# The millimeter IRAM-30 m line survey toward IK Tauri ⚫ ⚫ ⚫

L. Velilla Prieto<fnref n="1" />,<fnref n="2" />, C. Sánchez Contreras<fnref n="2" />, J. Cernicharo<fnref n="1" />, M. Agúndez<fnref n="1" />, G. Quintana-Lacaci<fnref n="1" />, V. Bujarrabal<fnref n="3" />, J. Alcolea<fnref n="4" />, C. Balança<fnref n="5" />, F. Herpin<fnref n="6" />,<fnref n="7" />, K. M. Menten<fnref n="8" />, and F. Wyrowski<fnref n="8" />

Received 22 April 2016 / Accepted 24 August 2016

## ABSTRACT

**Aims.** We aim to investigate the physical and chemical properties of the molecular envelope of the oxygen-rich AGB star IK Tau.

**Methods.** We carried out a millimeter wavelength line survey between ~79 and 356 GHz with the IRAM-30 m telescope. We analysed the molecular lines detected in IK Tau using the population diagram technique to derive rotational temperatures and column densities. We conducted a radiative transfer analysis of the SO₂ lines, which also helped us to verify the validity of the approximated method of the population diagram for the rest of the molecules.

**Results.** For the first time in this source we detected rotational lines in the ground vibrational state of HCO⁺, NS, NO, and H₂CO, as well as several isotopologues of molecules previously identified, namely, C¹⁸O, Si¹⁷O, Si¹⁸O, ²⁹SiS, ³⁰SiS, Si³⁴S, H¹³CN, ¹³CS, C³⁴S, H₂³⁴S, ³⁴SO, and ³⁴SO₂. We also detected several rotational lines in vibrationally excited states of SiS and SiO isotopologues, as well as rotational lines of H₂O in the vibrationally excited state $v_2 = 2$. We have also increased the number of rotational lines detected of molecules that were previously identified toward IK Tau, including vibrationally excited states, enabling a detailed study of the molecular abundances and excitation temperatures. In particular, we highlight the detection of NS and H₂CO with fractional abundances of $f(\text{NS}) \sim 10^{-8}$ and $f(\text{H}_2\text{CO}) \sim [10^{-7}-10^{-8}]$. Most of the molecules display rotational temperatures between 15 and 40 K. NaCl and SiS isotopologues display rotational temperatures higher than the average (~65 K). In the case of SO₂ a warm component with $T_{\text{rot}} \sim 290$ K is also detected.

**Conclusions.** With a total of ~350 lines detected of 34 different molecular species (including different isotopologues), IK Tau displays a rich chemistry for an oxygen-rich circumstellar envelope. The detection of carbon bearing molecules like H₂CO, as well as the discrepancies found between our derived abundances and the predictions from chemical models for some molecules, highlight the need for a revision of standard chemical models. We were able to identify at least two different emission components in terms of rotational temperatures. The warm component, which is mainly traced out by SO₂, is probably arising from the inner regions of the envelope (at $\le 8 R_*$) where SO₂ has a fractional abundance of $f(\text{SO}_2) \sim 10^{-6}$. This result should be considered for future investigation of the main formation channels of this, and other, parent species in the inner winds of O-rich AGB stars, which at present are not well reproduced by current chemistry models.

**Key words.** astrochemistry – line: identification – stars: abundances – stars: AGB and post-AGB – circumstellar matter

## 1. Introduction

Asymptotic giant branch (AGB) stars are the main contributors to the interstellar medium (ISM) chemical enrichment. The physical conditions, that is, the high densities ($\ge 10^{12}$ cm⁻<fnref n="3" />) and temperatures (~2000–3000 K), in their atmospheres allow the formation of stable molecules. All this molecular material is driven by the slow AGB wind creating a circumstellar envelope (CSE) that surrounds the star, up to regions where the interstellar UV field photodissociates the molecules. Carbon and oxygen are

the two most abundant and reactive elements in the atmospheres and winds of AGB stars, after hydrogen. All the possible carbon monoxide, which is a very stable molecule, is formed and then depending on which element (carbon or oxygen) is in excess, other molecules will be formed. Hence, the chemistry in these objects mainly depends on the elemental carbon to oxygen ratio, being O-rich ([C]/[O] < 1), C-rich ([C]/[O] > 1) or S-type stars ([C]/[O] ~ 1) (e.g. Olofsson 1996).

Since the first detection of CO in the millimeter wavelength range toward the CSE of an AGB star (Solomon et al. 1971), the observations of the molecular emission of CSEs in that wavelength domain have increased (e.g. Morris et al. 1975; Bujarrabal & Alcolea 1991; Cernicharo et al. 2015). These studies have been mostly focused on C-rich CSEs given that carbon is more chemically active than oxygen and, therefore, C-rich envelopes are expected and observed to display a large

<footnote n="1">¹ Instituto de Ciencia de Materiales de Madrid, CSIC, c/ Sor Juana Inés de la Cruz 3, 28049 Cantoblanco, Madrid, Spain
e-mail: lvelilla@icmm.csic.es</footnote>

<footnote n="2">² Centro de Astrobiología, INTA-CSIC, 28691 Villanueva de la Cañada, Madrid, Spain</footnote>

<footnote n="3">³ Observatorio Astronómico Nacional (IGN), Ap 112, 28803 Alcalá de Henares, Madrid, Spain</footnote>

<footnote n="4">⁴ Observatorio Astronómico Nacional (IGN), Alfonso XII No 3, 28014 Madrid, Spain</footnote>

<footnote n="5">⁵ LERMA, Observatoire de Paris, Sorbonne Université, UPMC, UMR 8112, 92195 Meudon, France</footnote>

<footnote n="6">⁶ Université de Bordeaux, LAB, UMR 5804, 33270 Floirac, France</footnote>

<footnote n="7">⁷ CNRS, LAB, UMR 5804, 33270 Floirac, France</footnote>

<footnote n="8">⁸ Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, 53121 Bonn, Germany</footnote>

<footnote>* Based on observations carried out with the IRAM-30 m Telescope. The Institut de Radioastronomie Millimétrique (IRAM) is supported by INSU/CNRS (France), MPG (Germany) and IGN (Spain).
** Full Tables E.1 and E.2 and the reduced spectrum (FITS file) are only available at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/597/A25</footnote>
variety of different molecular species (e.g. Cernicharo et al. 2000; Smith et al. 2015). However, the number of studies in the millimeter wavelength range has increased in the last years, and these studies have evidenced that O-rich CSEs do also host a rich variety of molecules (Ziurys et al. 2007; Kim et al. 2010; De Beck et al. 2013; Sánchez Contreras et al. 2015, and references therein).

Our motivation is to observe and to study the molecular content of the oxygen-rich CSE IK Tauri which is one of the most studied O-rich CSEs, and is considered a reference of its class.

## 1.1. IK Tauri

IK Tauri (hereafter IK Tau), also known as NML Tau, is a Mira-type variable star with a period of 470 days and a spectral type ~M9 (Pesch 1967; Wing & Lockwood 1973; Alcolea et al. 1999). This star was discovered by Neugebauer et al. (1965) and it is located at α(J2000) = 3h53m28s87 and δ(J2000) = 11°24′21″7 (Cutri et al. 2003). The distance to IK Tau was estimated to be 250–265 pc (Hale et al. 1997; Olofsson et al. 1998). The systemic velocity of the star with respect to the local standard of rest is $V_{\text{sys}}^{\text{LSR}} \sim 34$ km s⁻¹ (Kim et al. 2010, and references therein). Its effective temperature is $T_{\text{eff}} \sim 2200$ K and the stellar radius is $R_{*} \sim 2.5 \times 10^{13}$ cm (Decin et al. 2010a).

The star is surrounded by a an O-rich CSE, composed of dust and gas, which is the result of mass loss at a rate that has been estimated by different methods. Neri et al. (1998) estimated $\dot{M} \sim 3.8 \times 10^{-6} M_{\odot}$ yr⁻¹ from the model of $^{12}$CO J = 1–0 and J = 2–1 lines. González Delgado et al. (2003) estimated $\dot{M} \sim 3.0 \times 10^{-5} M_{\odot}$ yr⁻¹ from the model of $^{12}$CO J = 1–0, J = 2–1, J = 3–2, and J = 4–3 lines. Recent modelling of the J = 3–2, J = 4–3, and J = 7–6 lines of $^{12}$CO yielded $\dot{M} \sim 4.7 \times 10^{-6} M_{\odot}$ yr⁻¹ (Kim et al. 2010). The terminal expansion velocity of the CSE is $v_{\infty} \sim 18.5$ km s⁻¹ as measured from De Beck et al. (2013) and references therein. The size of the CSE depends on the molecule used to trace it out. Bujarrabal & Alcolea (1991) gave a half-intensity diameter of $\theta_{1/2} \sim 16–17″$ measured for $^{12}$CO J = 1–0 and $^{12}$CO J = 2–1 emission detected with the IRAM-30 m telescope. Kim et al. (2010) measured a $\theta_{1/2} \sim 20″$ for $^{12}$CO J = 3–2 with the Atacama Pathfinder EXperiment (APEX) telescope. Recent observations with the Plateau de Bure Interferometer (PdBI), showed that $^{12}$CO (J = 1–0) displays a $\theta_{1/2} \sim 18″$ (Castro-Carrizo et al. 2010). Also, HCN J = 1–0 was observed with the Owens Valley millimeter-array by Marvel (2005), displaying a size of $\theta_{1/2} \sim 3′′85$. The size of the SiO v = 0 J = 2–1 emission is $\theta_{1/2} = 2′′2 \pm 0′′1$ as determined with PdBI (Lucas et al. 1992). Finally, the emission of several lines of PN and PO has been mapped with the SubMillimeter Array (SMA), with $\theta_{1/2} \le 0′′65$ (De Beck et al. 2013).

The O-rich CSE around IK Tau displays maser emission of OH, H₂O, and SiO (Lane et al. 1987; Bowers et al. 1989; Alcolea & Bujarrabal 1992; Kim et al. 2010, and references therein). It also shows thermal molecular emission of $^{12}$CO, $^{13}$CO, SiO, $^{29}$SiO, $^{30}$SiO, OH, SiS, HCN, HC₃N, H₂S, SO, SO₂, NaCl, H₂O, H₂¹⁷O, H₂¹⁸O, NH₃, CS, CN, PO, PN, AlO, and tentatively, HNC (Lindqvist et al. 1988; Omont et al. 1993; Bujarrabal et al. 1994; Milam et al. 2007; Kim et al. 2010; Decin et al. 2010b; Menten et al. 2010; Justtanont et al. 2012; De Beck et al. 2013, 2015, and references therein). Some of the molecules observed up to date in IK Tau have been compared with chemical models and their line emission analysed with radiative transfer models (Willacy & Millar 1997; Duari et al. 1999; Cherchneff 2006; Kim et al. 2010; Decin et al. 2010a; Danilovich et al. 2016; Gobrecht et al. 2016; Li et al. 2016).

Nevertheless, most of the reported abundances in previous studies were derived from the analysis of a moderated number of lines (e.g. Milam et al. 2007; De Beck et al. 2013). Additionally, discrepancies remain between the predicted abundances and the observations, for example for SO₂ (Decin et al. 2010a; Gobrecht et al. 2016).

## 1.2. This paper

In this article we report the millimeter wavelength survey between ~79 and ~356 GHz carried out with the IRAM-30 m telescope toward IK Tau, which allowed us to detect rotational lines of 34 different species (including isotopologues). We detected for the first time in this source HCO⁺, NS, H₂CO, and NO, as well as several isotopologues of previously identified molecules, such as C¹⁸O, Si¹⁷O, Si¹⁸O, ²⁹SiS, ³⁰SiS, Si³⁴S, H¹³CN, ¹³CS, C³⁴S, H₂³⁴S, ³⁴SO, and ³⁴SO₂. For molecules with previous detections reported in the literature, we increased significantly the number of transitions observed, which is needed for a robust estimate of the excitation conditions and molecular abundances. We report the results of our analysis based on population diagrams, used to derive rotational temperatures and column densities. We also estimated fractional abundances which have been compared with values derived from previous observations and with predictions by chemical models. In the particular case of SO₂, we performed a radiative transfer calculation to study the excitation conditions of the ~90 lines detected with more detail. This suggests that this molecule is rather abundant not only in the intermediate and outer envelope but also in the inner, hotter and more dense regions of the CSE, where we estimate an average fractional abundance of ~$10^{-6}$ (with respect to H₂). This radiative transfer model also allowed us to verify the validity of the population diagram analysis for the rest of the species detected.

## 2. Observations

The observations presented in this paper correspond to a sensitive millimeter-wavelength (~79–356 GHz) survey carried out with the IRAM-30 m telescope toward the CSEs of two O-rich evolved stars, IK Tau and OH231.8+4.2, during several observing runs from 2009 to 2014. Partial results from the survey toward OH231.8+4.2 are reported in Sánchez Contreras et al. (2014, 2015) and Velilla Prieto et al. (2013, 2015).

We used the heterodyne Eight Mlxr Receiver (EMIR) working at four different wavelengths bands: E090 = 3 mm, E150 = 2 mm, E230 = 1.3 mm, and E330 = 0.9 mm (Carter et al. 2012). This receiver system was operated in single-sideband (SSB) mode for the E150 band and in dual sideband (2SB) mode for bands E090, E230, and E330. Two polarizations – horizontal and vertical – were available per sideband. The typical EMIR value image band rejection is approximately –14 dB or better, this implies that the peak intensity of a line entering through the image band is only $\le 4\%$ of its real value. We verified this value for the image band rejection measuring the relative intensities of strong lines that appear both in the signal and image bands.

Four different backends or spectrometers were connected to each receiver depending on their availability: the WIde Lineband Multiple Autocorrelator (WILMA), the fast Fourier Transform Spectrometer (FTS), the VERSatile SPectrometer Array (VESPA) and the 4 MHz spectrometer. The capabilities of these spectrometers and their usage are summarised in Table 1.

The observational technique used was the wobbler switching with a single pointing toward the position of the source (see
<table><caption>**Table 1.** Specifications for the spectrometers used.</caption><thead><tr><th>Name</th><th>SR (MHz)</th><th>VR (km s<sup>-1</sup>)</th><th>IBWEP (GHz)</th><th>Usage</th></tr></thead><tbody><tr><td>WILMA</td><td>2.000</td><td>1.7–7.6</td><td>3.7</td><td>E090, E150, E230, E330</td></tr><tr><td>FTS</td><td>0.195</td><td>0.2–0.7</td><td>4.0</td><td>E230, E330</td></tr><tr><td>VESPA</td><td>1.250</td><td>1.0–4.7</td><td>0.4</td><td>E090, E150, E230, E330</td></tr><tr><td>4 MHz</td><td>4.000</td><td>3.4–15.2</td><td>4.0</td><td>E150, E230, E330</td></tr></tbody></table>

**Notes.** Column 2: spectral resolution; Col. 3: spectral resolution in velocity units, the highest velocity resolution (the first number of the range) corresponds to 356 GHz and the lowest resolution to 79 GHz; Col. 4: instantaneous bandwidth in each polarization; Col. 5: EMIR bands observed with the corresponding spectrometer.

Sect. 1.1) and a wobbler throw of 120" in azimuth. We configured different setups (tuning steps) to observe both polarizations simultaneously until we covered the total frequency range available for each EMIR band. We selected a small overlap between adjacent setups to ensure a uniform calibration across the bands. During the observations we checked regularly the pointing and focus of the antenna every ~1.5 and ~4 h, respectively, on strong nearby sources. On-source integration times per setup were ~1 h. Calibration scans on the standard two loads + sky system were taken every ~18 min using the atmospheric transmission model (ATM) adopted by IRAM-30 m (Cernicharo et al. 1985; Pardo et al. 2001). Errors in the absolute flux calibration are expected to be ≤25%.

The data reduction, analysis and also most of the graphic representation were done using the GILDAS<fnref n="1" /> software package. The standard procedure followed to reduce the data and obtain the final spectra consists of the flagging of bad channels, the flagging of low-quality scans, the baseline substracting, and finally, the averaging of individual scans.

The output spectra obtained from the antenna are calibrated in antenna temperature ($T_A^*$), which can be converted to main beam temperature ($T_{mb}$) and brightness temperature ($T_B$) according to:

$$T_B = T_A^* \eta^{-1} bff^{-1}, \quad (1)$$

$$\eta^{-1} = F_{\text{eff}}/B_{\text{eff}}, \quad (2)$$

$$bff^{-1} = (\theta_b^2 + \theta_s^2)/\theta_s^2, \quad (3)$$

where $\eta$ is the main beam efficiency, $bff$ is the beam-filling factor, $B_{eff}$ is the main-beam efficiency of the antenna, $F_{eff}$ is the forward efficiency of the antenna, $\theta_s$ is the size (diameter) of the emitting region of the source, and $\theta_b$ is the half power beamwidth (HPBW) of the main beam of the antenna. See Table 2 for a summary of the relevant telescope parameters.

The half power width of the main beam can be approximated, using the values in Table 2, to a good accuracy by the expression:

$$\theta_b'' = 2460/v(\text{GHz}), \quad (4)$$

and the inverse of the main beam efficiency can be fitted (see Fig. 1) using the parameters in Table 2, to obtain:

$$\eta^{-1} \equiv F_{\text{eff}}/B_{\text{eff}} = 1.114 \exp\{(v(\text{GHz})/399.5)^2\}. \quad (5)$$

<table><caption>**Table 2.** Main parameters of the IRAM-30 m antenna measured with EMIR between 2009 and 2013 at representative frequencies.</caption><thead><tr><th>Frequency (GHz)</th><th><i>B</i><sub>eff</sub> (%)</th><th><i>F</i><sub>eff</sub> (%)</th><th>HPBW (")</th><th>S/<i>T</i><sub>A</sub><sup>*</sup> (Jy/κ)</th></tr></thead><tbody><tr><td>86</td><td>81</td><td>95</td><td>29<sup>†</sup></td><td>5.9<sup>†</sup></td></tr><tr><td>115</td><td>78</td><td>94</td><td>—</td><td>—</td></tr><tr><td>145</td><td>73</td><td>93</td><td>16<sup>†</sup></td><td>6.4<sup>†</sup></td></tr><tr><td>210</td><td>63</td><td>94</td><td>11<sup>†</sup></td><td>7.5<sup>†</sup></td></tr><tr><td>230</td><td>59</td><td>92</td><td>10.7<sup>‡</sup></td><td>—</td></tr><tr><td>280</td><td>49</td><td>87</td><td>—</td><td>—</td></tr><tr><td>340</td><td>35</td><td>81</td><td>7.5<sup>†</sup></td><td>10.9<sup>†</sup></td></tr><tr><td>345</td><td>34</td><td>80</td><td>—</td><td>—</td></tr></tbody></table>

**Notes.** Column 1: representative frequency; Col. 2: beam efficiency; Col. 3: forward efficiency; Col. 4: half power beam width; Col. 5: flux density to antenna temperature conversion factor in Jansky per Kelvin for a point-like source. (†) 2009 values. (‡) 2012 value. The values without symbols were reported on 2013. Source: http://www.iram.es/IRAMES/mainWiki/Iram30mEfficiencies

<figure><img src="image_1.png" /><figcaption>**Fig. 1.** Fit of the inverse of the main beam efficiency for the IRAM-30 m with EMIR.</figcaption></figure>

## 2.1. Observational results

Our results are based mainly on the spectra obtained with WILMA and FTS given their better spectral resolution and bandwidth. The data obtained with the 4 MHz spectrometer were used to check the edges of the setups that were only observed with WILMA, given that the 4 MHz bandwidth is slightly larger than the bandwidth of WILMA, but it has the same bandwidth than that of the FTS (see Table 1). VESPA data were used only to check certain line profiles. However, only WILMA was available to cover the full EMIR wavelength range. For example, FTS was not available in the E150 band at the epoch of the observations and also some technical issues prevented us from using the FTS with the E090 band.

The spectra of the full mm-wavelength survey carried out with IRAM-30 m toward IK Tau with the WILMA and the FTS spectrometers can be seen in Fig. 2 and also in more detail in Fig. C.1. The ¹²CO, ¹³CO, and C¹⁸O line profiles are shown in Fig. 3. In Table 3 we show a summary of the observational results.

<footnote n="1">¹ GILDAS is a world-wide software to process, reduce and analyse astronomical single-dish and interferometric observations mainly. It is maintained by the Institut de Radioastronomie Millimétrique (IRAM). See http://www.iram.fr/IRAMFR/GILDAS</footnote>
<figure><img src="image_2.png" /><figcaption>**Fig. 2.** Overall view of the survey observed with WILMA (top) and FTS (bottom). The spectral resolution is $\Delta\nu = 2$ MHz.</figcaption></figure>

<table><caption>**Table 3.** Summary of the observational results.</caption><thead><tr><th>Band</th><th>SP</th><th>ν<sub>obs</sub><br>(GHz)</th><th>rms<br>(mK)</th><th>Opacity<br>—</th></tr></thead><tbody><tr><td>E090</td><td>WILMA</td><td>79.3–115.7</td><td>1.5 (0.5)</td><td>0.12 (0.05)</td></tr><tr><td>E150</td><td>WILMA</td><td>128.4–174.8</td><td>2.7 (1.3)</td><td>0.19 (0.11)</td></tr><tr><td>E230</td><td>FTS</td><td>202.1–270.7<sup>†</sup></td><td>4.7 (0.6)</td><td>0.18 (0.03)</td></tr><tr><td>E330</td><td>FTS</td><td>277.1–356.2<sup>‡</sup></td><td>12.8 (10.4)</td><td>0.26 (0.16)</td></tr></tbody></table>

**Notes.** Values given between parentheses represent $1\sigma$ of the value. Col. 1 EMIR band; Col. 2 spectrometer; Col. 3 observed frequency windows in GHz; Col. 4 root mean square (rms) noise in units of $T_a^*$ for a spectral resolution of 2 MHz; Col. 5 zenith atmospheric opacity at the observed frequency. (†) 217.5–217.8 gap. (‡) 325.0–329.5 gap.

## 3. Line identification

For the line identification, we used the public line catalogues from the Cologne Database for Molecular Spectroscopy (CDMS, Müller et al. 2005) and the Jet Propulsion Laboratory (JPL, Pickett et al. 1998), together with a private spectroscopic catalogue that assembles information for more than five thousand spectral entries (atoms and molecules, including vibrationally excited states), compiled from extensive laboratory and theoretical works (the MADEX code, Cernicharo 2012).

Given the wavelength range covered in our observations, we detected, mainly, rotational transitions in the ground vibrational state, but also, rotational transitions in higher vibrational states (i.e. SiO $v = 1$, SiO $v = 2$, SiO $v = 3$, $^{29}$SiO $v = 1$, $^{29}$SiO $v = 2$, $^{29}$SiO $v = 3$, $^{30}$SiO $v = 1$, $^{30}$SiO $v = 2$, H$_2$O $v_2 = 1$, and H$_2$O $v_2 = 2$). We established the detection limit at $\ge 5\sigma$ with respect to the integrated intensity for well detected features, and between $3\sigma$ and $5\sigma$ for tentative detections, although, these tentative detections may be more reliable when they belong to well-known species that have been identified through other stronger lines.

We detected ~450 spectral features in the spectra of IK Tau, ~90% of which are lines in the signal side band of the receivers. Of the ~400 signal band features, ~350 lines have been unambiguously identified with rotational transitions of 34 different species (including vibrationally excited states), which are reported in Tables A.1 and A.2, along with some of their spectroscopic parameters and their fitted parameters. The rest of the lines (~35) remain unidentified, although, we proposed a tentative identification for some of them (see Table B.1).

There were several lines that we assigned to spurious features produced in the receivers in the range 167 475–174 800 MHz

<figure><img src="image_3.png" /><figcaption>**Fig. 3.** $^{12}$CO, $^{13}$CO, and C$^{18}$O lines detected with our millimeter wavelength survey with a spectral resolution of $\Delta\nu = 2$ MHz. The fit of each line to a function of the type given by Eq. (6) is shown in blue.</figcaption></figure>

(Table B.2). These spurious features are symmetrical replicas at both sides of certain strong real emission lines, with the intensities of the replicas decreasing with the frequency distance to the real feature. We show in Fig. B.1 an example of this problem.
The features of the image band and the spurious features were blanked in the final data.

We identified for the first time toward IK Tau, rotational lines of: HCO+, NO, H₂CO, NS, C¹⁸O, SiO v = 2, ²⁹SiO v = 2, ²⁹SiO v = 3, ³⁰SiO v = 2, Si¹⁷O, Si¹⁸O, ²⁹SiS, ³⁰SiS, Si³⁴S, SiS v = 1, H¹³CN, ¹³CS, C³⁴S, H₂³⁴S, ³⁴SO, ³⁴SO₂, and H₂O v₂ = 2. We also detected rotational lines of: ¹²CO, ¹³CO, SiO, SiO v = 1, SiO v = 3, ²⁹SiO, ²⁹SiO v = 1, ³⁰SiO v = 1, SiS, HCN, HNC, CS, NaCl, H₂S, SO, SO₂, PN, PO, CN, H₂O, and H₂O v₂ = 1. The result of the identification can be seen in Fig. C.1.

# 4. Data analysis

## 4.1. Line profiles

Most of the lines show profiles that can be reasonably well fitted with the so-called shell profile provided by the software CLASS<fnref n="2" />:

$$f(v) = \frac{A}{\Delta v} \frac{1 + 4H[(v - v_o)/\Delta v]^2}{1 + H/3}, \quad (6)$$

where A is the area under the profile, $v_o$ is the central frequency, $\Delta v$ is the full width at zero intensity, and H is the horn to centre ratio. The expansion velocity ($v_{exp}$) can be related to the $\Delta v$ of a line through the expression:

$$v_{exp} = c \frac{\Delta v/2}{v_o}, \quad (7)$$

where c is the speed of light.

In the case of a spherical CSE, there are several typical line profiles which are commonly found: U-shaped, parabolic, flat-topped, Gaussian-like or triangular. Each type of profile has a particular interpretation in terms of the size of the emitting region compared to the $\theta_b$ of the telescope, the optical thickness of the line, and the kinematical properties of the gas responsible of the spectroscopic feature (e.g. Zuckerman 1987; Habing & Olofsson 2004). All these profiles are described to a good accuracy by the shell function described before in Eq. (6).

