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A&A
Volume 670, February 2023
Article Number A177
Number of page(s) 12
Section Interstellar and circumstellar matter
DOI https://doi.org/10.1051/0004-6361/202245442
Published online 24 February 2023

© The Authors 2023

Licence Creative CommonsOpen Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

This article is published in open access under the Subscribe to Open model.

Open Access funding provided by Max Planck Society.

1 Introduction

The number of multi-deuterated molecules detected in the interstellar medium (ISM) has increased substantially in the last years (e.g. CHD2OH and CD3OH (Parise et al. 2002, 2004), c-C3D2 (Spezzano et al. 2013), D2CO (Turner 1990), CHD2OHCHO (Manigand et al. 2019), D2O (Butner et al. 2007), and CH3OCHD2 (Richard et al. 2021)). In most recent years, the Atacama Large Millimeter/submillimeter Array (ALMA) telescope opened up the possibility of measuring the abundances of these species in a more unambiguous manner. The high spatial resolution of the interferometre allowed the warm gas around protostars to be zoomed into where these molecules appear. The ALMA Proto-stellar Interferometric Line Survey (PILS) towards the proto-stellar system IRAS 16293-2422 (Jørgensen et al. 2016) has allowed for the detection and accurate column density derivation of several multi-deuterated species (e.g. Persson et al. 2018 and Jensen et al. 2021). Doubly deuterated molecules are found to be more abundant than expected when taking the local ISM deuterium abundance into account (D/H = 2.0±0.1 × 10−5, Linsky 2003; Caselli & Ceccarelli 2012; Ceccarelli et al. 2014 and references therein). The enrichment of molecules with deuterium, known as deuterium fractionation, is an interesting diagnostics tool that can be used as a clock to trace molecules to the time and environment of their formation (Ceccarelli et al. 2014). For example, the D/H ratio for methanol found in comets agrees with the ratio derived in pre-stellar cores and low-mass proto-stellar regions linking the cometary methanol to the first stages of star formation (Drozdovskaya et al. 2021). Furthermore, the water D/H ratio on Earth is found to be more similar to the one observed in proto-stellar cores, in clustered star-forming regions, than that in isolated proto-stellar cores (Jensen et al. 2019), supporting the interpretation that the Sun was formed in a clustered star-forming environment (Adams 2010).

Deuteration is most effective in the pre-stellar core environment due to the low temperatures present (<10 K; e.g. Caselli et al. 2002 and Crapsi et al. 2007). Due to the lower zero point energy (ZPE) of deuterium, this forms stronger bonds than hydrogen at low temperatures, making the equilibrium of the reaction H3++HD ⇋ H2D++H2 shift to the right-hand side in pre-stellar cores (e.g. Pagani et al. 1992). Moreover, in these environments, CO, which is the main destructor of H3+${\rm{H}}_3^ + $ and H2D+, is heavily frozen onto the surface of dust grains (e.g. Caselli et al. 1999). As a consequence, pre-stellar cores have a higher H2D+/H3+ ratio (Dalgarno & Lepp 1984). The H2D+ and other multi-deuterated forms of H3+ are the main deuteration agent in the gas phase. On the other hand, H-D substitution reactions on the surface of dust grains have been proposed to explain the observed deuterium fractionation (Drozdovskaya et al. 2022 and references therein). In Ambrose et al. (2021), deuterated methanol (CH2DOH) was observed towards nine of the 12 starless and pre-stellar sources observed, deriving a median value [CH2DOH]/[CH3OH] ratio of 0.11.

Deuterated molecules found in sources at later stages of the star formation process are thought to be inherited from the pre-stellar core phase. The molecules trapped in the ice mantles of dust grains are released into the gas phase due to the heating of the central protostar, making their detection possible (Taquet et al. 2014). Observation of the D/H ratios towards the proto-stellar system IRAS 16293-2422 has revealed a generalised trend with smaller molecules (e.g. methanol, formic acid, formaldehyde) having a D/H ~2% and larger molecules (e.g. dimethyl ether, ethanol) displaying a D/H ~4–8% (Jørgensen et al. 2018). van Gelder et al. (2022) compared observations of deuterated methanol towards high-mass protostars with literature observations encompassing multiple stages and masses of the star formation process. They observe that the [CH2DOH]/[CH3OH] ratio for high-mass protostars is lower than the one for the low-mass protostars. However, the [CHD2OH]/[CH2DOH] ratio is found to be similar amongst high- and low-mass protostars. In the same paper, by using the gas-grain chemical model GRAINOBLE (Taquet et al. 2012, 2013, 2014), the authors suggest that the methanol deuteration levels in high-mass protostars could indicate that this molecule was formed in a warm environment (>20 K) or that the pre-stellar phase within which they formed was short lived.

