ATOMIUM: Molecular inventory of 17 oxygen-rich evolved stars observed with ALMA ⋆

Context. The dusty winds of cool evolved stars are a major contributor of the newly synthesised material enriching the Galaxy and future generations of stars. However, the details of the physics and chemistry behind dust formation and wind launching have yet to be pinpointed. Recent spatially resolved observations show the importance of gaining a more comprehensive view of the circumstellar chemistry, but a comparative study of the intricate interplay between chemistry and physics is still difficult because observational details such as frequencies and angular resolutions are rarely comparable. Aims. Aiming to overcome these deficiencies, ATOMIUM is an ALMA Large Programme to study the physics and chemistry of the circumstellar envelopes of a diverse set of oxygen-rich evolved stars under homogeneous observing conditions at three angular resolutions between ∼ 0.02 ′′ − 1 . 4 ′′ . Here we summarize the molecular inventory of these sources, and the correlations between stellar parameters and molecular content. Methods. Seventeen oxygen-rich or S-type asymptotic giant branch (AGB) and red supergiant (RSG) stars have been observed in several tunings with ALMA Band 6, targeting a range of molecules to probe the circumstellar envelope and especially the chemistry of dust formation close to the star. We systematically assigned the molecular carriers of the spectral lines and measured their spectroscopic parameters and the angular extent of the emission of each line from integrated intensity maps. Results. Across the ATOMIUM sample, we detect 291 transitions of 24 different molecules and their isotopologues. This includes several first detections in oxygen-rich AGB/RSG stars: PO (cid:51) = 1, SO 2 (cid:51) 1 = 1 and (cid:51) 2 = 2, and several high energy H 2 O transitions. We also find several first detections in S-type AGB stars: vibrationally excited HCN (cid:51) 2 = 2 , 3 and SiS (cid:51) = 4 , 5 , 6, as well as first detections of the molecules SiC, AlCl, and AlF in W Aql. Overall, we find strong correlations between the following molecular pairs: CS and SiS, CS and AlF, NaCl and KCl, AlO and SO, SO 2 and SO, and SO 2 and H 2 O; meaning both molecules tend to have more detected emission lines in the same sources. The measured isotopic ratios of Si and S are found to be consistent with previous measurements, except for an anomalously high 29 Si/ 30 Si ratio of 4 ± 1 in the RSG VX Sgr. Conclusions. This paper presents the overall molecular inventory and an initial analysis of the large ATOMIUM dataset, laying the groundwork for future work deriving molecular abundances and abundance profiles using radiative transfer modeling which will provide more rigorous tests for chemical models.


Introduction 1
Cool evolved stars are a major contributor of the gas and 2 dust returned to the interstellar medium (Tielens 2005) through Tables A.1-A.5 are only available in electronic form at the CDS via anonymous ftp to cdsarc.cds.unistra.fr(130.79.128.5) or via https://cdsarc.cds.unistra.fr/cgi-bin/qcat?J/A+A/ email: sofia.wallstrom@kuleuven.beThese AGB and RSG stars and their accompanying circumstellar envelopes (CSEs) provide useful chemical laboratories for studying dust and molecule formation due to their relatively simple overall spherical structure and their (mostly) radial velocity fields.Other chemically interesting cool environments, such as star-forming regions or (proto)planetary disks, tend to have more complex spatial and velocity structures, making it more difficult to disentangle the effects of chemistry.The overall chemical composition of an AGB CSE depends on the C/O ratio of the central star (see, for example, Habing & Olofsson 2003), as most of the less abundant element is locked up in CO.An oxygen-rich or M-type star (C/O < 1) has more free oxygen to form for example silicate dust and oxygen-bearing moleculessuch as SO, TiO, AlO -while a carbon-rich star (C/O > 1) has more free carbon to form for example amorphous carbon dust and molecules such as HC 3 N and SiC 2 .Stars with C/O ∼ 1 are called S-type stars and have a mixed chemistry.The more massive RSGs are all oxygen-rich stars, due to extra nucleosynthesis molecules, including AlCl, rotational emission from TiO for the first time in an oxygen-rich evolved star, and TiO 2 for the first time in space.A large number of lines of oxygen-rich molecules like SO 2 and SO are seen, as well as many lines of the relatively refractory NaCl including vibrationally excited transitions up to = 3.Most of the observed lines show multiple velocity components, and the molecular emission shows similar spatial complexity.Decin et al. (2017Decin et al. ( , 2018) ) observed two archetypal oxygenrich AGB stars, the high mass-loss rate (5×10 −6 M yr −1 ) IK Tau and the low mass-loss rate (1 × 10 −7 M yr −1 ) R Dor, at ∼0.15 angular resolution with the Atacama Large Millimeter and submillimeter Array (ALMA).They detect ∼200 lines from 15 different molecules, including dust precursors such as SiO, AlO, AlOH, TiO, and TiO 2 .Highly vibrationally excited SiO (up to = 5) is detected in both sources close to the star, and AlO is detected far beyond the dust condensation radius showing that this molecule does not become entirely locked up in dust grains.The data is also used to characterise the wind acceleration of both sources, showing much slower accelerations than for the carbon-rich CW Leo (β ∼ 5 − 10).
These interferometric surveys demonstrate the importance of spatially resolved observations for obtaining a more comprehensive view of the circumstellar chemistry, as different molecules and transitions can show emission at different spatial scales and with different morphologies.However, it is difficult to draw more general conclusions about AGB or RSG stars from the study of single sources.Even in aggregate, various studies have different sensitivities, frequency coverage, and angular resolutions, and hence are difficult to compare.The next step to elucidate the circumstellar chemistry is to observe a sample of stars with a range of stellar parameters, with identical observing setups.By performing homogeneous high-angular-resolution observations, we can directly compare the chemical inventories of different sources, and compare them with stellar parameters.
ALMA Tracing the Origins of Molecules formIng dUst in oxygen-rich M-type stars (ATOMIUM, Program ID: 2018.1.00659.L) is an ALMA Large Programme to observe 17 oxygen-rich AGB and RSG stars at high angular resolution in a range of molecular transitions (Decin et al. 2020;Gottlieb et al. 2022).The ATOMIUM targets were chosen to represent a range of AGB mass-loss rates, chemical types (M-type and S-type stars), and pulsation behaviors (semi-regular variables (SR), long-period variables (LPV), and regular Mira variables).The sample also includes three RSG stars, and is summarised in Table 1.ATOMIUM is the first ALMA Large Programme for stellar evolution, and consists of a set of homogeneous highresolution observations that allow unambiguous comparison of the physicochemical properties of the winds of the 17 evolved stars, expanding the sample of evolved stars studied at such high angular resolution by a factor of four.It also provides a detailed picture of the chemical and dynamical processes throughout the stellar wind, including measurements of isotopic ratios which provide an important tracer of nucleosynthesis in the core of the star.Alongside the ATOMIUM overview paper (Gottlieb et al. 2022), several in-depth studies of individual sources (Homan et al. 2020(Homan et al. , 2021;;Danilovich et al. 2023), specific molecules (Danilovich et al. 2021;Baudry et al. 2023), and comparisons with optical polarized light (Montargès et al. 2023) have already resulted from this data.tion are described fully in Gottlieb et al. (2022), and the charac-215 teristics such as the rms noise level, σ rms , and angular resolution 216 of each spectral cube are given in their Table E.3.Note that in 217 some cases (such as very bright, compact emission or weak, ex-218 tended emission) the standard reduction parameters may leave 219 low-level artefacts in the images for individual lines; papers on 220 specific lines or targets, using optimised imaging and combination of the different spatial resolutions, may give slightly different values from those reported here (and in Gottlieb et al. 2022).To allow for this and for the propagation of errors when combining data taken at different epochs, we adopt a conservative flux scale uncertainty of 15% (although in some cases it may be much better than this).