In Fig. 4 we show a sample of the line profiles observed. Most of the lines display profiles that match one of the types mentioned before, although, some profiles are complex and have to be considered carefully in the analysis. We also observed lines that are significatively narrower and more intense than the average, that is, they show maser like spectral profiles (see Fig. 4 bottom-right panel). For the sake of consistency we used the shell profile described in Eq. (6) to fit all the lines detected, even for the narrow lines since that should give us an approximated idea of the characteristic velocity in the regions of the wind acceleration. The aim of the fit is to estimate the centroids and linewidths, however, the velocity integrated intensities given in Tables A.1, A.2, and B.1 were obtained integrating the whole line profiles. The line profiles observed are discussed in detail for each detected molecule in Sect. 6.

## 4.2. Population diagrams and fractional abundances

Using the population diagram technique (Goldsmith & Langer 1999), we derived rotational temperatures and column densities averaged in the emitting region of the molecules detected. These values were derived using the following equation:

$$\ln \left( \frac{N_u}{g_u} \right) = \ln \left( \frac{3k_B W}{8\pi^3 v S_{ul} \mu^2} \right) = \ln \left( \frac{N}{Z} \right) - \frac{E_u}{k_B T_{rot}}, \quad (8)$$

<figure><img src="image_4.png" /><figcaption>Fig. 4. Representative profiles of the lines observed. From top-left to bottom-right: U-shaped, Gaussian-like, triangular, flat-topped, parabolic, complex, flat-topped, and a narrow maser-like line. The spectral resolution is $\Delta v = 2$ MHz. The fit of each line to a function of the type given by Eq. (6) is shown in blue.</figcaption></figure>

where $N_u$ is the column density of the upper level, $g_u$ is the degeneracy of the upper level, W is the velocity-integrated intensity of the line, $k_B$ is the Boltzmann constant, v is the rest frequency of the transition, $S_{ul}$ is the line strength, $\mu$ is the dipole moment of the molecule, N is the total column density, Z is the partition function, $E_u$ is the upper level energy of the transition, and $T_{rot}$ is the rotational temperature. The results of the populations diagrams are reported in Sect. 5.2 and Appendix D.

This method relies on local thermodynamical equilibrium (LTE), optically thin emission, as well as an uniform rotational temperature for the gas shell, and it permits the analysis of all the molecules using a homogeneous criteria. Also, the size of the emitting region for each molecule has to be known to account for the proper dilution of the emission. We have adopted approximate sizes of the emitting regions of $\theta_s(^{12}\text{CO},^{13}\text{CO}) = 18''$ which is a representative value for the sizes measured in Bujarrabal & Alcolea (1991), Castro-Carrizo et al. (2010), and Kim et al. (2010). We also adopted the sizes $\theta_s(\text{HCN}, \text{H}^{13}\text{CN}) = 4''$ (Marvel 2005), $\theta_s = 2''$ for SiO isotopologues (Lucas et al. 1992), and $\theta_s \lesssim 0.7''$ for PO and PN (De Beck et al. 2013). Similar values have been also used for these molecules by Kim et al. (2010). For the rest of the molecules, which have not been mapped, we assumed emitting

<footnote n="2">² See http://www.iram.fr/IRAMFR/GILDAS</footnote>
region sizes according to observational constraints, previous estimations, or predictions by radiative transfer and chemical models. These values are given in Table 5 and discussed in Sect. 6. We note that the adopted sizes are uncertain for some molecules and also that the emitting region size may vary for each transition of a given molecule. In general, an underestimation of the size of any emitting region will cause an underestimation of the beam filling factor (see Eq. (3)) and, thus, an overestimation of the abundance, and vice versa.

There are additional sources of uncertainty in the values derived from the population diagrams. In particular, the kinetic temperature ($T_{kin}$) throughout the CSE is not expected to be constant. This effect is less important for the molecules whose emission arises from regions with very uniform physical conditions (inner layers, photodissociation layers, etc.), and it must be more important for species whose emission extends through the whole envelope, such as probably SO$_2$, for which we did a more detailed radiative transfer analysis (see Sect. 4.3).

In the population diagrams, we have included lines (unambiguously identified and unblended) with fluxes above $5\sigma$. For those molecules well known to be present in the envelope of IK Tau, we have also included lines with $3-5\sigma$ detections. In the case of molecules with a hyperfine structure that cannot be specifically resolved with the spectral resolution achieved, that is, CN, NS, and NO, we measured the total integrated intensity of the blend of the hyperfine components and we calculated the sum of the strength of the hyperfine components to compute their population diagrams. In the case of H$_2$S we fitted together the lines of the ortho and para species due to the scarce number of lines detected for each species individually.

We have not calculated population diagrams for the molecules SiO $v = 1$, SiO $v = 2$, SiO $v = 3$, $^{29}$SiO $v = 1$, $^{29}$SiO $v = 2$, $^{29}$SiO $v = 3$, $^{30}$SiO $v = 1$, $^{30}$SiO $v = 2$, H$_2$O, H$_2$O $v_2 = 1$ or H$_2$O $v_2 = 2$. Some of these lines are masers and their populations are expected to strongly deviate from a Boltzmann distribution. Also, the intensity of the lines of these molecules may vary with the stellar pulsation phase and, given that the observations spread over a period of time of approximately five years, the excitation conditions may have changed along the observational runs (see Sect. 6.1).

The fractional abundances averaged in the emitting region for the molecules detected are calculated using the following equation:

$$f(X) = N(X) \frac{f(^{13}\text{CO})}{N(^{13}\text{CO})}, \qquad (9)$$

where $f(X)$ and $N(X)$ represent the fractional abundance (with respect to H$_2$) and column density of the molecule analysed, respectively. $N(^{13}\text{CO})$ is the column density that we derived from the $^{13}\text{CO}$ population diagram, and $f(^{13}\text{CO}) = 1.4 \times 10^{-5}$ (Decin et al. 2010a).

### 4.3. Radiative transfer model: MADEX

MADEX (Cernicharo 2012) is a radiative transfer code which is able to operate under LTE and large velocity gradient (LVG) approximation (Goldreich & Kwan 1974). It solves the radiative transfer problem coupled with statistical equilibrium equations to derive the radiation field and populations of the levels on each point of a gas cloud. Then, the emergent profile of the lines is obtained through ray-tracing.

We used MADEX to calculate line opacities, excitation temperatures, and critical densities for the physical conditions expected at a given distance from the star, that is, $n(r)$ and $T_{kin}(r)$

<table><caption>**Table 4.** Parameters of the central Mira-type star and the CSE of IK Tau.</caption><thead><tr><th>Parameter</th><th>Value</th><th>Reference</th></tr></thead><tbody><tr><td>Distance (d)</td><td>265 pc</td><td>a</td></tr><tr><td>Stellar radius (R<sub>*</sub>)</td><td>2.5 × 10<sup>13</sup> cm</td><td>c</td></tr><tr><td>Stellar effective temperature (T<sub>*</sub>)</td><td>2200 K</td><td>c</td></tr><tr><td>Terminal expansion velocity (v<sub>∞</sub>)</td><td>18.5 km s<sup>-1</sup></td><td>e</td></tr><tr><td>AGB mass loss rate (M&#775;)</td><td>8 × 10<sup>-6</sup> M<sub>☉</sub> yr<sup>-1</sup></td><td>c</td></tr><tr><td>Gas kinetic temperature (T<sub>kin</sub>)</td><td>T<sub>*</sub> (r/R<sub>*</sub>)<sup>-0.6</sup></td><td>c</td></tr><tr><td>Dust temperature (T<sub>d</sub>)</td><td>T<sub>*</sub>(2r/R<sub>*</sub>)<sup>-0.4</sup></td><td>b</td></tr><tr><td>Dust condensation radius (R<sub>c</sub>)</td><td>8 R<sub>*</sub></td><td>d</td></tr><tr><td>Density of particles (n)</td><td>M&#775;/(4πr<sup>2</sup>(m<sub>g</sub>)v<sub>exp</sub>)</td><td>—</td></tr></tbody></table>

**Notes.** The density of particles is calculated with the law of conservation of mass, where $\langle m_g \rangle$ is the mean mass of gas particles (2.3 amu, after considering H$_2$, He, and CO). (a): Hale et al. (1997); (b): Decin et al. (2006); (c): Decin et al. (2010a); (d): Gobrecht et al. (2016); (e): this work (see Sect. 5.1).

(see Table 4), along with the column densities derived from the population diagrams (given in Table 5), and the $v_{exp}$ derived from the line fitting (given in Table A.1) for all the molecules detected. We systematically used this procedure to compare the line opacities obtained from the interpretation of the line profiles and to verify if a given molecule could be sub-thermally excited or not. These calculations are detailed in each subsection of the Sect 6. The sets of the collisional coefficients used for these calculations (when available) are: CO (Yang et al. 2010), SiO (Dayou & Balança 2006), H$_2$O (Daniel et al. 2011), HCN (Ben Abdallah et al. 2012), CS (Lique & Spielfiedel 2007), SiS (Toboła et al. 2008), NaCl (Quintana-Lacaci et al. 2016), SO (Lique et al. 2007), PN (Toboła et al. 2007), CN (Lique & Klos 2011), HCO$^+$ (Flower 1999), and H$_2$CO (Schöier et al. 2005, and references therein). We also obtained synthetic spectra that helped us to correctly identify the spectral features.

As it is shown in Sect 5.2, the detected SO$_2$ transitions have a large span in energies (i.e. from 7.7 up to 733.4 K). The population diagram analysis of this molecule indicates that it is possibly tracing out an inner region of the CSE, with a $T_{kin} \ge 290$ K which is not observed for other molecules, and also a more external region with $T_{rot} \sim 40$ K from where most of the emission of the rest of the molecules arises. To investigate more precisely the excitation conditions of SO$_2$ and to confirm or not the temperature stratification inferred from the population diagrams, we have performed a detailed radiative transfer calculation for SO$_2$. Our main goal is to investigate the presence of SO$_2$ in the innermost regions of the CSE.

The physical model consists on a spherical expanding envelope of dust and gas with a constant mass loss rate, similar to the model presented in Agúndez et al. (2012) but corrected for IK Tau (see Table 4). The radius of the star is $2.5 \times 10^{13}$ cm (Decin et al. 2010a). The density of particles is calculated with the law of conservation of mass, that is, $n \propto r^{-2}$ (valid for a CSE expanding at constant velocity). In terms of $v_{exp}$, the envelope is divided in three regions: (i) from 1 to 5 $R_*$ where $v_{exp} = 5$ km s$^{-1}$ as an average value in this region (Decin et al. 2010b), (ii) from 5 to 8 $R_*$ where $v_{exp} = 10$ km s$^{-1}$ according to the dust condensation radius (Gobrecht et al. 2016), and (iii) from 8 $R_*$ to the end of the CSE where $v_{exp} = 18.5$ km s$^{-1}$ (see Sect. 5.1). Concerning dust, we adopted a dust-to-gas ratio of $1.3 \times 10^{-4}$ for the region (i), a value of $1.2 \times 10^{-3}$ for region (ii) and a value of $2.3 \times 10^{-3}$ for the region (iii), according to the values given by Gobrecht et al. (2016) for silicates. The dust temperature has been taken from Decin et al. (2006; see Table 4). The optical
<table><caption>**Table 5.** Results from the population diagrams, sorted according to the molecular fractional abundance (relative to H₂) in descending order.</caption><thead><tr><th>Molecule</th><th>T<sub>rot</sub><br>(K)</th><th>Column density<br>(cm<sup>-2</sup>)</th><th>Abundance<br>—</th><th>θ<sub>s</sub><br>"</th><th>Lit. observational f(X)</th><th>Ref.<br>—</th><th>Lit. chemical model f(X)</th><th>Ref.<br>—</th></tr></thead><tbody><tr><td>CO</td><td>18 (4)</td><td>≥1.3 (0.3) × 10<sup>17</sup></td><td>≥1.1 × 10<sup>-4</sup></td><td>18</td><td>[2–3] × 10<sup>-4</sup></td><td>d, f</td><td>7 × 10<sup>-4</sup>–1 × 10<sup>-3</sup></td><td>γ</td></tr><tr><td><sup>13</sup>CO</td><td>21 (8)</td><td>1.6 (0.6) × 10<sup>16</sup></td><td>1.4 × 10<sup>-5</sup>†</td><td>18</td><td>[1–3] × 10<sup>-5</sup></td><td>d, f</td><td>—</td><td>—</td></tr><tr><td>SO<sub>2</sub> cold</td><td>40 (2)</td><td>>1.1 (0.1) × 10<sup>16</sup>‡</td><td>>9.6 × 10<sup>-6</sup>‡</td><td>2‡</td><td>2 × 10<sup>-6</sup>–1 × 10<sup>-5</sup></td><td>b, f</td><td>2 × 10<sup>-7</sup></td><td>ε</td></tr><tr><td>SiO</td><td>17 (2)</td><td>>9.1 (3.3) × 10<sup>15</sup></td><td>>8.0 × 10<sup>-6</sup></td><td>2</td><td>4 × 10<sup>-7</sup>–2 × 10<sup>-5</sup></td><td>e, d</td><td>2 × 10<sup>-5</sup>–9 × 10<sup>-5</sup></td><td>γ</td></tr><tr><td>SO</td><td>17 (1)</td><td>≥8.9 (1.6) × 10<sup>15</sup></td><td>≥7.8 × 10<sup>-6</sup></td><td>2</td><td>3 × 10<sup>-7</sup>–3 × 10<sup>-6</sup></td><td>f, a</td><td>2 × 10<sup>-12</sup>–9 × 10<sup>-7</sup></td><td>γ, ε</td></tr><tr><td>SiS</td><td>64 (5)</td><td>5.2 (0.6) × 10<sup>15</sup></td><td>4.6 × 10<sup>-6</sup></td><td>2</td><td>8 × 10<sup>-9</sup>–1 × 10<sup>-5</sup></td><td>d</td><td>8 × 10<sup>-10</sup>–3 × 10<sup>-6</sup></td><td>β, ε</td></tr><tr><td>SO<sub>2</sub> warm</td><td>290 (60)</td><td>>3.1 (1.0) × 10<sup>15</sup>‡</td><td>>2.7 × 10<sup>-6</sup>‡</td><td>2‡</td><td>—</td><td>—</td><td>2 × 10<sup>-14</sup>–4 × 10<sup>-9</sup></td><td>γ</td></tr><tr><td><sup>29</sup>SiO</td><td>17 (2)</td><td>≥2.1 (0.6) × 10<sup>15</sup></td><td>≥1.8 × 10<sup>-6</sup></td><td>2</td><td>—</td><td>—</td><td>—</td><td>—</td></tr><tr><td>PO</td><td>17 (2)</td><td>2.0 (0.4) × 10<sup>15</sup></td><td>1.7 × 10<sup>-6</sup></td><td>0.7</td><td>5 × 10<sup>-8</sup>–6 × 10<sup>-7</sup></td><td>c</td><td>2 × 10<sup>-10</sup>–1 × 10<sup>-7</sup></td><td>γ</td></tr><tr><td><sup>30</sup>SiO</td><td>17 (2)</td><td>≥1.5 (0.5) × 10<sup>15</sup></td><td>≥1.3 × 10<sup>-6</sup></td><td>2</td><td>—</td><td>—</td><td>—</td><td>—</td></tr><tr><td>H<sub>2</sub>S</td><td>39 (3)</td><td>1.4 (0.3) × 10<sup>15</sup></td><td>1.2 × 10<sup>-6</sup></td><td>2</td><td>—</td><td>—</td><td>6 × 10<sup>-13</sup>–3 × 10<sup>-5</sup></td><td>β, γ</td></tr><tr><td><sup>34</sup>SO<sub>2</sub></td><td>35 (6)</td><td>1.1 (0.3) × 10<sup>15</sup></td><td>9.6 × 10<sup>-7</sup></td><td>2</td><td>—</td><td>—</td><td>—</td><td>—</td></tr><tr><td>CS</td><td>25 (2)</td><td>9.2 (1.0) × 10<sup>14</sup></td><td>8.0 × 10<sup>-7</sup></td><td>2</td><td>8 × 10<sup>-8</sup>–3 × 10<sup>-7</sup></td><td>f, g</td><td>2 × 10<sup>-11</sup>–2 × 10<sup>-5</sup></td><td>γ, β</td></tr><tr><td><sup>34</sup>SO</td><td>14 (1)</td><td>8.9 (2.4) × 10<sup>14</sup></td><td>7.8 × 10<sup>-7</sup></td><td>2</td><td>—</td><td>—</td><td>—</td><td>—</td></tr><tr><td>PN</td><td>18 (2)</td><td>8.3 (1.7) × 10<sup>14</sup></td><td>7.3 × 10<sup>-7</sup></td><td>0.7</td><td>3 × 10<sup>-7</sup></td><td>c</td><td>4 × 10<sup>-10</sup>–6 × 10<sup>-7</sup></td><td>γ</td></tr><tr><td>HCN</td><td>10 (1)</td><td>>7.6 (2.9) × 10<sup>14</sup></td><td>>6.6 × 10<sup>-7</sup></td><td>4</td><td>4 × 10<sup>-7</sup>–1 × 10<sup>-6</sup></td><td>i, f</td><td>6 × 10<sup>-12</sup>–3 × 10<sup>-4</sup></td><td>γ, β</td></tr><tr><td><sup>29</sup>SiS</td><td>78 (5)</td><td>4.9 (0.4) × 10<sup>14</sup></td><td>4.3 × 10<sup>-7</sup></td><td>2</td><td>—</td><td>—</td><td>—</td><td>—</td></tr><tr><td>Si<sup>34</sup>S</td><td>70 (10)</td><td>4.5 (0.8) × 10<sup>14</sup></td><td>3.9 × 10<sup>-7</sup></td><td>2</td><td>—</td><td>—</td><td>—</td><td>—</td></tr><tr><td>NaCl</td><td>67 (7)</td><td>3.5 (0.6) × 10<sup>14</sup></td><td>3.1 × 10<sup>-7</sup></td><td>0.3</td><td>4 × 10<sup>-9</sup></td><td>h</td><td>4 × 10<sup>-12</sup>–1 × 10<sup>-8</sup></td><td>γ</td></tr><tr><td><sup>30</sup>SiS</td><td>83 (9)</td><td>3.5 (0.5) × 10<sup>14</sup></td><td>3.1 × 10<sup>-7</sup></td><td>2</td><td>—</td><td>—</td><td>—</td><td>—</td></tr><tr><td>H<sub>2</sub>CO</td><td>10 (2)</td><td>2.8 (0.5) × 10<sup>14</sup></td><td>2.4 × 10<sup>-7</sup></td><td>2</td><td>—</td><td>—</td><td>1 × 10<sup>-9</sup>–5 × 10<sup>-7</sup></td><td>α, ε</td></tr><tr><td>CN</td><td>9 (2)</td><td>1.5 (0.7) × 10<sup>14</sup></td><td>1.3 × 10<sup>-7</sup></td><td>6</td><td>2 × 10<sup>-10</sup>–2 × 10<sup>-7</sup></td><td>d, f</td><td>3 × 10<sup>-13</sup>–3 × 10<sup>-7</sup></td><td>β, δ</td></tr><tr><td>Si<sup>18</sup>O</td><td>24 (8)</td><td>1.5 (0.8) × 10<sup>14</sup></td><td>1.3 × 10<sup>-7</sup></td><td>2</td><td>—</td><td>—</td><td>—</td><td>—</td></tr><tr><td>Si<sup>17</sup>O</td><td>12 (2)</td><td>1.0 (0.4) × 10<sup>14</sup></td><td>8.7 × 10<sup>-8</sup></td><td>2</td><td>—</td><td>—</td><td>—</td><td>—</td></tr><tr><td><sup>13</sup>CS</td><td>34 (3)</td><td>9.6 (0.8) × 10<sup>13</sup></td><td>8.4 × 10<sup>-8</sup></td><td>2</td><td>—</td><td>—</td><td>—</td><td>—</td></tr><tr><td>H<sup>13</sup>CN</td><td>11 (2)</td><td>9.2 (2.5) × 10<sup>13</sup></td><td>8.0 × 10<sup>-8</sup></td><td>4</td><td>—</td><td>—</td><td>—</td><td>—</td></tr><tr><td>C<sup>34</sup>S</td><td>24 (1)</td><td>6.9 (0.6) × 10<sup>13</sup></td><td>6.0 × 10<sup>-8</sup></td><td>2</td><td>—</td><td>—</td><td>—</td><td>—</td></tr><tr><td>NS</td><td>18 (2)</td><td>2.6 (0.5) × 10<sup>13</sup></td><td>2.3 × 10<sup>-8</sup></td><td>6</td><td>—</td><td>—</td><td>7 × 10<sup>-13</sup>–8 × 10<sup>-9</sup></td><td>β, δ</td></tr></tbody></table>

**Notes.** We give the formal uncertainties derived from the population diagram fits within parentheses. Column 5: size adopted for the emitting region. Columns 6 and 7: range of the fractional abundances given in the literature, derived from the following works based on observations: (a): Bujarrabal et al. (1994); (b): Danilovich et al. (2016); (c): De Beck et al. (2013); (d): Decin et al. (2010a); (e): González Delgado et al. (2003); (f): Kim et al. (2010); (g): Lindqvist et al. (1988); (h): Milam et al. (2007); (i): Schöier et al. (2013). Columns 8 and 9: range of the fractional abundances given in the literature, which were derived from the following chemical and shock models: (α): Agúndez et al. (2010); (β): Duari et al. (1999); (γ): Gobrecht et al. (2016); (δ): Li et al. (2016); (ε): Willacy & Millar (1997). (†) Value given in Table 6 in Decin et al. (2010a). (‡) See Sect. 6.5.1.

properties of the silicate dust and the size of the grains (0.1 µm) have been adopted from Suh (1999). For the microturbulence velocity we adopted the values given in Agúndez et al. (2012) for the C-rich CSE IRC+10216. We used different SO₂ abundance profiles (see Fig. 5) in order to investigate the presence of warm SO₂ in the inner regions of the CSE. For the calculations we used a set of collisional coefficients which are described in Appendix E. The results of the radiative transfer model are shown in Fig. 11 and discussed in Sect. 6.5.1.

# 5. Results

Here we present the general results from the analysis, which are summarised in Table 5 and Fig. 6.

## 5.1. Expansion velocity

The terminal expansion velocity of the CSE ($v_{\infty}$) can be estimated from the linewidths of the spectral features that arise from the outer ($r > 8 R_{*}$, Gobrecht et al. 2016) envelope regions where the gas has been fully accelerated to this maximal velocity. We estimated the $v_{\infty}$ from the <sup>13</sup>CO linewidths (see Table A.1) given that <sup>13</sup>CO emission certainly extends beyond the wind acceleration region, and the line profiles display a clear U-shaped profile (see Fig. 3) and, thus, no significant

<figure><img src="image_5.png" /><figcaption>**Fig. 5.** Radial profiles of the abundance adopted for the radiative transfer model of the lines of SO₂. We tested three different radial profiles: (i) an inner distribution of SO₂ with $f(\text{SO}_2) = 3 \times 10^{-6}$ between 1–8 R<sub>*</sub> (red line); (ii) a constant radial profile with $f(\text{SO}_2) = 2 \times 10^{-6}$ between 8–640 R<sub>*</sub> (blue line); and (iii) a two component profile (green line) which includes an inner warm component plus an extended component of SO₂. The results of the different models are shown in Fig. 11.</figcaption></figure>

opacity broadening is expected (Phillips et al. 1979). Assuming a mean density of $n(H_2) = 10^5$ cm⁻³, and the temperature and column density given in Table 5, the highest opacity measured
<figure><img src="image_6.png" /><figcaption>**Fig. 6.** Graph of the rotational temperatures (orange bars) and column densities (blue bars), with their formal uncertainties (black lines), derived from the population diagrams. Vertical blue arrows are plotted to indicate column density lower limits over each corresponding molecule. The temperature scale is represented on the left vertical axis, and the column density logarithmic scale is represented on the right vertical axis. The limits of the temperature scale are different in both boxes to improve the visual aspect of the figures. The values represented are tabulated in Table 5.</figcaption></figure>

with MADEX is $\tau = 0.13$ for the $^{13}$CO J = 3–2 line. We derived $v_{\infty} = 18.6 \pm 1.2$ km s$^{-1}$ which is in good agreement with previous measurements (e.g. De Beck et al. 2013).

Most of the rest of the lines detected display linewidths consistent with $v_{\infty}$ like for example SiS (see Tables A.1, A.2 and Fig. 7). In the particular case of H$_2$CO, we stacked the lines with K = 0, K = 1, and K = 2 to confirm that H$_2$CO linewidths are consistent with $v_{\exp} = v_{\infty}$ (Fig. 8). There are also several lines with linewidths larger than $v_{\infty}$, due to a blend of several hyperfine components (as occurs for NO and NS), or a poor fitting for lines detected below $5\sigma$.

Additionally, the lines with $E_u \ge 160$ K, that is, the lines of vibrationally excited states (Table A.2), H$_2$O, PO, NaCl, and several high-$E_u$ SO$_2$ lines, have line profiles indicative of $v_{\exp} \lesssim 10$ km s$^{-1}$, consistent with emission from the inner regions

of the CSE where the gas is still being accelerated ($r < 8 R_*$, i.e. $\sim 2 \times 10^{14}$ cm$^{-2}$, Decin et al. 2010b; Gobrecht et al. 2016). In order to obtain a more reliable estimate of the NaCl linewidths, we stacked the lines with $E_u = [22.5–56.9]$ K (group 1), $E_u = [85.0–118.7]$ K (group 2), and $E_u = [131.2–187.4]$ K (group 3) (see Fig. 8). The linewidths measured are consistent with $v_{\exp} = 14.8 \pm 2.2$ km s$^{-1}$ (group 1), $v_{\exp} = 20.1 \pm 1.1$ km s$^{-1}$ (group 2), and $v_{\exp} = 11.8 \pm 1.1$ km s$^{-1}$ (group 3). Therefore, it seems that $v_{\exp} < v_{\infty}$ at least for the lines of the group 3, that is to say, the high-$E_u$ lines.