The fact that D2/D ratios are observed to be higher than D/H ratios implies that multiple deuteration is more favourable than the first deuteration, which is supported by laboratory experiments (Nagaoka et al. 2005, 2007; Hidaka et al. 2009). In the case of methanol, from the observed D/H and D2/D column density ratios in the comet 67P/Churyumov–Gerasimenko, the formation of singly deuterated methanol (CH2DOH) is constrained to happen via the H–D substitution of the main isotopologue (CH3OH; Drozdovskaya et al. 2021). On the other hand, doubly deuterated methanol (CHD2OH) is deduced to form from the hydrogenation of doubly deuterated formaldehyde (D2CO; Drozdovskaya et al. 2021). The study of methanol deuteration sets an example as to the importance of deriving column density ratios of singly and multi-deuterated species for the purpose of understanding the nature of deuterium fractionation, and the interplay of the chemistry in the gas phase and on the surface of dust grains.

The astrophysically relevant molecule acetaldehyde and its isotopologues have been the focus of numerous spectroscopic studies due to the internal rotation of their methyl group. The microwave spectrum of the main isotopologue (CH3CHO) was first analysed by Kilb et al. (1957). Subsequently, its analysis was extended up to the υt = 4 torsional state (Hershbach 1959; Iijima & Tsuchiya 1972; Bauder & Günthard 1976), enabling its first detection in the ISM by Gilmore et al. (1976). The isotopic species with either a deuterated COD aldehyde group or a fully deuterated CD3 methyl group were also investigated (Coudert & López 2006; Elkeurti et al. 2010; Zaleski et al. 2017), of which the CH3CDO species has been detected in the ISM by Jørgensen et al. (2018). Spectroscopic results are also available for isotopic species with a partially deuterated CH2D or CHD2 asymmetrical methyl group. The monodeuterated species CH2DCHO has been the subject of several investigations (Turner & Cox 1976; Turner et al. 1981; Coudert et al. 2019) which led to its detection in the ISM (Coudert et al. 2019). The doubly deuterated species CHD2CHO has also been studied (Turner & Cox 1976; Turner et al. 1981), but only a few transitions characterised by low Ka values were assigned in a microwave spectrum. Due to the high levels of confusion in the observational spectra towards star-forming regions, high-accuracy spectroscopic catalogues are crucial for the detection of species in the ISM, which stresses the need to extend the study on CHD2CHO beyond the work done by Turner & Cox (1976) and Turner et al. (1981) towards higher J and Ka.

The doubly deuterated isotopic variant of acetaldehyde CHD2CHO is investigated in this article. The analysis of its microwave and sub-millimetre wave spectra is reported in Sect. 2, where a spectroscopic catalogue is also built. Section 3 deals with the astrophysical search in ALMA PILS and the detection of this species. In Sect. 4, we present the discussion. Lastly, our conclusions can be found in Sect. 5.

2 Spectroscopic investigation of CHD2CHO

Theoretical models aimed at accounting for the internal rotation of molecules displaying internal rotation of a symmetrical CH3 or CD3 methyl group were developed a long time ago (Koehler & Dennison 1940; Burkhard & Dennison 1951; Ivash & Dennison 1953; Hecht & Dennison 1957a,b; Lees & Baker 1968; De Lucia et al. 1989) and successfully applied to the main isotopic species of methanol and acetaldehyde. The efforts to characterise the internal rotation of symmetrical methyl groups is still under study (Ilyushin et al. 2020; Kleiner & Hougen 2020; Xu et al. 2021). These models cannot be used for molecules displaying internal rotation of a partially deuterated CH2D or CHD2 methyl group. Alternate models were designed for such molecules and applied to mono and doubly deuterated methyl formate and methanol (Margulès et al. 2009; Coudert et al. 2012, 2014, 2021; Pearson et al. 2012; Ndao et al. 2015). The Hamiltonian used in the present investigation is based on the theoretical model developed for monodeuterated methyl formate by Margulès et al. (2009), which relies on the high-barrier internal axis method (IAM) approach of Hougen (1985) and Coudert & Hougen (1988). In this section, the experimental spectrum is described and, after briefly outlining the IAM approach, the fitting of previously available microwave transitions (Turner & Cox 1976; Turner et al. 1981) and of the newly measured sub-millimetre ones are reported.

