Rotation-tunnelling spectrum and astrochemical modelling of dimethylamine, CH3NHCH3, and searches for it in space

ABSTRACT

1 INTRODUCTION

Methylamine, CH3NH2, was among the earliest molecules to be discovered by radio-astronomical means; Kaifu et al. (1974) and Fourikis, Takagi & Morimoto (1974) reported detections towards Sagittarius (Sgr) B2 and Orion A, although the detection towards Orion A was dismissed a few years later (Johansson et al. 1984). Despite being a fairly small molecule, searches for methylamine towards other sources remained fruitless for quite some time. It was ultimately identified in the course of a spectral line survey of a z ≈ 0.89 foreground galaxy located in front of the quasar PKS 1830 − 211 (Muller et al. 2011). Surprisingly, CH3NH2 emission was detected towards the peculiar molecule-rich circumstellar environment of the ‘red nova’ CK Vul, thought to be the remnant of a stellar merger (Kamiński et al. 2017), and imaged with the Atacama Large Millimeter/submillimeter Array (ALMA) (Kamiński et al. 2020). Recently, CH3NH2 was detected in the molecular cloud G+0.693−0.027 close to Sgr B2(N) (Zeng et al. 2018). Shortly thereafter, it was also found towards the high-mass star forming regions NGC6334I (Bøgelund et al. 2019) and G10.47+0.03 (Ohishi et al. 2019) and later towards several other high-mass protostars (Nazari et al. 2022).

Zeng et al. (2021) detected vinylamine, C2H3NH2, securely and ethylamine, C2H5NH2, tentatively in a spectral line survey of G+0.693−0.027. Dimethylamine, CH3NHCH3, (DMA for short) is an isomer of ethylamine and related to methylamine, making it a viable candidate for searches in space. These relationships are similar to the relationships of dimethyl ether, CH3OCH3, with respect to ethanol, C2H5OH, and methanol, CH3OH, all three species being well-known interstellar molecules.

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Wollrab & Laurie (1968) investigated the rotation-tunnelling spectra of several isotopologs of DMA in its ground vibrational state up to 45 GHz with J ≤ 8 and Ka ≤ 3. They determined hyperfine structure (HFS) parameters, dipole moment components, and structural parameters. Since they did not resolve any splitting caused by the internal rotation of the two equivalent methyl rotors, they studied the spectra of several isotopologs in their two fundamental torsional states (Wollrab & Laurie 1971).

Very recently, Koziol, Stahl & Nguyen (2021) analysed the ground state rotation-tunnelling spectrum of the DMA main isotopic species applying microwave Fourier transform spectroscopy. They were able to resolve internal rotation splitting of the order of 0.2 MHz and improved the HFS parameters. But because of the limitations in frequency (≤32 GHz) and the low rotational temperatures, their quantum number range is limited to J ≤ 10 and Ka ≤ 1.

Since the available data are insufficient to calculate accurate transition frequencies in the millimeter, let alone the submillimeter region, we carried out an extensive study of the ground state rotation-tunnelling spectrum of the DMA main isotopolog in sections between 76 and 1091 GHz.

We use the results of this spectroscopic study to search for DMA in the interstellar medium, employing two spectral line surveys performed towards the Sgr B2 molecular cloud complex: a survey obtained with ALMA towards hot molecular cores of the Sgr B2(N) star forming region (e.g. Belloche et al. 2019) and a survey obtained with single-dish telescopes towards the Giant Molecular Cloud G+0.693−0.027, also located in the Sgr B2 molecular cloud complex and that is experiencing a cloud-cloud collision (Zeng et al. 2018, 2020; Rivilla et al. 2021a, 2022b).

We also present here the results of astrochemical models under generic hot-core conditions, using a new chemical network that includes DMA. Methylamine was included in the early interstellar grain-surface chemistry network of Allen & Robinson (1977); the radicals CH3 and NH2 could directly recombine to form methylamine, while related atoms and radicals could also react to form the various hydrogenation states CHxNHy, which could then be further hydrogenated all the way to CH3NH2. Similar schemes have been used in later gas-grain chemical networks, including those intended specifically for hot cores (e.g. Garrod, Widicus Weaver & Herbst 2008). Although some of the species accessible in the Allen & Robinson (1977) network (e.g. CH2NCH3) came close in structure to DMA, the latter molecule does not appear to be present in any existing astrochemical networks up to now. Here, we adapt the hot-core model and chemical network used by Garrod et al. (2022), which already includes methylamine chemistry, to trace the production of DMA through a small selection of grain-surface/bulk-ice reaction pathways. The network also includes the usual mechanisms for grain-surface and gas-phase destruction of DMA and other associated species.

2 EXPERIMENTAL DETAILS

The investigation of the rotation-tunnelling spectrum of DMA was carried out with three different spectrometers. All absorption cells were made of Pyrex glass, had an inner diameter of 10 cm, and were kept at room temperature. The cells were filled to a certain nominal pressure from an aqueous solution of DMA; after a few hours to about a day, the sample was pumped off and the cell refilled because of the pressure rise caused by small leakages.

We used two 7 m coupled glass cells in a double path arrangement for measurements in the 76 − 124 GHz region, yielding an optical path length of 28 m. We employed a 5 m double path cell for the 159 − 375 GHz range. The cells of both spectrometers are equipped with Teflon windows. Additional information on these spectrometers is available in Ordu et al. (2012) and Martin-Drumel et al. (2015), respectively. The measurements between 793 and 1091 GHz were carried out in a 5 m long single path cell equipped with high-density polyethylene windows. Additional information on this spectrometer system is available in Xu et al. (2012). All spectrometers utilize Virginia Diode, Inc. (VDI), frequency multipliers driven by Roh-de & Schwarz SMF 100A synthesizers as sources. Schottky diode detectors are used up to 375 GHz while a closed cycle liquid He-cooled InSb bolometer (QMC Instruments Ltd) is employed around 1 THz. Frequency modulation is applied to reduce baseline effects with demodulation at twice the modulation frequency. This causes absorption lines to appear approximately as second derivatives of a Gaussian.

We recorded mostly individual transitions in all frequency windows covering 5, 6, and 10 MHz around 100, 250, and 900 GHz, respectively at pressures of about 1, 2, and 3−5 Pa. Larger sections were also covered, in particular at higher frequencies. Uncertainties were evaluated mostly based on the symmetry of the line shape. The lines around 100 GHz were quite weak because of HFS, internal rotation splitting or intrinsically. Assigned uncertainties were between 5 and 30 kHz in this region. We applied uncertainties of 3-10 kHz for lines that were very symmetric or nearly so in the 159−375 GHz range and 15-50 kHz for moderately to less symmetric lines, lines closer to other lines or fairly weak lines. Similar uncertainties were achieved earlier, for example, in the case of 2-cyanobutane, which has a much richer rotational spectrum (Müller et al. 2017). Uncertainties for very good lines were 5−10 kHz, and larger uncertainties up to ∼300 kHz were assigned for example to weaker lines and lines close to other lines in the 793−1091 GHz region. Similar uncertainties at these frequencies were achieved for excited vibrational lines of CH3CN (Müller et al. 2021) or for isotopic oxirane (Müller et al. 2022, 2023).