There are also some lines with low $E_u$ (<200 K) which appear to have expansion velocities of $\sim 10$ km s$^{-1}$ (e.g. SO$_2$, see Fig. 7). Such low values of the $v_{\exp}$ were measured for weak SO$_2$ lines with low S/N, thus, the linewidths observed in their profiles are uncertain.
<figure><img src="image_7.png" /><figcaption>**Fig. 7.** Plot of the $v_{\text{exp}}$ derived from the fit of the lines as a function of the $E_u$ of the corresponding transition for several molecules. In the top, we did not represent each error bar to improve the visualization of the figure. A typical error bar of 4 km s$^{-1}$ is plotted in the top left corner of the box. The values and uncertainties of the bottom correspond to the values given in Table A.2. For those lines that were observed in different epochs, we adopted an average value of the different measurements for the $v_{\text{exp}}$ and its uncertainty.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>**Fig. 8.** Line stacking of the H$_2$CO (left) and the NaCl (right) lines detected, with a spectral resolution of 2 MHz. Black spectrum correspond to the H$_2$CO $K_a = 0$ lines and the NaCl lines with $E_u = [22.5–56.9]$ K, pink spectrum correspond to the H$_2$CO $K_a = 1$ lines and the NaCl lines with $E_u = [85.0–118.7]$ K, and blue spectrum correspond to the H$_2$CO $K_a = 2$ lines and the NaCl lines with $E_u = [131.2–187.4]$ K.</figcaption></figure>

## 5.2. Rotational temperatures, column densities and fractional abundances

The population diagrams for all the molecules detected are shown in Appendix D, in Figs. D.1–D.13. Most diagrams display a linear trend, however, the population diagrams of, for example, SiO, $^{29}$SiO, or SO, display departures from a linear behaviour, which are more notable for low *J* transitions (see e.g. Fig. D.2). These departures are discussed in detail in Sect. 6

<table><caption>**Table 6.** Isotopic ratios obtained from the abundances derived with the population diagrams.</caption><thead><tr><th>Ratio</th><th>Value</th><th>From</th></tr></thead><tbody><tr><td><sup>12</sup>C/<sup>13</sup>C</td><td>&gt;8 (~10)</td><td>CO</td></tr><tr><td><sup>12</sup>C/<sup>13</sup>C</td><td>10</td><td>CS</td></tr><tr><td><sup>12</sup>C/<sup>13</sup>C</td><td>&gt;8 (~15)</td><td>HCN</td></tr><tr><td><sup>16</sup>O/<sup>18</sup>O</td><td>≈61</td><td>SiO</td></tr><tr><td><sup>16</sup>O/<sup>17</sup>O</td><td>≈91</td><td>SiO</td></tr><tr><td><sup>28</sup>Si/<sup>29</sup>Si</td><td>&gt;4 (~18)</td><td>SiO</td></tr><tr><td><sup>28</sup>Si/<sup>29</sup>Si</td><td>11</td><td>SiS</td></tr><tr><td><sup>28</sup>Si/<sup>30</sup>Si</td><td>&gt;6 (~34)</td><td>SiO</td></tr><tr><td><sup>28</sup>Si/<sup>30</sup>Si</td><td>16</td><td>SiS</td></tr><tr><td><sup>32</sup>S/<sup>34</sup>S</td><td>&gt;8 (~15)</td><td>SO</td></tr><tr><td><sup>32</sup>S/<sup>34</sup>S</td><td>13</td><td>CS</td></tr><tr><td><sup>32</sup>S/<sup>34</sup>S</td><td>12</td><td>SiS</td></tr><tr><td><sup>32</sup>S/<sup>34</sup>S</td><td>&gt;10 (~13)<sup>†</sup></td><td>SO<sub>2</sub></td></tr></tbody></table>

**Notes.** Opacity corrected values are given between parentheses (see Sect. 6.10). (†) This value was computed using only the cold SO$_2$ component in Table 5.

and they reflect the effect of optically thick emission and/or sub-thermal excitation. For SO$_2$ we see two different trends for lines below and above $E_u = 160$ K. We fitted both separately and their implications are explained in Sect. 6.5.1.

The rotational temperatures derived range from 9 K (for CN) to 290 K (for the warm component of SO$_2$), with most of the molecules displaying rotational temperatures between 15 K and 40 K (see Fig. 6). The column densities range from $≥1.3 \times 10^{17}$ cm$^{-2}$ for $^{12}$CO, down to $2.6 \times 10^{13}$ cm$^{-2}$ for NS. We obtained averaged fractional abundances using the Eq. (9), which range between $>1.1 \times 10^{-4}$ for $^{12}$CO, down to $2.3 \times 10^{-8}$ for NS. We calculated the isotopic ratios of the molecules for which several isotopologues were detected. Results are presented in Table 6 and discussed in Sect. 6.10.

# 6. Discussion: an overall picture of the whole envelope

## 6.1. Variability

The excitation mechanisms of the lines are a mix of collisional and radiative processes, where the radiation emitted by the central star has an impact on the population of the rotational levels (e.g. H$_2$O Agúndez & Cernicharo 2006). Since AGB stars are variable with periods of one to two years, the net excitation mechanism for those molecules is variable and the results obtained from the analysis of the molecular lines of AGB CSEs could be affected by this variability. In the case of O-rich stars, the impact of radiative pumping effects on masers is well-known (e.g. Nakashima & Deguchi 2007). Thermal line observations of CSEs have also to be considered carefully in the sub-millimeter and far-IR domain, while for the millimeter wavelength range, specially for low-*J* lines, the variation of the stellar light has not a major impact (Cernicharo et al. 2014). Given that our observations spread over a period of approximately five years, we observed a few spectral ranges at different epochs and here we discuss the results observed.

For the spectra observed at different epochs we observed intensity variations of less than 25% for the rotational lines of the
<figure><img src="image_9.png" /></figure>

**Fig. 9.** Variability of some of the lines observed. The observation dates which correspond to the spectra are shown in the top right corner of each box with its corresponding colour. The spectral resolution is 2 MHz. As discussed in Sect. 6.1, variations of up to a 25% are within the uncertainties of the calibration, pointing and baseline subtraction (i.e. *left boxes*). Variations of intensity higher than a 25% are observed in vibrationally excited lines or masers (i.e. *right boxes*).

ground vibrational levels. This value (i.e. 25%) was taken as the calibration uncertainty (see Sect. 2), and considered in the results presented throughout this work (Fig. 9 left). However, we observed strong intensity variations (>25%) for several lines, like for example the SiO *v* = 1 *J* = 7–6, (see Table A.2 and Fig. 9). These strongly variable lines correspond to rotational transitions of vibrationally excited states with *v*<sub>exp</sub> ≲ 10 km s<sup>-1</sup>, which arise from very inner regions of the CSE. The excitation mechanism of these lines may be correlated with the stellar phase, thus, it is not possible to extract any information of their abundances. In Table A.2 we present the fit parameters for these vibrationally excited and maser lines, where we included the mean Julian date of the observation and, in case that the feature was observed in different epochs, multiple measurements of that spectral feature.

## 6.2. O-bearing molecules

CO is the most abundant molecule in IK Tau (after H₂). It is distributed along the whole CSE with a size of ~[7–8] × 10¹⁶ cm (see Sect. 1.1). The ¹²CO *J* = 2–1 and ¹²CO *J* = 3–2 lines display parabolic profiles typical of optically thick lines, while the ¹²CO *J* = 1–0 line, all the ¹³CO lines, and the C¹⁸O lines show U-shaped profiles typical of optically thin lines (Fig. 3). The emission of all the CO isotopologues is probably spatially resolved considering the typical beam size (Table 2) and the shape of the line profiles. The population diagrams of ¹²CO and ¹³CO hint small departures from a linear trend, owing to high optical depth and/or sub-thermal excitation (Fig. D.1). The results can be seen in Table 5 and Fig. 6. We derived a fractional abundance *f*(^12CO) ≳ 1.1 × 10⁻⁴ (with respect to H₂) in agreement with previous estimates. For C¹⁸O, we estimated *f*(C¹⁸O) ~ 4 × 10⁻⁸, assuming the same excitation temperature (20 K) and emitting size as for ¹³CO.

We used MADEX to estimate the opacities of the CO lines (using the $T_{\text{kin}}$, the $v_{\text{exp}}$ derived from the linewidths, the column density derived from the population diagram, and the $n(\text{H}_2)$ density at the outer radius of the shell according to the equation given in Table 4). With these input parameters, MADEX predicts

that the ¹²CO *J* = 2–1 and the *J* = 3–2 lines are moderately thick ($\tau \lesssim 1.4$), while the *J* = 1–0 line is optically thin ($\tau \sim 0.2$). This is consistent with CO tracing the coolest, outermost layers of the CSE and ¹³CO probing also regions deeper inside.

For SiO isotopologues we have adopted an emitting size equivalent to 7.9×10¹⁵ cm (2′′) at a distance of 265 pc (Sect. 1.1). All the line profiles of the different SiO isotopologues are parabolic, consistent with optically thick emission. The rotational diagrams of all the SiO isotopologues display small departures from a linear trend, except perhaps for Si¹⁷O (Fig. D.2). We found similar $T_{\text{rot}}$ for all the isotopologues, that is, $T_{\text{rot}} \sim 20$ K, which are much lower than the $T_{\text{kin}}$ expected at a distance of 1'' from the star (i.e. $T_{\text{kin}} \sim 105$ K). Hence, sub-thermal excitation may have an impact on the values derived from the population diagrams of SiO isotopologues.

MADEX (see Sect. 4.3) predicted $\tau>1$ for all of the SiO, ²⁹SiO and ³⁰SiO lines (except for the *J* = 2–1 lines of ²⁹SiO and ³⁰SiO, for which MADEX predicted $\tau \lesssim 0.6$.) These values are consistent with the observed line profiles. For Si¹⁸O and Si¹⁷O lines, MADEX predicted $\tau < 0.5$. Therefore, except for Si¹⁸O and Si¹⁷O, the column densities and the abundances derived for the SiO isotopologues, given in Table 5, should be considered lower limits. The lower limit obtained, $f(\text{SiO}) > 8.0 \times 10^{-6}$, is in good agreement with previous measures (Decin et al. 2010a, and references therein), and, in principle, is also consistent with the low SiO abundances predicted by the model by Gobrecht et al. (2016) that proposes the formation of SiO in abundance under thermodynamical equilibrium (TE) in the stellar photosphere, and a significant abundance decay (to $1.5 \times 10^{-5}$) already at 6 $R_*$ mainly due to dust condensation.

## 6.3. C-bearing molecules

We detected emission of molecules, like CS, HCN and HNC, that are typically found in C-rich CSEs (e.g. Bujarrabal et al. 1994; Cernicharo et al. 2000; Zhang et al. 2009).

According to Marvel (2005), the HCN emission arises from a compact region with $\theta_s \sim 4''$, which we adopted in this work.
For CS, there are no observational constraints on the size of the emission, therefore, we adopted a size of $\theta_s = 2''$ which is the same size used for SiO and it is consistent with the extent of the CSE emission predicted by chemical models (Li et al. 2016). Adopting these sizes we obtained $T_{\text{rot}}(\text{HCN}) \sim 10$ K and $T_{\text{rot}}(\text{CS}) \sim 25$ K, and $N_{\text{tot}}(\text{HCN}) \ge 8 \times 10^{14} \text{ cm}^{-2}$ and $N_{\text{tot}}(\text{CS}) \sim 9 \times 10^{14} \text{ cm}^{-2}$ (Figs. D.3 and D.4).

Using MADEX, we found optically thick lines ($\tau \ge 1.5$) for HCN, and moderately thick lines ($\tau \le 1.2$) for H$^{13}$CN. Therefore, the column density and the abundance of HCN should be considered as lower limits. In the case of CS isotopologues, with the physical conditions expected at $r \sim 1''$, MADEX predicted optically thin lines ($\tau \le 1.0$). Finally, given that $T_{\text{kin}}(r \le 1'') \ge 100$ K, the lines of HCN and CS isotopologues are most likely sub-thermally excited.

The rotational temperatures and abundances derived for HCN and CS isotopologues (see Table 5) are consistent with previous measurements in IK Tau (Lindqvist et al. 1988; Kim et al. 2010). The HCN abundance is in the high end of the abundance range deduced by Schöier et al. (2013) in a sample of M-type AGB stars. The TE models for O-rich CSEs do not account for the HCN and CS abundances observed in O-rich CSEs, predicting values of $f(\text{HCN}) \sim 10^{-11}$ and $f(\text{CS}) \sim 10^{-10}$ (Duari et al. 1999; Gobrecht et al. 2016). The inclusion of shocks can contribute to enhance the formation of HCN in O-rich stars (Duari et al. 1999; Cherchneff 2006; Gobrecht et al. 2016), but it also brings up a theoretical homogeneity on the expected HCN abundances among different chemical types of stars that it is not observed, as noted by Schöier et al. (2013). Other authors invoked the photochemistry to try to explain the abundances of C-bearing molecules observed in O-rich CSEs (Nercessian et al. 1989; Ziurys et al. 2009). In particular, the chemical model of Willacy & Millar (1997) predicts peak abundances of $f(\text{HCN}) \sim 1 \times 10^{-7}$ and $f(\text{CS}) \sim 3 \times 10^{-7}$, although the carbon source proposed by these authors is CH$_4$ which has been later on refuted (Marvel 2005). Additionally, it has been also proposed that CSEs could be clumpy, hence, photochemistry could be important also in the inner layers of the envelopes (Agúndez et al. 2010). Our results do not conclude clearly which is the most likely scenario, although, our derived abundances are more similar to those predicted by the models of Gobrecht et al. (2016).

Finally, we detected two HNC lines, in particular, the $J = 1-0$, and the $J = 3-2$ line, which is blended with the image of the SiO $J = 6-5$ line. We estimated $f \sim 8 \times 10^{-9}$, assuming an excitation temperature of ~30 K and a size of 2'' for the emitting region, which are average values for these parameters.

## 6.4. Refractory species

We confirmed the presence of two important refractory molecules which are mainly found in C-rich envelopes: SiS and NaCl. The emission of these molecules has not been mapped in previous studies and, therefore, the size of the emitting region is unknown. The NaCl line profiles, with $v_{\text{exp}} \sim 14$ km s$^{-1}$, are narrower than those of SiS, consistent with $v_{\text{exp}} \sim 18.5$ km s$^{-1}$, which suggests a more inner distribution of NaCl around the star (see Fig. 7). This molecule may condense onto the dust grains beyond the dust condensation radius, as proposed by Milam et al. (2007). The profiles of the lines of NaCl and SiS isotopologues indicate spatially unresolved emission, which is compatible with the Gaussian-like profiles observed in the case of NaCl, and the triangular or parabolic profiles observed for

the SiS isotopologues. Moreover, the Gaussian-like profiles observed for NaCl may support that the emission of this molecule arises from the innermost regions of the CSE, where the gas has not been fully accelerated.

We adopted a size of $\theta_s = 2''$ for SiS isotopologues, as a first guess considering the emission size of SiO ($\theta_s = 2''$). This size is also consistent with the size predicted by recent chemical model of IK Tau (Li et al. 2016). For NaCl we adopted a size of $\theta_s(\text{NaCl}) = 0.3''$ (Milam et al. 2007). We derived similar rotational temperatures for SiS and NaCl (i.e. $T_{\text{rot}} \sim 65$ K) even higher for $^{29}$SiS, $^{30}$SiS, and $^{33}$SiS (see Figs. D.5 and D.6). According to the size adopted for SiS (i.e. $r \le 4 \times 10^{15}$ cm), we estimated $T_{\text{kin}} \ge 105$ K, and $n(\text{H}_2) \ge 3.5 \times 10^5 \text{ cm}^{-3}$. For the size adopted for NaCl (i.e. $r \le 6 \times 10^{14}$ cm), we estimated $T_{\text{kin}} \ge 330$ K. Hence, SiS and NaCl are most likely sub-thermally excited. We estimated critical densities for the SiS lines of $n_{\text{crit}} \sim [10^4-10^6] \text{ cm}^{-3}$ for a temperature of ~105 K, therefore, $n \le n_{\text{crit}}$ for several lines of SiS confirming sub-thermal excitation. For NaCl the critical densities expected are even higher, $n_{\text{crit}} \ge 5 \times 10^7 \text{ cm}^{-3}$, due to the high dipole moment of NaCl. MADEX predicted optically thin lines for both SiS ($\tau < 0.6$) and NaCl ($\tau < 0.3$).

We derived $f(\text{SiS}) \sim 5 \times 10^{-6}$. This value is in good agreement with the estimations by Kim et al. (2010). The chemical model by Gobrecht et al. (2016) predicts a SiS abundance of $4 \times 10^{-8}$ under TE and up to ~3 $\times 10^{-7}$ including dust condensation and shocks due to the pulsation of the star, which is at least one order of magnitude lower than our results. Willacy & Millar (1997) used SiS in their chemical models as a parent molecule with an abundance consistent with our observations (see Table 5).

Concerning NaCl, Milam et al. (2007) derived a rotational temperature and a column density consistent with our results. However, Milam et al. (2007) derived a fractional abundance ~80 times lower than ours, through the population diagram of two low S/N NaCl emission lines, and also a radiative transfer calculation using the code by Bieging & Tafalla (1993), with a set of SiO-corrected collisional coefficients. We detected 13 NaCl lines which cover a wide range in $E_u$ and have better S/N, from which we derived an average fractional abundance of $f(\text{NaCl}) = 3 \times 10^{-7}$ (see Table 5 and Fig. D.6). We cannot rule out uncertainties in our estimation due to the emitting size, and the $^{13}$CO column density adopted, which could not be representative in the region of NaCl emission. Moreover, NaCl line profiles are not incompatible with $\theta_s(\text{NaCl}) \ge 0.3''$, in particular, if $\theta_s(\text{NaCl}) = 1''$ we would derive $f(\text{NaCl}) = 3 \times 10^{-8}$. TE calculations predict abundances of $10^{-11}$ up to $10^{-7}$ (Tsuji 1973; Milam et al. 2007), while Gobrecht et al. (2016) models (TE and shocks) predicts NaCl abundances between $4 \times 10^{-12}$ up to $1 \times 10^{-8}$. It would be necessary to obtain maps of the NaCl spatial distribution in order to clarify these discrepancies.

## 6.5. S-bearing molecules

Here we discuss the detected emission of H$_2$S, SO, and SO$_2$. The first detection of these molecules toward IK Tau and their chemistry in O-rich CSEs was presented in Omont et al. (1993) and references therein. Omont et al. (1993) only detected one line of H$_2$S, and they were not able to estimate its abundance toward IK Tau. The emission of SO and SO$_2$ molecules in O-rich CSEs, including IK Tau, has been recently reviewed and modelled by Danilovich et al. (2016).

We detected three ortho and one para lines of H$_2$S as well as one line of o-H$_2$$^{34}$S, which point out $v_{\text{exp}} \sim v_{\infty}$. The profiles of the
<figure><img src="image_10.png" /><figcaption>**Fig. 10.** Line profiles of some of the SO lines identified. The quantum numbers of each transition are plotted in red in each box. The spectral resolution is 2 MHz for all the spectra shown.</figcaption></figure>

lines indicate spatially unresolved emission. Since there are not maps of the H₂S emission, we adopted a size of θₛ(H₂S) = 2'' which is consistent with the size predicted by chemical models (Li et al. 2016). Given that we only detected two lines of o-H₂S with S/N > 5, we calculated the population diagram (Fig. D.7) of ortho and para species together adopting an ortho-to-para ratio of 3:1 which is the value that could be expected from the formation processes of H₂S. We derived Tᵣ₀t ~ 40 K and f(H₂S) ~ 1 × 10⁻⁶. This value is consistent with the chemical models presented by Gobrecht et al. (2016) at a few stellar radii. We found that the lines of H₂S are likely to be sub-thermally excited at the distances adopted for the H₂S emission (r ≲ 1''). However, we did not make further non-LTE calculations due to the lack of a set of collisional coefficients for H₂S. Under LTE conditions, MADEX predicts optically thin lines (τ < 0.6).

The profiles of the SO lines observed are varied (see Fig. 10). Most of them are flat-topped (optically thin and spatially unresolved emission), some of them display parabolic profiles (optically thick or moderately thick emission) and a few SO lines display profiles which seem to be composed of two components, at least: one dominant flat-topped or parabolic component with linewidths consistent with v<sub>∞</sub>, and an additional narrow feature which may indicate SO gas inside the gas acceleration region. These two components are more clearly seen in several SO₂ lines (Fig. 11) which display a broad component plus a bulge-like centred narrow component, which we interpreted as SO₂ emission arising from r < 8 R<sub>*</sub> (see Sect. 6.5.1). Nevertheless, we have not detected high-E<sub>u</sub> SO narrow lines or two different trends in the SO population diagram (see below) which could prove a very inner component of warm SO gas (contrary to SO₂ as discussed in Sect. 6.5.1). Thus we have no firm evidence that could prove the presence of warm SO gas in the innermost regions of the CSE with a noticeable abundance. Finally, the ³⁴SO flat-topped (optically thin emission) profiles yield also v<sub>exp</sub> ~ v<sub>∞</sub>.

The brightness distribution of SO has not been mapped before, thus, we adopted a size of θₛ(SO) = 2'' as well as for ³⁴SO, according to the models by Li et al. (2016). The population diagrams (Fig. D.8) display departures from a linear trend for SO. We obtained T<sub>rot</sub>(SO) ~ T<sub>rot</sub>(³⁴SO) ~ 15 K, N<sub>tot</sub>(SO) ≳ 9 × 10<sup>15</sup> cm<sup>-2</sup> and N<sub>tot</sub>(³⁴SO) ~ 9 × 10<sup>14</sup> cm<sup>-2</sup>. We verified with MADEX (see Sect. 4.3) that SO lines would be moderately thick (τ ≲ 1.5) with a T<sub>kin</sub> = 105 K and n ~ 4 × 10<sup>5</sup> cm<sup>-3</sup> at r = 1''. MADEX predicted optically thin lines for ³⁴SO (τ ≲ 0.2). Furthermore, we estimated n<sub>crit</sub>(SO) ~ [10<sup>5</sup>–10<sup>7</sup>] cm<sup>-3</sup> and similar values for ³⁴SO, which suggests sub-thermal excitation of several transitions.

We derived abundances of f(SO) ≳ 8 × 10⁻⁶ and f(³⁴SO) ~ 8 × 10⁻⁷. The abundance measured of SO is at least a factor three higher compared to previous observational works toward IK Tau (Omont et al. 1993; Bujarrabal et al. 1994; Kim et al. 2010). On the other hand, TE models predict abundances of f(SO) ~ [2–4] × 10⁻⁸ (Duari et al. 1999; Gobrecht et al. 2016). Willacy & Millar (1997) derived peak abundances up to f(SO) ~ 9 × 10⁻⁷ with a chemical model for an O-rich CSE that used only H₂S and SiS as parent S-bearing molecules. Compared to these models, our derived abundance is at least nine times higher than the highest value obtained from the models. Our analysis seems to overestimate the SO abundance compared to previous measurements and chemical models. These discrepancies may be explained given the uncertainty on the size of the SO emitting region adopted, and the f(¹³CO) adopted (see Eq. (9)). In particular, a size of θₛ(SO) ~ 5'' would fix this discrepancy.

### 6.5.1. SO₂ and ³⁴SO₂

We detected ~90 lines of SO₂ displaying complex profiles which can be grouped according to their v<sub>exp</sub>: (i) ~60 lines with v<sub>exp</sub> ~ 18 km s⁻¹ consistent with the v<sub>∞</sub> of the CSE; and (ii) ~30 lines with v<sub>exp</sub> < v<sub>∞</sub>, with velocities as low as ~5 km s⁻¹ (see Fig. 7). The lines of SO₂ display parabolic profiles, flat-topped profiles, and complex profiles. Several lines display a self-absorption in the blue side of the line (see Fig. 11). This self-absorption may be explained considering that part of the SO₂ emission arising from the inner and warm shells of the CSE, is absorbed by the external and cold shells of the CSE, which are located (within the line of sight) between us and the warm gas. The narrow lines seem to be spatially unresolved, although, for the lines that have v<sub>exp</sub> ~ v<sub>∞</sub> it is not clear whether they are spatially resolved or not. Most of the ³⁴SO₂ lines show flat-topped profiles with indicative of spatially unresolved emission.

The rotational diagram of SO₂ was done adopting an emission size of θₛ(SO₂) = 2'', which should be considered as an educated guess derived from the chemical models by Li et al. (2016). From the population diagram of SO₂ (Fig. D.9) we observed also two components, a cold component with T<sub>rot</sub> ~ 40 K traced out by ~60 lines with E<sub>u</sub> ≲ 160 K and a warm component with T<sub>rot</sub> ~ 290 K traced out by ~30 lines with E<sub>u</sub> > 160 K. The cold component displays a slight change in the trend for the lines with E<sub>u</sub> ≲ 50 K which may be explained as a result of moderate optically thick emission for those lines and/or sub-thermal excitation. Using Eq. (9) we derived f(SO₂, cold) ≳ 9.6 × 10⁻⁶ and f(SO₂, warm) ≳ 2.7 × 10⁻⁶. For ³⁴SO₂ we derived a T<sub>rot</sub> ~ 35 K and f(³⁴SO₂) ~ 9.6 × 10⁻⁷.

As we said in Sect. 4.3, the SO₂ lines detected span over a wide range of energies, thus, the parameters derived from the population diagram may be unreliable given that the
<figure><img src="image_11.png" /><figcaption>**Fig. 11.** Results of the radiative transfer models of SO₂ explained in Sects. 4.3 and 6.5.1. The coloured curves correspond to the models adopting the abundance profiles shown in Fig. 5. The spectral resolution is 2 MHz. The temperature scale is in main beam temperature.</figcaption></figure>

homogenous temperature assumption may turn out to be a very crude approximation. We carried out several LVG models adopt- ing different radial abundance profiles (see Sect. 4.3 and Fig. 5). As it is discussed below, the different abundance profiles were adopted mainly to illustrate the need of the presence of warm SO₂ at r < 8 R* in order to reproduce the profiles of the high-E_u lines. The results of the radiative transfer models are shown in Fig. 11 for several lines of SO₂.

The first model (red line in Figs. 5 and 11) reproduces to a good accuracy the profiles of the narrow high-$E_u$ (i.e. $E_u > 160$ K) lines observed. However, it is unable to reproduce the line profiles of the low-$E_u$ (i.e. $E_u < 160$ K) lines, underes- timating their emission completely. We created a second model (blue line in Figs. 5 and 11) which reproduces, within a factor two in intensity, most of the low-$E_u$ SO₂ lines observed. How- ever, this model is unable to explain the narrow profiles of the high-$E_u$ SO₂ lines, predicting wide flat-topped lines or even no emission for these high energy lines. We may note, that the frac- tional abundance adopted for this second model is approximately a factor five lower than the abundance derived from the pop- ulation diagram of the SO₂ cold component. If the abundance is increased up to a value consistent with the population dia- gram results for the cold component (i.e. $f(\text{SO}_2) = 9.6 \times 10^{-6}$),

the model highly overestimates the line profiles observed. This discrepancy may arise from the lack of precise information about the spatial distribution of SO₂ toward the CSE.