2.1 Experimental

The rotational transitions were recorded in the 82.5–450 GHz frequency range using the broadband Chirped-Pulse Fourier Transform Spectrometre (CP-FTS) as well as the high-resolution absorption experiment in the Center for Astrochemical Studies Laboratory of the Max-Planck-Institute für Extraterrestrische Physik in Garching, Germany.

The doubly deuterated acetaldehyde sample was synthesised by warming up a mixture of equal weights of CH3CHO and D2O in acidic medium (KHSO4, pH 1) with a silicone bath at 38°C for 2 weeks. Separation of the organic phase, where the molecule is dissolved in, from the water phase was done by manual decantation. The first low J and Ka line recordings were done with CP-FTS which allows for an instantaneous bandwidth of 20 GHz in the frequency range of 75–110 GHz. The Chirped-Pulse was produced by an arbitrary waveform generator (Keysight, M8190A). The signal was then upconverted and amplified by an image quality (IQ) modulator and a solid state amplifier, respectively, before entering the chamber. Thereafter, the signal was amplified, downconverted, and digitised.

For lines at higher J and Ka, which require an increased sensitivity, we moved on to recording with the frequency modulated absorption spectrometre (Bizzocchi et al. 2017). The radiation source is an active multiplier chain (Virginia Diodes, Inc.) connected to a synthesiser (Keysight E8257D PSG Analog Signal Generator) operating between 250 kHz and 67 GHz. The synthesiser is also connected to a 10 MHz rubidium frequency clock. A combination of frequency multipliers allowed us to access the range between 82.5 and 450 GHz covered by the measurements. The detector used is a liquid-He-cooled InSb hot electron bolometre (QMC Instr. Ltd.). Frequency modulation of the signal was applied to reduce the noise, and then the output signal was demodulated at 2f (where f denotes the modulation frequency) with a lock-in amplifier (Standford Research Systems SR830). The sample was at an average pressure of 1.2 × 10−2 mbar in the cell during measurements with both setups and the linewidth was limited by Doppler broadening. All of the measurements were carried out at room temperature. Figure 1 shows a sample of the measurement scans and Fig. 2 shows the Out configuration a-type 17Ka→16Ka${17_{{K_a}}} \to {16_{{K_a}}}$ transitions for Ka ranging from 6 to 9 (see Fig. 3 for a structural reference of the In and Out configurations.)

thumbnail Fig. 1

υ = 0 and 1 tunnelling components, arising from the two isoenergetic Out configurations, of several a-type transitions. The upper panel shows the υ =1 component of the unresolved K-type doublet 179 ← 169. The lower panel depicts the υ = 0 and 1 tunnelling components of the 191,19 ← 181,18 transition.

2.2 Theory

The theoretical model developed previously for monodeuterated methyl formate (Margulès et al. 2009) can be applied to doubly deuterated acetaldehyde CHD2CHO with only a few changes. The main one concerns the relative energy of the non-superimposable equilibrium configurations, defined in agreement with the IAM approach of Hougen (1985) and Coudert & Hougen (1988). As emphasised by Fig. 3, in doubly deuterated acetaldehyde, just as in monodeuterated methyl formate, there arise three equilibrium configurations which can be identified by their configuration number n, with n = 1, 2, and 3, and characterised by αeq(n)$\alpha _{{\rm{eq}}}^{\left( n \right)}$, the value of the torsional angle α=∠HCCO$\alpha = \angle {\rm{HCCO}}$ about which the reference function is localised. Configurations 1 and 2 are the two C1 symmetry Out configurations with the hydrogen atom outside the CCO plane. They are lower in energy than Configuration 3, the Cs symmetry In configuration with the hydrogen atom in the CCO plane. The energy difference Ed between the In and Out configurations is not known exactly as of yet, but it is expected to be very close to the zero-point vibrational energy difference: Ed=Ezpe(In, CHD2CHO)−Ezpe(Out, CHD2CHO).${E_{\rm{d}}} = {E_{{\rm{zpe}}}}\left( {{\rm{In,}}\,{\rm{CH}}{{\rm{D}}_2}{\rm{CHO}}} \right) - {E_{{\rm{zpe}}}}\left( {{\rm{Out,}}\,{\rm{CH}}{{\rm{D}}_2}{\rm{CHO}}} \right).$(1)