3 SPECTROSCOPIC PROPERTIES OF DIMETHYLAMINE

DMA is an asymmetric rotor with κ = (2B − A − C)/(A − C) = −0.9140 close to the prolate limit of −1. Fig. 1 shows that the molecule has CS symmetry in a static picture; the H atom attached to the N atom can be above or below the CNC plane. However, the barrier to exchange of these two positions is relatively low, such that the H atom is able to tunnel between these equivalent positions. Rotation lifts the degeneracy and causes a symmetric tunnelling state frequently labelled with 0+ and an antisymmetric tunnelling state then labelled with 0−. The symmetry of the molecule in this dynamical picture is C2v, as it is the symmetry of the transition state. The b-axis in this configuration is along the NH bond; the pure rotational transitions, those within each tunnelling state, obey b-type selection rules. The a-axis is parallel to the line through the C atoms, and the c-axis is perpendicular to the CNC plane. The rotation-tunnelling transitions, which connect the two tunnelling states, obey c-type selection rules as the tunnelling of the H atom takes place parallel to the c-axis. Wollrab & Laurie (1968) determined the dipole moment components as μb = 0.295 D and μc = 0.967 D. Fig. 2 demonstrates possible transitions among the lowest energy levels of DMA.

Coriolis-type interaction occurs between the two tunnelling states for levels with equal J which differ in Ka and Kc by an even and odd number, respectively. The interaction is strongest (resonant) when the levels are close in energy. The most common interactions in a prolate rotor are those with ΔKa = 0 and ΔKc = ±1. It is also shown in Fig. 2 that the first resonant interaction of this type occurs in DMA at Ka = 1 for J = 1. The figure demonstrates the general pattern of this type of resonance: the upper asymmetry level of the lower tunnelling state interacts with the lower asymmetry level of the upper tunnelling state. Since the asymmetry splitting decreases rapidly with increasing Ka for a given J, this type of interaction is resonant at increasing J for an increase in Ka. The usually one J with strongest interaction for a given Ka is listed in Table 1 for Ka ≤ 11. The parameter Fbc describes this interaction at lowest order.

The two equivalent methyl groups in DMA (Fig. 1) lead to ortho and para spin-statistics with intensity ratios of 9 : 7. The ortho and para levels are described by Ka + Kc being odd and even, respectively in υ = 0+ while it is opposite in υ = 0−, see Fig. 3.

The two methyl groups in DMA carry out hindered internal rotations, but this rotation is so strongly hindered that it was not resolved in the initial microwave study of the ground vibrational state (Wollrab & Laurie 1968). Fig. 4 shows weaker internal rotation components displaced by about 400 kHz to either side of the stronger central component.

The presence of the 14N nucleus (IN = 1) leads to HFS splitting. Each rotational level with J ≥ 1 splits into three, and the strongest HFS components are those with ΔF = ΔJ, where F represents the combination of the rotational and nuclear spin angular momenta. Transitions with ΔF ≠ ΔJ are also allowed as long as ΔF = 0, ±1 is fulfilled. These transitions are usually too weak to be observed except for transitions with low rotational quantum numbers or measured with very high signal-to-noise ratios (S/N). An example of HFS splitting is shown in Fig. 4. As one can see, the F = J ± 1 components nearly coincide in frequency, and the frequency modulation causes a reduction of their intensities because the two components are not completely separated. In fact, the F = J ± 1 components are frequently completely blended, whereas the F = J component may be separated from these. This causes an asymmetric intensity ratio of about 2 : 1 for partly resolved HFS patterns.

4 SPECTROSCOPIC RESULTS AND DETERMINATION OF SPECTROSCOPIC PARAMETERS

Fitting and calculation of the rotational spectrum of DMA was carried out with the SPFIT and SPCAT programs (Pickett 1991). The two interacting tunnelling states are commonly fit with a Hamiltonian that can be divided into a 2 × 2 matrix with the diagonal elements consisting of the usual Watson-type rotational Hamiltonians for 0+ and 0− on the diagonal; the one for 0− includes in addition the energy difference. The interaction Hamiltonian is off-diagonal. The treatment of the Coriolis interaction between the 0+ and 0− states requires additional consideration. Tanaka & Morino (1970), for example, discussed the need for two low order terms to treat the c-type Coriolis interaction between υ1 = 1 and υ3 = 1 of ozone: iDcJc + Fab(JaJb + JbJa)/2. Additional rotational correction terms to either low order term may be needed if a large range of high quantum numbers is accessed, as in the example of ClClO2 (Müller, Cohen & Christen 2002). Lide (1962) derived that both types of terms are allowed to treat the rotation-tunnelling interaction in cyanamide, H2NCN. Harris et al. (1966) showed in the analysis of the ring-puckering in trimethylene sulfide, c-C3H6S, that at least under certain circumstances only one type of terms is required and proposed to use the odd order terms iDj with j being a, b, or c, depending on the symmetry. Wollrab & Laurie (1968) followed this recommendation in their analysis of the rotation-tunnelling spectrum of DMA. Pickett (1972) proposed to use the reduced axis system in which the interaction Hamiltonian consists of appropriate axis-rotation terms Fij with i, j being a, b, or c and i ≠ j. He showed that this method minimizes the effects of Coriolis coupling and may thus reduce the number of required interaction terms. The reduced axis system was the preferred method to treat tunnelling-rotation and related spectra lately and was applied in all examples given below. The only non-zero interaction element in the case of DMA is Fbc supplemented with its distortion corrections: |$(F_{bc} + F_{bc,K}J_a^2 + F_{bc,J}J^2 + F_{2bc}(J_b^2-J_c^2) + …) times (J_bJ_c + J_cJ_b)/2$|⁠. Two separate rotational Hamiltonians are traditionally employed, which is appropriate if the parameters in the two Hamiltonians differ considerably. This approach was applied, for example, in the case of gauche-propanal (Zingsheim et al. 2022).

Noting that the two tunnelling states 0+ and 0− together comprise the ground vibrational state υ = 0, it can be advantageous to rearrange the Hamiltonians and fit average spectroscopic parameters X = (X(0+) + X(0−))/2 and differences ΔX = {X(0−) − X(0+)}/2, as was done by Christen & Müller (2003) in their treatment of the lowest energy conformer of ethylene glycol, also known as ethanediol. Christen & Müller (2003) also pointed out that the differences in spectroscopic parameters can be interpreted as rotational corrections to the energy difference, for example, EK is defined as Δ{A − (B + C)/2}, EJ as Δ{(B + C)/2}, E2 as Δ{(B − C)/4}, and so forth. We follow this interpretation in our current work. We should point out that in our definition of the differences, 0− is higher in energy by 2E than 0+. The advantage of this formulation is that an average parameter or its difference can be employed individually in the fit independent of each other. A rotation-tunnelling spectrum with a small energy difference may require fewer parameter differences than average parameters. On the other hand, the rotation-tunnelling spectrum of a symmetric top molecule, such as NH3, requires many differences in the fit to describe pure tunnelling transitions. In addition, the purely axial average parameters (here C, DK, etc.) are not determinable from regular (ΔK = 0) transitions. Examples applying such rearranged Hamiltonians include the treatments of ethanethiol (Müller et al. 2016), hydroxyacetonitrile (Margulès et al. 2017), the low-energy conformer of ethanediol (Melosso et al. 2020), and isotopic cyanamide (Coutens et al. 2019); the difference between the number of average parameters and their differences is very small in the last example, which may, at least in part, be related to the large energy splitting between the two tunnelling states.

The HFS splitting requires appropriate terms to be added to the Hamiltonian; these are the quadrupole coupling parameters χii with i = a, b, c on the diagonal and χbc off-diagonal. Since the quadrupole tensor is traceless, only two of the three χii are independent.

