Correlations of Methyl Formate (CH3OCHO), Dimethyl Ether (CH3OCH3) and Ketene (H2CCO) in High-mass Star-forming Regions

We present high-spatial-resolution (0.7 to 1.0 arcsec) submillimeter observations of continuum and molecular lines of CH3OCHO, CH3OCH3, and H2CCO toward 11 high-mass star-forming regions using the Atacama Large Millimetre/submillimetre Array (ALMA). A total of 19 separate cores from 9 high-mass star-forming regions are found to be line-rich, including high-, intermediate-, and low-mass line-rich cores. The three molecules are detected in these line-rich cores. We map the emission of CH3OCHO, CH3OCH3, and H2CCO in 9 high-mass star-forming regions. The spatial distribution of the three molecules is very similar and concentrated in the areas of intense continuum emission. We also calculate the rotation temperatures, column densities, and abundances of CH3OCHO, CH3OCH3, and H2CCO under the local thermodynamic equilibrium (LTE) assumption. The abundances relative to H2 and CH3OH, and line widths of the three molecules are significantly correlated. The abundances relative to H2, temperatures and line widths of the three molecules tend to be higher in cores with higher mass and outflows detected. The possible chemical links of the three molecules are discussed.


INTRODUCTION
The astrochemical networks of many species have gradually been revealed.These species range from simple neutral molecules, molecular radicals, and ions to complex organic molecules (COMs).COMs are defined as C-bearing molecules with at least six atoms (Herbst & van Dishoeck 2009).At present, two major pathways for producing organic molecules have been proposed: (i) grain-surface chemical reactions (Hasegawa et al. 1992;Ruffle & Herbst 2000;Garrod et al. 2008;Ruaud et al. 2015); (ii) gas-phase chemical reactions (Duley & Williams 1984;Vasyunin & Herbst 2013;Balucani et al. 2015).Comparing the abundance and spatial distribution correlations of different species is an important mean to test chemical models and determine their formation paths.For example, interferometric observations showed a difference in the spatial distribution of O-and N-bearing molecules (Friedel & Snyder 2008;Csengeri et al. 2019;Qin et al. 2015Qin et al. , 2022)), with N-bearing molecules tracing higher temperature gas than O-bearing molecules (Qin et al. 2010;Crockett et al. 2015;van 't Hoff et al. 2020).In particular, methyl formate (CH 3 OCHO) and dimethyl ether (CH 3 OCH 3 ) were found to have a ★ E-mail: lichuanshou2021@163.com potential similarity (Jaber et al. 2014;Coletta et al. 2020;Peng et al. 2022;Chen et al. 2023).Nevertheless, the spatial similarity between CH 3 OCHO and CH 3 OCH 3 has not been systematically confirmed by interferometric observations with large samples.
In this work, the correlations among CH 3 OCHO, CH 3 OCH 3 , and

