© The Authors 2024

1 Introduction

Stars of low to intermediate zero-age main sequence mass (~0.8 M_⊙ < M < 8 M_⊙) populate the asymptotic giant branch (AGB) during their late evolution, after the end of helium fusion in their cores. In this phase, stars are characterised by an inert carbon-oxygen core surrounded by shells of helium and hydrogen. Contraction of the core causes the outer layers of the star to expand, resulting in cool, luminous giants (T_eff ≲ 3000 K, L_* ~ 10³–10⁴L_⊙, R_* ~ 100 R_⊙; Herwig 2005). Microscopic dust grains (with radius a in the range 0.1 μm ≤ a ≤ 0.5 μm, e.g. Groenewegen 1997; Höfner 2008; Yasuda & Kozasa 2012) formed in the cool, dense upper stellar atmosphere are levitated by pulsations, accelerated by radiation pressure, and push gas radially outwards through dust-gas momentum exchange (Höfner 2015). This causes extensive mass loss from the stellar surface. AGB mass-loss rates (hereafter MLRs) range from 10⁻⁸ to 10⁻⁴ M_⊙ yr⁻¹, dominating the evolution on the AGB (e.g. Höfner & Olofsson 2018). The winds of AGB stars are major sources of gas and dust feedback into the interstellar medium (ISM, e.g. Matsuura et al. 2009; Tielens 2005).

The mass loss creates an expanding envelope of chemically rich material around the star, called the circumstellar envelope (CSE). The radial density distribution of material in the CSE is a tracer of the temporal variations in the mass loss. The elemental compositions of gas and dust in the CSE reflect the composition of the atmosphere of the star at the time of the ejection of the circumstellar material.

Based on their atmospheric carbon-to-oxygen elemental abundance ratio, AGB stars are classified into two main groups: C-type (C/O > 1) and M-type (C/O < 1). AGB stars in the mass range 1.5–4 M_⊙ (at solar composition) evolve into C-type stars in the absence of hot-bottom burning (Lattanzio et al. 1997), as the carbon produced in the helium-burning layer is brought up to the surface by convection (e.g. Di Criscienzo et al. 2016) during the third dredge-up (Herwig 2005). The excess of carbon over oxygen for C-type stars allows a wide range of C-bearing species to form in their CSEs, including long carbon chains and possibly also PAHs (e.g. Cherchneff et al. 1992; Allain et al. 1997), as well as carbonaceous dust (e.g. Kraemer et al. 2019; Sloan et al. 1998; Zijlstra et al. 2006). With 96 molecular species detected in carbon star CSEs so far, compared to only around 34 species found in oxygen-rich circumstellar environments, the CSEs of C-type stars are generally richer in chemistry than those of their M-type counterparts (Agúndez 2022; McGuire 2022; Cernicharo et al. 2023a,b).

The advent of high-angular-resolution mm/sub-mm interferometers like the Atacama Large Millimeter/submillimeter Array (ALMA) has made it possible to explore the chemical complexity of AGB CSEs in unmatched detail. However, notwithstanding these significant advances in instrumentation, much of our current knowledge of AGB circumstellar chemistry is still based on observational results and modelling focused on a single object, the C-type IRC +10216 (CW Leonis), owing primarily to its proximity (120–190 pc), high MLR (Ṁ = 2–4 × 10⁻⁵ M_⊙ yr⁻¹), and molecular richness (e.g. Andriantsaralaza et al. 2022; Agúndez et al. 2017; He et al. 2008; Cernicharo et al. 2000; Cordiner & Millar 2009; Groenewegen et al. 2012; Guélin et al. 2018; Pardo et al. 2022; Patel et al. 2011; Tenenbaum et al. 2010; Velilla-Prieto et al. 2019; Van de Sande et al. 2019).

Studies of the molecular chemistry in the CSE of IRC +10216, from single-dish spectral surveys (e.g. Cernicharo et al. 2000; Agúndez et al. 2012) to interferometric maps (e.g. Patel et al. 2011; Velilla Prieto et al. 2015a; Agúndez et al. 2017) have revealed a host of information about circumstellar chemical pathways and the physical structure of its CSE, including complex substructures within its molecular emitting shells. Radiative transfer and chemical models of AGB CSEs that take into account the clumps and arcs seen in the emission have also been presented (e.g. Cordiner & Millar 2009; Agúndez et al. 2017; Van de Sande et al. 2018; Van de Sande & Millar 2022). Chemical modelling of the photochemistry in AGB CSEs has shed light on their diverse chemical pathways (e.g. Li et al. 2014; Saberi et al. 2019), and the effects of potential binarity (e.g. Siebert et al. 2022; Van de Sande & Millar 2022).

There have only been very few detailed investigations into the circumstellar chemistry of C-rich AGB stars other than IRC +10216. Nyman et al. (1993); Woods et al. (2003) and Smith et al. (2015) performed single-dish spectral surveys in mm/sub-mm wavelengths towards selected C-type AGB stars. A few studies of larger source samples in fewer molecules have also been performed (e.g. Schöier et al. 2006, 2007, 2013; Massalkhi et al. 2019).

A large variety of molecules present in AGB CSEs have rotational transitions at mm/sub-mm wavelengths. Analysis of these lines can help to constrain the physics and chemistry of these sources. Therefore, spectral surveys in this wavelength regime offer an ideal method of studying both the chemical composition and the kinematic and thermodynamic properties of AGB CSEs.

The single-dish spectral line survey by Woods et al. (2003) observed the stars in our sample (Sect. 2) in the frequency range 85–266 GHz. However, to determine accurate molecular abundances, spatial information on the emitting regions is required. Woods et al. (2003) used indirect methods such as modelling of photodissociation radii and scaling of the known emitting-region sizes for IRC +10216 with the MLRs and expansion velocities of the respective sources, to estimate the sizes of the molecular emitting regions of their stars. It is in this context that the study of spatially resolved data of a subset of C-type AGB stars, as presented in this work, is highly relevant. Our interferomet-ric observations make it possible to directly obtain the spatial extents of the emitting regions for individual stars. Thus, along with mapping the physical conditions like density and temperature across the CSEs, the observations presented will also help to provide better estimates of molecular abundances and isotopic ratios.

This paper is the first in a series of planned publications that together aim to advance our understanding of the molecular chemistry in carbon-rich AGB CSEs by studying a sample of stars other than IRC +10216. The primary aim of this paper is to present ALMA spectral surveys of three carbon stars, showcasing the large number of detected spectral lines and their emission maps. Detailed non-LTE radiative transfer modelling is required to constrain molecular abundances to the best possible accuracy, and will be presented in a subsequent paper. In the current work, we adopted a qualitative approach using simplistic LTE models to obtain order-of-magnitude estimates of the abundances.

This paper is organised as follows. The sample is described in Sect. 2. The details of the observations and data processing procedures employed are described in Sect. 3. We present the line identifications and abundance estimates in Sect. 4 and end with a qualitative discussion of the chemical and morphological similarities and differences between the three stars, and in comparison to IRC +10216, in Sect. 5.

2 The sources

We have observed a sample of three C-type AGB stars, IRAS 15194–5115, IRAS 15082–4808, and IRAS 07454–7112, using ALMA. Owing to their high MLRs, they are expected to present strong emission from a large variety of molecules. The stars were chosen for their similar physical outflow properties (see Table 1), both among themselves and in comparison to IRC +10216. They possess expanding, largely spherical CSEs with similar expansion velocities, sampling roughly an order of magnitude in MLRs. They sample a broad range of ¹²C/¹³C ratios (Table 1), which may be due to differences in their nucleosynthetic histories. These properties make them ideal candidates for a comparative study of C-type CSEs. The MLRs listed were obtained by scaling the values from Woods et al. (2003) to the new distance estimates from Andriantsaralaza et al. (2022).

IRAS 15194–5115 (II Lup) is a J-type (Smith et al. 2015) Mira variable with a pulsation period of 575 days (Feast et al. 2003). It is the third brightest carbon star at 12 μm, surpassed only by IRC +10216 and CIT 6 (Nyman et al. 1993). IRAS 15082– 4808 (V358 Lup) is a Mira variable with a period of 632 days (Whitelock et al. 2006). It has an MLR comparable to that of IRAS 15194–5115 and IRC+10126. IRAS 07454–7112 (AI Vol) is also a Mira variable with a pulsational period of 511 days (Whitelock et al. 2006). It has a lower MLR than the other two stars, by approximately an order of magnitude. Based on their MLRs, all three stars in our sample are currently expected to be in the high-MLR phase at the end of their AGB evolution (Vassiliadis & Wood 1993).