Processing and analysis
We used spectra of each source at high, medium, and low angular resolution to identify the various molecular transitions.Spectra were extracted in circular apertures, centered on the continuum peak, with diameters of 0.04 , 0.08 , and 0.12 for the high-resolution data; diameters of 0.4 , 1.2 , and 3.6 for the medium-resolution data; and diameters of 1.2 , 3.6 , and 10.8 for the low-resolution data.At each resolution, the smallest aperture was chosen to be the average beam size rounded up to one significant figure, for consistency.
In each spectrum the line identification was carried out in a systematic way.Starting from a list of expected lines based on the line survey of IK Tau and R Dor by Decin et al. (2018), at the position of each potential line a soft parabola function (as defined in De Beck et al. 2010) was fit with a least squares fitting algorithm.A visual inspection then ruled out spurious fits, added missing lines, and adjusted the fit of weak and blended lines.The rms (σ) was measured from the parts of the spectrum more than three times the wind expansion velocity (v exp ) away from any line, and any potential lines below 2.5σ are considered nondetections.Any previously unknown lines were added to the line list, and identified if possible.Inspection of integrated intensity (moment 0) maps by eye further ensured any weak lines correspond to coherent emission across several channels rather than a noise fluctuation.We have also checked the intrinsic brightness (at 300 K) of the various transitions to ensure that the detected lines of each molecule are among the brightest lines in our frequency range.We do not exclude the possibility that further lines may be detected with a different data reduction method or by stacking data; however, we leave this to future papers.
Example medium and high angular resolution spectra of R Hya are shown in Appendix C, with molecular identifications, while Appendix A contains more detailed information about the identified lines.Additional information about the lines and molecular data can be found in Appendix A.1, Table A.1 gives a full list of identified molecules by source, Table A.2 gives the maximum radial extent of each molecule in each source, Table A.3 lists all identified molecular lines with references for the line parameters, and Table A.4 lists all the unidentified lines.Table A.5 list all detected lines in each source, and gives measurements taken at each spatial resolution (high, medium, low) where the line was detected.Each line was measured separately in the spectra extracted with the three different apertures given above.
Line parameters were extracted from each spectrum, and for each detected line its peak flux, integrated intensity, velocity width (full width at zero power), and angular extent (from its integrated intensity map, see below) was measured.The peak flux was taken to be the flux in the brightest channel included within the line extent.The spectral extent of a line was measured between the channels where each line wing reaches 2.5σ, with a minimum width of four channels (≈5 km s −1 ), thus defining the velocity width and integrated intensity.As this was done automatically, broad weak lines may have their velocity widths and hence integrated intensities underestimated.The uncertainty on the peak flux was taken to be the rms plus the 15% absolute Table 1: ATOMIUM sources and their stellar parameters.
(2) Calculated from the stellar angular diameter and distance.
(3) Scaled to the new distance estimate, see Section 2.3.
(4) Several distances have been updated with respect to the values given in Gottlieb et al. (2022).
References:  enclosing the star (centered on the peak of the continuum emission).The contours were azimuthally smoothed (in bins with at least ten samples, corresponding to angular ranges of ≥60 • ) to limit deviations due to noise, following the method in Danilovich et al. (2021).Note that for transitions with clumpy emission, this method may underestimate the extent of the emission.For transitions with no measured extent from this method an upper limit is given, equal to half the major axis of the restoring beam (b ma j /2).We also note that there may be diffuse extended emission of various molecules which is not properly imaged, or which is filtered out if its size is similar to (or greater than) the maximum recoverable scale.Such emission may be brought out with different data reduction techniques or spectral averaging. .
Updating the distances to these sources has changed the de-

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rived mass-loss rate by at most a factor of 2.5.However, we 332 expect the literature mass-loss rate values to have uncertainties 333 larger than this (though they are seldom quantified), with determinations frequently based on only one or two independent observations which makes it difficult to disentangle the degeneracies between for example the mass-loss rate, temperature profile, and the outer radius of the wind.Sources with derived mass-loss rates based on more than two independent observational data points are highlighted in green, which is the case for only five sources: IRC+10011, π 1 Gru, R Hya, VX Sgr, and W Aql. W Aql has undoubtedly the best constrained mass-loss rate as it is based on direct modeling of 21 individual CO lines, and even here the model has an estimated uncertainty of a factor ∼3 (Danilovich et al. 2014;Ramstedt et al. 2017).Furthermore, many of the mass-loss rates are derived using empirical formulae, based on CO line fluxes and some stellar parameters, rather than direct radiative transfer modelling of CO observations.These formulae involve a large number of assumptions resulting in uncertainties of at least a factor ∼3-5 (De Beck et al. 2010;Olofsson et al. 1993), when they are quantified at all.Two of the mass-loss rates are derived from empirical formulae using the observed 60 µm flux (labeled "a" in Table 3), which requires further assumptions about the wind velocity, dust properties, and gas-to-dust ratio.
The derived mass-loss rates also generally assume a constant and spherically symmetric mass loss, but the ATOMIUM observations have shown this is not true for any of our sources (Decin et al. 2020): they all show significant structure in their winds, and some -like π 1 Gru and R Hya -are highly asymmetric.This is interpreted as the likely presence of a companion.If the companion shapes the wind into an equatorial density enhancement, this could change the derived mass-loss rate by a factor of up to three if the system is seen face-on, and potentially much more if the system is seen edge-on (El Mellah et al. 2020).Furthermore, simply the assumption of a constant mass-loss rate has been shown to change the derived mass-loss rate by a factor of a few (Kemper et al. 2003;Decin et al. 2007).
Taken together, these factors result in typical uncertainties on the mass-loss rates of up to an order of magnitude.However, the mass-loss rate still provides a useful way to order the sources to look for general trends, and in the absence of more precise estimates we will continue to use the values in Table 1 in our analysis.Improving the mass-loss rate estimates for the ATOM-IUM sources will be undertaken in a future publication, using radiative transfer modelling of homogeneous single-dish observations of at least four CO transitions per source, combined with the spatial information from the ALMA observations.

Results and discussion
This section presents an overview of the molecular inventory in Section 3.1, molecular emission sizes in Section 3.2, correlations between various stellar parameters and their molecular content in Section 3.3, an analysis of the spatial distributions of SO and SO 2 in Section 3.4, isotopic ratios for a subset of the molecules in Section 3.5, and a discussion of the unidentified lines in Section 3.6

Overview of molecular inventory
Across the variety of 17 AGB and RSG sources in the ATOM-IUM sample, we detect 287 molecular lines of which 29 remain unidentified.Emission from a total of 24 molecules has been identified, namely: AlCl, AlF, AlO, AlOH, CO, CN, CS, H 2 O, H 2 S, HC 3 N, HCN, KCl, NaCl, OH, PO, SO, SO 2 , SiC, SiC 2 , SiN, SiO, SiS, TiO, and TiO 2 ; and 19 isotopologues thereof con-taining one or more of atoms of 13 C, 17 O, 29 Si, 30 Si, 33 S, 34 S, and From Figure 1 we can see that CO, HCN, and SiO are ubiquitous, as expected from previous studies, with similar numbers of lines detected in almost all sources (excepting the large number of vibrationally excited HCN lines in W Aql).All sources show vibrationally excited (up to = 4) lines of SiO except the line-poor KW Sgr (up to = 2) and U Del (up to = 1), and also SV Aqr (up to = 1).Three sources also show 30 SiO lines up to = 5: R Aql, R Hya, and S Pav.Note that the = 5 transitions of the main SiO isotopologue were not covered by our observations.Many of the SiO lines have maser components, especially the high-lines but also some = 0 lines (Pimpanuwat et al., in prep.).SO and SO 2 are detected in a majority of sources, excepting the line-poor U Del and KW Sgr (in which SO but not SO 2 is seen), and the S-type sources π 1 Gru and W Aql. A large number of SO 2 = 0 and 2 = 1 lines are detected in many sources, and the two RSGs AH Sco and VX Sgr also show a few highenergy 1 = 1 or 2 = 2 transitions.SO 2 is one of the most widespread species in our sample, partially due to its nature as an asymmetric top which exhibits many different energy levels throughout its energy ladder, which are fairly easily populated by radiation and collisions.The other sulfur-bearing molecules -H 2 S, SiS, and CS -are expected to have abundances that scale with mass-loss rate, and hence are more likely to be seen in high mass-loss-rate sources (Decin et al. 2018;Danilovich et al. 2017Danilovich et al. , 2018)).Indeed, we only see H 2 S in the highest mass-loss-rate sources, but for SiS and CS there is no clear trend with massloss rate.Danilovich et al. (2016Danilovich et al. ( , 2020a) also found a difference in the spatial distributions of SO and SO 2 in low-and high-massloss-rate sources, which is discussed further in Section 3.4.
SiS shows transitions from several isotopologues, and highlines (up to = 5 − 6) are seen in both S-type sources, π 1 Gru and W Aql, which are expected to have higher SiS abundances (Schöier et al. 2007;Danilovich et al. 2018).All other sources only show lines of SiS up to = 1, except IRC+10011 and IRC-10529 where = 3 is reached.
H 2 O is detected in all the sources in our sample except the two S-type stars, in several high-lying rotational transitions with lower state energy levels above ∼3900 K, including high vibrational energy states.Four OH hyperfine split transitions with similar high energies (E low 4800 K) are also detected.This includes many first detections of these transitions in space; they are discussed in detail in Baudry et al. (2023) and hence will not be extensively discussed here.
The halide-bearing molecules -AlF, NaCl, and KCl -are mostly found in high mass-loss-rate sources, although AlF (and AlOH) are also seen in the intermediate mass-loss-rate source U Her. Specifically the chlorine-bearing molecules KCl and NaCl are found only in IRC+10011, IRC-10529, and GY Aql.It is perhaps unexpected that the chlorides are missing in the RSGs AH Sco and VX Sgr, as NaCl is very strong in the RSG VY CMa (Tenenbaum et al. 2010;Quintana-Lacaci et al. 2023), however VY CMa is a more evolved RSG with a higher mass-loss rate than the RSGs in our sample.Furthermore, another chlorinebearing molecule, AlCl, is only found in the S-type star W Aql, in which we do not detect NaCl or KCl, so AlCl seems to require different formation and/or excitation conditions.W Aql is also the only source to show transitions of 13 CN, SiN, SiC, SiC 2 , and HC 3 N (note 12 CN was not covered by our observations).This is unsurprising as it is a bright, nearby Stype star with a fairly carbon-rich outflow (De Beck & Olofsson 2020).The other molecule only seen in a single source is TiO 2 in VX Sgr, which may be because VX Sgr is the highest-mass-