Finally, we tested the possibility of SO₂ being distributed as a sum of two components, in particular, the sum of a compact inner component plus an extended component with a shell-like enhancement in the outermost part of the CSE, in order to re- produce the whole set of SO₂ lines observed with a single radial abundance profile. This last model (green line in Figs. 5 and 11) is able to approximately reproduce both the low- and high-$E_u$ SO₂ lines observed, although, it does not reproduces perfectly all the line profiles. The discrepancies found between this best model and the observations are within a factor two or three in intensity for most of the lines observed. This disagreement emerges probably from the lack of precise information about the spatial distribution of SO₂. The radial abundance profile adopted for the model is consistent, within a factor two or three in inten- sity, with the results obtained from the population diagram for the SO₂ warm and cold components. Additionally, the best model predicts both optically thin and optically thick lines which is consistent with the variety of profiles observed.

Hence, we can conclude that SO₂ is distributed along the CSE with an average fractional abundance of $f(\text{SO}_2) \sim 10^{-6}$.
Our models evidenced the presence of an inner (1–8 $R_*$) warm (≥290 K) component of SO₂ with fractional abundances ~10⁻⁶, which produces most of the emission from SO₂ lines with $E_u \gtrsim 160$ K. This is also consistent with the narrow profiles of the high-$E_u$ SO₂ lines. Nevertheless, our model is not able to reproduce the complexity observed in the profiles, which probably indicates the simplicity of the approximated physical model. In particular, the outer radius of the SO₂ cold component is critical to control the expected intensities of the low-$E_u$ lines, which we adopted from the chemical model by Li et al. (2016). Therefore, it would be necessary to map the brightness distribution of this molecule in order to constrain the outer radius of SO₂ emission. High angular resolution observations are also required to map the innermost regions of the CSE, since the distribution of SO₂ in the region between 1–20 $R_*$ would improve the results obtained not only for the high-$E_u$ lines but also for those lines that display a narrow core component (e.g. SO₂ 7,3,5–7,2,6 in Fig. 11).

Previous works toward IK Tau pointed out SO₂ abundances in the intermediate and outer envelope consistent with our results (Omont et al. 1993; Kim et al. 2010; Decin et al. 2010a). Decin et al. (2010a) hinted the presence of SO₂ in the inner wind, since they were not able to reproduce with their radiative transfer model simultaneously the emission of a few lines with $E_u \sim 140$ K detected with APEX and the low-$E_u$ transitions observed with the IRAM-30 m telescope. Given the limited number of high-$E_u$ lines detected by Decin et al. (2010a), these authors were unable to reach conclusive results on the presence of SO₂ in the inner wind of IK Tau and its abundance. Recent research was conducted to investigate one SO₂ line with $E_u \sim 600$ K detected with Herschel/HIFI as well as other SO₂ lines reported in the literature toward IK Tau with a radiative transfer model by Danilovich et al. (2016). Their best-fit model has a peak abundance of $f(\text{SO}_2) = 2 \times 10^{-6}$ and an e-folding radius $R_e = 10^{16}$ cm, although, it is unable to reproduce all the SO₂ observed line profiles as indicated by these authors.

TE models predict the formation of SO₂ in the photosphere of the star with abundances of $f(\text{SO}_2) \sim 10^{-11}$ (Tsuji 1973; Gobrecht et al. 2016), which is approximately five orders of magnitude lower than our results. Willacy & Millar (1997) predicted a peak abundance of $f(\text{SO}_2) \sim 2 \times 10^{-7}$ in the intermediate and outer parts of the CSE, at $r \sim 10^{16}$ cm (i.e. ~500 $R_*$), and $f(r \le 3 \times 10^{15}$ cm) $\le 10^{-10}$, where they used H₂S and SiS as the S-bearing parent molecules of the model. This chemical model is also inconsistent with our results given that they do not predict the formation of SO₂ in the inner parts of the CSE and the abundance in the intermediate and outer parts is approximately two orders of magnitude lower than our measures. In the recent chemical model presented by Li et al. (2016), the authors explore the effect of including SO₂ as a parent molecule. In the absence of a reliable observational estimate of the SO₂ abundance in the inner envelope, these authors adopt $f(\text{SO}_2) = 2 \times 10^{-6}$, which is the value estimated from low-$E_u$ SO₂ transitions arising in the outer envelope regions (Decin et al. 2010a). In the innermost parts of the envelope ($r < 8 R_*$) the SO₂ abundance can be enhanced up to $f(\text{SO}_2) = 4 \times 10^{-9}$ including the effect of shocks and dust grains (Gobrecht et al. 2016). These authors suggest that the production of SO₂ triggers the formation of SO₂ at ~4 $R_*$ in the gas phase through the reaction with OH. Although, the SO₂ abundance obtained with the inclusion of shocks is approximately two or three orders of magnitude lower than our estimates. Photochemistry may also enhance the formation of SO₂ in the inner layers of the CSE, which would require an additional source of UV radiation to dissociate H₂O providing OH to react with the SO₂ formed leading to the enhancement of SO₂. This could be

plausible if the envelope of IK Tau is clumpy, as proposed for other objects (Agúndez et al. 2010).

## 6.6. N-bearing molecules

Besides HCN, HNC and PN, which are discussed in other sections, we detected CN, NS, and NO. The CN lines with unblended hyperfine components have widths consistent with $v_{\text{exp}} = v_{\infty}$ within errors. The spatial distribution of CN in IK Tau is unknown. CN has been observed in the outer shells of the C-rich CSE IRC+10216 (Lucas et al. 1995), and chemical models predict that it is formed as a result of the photodissociation of HCN and HNC in these outer shells (e.g. Nejad & Millar 1988). Given that the HCN size is $\theta_s(\text{HCN}) = 3.85$, CN would be expected to be in a shell external to the HCN. According to the chemical model by Li et al. (2016), the CN peak abundance occurs at $r \sim 1.5 \times 10^{16}$ cm. We converted the area between the HCN outer shell and the CN abundance peak to an equivalent emitting size, obtaining $\theta_s(\text{CN}) \sim 6''$. With this size, we calculated the population diagram of CN (Fig. D.10). We estimated $T_{\text{rot}} = 9 \pm 2$ and $N_{\text{tot}} \sim 1 \times 10^{14}$ cm⁻². At $r \sim 1.5 \times 10^{16}$ cm, $T_{\text{kin}}$ is ~50 K and $n(\text{H}_2) \sim 2 \times 10^4$ cm⁻³, thus, CN lines are probably sub-thermally excited ($n_{\text{crit}} \gtrsim 10^6$ cm⁻³). With these physical conditions MADEX predicted optically thin lines. We estimated $f(\text{CN}) \sim 1 \times 10^{-7}$ which is consistent with previous estimations (Kim et al. 2010). Chemical models predict abundances up to $3 \times 10^{-7}$ (Willacy & Millar 1997; Li et al. 2016), which are also in good agreement with our observations.

As far as we know, our discovery of NS emission toward IK Tau is the first detection of this molecule in this source. Given that we did not resolve its hyperfine structure we cannot extract information on the line profiles observed. There are not observational constraints on the emission size of this molecule. According to the chemical model by Li et al. (2016), which predicts that NS would be formed through the neutral-neutral reaction of NH and S in an external shell of the envelope, similar to the CN shell, we adopted a $\theta_s(\text{NS}) \sim 6''$. With this size, from its population diagram (Fig. D.11), we derive a $T_{\text{rot}} = 18 \pm 2$ K and a column density of ($2.6 \pm 0.5) \times 10^{13}$ cm. As for CN, the lines of NS may be sub-thermally excited. Since, we have not a set of collisional coefficients for NS we could neither estimate the opacities of the lines nor their critical densities. A rough estimation under LTE conditions with MADEX yields optically thin lines ($\tau < 0.1$). We derived an abundance of $f(\text{NS}) \sim 2 \times 10^{-8}$. The chemistry of NS in O-rich CSEs was discussed in Willacy & Millar (1997), although, these authors did not give a value for the predicted NS abundance. Recently, chemical models by Li et al. (2016) predicted $f(\text{NS}) \sim 8 \times 10^{-9}$, which is (within uncertainties) consistent with our results.

For NO, we only detected two lines with low S/N. One of them is a blend of several hyperfine components. For the NO hyperfine component spectrally resolved we derived $v_{\text{exp}} = v_{\infty}$. We estimated a rough value of the NO abundance adopting $\theta_s \sim 6''$ (like for CN and NS), and an excitation temperature of 30 K, which is representative of the $T_{\text{kin}}$ in the outer shells of the CSE ($r \sim [2-5] \times 10^{16}$ cm). With these considerations, we obtained $f(\text{NO}) \sim 2 \times 10^{-6}$, in agreement with the predictions of the chemical model by Li et al. (2016).

## 6.7. P-bearing molecules

PN and PO were detected for the first time toward IK Tau by De Beck et al. (2013), and we detected one additional line of
PN, and seven additional lines of PO. Concerning PO, which has hyperfine structure, we observed several spectrally resolved (as well as unresolved) lines with linewidths consistent with $v_{\text{exp}} \sim 9$ km s⁻¹. This suggests that PO emission lines arise from $r < 8 R_\odot$. De Beck et al. (2013) mapped the brightness distribution of both PN and PO toward IK Tau, and found $\theta_s \lesssim 0.7''$. With this size we calculated the rotational diagram of both molecules (Fig. D.12), and we derived low rotational temperatures ($T_{\text{rot}} \sim 20$ K), $N_{\text{tot}}(\text{PN}) \sim 8 \times 10^{14}$ cm⁻² and $N_{\text{tot}}(\text{PO}) \sim 2 \times 10^{15}$ cm⁻². The low $T_{\text{rot}}$ deduced for PN and PO is probably indicative of sub-thermal excitation since at the inner wind layers ($<0.7''$) where the emission is produced, the gas kinetic temperature is expected to be well above 200 K. We used our radiative transfer code (see Sect. 4.3) to confirm our results. MADEX predicted optically thin ($\tau \lesssim 0.4$) and sub-thermally excited lines for PN. In the case of PO, MADEX predicted optically thin ($\tau < 0.1$) PO lines, under LTE approximation given that there is not a set of PO collisional coefficients available. We derived $f(\text{PN}) \sim 7 \times 10^{-7}$ and $f(\text{PO}) \sim 2 \times 10^{-6}$, which are consistent with previous estimates considering uncertainties (De Beck et al. 2013).

Concerning chemical models, these P-bearing molecules are adopted as parent molecules and their abundances are assumed from observations of the inner region of the CSE (De Beck et al. 2013; Li et al. 2016). TE calculations predict abundances for PN compatible with our results, and one order of magnitude lower than our measurements for PO (Tsuji 1973; Agúndez et al. 2007; Milam et al. 2008).

## 6.8. HCO⁺

We detected the $J = 1-0$ line of the HCO⁺ ion. The $J = 3-2$ line was not detected probably due to an insufficient sensitivity. The $J = 2-1$ and the $J = 4-3$ lines lie in wavelength ranges that were not observed. The flat-topped profile of the HCO⁺ $J = 1-0$ line indicates $v_{\text{exp}} \sim v_{\infty}$, optically thin, and spatially unresolved emission. We estimated a very rough value of the $f(\text{HCO}^+)$ adopting an emission region and an excitation temperature equal to those adopted for NO (see Sect. 6.6) since both molecules are expected to be formed in the outer shells of the CSE. With these values, we obtained $f(\text{HCO}^+) \sim 10^{-8}$.

According to chemical models, this molecule is formed efficiently in the outer layers of O-rich CSEs as a result of reactions that involve CO, H₂O, and their photodissociation products, with abundances consistent with our results (Willacy & Millar 1997; Sánchez Contreras et al. 2015, and references therein).

## 6.9. The organic precursor missing link to carbon chemistry: H₂CO

This is the first detection of the organic precursor molecule H₂CO toward IK Tau. We detected ortho and para lines with flat-topped profiles, indicating optically thin and spatially unresolved emission, even for the lines at high frequencies with $\theta_b \sim 8''$ (see Eq. (4)). We adopted a size of $\theta_s(\text{H}_2\text{CO}) = 2''$, which is an educated guess, taking into account that most of the molecules detected are expected to emit in that region of the CSE.

In the population diagram of H₂CO (see Fig. D.13), the $K_a = 0, K_a = 1$, and $K_a = 2$ ladders were fitted separately. For $K_a = 2$ only two data were collected. The average rotational temperature indicated by the fits of the different $K_a$ ladders is ~10 K. For the $K_a = 3$ ladder we only detected two lines with the same upper energy level, therefore, we adopted

an average excitation temperature of ~10 K to derive a rough value of the $K_a = 3$ column density. Formaldehyde is an asymmetric rotor with its dipolar moment oriented along the *a* axis. Therefore, transitions between different $K_a$ levels are weakly connected through radiative processes. This explains why each of the $K_a$ ladders appears as separated lines in the rotational diagram. The column densities derived result in an ortho-to-para ratio of ~3:1, which has been computed dividing the sum of the $K_a = 1$ and $K_a = 3$ (ortho transitions) by the sum of the $K_a = 0$ and 2 (para transitions) column densities (see Fig. D.13). The total column density is $N_{\text{tot}}(\text{H}_2\text{CO}) \sim 3 \times 10^{14}$ cm⁻². Adding both o-H₂CO and p-H₂CO, we obtained a fractional abundance of $f(\text{H}_2\text{CO}) \sim 2 \times 10^{-7}$. In this case, MADEX predicted optically thin lines ($\tau < 0.3$) and sub-thermal excitation which is consistent with $T_{\text{kin}}(r = 1'') > T_{\text{rot}}$.

The origin of formaldehyde, as well as other C-bearing species, in O-rich envelopes has puzzled the scientific community since H₂CO was first detected in the O-rich CSE OH231.8+4.2, with a fractional abundance of $4 \times 10^{-8}$ (Lindqvist et al. 1992; Charnley et al. 1995). Millar & Olofsson (1993) proposed a formation route which requires methane to produce formaldehyde in the external envelope with abundances up to $10^{-7}$ depending on the mass loss rate of the star. Methane is a highly symmetric molecule with no permanent dipole, thus, indirect evidence for the presence of methane can be provided by the search of expected products of CH₄ chemistry, such as C₂H and CH₃OH. A previous search for these molecules toward IK Tau and other O-rich CSEs has resulted in non-detections of C₂H ($f(\text{C}_2\text{H}) < 9.7 \times 10^{-9}$) and methanol ($f(\text{CH}_3\text{OH}) < 3.2 \times 10^{-8}$; Charnley & Latter 1997; Marvel 2005). We also did not detect emission of these molecules consistent with the upper limits provided by Marvel (2005). If the correct scenario were that H₂CO is formed in the outer envelope, the size adopted for the calculation of the population diagram would result in an abundance overestimate. In that case, assuming $\theta_s = 6''$, like for CN, NS, or NO, we derive an abundance of $f(\text{H}_2\text{CO}) \sim 2 \times 10^{-8}$. Furthermore, a clumpy envelope may lead to an enhanced photochemistry in the inner layers of the CSE, which result in the formation of carbon molecules in the inner and intermediate layers of O-rich CSEs, and in particular formaldehyde with $f(\text{H}_2\text{CO}) \sim 10^{-9}$ (Agúndez et al. 2010).

## 6.10. Isotopic ratios

Isotopic ratios of different species can be measured from the column densities derived in the rotational diagrams (see Table 6). However, these ratios have to be considered as lower limits when the molecule used to calculate the ratio has optically thick lines. In case that the opacities are moderately high, the isotopic ratio can be corrected using the approach by Goldsmith & Langer (1999).

For ¹²C/¹³C ratio, we measured values of eight to ten depending on the molecule used (i.e. CO, CS or HCN). The opacity correction yielded a ¹²C/¹³C ratio of ~10 from CO. This value is in good agreement with that obtained by Ramstedt & Olofsson (2014) from their radiative transfer model of the ¹²CO and ¹³CO emission in IK Tau. This ratio is also compatible with other estimates in M-type stars like TX Cam or W Hya, consistent with a standard evolution for an M-type star (Ramstedt & Olofsson 2014, and references therein).

For the ¹⁶O/¹⁷O and ¹⁶O/¹⁸O ratios, we estimated lower limits of 90 and 60, respectively. MADEX predicted opacities as high as $\tau \sim 10$ for a few SiO lines that would result in opacity
corrected values of one order of magnitude higher, in agreement with previous estimates (Decin et al. 2010b).

The opacity corrected isotopic ratios of $^{28}$Si/$^{29}$Si and $^{28}$Si/$^{30}$Si are ~18 and ~34, respectively. Both isotopic ratios are (within uncertainties) in reasonable agreement with previous estimations toward IK Tau (Decin et al. 2010a), and also with the solar ratios ($[^{28}\text{Si}/^{29}\text{Si}] \sim 20$ and $[^{28}\text{Si}/^{30}\text{Si}] \sim 30$, Asplund et al. 2009). Therefore, it seems that in the case of IK Tau, Si isotopic ratios do not indicate significant alterations in the post-main sequence evolution.

Finally, we measured the isotopic ratio of $^{32}$S/$^{34}$S using SO, SiS, SO$_2$, and CS obtaining values between 10 and 13. We corrected the effect of optically thick emission and we estimated a $^{32}$S/$^{34}$S ratio of ~15. As far as we know, there are no previous observational constraints to this isotopic ratio toward IK Tau. The solar $^{32}$S/$^{34}$S ratio is ~22 (Asplund et al. 2009). Recently, Danilovich et al. (2016) reported $[^{32}\text{S}/^{34}\text{S}] \sim 32$ toward the O-rich CSE of R Dor. Both, Sun and R Dor isotopic ratios are, within uncertainties, compatible with our estimations.

## 6.11. Qualitative comparison with other O-rich objects

The molecular content of only a few O-rich CSEs has been studied so far. In particular, the best studied objects are the AGB CSE IK Tau, the CSE of the hypergiant VY CMa and the peculiar object OH231.8+4.2 (Alcolea et al. 2013; De Beck et al. 2013; Matsuura et al. 2014; Sánchez Contreras et al. 2015; Ziurys et al. 2007, and references therein).

IK Tau has, in terms of chemical composition, more similarities with VY CMa. AlOH and $H_3O^+$ are the only molecules present in the CSE of VY CMa that are not found in the CSE of IK Tau. Formaldehyde is found in the CSE of IK Tau but it is not found in the CSE of VY CMa. Regardless of the possible chemical processes at work in the CSE of IK Tau, the presence of CO, CN, CS, HCN, HNC, HCO$^+$, and $H_2CO$ in IK Tau indicates that the emission of C-bearing molecules in VY CMa is not so unique (Ziurys et al. 2009).

OH231.8+4.2 displays emission of several molecules that are not found toward IK Tau: HNCO, HNCS, OCS, $H^{13}CO^+$, $SO^+$, $N_2H^+$, and $H_3O^+$. The remarkable chemistry of OH231.8+4.2 probably reflects the molecular regeneration process within its envelope after the passage of fast (~100 km s$^{-1}$) shocks that accelerated and dissociated molecules in the AGB wind ~800 yr ago (Sánchez Contreras et al. 2015). In IK Tau there is no evidence of a similar molecular destruction process by fast (~100 km s$^{-1}$) velocity shocks. Instead, slower shocks due to stellar pulsation may have an impact on the chemistry of AGB CSEs (Gobrecht et al. 2016). However, the fact that these molecules are not observed toward IK Tau point out that slow shocks are not able to enhance the formation of these particular species, which are unexpectedly abundant in OH231.8+4.2 (Velilla Prieto et al. 2015). Nevertheless, slow shocks could enhance the formation of molecules like HCN or CS (see Sect. 6.3). Another difference with respect to OH231.8+4.2 is that IK Tau displays emission of NaCl and more intense lines of vibrationally excited SiO (Velilla Prieto et al., in prep.). The emission of these lines arises from very warm and inner regions of the CSE. The absence of NaCl and the weakness of the vibrationally excited SiO lines toward OH231.8+4.2, probably indicates that the mass loss rate of OH231.8+4.2 is decreasing at present (as suggested by Sánchez Contreras et al. 2002), which results in the progressive growth of a central cavity around the star.

## 7. Conclusion

In this work we present the detection toward IK Tau of ~350 rotational lines corresponding to a list of H-, O-, C-, N-, S-, Si- and P-bearing molecules, which evidences an active chemistry for an O-rich AGB CSE.

We detected for first time in this source emission of HCO$^+$, NO, $H_2CO$, and NS. We also detected for the first time toward IK Tau rotational lines of C$^{18}$O, Si$^{17}$O, Si$^{18}$O, $^{29}$SiS, $^{30}$SiS, Si$^{34}$S, $H^{13}$CN, $^{13}$CS, C$^{34}$S, $H_2^{34}$S, $^{34}$SO, $^{34}$SO$_2$, and $H_2O$ $v_2 = 2$, as well as several rotational lines of SiO isotopologues in vibrationally excited states. In addition, we significantly increased the number of lines detected for those molecules that were previously identified toward IK Tau. This has allowed us to deduce characteristic values of the rotational temperatures, column densities, and ultimately fractional abundances of the molecules present in its envelope. From our work we extract the following conclusions:

- The intensity of the rotational lines of molecules in the ground vibrational state do not show a significant variability as a function of time, for the spectral ranges that we could observe in different epochs. The small variations found for these lines can be explained owing to calibration or pointing uncertainties within a 25%. We confirmed the time variability of the intensity of the lines of molecules in vibrationally excited states (e.g. SiO $v = 1$) by an average factor of 60%.

- Most of the molecules display rotational temperatures between 15 and 40 K. NaCl and SiS isotopologues display rotational temperatures of ~65 K.

- We detected a warm component of $SO_2$ traced out by lines with upper energy levels between 160 and 730 K which display $v_{exp} < v_{\infty}$. This points out that $SO_2$ is present close to the stellar surface (~$8 R_*$) with an abundance of $f(SO_2) \sim 10^{-6}$.

- Among the species detected, we highlight the detection of $H_2CO$ and NS for the first time in this source with abundances of $f(H_2CO) \sim [10^{-7}-10^{-8}]$ and $f(NS) \sim 10^{-8}$. We also estimated fractional abundances for the first time detected (toward IK Tau) molecules HCO$^+$ and NO obtaining $f(HCO^+) \sim 10^{-8}$ and $f(NO) \sim 10^{-6}$.

- The detection of several C-bearing species like HCN, CS, $H_2CO$ or CN with abundances of ~$10^{-7}$ indicates an active carbon chemistry which is not expected given that most of the available carbon should be locked up into CO.

- The greatest discrepancies between our results and previous chemical models are found for PO, NaCl, and $SO_2$.

It would be necessary to obtain very high angular resolution observations to characterise the molecular emission in the inner parts of the CSE and the abundances and distribution of the molecules formed in this region. Further investigation is required to understand the nature of the discrepancies found between our derived values and chemical models, in particular, the discrepancies for S-bearing molecules and C-bearing molecules. The inclusion of photo-induced or shock-induced chemistry or maybe other processes is necessary to enhance the formation of these molecules up to values comparable to the abundances observed. Additionally, there are ~40 lines that still remain unidentified. We expect that future observations, supported by improvements in the molecular catalogues and chemical models, lead to fully understand the envelope of IK Tau and, more generally, in O-rich AGB envelopes.

*Acknowledgements.* We acknowledge the IRAM staff for the support and help offered during all the observational runs. We acknowledge the Spanish MICINN/MINECO for funding support through grants AYA2009-07304,
AYA2012-32032, the ASTROMOL Consolider project CSD2009-00038 and also the European Research Council funding support (ERC grant 610256: NANOCOSMOS). L.V.P. also acknowledges the support of the Universidad Complutense de Madrid Ph.D. programme. This research has made use of the The JPL Molecular Spectroscopy catalog, The Cologne Database for Molecular Spectroscopy, the SIMBAD database operated at CDS (Strasbourg, France), the NASA's Astrophysics Data System, the IRAM GILDAS software, and Aladin.

