Survey of CH₃NH₂ and its Formation Process

In Suzuki et al. (2016), we performed a survey of CH₂NH in CH₃OH-rich high-mass star-forming regions with the NRO 45 m telescope. As a result, we detected CH₂NH in eight sources. From this survey, we selected four CH₂NH-rich sources: G10.47+0.03, G31.41+0.3, NGC 6334I, and W51 e1/e2. The coordinates, source velocities, distances, and previously reported CH₂NH fractional abundances of the selected sources are summarized in Table 1. A more detail description of the four regions is presented in Section 3.1. We note that the spatial resolution of the CH₂NH survey was ∼16'', which is much larger than the current study (∼1'').

Our observations were carried out during Cycle 5 of ALMA in 2018 May, using the ALMA Band 5 and 6 receivers. Our configuration was C43-2. Other observation parameters, such as the phase centers, the spectral resolutions, the maximum recoverable scales, the angular resolutions, and the sources and the signal-to-noise ratios (S/Ns) of the calibrations are summarized in Table 2.

The observed frequency ranges are the same for all sources. The center frequencies, the bandwidths, and the number of channels are summarized in Table 3. We designed these receiver setups to cover a number of molecular transitions of CH₃OH, CH₃NH₂, and CH₂NH with a wide range of upper state energy levels (see the Appendix).

In our analysis, we directly use the pipeline-calibrated data. The total calibration errors are less than 10% in Bands 5 and 6 (ALMA technical handbook). Our data were calibrated by Common Astronomy Software Applications (CASA) V.5.1.1 (McMullin et al. 2007), with the ALMA Cycle 5 pipeline. Then, we subtract the continuum emission in the (u, v) domain using first the methodology described in Jørgensen et al. (2016) to determine the continuum level. We first create an image cube for each source and extract the spectrum with the task imval of the peak position. With all the channels of the extracted spectra we create histograms of the frequency distribution of intensity. We derive the continuum level and its standard deviation by performing Gaussian fits to the peak of the histogram (see Figure 1). We then select the line-free channels if the intensity of the channel is within the 3σ level of the derived continuum level. We use the line-free channels to subtract the continuum emission in the (u, v) domain using the CASA task uvcontsub. We note that the error in the determination of the continuum level using the histogram of intensities is typically 5% (Jørgensen et al. 2016; Sánchez-Monge et al. 2018). For the regions NGC 6334I and W51, which contain several bright sources, we determine the continuum level and line-free channels independently for each source

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After subtracting continuum emission in the (u, v) domain, spectral cubes are obtained by the CASA task tclean by applying natural weighting. We also create continuum emission maps with tclean. We show examples of continuum maps in Figure 2, which are created from the spectral window of Band 5, whose center frequency of 203.050 GHz. These continuum maps are used to estimate the hydrogen column densities in the following section. With the CASA task imfit, we performed Gaussian fitting on the continuum peak positions, where we extract the spectra. We create the continuum emission maps and continuum-free spectra through the CASA task immoment.

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We show the continuum emission maps and the contamination-free transitions in Figures 2 through 6. Their upper energy levels are shown on the lower right of each figure. Using the CASA task imfit, we performed Gaussian fitting of the peaks of integrated intensity to determine the FWHMs of the source sizes. These source sizes are converted to physical sizes considering the distances to the sources. We summarize our results in Table 4. We note that some species show different excitation temperatures and velocities, suggesting the existence of unresolved spatial components. Therefore, our abundances should be regarded as the average of the unresolved components. Though we discuss the molecular ratios with this limitation in this article, future high-resolution mapping would improve their accuracy.

In NGC 6334I, Hunter et al. (2006) performed mapping observations of 1.3 mm continuum emission with the Submillimeter Array (SMA), and reported the structures named SMA1, SMA2, SMA3, and SMA4. Later, Brogan et al. (2016) carried out mapping with angular resolution as high as 017 (220 AU) from 5 cm to 1.3 mm with the Karl G. Jansky Very Large Array (VLA) and ALMA. They found the continuum peaks of MM1, MM2, MM3, MM4, MM6, MM7, MM9, and CM2, where MM1, MM2, MM3, and MM4 respectively correspond to the previously known SMA1, SMA2, SMA3, and SMA4. Of these components, MM1 is known as a dramatic outburst source, associated with 6.7 GHz methanol maser and mid-infrared emission (Hunter et al. 2018, 2021). MM3 is known to be a UCHII region associated with free–free emission (Hunter et al. 2006). Many organic molecules have been reported in MM1 and MM2 (e.g., Walsh et al. 2010; Zernickel et al. 2012; El-Abd et al. 2019).