An approximate value of this difference was retrieved from E′d${{E'}_{\rm{d}}}$, the equivalent energy difference for the monodeuterated species CH2DCHO (we refer to Fig. 2 in Coudert et al. 2019 for a visual representation of these conformers): E′d=Ezpe(Out, CH2DCHO)−Ezpe(In, CH2DCHO).${E'_{\rm{d}}} = {E_{{\rm{zpe}}}}\left( {{\rm{Out,}}\,{\rm{C}}{{\rm{H}}_2}{\rm{DCHO}}} \right) - {E_{{\rm{zpe}}}}\left( {{\rm{In,}}\,{\rm{C}}{{\rm{H}}_2}{\rm{DCHO}}} \right).$(2)

The ratio r=Ed/E′d$r = {E_{\rm{d}}}/{{E'}_{\rm{d}}}$ was computed using ab initio calculations. A calculation at the B3LYP/6-31G(d) level of theory with the Gaussian 16 package (Frisch et al. 2016) yielded r = 0.9311. Since E′d${{E'}_{\rm{d}}}$, which was first estimated by Turner et al. (1981) and Cox et al. (2003) and determined later with a higher accuracy by Coudert et al. (2019), is 15.558 66(4) cm−1, we obtain Ed = 14.487 cm−1.

The theoretical results in Sects. 3.2 and 3.3 of Margulès et al. (2009) can be used in the case of CHD2CHO provided a few changes, due to the definition of Ed in this work, are made. Equation (8) of these authors should be changed to: 〈 ψ3| Ht |ψ3 〉=〈 ψ1| Ht |ψ1 〉+Ed=〈 ψ2| Ht |ψ2 〉+Ed$\left\langle {{\psi _3}\left| {{H_{\rm{t}}}} \right|{\psi _3}} \right\rangle = \left\langle {{\psi _1}\left| {{H_{\rm{t}}}} \right|{\psi _1}} \right\rangle + {E_{\rm{d}}} = \left\langle {{\psi _2}\left| {{H_{\rm{t}}}} \right|{\psi _2}} \right\rangle + {E_{\rm{d}}}$(3)

and Ed should be ignored in their Eq. (21) and in their Table 2; in their Table 1, it should only appear for diagonal matrix elements involing two wavefunctions corresponding to Configuration 3. Table 1 of the present paper lists the computed values for the rotational constants and dipole moment components of the In and Out configurations as retrieved from the structure of Kilb et al. (1957) and the dipole moment components reported in Table 16 of Turner & Cox (1978) for CH3CHO. Equations (12) and (13) of Margulès et al. (2009) should be used with no change being made to obtain the tunnelling matrix element HJKγ1;JK′γ′2${H_{JK\gamma 1;JK'\gamma '2}}$ of the 1 → 2 tunnelling path connecting the isoenergetic Configurations 1 and 2. Similarly, Eqs. (14) and (15) should be used for the tunnelling of matrix element HJKγ1;JK′γ′3${H_{JK\gamma 1;JK'\gamma '3}}$ of the 1 → 3 tunnelling path connecting Configurations 1 and 3. The rotational dependence of these tunnelling matrix elements was parame-terised by two sets of Eulerian-type angles, O2, ∅2 and χ3, θ3, ∅3, which were numerically evaluated using the structure of Kilb et al. (1957) and which are also given in Table 1. In Eqs. (12)–(15) of Margulès et al. (2009), h2 and h3 are the magnitude of the tunnelling splittings. These parameters – the Eulerian-type angles θ2, ∅2, χ3, θ3, and ∅3; the rotational constants of the In and Out configurations; and the energy difference Ed – allowed us to compute the rotation-torsion energy of the first three torsional states of CHD2CHO to zeroth order.

When tunnelling effects are small, the In configuration displays asymmetric-top rotational energies shifted by +Ed. For the + and − sub-levels arising from the Out configurations, Eq. (21) of Margulès et al. (2009) shows that ±h2 should be added to the asymmetric-top rotational energies, where the upper (lower) sign is for the + (−) sub-level. As h2 is negative (Hougen 1985; Coudert & Hougen 1988), the + sub-level is below the – sub-level. The resulting tunnelling pattern for J = 0 is drawn in Fig. 4 where it is compared to that of the monodeuterated species CH2DCHO. In agreement with the energy level diagram for CHD2CHO in this figure, the vibrational quantum number υ, with 0 ≤ υ ≤ 2, was introduced. Furthermore, υ = 0 and 1 refer to rotational levels arising from the + and − tunnelling sub-levels, respectively, and υ = 2 to those arising from the In configuration. The results presented for CH2DCHO by Coudert et al. (2019) concerning selection rules, distortion terms for the tunnelling matrix elements, and the assignment of the levels arising from numerical diagonalisation of the Hamiltonian matrix also apply for CHD2CHO and readers are referred to that paper for further information.