3 Observations and data reduction

3.1 Observations

Interferometric spectral survey observations in the frequency range 85–116 GHz towards the three sources were carried out with angular resolutions in the range 0.″7-1.″7 using the Band 3 receiver (Claude et al. 2005) of the ALMA 12 m array in Cycle 2 (project code: 2013.1.00070.S; PI: Nyman, L. Å.). A detailed list of the observational and technical parameters is given in Table 2. The maximum recoverable scale (MRS) of the observations ranges from 4.3″–9.3″, and the field of view from 54″–63″. Each source was observed in five tunings, each with four 1.875 GHz wide spectral windows, together covering the entire Band 3 frequency range (Table 3). Based on the expected line widths (Table 1), a spectral resolution of 0.49 MHz (~ 1.6 km s⁻¹) was chosen for IRAS 07454-7112, while 0.98 MHz (~3.2 km s⁻¹) was used for the other two stars, in order to resolve structure in the line profiles to a similar detail for the three sources.

We also observed the three stars and IRC +10216 using the Atacama Pathfinder Experiment telescope (APEX; Güsten et al. 2006). All stars were observed in the full band-widths of APEX Bands 5 (159–211 GHz) and 6 (200–270 GHz). The SEPIA receiver was used for the Band 5 observations (Billade et al. 2012; Belitsky et al. 2018). For Band 6, the SHeFI receiver (Vassilev et al. 2008) was used for IRAS 15194–5115, whereas the PI230 receiver¹ was used for the other stars. Additionally, IRAS 15194–5115 was also observed in APEX Band 7 (SHeFI, 272–376 GHz). The Kelvin-to-Jansky conversion factor² for the APEX lines is 34 (Band 5) and 40 (Bands 6 and 7), with 5–10% uncertainty in each case (Güsten et al. 2006). Several lines from the APEX surveys have been used in this work (Table B.2, Figs. C.109–C.185). The integrated intensities of these lines are listed in Table B.2. The spectra of these lines are shown in Figs. C.109–C.185. The full APEX surveys will be presented in a forthcoming paper.

3.2 Data reduction

We retrieved the data stored in the ALMA Science Archive, which were calibrated and imaged using the Common Astronomy Software Applications (CASA) package (McMullin et al. 2007) versions 4.3 and 4.4. The archival image cubes of IRAS 15194–5115 exhibited weak, extended, symmetric artefacts that were not associated with the actual source structure (Fig. 1). Also, for this source, some of the spectral windows in tunings a and d (Table 3) show intensity mismatches for the lines falling within their overlapping frequency ranges. Such issues were partly caused by the fact that the archival images were produced using a now deprecated version of the CASA task clean, probably leading to inadequate cleaning at different spatial scales. In addition, we found that the flux scales used for the calibration of the archival data of several tunings of IRAS 15194-5115 and IRAS 15082-4808 were obtained using a model of the Solar System object Ceres that was poorly defined (see Butler 2012). This led us to use quasars (Table 3), originally serving as phase calibrators, instead of Ceres to calibrate the flux scales of these tunings. The spectral indices of these quasars were obtained by interpolating the corresponding flux values from the ALMA calibrator source catalogue³.

With this change, we manually re-calibrated the whole dataset using CASA version 4.3.1. Water vapour radiometer data was used to correct atmospheric variations at the time of observations. The continuum was estimated using a first-order polynomial fit to the line-free channels, and subtracted from the calibrated visibilities. Imaging was performed with the newer CASA version 6.3.0-48, using the Multi-Scale deconvolving parameter of the CASA task tclean (Cornwell 2008), and adopting a Briggs weighting scheme with a robust parameter of 0.5. The clean masks were set automatically using the auto-multithresh algorithm (Kepley et al. 2020). This significantly improved the image quality over the archival image cubes (Fig. 1), and the extended artefacts present in the archival images of IRAS 15194–5115 were successfully removed by the reprocessing.

The use of quasars instead of Solar System objects as flux calibrators implies an absolute flux calibration uncertainty of ~5–10% (e.g. Goddi et al. 2019; Guzmán et al. 2019). In this work, we adopted a conservative estimate of 10%, also considering the fact that the observation times of our data and the measurements from the calibrator catalogue often differ by several days. With the reprocessing, the intensity mismatches between the lines in the overlapping tunings for IRAS 15194–5115 were reduced to within the absolute calibration uncertainty (10%). In addition, given that the channel maps in tuning d have more significant residuals after cleaning and the channel maps in tuning a show a better signal-to-noise ratio, we estimated a 20% calibration uncertainty for the lines from tuning d of IRAS 15194–5115.

Self-calibration was attempted in tunings with bright and compact lines available, but did not result in any significant improvement in the signal-to-noise ratio, and was hence not implemented. The observed continuum emission could not be used for self-calibration due to its low intensity. The average beam sizes and spectral resolution of the final processed data are listed in Table 2. Figure 2 shows the variation in the achieved rms in the different spectral windows, as a function of frequency. The atmospheric transmission in ALMA Band 3 is also shown, which corresponds well to the increase in rms at higher frequencies.

3.3 Data combination

For IRAS 15194–5115 and IRAS 15082–4808, observations with a higher spatial resolution (0″.4) were available in the ALMA archive (project code: 2015.1.01271.S, PI: Keller, D.), but covering only the frequency ranges 87.27–90.97 GHz and 99.14–102.89 GHz. The details of this dataset are given in Table 2. This dataset includes observations with both more extended (hereafter high-angular-resolution dataset) and more compact (hereafter low-angular-resolution dataset) baseline configurations compared to our data (hereafter intermediate-angular-resolution dataset). We therefore combined the corresponding visibilities from this project with our observations to increase the sensitivity to the emission on compact and extended spatial scales. This helped to increase the MRS of the observations, enabling us to recover the weak, extended molecular emission on large spatial scales that could have been filtered out due to the lack of very short baselines in the intermediate resolution data before combination, while also lowering the rms noise in the combined maps. The data combination was performed using the task concat in CASA version 6.3.0-48. Figure 3 shows the combined visibilities towards IRAS 15082–4808, depicting the extended and compact baseline coverages added.

As these two datasets were observed several months apart, it can be argued that they might not be compatible due to a possible time variation in the sources related to (1) the evolution of the ejected material and (2) changes in the molecular excitation. We note that any spatial variation in the circumstellar gas distribution occurring during the interval between these observations (≤ 1 yr) will be far below the spatial resolution of both datasets. For example, in the case of IRAS 15194–5115, given the expansion velocity of 21.5 km s⁻¹ at a distance of ~696 pc (Table 1), the increase in angular size in 1 year is only 6 mas, around two orders of magnitude less than the angular resolution of the observations. In contrast, by comparing the line intensities from the two epochs used in the data combination, we do detect line variability likely connected to the variability in the stellar radiation field in two species, C₂H and HC₃N, for both IRAS 15194–5115 and IRAS 15082–4808. The observed variability is quantified in Sect. 4.2, and its impact on our results is discussed in Sect. 5. We still combine the two datasets for these lines, in order to trace the spatial structure in as much detail as possible, while increasing the uncertainty in the line intensities of these species by the observed percentage of variability.

4 Analysis and results

4.1 Line detection and identification

Continuum maps were produced from the line-free channels across the survey bandwidth (85–116 GHz) using multi-frequency synthesis (Rau & Cornwell 2011). The continuum emission is spatially unresolved for all three stars. The peak positions and total flux of the continuum maps are given in Table 4. The continuum was then removed from the data to obtain the continuum-subtracted line spectra.

Figure 4 shows an overview of the ALMA Band 3 spectra for all three stars. The full line-labelled ALMA Band 3 spectra of the three sources, extracted by integrating the intensity in a circular aperture of 12.5″ radius centred on the respective continuum peaks, so as to recover emission from all molecules, are presented in Appendix A. We used the Weeds (Maret et al. 2011) package in GILDAS⁴ to identify the emission lines. The Cologne Database for Molecular Spectroscopy (CDMS⁵; Müller et al. 2005) catalogue was referred to for line identification. Splatalogue⁶ (Remijan et al. 2007) was also used as an interface to obtain spectral line parameters. We detect, above the 3σ noise level, a total of 314 spectral emission features across the three stars, out of which 311 could be identified and assigned to 132 known rotational transitions of 49 molecular species, including various isotopologues (see Fig. A.1 and Table B.1). All detected lines, along with the associated spectroscopic parameters and observed integrated intensities towards the three stars, are tabulated in Table B.1. Figures in Appendix C show the brightness distributions at the systemic velocity and the spectra of the detected lines.