The rotation-tunnelling spectrum of DMA is relatively sparse on the level of the strongest transitions. In addition, several of the stronger series of transitions display HFS splitting that is neither well resolved, be it into the three strong components or be it into the F = J and the overlapping F = J ± 1 components, nor fully collapsed. Such patterns make it more difficult to determine rest frequencies very accurately. And finally, several series of interest are very weak such that their S/N may be insufficient in spectral recordings that cover large frequency regions in a reasonable amount of time. Therefore, we decided to search in most cases only for individual rotation-tunnelling transitions.

An initial catalogue file was created from the transition frequencies by Wollrab & Laurie (1968) applying 100 kHz as uncertainty for all lines as reported. We carried out exploratory measurements between 76 and 124 GHz to evaluate the quality of the model. The transitions cover almost exclusively low or very low values in J (1 ≤ J ≤ 11), notably the R-branch (ΔJ = +1) transitions with Ka = 1 − 0, 0 − 1, 2 − 1, and 1 − 2 as well as Q-branch (ΔJ = 0) transitions with Ka = 2 − 1. Most of these transitions displayed fully (Fig. 4) or partially resolved HFS splitting. Internal rotation splitting affected sometimes the positions of the strongest central component; the uncertainty of the corresponding line was increased somewhat as long as the effect appeared to be small, otherwise, the line was not used in the fit.

In the course of the investigation, three of the initial transition frequencies (Wollrab & Laurie 1968) showed large residuals that were eventually interpreted as typographical errors as two residuals were very close to 1.0 MHz and one very close to 2.0 MHz.

The majority of the measurements were made between 159 and 375 GHz, fairly extensive recordings were also carried out between 793 and 1091 GHz. We focused on transitions that had a splitting between the F = J and the overlapping F = J ± 1 components of at least one line width up to 254 GHz or on transitions having HFS splitting well within half of the estimated line width throughout the entire frequency region. We tried to record as many members of specific series as possible with limitations caused by the intrinsic weakness of a series, the reduced sensitivity of the spectrometer in certain regions, especially at the edges, or by accidental blending. We covered several different series of transitions pertaining to adjacent Ka for low values of Ka. The strong rR-branch transitions were covered up to J = Ka = 16 − 15 around 1067 GHz. All Ka values were covered up to Ka = 21 − 20, which was accessed through both Q-branches, with 0+ or with 0− representing the lower state level; part of the former one is shown in Fig. 5. The highest J level that we accessed had J = 61. The highest J value with partially resolved HFS was 44 for the Ka = 4 − 3 Q-branch transitions within 0+ and 0− near 252 565 MHz; we only used the overlapping F = J ± 1 components because the uncertainties of the F = J components were much larger. The F = J components were also kept in the line list for several Ka = 6 − 5 Q-branch transitions between 0+ and 0− with 38 being the highest J value near 163 889MHz.

We took care to describe the rotation-tunnelling interaction in DMA well. To this end, we tried to cover as many near-degenerate levels as available. We accessed several transitions for each Ka between 1 and 8, as can be seen in Table 1; we reached only one J below the strongest interaction for Ka = 9. The interaction transfers intensity from c-type transitions to some of the weaker b-type transitions. This is best described with Fbc being positive when μb and μc are chosen to be positive. The parameter χbc affects in particular the line positions in the transitions involving the J = Ka = 1 levels. Its value needed to be negative once Fbc was chosen to be positive.

The determination of the spectroscopic parameters was carried out in the usual way. We tested after each round of assignments if one or more spectroscopic parameters would improve the quality of the fit by amounts that warranted keeping the respective parameter in the fit. Care was taken to try only parameters that are reasonable with respect to those already used in the fit. If at least one parameter improved the quality of the fit sufficiently, we chose the one that improved the quality the most and searched for additional parameters. Correlation among the parameters may cause a parameter that looked well determined, that is, with a magnitude at least several times its uncertainty, to be not well determined. It was omitted from the fit, often only temporarily, if its omission did not cause a large deterioration of the fit.

Some of our spectral recordings resolved internal rotation splitting, as can be seen in Fig. 4. DMA is isoelectronic to dimethyl ether; the internal rotation patterns for this molecule were described in detail for example by Endres et al. (2009). Briefly, the nine equivalent internal rotation positions caused by the two equivalent methyl rotors in DMA and dimethyl ether lead to four distinct internal rotation substates AA, AE, EA, and EE. The lines pertaining to AE and EA are frequently blended, in particular in dimethyl ether and even more so in DMA with their small internal rotation splittings. The combined AE and EA peak has then the same intensity as the AA peak, and the two peaks occur to either side of the central EE peak displaced by essentially the same amount in the absence of strong torsion-rotation interaction. Information on the internal rotation splitting in DMA is provided in the microwave study on torsionally excited DMA (Wollrab & Laurie 1971). We did not use the internal rotation splitting of ground state DMA in almost all of our fits and only used the central, strong internal rotation peak (EE).

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The SPFIT program is capable of fitting spectra with small internal rotation splitting (Drouin et al. 2006; Endres et al. 2009), but attempts to introduce internal rotation into the treatment of the rotation-tunnelling spectrum of DMA failed. The transition frequencies calculated with internal rotation splitting differed from those calculated without splitting by a few to several tens of kilohertz, often well outside the experimental uncertainties, and we were unable to reduce this difference. The reason is that the internal rotation splitting affects the tunnelling splitting differently for different values of Ka. Therefore, we also used only the frequencies of the central internal rotation components from the Fourier transform microwave measurements (Koziol et al. 2021). Four of the c-type HFS components and most of the few b-type HFS components showed larger residuals of around 10 kHz or more than the majority of the data, so the b-type transitions and the four c-type HFS components were omitted from the final fit. The residuals are a result of the density of lines for b-type transitions with low values of J and for some of the c-type transitions. The Fourier transform microwave data did not require any additional parameters in the fit, such as nuclear spin-rotation parameters, but improved some of the lower order parameters substantially, in particular χaa and χcc as well as the rotational parameters and χbc; effects were smaller for most other parameters. The resulting spectroscopic parameters are listed in Table 2.

The 48 transition frequencies from Wollrab & Laurie (1968) were fit to 103 kHz on average, acceptably close to the assigned 100 kHz uncertainty. The more recent microwave data from Koziol et al. (2021) were fit to 1.39 kHz on average. We had chosen 1.5 kHz as final uncertainties for these 88 transition frequencies after we recognized that the value of 1.0 kHz, initially assumed by us, was too optimistic. Our 1294 transitions were reproduced to an rms error, also known as weighted or normalized rms, of 0.952. As we employed a substantial range of different uncertainties, the rms value of 28.7 kHz is dominated by the data with larger uncertainties. The number of different frequencies is 943 because of overlapping HFS components, unresolved asymmetry splitting or accidental blending.