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The largest angular extents, >1.5 , are mainly found for molecules which are seen in a majority of sources: CO, SiO, SO, SO 2 , CS, SiS, and HCN.However, for almost all molecules there are some sources where the maximum measured extent is very small.Which source it is varies by molecule, and its value is often an outlier among the sample.For example, in CO the smallest r max of 29 R in the line-poor RSG KW Sgr is much smaller than the next smallest value of 530 R in AH Sco.V PsA has the smallest measured r max in HCN, SO, and SO 2 ; R Hya shows the smallest extents in SiS and CS; and the smallest measured r max in SiO is in π 1 Gru.
There are some interesting observations to be made from this summary from a chemical standpoint.First, AlO extends further out than AlOH, though this is only true for the RSGs VX Sgr and AH Sco, which have much larger AlO extents than the other sources: ≥100 R .They also have the largest r max in AlOH, at 45 and 8 R , respectively -smaller than their AlO extents.This is unexpected as AlOH is formed from AlO (by reaction with H 2 O and H 2 ), although AlOH is also easily photolysed back to AlO (Mangan et al. 2021).The other three AGB sources with detections of both AlOH and AlO show slightly larger extents in AlOH.So here we have a dichotomy between the RSG and AGB sources, where perhaps the photolysis of AlOH to AlO is more efficient in the RSGs explaining their large AlO extents.
Another surprising observation is that TiO extends further out than TiO 2 in the only star where TiO 2 is detected: the RSG VX Sgr.VX Sgr shows a maximum extent in TiO of 65 R , larger than the 14 R extent in TiO 2 .This might indicate that TiO 2 is depleted because it is taking part in the formation of dust particles in the inner wind.Notes: Maximum extents in CO are likely underestimated and are marked with † .Transitions with no measurable extent are noted as upper limits equal to the radius of the beam (b ma j /2).The molecules are arranged according to the maximum measured r max in R .

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To get an overview of how the molecular content varies by ship between the two variables can be described by a monotonic function, that is, whether the first variable tends to increase as the second does and vice versa.The variables being correlated are the effective temperatures, mass-loss rates, terminal expansion velocities, and pulsation periods (as given in Table 1), and the number of lines detected for each molecule and its isotopologues.Molecules which are found in only one source (TiO 2 in VX Sgr, and AlCl, HC 3 N, SiC 2 , SiN, and 13 CN in W Aql) have not been included.Generally, we assume that a larger number of detected lines of a given molecule implies a higher molecular abundance; however there may be additional effects making the detection of, for example, highly vibrationally excited lines more likely.These will be discussed for each molecule in the following sections.
As we have more than ten sources to compare, the sampling distribution of Kendall's τ b is approximately a normal Gaussian distribution (Kendall 1938).We therefore use p-values1 corresponding to 1σ (p < 0.15865), 2σ (p < 0.02275), and 3σ (p < 0.00135) to determine which correlations are significant.We consider a correlation coefficient 0.5 to be a strong correlation, which is generally only seen for correlations with at least 2σ significance.Correlations with 3σ significance have coefficients ≥0.64 and hence will be termed very strong correlations.For simplicity, we use a single term to refer to both significance and strength of correlation, as they are strongly related, and will refer to correlations with 2σ significance as strong correlations, and those with 1σ significance as weak correlations.Figure 2 is colorized by the value of the correlation coefficient, with stronger positive correlations in a darker blue.For further visual differentiation, 3σ correlation coefficients are written in boldface, 2σ in regular font, and 1σ in small italics.Correlation coefficients with p-values above 0.15865 (that is lower than 1σ significance) are not included in our analysis or in the figure .The molecular correlations with at least a 1σ significance were then used to calculate a dendrogram (see Figure 3) of the hierarchical relationships between the different parameters, using the farthest point (a.k.a.complete linkage) algorithm for hierarchical clustering.This dendrogram shows which parameters are most similar to each other in terms of their correlations to all the other parameters, and groups them into seven clusters shown with different colors.Note that this grouping may split up pairs of parameters that are strongly correlated with each other but have dissimilar correlations with other parameters.These clusters are reflected in Figure 2, and the calculated correlations will now be discussed cluster by cluster for simplicity.
Cluster 1: HCN and CO is shown with green lines in Figure 3 and discussed in Sect 3.3.1;Cluster 2: AlF, CS, H 2 S, and AlOH is shown with red lines and discussed in Sect 3.3.2;Cluster 3: v exp and P is shown with cyan lines and discussed in Sect 3.3.3;Cluster 4: SiS, Ṁ, NaCl, and KCl is shown with purple lines discussed in Sect 3.3.4;Cluster 5: AlO and SO is shown with yellow lines and discussed in Sect 3.3.5;Cluster 6: PO, TiO, SO 2 , H 2 O, OH, and SiO is shown with black lines and discussed in Sect 3.3.6;and Cluster 7: T eff is discussed in Sect 3.3.7.

665
The isotopologues of HCN and CO tend to be detected in the 666 same sources, as one might expect for both isotopologues with 667 13 C. 13 CO is detected in all sources except SV Aqr, and H 13 CN 668 is detected in all sources except SV Aqr, U Del, and V PsA.Detecting more lines of HCN and CO is correlated with more 681 detected lines of AlF, CS, SiS, AlO, TiO, and SiO, as well as a this cluster are strongly correlated with each other and tend to be detected in the same sources.4/5 sources showing H 2 S also show AlOH, and all sources with either molecule also show AlF.All four molecules are also correlated with a longer pulsation period (P), higher mass-loss rate ( Ṁ), and detecting more lines of SiS, NaCl, AlO, and SO.Three-out-of-four molecules are further correlated with detecting more lines of HCN, CO, KCl, and PO, as well as a larger expansion velocity (v exp ).
These correlations can largely be explained by the similarities between the four sources AH Sco, GY Aql, IRC+10011, and VX Sgr.These sources have the second to eighth longest periods, and highest to seventh highest mass-loss rates.They all show a fair number of SiS lines, and include two of the three sources with detections of NaCl (see Sect 3.3.4).The RSGs AH Sco and VX Sgr are the two sources which show the most lines of both AlO and SO (see further discussion in Sect 3.3.5).Regarding HCN and CO: all four sources show their 13 C isotopologues and the CO = 1 transition, three show vibrationally excited HCN and two also show vibrationally excited H 13 CN.IRC+10011 is one of two sources showing KCl emission.All four sources are among the 11 showing PO emission, and the group contains 2/5 sources showing vibrationally excited transitions of PO.Finally, these four sources have the third to ninth largest expansion velocities.
The strong correlation between AlOH and AlO is expected due to their close chemical coupling (Mangan et al. 2021;Gobrecht et al. 2022).The strong correlation between AlOH and AlF probably comes from AlF's formation reaction AlOH + HF → AlF + H 2 O; and the correlation between AlO and AlF also follows from the lesser formation reaction AlO + HF → AlF + OH (Danilovich et al. 2021).

Cluster 3: v exp , P
The third cluster contains expansion velocity (v exp ) and pulsation period (P), which are weakly correlated with each other.The clustering of these parameters is not unexpected, as for AGB stars both expansion velocity and pulsation period tend to increase as they evolve (Habing & Olofsson 2003), along with the mass-loss rate.In fact, for a constant and spherical mass loss we expect a perfect correlation between v exp and the mass-loss rate, so the correlation of 0.48 seen here is further evidence of wind asymmetries.
A larger expansion velocity and longer pulsation period is correlated with detecting more lines of AlF, H 2 S, AlOH, and SiS, as well as a larger mass-loss rate.The expansion velocity is also correlated with detecting more lines of HCN, while the pulsation period is correlated with detecting more lines of CS, AlO, and SO.As discussed in Section 3.3.1,most of these molecules are preferentially detected in a dense (higher Ṁ) wind.