thumbnail Fig. 2

υ = 0 and 1 tunnelling components of the a-type 17Ka ← 16Ka transitions, displaying no resolved asymmetry splitting, with 6 ≤ Ka ≤ 9. The line at 295–312 MHz in the second panel is unidentified.
thumbnail Fig. 3

Two energetically equivalent Out configurations and the higher energy In configuration are identified by their configuration number n = 1, 2, and 3. The two deuterium atoms are labelled 2 and 3. Furthermore, αeq(n)$\alpha _{{\rm{eq}}}^{\left( n \right)}$ is the equilibrium value of the torsional angle α=∠HCCO$\alpha = \angle {\rm{HCCO}}$. Configuration 3, displaying a symmetry plane and therefore having Cs symmetry, is approximately 14.487 cm−1 above Configurations 1 and 2 with C1 symmetry.
Table 1

Calculated molecular parameters.

thumbnail Fig. 4

J = 0 tunnelling pattern of CH2DCHO and CHD2CHO as retrieved by Margulès et al. (2009). The tunnelling parameter h2 and the energy differences Ed and E′d${{E'}_{\rm{d}}}$ are defined in Sect. 2.2. The tunnelling sub-levels for CHD2CHO are also labelled with the quantum number υ such that υ = 0 and 1 correspond to the + and − tunnelling sub-levels, respectively, and υ = 2 to the In conformation level.

2.3 Line assignment and line analysis

Starting from the results of Turner & Cox (1976), parallel a-type and perpendicular b-type transitions within the In configuration were assigned up to J = 20 and Ka = 5. This first set of transitions was fitted with a Watson-type Hamiltonian. Parallel a-type and perpendicular b- and c-type transitions within and between the + and − sub-levels of the Out configurations were assigned afterwards up to J = 27 and Ka = 16, using the results of Turner et al. (1981). Fitting this second set of transitions yielded rotational constants for the Out configurations, the magnitude of the tunnelling splitting h2, and the Eulerian-type angles θ2 and ∅2. No unaccountably large residuals, which could have been attributed to couplings between the In and Out configurations, were found. As a result, unlike in the monodeuterated species CH2DCHO, the value of Ed and of the parameters describing the 1 → 3 tunnelling parameter could not be retrieved. Both sets of transitions were then fitted and new transitions were predicted and searched for. For the In configuration, it was possible to assign a- and b-type transitions up to J = 26 and Ka = 17. For the Out configurations, a-, b-, and c-type transitions were assigned up to J = 27 and Ka = 14. Table 2 lists the number of assigned transitions for each configuration, counting even forbidden ΔKa and ΔKc transitions (Turner et al. 1981) of the Out configurations as a-type transitions. In the final analysis, experimental frequencies were introduced in a least-squares-fit procedure where they were given a weight equal to the inverse of their experimental uncertainty squared. Unresolved K-type doublets were treated as in Margulès et al. (2009). The rotational Watson-type Hamiltonians used for the In and Out configurations were written using Watson’s A set of distortion parameters (Watson 1967, 1968a,b). The root mean square value of the observed minus calculated frequency is 81 kHz for transitions within the ‘In’ configuration, 88 kHz for transitions within the ‘Out’ configurations, and 83 kHz for all transitions. The unit-less standard deviation of this final analysis is 1.7. With the selected set of spectroscopic parameters, most line frequencies are reproduced within their experimental uncertainty of 50 kHz. Also, a-type lines characterised by a large J and Ka value tend to display residuals larger than this value and this may be due to the effects that are unaccounted for from the 1 → 3 tunnelling motion. For the whole dataset, assignments, observed and calculated frequencies, and residuals are listed in Table 3, available at the Centre de Données astronomiques de Strasbourg (CDS). Table 4 lists the parameters determined in the analysis. This table displays two columns. Column 1 gives the parameter name and Col. 2 its value and uncertainty. For the rotational constants, the calculated values in Table 1 are within 300 MHz from the experimental values in Table 4. For the Eulerian-type angles describing the rotational dependence of the tunnelling matrix elements, the discrepancies are 0.2 and 1° for θ2 and ∅2, respectively.

Table 2

Assigned transitions.

