-10	3.00E-10	4.72E-10	2.83E-10	4.60E-10	2.83E-10	4.60E-10
${X}_{{{\rm{H}}}_{2}\mathrm{CO}}$	5.20E-11	6.88E-11	8.09E-11	8.74E-11	1.59E-10	2.40E-10	1.76E-10	2.80E-10	1.53E-10	2.32E-10	8.87E-11	1.57E-10
${X}_{{}^{13}\mathrm{CS}}$	6.03E-11	6.03E-11	7.94E-11	7.94E-11	⋯	⋯	1.52E-11	1.52E-11	4.73E-11	4.73E-11	5.41E-11	5.38E-11
${X}_{\mathrm{DCN}}$	⋯	⋯	⋯	⋯	⋯	⋯	8.30E-12	8.55E-12	8.30E-12	8.55E-12	8.30E-12	8.55E-12
${X}_{{{\rm{C}}}_{2}{\rm{D}}}$	1.79E-10	2.50E-10	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	1.79E-10	2.50E-10
XSiO	⋯	⋯	4.05E-11	4.38E-11	⋯	⋯	3.26E-11	5.69E-11	3.35E-11	5.54E-11	3.35E-11	5.54E-11

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Assuming LTE and optically thin molecular emission, the molecular column density (N_mol) can be estimated from the velocity-integrated intensity (see Appendix C for a detailed derivation of the column density). To study the properties of the molecules, we also calculated the molecular abundances, ${X}_{\mathrm{mol}}={N}_{\mathrm{mol}}/{N}_{{{\rm{H}}}_{2}}$, using the updated H₂ column density and the derived molecular column densities.

The derived N₂D⁺ column densities range from 5.9 × 10¹⁰ to 1.3 × 10¹² cm⁻², resulting in N₂D⁺ abundances of 2.2 × 10⁻¹²–1.7 × 10⁻¹¹. The N₂D⁺ column densities are similar to the value of 6.2 × 10¹¹ cm⁻² obtained for other IRDCs (e.g., Chen et al. 2010; Gerner et al. 2015; Barnes et al. 2016), and the N₂D⁺ abundances are comparable to the values of ∼10⁻¹² in other massive clumps (Giannetti et al. 2019). The estimated DCO⁺ column densities are between 4.7 × 10¹⁰and 6.5 × 10¹¹ cm⁻², leading to DCO⁺ abundances of 1.3 × 10⁻¹²–2.4 × 10⁻¹¹. ${N}_{{\mathrm{DCO}}^{+}}$ is similar to the values reported in other IRDCs (≤3 × 10¹¹ cm⁻²; Gerner et al. 2015). The derived DCN column densities and abundances are 2.7 × 10¹¹–2.0 × 10¹² cm⁻² and 5.6 × 10⁻¹²–1.2 × 10⁻¹¹, respectively. The DCN abundances are significantly lower than those in more evolved dense cores in W3 (>10⁻¹⁰; Mottram et al. 2020). C₂D has column densities of 4.8 × 10¹²–1.1 × 10¹³ cm⁻² and abundances of 1.5 × 10⁻¹⁰–4.2 × 10⁻¹⁰.

Given that these dense cores are still in very early evolutionary phases and are characterized by a cold environment, H₂CO is expected to form in ice on the grain surface and to subsequently be released to the gas phase (Jørgensen et al. 2005). We assumed an ortho-to-para ratio of 1.6, which is consistent with thermalization at a low temperature of T ∼ 15 K (Jørgensen et al. 2005). The derived H₂CO column densities and abundances are 4.1 × 10¹¹–9.3 × 10¹³ cm⁻² and 1.2 × 10⁻¹¹–1.1 × 10⁻⁹, respectively. CH₃OH has column densities of 2.4 × 10¹²–1.9 × 10¹⁴ cm⁻² and abundances of 7.3 × 10⁻¹¹–2.3 × 10⁻⁹ for the detected dense cores. The abundances of H₂CO and CH₃OH are similar to those in dense cores prior to the hot-core phase in other IRDCs (a few 10⁻¹⁰ for H₂CO and CH₃OH; Gerner et al. 2014; Mottram et al. 2020), but lower than those in hot-core and UCHII regions ( ≥ 10⁻⁹; e.g., Gerner et al. 2014; Mottram et al. 2020).