The fit file and calculations of the rotational spectrum of DMA with and without HFS have been deposited as supplementary material to this paper together with an explanatory file. These files as well as additional files are also available in the Cologne Database for Molecule Spectroscopy (CDMS.1; Müller et al. 2005; Endres et al. 2016). The partition function Qrot was calculated for selected temperatures beyond the standard temperatures in the CDMS by summation over the ground state energies up to J = 130 and Ka = 60. Spin-statistics and the spin-weight from the 14N nucleus were taken into account. In the warm ISM (T ≳ 100 K), excited vibrational states are populated non-negligibly. We evaluated the vibrational partition function for a posteriori correction in the harmonic approximation. Gamer & Wolff (1973) and Durig, Groner & Griffin (1977) reported on gas phase infrared and Raman measurements. These reports are, however, not always consistent with each other and are incomplete as not all of the 24 fundamental vibrations were identified. Explanations for the incompleteness and inconsistency are that some fundamentals are very weak and may be blended with potentially stronger overtone and combination bands. Moreover, some fundamentals occur in a very narrow energy range. We carried out quantum-chemical calculations at the Regionales Rechenzentrum der Universität zu Köln (RRZK) using the commercially available program Gaussian 09 (Frisch et al. 2013) in order to calculate the harmonic and anharmonic fundamentals of DMA. We employed the B3LYP hybrid density functional (Lee, Yang & Parr 1988; Becke 1993) for that matter together with the correlation consistent basis set augmented with diffuse basis functions commonly denoted aug-cc-pVTZ (Dunning, Jr 1989). There are 17 fundamentals below ∼1500 cm−1; the highest ones correspond to a Boltzmann factor of ∼10−3 at 300 K; the remaining fundamentals are above 2700 cm−1. Wherever fundamentals are isolated and not too weak, there is usually good to reasonable agreement between experimental and calculated values. Gamer & Wolff (1973) and Durig et al. (1977) reported also vibrations around ∼1450 cm−1, but fewer than 7, and some of their values may correspond to overtones or combination bands. The experimental and quantum-chemically evaluated fundamentals are presented in Table 3, and the resulting values for Qrot and Qvib are summarized in Table 4.

5 DISCUSSION OF THE SPECTROSCOPIC PARAMETERS

The spectroscopic parameters of DMA are prototypical for an asymmetric top molecule close to the prolate limit, as the series of parameters describing the asymmetry (the d’s and h’s) converge faster than that of the purely J-dependent parameters (DJ, HJ, LJ), and that, in turn, converges faster than the series of purely K-dependent parameters (DK, HK, LK, PK). In addition, the magnitudes of the diagonal distortion parameters within a given order decrease considerably from the purely K-dependent parameters to the purely J-dependent parameters with the minor exception of PK and PKKJ. A strong decrease is also seen for d1 and d2 as well as for h1 to h3. The distortion corrections to the energy behave in a similar way, and their number is smaller than that of the regular distortion parameters, commensurate with the moderate energy difference between 0+ and 0−.

The value of Fbc is quite small, and only two distortion corrections are required to fit this fairly large data set well. The HFS parameters are very well determined, including the interaction parameter χbc. It is not surprising that the 14N nuclear spin-rotation parameters could not be determined, as the magnetic moment of 14N is quite small. Inclusion of resolved internal rotation components other than the central EE components into a fit should not only enable the direct determination of a probably small number of internal rotation parameters, but may also reduce the uncertainties of some of the lower order parameters slightly.

Our present spectroscopic parameters are sufficiently accurate for all kinds of astronomical observations. The neglect of the internal rotation does not pose a limitation in sources such as Sgr B2(N) or G+0.693−0.027. Moreover, it should affect our current parameter values negligibly. Internal rotation may need to be considered around 100 GHz for sources with line widths less than 2 km s−1. The internal rotation splitting is likely too small to be resolved at much higher frequencies. Conversely, the DMA lines are probably too weak at lower frequencies in the warm ISM (around 100 – 200 K).

6 SEARCH FOR DIMETHYLAMINE TOWARDS G+0.693-0.027

6.1 Observations

We searched for DMA towards the G+0.693−0.027 molecular cloud, located in the Sgr B2 Giant Molecular Cloud of the galactic centre region. This source exhibits an extremely rich molecular complexity, and numerous molecular species have been detected for the first time towards it (see e.g. Rivilla et al. 2019; Bizzocchi et al. 2020; Rivilla et al. 2020, 2021a, b, 2022a, c; Zeng et al. 2021; Rodríguez-Almeida et al. 2021a, b; Jiménez-Serra et al. 2022). We used a sensitive unbiased spectral survey performed with the Yebes 40 m (Guadalajara, Spain) and the IRAM 30 m (Granada, Spain) telescopes. The position switching observations were centred at α(J2000.0) = |$, 17^{rm h}47^{rm m}22^{rm s}$|⁠, δ(J2000.0) = |$, -28^{circ }21^{prime }27^{prime prime }$|⁠. The Yebes 40 m observations cover a spectral range from 31.0 GHz to 50.4 GHz, while the IRAM 30 m observations cover the spectral ranges 71.77 − 116.72 GHz, 124.8-175.5 GHz, and 199.8 − 238.3 GHz. The line intensity of the spectra was measured in units of |$T_{mathrm{A}}^{ast }$| as the molecular emission towards G+0.693 is extended over the beam (Requena-Torres et al. 2006, 2008; Zeng et al. 2018, 2020). The noise of the spectra (in |$T_{A}^{*}$|⁠) depends on the frequency range, and varies from 1 to 10 mK. The spectra were smoothed to velocity resolutions of 1.0 − 2.6 km s−1, depending on the frequency. For more detailed information of the observational survey we refer to Rivilla et al. (2022b).

6.2 Non-detection of dimethylamine towards G+0.693-0.027

We implemented the spectroscopic entry of DMA presented in this work into the MADCUBA package2 (version 28/10/2022; Martín et al. 2019). Using the SLIM (Spectral Line Identification and Modelling) tool of MADCUBA, we generated a synthetic spectrum of DMA under the assumption of local thermodynamic equilibrium (LTE) and compared it with the observed spectra. The molecule is not detected in the observational survey. Most of the DMA transitions appear heavily blended with brighter transitions from other molecules already identified in the survey. To derive the upper limit to the column density, we have used the brightest emission according to the simulated LTE model that appears unblended, which are three unresolved HFS components of the υ = 0− − 0+ 11, 0 − 00, 0 transition with F = 0 − 1, 2 − 1, and 1 − 1 that fall in the Q-band survey performed with the Yebes telescope and that are shown in Fig. 6. For the LTE simulated spectrum, we have used the excitation temperature derived for CH3NH2 by Zeng et al. (2018), 16 K, which is similar to those derived for C2H3NH2 and C2H5NH2 (18 and 12 K, respectively; Zeng et al. 2021). We also used the velocity and linewidth found for the latter species: VLSR = 67 km s−1 and FWHM = 18 km s−1; the beam size at 44.9 GHz is 39″. Unfortunately, the predicted emission just appears in a spectral region which shows a local minimum in the data with respect to the adjusted broad band baseline. Considering the noise of the data, we obtained a 3σ upper limit in integrated area of N < 7.6 × 1013 cm−2, which corresponds to an abundance compared to H2 of < 5.6 × 10−10, using N(H2) = 1.35 × 1023 cm−2 (Martín et al. 2008). This upper limit as well as column densities of methylamine, methanol and dimethyl ether are summarized in Table 5 together with derived quantities. The upper limit to the column density of DMA could be affected by the local baseline by less than a factor of two when the local baseline uncertainty is considered. The rms noise level in the Yebes spectrum near 44.9 GHz is 1.6 mK in a 1.5 km s−1 channel. Fortunately, the spectral region of these transitions seems to be clean from contamination, opening the possibility of a detection in future more sensitive Q band searches.

7 SEARCH FOR DIMETHYLAMINE TOWARDS SGR B2(N)

7.1 Observations

We also used the imaging spectral line survey Re-exploring Molecular Complexity with ALMA (ReMoCA) that targeted the high-mass star forming protocluster Sgr B2(N) with ALMA to search for dimethylamine in the interstellar medium. The data reduction and the method of analysis of this survey were described in Belloche et al. (2019). We summarize the main features of the survey below. The phase centre is located at the equatorial position (α, δ)J2000 = (⁠|$17^{rm h}47^{rm m}19{_{.}^{rm s}}87, -28^circ 22^{prime }16{{_{.}^{primeprime}} }0$|⁠). This position is half-way between the two hot molecular cores Sgr B2(N1) and Sgr B2(N2). The survey covers the frequency range from 84.1 to 114.4 GHz at a spectral resolution of 488 kHz (1.7 – 1.3 km s−1). This frequency coverage was obtained with five different tunings of the receivers. The observations achieved a sensitivity per spectral channel ranging between 0.35 and 1.1 mJy beam−1 (rms) depending on the setup, with a median value of 0.8 mJy beam−1. The angular resolution (HPBW) varies between ∼0.3″ and ∼0.8″ with a median value of 0.6″. This corresponds to ∼4900 au at the distance of Sgr B2 (8.2 kpc, Reid et al. 2019). We further improved the process that separates the line and continuum emission by adding two reference positions to the pool of positions that were used to find the frequency ranges that contain absorption features (for more details about the separation of line and continuum emission, see Belloche et al. 2019).