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# Appendix A: Table of measured lines

<table><caption>**Table A.1.** Measured and spectroscopic parameters of the detected lines.</caption><thead><tr><th>Molecule</th><th>Transition QNs</th><th>ν<sub>rest</sub> (MHz)</th><th>E<sub>u</sub> (K)</th><th>A<sub>ul</sub> (s<sup>-1</sup>)</th><th>∫ T<sup>*</sup><sub>ant</sub> dv (K km s<sup>-1</sup>)</th><th>v<sub>exp</sub> (km s<sup>-1</sup>)</th></tr></thead><tbody><tr><td>CO</td><td>1–0</td><td>115 271.202</td><td>5.5</td><td>7.205 × 10<sup>-8</sup></td><td>49.14 (0.04)</td><td>18 (3)</td></tr><tr><td>CO</td><td>2–1</td><td>230 538.000</td><td>16.6</td><td>6.916 × 10<sup>-7</sup></td><td>121.61 (0.06)</td><td>16.7 (1.3)</td></tr><tr><td>CO</td><td>3–2</td><td>345 795.990</td><td>33.2</td><td>2.501 × 10<sup>-6</sup></td><td>103.38 (0.07)</td><td>16.7 (1.0)</td></tr><tr><td><sup>13</sup>CO</td><td>1–0</td><td>110 201.354</td><td>5.3</td><td>6.336 × 10<sup>-8</sup></td><td>5.08 (0.02)</td><td>19 (3)</td></tr><tr><td><sup>13</sup>CO</td><td>2–1</td><td>220 398.684</td><td>15.9</td><td>6.082 × 10<sup>-7</sup></td><td>13.11 (0.05)</td><td>18.6 (1.4)</td></tr><tr><td><sup>13</sup>CO</td><td>3–2</td><td>330 587.964</td><td>31.7</td><td>2.199 × 10<sup>-6</sup></td><td>15.37 (0.12)</td><td>18.1 (1.0)</td></tr><tr><td>C<sup>18</sup>O</td><td>1–0</td><td>109 782.176</td><td>5.3</td><td>6.263 × 10<sup>-8</sup></td><td>0.07 (0.02)</td><td>14 (6)</td></tr><tr><td>C<sup>18</sup>O</td><td>2–1</td><td>219 560.358</td><td>15.8</td><td>6.013 × 10<sup>-7</sup></td><td>0.39 (0.03)</td><td>19.8 (1.4)</td></tr><tr><td>SiO</td><td>2–1</td><td>86 846.986</td><td>6.3</td><td>2.927 × 10<sup>-5</sup></td><td>31.16 (0.03)</td><td>17 (3)</td></tr><tr><td>SiO</td><td>3–2</td><td>130 268.687</td><td>12.5</td><td>1.059 × 10<sup>-4</sup></td><td>50.51 (0.03)</td><td>18 (2)</td></tr><tr><td>SiO</td><td>4–3</td><td>173 688.237</td><td>20.8</td><td>2.602 × 10<sup>-4</sup></td><td>48.63 (0.06)</td><td>18 (2)</td></tr><tr><td>SiO</td><td>5–4</td><td>217 104.920</td><td>31.3</td><td>5.197 × 10<sup>-4</sup></td><td>59.86 (0.04)</td><td>17.0 (1.4)</td></tr><tr><td>SiO</td><td>6–5</td><td>260 518.018</td><td>43.8</td><td>9.117 × 10<sup>-4</sup></td><td>56.51 (0.07)</td><td>14.4 (1.2)</td></tr><tr><td>SiO</td><td>7–6</td><td>303 926.814</td><td>58.4</td><td>1.464 × 10<sup>-3</sup></td><td>56.96 (0.06)</td><td>17.6 (1.0)</td></tr><tr><td>SiO</td><td>8–7</td><td>347 330.592</td><td>75.0</td><td>2.203 × 10<sup>-3</sup></td><td>40.76 (0.15)</td><td>17.3 (1.0)</td></tr><tr><td><sup>29</sup>SiO</td><td>2–1</td><td>85 759.194</td><td>6.2</td><td>2.819 × 10<sup>-5</sup></td><td>5.85 (0.03)</td><td>17 (3)</td></tr><tr><td><sup>29</sup>SiO</td><td>3–2</td><td>128 637.044</td><td>12.3</td><td>1.019 × 10<sup>-4</sup></td><td>10.71 (0.03)</td><td>15 (2)</td></tr><tr><td><sup>29</sup>SiO</td><td>4–3</td><td>171 512.796</td><td>20.6</td><td>2.505 × 10<sup>-4</sup></td><td>13.05 (0.05)</td><td>18 (2)</td></tr><tr><td><sup>29</sup>SiO</td><td>5–4</td><td>214 385.752</td><td>30.9</td><td>5.004 × 10<sup>-4</sup></td><td>14.82 (0.04)</td><td>17.8 (1.4)</td></tr><tr><td><sup>29</sup>SiO</td><td>6–5</td><td>257 255.213</td><td>43.2</td><td>8.779 × 10<sup>-4</sup></td><td>12.88 (0.05)</td><td>17.9 (1.2)</td></tr><tr><td><sup>29</sup>SiO</td><td>7–6</td><td>300 120.480</td><td>57.6</td><td>1.409 × 10<sup>-3</sup></td><td>10.60 (0.08)</td><td>17.1 (1.0)</td></tr><tr><td><sup>29</sup>SiO</td><td>8–7</td><td>342 980.854</td><td>74.1</td><td>2.121 × 10<sup>-3</sup></td><td>10.27 (0.09)</td><td>16.7 (1.0)</td></tr><tr><td><sup>30</sup>SiO</td><td>2–1</td><td>84 746.165</td><td>6.1</td><td>2.720 × 10<sup>-5</sup></td><td>3.74 (0.03)</td><td>18 (3)</td></tr><tr><td><sup>30</sup>SiO</td><td>4–3</td><td>169 486.869</td><td>20.3</td><td>2.418 × 10<sup>-4</sup></td><td>8.72 (0.03)</td><td>19 (2)</td></tr><tr><td><sup>30</sup>SiO</td><td>5–4</td><td>211 853.467</td><td>30.5</td><td>4.829 × 10<sup>-4</sup></td><td>11.78 (0.06)</td><td>16.1 (1.4)</td></tr><tr><td><sup>30</sup>SiO</td><td>6–5</td><td>254 216.652</td><td>42.7</td><td>8.472 × 10<sup>-4</sup></td><td>8.96 (0.03)</td><td>17.0 (1.2)</td></tr><tr><td><sup>30</sup>SiO</td><td>7–6</td><td>296 575.741</td><td>56.9</td><td>1.360 × 10<sup>-3</sup></td><td>10.39 (0.03)</td><td>20.0 (1.0)</td></tr><tr><td><sup>30</sup>SiO</td><td>8–7</td><td>338 930.052</td><td>73.2</td><td>2.047 × 10<sup>-3</sup></td><td>6.78 (0.15)</td><td>16.8 (1.1)</td></tr><tr><td>Si<sup>18</sup>O</td><td>2–1</td><td>80 704.922</td><td>5.8</td><td>2.349 × 10<sup>-5</sup></td><td>0.21 (0.03)</td><td>19 (4)</td></tr><tr><td>Si<sup>18</sup>O</td><td>4–3</td><td>161 404.893</td><td>19.4</td><td>2.088 × 10<sup>-4</sup></td><td>0.82 (0.02)</td><td>16 (2)</td></tr><tr><td>Si<sup>18</sup>O</td><td>6–5</td><td>242 094.961</td><td>40.7</td><td>7.317 × 10<sup>-4</sup></td><td>1.34 (0.05)</td><td>16.9 (1.3)</td></tr><tr><td>Si<sup>18</sup>O</td><td>7–6</td><td>282 434.735</td><td>54.2</td><td>1.175 × 10<sup>-3</sup></td><td>2.56 (0.04)</td><td>16.8 (1.1)</td></tr><tr><td>Si<sup>17</sup>O</td><td>4–3</td><td>167 171.991</td><td>20.1</td><td>2.320 × 10<sup>-4</sup></td><td>0.89 (0.02)</td><td>11 (3)</td></tr><tr><td>Si<sup>17</sup>O</td><td>5–4</td><td>208 960.009</td><td>30.1</td><td>4.634 × 10<sup>-4</sup></td><td>0.52 (0.04)</td><td>21.9 (1.4)</td></tr><tr><td>Si<sup>17</sup>O</td><td>6–5</td><td>250 744.706</td><td>42.1</td><td>8.129 × 10<sup>-4</sup></td><td>0.43 (0.05)</td><td>18 (3)</td></tr><tr><td>Si<sup>17</sup>O</td><td>7–6</td><td>292 525.420</td><td>56.2</td><td>1.305 × 10<sup>-3</sup></td><td>0.27 (0.04)</td><td>9 (2)</td></tr><tr><td>SiS</td><td>5–4</td><td>90 771.566</td><td>13.1</td><td>1.191 × 10<sup>-5</sup></td><td>1.02 (0.02)</td><td>20 (3)</td></tr><tr><td>SiS</td><td>6–5</td><td>108 924.303</td><td>18.3</td><td>2.090 × 10<sup>-5</sup></td><td>2.04 (0.03)</td><td>18 (3)</td></tr><tr><td>SiS</td><td>8–7</td><td>145 227.054</td><td>31.4</td><td>5.050 × 10<sup>-5</sup></td><td>4.23 (0.02)</td><td>18 (2)</td></tr><tr><td>SiS</td><td>9–8</td><td>163 376.782</td><td>39.2</td><td>7.238 × 10<sup>-5</sup></td><td>5.88 (0.02)</td><td>19 (2)</td></tr><tr><td>SiS</td><td>12–11</td><td>217 817.656</td><td>68.0</td><td>1.738 × 10<sup>-4</sup></td><td>9.36 (0.05)</td><td>19.2 (1.4)</td></tr><tr><td>SiS</td><td>13–12</td><td>235 961.366</td><td>79.3</td><td>2.216 × 10<sup>-4</sup></td><td>11.13 (0.06)</td><td>19.1 (1.3)</td></tr><tr><td>SiS</td><td>14–13</td><td>254 103.213</td><td>91.5</td><td>2.775 × 10<sup>-4</sup></td><td>11.68 (0.04)</td><td>18.8 (1.2)</td></tr><tr><td>SiS</td><td>15–14</td><td>272 243.055</td><td>104.5</td><td>3.421 × 10<sup>-4</sup></td><td>7.50 (0.07)</td><td>19.0 (1.1)</td></tr><tr><td>SiS</td><td>16–15</td><td>290 380.747</td><td>118.5</td><td>4.159 × 10<sup>-4</sup></td><td>13.18 (0.04)</td><td>18.6 (1.0)</td></tr><tr><td>SiS</td><td>17–16</td><td>308 516.147</td><td>133.3</td><td>4.997 × 10<sup>-4</sup></td><td>10.28 (0.05)</td><td>17.9 (1.0)</td></tr><tr><td>SiS</td><td>19–18</td><td>344 779.495</td><td>165.5</td><td>6.996 × 10<sup>-4</sup></td><td>11.87 (0.10)</td><td>17.3 (1.0)</td></tr></tbody></table>

**Notes.** Column 2: quantum numbers; Col. 6: integrated intensity (in antenna temperature) of the line with its formal uncertainty; Col. 7: expansion velocity derived from the linewidth with its uncertainty which includes the width of half a channel (1 MHz) except for the lines with a low S/N where a full channel (2 MHz) is included. The uncertainties given (within parentheses) do not include additional uncertainties derived from the absolute flux calibration. (HB) Hard blend, thus, we cannot estimate the contribution of the line to the spectral feature observed. (BF) Bad fit.
Table A.1. continued.