Continuum Emission
We perform multi-component two-dimensional Gaussian fits to 870 m continuum emission using the CASA-   function.A total of 145 dense cores were resolved in 11 high-mass star-forming regions (Chen et al. 2024).We have checked the spectra towards the 145 cores one by one, and found that 19 separate cores in 9 regions have multiple line emissions of CH 3 OCHO or CH 3 OCH 3 or H 2 CCO.
From Figure 1 and A1, these 19 cores show rich line emission.The ALMA 870 m continuum emission from 9 high-mass star-forming regions is shown in Figure 2. The positions of 19 line-rich cores are labeled.For the other two of the 11 high-mass star-forming regions (IRAS 14382-6017 and IRAS 17204-3636), the line transitions of the three molecules were not detected.The absence of HMCs from these two sources was affirmative by cross-matching with the ALMA Band 3 dataset (Qin et al. 2022).
For the estimation of the core masses and the molecular hydrogen column densities, the commonly used method assumes that the dust emission is optically thin and in local thermodynamic equilibrium (LTE).Under these assumptions, the core masses and sourceaveraged H 2 column densities can be estimated by the expressions (Kauffmann et al. 2008): where S  is integrated flux density,  = 100 is gas-to-dust mass ratio (Lis et al. 1991;Hasegawa et al. 1992), D is the distance to the core (Liu et al. 2020) and the uncertainty takes 10% (Baug et al. 2020;Liu et al. 2022) when calculating the uncertainty of the core mass,   is the dust mass absorption coefficient, B  (T) is the Planck function at dust temperature T,  = 2.8 is the mean molecular weight of the gas (Kauffmann et al. 2008), m H is the mass of the hydrogen atom, and Ω is the solid angle corresponding to the deconvolved size of the core.In our case,  870 takes a value of 1.89 cm 2 g −1 , which is interpolated from the table given in Ossenkopf & Henning (1994), assuming grains with thin ice mantles and a gas density of 10 6 cm −3 .The dust temperatures of dense cores are assumed to be the rotation temperatures of CH 3 OCHO, which is considered to be dust temperature probe (Favre et al. 2011).The parameters of 19 line-rich cores are listed in Table 1.In Table 1, we also list whether these cores are associated with outflows.The presence of outflows is identified by searching for red-blue lobes around continuum sources using the CO (3-2), HCN (4-3), and SiO (2-1) lines (Baug et al. 2020).
The source-averaged optical depths of the continuum can be calculated by the following formula (Frau et al. 2010;Gieser et al. 2021): The derived  870 ranges from 6.2 × 10 −3 to 1.4 × 10 −1 for the 19 dense cores, so the optically thin assumption is reasonable.I15520, I16060, I16071, I16076, I16351, and I17220 were found to be associated with the ultra-compact (UC) Hii regions traced by the H40 lines (Qin et al. 2022;Liu et al. 2022 Frequency (MHz) 0.0 0.2 0.4

Line Identifications
We extracted the spectra from the continuum peak positions of these dense cores.Then the spectral line transitions are identified using the eXtended CASA Line Analysis Software Suite (XCLASS1 ; Möller et al. 2017).XCLASS searches for molecular line parameters in the Jet Propulsion Laboratory (JPL2 ; Pickett et al. 1998) and the Cologne Database for Molecular Spectroscopy (CDMS3 ; Müller et al. 2001Müller et al. , 2005)).The value of the partition functions in the XCLASS have 110 different temperature intervals between 1.072 and 1000 K. Assuming that the molecular gas satisfies the LTE condition, the XCLASS solves the radiative transfer equation and produces synthetic spectra for specific molecular transitions by taking into account beam dilution, dust attenuation, line opacity, and line blending.In the XCLASS modeling, the input parameters are the size (), rotational temperature (T), column density (N), line width (ΔV), and velocity offset (V off ) of each molecule.In our study, we took the deconvolved sizes (see Table 1) of the continuum sources as molecular component sizes.To better fit the rotation temperature, column density, and line width parameters, we further employed Modeling and Analysis Generic Interface for eXternal numerical codes (MAGIX; Möller et al. 2013).The MAGIX optimizes these molecular component parameters within the given range and provides the corresponding error estimates.The parameter ranges are set based on the initial guesses provided by XCLASS fitting.Note that in our case the optical depths of the continuum cores are less than 1.4 × 10 −1 and then the dust attenuation effect can be ignored.
Transitions are considered as detection if the line intensities exceed 3 noise level.CH 3 OCHO, CH 3 OCH 3 , H 2 CCO, and CH 3 OH lines are detected in all 19 line-rich cores, and 13 CH 3 OH lines are detected in 16 line-rich cores.Figure 1 shows the sample spectra and optical depths of molecular transitions toward I14498 C1.The spectra and optical depths of molecular transitions toward the other 18 cores are presented in Figure A1 of Appendix A. The overall results of the detected spectral lines are summarized as follows: Notes.The distances of the 9 high-mass star-forming regions are taken from Liu et al. (2020).The positions, deconvolved sizes, peak flux densities, and integrated flux densities of 19 dense cores are obtained from multi-component 2D Gaussian fitting of the 870 m continuum with CASA.The radii are derived from the equation R core = √︁  maj  min / 3600 ×  / 180 × D. The core masses and molecular hydrogen column densities are calculated in Eq. (1) and Eq.(2) of Section 3.1.The mass classification is discussed in Section 4.1.Outflows.0 = the outflows are not detected, 1 = the outflows are detected (taken from Baug et al. 2020).Notes.The rotation temperatures T and column densities N are model fitting results.The ΔV dec is deconvolved line widths. The column densities of CH 3 OH in these cores are obtained from the column densities of 13 CH 3 OH using Eq. ( 7).
1. Most transitions in each core are optically thin ( < 1). 2. In each core, more than three lines are detected for CH 3 OCHO, CH 3 OCH 3 , and H 2 CCO, and CH 3 OCHO presents more lines than CH 3 OCH 3 and H 2 CCO.
3. In all cores, the CH 3 OCHO and CH 3 OCH 3 have larger line intensities, while the line intensities of H 2 CCO are generally smaller.
The rotational transitions of CH 3 OCHO, CH 3 OCH 3 , and H 2 CCO detected in 19 dense cores are listed in Table B1 of Appendix B. The upper level energy ranges of CH 3 OCHO, CH 3 OCH 3 , and H 2 CCO are 80 to 590 K, 73 to 167 K and 148 to 474 K, respectively.These three molecules, especially CH 3 OCHO and H 2 CCO, cover a wide range of upper level energies, which is conducive to the constraints of rotational temperatures and column densities.