For this work we analysed the spectra of two positions. The first one, Sgr B2(N1S), is located at (α, δ)J2000 = (⁠|$17^{rm h}47^{rm m}19{_{.}^{rm s}}87$|⁠, −28°22′19|${_{.}^{primeprime}}$|5). It is offset by about 1″ to the south of the main hot core Sgr B2(N1). This position was chosen by Belloche et al. (2019) for its lower continuum opacity compared to the peak of the hot core. The second position is the position called Sgr B2(N2b) by Belloche et al. (2022). It is located in the secondary hot core Sgr B2(N2) at (α, δ)J2000 = (⁠|$17^{rm h}47^{rm m}19{_{.}^{rm s}}83, -28^circ 22^{prime }13{{_{.}^{primeprime}} }6$|⁠). This position was chosen as a compromise between getting narrow line widths to reduce the level of spectral confusion and keeping a high enough H2 column density to detect less abundant molecules.

Like in our previous ReMoCA studies (e.g. Belloche et al. 2019, 2022), we compared the observed spectra to synthetic spectra computed under the assumption of LTE with the astronomical software weeds (Maret et al. 2011). This assumption is justified by the high densities of the regions where hot-core emission is detected in Sgr B2(N) (>1 × 107 cm−3, see Bonfand et al. 2019). The calculations take into account the finite angular resolution of the observations and the optical depth of the rotational transitions. For each position, we derived by eye a best-fit synthetic spectrum for each molecule separately, and then added together the contributions of all identified molecules. Each species was modelled with a set of five parameters: size of the emitting region (θs), column density (N), temperature (Trot), linewidth (ΔV), and velocity offset (Voff) with respect to the assumed systemic velocity of the source, Vsys = 62.0 km s−1 for Sgr B2(N1S) and Vsys = 74.2 km s−1 for Sgr B2(N2b). The linewidth and velocity offset are obtained directly from the well detected and not contaminated lines. The emission of complex organic molecules is extended over several arcseconds around Sgr B2(N1) (see Busch et al. 2022). For the LTE modelling, we assumed like in Belloche et al. (2019) an emission size of 2″, which is much larger than the beam, meaning that the derived column densities do not depend on the exact value of this size parameter. In the case of Sgr B2(N2b), the size of the emission of a given molecule was estimated from integrated intensity maps of transitions of this given molecule that were found to be relatively free of contamination from other species.

7.2 Search for DMA towards Sgr B2(N1S) and Sgr B2(N2b)

Before searching for dimethylamine, CH3NHCH3, towards Sgr B2(N1S) and Sgr B2(N2b), we modelled the rotational emission of the similar molecule dimethyl ether, CH3OCH3. We used the spectroscopic calculations available in the CDMS (Müller et al. 2005) for the vibrational ground state (version 1 of entry 46514), which are based on Endres et al. (2009) and references therein. For the vibrationally excited states υ11 = 1 and υ15 = 1, we used like in Belloche et al. (2013) predictions provided by C. Endres. Dimethyl ether is well detected towards both Sgr B2(N1S) and Sgr B2(N2b), with dozens of lines in its vibrational ground state easily identified (see Figs A1 and A4). Two dozen lines in each of its vibrationally excited states υ11 = 1 and υ15 = 1 are also clearly detected towards Sgr B2(N2b) (Figs A5-A6). Because of the broader line widths that increase the level of spectral confusion (5 km s−1 versus 3.5 km s−1 towards Sgr B2(N2b)), only a few lines from within υ11 = 1 and υ15 = 1 are sufficiently free of contamination to be identified towards Sgr B2(N1S) (Figs A2-A3). As explained in Section 7.1, we assumed an emission size of 2″ to model the emission of dimethyl ether towards Sgr B2(N1S). In the case of Sgr B2(N2b), integrated intensity maps of lines of dimethyl ether that are free of contamination suggest an emission size on the order of 0.8″. Figs 7 and 8 show population diagrams of dimethyl ether for Sgr B2(N1S) and Sgr B2(N2b), respectively. A fit to these population diagrams yields rotational temperatures of ∼170 and ∼130 K, respectively (see Tables 6 and 7). Assuming these temperatures, we adjusted synthetic LTE spectra to the observed spectra and obtained the column densities reported in Tables 8 and 9 for dimethyl ether. We also list in these tables the parameters that we previously obtained from the ReMoCA survey for methanol towards both positions (Motiyenko et al. 2020; Belloche et al. 2022), as well as the parameters that we recently obtained for methylamine, CH3NH2, towards Sgr B2(N1S) (Gyawali et al., in preparation), using the spectroscopic predictions available in the Lille Spectroscopic Database (version 2021.08.hfs of entry 31802), which are based on Motiyenko et al. (2014).

Methylamine turns out to be more difficult to identify towards Sgr B2(N2b) than towards Sgr B2(N1S). Methylamine has a similar rotational temperature as methanol towards Sgr B2(N1S), which led us to assume the same rotational temperature and emission size as methanol towards Sgr B2(N2b). The best-fit synthetic LTE spectrum of methylamine using these parameters is shown in Fig. A7. Most transitions of this molecule are contaminated by emission from other species. Only two transitions are relatively free of contamination (at 84 306 and 112 273 MHz). As a result, we only claim a tentative detection of methylamine towards Sgr B2(N2b). The parameters of its best-fit LTE model are given in Table 9.

To search for dimethylamine towards each position using the spectroscopic predictions obtained in Section 4, we computed synthetic LTE spectra assuming the same emission size and rotational temperature as those derived for dimethyl ether. We did not find any evidence for dimethylamine in either source. The upper limit to the column density of DMA was evaluated for each source by varying the column density by hand and comparing the synthetic and observed spectra by eye, using the 3σ level (dashed lines in Figs 9 and 10) as a guide, but also accounting for the blends with other species and the uncertainties on the baseline level. The synthetic spectra used to estimate the upper limit to its column density are shown in Figs 9 and 10 for Sgr B2(N1S) and Sgr B2(N2b), respectively. These upper limits are reported in Tables 8 and 9, respectively.

8 ASTROCHEMICAL MODELLING

To explore the possible chemistry of DMA and its likely yield in the interstellar medium, we adapt the astrochemical models presented by Garrod et al. (2022) to include DMA and a selection of related species. The physical treatment and chemical framework of the models correspond to the final model of Garrod et al. (2022), which uses a three-phase (gas, grain/ice-surface and bulk-ice) treatment of the coupled gas and grain chemistry of hot cores. The grain chemistry framework (explained in detail by Jin & Garrod 2020) includes non-diffusive mechanisms for surface and bulk-ice reactions, which allows the production of complex organic molecules to occur on the grains even at very low temperatures. The physical modelling uses a two-stage treatment, in which relatively diffuse gas (nH = 3000 cm−3) first collapses to high density (2 × 108 cm−3); as the visual extinction increases from 3 to 500 mag., the dust cools from ∼14.6 to 8 K, while the gas temperature is held steady at 10 K during the collapse as in past models. Much of the grain-surface ice builds up towards the end of the collapse stage. During the subsequent warm-up stage, this material is heated such that the gas and dust temperatures rise monotonically to a maximum of 400 K. Following various past models that have used the same physical treatment, the warm-up occurs over one of three characteristic time-scales, labelled fast (5 × 104 yr), medium (2 × 105 yr), and slow (1 × 106 yr), where the time-scale technically corresponds to the time required to reach a representative hot-core temperature of 200 K. Desorption of the ice mantles into the gas phase takes place mainly in the 100 – 200 K temperature range.