2.4 Spectroscopic catalogue

The spectroscopic catalogue was built using the results of the previous sections. The energy difference Ed was set to the value computed in Sect. 2.2. Transitions were calculated up to J = 28 and their line strength and line intensity were computed using the dipole moment components in Table 1. The partition functions Qrot, listed in Table 5, were computed for several temperatures using degeneracy factors equal to (2J + 1). A zero energy was taken for the Out configurations 000, + level. Lines were selected using an intensity cutoff depending on the line frequency (as is commonly done in the Jet Propulsion Laboratory (JPL) database catalogue line files; Pickett et al. 1998). Its value in nm2·MHz units at 300 K is 10LOGSTR0+(F/300 000)2×10LOGSTR1,${10^{{\rm{LOGSTR0}}}} + {\left( {{F \mathord{\left/ {\vphantom {F {300\,000}}} \right. \kern-\nulldelimiterspace} {300\,000}}} \right)^2} \times {10^{{\rm{LOGSTR1}}}},$(4)

where F is the frequency in MHz, and LOGSTR0 and LOGSTR1 are two dimensionless constants both set to −8. The linelist, given in Table 6, is available at the CDS and is formatted in the same way as the catalogue line files of the JPL database (Pickett et al. 1998). A minimum value of 10 kHz was selected for the calculated error (ERR). For observed unblended microwave lines, the line frequency (FREQ) and the error (ERR) were replaced by their experimental values. This is then indicated by a negative species tag. The catalogue is available on CDMS1 (Endres et al. 2016).

Table 4

Spectroscopic parameters.

Table 5

Partition functions (Qrot) of CHD2CHO.

thumbnail Fig. 5

Example of the CHD2CHO fits in a selected frequency range. The synthetic spectra fitted to CHD2CHO is shown in red and all other species identified in PILS are in blue.

3 Astrophysical observations

Based on the new spectroscopic measurements, we searched for CHD2CHO towards the B component of the proto-stellar system IRAS 16293–2422 in data from the ALMA PILS (Jørgensen et al. 2016). PILS represents an unbiased molecular line survey of IRAS 16293-2422 which was carried out during ALMA’s Cycle 2 (project id: 2013.1.00278.S, PI: J. K. Jørgensen), covering one of the prominent atmospheric windows in ALMA’s Band 7 between 329.1 and 362.9 GHz with a spectral resolution of ≈0.2 km s−1 and angular resolution of ≈0.5″ (70 au at the distance of IRAS 16293-2422). The high sensitivity of the PILS data and relatively narrow lines towards one component of IRAS 16293–2422 have enabled the detections of a number of species for the first time in the ISM (e.g. CH3Cl by Fayolle et al. 2017 and HONO by Coutens et al. 2019) as well as having made it possible to systematically survey the content of deuterated isotopologues of complex organic molecules (Jørgensen et al. 2018). The latter also includes the detection of doubly deuterated organics including CHD2CN (Calcutt et al. 2018), CHD2OCHO (Manigand et al. 2019), and CHD2OCH3 (Richard et al. 2021) as well as new and better constraints on the column densities of doubly and triply deuterated methanol (Drozdovskaya et al. 2022; Ilyushin et al. 2022). For details about the data and their reduction, we refer readers to Jørgensen et al. (2016).

For our search we analysed the position offset by one beam (0.5″) from the B component of IRAS 16293–2422, where line and continuum opacity is limited. This position was also the one studied in the above-mentioned papers from PILS (Jørgensen et al. 2016, 2018). We adopted a similar approach to previous works by fitting synthetic spectra for CHD2CHO calculated under the assumption that its excitation is characterised by local thermodynamical equilibrium (LTE), which is reasonable at the densities of the warm gas where these species are present (Jørgensen et al. 2016). The free parameters in the fits are the column density of the molecule N, and its rotational temperature, Trot. For the line width and velocity offset relative to the local standard of rest, we adopted values of 1 km s−1 (FWHM) and of 2.6 km s−1, respectively, which match the spectra well at this position. For Trot we assumed a temperature of 125 K similar to that of the non-deuterated and singly deuterated isotopologues of acetaldehyde. An example of the fit to a selected frequency range is shown in Fig. 5 while the fits to the lines predicted to be brighter than 40 mJy beam−1 km s−1 (68 transitions; the root mean square noise in the spectra is about 4–5 mJy beam−1 per 1 km s−1) over the entire frequency range are shown in Fig. A.1. Several clean and unblended transitions are seen to provide a good constraint on the CHD2CHO column density of 1.3 × 1015 cm−2 with an uncertainty of 10–20% (for the discussion on the uncertainty derivation, we refer readers to Jørgensen et al. 2018). The few lines that are either under- or over-produced with the synthetic spectra are due to blends with brighter lines of more prominent species (e.g. the two lines seen at 330.71 GHz with an upper energy level of 202 K that are blended with glyco-laldehyde) or absorption due to optically thick emission (e.g. the transition at 347.86 GHz falling close to a transition of formic acid).