<table><thead><tr><th>Molecule</th><th>Transition QNs</th><th>ν<sub>rest</sub> (MHz)</th><th>E<sub>u</sub> (K)</th><th>A<sub>ul</sub> (s<sup>-1</sup>)</th><th>∫ T<sup>*</sup><sub>ant</sub> dv (K km s<sup>-1</sup>)</th><th>ν<sub>exp</sub> (km s<sup>-1</sup>)</th></tr></thead><tbody><tr><td><sup>29</sup>SiS</td><td>6–5</td><td>106 922.982</td><td>18.0</td><td>1.977 × 10<sup>-5</sup></td><td>0.14 (0.02)</td><td>17 (4)</td></tr><tr><td><sup>29</sup>SiS</td><td>8–7</td><td>142 558.821</td><td>30.8</td><td>4.777 × 10<sup>-5</sup></td><td>0.29 (0.03)</td><td>18 (3)</td></tr><tr><td><sup>29</sup>SiS</td><td>9–8</td><td>160 375.153</td><td>38.5</td><td>6.846 × 10<sup>-5</sup></td><td>0.50 (0.02)</td><td>17 (2)</td></tr><tr><td><sup>29</sup>SiS</td><td>12–11</td><td>213 816.142</td><td>66.7</td><td>1.644 × 10<sup>-4</sup></td><td>1.02 (0.04)</td><td>18 (2)</td></tr><tr><td><sup>29</sup>SiS</td><td>13–12</td><td>231 626.676</td><td>77.8</td><td>2.096 × 10<sup>-4</sup></td><td>1.22 (0.06)</td><td>18.8 (1.5)</td></tr><tr><td><sup>29</sup>SiS</td><td>14–13</td><td>249 435.415</td><td>89.8</td><td>2.625 × 10<sup>-4</sup></td><td>1.10 (0.05)</td><td>17.6 (1.3)</td></tr><tr><td><sup>29</sup>SiS</td><td>15–14</td><td>267 242.221</td><td>102.6</td><td>3.236 × 10<sup>-4</sup></td><td>1.15 (0.05)</td><td>16 (2)</td></tr><tr><td><sup>29</sup>SiS</td><td>16–15</td><td>285 046.956</td><td>116.3</td><td>3.934 × 10<sup>-4</sup></td><td>1.28 (0.06)</td><td>14.5 (1.2)</td></tr><tr><td><sup>29</sup>SiS</td><td>17–16</td><td>302 849.482</td><td>130.8</td><td>4.727 × 10<sup>-4</sup></td><td>1.23 (0.03)</td><td>17.7 (1.1)</td></tr><tr><td><sup>29</sup>SiS</td><td>18–17</td><td>320 649.661</td><td>146.2</td><td>5.619 × 10<sup>-4</sup></td><td>0.99 (0.11)</td><td>15 (2)</td></tr><tr><td><sup>29</sup>SiS</td><td>19–18</td><td>338 447.355</td><td>162.5</td><td>6.617 × 10<sup>-4</sup></td><td>1.17 (0.12)</td><td>16 (2)</td></tr><tr><td><sup>30</sup>SiS</td><td>8–7</td><td>140 073.964</td><td>30.3</td><td>4.532 × 10<sup>-5</sup></td><td>0.26 (0.02)</td><td>20 (2)</td></tr><tr><td><sup>30</sup>SiS</td><td>9–8</td><td>157 579.811</td><td>37.8</td><td>6.494 × 10<sup>-5</sup></td><td>0.27 (0.02)</td><td>19 (2)</td></tr><tr><td><sup>30</sup>SiS</td><td>12–11</td><td>210 089.621</td><td>65.5</td><td>1.560 × 10<sup>-4</sup></td><td>0.67 (0.05)</td><td>12 (2)</td></tr><tr><td><sup>30</sup>SiS</td><td>13–12</td><td>227 589.870</td><td>76.5</td><td>1.989 × 10<sup>-4</sup></td><td>0.62 (0.04)</td><td>17 (2)</td></tr><tr><td><sup>30</sup>SiS</td><td>14–13</td><td>245 088.386</td><td>88.2</td><td>2.490 × 10<sup>-4</sup></td><td>0.67 (0.04)</td><td>16.7 (1.5)</td></tr><tr><td><sup>30</sup>SiS</td><td>15–14</td><td>262 585.036</td><td>100.8</td><td>3.070 × 10<sup>-4</sup></td><td>0.86 (0.06)</td><td>17.6 (1.2)</td></tr><tr><td><sup>30</sup>SiS</td><td>16–15</td><td>280 079.687</td><td>114.3</td><td>3.732 × 10<sup>-4</sup></td><td>1.17 (0.04)</td><td>20.3 (1.3)</td></tr><tr><td><sup>30</sup>SiS</td><td>17–16</td><td>297 572.206</td><td>128.6</td><td>4.484 × 10<sup>-4</sup></td><td>0.88 (0.05)</td><td>13.6 (1.0)</td></tr><tr><td><sup>30</sup>SiS</td><td>18–17</td><td>315 062.459</td><td>143.7</td><td>5.331 × 10<sup>-4</sup></td><td>0.71 (0.06)</td><td>17 (2)</td></tr><tr><td><sup>30</sup>SiS</td><td>19–18</td><td>332 550.312</td><td>159.6</td><td>6.278 × 10<sup>-4</sup></td><td>0.85 (0.09)</td><td>15 (2)</td></tr><tr><td>Si<sup>34</sup>S</td><td>5–4</td><td>88 285.830</td><td>12.7</td><td>1.096 × 10<sup>-5</sup></td><td>0.09 (0.02)</td><td>7 (7)</td></tr><tr><td>Si<sup>34</sup>S</td><td>6–5</td><td>105 941.505</td><td>17.8</td><td>1.923 × 10<sup>-5</sup></td><td>0.18 (0.02)</td><td>24 (5)</td></tr><tr><td>Si<sup>34</sup>S</td><td>8–7</td><td>141 250.280</td><td>30.5</td><td>4.647 × 10<sup>-5</sup></td><td>0.18 (0.02)</td><td>15 (2)</td></tr><tr><td>Si<sup>34</sup>S</td><td>9–8</td><td>158 903.109</td><td>38.1</td><td>6.659 × 10<sup>-5</sup></td><td>0.44 (0.02)</td><td>20 (2)</td></tr><tr><td>Si<sup>34</sup>S</td><td>13–12</td><td>229 500.871</td><td>77.1</td><td>2.039 × 10<sup>-4</sup></td><td>0.96 (0.05)</td><td>15.2 (1.5)</td></tr><tr><td>Si<sup>34</sup>S</td><td>14–13</td><td>247 146.245</td><td>89.0</td><td>2.553 × 10<sup>-4</sup></td><td>0.96 (0.03)</td><td>17.1 (1.3)</td></tr><tr><td>Si<sup>34</sup>S</td><td>15–14</td><td>264 789.722</td><td>101.7</td><td>3.147 × 10<sup>-4</sup></td><td>0.97 (0.05)</td><td>17.2 (1.3)</td></tr><tr><td>Si<sup>34</sup>S</td><td>17–16</td><td>300 070.442</td><td>129.6</td><td>4.598 × 10<sup>-4</sup></td><td>1.01 (0.11)</td><td>16 (2)</td></tr><tr><td>Si<sup>34</sup>S</td><td>18–17</td><td>317 707.414</td><td>144.9</td><td>5.466 × 10<sup>-4</sup></td><td>1.07 (0.13)</td><td>13 (2)</td></tr><tr><td>HCO<sup>+</sup></td><td>1–0</td><td>89 188.526</td><td>4.3</td><td>4.234 × 10<sup>-5</sup></td><td>0.45 (0.03)</td><td>20 (3)</td></tr><tr><td>HNC</td><td>1–0</td><td>90 663.563</td><td>4.4</td><td>2.690 × 10<sup>-5</sup></td><td>0.13 (0.02)</td><td>20 (7)</td></tr><tr><td>HNC</td><td>3–2</td><td>271 981.107</td><td>26.1</td><td>9.336 × 10<sup>-4</sup></td><td>HB</td><td>HB</td></tr><tr><td>HCN</td><td>1–0</td><td>88 631.602</td><td>4.3</td><td>2.406 × 10<sup>-5</sup></td><td>8.09 (0.02)</td><td>18 (3)</td></tr><tr><td>HCN</td><td>3–2</td><td>265 886.433</td><td>25.5</td><td>8.352 × 10<sup>-4</sup></td><td>33.02 (0.04)</td><td>18.2 (1.1)</td></tr><tr><td>HCN</td><td>4–3</td><td>354 505.476</td><td>42.5</td><td>2.053 × 10<sup>-3</sup></td><td>20.5 (0.2)</td><td>17.6 (1.0)</td></tr><tr><td>H<sup>13</sup>CN</td><td>1–0</td><td>86 339.921</td><td>4.1</td><td>2.224 × 10<sup>-5</sup></td><td>0.85 (0.04)</td><td>18 (4)</td></tr><tr><td>H<sup>13</sup>CN</td><td>2–1</td><td>172 677.851</td><td>12.4</td><td>2.135 × 10<sup>-4</sup></td><td>3.90 (0.09)</td><td>16 (2)</td></tr><tr><td>H<sup>13</sup>CN</td><td>3–2</td><td>259 011.798</td><td>24.9</td><td>7.721 × 10<sup>-4</sup></td><td>6.43 (0.05)</td><td>16.4 (1.2)</td></tr><tr><td>H<sup>13</sup>CN</td><td>4–3</td><td>345 339.769</td><td>41.4</td><td>1.898 × 10<sup>-3</sup></td><td>HB</td><td>HB</td></tr><tr><td>NaCl</td><td>8–7</td><td>104 189.669</td><td>22.5</td><td>5.020 × 10<sup>-4</sup></td><td>0.05 (0.01)</td><td>10 (8)</td></tr><tr><td>NaCl</td><td>10–9</td><td>130 223.637</td><td>34.4</td><td>9.919 × 10<sup>-4</sup></td><td>0.10 (0.01)</td><td>15 (5)</td></tr><tr><td>NaCl</td><td>11–10</td><td>143 237.371</td><td>41.3</td><td>1.326 × 10<sup>-3</sup></td><td>0.18 (0.02)</td><td>20 (4)</td></tr><tr><td>NaCl</td><td>12–11</td><td>156 248.639</td><td>48.8</td><td>1.727 × 10<sup>-3</sup></td><td>0.21 (0.02)</td><td>14 (4)</td></tr><tr><td>NaCl</td><td>13–12</td><td>169 257.217</td><td>56.9</td><td>2.202 × 10<sup>-3</sup></td><td>0.27 (0.02)</td><td>16 (2)</td></tr><tr><td>NaCl</td><td>16–15</td><td>208 264.570</td><td>85.0</td><td>4.131 × 10<sup>-3</sup></td><td>0.15 (0.02)</td><td>8 (3)</td></tr><tr><td>NaCl</td><td>17–16</td><td>221 260.147</td><td>95.6</td><td>4.962 × 10<sup>-3</sup></td><td>0.24 (0.03)</td><td>10 (4)</td></tr><tr><td>NaCl</td><td>18–17</td><td>234 251.912</td><td>106.9</td><td>5.898 × 10<sup>-3</sup></td><td>0.27 (0.04)</td><td>11 (3)</td></tr><tr><td>NaCl</td><td>19–18</td><td>247 239.643</td><td>118.7</td><td>6.945 × 10<sup>-3</sup></td><td>0.40 (0.03)</td><td>17 (2)</td></tr><tr><td>NaCl</td><td>20–19</td><td>260 223.113</td><td>131.2</td><td>8.108 × 10<sup>-3</sup></td><td>0.27 (0.06)</td><td>11 (3)</td></tr><tr><td>NaCl</td><td>22–21</td><td>286 176.379</td><td>158.1</td><td>1.081 × 10<sup>-2</sup></td><td>0.28 (0.05)</td><td>20 (3)</td></tr><tr><td>NaCl</td><td>23–22</td><td>299 145.726</td><td>172.4</td><td>1.236 × 10<sup>-2</sup></td><td>0.25 (0.02)</td><td>13.8 (1.5)</td></tr><tr><td>NaCl</td><td>24–23</td><td>312 109.915</td><td>187.4</td><td>1.405 × 10<sup>-2</sup></td><td>0.28 (0.06)</td><td>14 (2)</td></tr></tbody></table>
<table><caption>Table A.1. continued.</caption><thead><tr><th>Molecule</th><th>Transition QNs</th><th>ν<sub>rest</sub> (MHz)</th><th>E<sub>u</sub> (K)</th><th>A<sub>ul</sub> (s<sup>-1</sup>)</th><th>∫ T<sup>*</sup><sub>ant</sub> dv (K km s<sup>-1</sup>)</th><th>ν<sub>exp</sub> (km s<sup>-1</sup>)</th></tr></thead><tbody><tr><td>CS</td><td>2–1</td><td>97 980.953</td><td>7.1</td><td>1.679 × 10<sup>-5</sup></td><td>0.79 (0.01)</td><td>22 (3)</td></tr><tr><td>CS</td><td>3–2</td><td>146 969.026</td><td>14.1</td><td>6.071 × 10<sup>-5</sup></td><td>2.11 (0.02)</td><td>17 (2)</td></tr><tr><td>CS</td><td>5–4</td><td>244 935.555</td><td>35.3</td><td>2.981 × 10<sup>-4</sup></td><td>5.77 (0.04)</td><td>16.1 (1.2)</td></tr><tr><td>CS</td><td>6–5</td><td>293 912.089</td><td>49.4</td><td>5.229 × 10<sup>-4</sup></td><td>5.87 (0.04)</td><td>17.4 (1.0)</td></tr><tr><td>CS</td><td>7–6</td><td>342 882.854</td><td>65.8</td><td>8.395 × 10<sup>-4</sup></td><td>5.30 (0.07)</td><td>19.6 (1.0)</td></tr><tr><td><sup>13</sup>CS</td><td>3–2</td><td>138 739.264</td><td>13.3</td><td>5.107 × 10<sup>-5</sup></td><td>0.17 (0.01)</td><td>13 (3)</td></tr><tr><td><sup>13</sup>CS</td><td>5–4</td><td>231 220.684</td><td>33.3</td><td>2.507 × 10<sup>-4</sup></td><td>0.63 (0.05)</td><td>23 (3)</td></tr><tr><td><sup>13</sup>CS</td><td>6–5</td><td>277 455.398</td><td>46.6</td><td>4.399 × 10<sup>-4</sup></td><td>0.70 (0.06)</td><td>15.4 (1.1)</td></tr><tr><td>C<sup>34</sup>S</td><td>3–2</td><td>144 617.101</td><td>13.9</td><td>5.784 × 10<sup>-5</sup></td><td>0.18 (0.02)</td><td>18 (4)</td></tr><tr><td>C<sup>34</sup>S</td><td>5–4</td><td>241 016.089</td><td>34.7</td><td>2.840 × 10<sup>-4</sup></td><td>0.41 (0.04)</td><td>22 (4)</td></tr><tr><td>C<sup>34</sup>S</td><td>6–5</td><td>289 209.067</td><td>48.6</td><td>4.982 × 10<sup>-4</sup></td><td>0.43 (0.03)</td><td>19 (2)</td></tr><tr><td>o-H<sub>2</sub>S</td><td>1<sub>1,0</sub>–1<sub>0,1</sub></td><td>168 762.754</td><td>8.1</td><td>2.677 × 10<sup>-5</sup></td><td>6.35 (0.02)</td><td>18 (2)</td></tr><tr><td>o-H<sub>2</sub>S</td><td>4<sub>1,4</sub>–3<sub>2,1</sub></td><td>204 140.204</td><td>144.5</td><td>3.006 × 10<sup>-8</sup></td><td>0.14 (0.03)</td><td>BF</td></tr><tr><td>o-H<sub>2</sub>S</td><td>3<sub>3,0</sub>–3<sub>2,1</sub></td><td>300 505.524</td><td>149.1</td><td>1.024 × 10<sup>-4</sup></td><td>1.05 (0.07)</td><td>17.3 (1.1)</td></tr><tr><td>p-H<sub>2</sub>S</td><td>2<sub>2,0</sub>–2<sub>1,1</sub></td><td>216 710.444</td><td>84.0</td><td>4.870 × 10<sup>-5</sup></td><td>0.66 (0.05)</td><td>18.3 (1.4)</td></tr><tr><td>o<sup>34</sup>H<sub>2</sub>S</td><td>1<sub>1,0</sub>–1<sub>0,1</sub></td><td>167 910.516</td><td>8.1</td><td>2.616 × 10<sup>-5</sup></td><td>0.89 (0.02)</td><td>22 (2)</td></tr><tr><td>SO</td><td>(2, 2)–(1, 1)</td><td>86 093.959</td><td>19.3</td><td>5.250 × 10<sup>-6</sup></td><td>0.70 (0.03)</td><td>17 (3)</td></tr><tr><td>SO</td><td>(2, 3)–(1, 2)</td><td>99 299.891</td><td>9.2</td><td>1.125 × 10<sup>-5</sup></td><td>7.50 (0.02)</td><td>16 (3)</td></tr><tr><td>SO</td><td>(3, 2)–(2, 1)</td><td>109 252.184</td><td>21.1</td><td>1.080 × 10<sup>-5</sup></td><td>1.11 (0.02)</td><td>17 (3)</td></tr><tr><td>SO</td><td>(3, 3)–(2, 2)</td><td>129 138.904</td><td>25.5</td><td>2.250 × 10<sup>-5</sup></td><td>2.19 (0.03)</td><td>17 (2)</td></tr><tr><td>SO</td><td>(3, 4)–(2, 3)</td><td>138 178.659</td><td>15.9</td><td>3.166 × 10<sup>-5</sup></td><td>12.43 (0.02)</td><td>17 (2)</td></tr><tr><td>SO</td><td>(4, 3)–(3, 2)</td><td>158 971.816</td><td>28.7</td><td>4.233 × 10<sup>-5</sup></td><td>2.79 (0.02)</td><td>17 (2)</td></tr><tr><td>SO</td><td>(4, 4)–(3, 3)</td><td>172 181.407</td><td>33.8</td><td>5.833 × 10<sup>-5</sup></td><td>2.77 (0.05)</td><td>17 (2)</td></tr><tr><td>SO</td><td>(5, 4)–(4, 3)</td><td>206 176.019</td><td>38.6</td><td>1.010 × 10<sup>-4</sup></td><td>3.23 (0.04)</td><td>17.4 (1.5)</td></tr><tr><td>SO</td><td>(5, 5)–(4, 4)</td><td>215 220.653</td><td>44.1</td><td>1.193 × 10<sup>-4</sup></td><td>3.76 (0.04)</td><td>16.9 (1.4)</td></tr><tr><td>SO</td><td>(5, 6)–(4, 5)</td><td>219 949.396</td><td>35.0</td><td>1.335 × 10<sup>-4</sup></td><td>10.68 (0.03)</td><td>17.7 (1.4)</td></tr><tr><td>SO</td><td>(6, 5)–(5, 4)</td><td>251 825.767</td><td>50.7</td><td>1.925 × 10<sup>-4</sup></td><td>3.15 (0.04)</td><td>16.1 (1.2)</td></tr><tr><td>SO</td><td>(6, 6)–(5, 5)</td><td>258 255.830</td><td>56.5</td><td>2.120 × 10<sup>-4</sup></td><td>3.44 (0.05)</td><td>17.4 (1.2)</td></tr><tr><td>SO</td><td>(6, 7)–(5, 6)</td><td>261 843.713</td><td>47.6</td><td>2.282 × 10<sup>-4</sup></td><td>7.54 (0.07)</td><td>16.2 (1.1)</td></tr><tr><td>SO</td><td>(1, 1)–(0, 1)</td><td>286 340.151</td><td>15.2</td><td>1.403 × 10<sup>-5</sup></td><td>0.54 (0.05)</td><td>19 (2)</td></tr><tr><td>SO</td><td>(7, 6)–(6, 5)</td><td>296 550.061</td><td>64.9</td><td>3.230 × 10<sup>-4</sup></td><td>2.31 (0.03)</td><td>16.7 (1.2)</td></tr><tr><td>SO</td><td>(7, 7)–(6, 6)</td><td>301 286.123</td><td>71.0</td><td>3.429 × 10<sup>-4</sup></td><td>3.38 (0.04)</td><td>19.2 (1.0)</td></tr><tr><td>SO</td><td>(7, 8)–(6, 7)</td><td>304 077.867</td><td>62.1</td><td>3.609 × 10<sup>-4</sup></td><td>7.23 (0.05)</td><td>16.2 (1.0)</td></tr><tr><td>SO</td><td>(2, 2)–(1, 2)</td><td>309 502.443</td><td>19.3</td><td>1.419 × 10<sup>-5</sup></td><td>0.46 (0.03)</td><td>17.6 (1.0)</td></tr><tr><td>SO</td><td>(3, 3)–(2, 3)</td><td>339 341.457</td><td>25.5</td><td>1.455 × 10<sup>-5</sup></td><td>0.45 (0.06)</td><td>16 (2)</td></tr><tr><td>SO</td><td>(8, 7)–(7, 6)</td><td>340 714.295</td><td>81.2</td><td>4.985 × 10<sup>-4</sup></td><td>2.46 (0.06)</td><td>18.1 (1.0)</td></tr><tr><td>SO</td><td>(8, 8)–(7, 7)</td><td>344 310.717</td><td>87.5</td><td>5.186 × 10<sup>-4</sup></td><td>2.72 (0.08)</td><td>18.2 (1.0)</td></tr><tr><td>SO</td><td>(8, 9)–(7, 8)</td><td>346 528.537</td><td>78.8</td><td>5.382 × 10<sup>-4</sup></td><td>HB</td><td>HB</td></tr><tr><td><sup>34</sup>SO</td><td>(2, 3)–(1, 2)</td><td>97 715.405</td><td>9.1</td><td>1.073 × 10<sup>-5</sup></td><td>0.51 (0.02)</td><td>18 (3)</td></tr><tr><td><sup>34</sup>SO</td><td>(3, 2)–(2, 1)</td><td>106 743.368</td><td>20.9</td><td>1.007 × 10<sup>-5</sup></td><td>0.07 (0.01)</td><td>6 (9)</td></tr><tr><td><sup>34</sup>SO</td><td>(3, 4)–(2, 3)</td><td>135 775.651</td><td>15.6</td><td>3.004 × 10<sup>-5</sup></td><td>0.93 (0.02)</td><td>18 (2)</td></tr><tr><td><sup>34</sup>SO</td><td>(4, 3)–(3, 2)</td><td>155 506.808</td><td>28.4</td><td>3.961 × 10<sup>-5</sup></td><td>0.16 (0.02)</td><td>17 (4)</td></tr><tr><td><sup>34</sup>SO</td><td>(4, 4)–(3, 3)</td><td>168 815.114</td><td>33.4</td><td>5.498 × 10<sup>-5</sup></td><td>0.17 (0.02)</td><td>20 (4)</td></tr><tr><td><sup>34</sup>SO</td><td>(5, 5)–(4, 4)</td><td>211 013.024</td><td>43.5</td><td>1.124 × 10<sup>-4</sup></td><td>0.34 (0.05)</td><td>21 (5)</td></tr><tr><td><sup>34</sup>SO</td><td>(5, 6)–(4, 5)</td><td>215 839.917</td><td>34.4</td><td>1.262 × 10<sup>-4</sup></td><td>0.74 (0.04)</td><td>17.6 (1.4)</td></tr><tr><td><sup>34</sup>SO</td><td>(6, 5)–(5, 4)</td><td>246 663.403</td><td>49.9</td><td>1.809 × 10<sup>-4</sup></td><td>0.26 (0.03)</td><td>19 (2)</td></tr><tr><td><sup>34</sup>SO</td><td>(6, 6)–(5, 5)</td><td>253 207.022</td><td>55.7</td><td>1.998 × 10<sup>-4</sup></td><td>0.28 (0.04)</td><td>21 (3)</td></tr><tr><td><sup>34</sup>SO</td><td>(7, 6)–(6, 5)</td><td>290 562.257</td><td>63.8</td><td>3.037 × 10<sup>-4</sup></td><td>0.27 (0.03)</td><td>22 (4)</td></tr><tr><td><sup>34</sup>SO</td><td>(7, 8)–(6, 7)</td><td>298 257.973</td><td>61.0</td><td>3.406 × 10<sup>-4</sup></td><td>0.50 (0.03)</td><td>15.6 (1.4)</td></tr></tbody></table>
<table><caption>Table A.1. continued.</caption><thead><tr><th>Molecule</th><th>Transition QNs</th><th>ν<sub>rest</sub> (MHz)</th><th>E<sub>u</sub> (K)</th><th>A<sub>ul</sub> (s<sup>-1</sup>)</th><th>∫ T<sup>*</sup><sub>ant</sub> dv (K km s<sup>-1</sup>)</th><th>ν<sub>exp</sub> (km s<sup>-1</sup>)</th></tr></thead><tbody><tr><td>SO<sub>2</sub></td><td>8<sub>1,7</sub>–8<sub>0,8</sub></td><td>83 688.092</td><td>36.7</td><td>6.825 × 10<sup>-6</sup></td><td>1.32 (0.03)</td><td>20 (4)</td></tr><tr><td>SO<sub>2</sub></td><td>2<sub>2,0</sub>–3<sub>1,3</sub></td><td>100 878.107</td><td>12.6</td><td>1.026 × 10<sup>-6</sup></td><td>0.11 (0.01)</td><td>20 (6)</td></tr><tr><td>SO<sub>2</sub></td><td>3<sub>1,3</sub>–2<sub>0,2</sub></td><td>104 029.420</td><td>7.7</td><td>1.006 × 10<sup>-5</sup></td><td>1.73 (0.03)</td><td>21 (3)</td></tr><tr><td>SO<sub>2</sub></td><td>10<sub>1,9</sub>–10<sub>0,10</sub></td><td>104 239.299</td><td>54.7</td><td>1.122 × 10<sup>-5</sup></td><td>1.12 (0.02)</td><td>19 (3)</td></tr><tr><td>SO<sub>2</sub></td><td>12<sub>2,10</sub>–12<sub>1,11</sub></td><td>128 605.111</td><td>82.6</td><td>2.615 × 10<sup>-5</sup></td><td>0.64 (0.02)</td><td>16 (2)</td></tr><tr><td>SO<sub>2</sub></td><td>12<sub>1,11</sub>–11<sub>2,10</sub></td><td>129 105.786</td><td>76.4</td><td>9.029 × 10<sup>-6</sup></td><td>0.64 (0.02)</td><td>19 (2)</td></tr><tr><td>SO<sub>2</sub></td><td>10<sub>2,8</sub>–10<sub>1,9</sub></td><td>129 514.799</td><td>60.9</td><td>2.502 × 10<sup>-5</sup></td><td>0.92 (0.03)</td><td>16 (2)</td></tr><tr><td>SO<sub>2</sub></td><td>12<sub>1,11</sub>–12<sub>0,12</sub></td><td>131 014.841</td><td>76.4</td><td>1.856 × 10<sup>-5</sup></td><td>1.00 (0.01)</td><td>22 (2)</td></tr><tr><td>SO<sub>2</sub></td><td>14<sub>2,12</sub>–14<sub>1,13</sub></td><td>132 744.832</td><td>108.1</td><td>2.933 × 10<sup>-5</sup></td><td>0.47 (0.03)</td><td>18 (2)</td></tr><tr><td>SO<sub>2</sub></td><td>8<sub>2,6</sub>–8<sub>1,7</sub></td><td>134 004.812</td><td>43.1</td><td>2.501 × 10<sup>-5</sup></td><td>1.28 (0.02)</td><td>16 (2)</td></tr><tr><td>SO<sub>2</sub></td><td>5<sub>1,5</sub>–4<sub>0,4</sub></td><td>135 696.017</td><td>15.7</td><td>2.208 × 10<sup>-5</sup></td><td>3.78 (0.03)</td><td>17 (2)</td></tr><tr><td>SO<sub>2</sub></td><td>6<sub>2,4</sub>–6<sub>1,5</sub></td><td>140 306.166</td><td>29.2</td><td>2.528 × 10<sup>-5</sup></td><td>1.76 (0.02)</td><td>17 (2)</td></tr><tr><td>SO<sub>2</sub></td><td>16<sub>2,14</sub>–16<sub>1,15</sub></td><td>143 057.080</td><td>137.5</td><td>3.572 × 10<sup>-5</sup></td><td>0.31 (0.02)</td><td>18 (3)</td></tr><tr><td>SO<sub>2</sub></td><td>4<sub>2,2</sub>–4<sub>1,3</sub></td><td>146 605.520</td><td>19.0</td><td>2.470 × 10<sup>-5</sup></td><td>1.81 (0.03)</td><td>17 (2)</td></tr><tr><td>SO<sub>2</sub></td><td>2<sub>2,0</sub>–2<sub>1,1</sub></td><td>151 378.663</td><td>12.6</td><td>1.875 × 10<sup>-5</sup></td><td>1.11 (0.03)</td><td>18 (2)</td></tr><tr><td>SO<sub>2</sub></td><td>3<sub>2,2</sub>–3<sub>1,3</sub></td><td>158 199.781</td><td>15.3</td><td>2.532 × 10<sup>-5</sup></td><td>1.58 (0.02)</td><td>17 (2)</td></tr><tr><td>SO<sub>2</sub></td><td>18<sub>2,16</sub>–18<sub>1,17</sub></td><td>160 342.971</td><td>170.8</td><td>4.692 × 10<sup>-5</sup></td><td>0.33 (0.02)</td><td>13 (2)</td></tr><tr><td>SO<sub>2</sub></td><td>4<sub>3,1</sub>–5<sub>2,4</sub></td><td>160 543.024</td><td>31.3</td><td>4.321 × 10<sup>-6</sup></td><td>0.06 (0.01)</td><td>8 (4)</td></tr><tr><td>SO<sub>2</sub></td><td>10<sub>0,10</sub>–9<sub>1,9</sub></td><td>160 827.841</td><td>49.7</td><td>3.954 × 10<sup>-5</sup></td><td>3.37 (0.02)</td><td>17 (2)</td></tr><tr><td>SO<sub>2</sub></td><td>14<sub>1,13</sub>–14<sub>0,14</sub></td><td>163 605.533</td><td>101.8</td><td>3.006 × 10<sup>-5</sup></td><td>1.33 (0.03)</td><td>18 (2)</td></tr><tr><td>SO<sub>2</sub></td><td>5<sub>2,4</sub>–5<sub>1,5</sub></td><td>165 144.652</td><td>23.6</td><td>3.122 × 10<sup>-5</sup></td><td>2.47 (0.02)</td><td>18 (2)</td></tr><tr><td>SO<sub>2</sub></td><td>7<sub>1,7</sub>–6<sub>0,6</sub></td><td>165 225.452</td><td>27.1</td><td>4.135 × 10<sup>-5</sup></td><td>6.14 (0.02)</td><td>17 (2)</td></tr><tr><td>SO<sub>2</sub></td><td>12<sub>0,12</sub>–11<sub>1,11</sub></td><td>203 391.484</td><td>70.1</td><td>8.805 × 10<sup>-5</sup></td><td>4.04 (0.06)</td><td>16.4 (1.5)</td></tr><tr><td>SO<sub>2</sub></td><td>18<sub>3,15</sub>–18<sub>2,16</sub></td><td>204 246.762</td><td>180.6</td><td>9.267 × 10<sup>-5</sup></td><td>0.38 (0.05)</td><td>15 (3)</td></tr><tr><td>SO<sub>2</sub></td><td>11<sub>2,10</sub>–11<sub>1,11</sub></td><td>205 300.539</td><td>70.2</td><td>5.318 × 10<sup>-5</sup></td><td>1.54 (0.06)</td><td>17.1 (1.5)</td></tr><tr><td>SO<sub>2</sub></td><td>3<sub>2,2</sub>–2<sub>1,1</sub></td><td>208 700.337</td><td>15.3</td><td>6.719 × 10<sup>-5</sup></td><td>3.08 (0.03)</td><td>17.2 (1.4)</td></tr><tr><td>SO<sub>2</sub></td><td>26<sub>3,23</sub>–26<sub>2,24</sub></td><td>213 068.427</td><td>350.8</td><td>1.156 × 10<sup>-4</sup></td><td>0.19 (0.04)</td><td>5 (3)</td></tr><tr><td>SO<sub>2</sub></td><td>16<sub>3,13</sub>–16<sub>2,14</sub></td><td>214 689.395</td><td>147.8</td><td>9.902 × 10<sup>-5</sup></td><td>0.32 (0.03)</td><td>19 (2)</td></tr><tr><td>SO<sub>2</sub></td><td>22<sub>2,20</sub>–22<sub>1,21</sub></td><td>216 643.304</td><td>248.5</td><td>9.271 × 10<sup>-5</sup></td><td>0.40 (0.04)</td><td>11 (2)</td></tr><tr><td>SO<sub>2</sub></td><td>11<sub>1,11</sub>–10<sub>0,10</sub></td><td>221 965.221</td><td>60.4</td><td>1.138 × 10<sup>-4</sup></td><td>5.81 (0.06)</td><td>16.2 (1.4)</td></tr><tr><td>SO<sub>2</sub></td><td>13<sub>2,12</sub>–13<sub>1,13</sub></td><td>225 153.705</td><td>93.0</td><td>6.523 × 10<sup>-5</sup></td><td>0.94 (0.07)</td><td>17.3 (1.4)</td></tr><tr><td>SO<sub>2</sub></td><td>14<sub>3,11</sub>–14<sub>2,12</sub></td><td>226 300.028</td><td>119.0</td><td>1.068 × 10<sup>-4</sup></td><td>HB</td><td>HB</td></tr><tr><td>SO<sub>2</sub></td><td>4<sub>2,2</sub>–3<sub>1,3</sub></td><td>235 151.721</td><td>19.0</td><td>7.691 × 10<sup>-5</sup></td><td>4.41 (0.05)</td><td>17.2 (1.3)</td></tr><tr><td>SO<sub>2</sub></td><td>16<sub>1,15</sub>–15<sub>2,14</sub></td><td>236 216.688</td><td>130.7</td><td>7.505 × 10<sup>-5</sup></td><td>0.66 (0.05)</td><td>17.0 (1.4)</td></tr><tr><td>SO<sub>2</sub></td><td>12<sub>3,9</sub>–12<sub>2,10</sub></td><td>237 068.834</td><td>94.0</td><td>1.141 × 10<sup>-4</sup></td><td>0.85 (0.04)</td><td>18.6 (1.4)</td></tr><tr><td>SO<sub>2</sub></td><td>18<sub>1,17</sub>–18<sub>0,18</sub></td><td>240 942.792</td><td>163.1</td><td>7.024 × 10<sup>-5</sup></td><td>0.47 (0.04)</td><td>18 (3)</td></tr><tr><td>SO<sub>2</sub></td><td>5<sub>2,4</sub>–4<sub>1,3</sub></td><td>241 615.798</td><td>23.6</td><td>8.455 × 10<sup>-5</sup></td><td>4.74 (0.06)</td><td>17.6 (1.2)</td></tr><tr><td>SO<sub>2</sub></td><td>14<sub>0,14</sub>–13<sub>1,13</sub></td><td>244 254.220</td><td>93.9</td><td>1.639 × 10<sup>-4</sup></td><td>3.71 (0.04)</td><td>17.3 (1.2)</td></tr><tr><td>SO<sub>2</sub></td><td>10<sub>3,7</sub>–10<sub>2,8</sub></td><td>245 563.423</td><td>72.7</td><td>1.191 × 10<sup>-4</sup></td><td>1.31 (0.04)</td><td>17.0 (1.2)</td></tr><tr><td>SO<sub>2</sub></td><td>15<sub>2,14</sub>–15<sub>1,15</sub></td><td>248 057.403</td><td>119.3</td><td>8.056 × 10<sup>-5</sup></td><td>0.66 (0.05)</td><td>16.0 (1.3)</td></tr><tr><td>SO<sub>2</sub></td><td>13<sub>1,13</sub>–12<sub>0,12</sub></td><td>251 199.676</td><td>82.2</td><td>1.756 × 10<sup>-4</sup></td><td>HB</td><td>HB</td></tr><tr><td>SO<sub>2</sub></td><td>8<sub>3,5</sub>–8<sub>2,6</sub></td><td>251 210.586</td><td>55.2</td><td>1.198 × 10<sup>-4</sup></td><td>HB</td><td>HB</td></tr><tr><td>SO<sub>2</sub></td><td>6<sub>3,3</sub>–6<sub>2,4</sub></td><td>254 280.537</td><td>41.4</td><td>1.136 × 10<sup>-4</sup></td><td>2.02 (0.03)</td><td>16.7 (1.2)</td></tr><tr><td>SO<sub>2</sub></td><td>4<sub>3,1</sub>–4<sub>2,2</sub></td><td>255 553.303</td><td>31.3</td><td>9.284 × 10<sup>-5</sup></td><td>1.62 (0.06)</td><td>17.2 (1.2)</td></tr><tr><td>SO<sub>2</sub></td><td>3<sub>3,1</sub>–3<sub>2,2</sub></td><td>255 958.045</td><td>27.6</td><td>6.626 × 10<sup>-5</sup></td><td>1.09 (0.06)</td><td>17.6 (1.2)</td></tr><tr><td>SO<sub>2</sub></td><td>5<sub>3,3</sub>–5<sub>2,4</sub></td><td>256 246.946</td><td>35.9</td><td>1.074 × 10<sup>-4</sup></td><td>1.94 (0.04)</td><td>17.2 (1.2)</td></tr><tr><td>SO<sub>2</sub></td><td>7<sub>3,5</sub>–7<sub>2,6</sub></td><td>257 099.967</td><td>47.8</td><td>1.223 × 10<sup>-4</sup></td><td>1.78 (0.04)</td><td>16.5 (1.2)</td></tr><tr><td>SO<sub>2</sub></td><td>32<sub>4,28</sub>–32<sub>3,29</sub></td><td>258 388.714</td><td>531.1</td><td>2.102 × 10<sup>-4</sup></td><td>0.19 (0.03)</td><td>6.2 (1.4)</td></tr><tr><td>SO<sub>2</sub></td><td>9<sub>3,7</sub>–9<sub>2,8</sub></td><td>258 942.200</td><td>63.5</td><td>1.318 × 10<sup>-4</sup></td><td>1.53 (0.04)</td><td>17.2 (1.2)</td></tr><tr><td>SO<sub>2</sub></td><td>30<sub>4,26</sub>–30<sub>3,27</sub></td><td>259 599.446</td><td>471.5</td><td>2.072 × 10<sup>-4</sup></td><td>0.16 (0.02)</td><td>6 (2)</td></tr><tr><td>SO<sub>2</sub></td><td>11<sub>3,9</sub>–11<sub>2,10</sub></td><td>262 256.907</td><td>82.8</td><td>1.408 × 10<sup>-4</sup></td><td>0.88 (0.09)</td><td>18 (2)</td></tr><tr><td>SO<sub>2</sub></td><td>30<sub>3,27</sub>–30<sub>2,28</sub></td><td>263 543.954</td><td>459.1</td><td>1.894 × 10<sup>-4</sup></td><td>0.21 (0.02)</td><td>5.1 (1.4)</td></tr><tr><td>SO<sub>2</sub></td><td>34<sub>4,30</sub>–34<sub>3,31</sub></td><td>265 481.970</td><td>594.7</td><td>2.277 × 10<sup>-4</sup></td><td>0.12 (0.02)</td><td>8.6 (1.2)</td></tr></tbody></table>
<table><caption>Table A.1. continued.</caption><thead><tr><th>Molecule</th><th>Transition QNs</th><th>v<sub>rest</sub> (MHz)</th><th>E<sub>u</sub> (K)</th><th>A<sub>ul</sub> (s<sup>-1</sup>)</th><th>∫ T<sup>*</sup><sub>ant</sub> dv (K km s<sup>-1</sup>)</th><th>v<sub>exp</sub> (km s<sup>-1</sup>)</th></tr></thead><tbody><tr><td>SO<sub>2</sub></td><td>13<sub>3,11</sub>-13<sub>2,12</sub></td><td>267 537.453</td><td>105.8</td><td>1.513 × 10<sup>-4</sup></td><td>0.88 (0.05)</td><td>15.8 (1.2)</td></tr><tr><td>SO<sub>2</sub></td><td>28<sub>4,24</sub>-28<sub>3,25</sub></td><td>267 719.839</td><td>415.9</td><td>2.157 × 10<sup>-4</sup></td><td>0.11 (0.04)</td><td>12 (2)</td></tr><tr><td>SO<sub>2</sub></td><td>7<sub>2,6</sub>-6<sub>1,5</sub></td><td>271 529.016</td><td>35.5</td><td>1.107 × 10<sup>-4</sup></td><td>2.53 (0.07)</td><td>16.8 (1.1)</td></tr><tr><td>SO<sub>2</sub></td><td>17<sub>2,16</sub>-17<sub>1,17</sub></td><td>273 752.962</td><td>149.2</td><td>9.966 × 10<sup>-5</sup></td><td>0.29 (0.06)</td><td>12 (2)</td></tr><tr><td>SO<sub>2</sub></td><td>15<sub>3,13</sub>-15<sub>2,14</sub></td><td>275 240.185</td><td>132.5</td><td>1.645 × 10<sup>-4</sup></td><td>0.64 (0.08)</td><td>8 (4)</td></tr><tr><td>SO<sub>2</sub></td><td>26<sub>4,22</sub>-26<sub>3,23</sub></td><td>280 807.246</td><td>364.3</td><td>2.329 × 10<sup>-4</sup></td><td>0.22 (0.05)</td><td>4.8 (1.3)</td></tr><tr><td>SO<sub>2</sub></td><td>36<sub>4,32</sub>-36<sub>3,33</sub></td><td>281 688.930</td><td>662.1</td><td>2.636 × 10<sup>-4</sup></td><td>0.22 (0.03)</td><td>9 (2)</td></tr><tr><td>SO<sub>2</sub></td><td>15<sub>1,15</sub>-14<sub>0,14</sub></td><td>281 762.602</td><td>107.4</td><td>2.609 × 10<sup>-4</sup></td><td>4.64 (0.05)</td><td>17.1 (1.1)</td></tr><tr><td>SO<sub>2</sub></td><td>6<sub>2,4</sub>-5<sub>1,5</sub></td><td>282 036.568</td><td>29.2</td><td>1.003 × 10<sup>-4</sup></td><td>4.33 (0.05)</td><td>17.7 (1.1)</td></tr><tr><td>SO<sub>2</sub></td><td>20<sub>1,19</sub>-20<sub>0,20</sub></td><td>282 292.806</td><td>198.9</td><td>1.002 × 10<sup>-4</sup></td><td>0.40 (0.05)</td><td>16 (2)</td></tr><tr><td>SO<sub>2</sub></td><td>16<sub>0,16</sub>-15<sub>1,15</sub></td><td>283 464.770</td><td>121.0</td><td>2.700 × 10<sup>-4</sup></td><td>3.80 (0.03)</td><td>22.0 (1.1)</td></tr><tr><td>SO<sub>2</sub></td><td>17<sub>3,15</sub>-17<sub>2,16</sub></td><td>285 743.589</td><td>162.9</td><td>1.816 × 10<sup>-4</sup></td><td>0.78 (0.06)</td><td>17.5 (1.0)</td></tr><tr><td>SO<sub>2</sub></td><td>22<sub>2,20</sub>-21<sub>3,19</sub></td><td>286 416.272</td><td>248.5</td><td>9.293 × 10<sup>-5</sup></td><td>0.30 (0.06)</td><td>16 (2)</td></tr><tr><td>SO<sub>2</sub></td><td>18<sub>1,17</sub>-17<sub>2,16</sub></td><td>288 519.997</td><td>163.1</td><td>1.570 × 10<sup>-4</sup></td><td>1.00 (0.06)</td><td>16.3 (1.1)</td></tr><tr><td>SO<sub>2</sub></td><td>26<sub>2,24</sub>-26<sub>1,25</sub></td><td>296 168.675</td><td>340.6</td><td>1.873 × 10<sup>-4</sup></td><td>0.21 (0.02)</td><td>10.2 (1.4)</td></tr><tr><td>SO<sub>2</sub></td><td>9<sub>2,8</sub>-8<sub>1,7</sub></td><td>298 576.309</td><td>51.0</td><td>1.442 × 10<sup>-4</sup></td><td>3.35 (0.04)</td><td>17.1 (1.0)</td></tr><tr><td>SO<sub>2</sub></td><td>19<sub>3,17</sub>-19<sub>2,18</sub></td><td>299 316.820</td><td>197.0</td><td>2.037 × 10<sup>-4</sup></td><td>0.55 (0.06)</td><td>17 (2)</td></tr><tr><td>SO<sub>2</sub></td><td>32<sub>3,29</sub>-32<sub>2,30</sub></td><td>300 273.420</td><td>518.7</td><td>2.547 × 10<sup>-4</sup></td><td>0.13 (0.03)</td><td>6 (2)</td></tr><tr><td>SO<sub>2</sub></td><td>19<sub>2,18</sub>-19<sub>1,19</sub></td><td>301 896.629</td><td>182.6</td><td>1.229 × 10<sup>-4</sup></td><td>0.35 (0.06)</td><td>20 (3)</td></tr><tr><td>SO<sub>2</sub></td><td>38<sub>4,34</sub>-38<sub>3,35</sub></td><td>307 185.315</td><td>733.4</td><td>3.228 × 10<sup>-4</sup></td><td>0.41 (0.06)</td><td>9 (2)</td></tr><tr><td>SO<sub>2</sub></td><td>22<sub>4,18</sub>-22<sub>3,19</sub></td><td>312 542.520</td><td>272.8</td><td>2.819 × 10<sup>-4</sup></td><td>0.27 (0.03)</td><td>9 (2)</td></tr><tr><td>SO<sub>2</sub></td><td>3<sub>3,1</sub>-2<sub>2,0</sub></td><td>313 279.719</td><td>27.6</td><td>3.396 × 10<sup>-4</sup></td><td>3.77 (0.07)</td><td>18.2 (1.0)</td></tr><tr><td>SO<sub>2</sub></td><td>17<sub>1,17</sub>-16<sub>0,16</sub></td><td>313 660.853</td><td>136.1</td><td>3.747 × 10<sup>-4</sup></td><td>1.87 (0.05)</td><td>16.5 (1.0)</td></tr><tr><td>SO<sub>2</sub></td><td>21<sub>3,19</sub>-21<sub>2,20</sub></td><td>316 098.875</td><td>234.7</td><td>2.319 × 10<sup>-4</sup></td><td>0.35 (0.04)</td><td>5 (2)</td></tr><tr><td>SO<sub>2</sub></td><td>18<sub>0,18</sub>-17<sub>1,17</sub></td><td>321 330.168</td><td>151.5</td><td>4.087 × 10<sup>-4</sup></td><td>1.5 (0.2)</td><td>11 (2)</td></tr><tr><td>SO<sub>2</sub></td><td>4<sub>3,1</sub>-3<sub>2,2</sub></td><td>332 505.243</td><td>31.3</td><td>3.290 × 10<sup>-4</sup></td><td>3.01 (0.09)</td><td>17.0 (1.0)</td></tr><tr><td>SO<sub>2</sub></td><td>8<sub>2,6</sub>-7<sub>1,7</sub></td><td>334 673.355</td><td>43.1</td><td>1.270 × 10<sup>-4</sup></td><td>2.5 (0.2)</td><td>21 (2)</td></tr><tr><td>SO<sub>2</sub></td><td>18<sub>4,14</sub>-18<sub>3,15</sub></td><td>338 305.994</td><td>196.8</td><td>3.266 × 10<sup>-4</sup></td><td>0.44 (0.06)</td><td>17 (2)</td></tr><tr><td>SO<sub>2</sub></td><td>20<sub>1,19</sub>-19<sub>2,18</sub></td><td>338 611.811</td><td>198.9</td><td>2.868 × 10<sup>-4</sup></td><td>0.48 (0.06)</td><td>9 (2)</td></tr><tr><td>SO<sub>2</sub></td><td>28<sub>2,26</sub>-28<sub>1,27</sub></td><td>340 316.406</td><td>391.8</td><td>2.580 × 10<sup>-4</sup></td><td>0.36 (0.04)</td><td>10.8 (1.0)</td></tr><tr><td>SO<sub>2</sub></td><td>36<sub>5,31</sub>-36<sub>4,32</sub></td><td>341 673.955</td><td>678.5</td><td>4.344 × 10<sup>-4</sup></td><td>0.18 (0.03)</td><td>4 (2)</td></tr><tr><td>SO<sub>2</sub></td><td>34<sub>3,31</sub>-34<sub>2,32</sub></td><td>342 761.629</td><td>581.9</td><td>3.447 × 10<sup>-4</sup></td><td>0.18 (0.03)</td><td>4 (2)</td></tr><tr><td>SO<sub>2</sub></td><td>13<sub>2,12</sub>-12<sub>1,11</sub></td><td>345 338.540</td><td>93.0</td><td>2.381 × 10<sup>-4</sup></td><td>HB</td><td>HB</td></tr><tr><td>SO<sub>2</sub></td><td>16<sub>4,12</sub>-16<sub>3,13</sub></td><td>346 523.879</td><td>164.5</td><td>3.390 × 10<sup>-4</sup></td><td>HB</td><td>HB</td></tr><tr><td>SO<sub>2</sub></td><td>19<sub>1,19</sub>-18<sub>0,18</sub></td><td>346 652.171</td><td>168.1</td><td>5.219 × 10<sup>-4</sup></td><td>1.43 (0.12)</td><td>19 (3)</td></tr><tr><td>SO<sub>2</sub></td><td>5<sub>3,3</sub>-4<sub>2,2</sub></td><td>351 257.225</td><td>35.9</td><td>3.357 × 10<sup>-4</sup></td><td>2.05 (0.12)</td><td>17.2 (1.0)</td></tr><tr><td><sup>34</sup>SO<sub>2</sub></td><td>3<sub>1,3</sub>-2<sub>0,2</sub></td><td>102 031.880</td><td>7.6</td><td>9.495 × 10<sup>-6</sup></td><td>0.17 (0.02)</td><td>24 (6)</td></tr><tr><td><sup>34</sup>SO<sub>2</sub></td><td>8<sub>2,6</sub>-8<sub>1,7</sub></td><td>128 668.791</td><td>42.8</td><td>2.245 × 10<sup>-5</sup></td><td>0.054 (0.015)</td><td>10 (6)</td></tr><tr><td><sup>34</sup>SO<sub>2</sub></td><td>5<sub>1,5</sub>-4<sub>0,4</sub></td><td>133 471.429</td><td>15.5</td><td>2.107 × 10<sup>-5</sup></td><td>0.19 (0.02)</td><td>16 (6)</td></tr><tr><td><sup>34</sup>SO<sub>2</sub></td><td>4<sub>3,1</sub>-5<sub>2,4</sub></td><td>151 917.559</td><td>30.5</td><td>3.663 × 10<sup>-6</sup></td><td>0.07 (0.02)</td><td>13 (5)</td></tr><tr><td><sup>34</sup>SO<sub>2</sub></td><td>3<sub>2,2</sub>-3<sub>1,3</sub></td><td>153 015.053</td><td>15.0</td><td>2.290 × 10<sup>-5</sup></td><td>0.11 (0.02)</td><td>12 (5)</td></tr><tr><td><sup>34</sup>SO<sub>2</sub></td><td>18<sub>2,16</sub>-18<sub>1,17</sub></td><td>160 802.573</td><td>170.3</td><td>4.611 × 10<sup>-5</sup></td><td>0.04 (0.01)</td><td>4 (4)</td></tr><tr><td><sup>34</sup>SO<sub>2</sub></td><td>10<sub>0,10</sub>-9<sub>1,9</sub></td><td>162 020.378</td><td>49.5</td><td>4.100 × 10<sup>-5</sup></td><td>0.24 (0.02)</td><td>17 (2)</td></tr><tr><td><sup>34</sup>SO<sub>2</sub></td><td>7<sub>1,7</sub>-6<sub>0,6</sub></td><td>162 775.882</td><td>26.9</td><td>3.976 × 10<sup>-5</sup></td><td>0.35 (0.02)</td><td>17 (2)</td></tr><tr><td><sup>34</sup>SO<sub>2</sub></td><td>11<sub>1,11</sub>-10<sub>0,10</sub></td><td>219 355.012</td><td>60.1</td><td>1.110 × 10<sup>-4</sup></td><td>0.32 (0.02)</td><td>15.2 (1.4)</td></tr><tr><td><sup>34</sup>SO<sub>2</sub></td><td>13<sub>1,13</sub>-12<sub>0,12</sub></td><td>248 698.698</td><td>81.8</td><td>1.721 × 10<sup>-4</sup></td><td>0.26 (0.04)</td><td>18 (2)</td></tr><tr><td><sup>34</sup>SO<sub>2</sub></td><td>7<sub>2,6</sub>-6<sub>1,5</sub></td><td>265 554.053</td><td>35.1</td><td>1.038 × 10<sup>-4</sup></td><td>0.52 (0.04)</td><td>27 (2)</td></tr><tr><td>PN</td><td>2-1</td><td>93 979.768</td><td>6.8</td><td>2.916 × 10<sup>-5</sup></td><td>0.18 (0.02)</td><td>16 (3)</td></tr><tr><td>PN</td><td>3-2</td><td>140 967.690</td><td>13.5</td><td>1.054 × 10<sup>-4</sup></td><td>0.48 (0.02)</td><td>17 (2)</td></tr><tr><td>PN</td><td>5-4</td><td>234 935.691</td><td>33.8</td><td>5.177 × 10<sup>-4</sup></td><td>0.82 (0.05)</td><td>14.2 (1.4)</td></tr><tr><td>PN</td><td>6-5</td><td>281 914.200</td><td>47.4</td><td>9.083 × 10<sup>-4</sup></td><td>0.99 (0.06)</td><td>18.6 (1.1)</td></tr></tbody></table>
Table A.1. continued.