Most of the detected spectral lines are thermal emission lines from transitions in the vibrational ground states. However, some of the lines we detect, including HCN ν₂ =2, J = 1−0, l = 0 and ν₂ = 1, J =2−1, l =1, are known to display maser emission towards carbon stars, including IRAS 15082–4808 (e.g. Guilloteau et al. 1987; Smith et al. 2014; Menten et al. 2018; Jeste et al. 2022). We find both these lines to be masering towards all three stars in our observations as well, based on their extremely narrow line widths and significantly different line shapes in comparison to other non-masering lines. These maser lines are not a target of study in this paper and are not considered in the morphological or abundance analysis presented below. In addition, SiS maser action has been reported for v = 0 rotational lines towards IRC +10216 using 3D radiative transfer modelling based on mm observations (Fonfría et al. 2018). In the SiS lines that we detect in our ALMA/APEX surveys, there are no apparent maser spikes. In this work, we have therefore assumed that all of the observed SiS line emissions are of a primarily thermal nature. We will come back on this issue in a forthcoming radiative transfer analysis. Two of the three unidentified features in our data, at 86.886 and 100.407 GHz, present narrow line profiles (Fig. C.108), indicating that they could be masers and/or originate in the inner parts of the CSE.

Owing to the increased sensitivity and better coverage of spatial scales in the combined data (see Sect. 3.3), we detected several additional lines, including lines from C₅H, C₆H, C₂S, and 1-C₄H₂, which were not detected in the intermediate resolution data alone. Further, the emission maps of several lines, including those of HC₃N, HCN, HNC, C₃N, and their ¹³C isotopologues, were enhanced by the data combination (e.g. Figs. C.21, C.25, C.27, C.34, C.69), owing to the same reasons as above.

We report the first detections of lines of ²⁹SiO, ³⁰SiO, ²⁹SiS, ³⁰SiS, Si³⁴S, and C³³S towards the three sources. The source with the largest number of detections is IRAS 15194–5115, presenting lines from 119 rotational transitions, compared to the 56 and 67 of IRAS 15082–4808, and IRAS 07454–7112, respectively (see Table B.1). This is largely due to the high abundance of ¹³C in its CSE, which leads to a large number of molecules containing ¹³C atoms, most of which are not detected towards the other two stars. We report the first detection of Si¹³CC, and doubly ¹³C-substituted isotopologues of HC₃N towards IRAS 15194–5115, along with the long-chain hydrocarbons C₆H, C₈H, 1–C₄H₂, which have not been detected towards this source in previous observations.

4.2 Line variability

The two datasets used for data combination (Sect. 3.3) were observed several months apart (see Table 2). Hence, to check for potential variability, we compared spectra produced from a subset of visibilities that have the same uv-coverage in both datasets. This removes any difference in amplitudes caused by the larger uv-coverage of one of the datasets, and would reflect only time-dependent amplitude variations, connected to the variability in the stellar radiation field.

Owing to the 10% absolute calibration uncertainty of our data (see Sect. 3.2), and the ALMA Band 3 standard calibration uncertainty of 5%⁷ for the high- and low-angular-resolution datasets (see Sect. 3.3), we estimate a relative calibration uncertainty of ~11% between the two observations. For both IRAS 15194–5115 and IRAS 15082–4808, we find differences in line intensity greater than the relative calibration uncertainty for only two species, C₂H and HC₃N. For IRAS 15194–5115, we find a ~ 15–20% change in the integrated line intensity of the strongest hyperfine component of the C₂H, N =1−0 line, and a change of ~10–15% in the HC₃N, J = 11−10 line. For IRAS 15082–4808, we find a ~25–30% change for C₂H, N =1−0, while for HC₃N, J = 11−10, the change is ~10–15%. The phase of the variability is also opposite for C₂H and HC₃N (see Sect. 5 for a brief discussion of the detected variability in comparison with that found in IRC +10216).

4.3 Morphological diversity

Estimation of the extents of the emitting regions is needed in order to calculate molecular fractional abundances and constrain the chemical models. Fourteen species (see Table 5) were found to have non-blended lines with sufficiently high signal-to-noise ratios (≥3σ) in the channel maps to allow extracting information about the spatial distributions of the emission towards all three stars by producing azimuthally averaged radial profiles (hereafter AARPs; see Sect. 4.3.2) of the line brightness distributions.

Four of these species, HCN, SiO, SiS, and CS, have line brightness distributions that peak close to the central star and extend radially outwards (Fig. 5, top panel and Figs. C.10, C.21, C.35, C.60). These molecules are termed centrally peaked species. These encompass the so-called parent molecules formed in the stellar photosphere or the extended atmosphere, or molecules formed through circumstellar chemistry in the inner layer of the CSE (see Millar & Herbst 1994; Cordiner & Millar 2009; Agúndez et al. 2017, Agúndez et al. 2020). Eight species, C₂H, C₃H, C₄H, c-C₃H₂, CN, C₃N, HC₅N, and HNC, present brightness distributions in the form of rings at the systemic velocity (e.g. Fig. 5, bottom panel and Figs. C.14, C.18, C.24, C.34, C.53, C.61, C.101). Our observations indicate that these species are distributed around the stars as hollow spherical shells with widths and peak radii that vary between molecules and stars. Hereafter we call these molecules shell species. The shell species are daughter molecules formed in the external layers of the CSE (see Agúndez et al. 2020) from centrally peaking parent molecules by photodissociation (e.g. C₂H and CN) or due to photo-induced chemistry (e.g. HNC and HC₅N), either directly or through series of intermediate steps (e.g. Daniel et al. 2012; Agúndez et al. 2017). Two species, HC₃N and SiC₂, show compound brightness distributions that have both centrally peaked and shell characteristics (Fig. 6, top-left panel and Figs. C.45, C.69). Maps of the emission at the systemic velocity for all the above species are shown in Appendix C.

4.3.1 Complex morphology in the CSEs of IRAS 15194–5115 and IRAS 15082–4808

The systemic velocity brightness distributions of HC₃N, SiC₂, HNC, and C₂H towards IRAS 15194–5115 and IRAS 15082–4808 are shown in Fig. 6. The lower spatial resolution in the maps of IRAS 07454–7112 limits the detection of any similar substructure around this star. The maps in Fig. 6 have been produced by stacking the systemic velocity emission from all detected transitions in the ALMA Band 3 for each of these molecules. We regridded the line cubes to be stacked to ensure that they have the same spectral resolution (3.3 km s⁻¹) and velocity grid, and used the software LineStacker (Jolly et al. 2020) to stack the cubes to extract the rms-weighted mean emission of the channels centred on the systemic velocity for each molecule. No channel averaging was performed as it would lead to the substructure visible at the systemic velocity to be smeared out. The spatial profiles obtained through radial cuts at different position angles on these maps are shown in Figs. 7 and 8.

For IRAS 15194–5115, the maps in Fig. 6 reveal well-defined arc structures within the emitting shell at the same locations in the HC₃N and SiC₂ maps. The approximate radial coincidence of the arcs seen in HC₃N and SiC₂ emission towards IRAS 15194–5115 can also be seen from the spatial profiles in Fig. 7. However, the SiC₂ emission does not appear to fully trace the HC₃N emission towards the southwest part of the image, and also around position angle (PA) ≈ 110° (Fig. 6, top-left panel). This could be due to the higher sensitivity of the HC3N data as compared to those of SiC₂, since we have an HC₃N line in the combined dataset (Sect. 3.3) with better uv-coverage than in the case of SiC₂. Clumpiness cannot be ruled out either as a potential cause of this difference, as there exist significant differences in the chemical pathways of the two species. The C₂H emission presents a main shell and a faint extended arc at larger radii (~10″), from the north down to the northeast part of the map. The same arc is traced by the HNC emission as well (Fig. 6, bottom-left panel), though this is somewhat hidden in the figure by the C₂H contours. Notably, there is C₂H and HNC emission visible even in areas between the arcs of the HC₃N and SiC₂ emission, towards IRAS 15194-5115 (Fig. 6, middle-left and bottom-left panels). The maps of the lines of C₂H and HNC have a higher sensitivity in comparison to the SiC₂ maps, as they are imaged from the combined data, and thus recover emission on more spatial scales.

In the case of IRAS 15082–4808, the SiC₂ emission appears confined to only the main shell region of the HC₃N map, and does not trace the outer arcs seen in the HC₃N emission (Fig. 6, top-right panel). This could be due to the lower signal-to-noise ratio of the SiC₂ maps, as in the case of IRAS 15194–5115. However, C₂H and HNC trace both the main shell and the arcs to the southwest in the HC₃N image (Fig. 6, middle-right and bottom-right panels).

4.3.2 Azimuthally averaged radial brightness profiles

Despite the complex morphology seen for some of the molecular line emissions, we used AARPs to study the radial structure of the emission for all sources, as is discussed below. This is the strategy used also by Agúndez et al. (2017) in their study of IRC +10216.

To obtain the inner (R_i) and outer (R_e) radii of the line-emitting regions for different species, we constructed the mean AARPs (Appendix D) for the 14 molecules listed in Table 5. Several detected isotopologues of HCN, CS, SiO, and HC₃N₁₃(H¹³CN, ¹³CS, C³⁴S, ²⁹SiO, H¹³CCCN, HC¹³CCN, and HCC¹³CN) present emission with signal-to-noise ratios >3σ in their channel maps. Since the photodissociation of these molecules occurs throughout the broadband continuum (van Dishoeck 1988), and is not limited to narrow frequency ranges of discrete UV lines, their rarer isotopologues are expected to be present in the same spatial range as the main counterparts. Hence, to generate the mean AARPs for these species, we have averaged together emission from the detected lines of their non-blended isotopologues where such averaging increases the signal-to-noise ratio of the resulting profile.