Cluster 4: SiS, Ṁ, NaCl, KCl
The fourth cluster contains the molecules SiS, NaCl, and KCl, along with the mass-loss rate ( Ṁ). NaCl is detected in three sources: GY Aql, IRC+10011, and IRC-10529, of which IRC+10011 and IRC-10529 also show vibrationally excited transitions and transitions of Na 37 Cl.KCl is detected only in these same two sources: IRC+10011 and IRC-10529.SiS is detected in 10/17 sources, while its various isotopologues of 29 Si, 30 Si, 33 S, and 34 S are detected in between five and seven sources, including GY Aql, IRC+10011, and IRC-10529.GY Aql also shows vibrationally excited transitions of SiS up to = 1, while tions up to = 3.The only sources showing higher vibrationally all, AlO and SO are correlated with the other oxygen-bearing molecules, as expected, but also with the molecules in Cluster 1 (HCN, CO) and Cluster 2 (AlF, CS, H 2 S, AlOH).As explained in Sect 3.3.2, the strong correlation between AlO and AlOH stems from their close chemical coupling, but the chemical links to SO and H 2 S are less clear.One might suspect a connection through the sulfur chemistry, as both AlO and SO are also correlated with CS, but neither is correlated with SiS.However, it may be that the conditions required to populate the higher energy levels of SiS (and hence have more detected lines of SiS) differ from the conditions that excite more transitions of (vibrationally excited) AlO and (vibrationally excited and/or isotopologues of) SO.Overall, both Cluster 1 and Cluster 2 molecules tend to have many detected lines in the three sources showing the most lines of AlO and SO -AH Sco, U Her, and VX Sgr -which may explain the correlations.The grouping of the low mass-loss rate AGB star U Her with the high mass-loss rate RSGs AH Sco and VX Sgr here is unexpected, and will be explored further in a future paper.
3.3.6.Cluster 6: PO, TiO, SO 2 , H 2 O, OH, SiO The sixth cluster contains the remaining oxygen-bearing molecules: PO, TiO, SO 2 , H 2 O, OH, and SiO.A PO doublet is detected in 11/17 sources, of which five sources -IRC+10011, IRC-10529, R Hya, S Pav, and the RSG AH Sco -also show the corresponding = 1 doublet.TiO is detected in 7/17 sources, with vibrationally excited transitions detected in three sources: R Hya, and the RSGs AH Sco and VX Sgr.SO 2 is detected in 13/17 sources, with 34 SO 2 in nine sources and vibrationally excited transitions detected in seven sources.Six of these sources have detections of both 34 SO 2 and vibrationally excited SO 2 : AH Sco, R Aql, R Hya, RW Sco, U Her, and VX Sgr.H 2 O is detected in 15/17 sources, with intrinsically fainter and/or higher energy transitions in progressively fewer sources.OH is detected in 6/17 sources, of which five show both detected = 0 doublets: R Aql, R Hya, S Pav, T Mic, and VX Sgr.SiO is detected in all sources: the main isotopologue in = 0 and = 1 and both 29 SiO and 30 SiO in a = 0 transition.So more detected transitions implies the detection of more highly vibrationally excited transitions: up to = 4 in the main isotopologue, which is seen in 13/17 sources; up to 29 SiO = 3 which is seen in six sources -IRC+10011, IRC-10529, R Aql, R Hya, S Pav, and W Aql; and up to 30 SiO = 5 which is seen in four sources -IRC+10011, R Aql, R Hya, and S Pav.
The molecules in this cluster are all correlated with each other, as expected, and most also show correlations with the other oxygen-bearing molecules.PO, TiO, and SiO are correlated with CO; PO, TiO, SO 2 , and H 2 O are correlated with AlOH; and all except SiO are correlated with AlO and SO.
PO is very strongly correlated with H 2 O, which supports experimental findings that the reaction of excited P atoms with H 2 O is a major formation route for PO (Douglas et al. 2022) As SO 2 is created from SO, one would expect these molecules to be anticorrelated, but this is probably ameliorated by photolysis of SO 2 back to SO.This reaction also helps explain the strong correlation between SO 2 and OH, and its correlation with H 2 O as observationally the photodissociation of H 2 O into OH is linked with an abundance peak in SO (Danilovich et al. 2016).We detect up to 66 lines of SO 2 in our sources, with vibrational levels up to 2 = 2.A majority (∼65%) of all the detected SO 2 lines are in the = 0 state, and most of the rest are in the 2 = 1 state.
The energy of the lower transition level (E low ) values are up to 2300 K, with the = 0 transitions spanning the whole range, while the 2 = 1 transitions have E low values above 750 K, and the four 1 = 1 and three 2 = 2 transitions all have energies above 1500 K.The single vibrationally excited transition of SO has an E low value around 1600 K.The ten detected H 2 O lines have much higher E low values (≥3900 K) and many are in vibrationally excited states.There is some indication that in sources with more detected transitions of SO 2 , SO, and H 2 O, these transitions are probing a hotter gas as they generally have high E low values.However, the H 2 O transitions we can detect have much higher energies than any SO 2 or SO transitions, implying they are probing a different region of the wind, and furthermore these sources also show more transitions of 33 S and 34 S isotopologues.
Therefore, the strong correlations between SO 2 and SO, and SO 2 and H 2 O seem to also reflect increased abundances of all three molecules in certain sources.
OH only shows significant correlations with the other 960 oxygen-bearing molecules: strong correlations with SO 2 , H 2 O, 961 and TiO, and weak correlations with AlO, SO, PO, and SiO.962 The strong correlation between OH and SO 2 can be explained 963 by the fast SO 2 formation reaction described above.OH and 964 H 2 O are expected to be chemically related, we only detect tran-965 sitions at high energies -≥3900 K for H 2 O, and ≥4700 K for 966 OH -which are likely to be excited in similar regions around 967 the star.The strong correlation between OH and TiO is surpris-968 ing from a chemical standpoint as they would be expected to be 969 anti-correlated due to the fast reaction TiO + OH → TiO 2 + H. 970 However, the two molecules are not necessarily co-located even 971 if they are found in the same sources, so this reaction may not be 972 very prominent.The detection of TiO 2 does not help resolve this 973 issue as its transitions are inherently fairly weak, and hence not 974 unexpectedly TiO 2 is detected in only the highest mass-loss rate 975 source, VX Sgr, 976 SiO shows strong correlations with CO, H 2 O, and PO; and 977 weak correlations with larger pulsation amplitudes, and detect-978 ing more lines of HCN, SO 2 , TiO, and OH.SiO is seen in ev-979 ery source due to its strong = 0 and = 1 lines, but some 980 sources show more highly vibrationally excited transitions up 981 to = 5, and lines from the 29 SiO and 30 SiO isotopologues.The 982 five sources with the most PO transitions -AH Sco, IRC+10011, 983 IRC-10529, R Hya, and S Pav -are among the seven sources 984 with the most SiO transitions.These sources also have among 985 the most CO and H 2 O transitions.Most of the SiO transitions 986 with > 0 are dominated by maser emission and weak masers 987 are seen even in = 0 for some stars (Pimpanuwat et al., in 988 prep).The strong correlations with CO, H 2 O and PO may indi-989 cate these high-SiO masers, with E low values up to ∼8600 K, 990 form in similar regions around the star as the high-energy lines 991 of H 2 O and PO, and the = 1 line of CO.Similarly, sources with 992 more detected transitions of HCN, SO 2 , TiO, and OH also tend to 993 show vibrationally excited lines of these molecules, which may 994 also form in similar regions.Finally, we have a cluster containing only the effective temper-997 ature of the star, T eff , which shows the only significant nega-998 tive correlation: a weak negative correlation with detecting more 999 lines of AlOH.There are two detected lines of AlOH, and both 1000 are low energy = 0 transitions.Two lines of AlOH are de-1001 tected in GY Aql, IRC+10011, and the RSG VX Sgr, while a 1002 single line is detected in U Her and the RSG AH Sco.GY Aql, 1003 IRC+10011, and U Her have effective temperatures at or below 1004 the median value for our sources, while the RSGs VX Sgr and 1005 AH Sco have the highest effective temperatures.So this nega-1006 tive correlation between effective temperature and detections of 1007 AlOH seems to mainly hold for AGB sources.The correlation 1008 might potentially be explained by a relative lack of alumina dust 1009 (and hence more free Al to form AlOH) in these sources.There 1010 is some evidence for alumina dust being the major dust compo-1011 nent in warmer semi-regular variable AGB stars, as it can form 1012 and survive at higher temperatures than silicate dust (Gobrecht 1013(Gobrecht et al. 2016, and references therein), and GY Aql, IRC+10011, 1014 and U Her are all relatively cool Mira variables.The two brightest SO lines covered by our frequency setup are N J = 5 5 − 4 4 at 215.221 GHz and N J = 6 5 − 5 4 at 251.826 GHz, the two lines with ∆N = ∆J = −1 and = 0.These two lines are detected for all 14 stars with any SO detections.Overall six SO lines in the = 0 vibrational ground state are detected in our sample, with E low ∼ 10 − 90 K.The most energetic line detected in our sample is the N J = 6 7 − 5 6 line at 259.857 GHz (E low = 1635 K) in the first vibrationally excited state ( = 1), which was detected for ten stars.The only other line in = 1 that was covered by our observations has a predicted intensity (following the intensity calculations of Pickett et al. 1998, at 300 K) almost three orders of magnitude lower than the detected line, so we do not expect to detect it.With such a small number of SO lines covered over a relatively narrow range of energies, aside from the single line in = 1, it is difficult to draw any firm conclusions about trends across the sample.Without a more detailed analysis involving radiative transfer modelling, which is beyond the scope of the present work, we cannot easily determine which lines were not detected for a particular source because of excitation conditions in the CSE or because of the sensitivity of our observations.SO 2 gives us more opportunity for such an analysis since many more lines, coming from a wide range of energy levels, fall in the covered frequency range and many of these were detected by our observations.One source, V PsA shows only two detected SO 2 lines: J K a ,K c = 14 0,14 − 13 1,13 at 244.254 GHz and J K a ,K c = 30 4,26 − 30 3,27 at 259.599 GHz.These are the lines with the highest predicted intensities (at 300 K) suggesting that sensitivity is the main limitation to detecting further SO 2 lines.With so few lines, we cannot draw any further conclusions for V PsA and exclude it from further discussion of SO 2 .The other ten AGB stars for which we detect SO 2 (GY Aql, IRC+10011, IRC−10529, R Aql, R Hya, RW Sco, S Pav, SV Aqr, T Mic, and U Her), all have detections of at least six lines in the ground vibrational state (with 30 K ≤ E low ≤ 280 K).Four stars (R Aql, R Hya, U Her and S Pav) also have detections of at least four lines in the 2 = 1 vibrational state.
The observational categories defined above, with shell-like or centralized SO 2 distributions, approximately correspond to the categories put forward by Danilovich et al. (2016) for SO, and are applicable to SO 2 as the emission of these two molecules for the same star tends to be broadly similar.Ordering the sources with SO 2 detections by mass-loss rate, as in Table 5, shows a general tendency for the low mass-loss-rate sources to have centralized distributions and higher mass-loss-rate sources to have shell-like distributions.We note, however, that the massloss rates for many of the stars in the ATOMIUM sample are uncertain (see Section 2.3).
From an examination of the detected SO 2 lines for each AGB source, we also found a tendency for the sources with shelllike emission to be detected in lower-energy SO 2 lines, while the sources with centralized emission tended to be detected in more higher-energy lines (in addition to the lower-energy lines).Three out of the six stars with centralized distributions (R Hya, U Her and S Pav) also show vibrationally excited emission.In contrast, only one star with shell-like emission (R Aql) has vibrationally excited SO 2 detections.Furthermore, some of the highest energy SO 2 lines in the ground vibrational state (such as J K a ,K c = 45 6,40 − 44 7,37 at 229.750 GHz with E low = 1034 K) are only detected in the centralized AGB sources.To quantify this trend, Table 5 includes the average of the lower energy levels of each detected line for each star.Overall, there is a trend for  The observed trend between SO 2 line energy and spatial distribution is not a consequence of naturally having greater spatial resolution for the nearest sources, since our two most distant sources (IRC−10529 and IRC+10011 see Table 1) have shelllike distributions of SO 2 lines, while two of the nearest sources (T Mic and R Hya) have centralized SO 2 lines.It is also not caused by lines with different energies being excited at different distances from the star, since this dichotomy holds if we use only the J K a ,K c = 14 0,14 − 13 1,13 line at 244.254 GHz, which is one of the brightest and most frequently detected lines, to make the determination.We also note that there is a general tendency for centralized sources to have more SO 2 lines detected than the shell-like sources: the maximum radial extent of SO 2 is found to be negatively correlated (r ∼ −0.3) with the median E low values and the number of SO 2 lines detected in each source.This is most likely a consequence of the excitation conditions.The SO 2 in centralized sources is found closer to the star and hence in a warmer environment, while a significant portion of the shell-like emission originates further out in a cooler region of the wind.At higher temperatures where there are more potential SO 2 transitions to be excited, and hence unsurprising that more (and more energetic) SO 2 lines are detected.
We can also compare the measured extents of SO 2 in our AGB sources with what is expected from the chemical model of Van de Sande et al. (2018), for which calculations for each ATOMIUM source (using the stellar parameters in Table 1) is shown in Figure 4.The sources are arranged as in Table 5, in order of increasing mass-loss rate, and for each the colored bar shows the modeled e-folding radius of the SO 2 abundance, and the black line the maximum measured 3σ extent of SO 2 lines from our observations.The chemical model assumes a powerlaw temperature profile with exponent ε, as implemented in where T is the surface temperature of the AGB star and R 1185 the stellar radius.As the temperature profile in the outflows is 1186 generally not known, a range of models with different tempera-1187 ture profiles, varying ε from 0.3 to 1.0 (in steps of 0.05), were 1188 calculated.This range of models is included in Figure 4 as an 1189 uncertainty on the model result.