Column Densities, Rotation Temperatures, Line Widths, and Molecular Abundances
The  B1) and then the hot components of the cores are not sampled.CH 3 OCHO and H 2 CCO should trace hotter components than CH 3 OCH 3 .Considering the overestimation of line widths due to velocity resolution of 0.98 km s −1 (see Section 2), we adopt the deconvolved line widths by the following formula: where ΔV is the fitted line width convolved with the velocity resolution Δv.We computed the molecular abundances relative to H 2 and CH 3 OH by the following formula: where N is the column density of the specific molecule, N (H 2 ) is the column density of H 2 (see Table 1), and N (CH 3 OH) is the column density of CH 3 OH (see Table 2).Due to the blending of CH 3 OH lines with other molecular lines in 16 line-rich cores, we then fit13 CH 3 OH line transitions and derive the column densities of CH 3 OH by the column densities of 13 CH 3 OH (see Table 2) multiplied by the12 C/ 13 C ratios from the following formula (Yan et al. 2019): where R GC (in kpc) represents the distance from the Galactic Center (Liu et al. 2020).In the other 3 line-rich cores without 13 CH 3 OH detected, the column densities of CH 3 OH are obtained through direct fitting, where the CH 3 OH lines are not blended.The abundances of CH 3 OCHO, CH 3 OCH 3 , and H 2 CCO relative to H 2 and CH 3 OH are listed in Table 3.

The Molecular Emission Maps
The integrated intensity maps of CH 3 OCHO at 342572 MHz (E u = 81 K), CH 3 OCH 3 at 344358 MHz (E u = 167 K), and H 2 CCO at 343173 MHz (E u = 148 K) in 9 high-mass star-forming regions are shown in Figure 2. The emission peaks of CH 3 OCHO, CH 3 OCH 3 , and H 2 CCO are consistent, and the spatial distribution of the three molecules is similar.These results suggest that there may be physical or chemical links among the three molecules.In addition, there is no difference in the spatial distributions of different energy level transitions of CH 3 OCHO in the 9 high-mass star-forming regions, as shown in Figure C1 of Appendix C. From Figure 2 and Figure C1, the line emissions of CH 3 OCHO, CH 3 OCH 3 , and H 2 CCO are primarily distributed around intense continuum emission.I15520, I16060, and I17220 are found to be associated with intense UC Hii regions, while I16071, I16076, and I16351 are associated with weaker UC Hii regions (Qin et al. 2022;Zhang et al. 2023).In I15520, I16060, and I17220, the line emissions are offset from the continuum cores, and CH 3 OCHO, CH 3 OCH 3 , and H 2 CCO also show irregular emissions in these regions, likely due to the influence of UC Hii regions.