The chemical network is based on that of Belloche et al. (2022), which included propanol chemistry and which is itself derived from the Garrod et al. (2022) network. The new chemistry for DMA is based around production on grain surfaces or in the bulk ices, through the radical recombination reaction

and the two-stage reaction process,

The intermediate radical CH3NH may be produced by the hydrogenation of other species of the form CHxNHy, or through the addition of other radicals leading to such species. Crucially, the CH3NH radical may additionally be formed through the photodissociation of methylamine, while CH2 and CH3 can be formed via repetitive H-addition to atomic carbon, or by the photodissociation of methane or other species containing a methyl group.

Each of the reaction sequences (1) and (2) may occur either on the grain/ice surfaces or within the bulk ice. On surfaces, reactions may be driven by diffusion or by non-diffusive encounters resulting from prior reactions (labelled ‘three-body’ reactions, 3-B) or photodissociation events (labelled ‘photodissociation-induced’ reactions, PDI). At the low temperatures (i.e. <20 K) achieved during the collapse stage and early in the warm-up stage, surface reactions such as (1) and (2a) occur mainly through non-diffusive processes, due to the immobility of the reactants, while reaction (2b) is driven by the diffusion of mobile atomic H. At higher temperatures, surface diffusion of radicals also contributes somewhat to the production of large molecules. Within the bulk ice, diffusive motions are restricted to H and H2 only, which can occur through quantum tunnelling as well as thermal diffusion. Thus, in the bulk ice, reactions between radicals (i.e. not H) may only occur through the non-diffusive 3-B and PDI mechanisms.

Based on the earlier chemistry, two new neutral species are added to the network: DMA and its radical precursor CH2NHCH3. Following past grain-surface chemistry treatments (e.g. Garrod 2013), both of these species may also be destroyed by reactions with radicals; DMA may undergo H-abstraction by, for example, the OH radical, forming water and CH2NHCH3, while CH2NHCH3 may abstract H from a selection of other radical species such as HCO, to form DMA and the stable molecule CO. DMA and CH2NHCH3 can also be photodissociated on the grains or in the gas phase.

Grain-surface/ice reactions included in the network that are relevant to DMA are listed in Table 10. Subject to the caveats outlined earlier, each may occur as the result of diffusive meetings, the 3-B and PDI processes, or by the Eley-Rideal (E-R) mechanism (surface only). Adsorption onto the grains, as well as thermal and non-thermal desorption mechanisms (photo- and chemical desorption) are treated as per past models. The surface binding energies of DMA and CH2NHCH3 used in the model are 5856 and 5731 K, respectively, based on extrapolation from other species/functional groups in the network, as per previous models (Garrod et al. 2008; Belloche et al. 2017, 2019). Molecular desorption driven by the direct impingement of cosmic rays on dust grains is not included in the present model, although the photodesorption mechanism includes a contribution from the cosmic ray-induced photon field.

The main destruction mechanisms for most complex organic molecules in the network are gas-phase ion-molecule reactions that take place following the desorption of the ice mantles into the gas. These are dominated by proton transfer from ions H|$_3^+$|⁠, HCO+, and H3O+; the resulting protonated molecule (⁠|$mathrm{CH_3NH_2CH_3^+}$|⁠, in the case of DMA) may then recombine with electrons, fragmenting the molecule. A description of the procedures for the construction of this basic gas-phase chemistry may be found in Garrod et al. (2008) and Garrod (2013).

Following Taquet, Wirström & Charnley (2016), Garrod et al. (2022) added to their reaction network a number of gas-phase proton-transfer reactions between ammonia and various protonated complex organics, producing NH|$_4^+$| while returning the original complex molecule unscathed. The inclusion of this mechanism was found to provide a competitive alternative to the destructive electronic recombination of protonated complex organics, thus enhancing their post-desorption gas-phase lifetimes. However, the proton affinity of DMA is greater than that of ammonia (929.5 versus 853.6 kJ mol−1 Hunter & Lias 1998), meaning that protonated DMA cannot transfer its proton in this way; such a mechanism is therefore not included in the present chemical network. The possible importance of the converse process of proton transfer from NH|$_4^+$| to certain complex organics is explored by Garrod & Herbst (2023) (submitted).

The new chemical network already incorporates the chemistry of a large selection of simple and complex molecules, including methylamine, methanol, dimethyl ether, and ethylamine; hot-core chemical model results for each of these are presented with those of DMA in order to compare with observations towards Sgr B2(N).

In order to test the effects on molecular ratios of the elevated cosmic ray ionization rates expected towards the galactic centre (Goto et al. 2014), the hot-core models are run using a selection of logarithmically spaced rates ranging from ζ = ζ0 to 101.5 ζ0, where ζ0 = 1.3 × 10−17 s−1.

For comparison with the gas-phase abundances observed towards G+0.693−0.027, the most appropriate modelling approach would include an explicit treatment of the passage of a shock (e.g. Requena-Torres et al. 2006; Zeng et al. 2018; Rivilla et al. 2022a), including the grain-heating and sputtering processes, as well as post-desorption gas-phase chemistry. Here, to allow a simpler comparison between the modelled abundances in the ices and the post-shock gas-phase abundances, we run collapse models similar to the first stage of the hot-core models, that would correspond to the pre-shock evolution of the dust and gas in G+0.693−0.027. The shock models of Rivilla et al. (2022a) suggest cosmic-ray ionization rates in this molecular cloud ranging from 100 to 1000 ζ0; we run collapse models with ζ using the two extremes of this range. To better represent the pre-shock gas density of G+0.693−0.027, the final gas density at the end of the collapse is reduced to nH = 2 × 104 cm−3, as inferred by Zeng et al. (2020).

8.1 Chemical model results

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Fig. 11 shows fractional abundances for DMA and other molecules during the warm-up stage, using the three typical warm-up time-scales, under conditions of ζ = ζ0. Each of the molecules shown inherits a substantial solid-phase abundance (indicated by dotted lines) from the cold collapse stage. The material remains on the grains until the ice begins to desorb strongly into the gas phase at temperatures greater than 100 K. Much of this release is driven by the thermal desorption of water, which comprises much of the ice abundance; it begins to be lost substantially at temperatures around 114 K, as noted by Garrod et al. (2022), and this continues until most water has been released by around 164 K. This desorption model is supported by observational results from Busch et al. (2022). They found in a study of Sgr B2(N1) that COMs formed on grains desorb thermally from the grain surface at ∼100 K, concomitantly with water. Because the model treats the ice as a distinct surface layer with a separate bulk ice beneath, the loss of water helps to release other species within the same time/temperature range. As a result, DMA, along with methanol and methylamine, reach their peak gas-phase abundances at around the temperature when water desorption reaches its maximum. These peak abundances and corresponding temperatures are shown in Table 11. The behaviour of other molecules not shown in the figures are well represented by the extensive results presented by Belloche et al. (2022) and Garrod et al. (2022).