1190
An increase in the SO 2 radius with increasing mass-loss rate 1191 is clearly seen from the model results, and the observationally 1192 measured extents broadly follow the same trend.In general, 1193 the measured SO 2 extents are larger than the modeled e-folding 1194 radii, and some discrepancy is expected when comparing mod-1195 eled abundances with measured emission intensities, which does 1196 not take, for example, excitation effects into account.There are, 1197 however, two significant outliers: RW Sco which has a much 1198 larger measured SO 2 extent than expected from the models, and 1199 R Hya whose measured extent is much smaller than expected.1200 There are several reasons to suspect the mass-loss rate we use for 1201 RW Sco is underestimated, which would explain its larger mea-1202 sured extent.First, its SO 2 distribution is shell-like rather than 1203 centralized, suggesting it should have a relatively high mass-loss 1204 rate to follow the SO 2 distribution trend.Second, the mass-loss 1205 rate value is taken from Groenewegen et al. (1999), who use an 1206 empirical formula from Olofsson et al. (1993) linking the in-1207 tegrated CO intensity with the mass-loss rate.Olofsson et al. 1208Olofsson et al. (1993) ) see evidence that their formula underestimates the mass-1209 loss rates for low mass-loss rate objects, like RW Sco.This is 1210 in addition to the inherent uncertainties in the formula, which 1211 are a factor of ∼5.The discrepancy between the measured extent 1212 of SO 2 and the prediction from the chemical model is further 1213 evidence that the mass-loss rate of RW Sco may be underesti-1214 mated.As for the unexpectedly small observed extent of SO 2 in 1215 R Hya, its geometry may provide an explanation: Homan et al. 1216 (2021) find evidence for an equatorial density enhancement, and 1217 possible rotating disk, in the inner 0.4 of the wind, which cor-1218 responds to ∼35 R .This is similar to the maximum measured 1219 extent of SO 2 (51 R ), so it may be that SO 2 is largely confined 1220 to this disk, or not abundant enough to be detected outside it.1221 Furthermore, the equatorial density enhancement increases the uncertainty of the calculated mass-loss rate by a factor of a few (El Mellah et al. 2020).Some discrepancy may also be caused by the limitations of the chemical model: it assumes a smooth, spherically symmetric outflow, with a constant expansion velocity and mass-loss rate.R Hya, with its equatorial density enhancement, deviates significantly from these assumptions.Additionally, most of the ATOMIUM sources show additional structure or deviations from spherical symmetry (Decin et al. 2020;Gottlieb et al. 2022) which may affect the chemistry in the wind.

RSG stars
The two red supergiants, VX Sgr and AH Sco, are detected in seven and six SO transitions, respectively, out of the seven total detected in ATOMIUM.They are also extensively detected in SO 2 , with more than 45 lines seen for each star, and approximately a third of this count lying in the 2 = 1 excited state.
There are additionally three tentative detections of SO 2 towards AH Sco in the 2 = 2 state and four tentative detections towards VX Sgr in the 1 = 1 state.Previous studies of the more massive and highly evolved red supergiants VY CMa and NML Cyg (Adande et al. 2013;Andrews et al. 2022) report asymmetric and localised emission for both stars, including multiple components of SO and SO 2 .In contrast, when considering only the lowerenergy ground vibrational state SO and SO 2 emission observed by ATOMIUM, we do not see directed outflows for VX Sgr or AH Sco.Based on observations of other molecular lines, it is likely that both of these stars have complex circumstellar structures.However, when considering only the SO and SO 2 lines, we can place both RSGs into the categories we have defined here for AGB stars: VX Sgr has shell-like SO 2 and SO emission, while AH Sco has more uniform emission resembling the centralized AGB stars.Since both stars have high mass-loss rates and many high-energy SO 2 line detections, making them the two stars with the highest mean energy levels across the SO 2 lines, they do not fit the trends observed for AGB stars.In light of this and the previous studies of SO and SO 2 for RSGs, it is likely that different factors contribute to RSG SO and SO 2 distributions, possibly including different formation mechanisms, compared with the AGB stars.However, a more detailed analysis of the ATOM-IUM RSGs is beyond the scope of this paper.