Our molecular distributions overlap with the positions of MM1, MM2, and MM3. The distributions of the CH₃OH transitions extend over ∼10''. This scale is close to the maximum recoverable scale. These maps suggest the existence of these species not only in the hot cores but also in the surrounding warm envelopes. As the results of Gaussian fitting to the compact components, the deconvolved source size for CH₃OH is 4''. The source sizes for CH₃NH₂ and CH₂NH are 2'', which correspond to ∼0.02 pc.

Though the previous continuum mapping observations by Brogan et al. (2016) suggested the existence of at least seven cores in MM1, our spatial resolution is not sufficient to resolve such structures. We analyze the molecular abundances assuming that molecular emission fills our synthesized beam. Future higher-resolution mapping observations of CH₃OH would enable us to investigate the detailed distributions of CH₃OH, CH₃NH₂, and CH₂NH.

Bøgelund et al. (2019) reported the distributions of CH₃NH₂ and CH₂NH in MM1 and MM2 with ALMA Band 7 receivers, which are consistent with our results. We note that the location of the continuum peak position of NGC 6334I MM1 is offset from that of Bøgelund et al. (2019) by about 2''. This difference may arise from the complex structure of this source due to the embedded cores. High-resolution mappings would be helpful to resolve such sources. As the molecular peak positions are close to that of our continuum peak, we extract the spectra of our continuum peak position of MM1 in the analysis of molecular abundance. Though our continuum peak position of MM2 is almost identical with Bøgelund et al. (2019), we find that the molecular peak positions are offset from the continuum peak position by about 1'' (see Figure 3). Since the difference of peak positions of molecules are small compared to the synthesized beam size, we extract the spectra from the peak integrated intensity position of CH₃OH 13₃ A⁻ → 13₂ A⁺. The continuum peak position of MM3 is offset to the north by ∼3'' from the molecular peak positions. We extracted the spectra from the peak position of the CH₃OH 13₃ A⁻ → 13₂ A⁺ transition.

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G10.47+0.03 is a well-known massive star-forming region associated with several UCHII and HCHII regions. Wood & Churchwell (1989) reported the UCHII regions A, B, and C via 2 and 6 cm mapping with the VLA (see Figure 4). Cesaroni et al. (1998) further resolved component B into HCHII regions B1 and B2 with 1.3 cm VLA observations. They interpreted these sources as face-on rotating disks. The absorption of the NH₃(4, 4) transition in these B1 and B2 cores is probably due to molecular outflows originating from HCHII regions. Cesaroni et al. (2010) resolved components A, B1, and B2 with 6, 2, and 1.3 cm continuum emission as well, and newly detected component D with 3.6 cm continuum emission. Cesaroni et al. (2010) also provided evidence of infalling gas toward the embedded cores associated with the outflows. Our maps show that the molecules are distributed around the B1 and B2 positions. In our maps, the distribution of CH₃OH 4₀ A⁺ → 3₀ A⁺ is slightly extended. The source sizes of other CH₃OH lines are comparable to this transition and independent of the upper energy level. The typical FWHM source size for the compact components is ∼2'', which corresponds to ∼0.08 pc. As our peak positions of the continuum emission coincide with those of the peaks of molecular emission, we extract the spectra from the peak positions of the continuum emission.

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G31.41+0.3 is a massive star-forming region similar to G10.47+0.03. Although this source has a UCHII region, the position of the hot molecular core is offset from the UCHII region by about 5'' (Cesaroni et al. 1994), which is outside of Figure 5. Cesaroni et al. (2010) detected weak continuum sources A and B inside the hot molecular core of G31.41+0.3, though we could not distinguish them with our spatial resolution. This continuum emission is thought to originate from a thermal jet rather than UCHII regions. The nondetection of UCHII regions inside the hot molecular core of G31.41+0.3 implies that this source is less evolved than G10.47+0.03 (Cesaroni et al. 2010). Our continuum emission and the molecular distributions extend around the continuum sources A and B. Through Gaussian fitting to the peaks, we found that the typical FWHM source sizes are ∼2'', which corresponds to ∼0.05 pc. Therefore the physical characteristics of the observed region relative to the synthesized source are similar to G10.47+0.03. We extract the spectra from the peak integrated intensity position of CH₃NH₂, which includes the continuum sources A and B.