Non-blended line cubes for a given species were convolved to a common circular beam with a size equal to the largest major axis among the individual beams. For each of these common-beam cubes, the emission from within a range of ±20% of the expansion velocity centred on the systemic velocity was averaged together to increase the signal-to-noise ratio, as we were now focusing on the overall size of the emitting shell and not the substructure within. The resulting maps were divided into successive concentric circular rings of increasing radii, centred on the continuum peak, with widths equal to the common restoring beam. The emission within each shell was averaged to obtain the azimuthally averaged brightness at the corresponding radius. These average brightnesses were plotted against the radii of the corresponding shells to produce one AARP per line. The uncertainty in the radial average for each shell corresponds to the rms noise in the channel map divided by the square root of the number of beams in the respective shell. The mean of these individual line AARPs was calculated for each species, weighted by the reciprocal of the squared uncertainty, to obtain the mean AARPs of the species shown in Fig. 9.

As part of this method, we verified for each species that the different transitions of all isotopologues are emitted from the same region around the central star. Fewer pixels were used in the azimuthal averaging as we calculated the AARP closer to the centre. This increased the chance that noise at the innermost radii might not be effectively suppressed, and could give rise to artefacts that need not correspond to actual emission. This is the reason why the error bars increase in size towards the inner part of the AARPs.

In order to estimate the radial extents of the emitting regions, the mean AARPs of each molecule were fitted with Gaussian profiles. We believe that Gaussian fits to the AARPs provide a reasonable way to systematically estimate the extent of the various emitting regions, to a first approximation. For instance, Fig. 10 shows such fits for the HCN and CN AARPs of IRAS 07454–7112. The Gaussian fits to the AARPs of the 14 selected species for all three sources are shown in Appendix D. The common restoring beam was used to obtain the beam-deconvolved sizes of the brightness distributions. For centrally peaked morphologies, the peak position (R_p) of the emission, and hence the inner radius (R_i), was set to 0. In this case, the outer radius (R_e) is estimated as the half width at half maximum (HWHM) of the Gaussian fit to the mean AARP. In the case of shell emission, the inner and outer radii of the emission regions are given by the half maxima points on either side of the peak position of the Gaussian fit to the AARP. For each molecule, the aperture from which line spectra were extracted was set to a circular region with a radius equal to the peak position + 3σ of the Gaussian fit to the AARP (i.e. R_p + 2.5×HWHM) of the corresponding molecule, in order to extract the maximum amount of emission while including only a minimum number of pixels with only noise and no emission.

Figure 11 shows the radial extent estimates of the average brightness distributions of each of the 14 analysed molecules, calculated using the Gaussian fits to their mean AARPs, as was discussed above. The observed values on an angular scale have been converted to a spatial scale using the distances provided in Table 1. The values of R_i and R_e, and the corresponding uncertainties are tabulated in Table 5. We present the qualitative results of the morphological analysis below, taking into account the calculated uncertainties.

4.3.3 Centrally peaked species

The AARPs of the centrally peaked species (SiO, SiS, CS, HCN) show clear deviations from a Gaussian profile in both IRAS 15194–5115 and IRAS 15082–4808, whereas they are fit well using Gaussians for IRAS 07454–7112 (an effect of the lower spatial resolution in this case; see Figs. D.1, D.2 (right), and D.3 (left)). For IRAS 15194–5115 and IRAS 15082–4808, the emissions from these molecules peak sharply at the centre and then gradually fall off at larger radii. Due to this, the Gaussian fits underestimate the radii of the actual emitting regions, as can be seen from Figs. D.1, D.2 (right), and D.3 (left).

The SiO and SiS emission regions are roughly co-spatial in each source. The CS emission region is more extended than those of SiO and SiS, while the HCN emission is the most extended of the centrally peaked species for all stars (see Fig. 9).

4.3.4 Shell species

Hydrocarbons: Within the calculated uncertainties (see Table 5), the shells of C₂H and C₄H peak at the same radii (Fig. 9) and have the same widths (Fig. 11) for the three stars, possibly with the exception of IRAS 15082-4808, where the C₂H emission appears to extend further out than that of C₄H by roughly 10% (see Table 5). The main hydrocarbon shells are of roughly the same thickness (~5500 AU) towards IRAS 15194–5115 and IRAS 15082–4808, but there are cases of faint extended emission beyond the main shell up to around 9300 AU for IRAS 15194–5115 (Fig. 9). IRAS 07454-7112 presents much thinner shells for the hydrocarbons, with a thickness of only ~1300 AU (Table 5). C₅H, C₆H, and C₈H have also been detected towards IRAS 15082–4808 and/or IRAS 15194–5115 in the combined data, but the lines are too weak for any morphological information to be extracted.

Cyanides: In addition to the expected shell emission (see e.g. Agúndez et al. 2017, for the HC₃N shell distribution for IRC + 10216), HC₃N also shows significant central emission components towards all three stars. This is discussed in more detail in Sect. 4.3.5. In the cases of IRAS 15082–4808 and IRAS 07454–7112, the shell-HC₃N and HC₅N emissions trace roughly the same radial range (Fig. 11 and Table 5), and peak at around the same distance from the centre (Fig. 9). In the case of IRAS 15194–5115 the HC₃N emission appears to peak at a slightly smaller radius than the HC₅N emission, by ~30% (Fig. 9). However, this could be due to contamination from the central component of the HC₃N emission and the low signal-to-noise in the HC₅N maps towards this star. Compared to C₂H and C₄H, the HC₃N and the HC₅N emissions peak at slightly smaller radii in all three CSEs, by an estimated 10–40% (Fig. 9).

In general, CN, HNC, and the hydrocarbons present the most extended emission among the observed molecules. The peaks of the CN and C₃N emissions are located roughly at the outer edges of the HCN and the shell-HC₃N emissions, respectively (Figs. 9, 11 and Table 5). The CN AARP of IRAS 15194–5115 shows a secondary peak at larger radii (~11″, Fig. 9), which is not present in the other two stars. For IRAS 15194–5115, we also see weak emission structures at roughly the same location as the CN secondary peak in SiC₂, HNC, C₃N, C₂H, C₄H, and possibly C₃H (Fig. 9). The fact that these arcs are traced by multiple species suggests that they are most likely the result of density enhancements (see also Sect. 5). The radial range of the HNC emission is roughly coincident with that of the C₂H and C₄H emission for all three stars (Fig. 11).

SiC₂: SiC₂ is the only silicon-bearing molecule out of the species studied in this paper that emits in a shell, whereas the others (SiO and SiS) are centrally peaked. The peak of the SiC₂ emission is close to those of the HC₃N and HC₅N emissions for all three stars (Fig. 9). However, SiC₂ also presents a central component that is further discussed below. We note that towards IRAS 15082–4808, the SiC₂ AARPs show negative dips at larger radii (see Fig. 9), which is evidence of interferometric filtering out of extended emission. A similar behaviour is exhibited by C₄H towards both IRAS 15194–5115 and IRAS 15082–4808, and possibly by HC₅N towards IRAS 15194–5115.

4.3.5 Central emission components of HC₃N and SiC₂

For IRAS 15194–5115 and IRAS 15082–4808, HC₃N and SKC₂ show central components above the respective 3σ noise levels (Fig. 9). We stress that what we call central emission need not necessarily originate in the extended atmosphere, but can instead emanate from roughly anywhere within a synthesised beam (~700 AU for IRAS 15194–5115 and ~1000 AU for IRAS 15082–4808, see Table 2) centred on the star. The central components of these species can be seen in the spatial profile plots shown in Figs. 7 and 8 also. We note that even though C₂H appears to have a central component towards IRAS 15082–4808 (see Fig. 6, middle-right panel and Fig. 8), this is due to the contamination from the blended hyperfine components of C₂H, and potentially also weak lines of c-C₃H₂ and C₆H (see Fig. A.1). In the case of IRAS 07454–7112, the angular resolution compared to the size of the emitting region is too poor to draw any conclusions about the behaviour of the brightness distributions in the inner part of the CSE. The possible formation mechanisms of these central components are discussed in more detail in Sect. 5.

4.4 Column density and rotation temperature estimates

We produced population diagrams (also referred to as rotation diagrams) to obtain the rotational temperature (T_rot) and the column density (N_tot) for molecules with detected lines from three or more rotational transitions. We made a first-order correction for the optical depths. The method is described in detail in Appendix E.1. The minimum and maximum line optical depths of each molecule for which we have made population diagrams are listed in Table E.1. In this section, we present the column densities and rotation temperatures obtained from the population diagram analysis. All the population diagrams produced are shown in Figs. E.1–E.18. The rotational temperatures and column densities thus obtained are tabulated in Table 6 and shown in Fig. 12.