Isotopic ratios
In order to calculate molecular abundances from our observational data, extensive radiative transfer modeling would be required.However, with a few assumptions we can calculate isotopic ratios from observations of different isotopologues in the same transitions.These ratios provide constrains on the nucleosynthesis within AGB and RSG stars, their stellar mass and age, and the Galactic environment in which they were born.We have limited the calculation of isotopic ratios to pairs of transitions in = 0 with at least one minor isotope in both molecules, to avoid the problem of potential missing flux or high optical depth in the main isotopologue lines.Hence we assume all the lines used to calculate isotopic ratios are optically thin and have no missing flux; assumptions which are supported by their narrow line shapes and limited angular extents.We have also checked that the chosen lines don't appear to be masing, as none are excessively bright or narrow.In practise, this limits us to calculations with isotopologues of SiS, as some lines of for example SiO isotopologues fall outside our observed frequency ranges.We also need to account for the differences in line strength 1281 between different isotopologues, so to calculate the isotopic ra-1282 tio between example isotopologues a X and b X we have used the 1283 following formula (Danilovich et al. 2020b): where I is the integrated intensity and ν the transition frequency 1285 for each isotopologue.For each pair of transitions we measured 1286 the integrated intensity in the spectrum where the sum of the 1287 intensities of both transitions is maximized.By taking the in-1288 tegrated intensities from spectra extracted at the same angular 1289 resolution and aperture size, the beam filling factors should be 1290 the same for both transitions.The calculated ratios are given in 1291 Table 6.In cases where an isotopic ratio can be calculated from 1292 multiple pairs of transitions for a single source, Table 6 contains 1293 the weighted average of these ratios.

1294
The silicon 29 Si/ 30 Si isotopic ratios are found to be generally 1295 in the range 1-2 for our oxygen-rich and S-type AGB stars, with 1296 the RSG VX Sgr showing a larger ratio of ∼4.Previously mea-1297 sured values in oxygen-rich sources are also in the range 1-2: 1298 1.7 in IK Tau (Danilovich et al. 2019); 1.58 in R Dor (De Beck 1299 & Olofsson 2018); between 0.99 and 1.35 in a sample of ten M-1300 type AGB stars, and around 1.5 in two RSG stars (Peng et al. 1301(Peng et al. 2013)).The solar value of 1.52 (Asplund et al. 2021) is similarly 1302 in the same range as the AGB stars.

1303
The high 29 Si/ 30 Si ratio of 4 ± 1 measured in VX Sgr is out-1304 side the range of almost all measured Si ratios in evolved stars 1305 and in the local galaxy in general. 29Si/ 30 Si ratios measured from 1306 presolar SiC grains are all close to the solar ratio of 1.52 (Zinner 1307(Zinner et al. 2006)), as are measurements of various sources at different 1308 Galactic radii (Monson et al. 2017).The only literature ratio we 1309 were able to find that matches VX Sgr are ratios ∼1-10 from 1310 infrared observations of the red giant EU Del (Pavlenko et al. 1311(Pavlenko et al. 2020)).EU Del is a very low-mass and metal-poor star, located 1312 below the tip of the red giant branch (McDonald et al. 2016), so 1313 it is not similar to the high mass-loss rate RSG VX Sgr. 29 Si/ 30 Si 1314 ratios above 2 have also been measured in the AGB stars χ Cyg 1315 (2.4) and V1111 Oph (2.9) by Ukita & Kaifu (1988), as well 1316 as a measured value of 3 ± 1.5 in IK Tau by Decin et al. (2010), 1317 consistent with the value of 1.7 cited above.We note that VX Sgr 1318 has been shown to have some puzzling characteristics (Tabernero 1319(Tabernero et al. 2021)), so this anomalous 29 Si/ 30 Si ratio may be another sig-1320 nature of its odd nature.

1336
The sulfur 33 S/ 34 S isotopic ratio is only measured in the S-1337 type star W Aql, where it is found to be 0.4 ± 0.3.This ratio has 1338 been measured to be 0.19 ± 0.03 in IK Tau (Danilovich et al. 1339 2019), and 0.17 ± 0.02 in R Dor (Danilovich et al. 2020b).The 1340 solar value is 0.17 (Asplund et al. 2021), consistent with the two 1341 oxygen-rich AGB stars and also with W Aql within the uncer-1342 tainties.

1343
The sulfur 34 S/ 32 S isotopic ratio is found to be 0.06 ± 0.02  Comparing all the U-line frequencies with the rotational lines of the following species -MgO, CaO, NaO, FeO, ZrO, MgOH, CaOH, NaOH, ZrS, MgS, and CaS -we tentatively conclude that there is no evidence for new metal oxides, hydroxides, and sulfides in the ATOMIUM survey.Furthermore, we would not expect most of these species to exist at observable levels because of the high concentrations of H and H 2 in the winds of these stars (Decin et al. 2018).