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W51 e1/e2 is a well-known protoclustar region, with the UCHII regions e1, e2, e3, e4, and e8 covered in our mapping region (Gaume et al. 1993; Zhang & Ho 1997), as shown in Figure 6. Through the mapping observation of 870 μm dust continuum emission with SMA, Tang et al. (2009) detected the extension of dust ridges northwest of e2 with an overall length of ∼2'', and southwest of e8 with an overall length of ∼3''. They suggest that the gravitational collapse would be slowed down by magnetic fields, affecting the morphology of the source. W51 e2 is the strongest H ii region, which is thought to be powered by an O8-type star (Shi et al. 2010). Shi et al. (2010) performed continuum mapping of W51 e2 at 0.85 and 1.3 mm with ALMA, and at 7 and 13 mm with VLA. They identified the subcores named e2-N, e2-W, e2-E, and e2-NW. The emission from e2-N is free–free emission from the H ii region, while the other continuum emission may be from dust. Of the four sources, e2-E was the only source associated with hydrogen recombination lines (H26α, H53α, and H66α). Goddi et al. (2016) found that e2-E and e2-NW are associated with NH₃ and CH₃OH emission, respectively, while e2-W is traced by absorption. The detailed structure in e2 is not resolved in our maps. The emission of CH₃OH 4₀ A⁺ → 3₀ A⁺ and CH₂NH 3_0,3 → 2_0,2 overlap with the dust ridges detected by Tang et al. (2009). The FWHM source sizes of CH₃OH and CH₂NH are larger than for CH₃NH₂. The typical FWHM source sizes are ∼3'' for CH₃OH and CH₂NH, which corresponds to ∼0.08 pc. This physical scale is larger than for NGC 6334I, but comparable to G10.47+0.03 and G31.41+0.3. Our molecular emission peaks are close to the continuum peak positions. Therefore, we extract the spectra from the continuum peak positions, which correspond to W51 e2-E and e8, and hereafter we call W51 e2-E as simply W51 e2.

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Given our synthesized beam size, the peak positions of the integrated intensities of the different species are close enough for the G10.47+0.03, G31.41+0.3, and W51 e1/e2 regions. On the other hand, the complex spatial morphology of NGC 6334I suggests the existence of unresolved hot cores. In this paper, we do not consider the diversity of the column densities for the unresolved cores. We note that the CH₃NH₂/CH₃OH ratio of this source may change if the cores are sufficiently resolved by future observations. Future higher-resolution observations would be important to obtain more detailed chemical characteristics of these cores.

We show the spectra of potentially strong CH₂NH and CH₃NH₂ transitions with black lines in Figure 7 through 12. The CH₂NH 7_1,6 → 7_0,7 transition at 250.16168 GHz and CH₃NH₂ 2₂ B2 → 2₁ B1 transition at 250.1594 GHz are blended with each other.

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We use the CASSIS line analysis package (Centre d'Analyze Scientifique de Spectres Instrumentaux et Synth'etiques) 6.2 to model the emission and absorption lines with the LTE approximation (Vastel et al. 2015). First of all, we create the best-fit model of CH₃OCHO, CH₃OCH₃, CH₃COCH₃, C₂H₃CN, C₂H₅CN, and NH₂CHO to exclude the possibility of contamination. As these COMs are known to be present in typical hot core environments and have rich molecular lines in our observed frequency range, we carefully select contamination-free transitions of CH₃OH, CH₃NH₂, and CH₂NH. Then, we performed least-squares fitting with the j thon scripting tool in CASSIS. We simulate the line shape from the given parameters, and the best column densities, excitation temperatures, line widths, and radial velocities are given by minimizing the residuals relative to the observed spectrum. With Markov Chain Monte Carlo methods, the initial values of the parameters are randomly given. We found that 3000 iterations are good enough to obtain the best parameters. The errors were given from the standard deviation of the best-fit parameters. The best-fitted synthesized spectra, including CH₃OH, CH₃NH₂, and CH₂NH, are shown overlapping with the observed spectra by the red line in Figures 7 through to 11. The column density of molecular hydrogen is estimated from the continuum emission from the dust in the same way as Hernández-Hernández et al. (2014). In this method, the gas mass is calculated as

$$\begin{eqnarray}&&{M}_{{\rm{gas}}}=\displaystyle \frac{{S}_{\nu }{D}^{2}{R}_{{\rm{d}}}}{{B}_{\nu }({T}_{{\rm{d}}}){\kappa }_{\nu }},\end{eqnarray} \tag{ 1 }$$

where S_ν , D, R_d, κ_ν , and B_ν (T_d) are the flux density, distance to the source, the gas-to-dust ratio, the dust opacity per unit dust mass, and the Planck function at the dust temperature T_d, respectively. First, from Ossenkopf & Henning (1994), we use a κ_ν of 2.0 cm² g⁻¹ at 1.3 mm, which corresponds to 230 GHz. We estimate κ_ν at the other frequencies with the emissivity spectral index of dust of 1.5 as

$$\begin{eqnarray}&&{\kappa }_{\nu }=2.0\times {\left[\displaystyle \frac{\nu \,\mathrm{GHz}}{230\,\mathrm{GHz}}\right]}^{1.5}.\end{eqnarray} \tag{ 2 }$$