Core Classification
Unlike HMCs, which are associated with the formation of massive stars, hot corinos are found around low-mass protostars.Typical hot corinos are small in size (≲ 200AU) and show a rich chemistry (Cazaux et al. 2003;Bottinelli et al. 2004;Maret et al. 2004;Bottinelli et al. 2007).Intermediate-mass hot cores (IMHCs) provide the link between HMCs and hot corinos, although it has rarely been reported (Sánchez-Monge et al. 2010;Palau et al. 2011;Fuente et al. 2014).
In high-mass star-forming regions, dense cores exist within massive reservoirs, and the mass of the stars formed is uncertain.Therefore, it is difficult to identify hot corinos and IMHCs (sometimes they are simply assumed to be HMCs) in high-mass star-forming regions.
In Table 1, we classify 19 line-rich cores into three groups according to their mass (further material accretion or loss may occur), namely 12 high-mass line-rich cores (H; > 8 M ), 6 intermediatemass line-rich cores (I; 2 -8 M ), and 1 low-mass line-rich core (L; < 2 M ).Moreover, the 11 high-mass star-forming regions are subsamples of Qin et al. (2022), who reported 60 HMCs from 146 high-mass star-forming regions at ALMA resolutions of ∼ 1.2 -1.9 arcsec.Our currently higher spatial resolution observations reveal that part of the HMCs detected in previous works actually host multiple line-rich cores with different masses.(see Qin et al. 2022 and our Figure 2).

Abundance, Temperature and Line Width Correlations
In Figure 3, we compare the CH 3 OCHO, CH 3 OCH 3 , and H 2 CCO abundances relative to H 2 in 19 dense cores.CH 3 OCHO and CH 3 OCH 3 show a strong abundance correlation (the Pearson correlation coefficient r = 0.82).The abundance correlation between CH 3 OCH 3 and H 2 CCO is significant (r = 0.80).CH 3 OCHO and H 2 CCO show the stronger abundance correlation (r = 0.93) than the other two pairs of molecules.Figure 4 shows the relationships of the abundances of the three molecules relative to CH 3 OH in 19 dense cores.The abundances of CH 3 OCHO and CH 3 OCH 3 relative to CH 3 OH mainly range from 10 −2 to 10 −1 , while the abundance of H 2 CCO relative to CH 3 OH mainly ranges from 10 −3 to 10 −2 .3 and Figure 4, the relative abundances of CH 3 OCHO to CH 3 OCH 3 are almost constant equal to 1. Chen et al. ( 2023) also found a constant relative abundance of ∼ 1 between CH 3 OCHO and CH 3 OCH 3 toward 19 protostars with different luminosities.This ratio is consistent with the observations from low-, intermediate-and high-mass star-forming regions (Jaber et al. 2014;Rivilla et al. 2017;Ospina-Zamudio et al. 2018;Coletta et al. 2020;Peng et al. 2022).In Figure 3 and Figure 4, we also compared our results with the molecular abundances relative to H 2 and CH 3 OH in other HMCs and hot corinos.The abundance correlations relative to H 2 and CH 3 OH in these sources agree with the results in our observations but more dispersed than our samples, which is most likely due to different spatial resolution and spectral setup of these observations.These results suggest that the formation of the three molecules may be closely related, i.e., they may have similar production conditions, or even share a common chemical reaction network.
In Figure 5, we compare the rotation temperatures of the three molecules.The temperature correlation coefficient of CH 3 OCHO and CH 3 OCH 3 is 0.62, CH 3 OCH 3 and H 2 CCO is 0.47, and CH 3 OCHO and H 2 CCO is 0.64.The results indicate that the rotation temperatures have no significant correlations among the three molecules.The results observed by Coletta et al. ( 2020) toward 13 high-mass star-forming regions also showed a poor temperature correlation (r = 0.45) between CH 3 OCHO and CH 3 OCH 3 , but the overall temperature ranges of the two molecules are similar.In fact, most of the temperatures of the three molecules in our case are in the range of tens of Kelvin, which is probably the reason why there is no apparent trend in temperature.
The line width relationships of the three molecules are shown in Figure 6.The CH 3 OCHO and H 2 CCO show strong line width correlation (r = 0.95), followed by CH 3 OCHO and CH 3 OCH 3 (r = 0.88), and by CH 3 OCH 3 and H 2 CCO (r = 0.79).This agrees with the line width correlation of CH 3 OCHO and CH 3 OCH 3 observed in 13 high-mass star-forming regions (Coletta et al. 2020).This implies that the three molecules may trace the similar kinematics. 4n Figures 3, 5, and 6, the H cores are shifted to the upper right relative to the I and L cores, indicating a tendency for the abundances relative to H 2 , temperatures and line widths of the three molecules to be higher in massive line-rich cores.In Figure 7, we also compare molecular abundances relative to H 2 and CH 3 OH, rotation temperatures and line widths of the cores with and without detected outflows (see Table 1).The abundances relative to H 2 , temperatures and line contributed by non-thermal motions: Δ V dec ∼ Δ V NT =