As the centrally peaked species are located close to the star, they are expected to have relatively high rotational temperatures. However, for all centrally peaked species, except SiS, the population diagrams yield much lower temperatures than expected (~ 10–20 K; Fig. 12, left panel). This is most likely due to three effects: (1) the limited range of energy levels covered (e.g. the highest energy level observed for HCN is at ~42 K, see Table B.2), where, in particular, high-excitation transitions are missing, yielding only a very limited sampling of the excitation properties, (2) the contribution from different lines may come from different regions based on their excitation conditions, and thus may not sample regions with the same temperature, and (3) the assumption of optically thin lines is not always fulfilled. For the SiS emission, where the energy range covered is larger, we obtain a somewhat higher rotational temperature of ~40 K.

The shell species often cover a large range of energy levels (e.g. 20–187 Κ for C₄H, see Tables B.1 and B.2), and the emission from different lines of a species come from roughly the same region. They are therefore are expected to produce reliable estimates of rotation temperatures. HC₃N and HC₅N yield rotation temperatures in the range of 15–30 K, whereas C₄H and C₃N give slightly higher temperatures, around 30–45 K. Based on these results, we use rotational temperatures of 40 and 20 Κ for centrally peaked and shell species, respectively, in the abundance estimates based on single lines in Appendix E.3. We also note that, in general, the obtained rotational temperatures are highest for IRAS 07454–7112 (Fig. 12, left panel).

4.5 Abundance estimates

For the species for which we could produce population diagrams (see Table 6 and Appendix E), we calculated fractional abundances from the corresponding column densities, using Eq. (E.6). For all the other species, we obtained a rough estimate of the abundance analytically using Eq. (E.7). These two methods are described in Appendix E.

The fractional abundances estimated towards our stars are listed in Table 7 and shown in Fig. 13, along with the corresponding abundances for IRC +10216 obtained from the literature. We also show the abundances normalised with those of IRC +10216, for an easier source-to-source comparison, and normalised to each star’s C³⁴S abundance, to eliminate source-specific uncertainties on distance and MLR. We chose C³⁴S in particular, since the S and³⁴ S abundances are not expected to vary between the sample stars, nor with respect to IRC +10216 (Henry et al. 2012). Whereas we find similar CS abundances for all of the stars, we note that Massalkhi et al. (2019) have reported a decreasing CS peak abundance for increasing density in carbon-rich CSEs.

We made first-order corrections for optical depths, which are particularly significant for HCN, SiO, and CS. However, the estimated rotational temperatures are much lower than expected for these centrally peaked species (see Table 6 and Fig. 12, left panel), and we therefore believe that for these species the reported abundances are lower limits.

The abundances of the shell species are in general comparable, within the uncertainties, in the three stars. Since extended emission appears to have been resolved out for SiC₂ and C₄H towards IRAS 15194–5115 and IRAS 15082–4808 (see Sect. 4.3.4), the ALMA points in the population diagrams of these species for these sources could be slightly underestimated.

We do not expect this to change the abundances beyond the estimated uncertainties.

Uncertainties of abundance estimates

The accuracy of a determined absolute abundance depends on the method used to estimate it, the validity of the assumptions that went into the calculations, and the uncertainties of the input parameters. We have assumed a simple circumstellar model (including the shape of the radial abundance distributions), and excitation in LTE of the molecular energy levels. Among the input parameters, we have the adopted distances and the mass-loss rates. In addition, the amount and quality (including calibration uncertainties) of the observational data contribute to the uncertainty, through the measured fluxes and estimated emitting-region sizes. This makes it difficult to estimate formal errors of the abundances.

The arcs seen in the molecular emission towards IRAS 15194–5115 and IRAS 15082–4808 suggest that there are density enhancements (see Sect. 4.3.4). These are not considered in the assumed smooth H₂ flow, as we do not have a well-constrained quantitative estimate of these enhancements.

This also adds to the uncertainty of the abundance estimates. Attempts to address this demand entailed modelling that is outside the scope of the present work.

In general, we estimate that the overall uncertainty, including all parameters and model assumptions, is about a factor of three to five for the absolute abundances estimated using population diagrams, depending on the quality of the population diagram. The single-line estimates are, at best, order-of-magnitude estimates. The uncertainty decreases to a factor of two to three and a factor of five in the cases of population diagram and single-line estimates, respectively, when comparing abundances that are normalised individually to the respective C³⁴S abundance for each source (Sect 4.5), since this means that the influences of distance, mass-loss rate, and the circumstellar model to a large extent are removed. The comparison abundances adopted for IRC +10216, which were obtained using different methods, have an uncertainty of at least a factor of two to three.

4.6 Isotopic ratios

Stellar elemental isotopic ratios are measures of the nucleosynthetic history (including dredge-up) of a star, and are, as such, important observational results. Spectral lines from our data can be used to estimate circumstellar isotopologue ratios. In most cases, there is every reason to think that these are also good estimates of the corresponding stellar isotope ratios, since the different isotopologues are produced, destroyed, and excited in a similar way, to first approximation. This applies, for instance, to silicon and sulphur. For carbon, the situation is special since the photo-dissociation process is isotope-selective in the case of CO (Saberi et al. 2019). However, the effect of this is estimated to be small for high-mass-loss-rate objects (Saberi et al. 2020), that is, the type of stars in this study.

For species for which we could make reliable population diagrams, the isotopic ratios were calculated from the abundance ratios of the relevant molecules. For all other species, the isotopic ratio was determined by calculating the corresponding line intensity ratios. This method assumes that the J – J′ transition is excited under the same conditions for both isotopo-logues. We refrained from performing any frequency corrections on the isotopic ratios, as the uncertainties in the estimated ratios are significantly greater than the magnitude of such corrections. We present estimates of the isotopic ratios for the three stars in Table 8, along with isotopic ratios for IRC+10216 and the Sun obtained from the literature for comparison.

Carbon: The ¹²C/¹³C ratios calculated from the optically thin lines of HNC, SiC₂, HC₃N, C₄H, and C₃N for all three stars are consistent with their respective values obtained from the CO radiative transfer modelling by Woods et al. (2003), though the C₄H ratio is slightly larger than the others.

Silicon: The ²⁸Si/²⁹Si, ²⁸Si/³⁰Si, and ²⁹Si/³⁰Si values in the three stars are similar to the expected values of 20, 30, and 1.5, the solar values (Asplund et al. 2009).

Sulphur: The ³²S/³³S and ³²S/³⁴S values, about 100 and 20, respectively, in the three stars, are close to the expected solar values of 125 and 22.

5 Discussion

A comparison of molecular radial brightness distributions and abundances between the three stars and with IRC +10216 enables us to understand whether and how the chemistry in C-type AGB CSEs is affected by variations in properties including the MLR and the stellar ¹²C/¹³C ratio. We compared the molecular radial brightness distributions of various molecules, focusing on Figs. 9 and 11 and the molecular abundances based on Fig. 13. Even though the AARPs show only the radial structure of the emission and average out all azimuthal variations, they still provide valuable information on the chemical stratification in the CSE, and thereby on the formation and destruction mechanisms of various molecules.

We started by analyzing whether the spatial extents of the molecular CSEs follow that expected from photodissociation by an external UV radiation field. The photodissociation radius of a molecule depends on how well it is shielded from the interstellar radiation field (ISRF). This is determined by the outward column density of dust, which in turn depends on the mass-loss rate, or rather the circumstellar density (proportional to Ṁ/υ_exp), and also on the gas-to-dust ratio. The circumstellar density is lowest for IRAS 07454–7112, and about three and five times higher for IRAS 15194–5115 and IRAS 15082–4808, respectively (Table 1). The gas-to-dust ratios for the three sources are likely similar (Groenewegen et al. 1998). Thus, we expect the sizes of the molecular shells to be smallest for IRAS 07454–7112, larger for IRAS 15194–5115, and largest for IRAS 15082–4808. Indeed, the shells of IRAS 07454–7112 are by far the smallest ones, by about a factor of three (Figs. 9, 11, Table 5). However, those of IRAS 15194–5115 and IRAS 15082–4808 are of about the same size. They are also comparable in size to the molecular shells seen towards IRC+10216, which has a circumstellar density roughly three times higher than that of IRAS 15194–5115 and 1.5 times that of IRAS 15082–4808. This could be attributed to errors in the distances (which affect mass-loss-rate estimates and spatial extents), differences in the gas-to-dust ratio, differences in the circumstellar dust properties, and/or to the CSEs being exposed to slightly different strengths of the ISRF. Thus, our results, which are also corroborated by the radial brightness profiles of the centrally peaked species, are not inconsistent with the expected sizes of molecular distributions affected by photo-dissociation by UV light from the outside. The next paper in the series will address this in a more quantitative way (see Sect. 1). As mentioned above, the lower circumstellar density of IRAS 07454–7112 leads to the parent molecules being photodis-sociated closer to the star than in the other two sources. This may be reflected in the higher rotation temperatures obtained for the daughter species for this object (Fig. 12, left panel).