Then, with an R_d of 100, and using the Rayleigh–Jeans approximation, we estimate the hydrogen column density with the following equation

$$\begin{eqnarray}&&\left[\displaystyle \frac{{N}_{{{\rm{H}}}_{2}}}{{\mathrm{cm}}^{2}}\right]=\displaystyle \frac{1.74\times {10}^{16}}{{\theta }^{2}{\kappa }_{\nu }}\left[\displaystyle \frac{{S}_{\nu }}{\mathrm{Jy}}\right]{\left[\displaystyle \frac{{T}_{{\rm{d}}}}{{\rm{K}}}\right]}^{-1},\end{eqnarray} \tag{ 3 }$$

where θ is the synthesized beam size (radians). In our work, we use the angular resolution of our observations as θ. Assuming that the source is uniformly filled within the beam, we ignore the frequency dependency of the source size. We obtain S_ν from the continuum maps (Figure 2), which are created in the procedure of continuum subtraction. We approximate the dust temperature by assuming it to be the excitation temperature of CH₃OH. We use all the spectral windows to obtain the mean hydrogen column densities, and the standard deviation of the hydrogen column densities to estimate the errors. As free–free emission is evident in NGC 6334I MM3, we subtract the contribution of free–free emission to estimate the hydrogen column density of this source. Utilizing VLA archival data, Hunter et al. (2006) estimated the fraction of free–free emission at 1.3 mm to be 62% of the total flux of continuum emission. With the caveat that this percentage is deduced from an observation of the 3.6 cm flux density, we multiply the observed flux of continuum emission by 0.62 to take into account the contribution of free–free emission in NGC 6334I MM3. We summarize our results in Table 5.

As a result of our fitting, we detected our species of interest in all sources. Especially, we report the first detection of CH₃NH₂ in G31.41+0.03, W51 e2, and W51 e8. Our column densities and the excitation temperatures of H₂, CH₃OH, CH₃NH₂, and CH₂NH are summarized in Table 6. In Table 5, we convert the column densities into fractional abundances compared to H₂.

The CH₃NH₂ abundances of G10.47+0.03, NGC 6334I MM1, and G31.41+0.3 show higher values of ∼1.0 × 10⁻⁷. On the other hand, NGC 6634I MM3 has low abundance of CH₃NH₂ and a high abundance of CH₃OH (3.4 × 10⁻⁷). Since the Gaussian-fitted source sizes of CH₃OH are larger than those of CH₂NH and CH₃NH₂, the abundances of N-bearing species may have been underestimated relative to those of O-bearing species in Suzuki et al. (2018) due to beam dilution. The excitation temperature of CH₃NH₂ in G10.47+0.03 is 172 K, which is much higher than that reported by Ohishi et al. (2019), where the excitation temperature was ∼46 K. The low excitation temperature of CH₃NH₂ given by Ohishi et al. (2019) implies that CH₂NH is in the extended envelope component structure surrounding the hot core. In Ohishi et al. (2019), the beam size of the NRO 45 m telescope was ∼20'', being larger than our maximum recoverable scale of ∼10''. Such a component would be unresolved with our interferometric observation since we did not use the ALMA Compact Array (ACA). In this case, it would be difficult to compare the column densities with those of Ohishi et al. (2019) in this study. Since we could not detect CH₂NH and CH₃NH₂ in the NGC 6334I MM3 region, we estimate the upper limit of the column densities using all transitions covered in our observations with an excitation temperature of 169 K, corresponding to that of CH₃OH, and a line width of 6.0 km s⁻¹. Through line simulation with CASSIS, we get an upper limit to the column density of 1.0 × 10¹⁶ cm⁻², which corresponds to a fractional abundance of 5.6 × 10⁻⁹. For CH₂NH, the upper limit of the column density for NGC 6334I MM3 is 1.5 × 10¹⁵ cm⁻², which corresponds to a fractional abundance of 8.3 × 10⁻¹⁰. The three cores in the NGC 6334I region, MM1, MM2, and MM3, are chemically interesting regions, as Bøgelund et al. (2019) reported that the abundances of CH₃NH₂ and CH₂NH differ by orders of magnitude in them. Our column densities of CH₂NH and CH₃NH₂ agree with Bøgelund et al. (2019) within a factor of three. Since our observed position of NGC 6334I is offset by about 2'' compared to Bøgelund et al. (2019), this difference would not be surprising. In addition, our receiver setup enables us to obtain the column density of CH₃OH in MM1, MM2, and MM3 simultaneously. The low CH₃NH₂/CH₃OH ratios of NGC 6334I MM2 and MM3 clearly show the depletion of only N-bearing species.

Finally, we show the spectra of the hydrogen recombination line H39β in Figure 13, which we could observe simultaneously in this work. While this line is evident in NGC 6334I MM3, it is very weak for the other sources. This result suggests the physical evolution of NGC 6334I MM1 and MM2 is in an early phase, as the ionization of hydrogen atoms by the stellar radiation field is not dominant.