Conclusions
We have observed 17 oxygen-rich AGB and RSG sources at high angular resolution (0.02 − 0.05 ), and complementary lower resolutions (up to 1.4 ), with the ALMA interferometer as part of the ATOMIUM Large Programme, detecting 291 transitions of 24 different molecules and their isotopologues.
We find a range of conclusions, both major and minor: -We have first detections in oxygen-rich AGB and RSG stars of several vibrationally excited transitions: PO = 1, SO 2 1 = 1 and 2 = 2, and high energy H 2 O transitions (as examined in more detail in Baudry et al. 2023).
-We also have several first detections in S-type AGB stars: vibrationally excited HCN 2 = 2, 3 and SiS = 4, 5, 6; as well as first detections of the molecules SiC, AlCl, and AlF in W Aql (Danilovich et al. 2021(Danilovich et al. , 2023, as examined in more detail in).
-We have calculated correlations between the molecular content of different sources, finding strong correlations (with 3σ significance and correlation coefficients above 0.64) between sources with more detected lines of: CS and SiS, CS and AlF, NaCl and KCl, AlO and SO, SO 2 and SO, and SO 2 and H 2 O.Some of these correlations are expected from previous results (for example, CS and SiS both trace more dense winds) or chemical reactions (for example, NaCl and KCl both form from reactions of the metal atom with HCl), while the correlations of, for example, CS and AlF, or AlO and SO, have less clear origins.
-Two of our sources are found to be extremely line-poor: the AGB star U Del and the RSG KW Sgr.We speculate this may be indicative of weak shocks in the inner wind.
-The spatial distributions of SO and SO 2 are found to be generally consistent with previous results, with a centralized distribution for low mass-loss rate sources and a shell-like distribution for high mass-loss rate sources.
-The isotopic ratios of Si and S are generally in line with previously measured ratios (including solar ratios) except for an anomalously high 29 Si/ 30 Si ratio of 4 ± 1 in the RSG VX Sgr.
This paper has presented the overall molecular inventory and an initial analysis of the large ATOMIUM dataset, laying the groundwork for future work deriving molecular abundances and abundance profiles using radiative transfer modeling which will provide more rigorous tests for chemical models.the main isotopologue were published by Mollaaghababa et al. (1991).Noteworthy are furthermore IR data from Campbell et al. (1995).
The current rest frequencies of SO rely mostly on Bogey et al. (1997) and Klaus et al. (1996), those of the isotopic species mostly on the latter work.Additional older data were also used at lower frequencies; some references are given in Table A.3.We point out that Hund's case (a) quantum numbers may be found in the older literature, usually designated as J N , whereas Hund's case (b) quantum numbers are more common in the more recent literature, designated as N J .
The SO 2 2 = 0 and 1 data were derived from Müller & Brünken (2005) with important additional rest frequencies for = 0 from Belov et al. ( 1998) and for both vibrational states from Alekseev et al. (1996) and Helminger & De Lucia (1985).The 2 = 2 and 1 = 1 data are based on an unpublished fit by one of us (HSPM) and employ besides own new data published rotational transition frequencies from Steenbeckeliers (1968), unpublished data communicated by the late Walter Lafferty, presumably associated with Pine et al. (1996), and IR data from Sattler et al. (1981) and Flaud et al. (1993).The 34 SO 2 = 0 data are largely based on Belov et al. ( 1998) with important additional rest frequencies from Alekseev et al. (1996) and Helminger & De Lucia (1985).
The SiS rest frequencies were derived from Müller et al. (2013) who performed Fourier transform microwave (FTMW) spectroscopy on several isotopic species up to very high vibrational states along with millimeter and submillimeter measurements of several isotopic species mostly in their ground vibrational states.Additional FTMW data of SiS, 29 SiS and Si 34 S) were taken from Sanz et al. (2003).Important were also IR data, in particular from Frum et al. (1990).
The H 2 O data pertaining to the lowest five vibrational states were based on the JPL catalog (Pickett et al. 1998;Pearson et al. 2010) entry which, in turn, is based on Yu et al. (2012).Besides extensive new data, this work employs additional rotational and rovibrational data from a plethora of sources.Coudert et al. (2014) presented a similar study including the next three vibrational states, but, unfortunately, calculated transition frequencies for these start only at 300 GHz.Therefore, we inspected the HI-TRAN2020 (Gordon et al. 2022) and W2020 (Furtenbacher et al. 2020) compilations for highly vibrationally excited H 2 O transitions.As these were deemed to be quite uncertain, we resorted to the transition frequencies determined in our study on H 2 O and OH (Baudry et al. 2023).
The initial OH data were taken from the JPL catalog and bear on Drouin (2013).This analysis is based on a plethora of laboratory spectroscopic investigations.The Λ-doubling transitions with high rotational quanta, however, are rather uncertain and display systematic deviations, see for example Khouri et al. (2019) and Baudry et al. (2023).In our study on H 2 O and OH (Baudry et al. 2023), we combined the data gathered in Drouin (2013) with Λ-doubling transition frequencies from our own astronomical observations and those from Khouri et al. (2019) to improve the calculations of the OH Λ-doubling transition frequencies in the upper millimeter and submillimeter regions (Baudry et al. 2023).
Calculations of the PO rest frequencies rely mainly on Bailleux et al. (2002) with additional = 0 data from Kawaguchi et al. (1983).
The TiO rest frequencies are based on an unpublished isotopic invariant fit by one of us (HSPM).The main source of experimental data are those from the minor Ti isotopologues from Lincowski et al. (2016).Additional important data relevant for our study are the ground state rotational data of 46,48,50 TiO from Kania et al. (2008), those of 48 TiO from Namiki et al. (1998), and the extensive IR data for all Ti isotopologues from Witsch et al. (2021).
Calculations on the rotational spectrum of TiO 2 are based on Kania et al. (2011).Besides our own upper millimeter and lower submillimeter data of 46,48,50 TiO 2 , the analysis also employs microwave data of the same isotopologues from Brünken et al. (2008).The rotational temperatures were of order of 30 K and 3 K, respectively, which limited the quantum number range accessed.Transition frequencies involving higher rotational excitation may be quite uncertain as a consequence.The K a = 6−5 Q-branch transitions with J = 25, 27, and 29 display larger uncertainties, such that their true transition freaquencies may differ from the calculated ones by more than 1 MHz.
The ground state rotational data of AlO were taken from Yamada et al. ( 1990) and from Törring & Herrmann (1989); transition frequencies of = 1 and 2 were published by Goto et al. (1994).
The AlOH data were taken from the JPL catalog; they are derived from Apponi et al. (1993).
The AlF rest frequencies are mainly based on the rotational data of Wyse et al. (1970).Additional rotational data are from Hoeft et al. (1970), and rovibrational data are mainly from Hedderich & Bernath (1992).
Calculations of the rotational spectrum of AlCl and Al 37 Cl depends mainly on rotational data of Wyse & Gordy (1972).
Very accurate frequencies of the J = 1 − 0 transitions by Hensel et al. (1993) were also employed as were rovibrational transitions taken from Hedderich et al. (1993).
The NaCl and KCl rest frequencies rely mainly on measurements by Caris et al. (2002) and Caris et al. (2004), respectively.
The SiN rest frequencies are based on Bizzocchi et al. (2006), with the important lower frequency data taken from Saito et al. (1983).
The SiC transition frequencies are based on Bogey et al. (1990) and on Cernicharo et al. (1989).
The current calculation of SiC 2 = 0 transition frequencies were derived from Müller et al. (2012).Important additional data besides HIFI-Herschel data from that work come from laboratory measurements by Gottlieb et al. (1989) and from astronomical observations by Cernicharo et al. (2000).

3
their dusty winds which can reach mass-loss rates of up 4 to 10 −4 M yr −1 (Höfner & Olofsson 2018).Low-and 5 intermediate-mass (∼0.8 -8 M ) asymptotic giant branch 6 (AGB) stars are known to have dust-driven winds, while the 7 mass-loss mechanism of the rarer, more massive red supergiant 8 (RSG) stars remains uncertain.In both cases, however, the de-9 tails of the physics and chemistry behind dust formation and 10 wind launching have yet to be pinpointed, a vital step in under-11 standing how newly synthesised material from AGB and RSG 12 stars enriches the Galaxy and future generations of stars.

---
PO in the vibrationally excited = 1 transition, detected 397 in the RSG AH Sco and the AGB stars IRC+10011, IRC-10529, R Hya, and S Pav.399 SO 2 in the high-energy vibrationally excited 2 = 2 and 400 1 = 1 transitions, detected in the RSGs AH Sco and VX Sgr, Of the ten detected rotational transitions from various vibra-403 tional states of H 2 O, all but one are the first identifications 404 in space, as is one high energy transition of OH (see Baudry

Fig. 1 :
Fig.1: Overview of how many lines of each molecule are detected in each source.The sources are listed in order of increasing mass-loss rate ( Ṁ), and molecules found in only a single source are not included.
analysis of the spatial distributions of various 521 molecules is beyond the scope of this paper, we found it useful as 522 a first step to simply compare their observationally measured ex-523 tents, as defined in Section 2.2.
578 source, we have calculated Kendall's τ b rank correlation coef-579 ficients (Kendall 1945) for various stellar parameters and the 580 molecular content of each source.These are shown in Figure 2. 581 Kendall's rank correlations are chosen as a non-parametric mea-582 sure of correlation, that does not assume linear relationships 583 between variables and is applicable to ordinal data.This al-584 lows us to use the differing number of detected lines of a given 585 molecule as a (very rough) proxy for its relative abundance in 586 different sources.The number of detected lines is a function 587 of molecular parameters and excitation conditions as well as 588 abundance, which we cannot properly take into account with-589 out radiative transfer modeling.However, by ranking the sources 590 by the number of detected lines we can nevertheless determine 591 which groups of molecules tend to coincide by having relatively 592 large numbers of lines in the same sources.We also negate the 593 need to normalize different molecules by the absolute number 594 of potentially detectable lines in our frequency range.Many al-595 ternative techniques, such as Pearson's correlations or principal 596 component analysis, assume linear relationships between vari-597 ables and hence are less applicable to our data at this initial anal-598 ysis stage.599 To calculate the Kendall's τ b correlation coefficients the 600 sources were ranked (by measured value for stellar parameters 601 and by number of detected lines for molecules) for each vari-602 able, and the ranks between every pair of variables were com-603 pared (adjusting for ties).This assesses how well the relation-604

Fig. 2 :
Fig. 2: Kendall's τ b rank correlation coefficients between the expansion velocity (v exp ), pulsation period (P), mass-loss rate ( Ṁ), effective temperature (T eff ), and number of detected lines of various molecules in each source.Correlation coefficients with 3σ significance are in boldface, 2σ in regular font, and 1σ in small italics.Coefficients with lower than 1σ significance are not included, and instead given as .The cells are colorized from perfect correlation (1) in blue, to perfect anti-correlation (-1) in red.
669C 17 O is only detected in two sources: IRC-10529 and W Aql.670From this we can assume that SV Aqr, U Del, and V PsA ei-671 ther have relatively low 13 C abundances or faint HCN emission, while IRC-10529 may have relatively high 17 O abundances and W Aql is the source with by far the brightest emission in the main CO isotopologue.Similarly, the vibrationally excited transitions in HCN and CO tend to coincide.Vibrationally excited HCN is detected in six sources: IRC+10011, π 1 Gru, R Hya, W Aql, and the RSGs AH Sco and VX Sgr, four of which also show vibrationally excited H 13 CN.These six sources are also among the 11 which show emission in the CO = 1 line.