√︃
ΔV 2 dec − 8ln2 kTex m , where ΔV NT is the line width contributed by non-thermal motions, k is the Boltzmann constant, T ex is the excitation temperature of the molecule, and m is the molecular mass.widths of the three molecules tend to be higher where outflows are detected.These results confirm that massive cores and cores with outflows may have richer chemistry (Jørgensen et al. 2020;Ceccarelli et al. 2023).

Implications for Chemistry
The spatial similarities, abundance correlations and line width correlations of CH 3 OCHO, CH 3 OCH 3 , and H 2 CCO are obvious.We briefly summarize the chemical models of these three molecules below.In gas-phase chemistry, protonated methanol (CH 3 OH + 2 ) can react with CH 3 OH to produce CH 3 OCH 3 as follows (Charnley et al. 1995;Taquet et al. 2016;Jørgensen et al. 2020): (8) Balucani et al. (2015) proposed that CH 3 OCH 3 could generate CH 3 OCHO in cold gas environments through the following reactions: where CH 3 OCH 3 is a precursor to CH 3 OCHO.In the case of grainsurface chemistry, the CH 3 OCHO and CH 3 OCH 3 follow the reactions (Garrod & Herbst 2006;Garrod et al. 2008): where methoxide (CH 3 O) is the common precursor of CH 3 OCHO and CH 3 OCH 3 .On the surface of the dust grains, the aldehyde (HCO) can produce H 2 CCO as follows (Charnley et al. 2001;Charnley & Rodgers 2005;Krasnokutski et al. 2017): where HCO is the common precursor of CH 3 OCHO and H 2 CCO through Eq. ( 10) (12).The spatial similarities, abundance correlations, and line width correlations of CH 3 OCHO, CH 3 OCH 3 , and H 2 CCO, combined with chemical models, suggest that three molecules are chemically related.Taquet et al. (2016) predicted the abundances of CH 3 OCH 3 relative to H 2 to be ∼ 10 −7 and relative to CH 3 OH to be ∼ 10 −2 using reaction (8).Our observed abundances of CH 3 OCH 3 relative to H 2 and CH 3 OH are consistent with this prediction.Garrod et al. (2022) showed a chemical network that includes reactions (8), ( 9), ( 10), (11), and (13) to predict the abundances of CH 3 OCHO, CH 3 OCH 3 , and H 2 CCO.The three warm-up timescales of 5 × 10 4 years (fast), 2 × 10 5 years (medium), and 1 × 10 6 years (slow) were employed in their models.At the medium timescale, the predicted abundances relative to H 2 are ∼ 10 −7 for CH 3 OCHO and CH 3 OCH 3 , ∼ 10 −8 for H 2 CCO, and relative to CH 3 OH are ∼ 10 −2 for CH 3 OCHO and CH 3 OCH 3 , ∼ 10 −3 for H 2 CCO.Our observed abundances of the three molecules relative to H 2 and CH 3 OH are consistent with the medium timescale predictions.In conclusion, our observed abundances of the three molecules support both grain-surface and gas-phase chemical pathways for the production of CH 3 OCHO and CH 3 OCH 3 , and grain-surface chemical pathways for the production of H 2 CCO.