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In this section, we evaluate our observational results using the chemical model described in Suzuki et al. (2018). In this previous work, we utilized the three-phase chemical model NAUTILUS (Ruaud et al. 2016, and references therein). We used the gas-phase chemical network kida.uva.2014 ¹⁰ (Wakelam et al. 2015), and the grain surface reactions in Garrod (2013). With these reaction sets, we updated the formation process of CH₃NH₂. We added the hydrogenation processes of HCN on the grain surface (HCN + 2H → H₂CN and H₂CN + 2H → CH₃NH₂), resulting in an increase of CH₃NH₂ abundance. In total, 489 species composed of 13 elements (H, He, C, N, O, Si, S, Fe, Na, Mg, Cl, P, and F) were included. We used the canonical cosmic-ray ionization rate of 1.3 × 10⁻¹⁷ s⁻¹. To simulate the physical conditions in hot cores, we assumed two stages for the physical model, where freefall collapse is followed by a dynamically static warm-up. The cold collapse phase started from ${n}_{{{\rm{H}}}_{2}}$ = 3 × 10³ cm⁻³ to a final postcollapse density of ${n}_{{{\rm{H}}}_{2}}$ = 2 × 10⁷ cm⁻³. In this phase, we use the formula of Nejad et al. (1990), where factor B controls the timescale of this phase. While B = 1 corresponds to freefall collapse, a smaller value of B describes the effects of turbulent, thermal, or magnetic resistance. In our model, the factor B only slows down the collapsing phase, without affecting any physical evolution during the warm-up phase. The factor B was set to unity, which corresponds to the case of freefall. The increase in visual extinction during collapse leads to a minimum dust-grain temperature of 8 K, followed by a warm-up to 400 K; during this phase, the gas and dust temperatures are assumed to be well coupled. The gas density during the warm-up phase is fixed to be the final gas density of the freefall collapse (i.e., ${n}_{{{\rm{H}}}_{2}}$ = 2 × 10⁷ cm⁻³). For the timescale, we employed the fast warm-up model since this model was prepared for the physical evolution of high-mass star-forming regions (Garrod 2013). The timescale for the warm-up phase is 7.12 × 10⁴ yr. After this time, the temperature remains fixed to the maximum value of 400 K. Since we achieved the best agreement after the end of the warm-up phase in Suzuki et al. (2018), we discuss the comparison beyond 7.12 × 10⁴ yr.

We test the parameter dependencies of our model by running our model with different cosmic-ray ionization rates, ζ. While the canonical value for ζ is 1.3 × 10⁻¹⁷ s⁻¹, Barger & Garrod (2020) suggested higher values for ζ up to 2 × 10⁻¹⁶ s⁻¹ to explain their observations of chemical species. In Models A, B, and C, we set ζ to be 1.3 × 10⁻¹⁷, 5.2 × 10⁻¹⁷, and 1.3 × 10⁻¹⁶ s⁻¹, respectively (see Table 7 for the detailed parameters). We present the time evolution of the fractional abundances of CH₃OH, CH₃NH₂, and CH₂NH in Figure 14. Cosmic rays efficiently destroy molecules when ζ is large. With an ζ of 1.3 × 10⁻¹⁷ s⁻¹, it takes ∼1 × 10⁶ yr after the beginning of warm-up to explain the observed CH₃OH and CH₃NH₂. On the other hand, this timescale decreases to less than 2 × 10⁵ yr with an ζ of 1.3 × 10⁻¹⁶ and 5.2 × 10⁻¹⁷ s⁻¹. Since the weak hydrogen recombination lines (Figure 13) suggest the younger evolutional phase, Models B and C would be reasonable. Considering that the typical timescale for hot cores to have a detectable UCHII region is ∼10⁵ yr (Churchwell 2002), ζ should be larger than 5.2 × 10⁻¹⁷ s⁻¹. Hereafter, we fix ζ to 5.2 × 10⁻¹⁷ s⁻¹ since this is the best value of ζ for NGC 6334I IRS1 (Barger & Garrod 2020).

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The other free parameters of our simulations are the factor B, peak temperature, peak density, and timescale of the warm-up phase. Based on Model B, we prepared physical models with different collapsing speeds, temperatures, densities, and warm-up timescales, as summarized in Table 7. We determine the peak temperature from the comparison with the theoretical model. As our sources are located at a different distances, the temperatures of the observed regions are different from source to source. We use the temperature profiles in Nomura & Millar (2004), which were predicted by a detailed radiative transfer model together with observations of the spectral energy distributions of hot molecular cores. Then, considering the distances to the sources and our synthesized beam size of ∼1'', the typical temperatures in our observations would be ∼500, ∼200, ∼300, and ∼300 K for NGC 6334I, G10.41+0.03, G31.41+0.3, and W51 e1/e2, respectively. Our synthesized beam would cover the hot regions where the frozen species would sufficiently sublimate. Therefore, in Models D and E, the peak temperature is changed to 200 and 600 K, respectively. In Models F and G, the final gas densities are 1 × 10⁶ and 1 × 10⁸ cm⁻³, respectively. We note that we used the same initial density in Models F and G. In Models H, I, and J, the factor B is set to 0.7, 0.2, and 0.1, respectively, to control the collapsing speed. We use the medium models in Garrod (2013) for Model K.