The derived column density can be compared to that of the singly deuterated variant, CH2DCHO, of 6.2 × 1015 cm−2 (Manigand et al. 2020). The ratio between the singly and doubly deuterated variants of 20% is very close to those for methyl formate (CHD2OCHO/CH2DOCHO) of 22% (Manigand et al. 2019), dimethylether (CH3OCHD2/CH2OCH2D) of 15–20% (Richard et al. 2021), and methanol (CHD2OH/CH2DOH) of 25% (Drozdovskaya et al. 2022) – in all cases it is significantly above the ratios for the singly deuterated to non-deuterated isotopologues (Jørgensen et al. 2018) by factors of 4–5.

4 Discussion of astronomical observational results

The similar doubly to singly deuterated column density ratios for acetaldehyde, methyl formate, dimethylether, and methanol presented in Sect. 3 suggest that doubly deuterated acetalde-hyde shares a common origin and was formed in an environment resembling the physical conditions with which doubly deuter-ated methyl formate, dimethylether, and methanol were formed. The pre-stellar core phase is a good candidate due to the low temperatures that promote deuterium fractionation through the enhancement of the H2D+/H3+${{\rm{H}}_2}{{\rm{D}}^ + }/{\rm{H}}_3^ + $ ratio as well as the larger atomic D/H ratio in the gas phase, which promotes deuteration of surface species.

Mechanisms for acetaldehyde main isotopologue formation have been suggested for both the gas phase as well as for the surface of grains. For the gas phase, Vazart et al. (2020) concluded that C2H5 + O(3P) and CH3CH2OH + OH/CH3CHOH + O(3P) are potentially efficient gas-phase formation routes. Fedoseev et al. (2022) studied grain surface reactions and proposed CH2CO + 2H as a plausible way of forming CH3CHO. Contrarily to deuterated methanol, whose formation pathway has been constrained (Drozdovskaya et al. 2021), the formation of deuterated acetaldehyde is still not clear. In the same line as doubly deuterated methanol, doubly deuterated acetaldehyde could be formed from a doubly deuterated reactant. The acetalde-hyde D2/D ratio found in this work and the D/H ratio from Manigand et al. (2020) combined with a gas-grain chemical model can potentially shed light on the formation mechanism of singly and multi-deuterated acetaldehyde.

Contrary to deuterated methanol, which has been observed in a variety of sources, deuterated acetaldehyde counts fewer detections. Acetaldehyde is less abundant than methanol in pre-stellar cores with [CH3CHO]/[CH3OH] ratios betweewn 0.02 and 0.26 (Scibelli & Shirley 2020). We estimate the line brightness of the most intense lines of the singly and doubly deuterated acetalde-hyde in the 3 mm band towards pre-stellar cores to be 4.3 mK and 0.5 mK, respectively. We base our estimate on the average column density of CH3CHO observed towards starless cores in Scibelli & Shirley 2020 (2 × 1012 cm−2), and assuming the D/H and D2/H ratio observed towards IRAS16293.

Based on our predictions, it will be unlikely to detect the doubly deuterated acetaldehyde towards pre-stellar cores, and this is possibly also true for other COMs. Nevertheless, one can use the diagnostic power of deuteration and derive the information on inheritance from pre-stellar cores by using state-of-the-art chemical models.

5 Conclusions

The rotation-torsion spectrum of doubly deuterated acetaldehyde (CHD2CHO) was experimentally and theoretically studied. Due to the tunnelling of the CHD2 methyl group, the ground state is split into three torsional sub-levels. Transitions were measured in the millimetre and sub-millimetre range (82.5–450 GHz), as described in Sect. 2.1. These, alongside previously measured ones, were fitted using IAM. A total of 853 transitions were fitted with a weighted root mean square deviation of 1.7. The resulting spectroscopic parameters computed with this fit can be found in Table 4. We built a spectroscopic catalogue for astrophysical purposes from the results of the analysis, which we publish in CDMS.