Post-desorption gas-phase abundances are seen to fall more strongly as a function of temperature in the longer warm-up time-scales runs, due to the longer period spent in the gas phase by those molecules. In all cases but for dimethyl ether, the peak gas-phase values of the molecules shown are seen to track fairly closely with the peak ice-mantle abundances of the same species. Thus, the relative abundances in the gas are more or less preserved from the much earlier and colder period when those molecules were formed on the grains. Dimethyl ether, as noted in various past modelling papers, has a strong gas-phase production mechanism based on the reaction of methanol with protonated methanol; its abundance therefore rises in the gas phase following desorption of the existing dimethyl ether in the ices.

Production of DMA in the models occurs during two main periods; the first occurs during the cold collapse stage and is thus a shared feature of all of the subsequent warm-up models. Reaction (1) occurs at very early times in the model, driven by a combination of PDI and 3-B processes within the bulk ice, in the proportion ∼2 : 1, respectively. The initial visual extinction of around 3 mag. is low enough to allow external UV photons to dissociate methane (CH4) and methylamine, producing CH3 and CH3NH and allowing one or other radical to be produced, on occasion, in the presence of the other, leading to immediate non-diffusive reaction. Since this process does not involve diffusion, most of the reactions leading to DMA production occur in the thicker bulk-ice layer, rather than on the surface. At this early stage, the ice is up to a few tens of monolayers in thickness in total. The 3-B reaction mechanism in the bulk ice occurs around the same time, when H atoms released in the bulk ice by other photodissociation processes diffuse to find the stable molecule methanimine, CH2NH, with which it reacts to form CH3NH; the latter radical may then react with any contiguous CH3 in the bulk ice.

Production of the related species ethylamine (C2H5NH2) occurs in a similar way, through the reaction of radicals CH3 and CH2NH2; however, CH2NH2 is formed mainly through H-atom abstraction from CH3NH2 by atomic H in the bulk ice. This abstraction reaction is substantially faster than the comparable photodissociation process by which it might form, because of the availability of diffusive atomic H in the bulk ice caused by the photodissociation of numerous different ice species, including water. Abstraction from the methyl group on methylamine to form CH2NH2 is expected to be strongly dominant over the alternative, CH3NH, at very low temperatures (see Kerkeni & Clary 2007, who calculated branching down to 200 K). The availability of this effective mechanism for producing CH2NH2 therefore leads to much greater production of ethylamine versus DMA in the model.

The second stage of DMA production occurs during the warm-up stage, and is most prevalent in the slow warm-up model, due to the longer period available for ice photochemistry. In this case, the DMA formation occurs through cosmic ray-induced photodissociation of methylamine and methane. The left panel of Fig. 12 shows the total rate of production of DMA in all phases (surface, ice-mantle, and gas phase) as a function of time through the full collapse stage followed by the slow warm-up stage. The first and second stages of DMA production are seen clearly in green. The second production stage becomes significant beginning around 30 K, and continues to produce DMA up until the point of desorption, which begins to occur strongly between the two vertical dashed lines that indicate the beginning and end of water desorption. The onset of DMA production around 30 K is related to the falling abundance of atomic H in the ice as temperatures increase, reducing its ability to recombine with simple radicals before they can form more complex species. The right panel of Fig. 12 shows the production and destruction of DMA in several key temperature regimes. The early production mechanism for DMA contributes around 60 per cent of total production. The blue sections of the left and right panels indicate where DMA is destroyed in the gas phase, mainly through proton-transfer from H3O+, followed by dissociative electronic recombination.

Table 11 also shows peak gas-phase abundances and associated temperatures for three additional sets of model-runs, using ζ = 100.5 ζ0, 10 ζ0, and 101.5 ζ0. Among the nitrogen-bearing species, the peak abundances fall somewhat with increased cosmic ray ionization rate, with the effect more pronounced with longer warm-up time-scales. The effect is caused by more rapid gas-phase destruction via ion-molecule reactions. The two highest ζ values, when combined with the longest warm-up time-scale, produce a more extreme degree of destruction for all the molecules. Outside of those two cases, the oxygen-bearing species methanol and dimethyl ether are more robust to changes in ζ, generally varying by less than a factor 2 between the various models. Although the peak values are less affected, however, both increased warm-up time-scale and ζ value lead to more rapid destruction in the gas phase for all species following attainment of the post-desorption peak.

Fig. 13 shows results from the low-density collapse model with ζ = 100 ζ0, which is intended to represent the pre-shock behaviour of G+0.693; time-dependent solid-phase abundances are shown for the same five species as in Fig. 11. During the collapse, the increases in gas density and decreases in dust temperature become more substantial after a time of around 0.5 Myr, which manifests as a steeper rise in methanol abundance in particular. DMA abundance is seen never to exceed that of methylamine, while ethylamine slightly exceeds the latter towards the end of the model run.

The final solid-phase abundances of these molecules are shown in Table 12, where the results for the ζ = 1000 ζ0 model are also shown. The abundance of methanol is notably affected in the highest ζ model, while the abundance of dimethyl ether is lower by a factor ∼4. The abundances of the N-bearing species shown are each lower by a factor ∼2 in the ζ = 1000 ζ0 model.

9 DISCUSSION OF THE ASTROCHEMICAL RESULTS

9.1 G+0.693

The column density upper limit derived for DMA is 7.6 × 1013 cm−2, slightly higher than the column density derived for C2H3NH2 and C2H5NH2, which are (4.5 ± 0.6) × 1013 cm−2 and (2.5 ± 0.7) × 1013 cm−2, respectively (Zeng et al. 2021). The abundance ratio compared to methylamine, whose abundance is 2.2 × 10−8 (Zeng et al. 2018), is CH3NH2/DMA >39. We can compare this ratio with other −H and −CH3 pairs already detected towards G+0.693, such as methanol (CH3OH) and dimethyl ether (CH3OCH3). The CH3OH abundance is 1.1 × 10−7 (Jiménez-Serra et al. 2022), and that of CH3OCH3 is 8.1 × 10−10 (Rivilla, private communication), which yields a ratio CH3OH/CH3OCH3 ∼135. This value is consistent with the lower limit found for the CH3NH2/DMA ratio (>39), see also Table 5. This might suggest, if the −H/−CH3 ratio also holds for amines, that the detection of DMA would still need a significant improvement of the sensitivity of the current observations.

9.2 Sgr B2(N)

Table 8 shows that dimethyl ether is 14 times less abundant than methanol in Sgr B2(N1S) and dimethylamine is at least 14 times less abundant than methylamine towards this position. This limit is not constraining enough to infer whether or not the formation routes that possibly relate methanol to dimethyl ether and methylamine to dimethylamine operate differently. Towards Sgr B2(N2b), dimethyl ether is 26 times less abundant than methanol (Table 9). Because the abundance ratio of methanol to methylamine is much higher in Sgr B2(N2b) than in Sgr B2(N1S) (300 versus 15), the upper limit obtained for dimethylamine is much less constraining towards Sgr B2(N2b): we can only say that dimethylamine is at least 4.5 times less abundant than methylamine towards this position.