As an example, we show our simulation results in Figure 15 with Model B. The simulated fractional abundances of CH₃OH, CH₃NH₂, and CH₂NH, compared to the total proton density in the gas phase and on grains (sum of the molecular abundances in the grain mantle and on the grain surface) are shown by solid and dotted lines, respectively. In the comparison between the simulated and observed abundances, we multiply the observed abundances by a factor of 2 since the observed abundances are the relative abundances compared to hydrogen molecules (two protons). A time of zero years corresponds to the beginning of the warm-up phase. The left panel of Figure 15 represents the fractional abundances until 1 × 10⁶ yr after the beginning of the warm-up phase. As we discussed in the previous studies, CH₂NH is efficiently formed in the gas-phase reaction CH₃ + NH → CH₂NH + H, while CH₃NH₂ is built on grain surfaces via successive hydrogenation processes of HCN (Suzuki et al. 2016, 2018). When the grain surface temperature gets high enough, these species sublimate from grains, leading to a sudden increase of the gas-phase abundances. The sublimation of CH₃NH₂ happens at ∼6.2 × 10⁴ yr, when the dust temperature is ∼130 K, while the sublimation of CH₃OH occurs when the dust temperature is ∼110 K due to the smaller binding energy. Since CH₃NH₂ is frozen before 6.2 × 10⁴ yr, the results before this age would be not meaningful.

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First of all, we compare Model B with the fast warm-up model of Garrod (2013). Our peak fractional abundances of CH₃OH, CH₃NH₂, and CH₂NH in the gas phase during the warm-up phase are 3.2 × 10⁻⁵, 3.4 × 10⁻⁶, and 2.3 × 10⁻⁶, respectively. Garrod (2013) reported the peak abundances of CH₃OH, CH₃NH₂, and CH₂NH in the gas phase to be 1.1 × 10⁻⁵, 8.0 × 10⁻⁸, and 1.1 × 10⁻⁸, respectively. Hence, there is a disagreement in the CH₃NH₂ and CH₂NH abundances. For CH₂NH, the disagreement is due to the update of the gas-phase formation process of CH₂NH with kida.uva.2014 (see Suzuki et al. 2016 for details). For CH₃NH₂, the difference is due to the inclusion of the hydrogenation processes of HCN and CH₂NH. We prepare Model B' where we switch off the series of hydrogenation processes to form CH₃NH₂ from Model B. The simulated fractional abundances from Models B and B' are compared in Figure 15. The peak abundance of CH₃NH₂ from Model B' is 4.3 × 10⁻⁸, which agrees with Garrod (2013).

We show the CH₃NH₂/CH₃OH ratio from Model B in the right panel of Figure 15. Both CH₃OH and CH₃NH₂ are formed on grains through the hydrogenation process during the warm-up phase and destroyed simultaneously in the gas phase after sublimation by reactive radicals, ions, and cosmic rays. However, there is a time variation in the CH₃NH₂/CH₃OH ratio. The CH₃NH₂/CH₃OH ratio is ∼0.01 at first, and it increases to 0.05 at ∼3 × 10⁵ yr. This increase is due to the formation of CH₃NH₂ in the gas phase through the following series of reactions: (1) CH₃ ⁺ + NH₃ → CH₃NH₃ ⁺ and then (2) CH₃NH₃ ⁺ + e⁻ → CH₃NH₂ + H. After ∼3 × 10⁵ yr, the CH₃NH₂/CH₃OH ratio drops dramatically due the formation of CH₃OH in the gas phase. First, the abundances of the ionized species increase due to cosmic rays. Then, CH₃OH forms through the recombination processes of these ions form CH₃OH. For example, CH₃OH₄ ⁺ + e⁻ → CH₃ + CH₃OH and CH₃COCH₄ ⁺ + e− → CH₃CO + HCO + H, then H + CH₃OCO → CH₃OH + CO. Though these reactions have to be considered with caution due to the lack of reliable measurements of the reaction rates, as we will see, the agreement with the observed abundances is achieved mainly before 3 × 10⁵ yr.

We compare the observed fractional abundances of CH₃OH, CH₃NH₂, and CH₂NH with the simulated fractional abundances derived from the chemical model. The errors of the observed fluxes during the calibration and the continuum subtraction should be ∼10% (ALMA technical handbook). On the other hand, the errors of the chemical model result should be propagated from thousands of reactions with the uncertain reaction rates along the time evolution. Hence, the errors of the chemical model are more significant. Since it is difficult to constrain the errors of the chemical model, we employ a criterion for the comparison as being within a factor of 10, which is often used for comparisons with simulations in previous studies (e.g., Wakelam et al. 2015).