A C¹⁸O optical correction factor, ${C}_{\tau }={\tau }_{{{\rm{C}}}^{18}{\rm{O}}}/[1-\exp (-{\tau }_{{{\rm{C}}}^{18}{\rm{O}}})]$, is applied in the calculation of the C¹⁸O column density. C_τ is derived following the approach described in Sabatini et al. (2019). The detailed estimation of the C¹⁸O correction factor is presented in Sabatini et al. (2022). The calculated C¹⁸O column densities vary from 1.3 × 10¹⁴ to 5.6 × 10¹⁵ cm⁻², resulting in C¹⁸O abundances of 3.7 × 10⁻⁹–4.8 × 10⁻⁷. The estimated SiO column densities vary from 2.3 × 10¹¹–3.2 × 10¹³ cm⁻², which are comparable to the values in the outflows, whereas the derived abundances of 3.0 × 10⁻¹²–3.4 × 10⁻¹⁰ are lower than those found in the outflows (≥1.1 × 10⁻⁹; see Paper II).

Figure 5 shows histograms of the molecular column densities and abundance ratio distributions for the prestellar and protostellar cores (see also Table 4). Except for C¹⁸O and N₂D⁺, which have similar column densities in the prestellar and protostellar cores, all other molecules have column densities in the prestellar cores that are relatively lower than those in the protostellar cores. On the other hand, the N₂D⁺, DCO⁺, and C¹⁸O abundances are higher in the prestellar cores than in the protostellar cores, indicating that the abundances of these molecules tend to decrease with the evolution of the dense cores. These abundance variations are dominated by the effect of the rapid H₂ density increase from the prestellar to protostellar phases (see Section 4.2). In contrast, the abundance of H₂CO in the protostellar cores is higher than in the prestellar ones, suggesting that its abundance can be enhanced with core evolution.

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To understand the impact of the missing flux on the line emission, we compared the 12m7m and 12m7mTP data sets. We investigated the integrated intensities, peak intensities, line widths, and central velocities of the line emissions between the two data sets.

For the N₂D⁺ line emission, we find that the 12m7m data have recovered about 92% of the 12m7mTP flux. The differences of the measured I and σ_obs are factors of 0.94 and 0.99, respectively. For the DCO⁺ line emission, the mean ratios of 12m7m to 12m7mTP are 0.89 for I and 0.9 for σ_obs, resulting a mean flux ratio (velocity-integrated intensity) of 0.79. The DCO⁺ emission behavior is very similar to that of N₂D⁺. These results indicate that most of the N₂D⁺ and DCO⁺ emission is compact and recovered without the addition of TP data from single-dish telescopes.

For the H₂CO (3_0,3 − 2_0,2) line emission, the 12m7m data recover about 71% of the 12m7mTP flux, and the mean ratios of 12m7m to 12m7mTP for I and σ_obs are 0.82 and 0.87, respectively. On the other hand, CH₃OH has similar flux, I, and σ_obs between the 12m7m and 12m7mTP data sets; the mean ratio (12m7m/12m7mTP) is 0.94 for flux, 0.94 for I, and 1.0 for σ_obs. This indicates that CH₃OH traces more spatially compact emission compared with H₂CO. This suggests that the observed CH₃OH transition may preferentially be concentrated near the protostars or in knots in outflows.

For C¹⁸O, the mean ratios of the 12m7m to 12m7mTP data are 0.54 for the intensity peak and 0.7 for the velocity dispersion, resulting in a mean flux ratio of 0.36. Among the detected lines (excluding CO), C¹⁸O suffers most severely from missing flux. This indicates that C¹⁸O probes a significant amount of diffuse molecular gas. For the remaining lines with relatively low detection rates, their 12m7m images are weakly affected by the missing flux. The mean flux ratios of 12m7m to 12m7mTP are 1.0 for SiO, 0.96 for ¹³CS, 0.9 for DCN, and 0.98 for C₂D.

N₂D⁺ is expected to be abundant in cold (<20 K) and dense (∼10⁵ cm⁻³) regions, in which its major destroyer, CO, is significantly depleted onto grain surfaces. N₂D⁺ can be formed via N₂ reacting with H₂D⁺ (dominant reaction: N₂ + H₂D⁺ → N₂D⁺ + H₂), D₂H⁺, or D₃ ⁺ (Pagani et al. 2009), and destroyed by CO (N₂D⁺ + CO → DCO⁺ + N₂) or electrons (N₂D⁺ + e⁻ → ND + N or D + N₂; Sakai et al. 2022). DCO⁺ is also considered to be a cold and dense gas tracer. However, DCO⁺ requires gas-phase CO for its formation at cold temperatures (T < 20–50 K), i.e., H₂D⁺ + CO → DCO⁺ + H₂ (Wootten & Loren 1987). Therefore, the DCO⁺ abundance does not decrease rapidly when CO is released to the gas phase from the grain mantles (Dalgarno & Lepp 1984). The different chemistry between N₂D⁺ and DCO⁺ may explain their different spatial distributions as seen in Figure 1 (e.g., Sakai et al. 2022). DCN and C₂D tend to form in warm environments (Turner 2001; Albertsson et al. 2013).