When looking at the AARPs of shell species in more detail, we conclude that the cyanopolyynes are located slightly inwards with respect to the hydrocarbons (see Figs. 9, 11 and Table 5). The average peak position of the cyanopolyynes falls inside that of the hydrocarbons by around 25–30% for both IRAS 15194–5115 and IRAS 15082–4808, and by roughly 10% for IRAS 07454–7112. We find no marked difference in the locations among the species of these respective groups. The largest spatial extents are found for HNC, CN, and possibly C₃N, and the hydrocarbons C₂H and C₄H. This is consistent with the results of Daniel et al. (2012) and Cernicharo et al. (2013), who found HNC emission extending to more than 30″ towards IRC +10216, and Agúndez et al. (2017), who found CN to present emission to similar radii, extending beyond that of the other cyanides and cyanopolyynes around this star. The shell of c-C₃H₂, detected only towards IRAS 15194–5115, appears roughly coincident with the C₂H and C₄H shells. In all of these respects, we reproduce the findings of Agúndez et al. (2017) in the case of IRC +10216. We note that, while Agúndez et al. (2017) find that the CN emission towards IRC +10216 clearly extends beyond that of the C₂H and C₄H radicals, we observe the faint extended emission from these radicals to have roughly the same radial extent as the CN towards IRAS 15194–5115 and IRAS 15082–4808 (Fig. 9). However, this is due to the most extended CN emission being filtered out due to the lack of very short baselines in our observations, in contrast to that of Agúndez et al. (2017), who used single dish observations to recover the flux filtered out by ALMA.

From our observations, we find that HC₃N is present within one synthesised beam around two of our stars, corresponding to ~700 AU and ~1000 AU for IRAS 15194–5115 and IRAS 15082–4808, respectively. For IRC +10216, Siebert et al. (2022) find significant emission from high-excitation (J = 38 − 37, 30 − 29, 28 − 27) lines of HC₃N within 350 AU from the star.

Herbst & Leung (1990), Howe & Millar (1990), and Agúndez et al. (2017) suggest that HC₃N is formed in C-type CSEs mainly through the reaction $$\text{CN}+{\text{C}}_2{\text{H}}_2\to {\text{HC}}_3\text{N}+\text{H}.$$(1)

Hence, it is expected to appear in the inner CSE if there is enough CN available. We cannot confirm this pathway as the main production channel, since we do not detect CN emission above the noise level in the innermost part in any of our CSEs. However, this could be a sensitivity effect, since the surface brightness of the CN emission is low at the systemic velocity for the two sources where we have sufficient spatial resolution to do this. Van de Sande & Millar (2022) suggest that a significant inner wind abundance of complex species, including HC₃N, can be indicative of the presence of a white dwarf binary companion. However, according to their models, this will also lead to severely reduced SiO and SiS abundances, an effect not seen in our data.

We find that the SiC₂ abundance distribution has both a central and a shell component. The presence of a central component has been discussed before by, for instance, Lucas et al. (1995); Fonfria et al. (2014); Velilla Prieto et al. (2015a); Massalkhi et al. (2018). It is most likely explained by SiC₂ being formed in the extended atmosphere, as was already suggested by MacKay & Charnley (1999), and predicted by the chemical models of Agúndez et al. (2020). The detection of hot SiC₂ ro-vibrational bands in the optical towards carbon stars (Sarre et al. 1996) supports this. The SiC₂ shell, on the other hand, is expected to be formed due to the fast reaction of Si with C₂H₂ in the low-temperature (< 100 K) conditions prevalent in the outer parts of the CSE (Canosa et al. 2001; Cernicharo et al. 2010): $$\text{Si}+{\text{C}}_2{\text{H}}_2\to \text{Si}{\left(\text{CH}\right)}_2\to {\text{SiC}}_2+{\text{H}}_2.$$(2)

Further out, it is photo-dissociated to form Si and C₂ (Harada et al. 2010).

The arcs seen in the HC₃N and SiC₂ emissions at the systemic velocity for IRAS 15194−5115 are clearly co-spatial (Fig. 6, top left panel), though these molecules themselves do not share any common chemistry. These arcs appear to be traced by a variety of other molecules as well (Sect. 4.3.1). This suggests that the arc structures seen are, predominantly, the result of density enhancements rather than abundance variations. Such thin shells in various cyanopolyynes and hydrocarbons are also seen in the CSE of IRC +10216 (Agúndez et al. 2017). Additionally, for IRC +10216, Mauron & Huggins (1999, 2000); Leão et al. (2006), and Dinh-V-Trung & Lim (2008) showed that the clumpy shells seen in cyanopolyyne emission coincide spatially with the dust arcs observed in dust-scattered optical light, and hence represent the same density enhancements in the CSE. This is in line with the suggestion by Lykou et al. (2018), based on CO, SiO, CS, and HC₃N emission and NACO/VLT near-infrared data, that IRAS 15194–5115 could be a binary system in which a spiral-like density structure would be imprinted in the CSE by an orbiting companion. Similar substructure was observed in CO, CN, and C₄H towards IRC +10216 by Cernicharo et al. (2015); Decin et al. (2015) and Guélin et al. (2018), which was attributed to episodic mass loss triggered by the existence of a putative binary companion. Towards IRAS 15194–5115, we find emission from C₂H also in the gaps between the arcs seen in HC₃N (Fig. 6, middle-left panel and Fig. 7). This need not be contrary to the proposition of density-enhanced shells but can rather be explained by the larger impact of density enhancements on the abundance of HC₃N (Cordiner & Millar 2009).

The rotation temperatures we estimate from our population diagrams match reasonably well with those estimated for IRC +10216. He et al. (2008) obtained a rotation temperature of 28 K for HC₃N, and Cernicharo et al. (2000) reported 35 K for C₄H and 20 K for C₃N, which align with our estimates. We note that Pardo et al. (2022) also present population diagrams of C₄H and HC₅N, among other species, towards IRC +10216 using lines from their 31.0–50.3 GHz spectral survey. These yield rotation temperatures of 4.9 and 10.1 K, respectively, much lower than our estimates for these species (Table 6).

We have estimated that the uncertainties of the relative abundances when comparing our three stars are a factor of two to three for population diagrams and a factor of five for singleline estimates. When comparing with IRC +10216 they increase to a factor of five for population diagrams and a factor of ten for single-line estimates. Considering this, there are no significant differences or trends in the abundances among our three stars, other than the possibly lower hydrocarbon abundances in IRAS 07454–7112 compared to the other two stars (Fig. 13). The latter could be a result of the lower density of the CSE of IRAS 07454–7112. When comparing with IRC +10216, all abundances except that of SiO are within a factor of ten, meaning that, except for this species, we find no significant differences with the abundances estimated for IRC +10216. The SiO abundances in our stars are higher than that for IRC +10216 by an order of magnitude. The same discrepancy was observed by Woods et al. (2003) in their single-dish line survey of these sources. The putative over-abundance of SiO in our stars needs to be confirmed through a proper radiative transfer analysis.

Time variability of the intensity of thermal (non-maser) line emission has been reported for several species in the case of IRC +10216 (Cernicharo et al. 2014; Pardo et al. 2018; He et al. 2019). By comparing the observations from two epochs, we find variability in the 3 mm line emission of C₂H and HC₃N towards IRAS 15194–5115 and IRAS 15082–4808. Our findings (Sect. 4.2) are in line with the conclusions of Cernicharo et al. (2014) and Pardo et al. (2018), who show that C₂H shows the highest variability at 3 mm, and that the phase of variability of the cyanopolyynes is opposite to that of C₂H, for IRC +10216 as well. We note that, in addition to C₂H and HC₃N, Pardo et al. (2018) also found time variability in the lines of CN, C₄H, C₅H, and HC₅N towards IRC +10216, which we are unable to ascertain for the stars in our sample from the current data. This could potentially be due to the intensity variation in the lines of these species being lower than the calibration uncertainty.