In Figure 16, we compare the simulated fractional abundances of CH₂NH from Models B, D, and E, where the peak temperatures are 400, 200, and 600 K, respectively. All models show a fractional abundance of CH₂NH higher than 1 × 10⁻⁷ after sublimation. We also display the observed CH₂NH abundances in blue, indicating the chemical models overproduce CH₂NH. As discussed in Suzuki et al. (2016), CH₂NH is efficiently produced by the reaction CH₃ + NH. The formation rate of CH₂NH from radicals is well investigated (see Hébrard et al. 2012; Loison et al. 2014; Wakelam et al. 2015 for details), and therefore this overproduction would not be due to the wrong formation rate. Our model considers the formation and destruction chemistry of CH2NH from the KIDA database. However, the destruction reactions of CH₂NH are largely dominated by ion–molecule reactions, which are mostly efficient in low-temperature environments. Therefore, additional high-temperature theoretical and experimental data exploring the possible neutral–neutral and radical–neutral destruction reactions of CH₂NH may provide a closer agreement with the observations.

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In Table 8, we summarize the ages where our models can explain the observed fractional abundances and the CH₃NH₂/CH₃OH ratio for each source. In this table, we set a criterion that the simulated fractional abundances of CH₃OH and CH₃NH₂ are within a factor of 10 compared to the observed abundances. The molecular ratio of CH₃NH₂/CH₃OH would be a more valid indicator as the uncertainty of the H₂ column densities disappears. We compare the observed CH₃NH₂/CH₃OH ratios with the simulations considering the error propagation of the observations. As a result, we can successfully explain the observation results with certain parameter sets, except for NGC 6334I MM3, where the CH₃NH₂ abundance was too low to detect.

In Figure 17, we show the time evolution of the fractional abundances of CH₃NH₂ and CH₃OH, and their ratio for the different Models D, E, F, G, H, I, J, and K. Though the overall trends of chemical evolution are similar to Model B, we can see that the molecular abundances are influenced by the physical environment. Especially, as we see in Models H, I, and J, the gravitational collapse speed controlled by B shows the largest effect on the CH₃NH₂/CH₃OH ratio. We also note that the observation results of NGC 6334I MM1, where CH₃NH₂ is especially abundant compared to CH₃OH, are reproduced only with Model J, where B is set to 0.7. Models H and J, where the smaller B slows down the collapse phase, the models overproduced the CH₃NH₂ abundance compared to the observations. Since the low binding energy of HCN is higher than for CO, a small value of B leads to a higher abundance of HCN on the grains. As a result, a large amount of CH₃NH₂ is built through the series of hydrogenation processes of HCN. This difference may give us important insight for CH₃NH₂ chemistry. Though Models H and I likely show too large CH₃NH₂ abundances, Model J where B = 0.7 shows a reasonably high CH₃NH₂/CH₃OH ratio. These results suggest that the differences of CH₃NH₂ abundances could be due to the different collapsing speeds of the core before the birth of the star.

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NGC 6334I MM3 is an interesting source where the fractional abundance of CH₃OH is exceptionally high, while CH₃NH₂ is not detected. We observed a strong hydrogen recombination line, H39β, in NGC 6334I MM3, suggesting a later phase of evolution when cosmic rays destroy gas-phase species. Though our simulation results after ∼3 × 10⁵ yr can explain the low observed CH₃NH₂ abundance of NGC 6334I MM3, the simulated gas-phase CH₃OH abundance is too low to explain the observed abundance at such phase. Our current model may not be suitable to explain the later phase of the chemical evolution due to a lack of reliable gas-phase chemistry of COMs.

To see the importance of the hydrogenation processes for the formation of CH₃NH₂, we compare the observed CH₃NH₂/CH₃OH ratios with Garrod (2013), where the hydrogenation processes of HCN and CH₂NH are not included. As we see in Table 5, the peak abundance ratio of CH₃NH₂/CH₃OH is 0.007 with the fast warm-up model, which is the highest among the three models in Garrod (2013). These values are too low to explain our observations. In addition, we run the chemical model turning off the hydrogenation processes for HCN and CH₂NH to see the importance of the hydrogenation processes. Our results are summarized in the lower part of Table 8. While we can explain the observed abundances and ratios for some sources based on the selected conditions and ages, we could not find any condition to reproduce the chemistry of NGC 6334I MM1, where CH₃NH₂ is the most abundant. With the caveat that we still have uncertain rate coefficients of the gas-phase reactions, these results suggest the importance of the hydrogenation processes of HCN and CH₂NH for the formation of CH₃NH₂.