The N₂D⁺ and DCO⁺ column densities exhibit a strong correlation (see Figure 15 in Appendix A), with a Spearman rank correlation coefficient ¹⁷ of r = 0.58. This is mostly because both lines trace cold and dense gas in the dense cores. The N₂D⁺ abundance appears to decrease with increasing volume densities ${n}_{{{\rm{H}}}_{2}}$, with a moderate correlation coefficient of −0.35 (see Figure 7). As mentioned in Section 3.4, the volume density increases with the evolution of the dense cores, which continue to accumulate mass via the accretion of material from natal clumps. The ${n}_{{{\rm{H}}}_{2}}$–${X}_{{{\rm{N}}}_{2}{{\rm{D}}}^{+}}$ anticorrelation suggests that the N₂D⁺ abundance decreases with core evolution. As the cores evolve, the gas temperature increases, thereby lowering the deuterium enhancement. In this case, one naively expects an anticorrelation between the N₂D⁺ abundance and ${T}_{{\mathrm{NH}}_{3}}$. As seen in Figure 7, there is no obvious trend between the N₂D⁺ abundance and ${T}_{{\mathrm{NH}}_{3}}$. These cores are still very cold, with temperatures between 10 and 20 K, which are lower than the sublimation temperature of CO (∼25 K). This may explain why the N₂D⁺ abundance does not vary significantly with ${T}_{{\mathrm{NH}}_{3}}$. In addition, this suggests that these cores are still at a very early evolutionary phase, in which the surrounding environment has not been significantly warmed up by young stellar objects. On the other hand, we cannot completely rule out the possibility that ${T}_{{\mathrm{NH}}_{3}}$ does not accurately reflect the true temperature of the dense molecular gas traced by N₂D⁺, because the spatial resolution of ${T}_{{\mathrm{NH}}_{3}}$ (∼5'') is coarser than the ALMA observations (∼12) and the critical density of NH₃ (1,1) is only of a few 10⁴ cm⁻³. Determinations of temperatures at ∼1'' scales would be necessary to verify whether the ${T}_{{\mathrm{NH}}_{3}}$ varies significantly down to the small scale. The ${n}_{{{\rm{H}}}_{2}}$–${X}_{{{\rm{N}}}_{2}{{\rm{D}}}^{+}}$ and ${X}_{{{\rm{N}}}_{2}{{\rm{D}}}^{+}}$–${T}_{{\mathrm{NH}}_{3}}$ results suggest that the N₂D⁺ abundance variation is dominated by the H₂ core density in the ASHES sample.

The column density ratio of ${N}_{{{\rm{N}}}_{2}{{\rm{D}}}^{+}}$/${N}_{{{\rm{H}}}_{2}\mathrm{CO}}$ appears to decrease as a function of increasing ${n}_{{{\rm{H}}}_{2}}$. However, a closer look reveals that this weak anticorrelation is mostly dominated by the protostellar cores. Both ${N}_{{{\rm{N}}}_{2}{{\rm{D}}}^{+}}$ and ${N}_{{{\rm{H}}}_{2}\mathrm{CO}}$ tend to increase with ${n}_{{{\rm{H}}}_{2}}$, and therefore the ${N}_{{{\rm{N}}}_{2}{{\rm{D}}}^{+}}$/${N}_{{{\rm{H}}}_{2}\mathrm{CO}}$-${n}_{{{\rm{H}}}_{2}}$ anticorrelation implies that ${N}_{{{\rm{H}}}_{2}\mathrm{CO}}$ is more sensitive to ${n}_{{{\rm{H}}}_{2}}$ than ${N}_{{{\rm{N}}}_{2}{{\rm{D}}}^{+}}$ toward the protostellar cores (see also Section 3.3). In addition, the ${N}_{{{\rm{N}}}_{2}{{\rm{D}}}^{+}}$/${N}_{{{\rm{H}}}_{2}\mathrm{CO}}$ ratio also appears to decrease with increasing ${T}_{{\mathrm{NH}}_{3}}$, with a correlation coefficient of −0.63. This is because the H₂CO abundance is enhanced by elevated temperatures. The ${N}_{{{\rm{N}}}_{2}{{\rm{D}}}^{+}}$/${N}_{{\mathrm{CH}}_{3}\mathrm{OH}}$ ratio shows no clear trend with ${n}_{{{\rm{H}}}_{2}}$ or ${T}_{{\mathrm{NH}}_{3}}$. In general, DCO⁺ shows a similar trend to those seen in N₂D⁺, except for ${n}_{{{\rm{H}}}_{2}}$–${N}_{{\mathrm{DCO}}^{+}}$/${N}_{{\mathrm{CH}}_{3}\mathrm{OH}}$ (r = −0.27), which presents a weak anticorrelation. The difference in N₂D⁺ and DCO⁺ may be a result of different chemistry.