The three stars in our sample have significantly different inferred ¹²C/¹³C ratios (Table 8), with IRAS 15194–5115 standing out with a very low value of six. For this star, Ramstedt & Olofsson (2014) report a ¹²CO/¹³CO ratio of ten, slightly higher than the value of six estimated by Woods et al. (2003) and us (still within the uncertainties of both estimates). The other two stars, and IRC +10216, have values in the range of 20–50, which is consistent with typical AGB evolution models (see e.g. Lattanzio & Boothroyd 1997, and references therein) where the surface ¹²C/¹³C ratio increases as the star evolves along the AGB. This has also been traced by observations (e.g. Lambert et al. 1986; Abia et al. 2001; Ramstedt & Olofsson 2014). It cannot be concluded with certainty that the low ratio in IRAS 15194–5115 is due to hot-bottom burning (HBB) and a subsequent evolution to a carbon star, as the star may not be massive enough for HBB to occur. Whereas HBB efficiently produces N, we find no indications of any N enhancement in the circumstellar species for this star. It has been suggested that the presence of a hot binary companion may alter the circumstellar ¹²CO/¹³CO through differential photodissociation so that it differs from the atmospheric ¹²C/¹³C, whereas this is not the case for the isotopo-logues of the other observed molecules in this study (see Vlemmings et al. 2013; Saberi et al. 2019). They are therefore expected to give good estimates of the stellar ¹²C/¹³C ratio. The models by Izzard & Tout (2003), combining nucleosynthesis and binary star evolution, have shown that the atmospheric ¹²C/¹³C can be lowered significantly in the presence of binary companions.

Finally, the observed similarity of the silicon isotopic ratios with the respective solar values is in line with AGB nucleosynthesis in lower-mass stars (≲4 M_⊙, Karakas & Lugaro 2016). In addition, the sulphur isotopic ratios being consistent with the corresponding solar ratios is in line with the fact that these isotopes are not expected to be influenced by nucleosynthesis in lower-mass stars (Shingles & Karakas 2013; Humire et al. 2020, and references therein).

6 Summary and conclusions

Our unbiased ALMA spectral survey mapped for the first time the 3 mm molecular rotational transitions in the CSEs of the C-type AGB stars IRAS 15194–5115, IRAS 15082–4808, and IRAS 07454–7112 at a high spatial resolution (0.″7-1.″7, corresponding to roughly 500–1000 AU). Extensive interferomet-ric surveys of this kind have previously been performed only towards IRC +10216. The survey yielded 311 identified lines (including hyperfine splitting components), from 132 rotational transitions of 49 molecular species, including various isotopo-logues, and three unidentified lines. Data with a sufficient signal-to-noise ratio (≳3σ in the emission maps), which enabled us to comparatively analyse the morphological characteristics across the three stars, was obtained for 14 species. We produced AARPs to obtain the radial brightness distributions of these species, and estimated the extents of their emitting regions. We used optical-depth-corrected population diagrams or single-line calculations to calculate the fractional abundances of these molecules and their less abundant isotopologues. Lines from our APEX single-dish surveys of the sources were used in the population diagrams to complement those from the ALMA observations. We also report several new detections towards these stars, namely ²⁹SiO, ³⁰SiO, ²⁹SiS, ³⁰SiS, Si³⁴S, C³³S, Si¹³CC, C₆H, C₈H, 1-C₄H₂, and doubly ¹³C-substituted isotopologues of HC₃N.

We find deviations from a smooth, spherically symmetric CSE towards IRAS 15194–5115 and IRAS 15082–4808 in several molecules, and detect density enhancements similar to what has previously been reported in the CSE of IRC +10216, which might indicate the presence of stellar or substellar companions of these stars. The very low ¹²C/¹³C ratio and the presence of a “central” emission component for HC₃N may also be indicative of the presence of a binary companion of IRAS 15194–5115.

By comparing our morphological results for the three sources amongst themselves and with results from the literature for IRC +10216, we find that the chemistry in the CSEs, as traced by the radial order in which different molecules exist around the central star, is very similar in our sources and IRC +10216. The chemistry does not seem significantly affected by the differences in the nucleosynthetic history of the individual stars, indicated by differences in their ¹²C/¹³C ratios, except for the expected increased abundance of singly and doubly ¹³C-substituted isotopologues in the CSE of IRAS 15194–5115, owing to its low ¹²C/¹³C ratio. We find that, within the uncertainties of our analysis, most of the estimated fractional abundances are similar across the source sample, and to the corresponding IRC +10216 values. The notable exception is SiO, which appears more abundant in the three stars in our sample in comparison to IRC +10216, by an order of magnitude. The calculated abundances of the shell species match reasonably well with the photochemical models for all sources. We also detect variability in the line emission of C₂H and HC₃N for two stars in our sample.

We estimated the carbon, silicon, and sulphur isotopic ratios for the three stars. The ¹²C/¹³C ratios match the values from the literature for all three stars, and the silicon and sulphur ratios of the three stars match reasonably well the corresponding IRC +10216 and solar values.

Overall, we conclude that the chemistry in the C-type AGB CSEs studied in this paper, as judged from radial brightness distributions and estimated abundances, is consistent across our small sample and with that of IRC +10216. This indicates that IRC +10216 serves reasonably well as an archetypal C-type AGB star, in terms of modelling C-type CSE chemistry, at least for MLRs within an order of magnitude of that of itself. However, we remind the reader of the possible binary nature of IRC +10216 and potentially also of some of the sources in our study. Binarity might influence the chemical properties differently for different sources, depending on the properties of the objects in the system.

Non-LTE radiative transfer modelling is necessary to more accurately determine the molecular abundances. This, and the subsequently updated chemical models, will be presented in a series of upcoming papers. More extensive observations, in terms of both sources and spectral coverage, are required to thoroughly constrain the chemical models and small-scale chemical variations in the CSEs. A detailed investigation of the morphology of the CSEs of the stars in our sample and the possible presence of binary companions will require observations with a higher angular resolution and sensitivity.

Acknowledgements

R.U. acknowledges data reduction support from the Nordic ALMA Regional Centre (ARC) node based at Onsala Space Observatory (OSO), Sweden. The Nordic ARC node is funded through Swedish Research Council grant No 2017-00648. E.D.B. acknowledges financial support from the Swedish National Space Agency. S.B.C. and M.A.C. were supported by the NASA Planetary Science Division Internal Scientist Funding Program through the Fundamental Laboratory Research work package (FLaRe). I.d.G. acknowledges support from grant PID2020-114461GB-I00, funded by MCIN/AEI/10.13039/501100011033. The work of M.G.R. is supported by NOIRLab, which is managed by the Association of Universities for Research in Astronomy (AURA) under a cooperative agreement with the National Science Foundation, USA. This paper makes use of the following ALMA data: ADS/JAO.ALMA#2013.1.00070.S, ADS/JAO.ALMA#2015.1.01271.S, ADS/JAO.ALMA#2011.0.00001.CAL. 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. This paper is based on observations with the Atacama Pathfinder Experiment (APEX) telescope. APEX is a collaboration between the Max Planck Institute for Radio Astronomy, the European Southern Observatory, and the Onsala Space Observatory. Swedish observations on APEX are supported through Swedish Research Council grant No 2017-00648. The APEX observations were obtained under project numbers O-0107.F-9310 (SEPIA/B5), O-0104.F-9305 (PI230), and O-087.F-9319, O-094.F-9318, O-096.F-9336, and O-098.F-9303 (SHeFI).

Appendix A ALMA Band 3 spectra

This appendix shows the entire ALMA Band 3 spectra of the three sources. The spectra were extracted by integrating the intensity in a circular aperture of 12.5″ radius centred on the respective continuum peaks, so as to recover emission from all molecules. Line detections (Table B.1) are labelled in the figure at the corresponding frequencies.

Appendix B Details of detected transitions

This appendix lists the detected emission lines along with their upper-level energies and integrated intensities for the three stars. Table B.1 presents the lines detected in the ALMA Band 3 spectra, and Table B.2 lists the lines from the APEX surveys (see Sect. 3.1) that were used in this work for abundance calculations.

Appendix C Emission maps and line spectra

The below figures show the line emission maps (top panels) averaged over ±20% of the expansion velocity around the systemic velocity, and the line spectra (bottom panels), for IRAS 15194–5115 (left), IRAS 15082–4808 (centre), and IRAS 07454–7112 (right). The figures are ordered in increasing order of line rest frequency, which is given in parentheses at the end of the figure caption. The white contours in the emission maps are at 3, 10, and 30 sigma. The synthesised beams are shown as filled white ellipses at the bottom left of each map. The grey shaded regions in the line spectra represent the channels used for calculating the integrated intensities of the lines, reported in Table B.1. The dotted vertical line in the line spectra marks the systemic velocity of the source. Missing plots indicate non-detection of the concerned line towards the particular source.

The below figures show the spectra of the lines from the APEX surveys that we have used in this work, for IRAS 15194−5115 (left), IRAS 15082−4808 (centre), and IRAS 07454−7112 (right). The figures are ordered in increasing order of line rest frequency, which is given in parentheses at the end of the figure caption. Missing plots indicate non-detection of the concerned line towards the particular source. The dotted vertical line marks the systemic velocity of the source. The grey shaded regions cover 1.2 times the expansion velocity on either side of the systemic velocity. For non-blended lines, this region represents the channels used for calculating the integrated line intensities, reported in Table B.2. For the lines of C₃N (Figs. C.113, C.147, C.158, C.165, C.183), where the line profile consists of blended hyperfine components, the whole line profile, not just the grey shaded region, has been integrated to obtain the integrated line intensity. For lines of C₂H and C₄H, which have hyperfine components, we have shown only the strongest or unblended component, but the total integrated intensity was calculated by summing up all the components per transition.