<table><thead><tr><th>Molecule</th><th>Transition QNs</th><th>ν<sub>rest</sub> (MHz)</th><th>E<sub>u</sub> (K)</th><th>A<sub>ul</sub> (s<sup>-1</sup>)</th><th>∫ T<sup>*</sup><sub>ant</sub> dv (K km s<sup>-1</sup>)</th><th>ν<sub>exp</sub> (km s<sup>-1</sup>)</th></tr></thead><tbody><tr><td>PO</td><td>Ω = 1/2,e,(5/2,3)-(3/2,2)</td><td>108 998.445</td><td>8.4</td><td>2.132 × 10<sup>-5</sup></td><td>0.08 (0.02)</td><td>6 (3)</td></tr><tr><td>PO</td><td>Ω = 1/2,f,(5/2,3)-(3/2,2)</td><td>109 206.200</td><td>8.4</td><td>2.143 × 10<sup>-5</sup></td><td>0.07 (0.02)</td><td>7 (3)</td></tr><tr><td>PO</td><td>Ω = 1/2,e,(7/2,4)-(5/2,3)</td><td>152 656.979</td><td>15.7</td><td>6.274 × 10<sup>-5</sup></td><td>0.28 (0.03)</td><td>BF</td></tr><tr><td>PO</td><td>Ω = 1/2,e,(7/2,3)-(5/2,2)</td><td>152 680.282</td><td>15.7</td><td>5.975 × 10<sup>-5</sup></td><td>0.14 (0.02)</td><td>BF</td></tr><tr><td>PO</td><td>Ω = 1/2,f,(7/2,4)-(5/2,3)</td><td>152 855.454</td><td>15.8</td><td>6.296 × 10<sup>-5</sup></td><td>0.14 (0.02)</td><td>13 (4)</td></tr><tr><td>PO</td><td>Ω = 1/2,f,(7/2,3)-(5/2,2)</td><td>152 888.128</td><td>15.7</td><td>5.998 × 10<sup>-5</sup></td><td>0.16 (0.02)</td><td>15 (4)</td></tr><tr><td>PO</td><td>Ω = 1/2,e,(11/2,5)-(9/2,5)</td><td>239 704.364</td><td>36.7</td><td>4.699 × 10<sup>-6</sup></td><td>0.06 (0.02)</td><td>5 (3)</td></tr><tr><td>PO</td><td>Ω = 1/2,f,(11/2,6)-(9/2,5)</td><td>239 948.978</td><td>36.7</td><td>2.583 × 10<sup>-4</sup></td><td rowspan="2">0.33 (0.04)</td><td rowspan="2">HB</td></tr><tr><td>PO</td><td>Ω = 1/2,f,(11/2,5)-(9/2,4)</td><td>239 958.096</td><td>36.7</td><td>2.536 × 10<sup>-4</sup></td></tr><tr><td>PO</td><td>Ω = 1/2,e,(11/2,6)-(9/2,5)</td><td>240 141.054</td><td>36.7</td><td>2.590 × 10<sup>-4</sup></td><td rowspan="2">0.25 (0.04)</td><td rowspan="2">HB</td></tr><tr><td>PO</td><td>Ω = 1/2,e,(11/2,5)-(9/2,4)</td><td>240 152.530</td><td>36.7</td><td>2.543 × 10<sup>-4</sup></td></tr><tr><td>PO</td><td>Ω = 1/2,f,(13/2,7)-(11/2,6)</td><td>283 586.816</td><td>50.3</td><td>4.330 × 10<sup>-4</sup></td><td rowspan="2">0.44 (0.03)</td><td rowspan="2">HB</td></tr><tr><td>PO</td><td>Ω = 1/2,f,(13/2,6)-(11/2,5)</td><td>283 593.166</td><td>50.3</td><td>4.274 × 10<sup>-4</sup></td></tr><tr><td>PO</td><td>Ω = 1/2,e,(13/2,7)-(11/2,6)</td><td>283 777.587</td><td>50.3</td><td>4.339 × 10<sup>-4</sup></td><td rowspan="2">0.44 (0.03)</td><td rowspan="2">HB</td></tr><tr><td>PO</td><td>Ω = 1/2,e,(13/2,6)-(11/2,5)</td><td>283 785.404</td><td>50.3</td><td>4.283 × 10<sup>-4</sup></td></tr><tr><td>NO</td><td>Ω = 1/2,e,(5/2,7/2)-(3/2,5/2)</td><td>250 436.842</td><td>19.2</td><td>1.841 × 10<sup>-6</sup></td><td rowspan="3">0.47 (0.05)</td><td rowspan="3">HB</td></tr><tr><td>NO</td><td>Ω = 1/2,e,(5/2,5/2)-(3/2,3/2)</td><td>250 440.653</td><td>19.2</td><td>1.547 × 10<sup>-6</sup></td></tr><tr><td>NO</td><td>Ω = 1/2,e,(5/2,3/2)-(3/2,1/2)</td><td>250 448.526</td><td>19.2</td><td>1.381 × 10<sup>-6</sup></td></tr><tr><td>NO</td><td>Ω = 1/2,e,(5/2,3/2)-(3/2,5/2)</td><td>250 517.704</td><td>19.2</td><td>1.841 × 10<sup>-8</sup></td><td>0.17 (0.04)</td><td>20 (2)</td></tr><tr><td>o-H<sub>2</sub>CO</td><td>2<sub>1,2</sub>-1<sub>1,1</sub></td><td>140 839.516</td><td>6.8</td><td>5.296 × 10<sup>-5</sup></td><td>0.41 (0.02)</td><td>20 (2)</td></tr><tr><td>o-H<sub>2</sub>CO</td><td>2<sub>1,1</sub>-1<sub>1,0</sub></td><td>150 498.335</td><td>7.5</td><td>6.462 × 10<sup>-5</sup></td><td>0.43 (0.03)</td><td>13 (2)</td></tr><tr><td>o-H<sub>2</sub>CO</td><td>3<sub>1,3</sub>-2<sub>1,2</sub></td><td>211 211.449</td><td>16.9</td><td>2.268 × 10<sup>-4</sup></td><td>0.71 (0.05)</td><td>16.6 (1.5)</td></tr><tr><td>o-H<sub>2</sub>CO</td><td>3<sub>1,2</sub>-2<sub>1,1</sub></td><td>225 697.772</td><td>18.3</td><td>2.767 × 10<sup>-4</sup></td><td>0.61 (0.06)</td><td>18 (3)</td></tr><tr><td>o-H<sub>2</sub>CO</td><td>4<sub>1,4</sub>-3<sub>1,3</sub></td><td>281 526.919</td><td>30.4</td><td>5.874 × 10<sup>-4</sup></td><td>0.75 (0.06)</td><td>25 (2)</td></tr><tr><td>o-H<sub>2</sub>CO</td><td>4<sub>3,2</sub>-3<sub>3,1</sub></td><td>291 380.441</td><td>125.8</td><td>3.040 × 10<sup>-4</sup></td><td>0.19 (0.02)</td><td>BF</td></tr><tr><td>o-H<sub>2</sub>CO</td><td>4<sub>3,1</sub>-3<sub>3,0</sub></td><td>291 384.360</td><td>125.8</td><td>3.040 × 10<sup>-4</sup></td><td>0.29 (0.02)</td><td>BF</td></tr><tr><td>o-H<sub>2</sub>CO</td><td>4<sub>1,3</sub>-3<sub>1,2</sub></td><td>300 836.630</td><td>32.7</td><td>7.168 × 10<sup>-4</sup></td><td>0.63 (0.11)</td><td>15.1 (1.0)</td></tr><tr><td>p-H<sub>2</sub>CO</td><td>2<sub>0,2</sub>-1<sub>0,1</sub></td><td>145 602.951</td><td>10.5</td><td>7.802 × 10<sup>-5</sup></td><td>0.28 (0.02)</td><td>25 (3)</td></tr><tr><td>p-H<sub>2</sub>CO</td><td>3<sub>0,3</sub>-2<sub>0,2</sub></td><td>218 222.187</td><td>21.0</td><td>2.814 × 10<sup>-4</sup></td><td>0.26 (0.03)</td><td>24 (3)</td></tr><tr><td>p-H<sub>2</sub>CO</td><td>3<sub>2,2</sub>-2<sub>2,1</sub></td><td>218 475.634</td><td>68.1</td><td>1.569 × 10<sup>-4</sup></td><td>0.41 (0.04)</td><td>17 (2)</td></tr><tr><td>p-H<sub>2</sub>CO</td><td>4<sub>0,4</sub>-3<sub>0,3</sub></td><td>290 623.412</td><td>34.9</td><td>6.891 × 10<sup>-4</sup></td><td>0.31 (0.03)</td><td>24 (2)</td></tr><tr><td>p-H<sub>2</sub>CO</td><td>4<sub>2,2</sub>-3<sub>2,1</sub></td><td>291 948.066</td><td>82.1</td><td>5.241 × 10<sup>-4</sup></td><td>0.15 (0.03)</td><td>14 (2)</td></tr><tr><td>CN</td><td>(1, 1/2, 1/2)-(0, 1/2, 3/2)</td><td>113 144.157</td><td>5.4</td><td>1.053 × 10<sup>-6</sup></td><td>0.19 (0.03)</td><td>11 (3)</td></tr><tr><td>CN</td><td>(1, 1/2, 3/2)-(0, 1/2, 1/2)</td><td>113 170.492</td><td>5.4</td><td>5.145 × 10<sup>-6</sup></td><td>0.18 (0.03)</td><td>15 (3)</td></tr><tr><td>CN</td><td>(1, 1/2, 3/2)-(0, 1/2, 3/2)</td><td>113 191.279</td><td>5.4</td><td>6.682 × 10<sup>-6</sup></td><td>0.20 (0.03)</td><td>18 (4)</td></tr><tr><td>CN</td><td>(1, 3/2, 3/2)-(0, 1/2, 1/2)</td><td>113 488.120</td><td>5.4</td><td>6.736 × 10<sup>-6</sup></td><td rowspan="2">0.47 (0.03)</td><td rowspan="2">HB</td></tr><tr><td>CN</td><td>(1, 3/2, 5/2)-(0, 1/2, 3/2)</td><td>113 490.970</td><td>5.4</td><td>1.192 × 10<sup>-5</sup></td></tr><tr><td>CN</td><td>(2, 3/2, 1/2)-(1, 3/2, 3/2)</td><td>226 298.943</td><td>16.3</td><td>8.227 × 10<sup>-6</sup></td><td rowspan="2">HB</td><td rowspan="2">HB</td></tr><tr><td>CN</td><td>(2, 3/2, 3/2)-(1, 3/2, 1/2)</td><td>226 303.037</td><td>16.3</td><td>4.169 × 10<sup>-6</sup></td></tr><tr><td>CN</td><td>(2, 3/2, 1/2)-(1, 1/2, 3/2)</td><td>226 616.571</td><td>16.3</td><td>1.073 × 10<sup>-5</sup></td><td>0.21 (0.03)</td><td>20.9 (1.5)</td></tr><tr><td>CN</td><td>(2, 3/2, 3/2)-(1, 1/2, 3/2)</td><td>226 632.190</td><td>16.3</td><td>4.259 × 10<sup>-5</sup></td><td>0.28 (0.02)</td><td>11 (3)</td></tr><tr><td>CN</td><td>(2, 3/2, 5/2)-(1, 1/2, 3/2)</td><td>226 659.558</td><td>16.3</td><td>9.467 × 10<sup>-5</sup></td><td rowspan="2">1.32 (0.04)</td><td rowspan="2">HB</td></tr><tr><td>CN</td><td>(2, 3/2, 1/2)-(1, 1/2, 1/2)</td><td>226 663.693</td><td>16.3</td><td>8.465 × 10<sup>-5</sup></td></tr><tr><td>CN</td><td>(2, 3/2, 3/2)-(1, 1/2, 1/2)</td><td>226 679.311</td><td>16.3</td><td>5.268 × 10<sup>-5</sup></td><td>0.26 (0.03)</td><td>10.9 (1.1)</td></tr><tr><td>CN</td><td>(2, 5/2, 5/2)-(1, 3/2, 3/2)</td><td>226 874.191</td><td>16.3</td><td>9.621 × 10<sup>-5</sup></td><td rowspan="4">1.60 (0.04)</td><td rowspan="4">HB</td></tr><tr><td>CN</td><td>(2, 5/2, 7/2)-(1, 3/2, 5/2)</td><td>226 874.781</td><td>16.3</td><td>1.143 × 10<sup>-4</sup></td></tr><tr><td>CN</td><td>(2, 5/2, 3/2)-(1, 3/2, 1/2)</td><td>226 875.896</td><td>16.3</td><td>8.587 × 10<sup>-5</sup></td></tr><tr><td>CN</td><td>(2, 5/2, 3/2)-(1, 3/2, 3/2)</td><td>226 887.420</td><td>16.3</td><td>2.731 × 10<sup>-5</sup></td></tr><tr><td>CN</td><td>(3, 5/2, 7/2)-(2, 5/2, 7/2)</td><td>339 516.635</td><td>32.6</td><td>2.535 × 10<sup>-5</sup></td><td>0.13 (0.03)</td><td>4.4 (0.4)</td></tr><tr><td>CN</td><td>(3, 5/2, 3/2)-(2, 3/2, 3/2)</td><td>340 019.626</td><td>32.6</td><td>9.270 × 10<sup>-5</sup></td><td rowspan="4">1.31 (0.05)</td><td rowspan="4">HB</td></tr><tr><td>CN</td><td>(3, 5/2, 7/2)-(2, 3/2, 5/2)</td><td>340 031.549</td><td>32.6</td><td>3.845 × 10<sup>-4</sup></td></tr><tr><td>CN</td><td>(3, 5/2, 3/2)-(2, 3/2, 1/2)</td><td>340 035.408</td><td>32.6</td><td>2.887 × 10<sup>-4</sup></td></tr><tr><td>CN</td><td>(3, 5/2, 5/2)-(2, 3/2, 3/2)</td><td>340 035.408</td><td>32.6</td><td>3.231 × 10<sup>-4</sup></td></tr></tbody></table>
<table><caption>Table A.1. continued.</caption><thead><tr><th>Molecule</th><th>Transition QNs</th><th>ν<sub>rest</sub> (MHz)</th><th>E<sub>u</sub> (K)</th><th>A<sub>ul</sub> (s<sup>-1</sup>)</th><th>∫ T<sup>*</sup><sub>ant</sub> dv (K km s<sup>-1</sup>)</th><th>ν<sub>exp</sub> (km s<sup>-1</sup>)</th></tr></thead><tbody><tr><td>CN</td><td>(3, 7/2, 7/2)–(2, 5/2, 5/2)</td><td>340 247.770</td><td>32.7</td><td>3.796 × 10<sup>-4</sup></td><td rowspan="5">0.83 (0.05)</td><td rowspan="5">HB</td></tr><tr><td>CN</td><td>(3, 7/2, 9/2)–(2, 5/2, 7/2)</td><td>340 247.770</td><td>32.7</td><td>4.131 × 10<sup>-4</sup></td></tr><tr><td>CN</td><td>(3, 7/2, 5/2)–(2, 5/2, 3/2)</td><td>340 248.544</td><td>32.7</td><td>3.674 × 10<sup>-4</sup></td></tr><tr><td>CN</td><td>(3, 7/2, 5/2)–(2, 5/2, 5/2)</td><td>340 261.773</td><td>32.7</td><td>4.479 × 10<sup>-5</sup></td></tr><tr><td>CN</td><td>(3, 7/2, 7/2)–(2, 5/2, 7/2)</td><td>340 264.949</td><td>32.7</td><td>3.350 × 10<sup>-5</sup></td></tr><tr><td>NS</td><td>Ω = 1/2,e,(7/2, 9/2)–(5/2, 7/2)</td><td>161 297.246</td><td>16.6</td><td>6.865 × 10<sup>-5</sup></td><td rowspan="5">0.35 (0.02)</td><td rowspan="5">HB</td></tr><tr><td>NS</td><td>Ω = 1/2,e,(7/2, 7/2)–(5/2, 5/2)</td><td>161 298.411</td><td>16.6</td><td>6.301 × 10<sup>-5</sup></td></tr><tr><td>NS</td><td>Ω = 1/2,e,(7/2, 5/2)–(5/2, 3/2)</td><td>161 301.747</td><td>16.6</td><td>6.108 × 10<sup>-5</sup></td></tr><tr><td>NS</td><td>Ω = 1/2,f,(7/2, 9/2)–(5/2, 7/2)</td><td>161 697.257</td><td>16.7</td><td>6.916 × 10<sup>-5</sup></td></tr><tr><td>NS</td><td>Ω = 1/2,f,(7/2, 7/2)–(5/2, 5/2)</td><td>161 703.404</td><td>16.7</td><td>6.348 × 10<sup>-5</sup></td></tr><tr><td>NS</td><td>Ω = 1/2,f,(7/2, 5/2)–(5/2, 3/2)</td><td>161 703.987</td><td>16.7</td><td>6.154 × 10<sup>-5</sup></td><td rowspan="5">0.31 (0.02)</td><td rowspan="5">HB</td></tr><tr><td>NS</td><td>Ω = 1/2,e,(9/2, 11/2)–(7/2, 9/2)</td><td>207 436.051</td><td>26.5</td><td>1.512 × 10<sup>-4</sup></td></tr><tr><td>NS</td><td>Ω = 1/2,e,(9/2, 9/2)–(7/2, 7/2)</td><td>207 436.636</td><td>26.5</td><td>1.436 × 10<sup>-4</sup></td></tr><tr><td>NS</td><td>Ω = 1/2,e,(9/2, 7/2)–(7/2, 5/2)</td><td>207 438.692</td><td>26.5</td><td>1.417 × 10<sup>-4</sup></td></tr><tr><td>NS</td><td>Ω = 1/2,f,(9/2, 11/2)–(7/2, 9/2)</td><td>207 834.866</td><td>26.6</td><td>1.521 × 10<sup>-4</sup></td></tr><tr><td>NS</td><td>Ω = 1/2,f,(9/2, 9/2)–(7/2, 7/2)</td><td>207 838.365</td><td>26.6</td><td>1.445 × 10<sup>-4</sup></td><td rowspan="5">0.35 (0.03)</td><td rowspan="5">HB</td></tr><tr><td>NS</td><td>Ω = 1/2,f,(9/2, 7/2)–(7/2, 5/2)</td><td>207 838.365</td><td>26.6</td><td>1.425 × 10<sup>-4</sup></td></tr><tr><td>NS</td><td>Ω = 1/2,e,(11/2, 13/2)–(9/2, 11/2)</td><td>253 570.476</td><td>38.7</td><td>2.824 × 10<sup>-4</sup></td></tr><tr><td>NS</td><td>Ω = 1/2,e,(11/2, 11/2)–(9/2, 9/2)</td><td>253 570.476</td><td>38.7</td><td>2.730 × 10<sup>-4</sup></td></tr><tr><td>NS</td><td>Ω = 1/2,e,(11/2, 9/2)–(9/2, 7/2)</td><td>253 572.148</td><td>38.7</td><td>2.711 × 10<sup>-4</sup></td></tr><tr><td>NS</td><td>Ω = 1/2,f,(11/2, 13/2)–(9/2, 11/2)</td><td>253 968.393</td><td>38.8</td><td>2.838 × 10<sup>-4</sup></td><td rowspan="5">0.47 (0.03)</td><td rowspan="5">HB</td></tr><tr><td>NS</td><td>Ω = 1/2,f,(11/2, 11/2)–(9/2, 9/2)</td><td>253 970.581</td><td>38.8</td><td>2.743 × 10<sup>-4</sup></td></tr><tr><td>NS</td><td>Ω = 1/2,f,(11/2, 9/2)–(9/2, 7/2)</td><td>253 970.581</td><td>38.8</td><td>2.723 × 10<sup>-4</sup></td></tr><tr><td>NS</td><td>Ω = 1/2,f,(15/2, 17/2)–(13/2, 15/2)</td><td>346 220.137</td><td>69.8</td><td>7.385 × 10<sup>-4</sup></td></tr><tr><td>NS</td><td>Ω = 1/2,f,(15/2, 15/2)–(13/2, 13/2)</td><td>346 221.163</td><td>69.8</td><td>7.250 × 10<sup>-4</sup></td></tr><tr><td>NS</td><td>Ω = 1/2,f,(15/2, 13/2)–(13/2, 11/2)</td><td>346 221.163</td><td>69.8</td><td>7.234 × 10<sup>-4</sup></td><td rowspan="3">0.15 (0.05)</td><td rowspan="3">HB</td></tr></tbody></table>
<table><caption>**Table A.2.** Line parameters for transitions that may present variability.</caption><thead><tr><th>Molecule</th><th>Transition QNs</th><th>ν<sub>rest</sub> (MHz)</th><th>E<sub>u</sub> (K)</th><th>A<sub>ul</sub> (s<sup>-1</sup>)</th><th>∫ T<sup>*</sup><sub>ant</sub> dv (K km s<sup>-1</sup>)</th><th>v<sub>exp</sub> (km s<sup>-1</sup>)</th><th>Julian date</th></tr></thead><tbody><tr><td>SiO v = 1</td><td>2–1</td><td>86 243.429</td><td>1775.4</td><td>2.903 × 10<sup>-5</sup></td><td>154.73 (0.04)</td><td>7 (3)</td><td>2 455 018.5</td></tr><tr><td>SiO v = 1</td><td>3–2</td><td>129 363.350</td><td>1781.6</td><td>1.050 × 10<sup>-4</sup></td><td>50.01 (0.02)</td><td>5 (2)</td><td>2 455 018.5</td></tr><tr><td>SiO v = 1</td><td>4–3</td><td>172 481.120</td><td>1789.9</td><td>2.580 × 10<sup>-4</sup></td><td>12.98 (0.02)</td><td>5 (2)</td><td>2 455 578.5</td></tr><tr><td>SiO v = 1</td><td>5–4</td><td>215 596.021</td><td>1800.3</td><td>5.154 × 10<sup>-4</sup></td><td>7.52 (0.03)</td><td>4 (1)</td><td>2 456 579.5</td></tr><tr><td>SiO v = 1</td><td>6–5</td><td>258 707.335</td><td>1812.7</td><td>9.042 × 10<sup>-4</sup></td><td>1.04 (0.07)</td><td>8 (1)</td><td>2 455 309.5</td></tr><tr><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>1.99 (0.05)</td><td>4 (1)</td><td>2 456 579.5</td></tr><tr><td>SiO v = 1</td><td>7–6</td><td>301 814.346</td><td>1827.2</td><td>1.452 × 10<sup>-3</sup></td><td>4.40 (0.08)</td><td>6 (1)</td><td>2 455 550.5</td></tr><tr><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>5.35 (0.10)</td><td>6 (1)</td><td>2 455 574.5</td></tr><tr><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>4.88 (0.05)</td><td>8 (1)</td><td>2 456 320.5</td></tr><tr><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>2.33 (0.12)</td><td>10 (1)</td><td>2 456 616.5</td></tr><tr><td>SiO v = 1</td><td>8–7</td><td>344 916.336</td><td>1843.7</td><td>2.185 × 10<sup>-3</sup></td><td>0.74 (0.08)</td><td>8 (1)</td><td>2 455 576.5</td></tr><tr><td>SiO v = 2</td><td>2–1</td><td>85 640.455</td><td>3527.5</td><td>2.879 × 10<sup>-5</sup></td><td>0.77 (0.02)</td><td>7 (3)</td><td>2 455 018.5</td></tr><tr><td>SiO v = 2</td><td>3–2</td><td>128 458.888</td><td>3533.6</td><td>1.041 × 10<sup>-4</sup></td><td>1.63 (0.01)</td><td>4.70 (2)</td><td>2 455 018.5</td></tr><tr><td>SiO v = 2</td><td>4–3</td><td>171 275.169</td><td>3541.9</td><td>2.559 × 10<sup>-4</sup></td><td>6.62 (0.04)</td><td>8 (2)</td><td>2 455 578.5</td></tr><tr><td>SiO v = 2</td><td>5–4</td><td>214 088.579</td><td>3552.1</td><td>5.110 × 10<sup>-4</sup></td><td>1.94 (0.03)</td><td>7 (1)</td><td>2 456 579.5</td></tr><tr><td>SiO v = 2</td><td>6–5</td><td>256 898.401</td><td>3564.5</td><td>8.966 × 10<sup>-4</sup></td><td>2.03 (0.05)</td><td>7 (1)</td><td>2 456 579.5</td></tr><tr><td>SiO v = 2</td><td>7–6</td><td>299 703.918</td><td>3578.9</td><td>1.439 × 10<sup>-3</sup></td><td>1.63 (0.09)</td><td>2 (1)</td><td>2 455 550.5</td></tr><tr><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>6.29 (0.06)</td><td>3 (1)</td><td>2 456 320.5</td></tr><tr><td>SiO v = 2</td><td>8–7</td><td>342 504.411</td><td>3595.3</td><td>2.166 × 10<sup>-3</sup></td><td>0.34 (0.07)</td><td>5 (1)</td><td>2 455 576.5</td></tr><tr><td>SiO v = 3</td><td>4–3</td><td>170 070.353</td><td>5276.8</td><td>2.536 × 10<sup>-4</sup></td><td>2.78 (0.02)</td><td>4 (2)</td><td>2 455 576.5</td></tr><tr><td>SiO v = 3</td><td>5–4</td><td>212 582.557</td><td>5287.0</td><td>5.066 × 10<sup>-4</sup></td><td>0.12 (0.03)</td><td>3 (1)</td><td>2 456 579.5</td></tr><tr><td>SiO v = 3</td><td>6–5</td><td>255 091.170</td><td>5299.2</td><td>8.888 × 10<sup>-4</sup></td><td>0.78 (0.03)</td><td>8 (1)</td><td>2 456 579.5</td></tr><tr><td>SiO v = 3</td><td>7–6</td><td>297 595.476</td><td>5313.5</td><td>1.427 × 10<sup>-3</sup></td><td>1.46 (0.03)</td><td>2 (3)</td><td>2 456 371.5</td></tr><tr><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>0.01 (0.02)</td><td>3 (1)</td><td>2 456 615.5</td></tr><tr><td>SiO v = 3</td><td>8–7</td><td>340 094.756</td><td>5329.8</td><td>2.148 × 10<sup>-3</sup></td><td>0.36 (0.05)</td><td>5 (1)</td><td>2 455 575.5</td></tr><tr><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>0.37 (0.10)</td><td>3 (1)</td><td>2 456 615.5</td></tr><tr><td><sup>29</sup>SiO v = 1</td><td>2–1</td><td>85 166.957</td><td>1764.3</td><td>2.796 × 10<sup>-5</sup></td><td>1.50 (0.03)</td><td>7 (3)</td><td>2 455 018.5</td></tr><tr><td><sup>29</sup>SiO v = 1</td><td>4–3</td><td>170 328.320</td><td>1778.6</td><td>2.485 × 10<sup>-4</sup></td><td>9.34 (0.02)</td><td>5 (2)</td><td>2 455 576.5</td></tr><tr><td><sup>29</sup>SiO v = 1</td><td>5–4</td><td>212 905.155</td><td>1788.8</td><td>4.963 × 10<sup>-4</sup></td><td>0.15 (0.03)</td><td>1 (2)</td><td>2 456 579.5</td></tr><tr><td><sup>29</sup>SiO v = 1</td><td>6–5</td><td>255 478.493</td><td>1801.1</td><td>8.707 × 10<sup>-4</sup></td><td>11.18 (0.04)</td><td>5 (2)</td><td>2 456 579.5</td></tr><tr><td><sup>29</sup>SiO v = 1</td><td>7–6</td><td>298 047.635</td><td>1815.4</td><td>1.398 × 10<sup>-3</sup></td><td>0.80 (0.06)</td><td>5 (1)</td><td>2 455 550.5</td></tr><tr><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>2.91 (0.04)</td><td>4 (1)</td><td>2 456 320.5</td></tr><tr><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>2.21 (0.04)</td><td>5 (1)</td><td>2 456 371.5</td></tr><tr><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>0.35 (0.03)</td><td>4 (1)</td><td>2 456 615.5</td></tr><tr><td><sup>29</sup>SiO v = 1</td><td>8–7</td><td>340 611.882</td><td>1831.8</td><td>2.104 × 10<sup>-3</sup></td><td>0.21 (0.06)</td><td>5 (1)</td><td>2 455 575.5</td></tr><tr><td><sup>29</sup>SiO v = 2</td><td>2–1</td><td>84 575.290</td><td>3505.6</td><td>2.773 × 10<sup>-5</sup></td><td>12.64 (0.02)</td><td>10 (3)</td><td>2 455 018.5</td></tr><tr><td><sup>29</sup>SiO v = 2</td><td>4–3</td><td>169 144.982</td><td>3519.8</td><td>2.464 × 10<sup>-4</sup></td><td>0.66 (0.02)</td><td>6 (2)</td><td>2 455 576.5</td></tr><tr><td><sup>29</sup>SiO v = 2</td><td>5–4</td><td>211 425.980</td><td>3529.9</td><td>4.922 × 10<sup>-4</sup></td><td>0.16 (0.02)</td><td>2 (2)</td><td>2 456 579.5</td></tr><tr><td><sup>29</sup>SiO v = 2</td><td>6–5</td><td>253 703.479</td><td>3542.1</td><td>8.635 × 10<sup>-4</sup></td><td>9.61 (0.03)</td><td>1 (2)</td><td>2 456 579.5</td></tr><tr><td><sup>29</sup>SiO v = 3</td><td>8–7</td><td>335 880.698</td><td>5296.5</td><td>2.069 × 10<sup>-3</sup></td><td>0.3 (0.3)</td><td>8 (2)</td><td>2 455 579.5</td></tr><tr><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>1.0 (0.2)</td><td>2 (2)</td><td>2 456 371.5</td></tr><tr><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>0.57 (0.10)</td><td>2 (2)</td><td>2 456 615.5</td></tr><tr><td><sup>30</sup>SiO v = 1</td><td>4–3</td><td>168 323.349</td><td>1768.0</td><td>2.398 × 10<sup>-4</sup></td><td>2.00 (0.02)</td><td>4 (5)</td><td>2 455 576.5</td></tr><tr><td><sup>30</sup>SiO v = 1</td><td>5–4</td><td>210 399.065</td><td>1778.1</td><td>4.790 × 10<sup>-4</sup></td><td>1.11 (0.04)</td><td>6 (2)</td><td>2 456 579.5</td></tr><tr><td><sup>30</sup>SiO v = 1</td><td>6–5</td><td>252 471.366</td><td>1790.3</td><td>8.403 × 10<sup>-4</sup></td><td>0.15 (0.04)</td><td>4 (2)</td><td>2 456 579.5</td></tr><tr><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>0.08 (0.03)</td><td>4 (2)</td><td>2 456 579.5</td></tr><tr><td><sup>30</sup>SiO v = 1</td><td>7–6</td><td>294 539.570</td><td>1804.4</td><td>1.349 × 10<sup>-3</sup></td><td>0.59 (0.04)</td><td>6 (2)</td><td>2 456 320.5</td></tr><tr><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>0.35 (0.04)</td><td>5 (1)</td><td>2 456 371.5</td></tr><tr><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>0.23 (0.03)</td><td>6 (1)</td><td>2 456 615.5</td></tr></tbody></table>