We present the first detection of CHD2CHO in the ISM through comparisons to observations of the B component of the proto-stellar system IRAS 16293-2422 from the ALMA PILS programme. This doubly deuterated variant is enhanced compared to its singly and non-deuterated counterparts at the same level as for other complex organics seen towards this source. Further comparison to chemical models may shed further light on the acetaldehyde formation during the earliest stages of star formation.

Acknowledgements

J.F.A., S.S., V.L., C.P.E. and P.C. gratefully acknowledge the support of the Max Planck Society. The research of J.K.J. is supported by the Independent Research Fund Denmark (grant no. 0135-00123B). This paper makes use of the following ALMA data: ADS/JAO.ALMA#2013.0.00278.S. ALMA is a partnership of ESO (representing its member states), NSF (USA) and NINS (Japan), together with NRC (Canada), MOST 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. We also thank the anonymous referee for their insightful comments.

Appendix A Additional material

In this section we present Table A.1, which lists the transitions of CHD2CHO detected in the PILS ALMA Band 7 frequency range. Moreover, we present the fits of these transitions assuming a rotational temperature of 125 K over the PILS ALMA Band 7 spectrum in Fig. A.1.

Table A.1

Detected CHD2CHO transitions towards IRAS 16293-2422.

thumbnail Fig. A.1

68 transitions of CHD2CHO predicted to be the brightest assuming a rotational temperature of 125 K. The red line indicates the predicted line intensities obtained by fitting to the lines with the synthetic spectra, thereby constraining the column density. In each panel, the numbers on the upper left corner indicate the excitation temperature Tex of the fitted transitions. An asterisk next to this number indicates situations where two lines from Table A.1 with similar values for Eu fall within 10 MHz of each other and are shown together in one panel.

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All Tables

Table 1

Calculated molecular parameters.

In the text
Table 2

Assigned transitions.

In the text
Table 4

Spectroscopic parameters.

In the text
Table 5

Partition functions (Qrot) of CHD2CHO.

In the text
Table A.1

Detected CHD2CHO transitions towards IRAS 16293-2422.

In the text

All Figures

thumbnail Fig. 1

υ = 0 and 1 tunnelling components, arising from the two isoenergetic Out configurations, of several a-type transitions. The upper panel shows the υ =1 component of the unresolved K-type doublet 179 ← 169. The lower panel depicts the υ = 0 and 1 tunnelling components of the 191,19 ← 181,18 transition.
In the text
thumbnail Fig. 2

υ = 0 and 1 tunnelling components of the a-type 17Ka ← 16Ka transitions, displaying no resolved asymmetry splitting, with 6 ≤ Ka ≤ 9. The line at 295–312 MHz in the second panel is unidentified.
In the text
thumbnail Fig. 3

Two energetically equivalent Out configurations and the higher energy In configuration are identified by their configuration number n = 1, 2, and 3. The two deuterium atoms are labelled 2 and 3. Furthermore, αeq(n)$\alpha _{{\rm{eq}}}^{\left( n \right)}$ is the equilibrium value of the torsional angle α=∠HCCO$\alpha = \angle {\rm{HCCO}}$. Configuration 3, displaying a symmetry plane and therefore having Cs symmetry, is approximately 14.487 cm−1 above Configurations 1 and 2 with C1 symmetry.
In the text
thumbnail Fig. 4

J = 0 tunnelling pattern of CH2DCHO and CHD2CHO as retrieved by Margulès et al. (2009). The tunnelling parameter h2 and the energy differences Ed and E′d${{E'}_{\rm{d}}}$ are defined in Sect. 2.2. The tunnelling sub-levels for CHD2CHO are also labelled with the quantum number υ such that υ = 0 and 1 correspond to the + and − tunnelling sub-levels, respectively, and υ = 2 to the In conformation level.
In the text
thumbnail Fig. 5

Example of the CHD2CHO fits in a selected frequency range. The synthetic spectra fitted to CHD2CHO is shown in red and all other species identified in PILS are in blue.
In the text
thumbnail Fig. A.1

68 transitions of CHD2CHO predicted to be the brightest assuming a rotational temperature of 125 K. The red line indicates the predicted line intensities obtained by fitting to the lines with the synthetic spectra, thereby constraining the column density. In each panel, the numbers on the upper left corner indicate the excitation temperature Tex of the fitted transitions. An asterisk next to this number indicates situations where two lines from Table A.1 with similar values for Eu fall within 10 MHz of each other and are shown together in one panel.
In the text

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