There is a weak anticorrelation between ${n}_{{{\rm{H}}}_{2}}$ and the ${N}_{{\mathrm{DCO}}^{+}}$/${N}_{\ {{\rm{N}}}_{2}{{\rm{D}}}^{+}}$ ratio (see Figure 6), with a correlation coefficient of r = −0.23. From Figures 7 and 8, one notes that both the N₂D⁺ and DCO⁺ abundances decrease with increasing ${n}_{{{\rm{H}}}_{2}}$, thereby causing the ratio of DCO⁺ to N₂D⁺ to change slightly with ${n}_{{{\rm{H}}}_{2}}$. In addition, the ${N}_{{\mathrm{DCO}}^{+}}$/${N}_{\ {{\rm{N}}}_{2}{{\rm{D}}}^{+}}$ ratio shows only minor changes with ${T}_{{\mathrm{NH}}_{3}}$, which gives a correlation coefficient of r = −0.11. This can be ascribed to the fact that the both DCO⁺ and N₂D⁺ abundances do not vary significantly with ${T}_{{\mathrm{NH}}_{3}}$ (see Figures 7 and 8).

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CH₃OH is considered to be mostly formed on the surface of dust grains, via the hydrogenation of CO with some intermediate products (e.g., H₂CO; Charnley et al. 1997; Watanabe et al. 2004; Fuchs et al. 2009):

$$\begin{eqnarray}&&\begin{array}{l}\mathrm{CO}\,\mathop{\longrightarrow }\limits_{{\rm{H}}}\,\mathrm{HCO}\mathop{\longrightarrow }\limits_{{\rm{H}}}\,{{\rm{H}}}_{2}\mathrm{CO}\mathop{\longrightarrow }\limits_{{\rm{H}}}\,{\mathrm{CH}}_{2}\mathrm{OH},\\ {\mathrm{CH}}_{3}{\rm{O}}\mathop{\longrightarrow }\limits_{{\rm{H}}}\,{\mathrm{CH}}_{3}\mathrm{OH}.\end{array}\end{eqnarray} \tag{ 2 }$$

Unlike CH₃OH, which forms entirely on the surfaces of dust grains, H₂CO can be formed efficiently through both grain surface reaction in cold environments and gas-phase reactions in warm/hot environments (Le Teuff et al. 2000; Garrod et al. 2006; Fuchs et al. 2009).

CH₃OH shows a dip in its emission distribution at the center of some dense cores, such as the protostellar core #15 in G337.54 (Appendix A). A similar feature has been observed in low-mass prestellar cores, e.g., L1498 and L1517B (Tafalla et al. 2006). These authors suggest that the weaker CH₃OH emission toward the center of the dense cores is due to the significant CH₃OH depletion in cold and dense environments. Therefore, the low detection rate of CH₃OH in dense cores may be partly ascribed to CH₃OH depletion.

Among the detected molecules, the H₂CO and CH₃OH column densities show the strongest correlation, with correlation coefficients of 0.83 (see Figure 15 in Appendix A). As mentioned in Section 3.3, both H₂CO and CH₃OH tend to probe dense and high-velocity molecular gas, and hence the protostellar activity may be partly responsible for the strong correlation of the two species. For example, outflows/shocks can release both H₂CO and CH₃OH from grain mantles to the gas phase. In addition, both the H₂CO and CH₃OH column densities show strong correlations with the SiO column density (see Figure 15 in Appendix A); the correlation coefficient is 0.73 for ${N}_{{{\rm{H}}}_{2}\mathrm{CO}}$–N_SiO and 0.84 for ${N}_{{\mathrm{CH}}_{3}\mathrm{OH}}$–N_SiO.

The derived abundance ratios of H₂CO/CH₃OH =0.1–2.3 are comparable to the values of 0.9–2.5 reported in dense clumps (${n}_{{{\rm{H}}}_{2}}\sim {10}^{6}$ cm⁻³; Leurini et al. 2010), hot corinos (0.7–4.3; Maret et al. 2004, 2005), and low-mass starless cores (1.1–2.2, e.g., L1498 and L1517B; Tafalla et al. 2006). These values are higher than the abundance ratios derived in hot cores (0.13–0.28; Bisschop et al. 2007) and the shocked gas in the Galactic Center clouds (0.01–0.1; Requena-Torres et al. 2006; Lu et al. 2021), whereas they are significantly lower than those in the interclump medium (H₂CO/CH₃OH = 14–1400; ${n}_{{{\rm{H}}}_{2}}\sim {10}^{4}$ cm⁻³; Leurini et al. 2010). The discrepancies could be attributed to either different dominant formation mechanisms or different chemical conditions. A detailed chemical modeling and observational comparison is needed to distinguish between these possibilities, which is beyond the scope of this paper.