Appendix D AzimuthaMy-averaged radial profiles (AARPs)

The figures below show the Gaussian fits to the AARPs of the systemic velocity emission maps of the 14 species shown in Fig. 9. The details of these profiles and fits are explained in Sect. 4.3.2.

Appendix E Column densities and abundances: Methods

The results in this section are based on a simple model for the CSE, assuming an isotropic, constant mass-loss rate and gas expanding at its terminal velocity. Nevertheless, there are clear indications of deviations from such a simple model, particularly in terms of the morphology, as is discussed in Sect. 4.3.1.

We express molecular abundances as fractional abundances relative to that of molecular hydrogen, H₂, which has the abundance distribution with the largest spatial extent (Huggins & Glassgold 1982). The fractional abundance profile of a molecular species, X, is defined as $$f_{\text{X}}(r)=\frac{n_{\text{X}}(r)}{n_{{\text{H}}_2}(r)},$$(E.1)

where n_X(r) and $n_{{\text{H}}_2}(r)$ are the number density distributions of the molecule and molecular hydrogen, respectively.

The excitation of a molecule in the CSE is determined by collisions and radiation, in particular the radiation fields of the central star and circumstellar dust. Non-local thermodynamic equilibrium (non-LTE) conditions can be prevalent in CSEs, which calls for a detailed radiative transfer analysis for the proper treatment of molecular excitation. Such a non-LTE treatment is outside the scope of the current work, and will be presented in an upcoming paper. A simpler analysis assuming LTE conditions can provide reasonable estimates of the molecular abundances and offer substantial insights into circumstellar chemistry, and is regularly employed as a first tool to analyse spectral surveys and other large datasets of evolved stars (e.g. Cernicharo et al. 2000; Justtanont et al. 2000; Wesson et al. 2010; Patel et al. 2011; Sanchez Contreras et al. 2015; Smith et al. 2015; Velilla Prieto et al. 2015b; Pardo et al. 2022). For molecules with multiple rotational transitions detected, the rotational temperature and column density can be estimated using a population diagram (Sect. E.1). The column densities thus obtained, together with the emission region sizes calculated from the AARPs, can be used to estimate molecular fractional abundances. In those cases where the population diagram method can not be employed, owing to the lack of a sufficient number of transitions covering a broad range of upper-level energies, we performed an approximate calculation of the fractional abundance using a single line for each species (Sect. E.3). We describe both methods below.

Appendix E.1 The population diagram method

The column density of each rotational energy level is related to the rotational temperature, T_rot, and total column density, N_tot, by the relation $$\ln \frac{N_{\text{u}}}{g_{\text{u}}}=\ln \frac{N_{\text{tot}}}{Z\left(T_{\text{rot}}\right)}-\frac{E_{\text{u}}}{k_{\text{B}}{T}_{\text{rot}}},$$(E.2)

where N_u is the column density of molecules in the upper energy level having energy E_u and statistical weight g_u, and Z and k_B are the partition function and the Boltzmann constant, respectively (Goldsmith & Langer 1999). For the calculation of partition functions, all molecules used for producing population diagrams (see Table 6) have been regarded as linear rigid rotors, except SiC₂ and c-C₃H₂, which are asymmetric tops. In order to use the integrated intensities summed over the hyperfine components wherever present (e.g. C₂H, C₃N), we calculated the partition functions, degeneracy factors, and Einstein A-coefficients under the assumption that the molecules do not possess a hyperfine structure. For the asymmetric tops, we interpolated the partition function values from the CDMS (Müller et al. 2005) catalogue to the rotation temperatures obtained from our analysis.

The source-averaged column density of the upper state, N_u, can be calculated from the observed velocity-integrated flux, ∫S_uldv, of the corresponding rotational emission line as $$N_{\text{u}}=\frac{4\pi {{\displaystyle \int }}^{\text{}}{S}_{\text{ul}}dv}{hc{A}_{\text{ul}}{\text{Ω}}_s}{C}_{{\tau }_v},$$(E.3)

where v_ul is the rest frequency of the transition, A_ul is the Einstein A-coefficient, Ω_s is the solid angle of the emitting region, h is the Planck constant, c is the speed of light in vacuum, and ${\text{C}}_{{\tau }_v}$ is the optical depth correction factor (see Goldsmith & Langer 1999), given by $$C_{{\tau }_v}=\left(\frac{{\tau }_v}{1-e^{-{\tau }_v}}\right),$$(E.4)

where τ_ν is the optical depth of the line.

If the assumptions are correct that, firstly, the populations of the corresponding energy levels follow a Boltzmann distribution that can be described by a single excitation temperature, T_rot, and, secondly, the lines are optically thin, then the points in the plot of ln(N_u/g_u) versus E_u/k_B are expected to lie on a straight line (see e.g. Fig. E.1). The rotational temperature and column density of each molecule are calculated from the slope and intercept, respectively, of a linear fit to such a plot.

Using this method, we first obtained estimates of the rotational temperature and total column density for each species without an optical depth correction (${\text{C}}_{{\tau }_v}=1$). From these values, we then calculated a preliminary estimate of the optical depth for each individual line of the species, using the standard equation $${\tau }_v=\frac{c^3{g}_u{A}_{ul}}{8\pi v^3}\frac{N_{tot}}{\text{Δ}vZ(T)}{e}^{-E_u/k_{\text{B}}T}\left(e^{hv/k_{\text{B}}T}-1\right)$$(E.5)

where Δυ is the full velocity width of the line. The range of optical depths thus calculated for each species for the three stars are given in Table E.1.

Employing the correction factors (see Eq. E.4) obtained from the calculated optical depths, we then produced optical-depth-corrected population diagrams, from which optical-depth-corrected rotation temperatures and total column densities were estimated. These values are presented in Table 6. The optical-depth-corrected population diagrams are shown in Figs. E.1 - E.18.

We note that along with the lines from the ALMA data, we have also included lines detected in our APEX surveys (Table B.2 and Figs. C.109–C.185) in the population diagrams, so that a wider range of energy levels can be sampled.

Appendix E.2 Abundance calculation from column densities

Using the estimates of the radial extents of the emitting regions of different species obtained from the Gaussian fits to the AARPs (see Sect. 4.3.2), we can estimate the molecular fractional abundances (Table 7) from the column densities of the respective species given by the population diagrams, using the equation $$f_{\text{X}}=\frac{2\pi m_{\text{H}}{v}_{\text{exp}}{N}_{\text{tot},\text{X}}}{\dot{M}}\left(\frac{R_{\text{e}}^2}{R_{\text{e}}-R_{\text{i}}}\right),$$(E.6)

where Ṁ is the hydrogen mass-loss rate, υ_exp the gas expansion velocity, and m_H the mass of the hydrogen atom, and where R_i and R_e are the inner and outer radii of the emitting region, respectively (Olofsson 2003).

Appendix E.3 Abundance calculation from single lines

Population diagrams cannot be used in the case of molecules for which only one or two lines are detected, or for which the detected transitions are very close together in upper-level energies. In such cases, we obtained a rough estimate of the fractional abundance, using the highest signal-to-noise line available, by assuming it to be constant in the radial range Ri to Re and zero outside it. Assuming an r⁻² density distribution and a constant, assumed excitation temperature throughout the emitting region, we used the following formula from Habing & Olofsson (2004, in rewritten form) $$f_{\text{X}}=1.3\times {10}^{-19}\frac{v_{\text{exp}}DZ\left(T_{\text{ex}}\right)}{g_{\text{u}}{A}_{\text{ul}}\dot{M}\left(R_{\text{e}}-R_{\text{i}}\right)}{e}^{E_1/k_{\text{B}}{T}_{\text{ex}}}{{\displaystyle \int }}^{\text{}}{S}_{\text{ul}}dv$$(E.7)

where υ_exp is given in km/s, Ṁ in M_⊙ yr⁻¹, D in kpc, R_i and R_e in cm, and ∫S _uldv in Jykm/s. The assumed T_ex values are 40 K for centrally peaked species and 20 K for shell species (see Sect. 4.4 for a justification of these values). We note that we did not perform optical depth corrections in the case of singleline abundance estimates, as the temperature we used for these calculations was an assumed value, and since the high uncertainties involved anyway deem the abundances thus calculated to be order of magnitude estimates.

The figures below show the population diagrams (see Sect. E.1) of various molecular species (listed in Table 6) towards the three stars.

References

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All Tables

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