Our conclusion that CH₃NH₂ is built through the successive hydrogenation processes of HCN is different from that of Bøgelund et al. (2019). In Bøgelund et al. (2019), the authors observed NGC 6334I and derived the CH₃NH₂ column densities to be 2.7 × 10¹⁷, 6.2 × 10¹⁶, and 3.0 × 10¹⁵ cm⁻² for MM1, MM2, and MM3, respectively. With these column densities, they obtained that the CH₃NH₂/CH₃OH ratio ranges from ∼5 × 10⁻³ to ∼5 × 10⁻⁴, which agrees with the peak abundance ratio from the fast warm-up model in Garrod (2013) within a factor of 5. Therefore they suggested that CH₃NH₂ is built via a recombination process of radical species (CH₃ + NH₂). Their very low CH₃NH₂/CH₃OH ratio for the NGC 6334I region is contrary to our result. Since our CH₃NH₂ column densities of the NGC 6334I region agree with Bøgelund et al. (2019), this disagreement comes from the CH₃OH column densities.

We believe our CH₃OH column densities are more reliable for a few reasons. First, Bøgelund et al. (2019) observed only one transition of the CH₃OH molecule, which would lead to uncertainty of the CH₃OH abundance. Second, if we apply their observational results and assume a CH₃NH₂ column density of 2.7 × 10¹⁷ cm⁻² and a CH₃NH₂/CH₃OH ratio of 1 × 10⁻³, the CH₃OH column density should be 2.7 × 10²⁰ cm⁻². This surprisingly high CH₃OH column density is not consistent with the previous studies. The column density of CH₃OH can be roughly estimated from the previous observation by a single dish telescope. Ikeda et al. (2001) found that the CH₃OH column density of NGC 6334I was 3.4 × 10¹⁶ cm⁻² under the assumption of the source size being 20''. Our mapping result suggests that the source size of CH₃OH is ∼5'' in the NGC 6334I region. Then, the CH₃OH column density is estimated to be 3.4 × 10¹⁶ × (20''/5'')² = 5.4 × 10¹⁷ cm⁻². Therefore, the column density of CH₃OH used in Bøgelund et al. (2019) appears to be overestimated. The column density of 5.4 × 10¹⁷ cm⁻² rather agrees with our CH₃OH column densities of the NGC 6334I region.

Belloche et al. (2013) and Neill et al. (2014) investigated the CH₃NH₂ and CH₃OH abundances of Sgr B2 (M) and (N). According to these studies, the CH₃NH₂/CH₃OH ratios of Sgr B2 (N) are 0.03 and 0.1, respectively. This difference would come from the smaller beam size of Neill et al. (2014) compared to that of Belloche et al. (2013). The CH₃NH₂/CH₃OH ratio of 0.1 is close to our values for NGC 6334I MM2 and G31.41+0.3. The CH₃NH₂/CH₃OH ratios for NGC 6334I MM1 and W51 e2 are higher than that of Sgr B2. On the other hand, the small value of CH₃NH₂/CH₃OH for Sgr B2(M) is close to that of NGC 6334I MM3. The similarity of Sgr B2(M) with NGC 6334I MM3, and of Sgr B2(N) with NGC 6334I MM1 and MM2 could be due to the fact that Sgr B2(M) is highly dominated by H ii regions, while Sgr B2(N) is more dominated by dust emission (Schmiedeke et al. 2016; Sánchez-Monge et al. 2017).

Pagani et al. (2017) reported the CH₃NH₂ column density of the Orion KL hot core to be 1 × 10¹⁶ cm⁻². The CH₃OH column density of the Orion KL-W region is reported in Peng et al. (2012). Their CH₃OH contour map suggests that the CH₃OH abundance at the position of the hot core would be close to the position of the KL-W region. In this case, the CH₃OH column density is 9.2 × 10¹⁷ cm⁻². Therefore we obtain a CH₃NH₂/CH₃OH ratio of 0.011 for the Orion KL hot core, which is similar to that of NGC 6334I MM3.

Finally, we note that we performed this survey of CH₂NH-rich sources reported in Suzuki et al. (2016). Therefore our source samples may be biased toward N-bearing species-rich sources. Further CH₃NH₂ surveys of other hot cores would be essential to reveal a more general picture of hot core chemistry. CH₃NH₂ surveys of low-mass protostars are also an interesting topic. For hot corinos, the CH₃NH₂/CH₃OH ratio was investigated only for IRAS16293-2422. The CH₃NH₂/CH₃OH ratio in this source is less than 5.3 × 10⁻⁵, which is dramatically lower than our result. Such a difference could be due to the higher binding energy of CH₃NH₂. Therefore the source size of CH₃NH₂ may be much smaller for low-mass stars, which require extremely high angular resolutions.