CONCLUSIONS
We have analyzed the spectra of 11 high-mass star-forming regions obtained by ALMA band 7 observations, and studied the correlations of complex organic molecules CH 3 OCHO and CH 3 OCH 3 as well as an important precursor of complex organic molecules H 2 CCO.We summarize the main results in the following: 1. CH 3 OCHO, CH 3 OCH 3 , and H 2 CCO lines were detected in 19 line-rich cores from 9 out of 11 high-mass star-forming regions.At our higher spatial resolution observations, some of the hot molecular cores found in previous observations are revealed to actually host multiple line-rich cores with different masses.
2. The integrated intensity maps of the 9 high-mass star-forming regions show that the emission peaks of the three molecules are consistent, and the spatial distribution of the molecules is similar.The emissions of the three molecules in the 9 high-mass star-forming regions are primarily distributed around intense continuum emission.
3. The abundances relative to H 2 and CH 3 OH, and line widths of the three molecules show obvious correlations in the 19 dense cores.The abundance correlations of the three molecules relative to H 2 and CH 3 OH in other hot molecular cores and hot corinos agree with the results in our observations.The molecular abundances of CH 3 OCHO and CH 3 OCH 3 are rather similar, while the molecular abundances of H 2 CCO are one order of magnitude lower.
4. The abundances relative to H 2 , temperatures and line widths of the three molecules tend to be higher in the cores with higher mass and with outflows.This confirms that massive cores and cores with outflows may have richer chemistry.
5. The spatial similarities, abundance correlations, and line width correlations of CH 3 OCHO, CH 3 OCH 3 , and H 2 CCO, combined with chemical models, suggest that three molecules are chemically related.Our results suggest that both grain-surface and gas-phase chemical pathways can be responsible for producing CH 3 OCHO and CH 3 OCH 3 , while H 2 CCO should be produced by grain-surface chemical pathways.

Figure 1 .
Figure 1.Sample spectra and optical depths of the three molecules for I14498 C1.The observed spectra are shown in gray curves and the XCLASS modeled spectra are shown in color curves.The small panel below each spectrum shows the optical depths of the XCLASS modeled spectra.The gray arrows represent the transitions used as integrated intensity maps in Figure 2. The spectra and optical depths of other line-rich cores are shown in Figure A1.

Figure 4 .
Figure 4. Comparison among the molecular abundances of CH 3 OCHO, CH 3 OCH 3 , and H 2 CCO relative to CH 3 OH.The colored circles represent the different types of cores in this work (H = high-mass line-rich core, I = intermediate-mass line-rich core, and L = low-mass line-rich core), while the colored squares represent the sources in the literature (References: HMCs: Bøgelund et al. 2019; Peng et al. 2022; hot corinos: Taquet et al. 2015; Lefloch et al. 2017; Ospina-Zamudio et al. 2018; Jørgensen et al. 2018).The orange areas indicate the relative abundance ranges of molecules.The black dashed lines and the gray dashed lines are linear least-squares fits of this work and all sources, respectively.The fitting results and Pearson correlation coefficients (r) are shown on the top left.

Figure 5 .Figure 6 .
Figure 5.Comparison among the rotation temperatures of CH 3 OCHO, CH 3 OCH , and H 2 CCO.The colored circles represent different types of cores (H = high-mass line-rich core, I = intermediate-mass line-rich core, and L = low-mass line-rich core).The black dashed lines are the linear leastsquares fits to the data.The fitting results and Pearson correlation coefficients (r) are shown on the top left.

)Figure 7 .
Figure 7.Comparison of molecular abundances relative to H 2 and CH 3 OH, rotation temperatures and line widths of the cores with and without detected outflows.The colored circles represent cores with and without outflows.The green triangles represent the averages and the green diamonds represent the medians.

Table 1 .
Physical Parameters of the Continuum Sources.
MAGIX optimization results for CH 3 OCHO, CH 3 OCH 3 , and H 2 CCO in 19 dense cores are shown in Table2.The column densities mainly range from 10 15 to 10 17 cm −2 for CH 3 OCHO and CH 3 OCH 3 , and from 10 14 to 10 16 cm −2 for H 2 CCO.The upper level energies of H 2 CCO lines are larger than 148 K (see Section 3.2), and the column densities of H 2 CCO are lower, which can explain its weaker line intensities than the other two molecules.The rotation temperature ranges of CH 3 OCHO, CH 3 OCH 3 , and H 2 CCO are 70 to 170 K, 50 to 137 K and 85 to 173 K, respectively.The rotation temperatures of CH 3 OCH 3 in most cores are generally lower than those of CH 3 OCHO and H 2 CCO, possibly because our 870 m observations of the CH 3 OCH 3 lines have lower upper level energies (see Table

Table B1 .
The Detected Transitions of CH 3 OCHO, CH 3 OCH 3 , and H 2 CCO with Signal Above 3 Noise Level.
Figure A1.Same as Figure1, but for the other 18 line-rich cores.