9.3 Comparison of chemical models with observations

As with the observational data themselves, molecular abundance ratios may be the most useful means of comparison between models and observations. Table 13 shows chemical model ratios between peak gas-phase abundance values for CH3OH : CH3OCH3, CH3NH2 : CH3NHCH3 and CH3OH : CH3NHCH3. The first of these, comparing with the ratios obtained for Sgr B2(N1S) and Sgr B2(N2b) of 14 and 26, respectively, provides an acceptable match with the observed values within the range of model outcomes, which range from 8 to 55. The modelled ratio CH3NH2 : CH3NHCH3, however, is rather more extreme, ranging from 37 to 75, with most values exceeding 50. Lower limits on this ratio for Sgr B2(N1S) and Sgr B2(N2b) are 14 and 4.5; thus the models predict abundances for DMA that are substantially below its observational upper limits in Sgr B2(N). The modelled ratio of methanol to DMA shows a similar picture, although the ratio for the high-ζ/slow warm-up model of 1410 is close to the observed lower limit for Sgr B2(N2b) of 1360. Either way, the chemical models are consistent with the non-detection of DMA towards Sgr B2(N).

Table 14 shows molecular ratios based on the ice-mantle abundances achieved for each molecule at the end of the low-density, high-ζ collapse models. We compare these ratios with those obtained from the gas-phase abundances observed towards G+0.693−0.027, on the assumption that the gas-phase abundances may retain the underlying ratios of the originating ice composition.

In comparison with the observed CH3OH : CH3OCH3 ratio of 135, the model ratios are too low, producing values of 16 and 4 for the ζ = 100 ζ0 and 1000 ζ0 models, respectively. At cosmic-ray ionization rates that are this high, the gas-phase survival of CO is substantially affected by ion-molecule reactions involving H|$_3^+$| and He+, such that the amount of CO available to produce grain-surface methanol, via hydrogenation by atomic H, is diminished. Furthermore, under these high-ζ, low-density conditions, in which photodissociation of ice-mantle species is quite rapid in comparison to the rate at which gas-phase CO and other species are deposited onto the grains, bulk-ice photochemistry involving CH3OH dominates dimethyl ether production on the grains, increasing its ratio relative to methanol.

Meanwhile the CH3NH2 : CH3NHCH3 ratios achieved in the models still slightly exceed the observational lower limit of 39, ranging from 56 to 60. These results are thus consistent with the non-detection of DMA towards G+0.693−0.027, although they also suggest that a detection may be rather easier to achieve towards this source than towards Sgr B2(N).

We note, however, that the ice-mantle abundance ratio for CH3NH2 : C2H5NH2 is close to unity in both the hot-core models and the lower-density, high-ζ models. This compares unfavourably with the observational ratio of ∼120 towards G+0.693−0.027, suggesting that the models substantially over-produce ethylamine. Furthermore, towards Sgr B2(N1S), this ratio has been found to be >6 (Margulès et al. 2022). Due to the similarities in the chemistry between ethylamine and DMA, this could indicate that DMA is also over-produced, rendering a possible future detection of this molecule even more challenging.

The rates used to simulate the production of DMA and related species are only poorly constrained, largely by comparison between photodissociation rates of similar molecules (under gas-phase conditions). There may therefore be a substantial amount of possible variation in model outcomes. The strongest mechanism for DMA production in the hot-core models also occurs early in the physical evolution, when visual extinction is low. It remains to be seen whether such a low initial visual extinction is appropriate to all regions of a hot core, thus DMA abundances could again be lower than the models predict.

There remains also the possibility that DMA could be formed in the gas phase, possibly through a similar mechanism to that which is so effective for the production of protonated dimethyl ether, |$mathrm{CH_3OH_2^+}$| + CH3OH → |$mathrm{CH_3OHCH_3^+}$| + H2O, followed by dissociative recombination. However, the authors are unaware of any experimental studies (Anicich 2003) of such a reaction between any combination of |$mathrm{CH_3OH_2^+}$|⁠, CH3OH, |$mathrm{CH_3NH_3^+}$|⁠, or CH3NH2 that would lead to protonated DMA. Furthermore, the gas-phase reaction producing dimethyl ether is especially effective due to the exceedingly high gas-phase abundances achieved by both methanol and protonated methanol (relative to other protonated complex organics), due to the presence of methanol in great abundance in the ice mantles. Even with a large reaction rate coefficient, the absolute reaction rate for an alternative process involving methylamine might not be great enough to compete with production of DMA on grains, limited as that may be.

While the DMA abundance produced by the low-density, high-ζ models is consistent with the non-detection, the behaviour of dimethyl ether with respect to methanol is not consistent with their observed ratio towards G+0.693−0.027. However, we emphasize that a fair comparison between models and observations should include the substantial influence of the shock chemistry and shock-induced grain-mantle release, which the present models do not do.

10 CONCLUSION AND OUTLOOK

We have investigated the rotation-tunnelling spectrum of DMA extensively in the millimeter and submillimeter regions. This yielded very accurate spectroscopic parameters which are well-suited for almost all searches for this molecule in space, except possibly in cases in which the methyl internal rotation needs to be taken into account.

Dimethylamine was not detected towards G+0.693−0.027. The lower limit to the CH3NH2/DMA ratio of >39 is constraining. But if the CH3NH2/DMA ratio is the same as the CH3OH/CH3OCH3 ratio of ∼135 an unambiguous identification of DMA in this source will require a considerable improvement in sensitivity.

We report non-detections of dimethylamine with ALMA towards Sgr B2(N1S) and Sgr B2(N2b). The non-detections imply that dimethylamine is at least 14 and 4.5 times less abundant than methylamine towards these sources, respectively, while dimethyl ether is 14 and 26 times less abundant than methanol, respectively.

Dimethylamine was included in astrochemical kinetic modelling calculations, assuming grain-surface and ice-mantle formation mechanisms. The calculated CH3NH2/DMA ratios are compatible with our observational non-detections. DMA in the models is formed mainly through an early mechanism that relies on photoprocessing of the young dust-grain ices by external UV under low-extinction conditions. Further processing of the ices by cosmic ray-induced UV photons allows DMA to be formed at higher temperatures. The models overproduce C2H5NH2 with respect to CH3NH2, suggesting that the abundance of DMA in the interstellar medium could be substantially lower than the predicted values if both DMA and ethylamine are similarly overproduced by the models. The calculated ratios of peak molecular abundances remain fairly stable for the range of cosmic-ray ionization rates tested here.

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ACKNOWLEDGEMENTS

We are grateful to H. V. L. Nguyen for communicating results of the Fourier transform microwave investigation prior to publication. We also thank C. P. Endres for providing SPFIT files of the ground state rotational spectrum of dimethyl ether. We acknowledge support by the Deutsche Forschungsgemeinschaft via the collaborative research center SFB 956 (project ID 184018867) project B3 as well as the Gerätezentrum SCHL 341/15-1 (‘Cologne Center for Terahertz Spectroscopy’). RTG thanks the Astronomy & Astrophysics program of the National Science Foundation (grant number AST 19-06489) for funding the chemical modelling presented here. VMR has received support from the project RYC2020-029387-I funded by MCIN/AEI /10.13039/501100011033. IJ-S and JM-P acknowledge funding from grant number PID2019-105552RB-C41 awarded by the Spanish Ministry of Science and Innovation/State Agency of Research MCIN/AEI/10.13039/501100011033. Our research benefited from NASA’s Astrophysics Data System (ADS). This paper makes use of the following ALMA data: ADS/JAO.ALMA#2016.1.00074.S. ALMA is a partnership of ESO (representing its member states), NSF (USA), and NINS (Japan), together with NRC (Canada), NSC and ASIAA (Taiwan), and KASI (Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO, and NAOJ. The interferometric data are available in the ALMA archive at https://almascience.eso.org/aq/.

DATA AVAILABILITY

The spectroscopic line lists and associated files are available as supplementary material through the journal and in the data section of the CDMS3 The underlying original spectral recordings will be shared on reasonable request to the corresponding author. The radio astronomical data on Sgr B2(N) are available through the ALMA archive.4

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References

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