Fig. 3 :
Fig. 3: Dendrogram of the correlations in Figure 2, showing the hierarchical relationships between the different parameters.A closer connection point (lower down in the diagram) between two parameters signals a stronger relationship.The dark blue lines indicate the top-level division into seven clusters, and the other colors are simply to guide the eye in distinguishing between the different clusters.
. The five sources with the most detected PO lines -that is the ones showing the = 1 transition: AH Sco, IRC+10011, IRC-10529, R Hya, and S Pav -are also among the sources with the most detected H 2 O lines, including R Hya which is the only source to show all ten H 2 O transitions.Conversely, the six sources with no detected PO transitions -KW Sgr, π 1 Gru, SV Aqr, U Del, V PsA, and W Aql -also show the fewest detected H 2 O lines.The two S-type sources, π 1 Gru and W Aql, show neither PO nor H 2 O lines, and the others only have one to two H 2 O lines and are overall quite line-poor.However, from the dendrogram in Figure 3 we can see that PO is less closely grouped with H 2 O thanSO 2 , TiO, and OH are.This is likely due to PO showing correlations that H 2 O lacks with a range of molecules -CO, CS, H 2 S, NaCl, and KCl -in addition to their shared correlations with the other oxygen-bearing molecules.This may be mostly due to IRC+10011 and IRC-10529 which are, for example, two of the three sources with detected NaCl or KCl, and two of the five sources showing H 2 S. Conversely, in R Hya and S Pav, which show the most H 2 O lines, we do not detect any transitions of NaCl, KCl, or H 2 S. Detecting more lines of TiO is correlated with detecting more lines of HCN, CO, and H 2 S, alongside its correlations with the other oxygen-bearing molecules.There are up to nine TiO lines, with vibrationally excited transitions in = 1, with E low values around 1500 K, and = 2, with E low values around 3000 K. Hence detecting more lines of TiO implies more vibrationally excited lines, as is also the case for HCN and CO.The three sources with the most TiO lines -AH Sco, R Hya, and VX Sgr -are also the only sources to show vibrationally excited TiO transitions.The 13 C isotopologues of HCN and CO are detected in all three of these sources, as are the CO = 1 and HCN 2 = 1 transitions.The vibrationally excited CO = 1 has an E low value around 3000 K, just as the = 2 transitions of TiO do, and the HCN 2 = 1 transitions have E low values around 1000 K, roughly similar to the = 1 transitions of TiO.This implies that these vibrationally excited transitions may originate in similar regions of the circumstellar envelope, potentially explaining their correlation.SO 2 and H 2 O are very strongly correlated with each other, and SO 2 is also very strongly correlated with SO.The four sources with the most transitions of SO 2 -AH Sco, R Hya, U Her, and VX Sgr -are also the four with the most SO transitions: this includes transitions of its 33 S and 34 S isotopologues, as well as the one vibrationally excited SO transition.These four sources are also in the half of the sample with the most detected H 2 O transitions, as indeed are all seven of the sources with the most SO 2 transitions.SO 2 and SO are chemically connected by the fast reaction SO + OH → SO 2 + H (DeMore et al. 1997).
Fig. B.13), but the SO emission is brighter closer to the contin-1067 the sources with a shell-like distribution to have lower median E low values than the sources with a centralized distribution.This trend is confounded by RW Sco and SV Aqr, two centralized sources with median E low values below 100 K.However, these sources both show faint SO 2 emission, making the classification of their emission distribution more difficult.They also have the fewest SO 2 detections among the centralized sources, tending to show only the brightest SO 2 lines which generally have low E low values.

Fig. 4 :
Fig. 4: Emission sizes of SO 2 as expected from chemical models, and our maximum measured line extents, for each source.

1321
For most oxygen-rich AGB stars we do not expect the 1322 29 Si/ 30 Si ratio to change during the AGB phase(Zinner et al. 1323   A&A proofs: manuscript no.output 2006), so the measured ratios reflect those from the stars' na-1324 tal clouds.The primary isotope of silicon, 28 Si, is an α-process 1325 element, while the two isotopes 29 Si and 30 Si form largely 1326 from 25 Mg and 26 Mg during Ne burning, which creates sim-1327 ilar amounts of both isotopes (within a factor ∼1.5, Woosley 1328 & Weaver 1995), as well as during core-collapse Type II su-1329 pernovae.According to the models of Kobayashi et al. (2011), 1330 29 Si/ 30 Si ratios of ∼2-4 can be formed in the core-collapse su-1331 pernovae of 25-30 M progenitors, though the supernovae of 1332 both lower and higher mass progenitors produce much lower ra-1333 tios.Some 29 Si and 30 Si also forms from 28 Si in the He-burning 1334 shells of AGB stars, but in small and similar amounts (Monson 1335 et al. 2017).
1344 in the S-type star W Aql, and 0.04 ± 0.02 and 0.11 ± 0.06 in 1345 IRC+10011 and IRC-10529, two high mass-loss rate oxygen-1346 rich sources.A slightly lower ratio of 0.03 is found in IK Tau 1347 (Danilovich et al. 2019), while a value of 0.04 is found in the 1348 oxygen-rich RN Cnc (Winters et al. 2022), and both R Dor and 1349 the Sun have similar values of 0.05 (Danilovich et al. 2020b; 1350 Asplund et al. 2021).Hence all our measured 34 S/ 32 S ratios are 1351 consistent with the solar value, within uncertainties.1352 Both the main sulfur isotope 32 S and the second most abun-1353 dant isotope 34 S are primarily produced through explosive nucle-1354 osynthesis during Type II supernovae, so these values measured 1355 in AGB stars reflect the abundances in the stars' natal clouds.1356 However, the abundance of the 33 S isotope may increase during 1357 the AGB phase via the slow neutron capture process (Anders & 1358 Grevesse 1989).This is consistent with its detection in the S-type 1359 star W Aql, which is more evolved than the oxygen-rich stars in 1360 our sample.1361 3.6.Unidentified lines 1362 Table A.4 lists the 28 unidentified lines in the ATOMIUM sam-1363 ple, and in which sources they are detected.Four of these lines 1364 -U221.507,U254.791,U255.023, and U259.329 -are coinci-1365 dent with calculated lines of SO 2 in its 3 =1 state.The lines were 1366 observed toward stars with SO 2 lines in = 0 and 2 = 1 such 1367 that the assignments appear to be reasonable.On the other hand, 1368 except for S Pav, toward which two such lines were detected, 1369 only one line was detected for the other stars and none of these 1370 stars displayed emissions in 2 = 2 or 1 = 1.We would therefore 1371 have to invoke very selective excitations, which appears to be too 1372 speculative at present even if this cannot be ruled out entirely.1373 Therefore, we refrain from viewing these assignments even as 1374 tentative ones.
The ground state rotational data of HC 3 N depend onThorwirth et al. (2000) with additional contributions mainly fromYamada et al. (1995).Article number, page 21 of 42Dec offset[arcsec]

Fig
Fig. B.5: Channel map of the SO 2 = 0 J K a ,K c = 14 0,14 − 13 1,13 line at 244.254 GHz observed towards SV Aqr at low angular resolution.The medium angular resolution map is too faint to show the emission distribution.See caption of Figure B.1.

Fig
Fig. B.6: Channel map of the SO 2 = 0 J K a ,K c = 14 0,14 − 13 1,13 line at 244.254 GHz observed towards U Her at medium angular resolution.See caption of Figure B.1.

Fig
Fig. B.7: Channel map of the SO 2 = 0 J K a ,K c = 14 0,14 − 13 1,13 line at 244.254 GHz observed towards R Aql at medium angular resolution.See caption of Figure B.1.

Fig
Fig. B.9: Channel map of the SO 2 = 0 J K a ,K c = 14 0,14 − 13 1,13 line at 244.254 GHz observed towards IRC-10529 at low angular resolution.The medium angular resolution map has too much resolved out flux to show the emission distribution.See caption of Figure B.1.

Table 2 :
Extract of TableA.5 which lists all measured lines in each source.

Table 3
lists the factor by which this has changed the literature 328 mass-loss rate, alongside more details about how the mass-loss 329 rates were derived.330

Table 3 :
Mass-loss rates from literature.

Table 4 :
Maximum measured radial extent of each molecule across all sources.
. H. J. Wallström et al.: ATOMIUM: Molecular inventory of 17 oxygen-rich evolved stars observed with ALMA HCN CO AlF CS H 2 S AlOH v exp P SiS M NaCl KCl AlO SO PO TiO SO 2 H 2 O OH SiO T eff S

Table 5 :
SO 2 spatial distributions, radial extents, and median lower level energies in all sources.Spatial distributions with uncertain classifications due to faint SO 2 emission are marked with † .AGB stars are listed above the horizontal line and RSGs below. Notes:

Table 6 :
Isotopic ratios calculated from single and double isotopologues of SiS.
ven C1 excellence grant C16/17/007 MAESTRO, and from the FWO research 1447 grant 6099720N.MVdS acknowledges support from the European Union's Hori-1448 zon 2020 research and innovation programme under the Marie Skłodowska-1449 Curie grant agreement No 882991.AB and FH acknowledge funding from the