**Notes.** Column 2: quantum numbers of the corresponding line; Col. 6: integrated intensity (in antenna temperature) of the line with its formal uncertainty; Col. 7: expansion velocity derived from the linewidth with its uncertainty which includes the width of half a channel (1 MHz) except for the lines with a low S/N where a full channel (2 MHz) is included. Column 8: Julian date. The uncertainties given (within parentheses) do not include additional uncertainties derived from the absolute flux calibration and baseline subtraction. The ellipsis symbol indicate that the field is equal to the same field of the previous row.
<table><caption>Table A.2. continued.</caption><thead><tr><th>Molecule</th><th>Transition QNs</th><th>ν<sub>rest</sub> (MHz)</th><th>E<sub>u</sub> (K)</th><th>A<sub>ul</sub> (s<sup>-1</sup>)</th><th>∫ T<sup>*</sup><sub>ant</sub> dv (K km s<sup>-1</sup>)</th><th>v<sub>exp</sub> (km s<sup>-1</sup>)</th><th>Julian date</th></tr></thead><tbody><tr><td><sup>30</sup>SiO v = 1</td><td>8–7</td><td>336 602.993</td><td>1820.6</td><td>2.031 × 10<sup>-3</sup></td><td>2.8 (0.3)</td><td>9 (1)</td><td>2 456 371.5</td></tr><tr><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>3.3 (0.3)</td><td>8 (1)</td><td>2 456 371.5</td></tr><tr><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>7.14 (0.11)</td><td>6 (1)</td><td>2 456 615.5</td></tr><tr><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>7.77 (0.13)</td><td>6 (1)</td><td>2 456 615.5</td></tr><tr><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>3.5 (0.3)</td><td>6 (1)</td><td>2 455 579.5</td></tr><tr><td><sup>30</sup>SiO v = 2</td><td>2–1</td><td>83 583.203</td><td>3485.0</td><td>2.676 × 10<sup>-5</sup></td><td>0.45 (0.02)</td><td>7 (7)</td><td>2 455 018.5</td></tr><tr><td><sup>30</sup>SiO v = 2</td><td>4–3</td><td>167 160.941</td><td>3499.1</td><td>2.379 × 10<sup>-4</sup></td><td>0.68 (0.01)</td><td>4 (3)</td><td>2 455 575.5</td></tr><tr><td>SiS v = 1</td><td>8–7</td><td>144 520.367</td><td>1102.4</td><td>5.034 × 10<sup>-5</sup></td><td>0.04 (0.01)</td><td>19 (5)</td><td>2 455 018.5</td></tr><tr><td>SiS v = 1</td><td>9–8</td><td>162 581.756</td><td>1110.2</td><td>7.215 × 10<sup>-5</sup></td><td>0.13 (0.01)</td><td>16 (4)</td><td>2 455 550.5</td></tr><tr><td>SiS v = 1</td><td>12–11</td><td>216 757.603</td><td>1138.8</td><td>1.733 × 10<sup>-4</sup></td><td>0.10 (0.03)</td><td>4 (3)</td><td>2 456 579.5</td></tr><tr><td>SiS v = 1</td><td>13–12</td><td>234 812.968</td><td>1150.1</td><td>2.209 × 10<sup>-4</sup></td><td>0.16 (0.03)</td><td>7 (3)</td><td>2 456 579.5</td></tr><tr><td>SiS v = 1</td><td>14–13</td><td>252 866.469</td><td>1162.2</td><td>2.766 × 10<sup>-4</sup></td><td>0.14 (0.03)</td><td>7 (3)</td><td>2 456 579.5</td></tr><tr><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>0.14 (0.02)</td><td>5 (2)</td><td>2 456 579.5</td></tr><tr><td>SiS v = 1</td><td>15–14</td><td>270 917.961</td><td>1175.2</td><td>3.410 × 10<sup>-4</sup></td><td>0.13 (0.04)</td><td>4 (3)</td><td>2 455 309.5</td></tr><tr><td>SiS v = 1</td><td>17–16</td><td>307 014.349</td><td>1203.8</td><td>4.982 × 10<sup>-4</sup></td><td>0.32 (0.06)</td><td>5 (2)</td><td>2 456 320.5</td></tr><tr><td>SiS v = 1</td><td>19–18</td><td>343 100.984</td><td>1235.9</td><td>6.974 × 10<sup>-4</sup></td><td>0.30 (0.05)</td><td>9 (2)</td><td>2 455 576.5</td></tr><tr><td>o-H<sub>2</sub>O</td><td>10<sub>2.9</sub>–9<sub>3.6</sub></td><td>321 225.640</td><td>1827.1</td><td>6.124 × 10<sup>-6</sup></td><td>1.0 (0.2)</td><td>5 (2)</td><td>2 455 574.5</td></tr><tr><td>o-H<sub>2</sub>O v<sub>2</sub> = 1</td><td>5<sub>5.0</sub>–6<sub>4.3</sub></td><td>232 686.700</td><td>3427.8</td><td>4.630 × 10<sup>-6</sup></td><td>0.18 (0.03)</td><td>4 (3)</td><td>2 456 579.5</td></tr><tr><td>o-H<sub>2</sub>O v<sub>2</sub> = 1</td><td>6<sub>6.1</sub>–7<sub>5.2</sub></td><td>293 664.442</td><td>3899.5</td><td>7.018 × 10<sup>-6</sup></td><td>0.48 (0.04)</td><td>5 (1)</td><td>2 456 320.5</td></tr><tr><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>0.26 (0.04)</td><td>4 (2)</td><td>2 456 371.5</td></tr><tr><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>0.22 (0.04)</td><td>8 (2)</td><td>2 456 615.5</td></tr><tr><td>p-H<sub>2</sub>O v<sub>2</sub> = 1</td><td>4<sub>4.0</sub>–5<sub>3.3</sub></td><td>96 259.644</td><td>3064.2</td><td>4.608 × 10<sup>-7</sup></td><td>0.10 (0.01)</td><td>7 (5)</td><td>2 455 019.5</td></tr><tr><td>p-H<sub>2</sub>O v<sub>2</sub> = 1</td><td>5<sub>5.1</sub>–6<sub>4.2</sub></td><td>209 118.370</td><td>3462.1</td><td>3.369 × 10<sup>-6</sup></td><td>0.21 (0.03)</td><td>7 (2)</td><td>2 456 372.5</td></tr><tr><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>0.06 (0.06)</td><td>8 (2)</td><td>2 456 579.5</td></tr><tr><td>p-H<sub>2</sub>O v<sub>2</sub> = 1</td><td>6<sub>6.0</sub>–7<sub>5.3</sub></td><td>297 439.107</td><td>3933.7</td><td>7.289 × 10<sup>-6</sup></td><td>0.12 (0.04)</td><td>5 (2)</td><td>2 456 320.5</td></tr><tr><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>0.17 (0.03)</td><td>7 (2)</td><td>2 456 371.5</td></tr><tr><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>0.08 (0.03)</td><td>5 (2)</td><td>2 456 615.5</td></tr><tr><td>o-H<sub>2</sub>O v<sub>2</sub> = 2</td><td>6<sub>5.2</sub>–7<sub>4.3</sub></td><td>268 149.175</td><td>6005.0</td><td>1.471 × 10<sup>-5</sup></td><td>2.38 (0.07)</td><td>2 (1)</td><td>2 455 309.5</td></tr><tr><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>0.12 (0.03)</td><td>7 (1)</td><td>2 456 579.5</td></tr><tr><td>p-H<sub>2</sub>O v<sub>2</sub> = 2</td><td>3<sub>3.1</sub>–4<sub>2.2</sub></td><td>137 048.521</td><td>5036.7</td><td>2.096 × 10<sup>-6</sup></td><td>0.03 (0.01)</td><td>8 (5)</td><td>2 455 019.5</td></tr></tbody></table>
## Appendix B: Unidentified lines

<table><caption>**Table B.1.** Unidentified features and, in some cases, tentative line identification.</caption><thead><tr><th>v<sub>rest</sub><br>(MHz)</th><th>Tentative assignment</th><th>∫ T<sup>*</sup><sub>ant</sub> dv<br>(K km s<sup>-1</sup>)</th><th>v<sub>exp</sub><br>(km s<sup>-1</sup>)</th></tr></thead><tbody><tr><td>81 166</td><td>—</td><td>0.08 (0.03)</td><td>16 (7)</td></tr><tr><td>83 825</td><td>SiO v = 5 J = 2–1</td><td>0.30 (0.03)</td><td>35 (5)</td></tr><tr><td>84 478</td><td>—</td><td>0.06 (0.02)</td><td>7 (7)</td></tr><tr><td>86 190</td><td>OH v = 1 J, Ω, p, F = 8/2,3/2,1,9–8/2,3/2,–1,9</td><td>0.71 (0.02)</td><td>7 (3)</td></tr><tr><td>87 385</td><td>—</td><td>0.23 (0.02)</td><td>17 (3)</td></tr><tr><td>108 892</td><td>—</td><td>0.09 (0.01)</td><td>11 (4)</td></tr><tr><td>128 883</td><td>TiO<sub>2</sub> J<sub>K,k</sub>=19<sub>10,10</sub>–20<sub>9,11</sub></td><td>0.10 (0.02)</td><td>13 (4)</td></tr><tr><td>131 195</td><td>SiN N, J, F = 3,7/2,7/2–2,5/2,7/2</td><td>0.05 (0.01)</td><td>7 (4)</td></tr><tr><td>136 946</td><td>—</td><td>0.15 (0.01)</td><td>27 (4)</td></tr><tr><td>139 065</td><td>—</td><td>0.05 (0.01)</td><td>13 (4)</td></tr><tr><td>143 997</td><td>—</td><td>0.05 (0.01)</td><td>7 (4)</td></tr><tr><td>145 101</td><td>N<sup>17</sup>O J = 3/2–1/2 hfs blend</td><td>0.11 (0.02)</td><td>18 (4)</td></tr><tr><td>149 968</td><td>—</td><td>0.12 (0.02)</td><td>18 (4)</td></tr><tr><td>150 165</td><td>—</td><td>0.13 (0.03)</td><td>20 (4)</td></tr><tr><td>158 409</td><td><sup>29</sup>Si<sup>18</sup>O J = 4–3</td><td>0.04 (0.01)</td><td>10 (4)</td></tr><tr><td>159 227</td><td><sup>29</sup>SiS v = 1 J = 9–8</td><td>0.08 (0.01)</td><td>13 (4)</td></tr><tr><td>159 607</td><td>—</td><td>0.08 (0.01)</td><td>4 (3)</td></tr><tr><td>161 197</td><td>—</td><td>0.06 (0.02)</td><td>8 (4)</td></tr><tr><td>165 641</td><td>Na<sup>37</sup>Cl J = 13–12</td><td>0.09 (0.01)</td><td>11 (4)</td></tr><tr><td>169 652</td><td>—</td><td>0.12 (0.02)</td><td>16 (3)</td></tr><tr><td>172 925</td><td>—</td><td>0.47 (0.04)</td><td>28 (3)</td></tr><tr><td>208 612</td><td>TiO<sub>2</sub> J<sub>K,k</sub> = 43<sub>10,34</sub>–42<sub>11,31</sub></td><td>0.09 (0.02)</td><td>3 (3)</td></tr><tr><td>209 295</td><td>—</td><td>0.22 (0.03)</td><td>17 (2)</td></tr><tr><td>216 602</td><td><sup>13</sup>CN J = 2–1 hfs blend</td><td>0.26 (0.03)</td><td>8 (2)</td></tr><tr><td>218 065</td><td>—</td><td>0.41 (0.02)</td><td>3 (3)</td></tr><tr><td>218 575</td><td>—</td><td>0.43 (0.03)</td><td>24 (2)</td></tr><tr><td>219 840</td><td><sup>34</sup>SO<sub>2</sub> J<sub>K,k</sub> = 6<sub>4,2</sub>–7<sub>3,5</sub></td><td>0.35 (0.04)</td><td>3 (2)</td></tr><tr><td>221 614</td><td>—</td><td>0.48 (0.04)</td><td>18 (2)</td></tr><tr><td>223 370</td><td>SO<sup>18</sup>O J<sub>K,k</sub> = 6<sub>4,2</sub>–7<sub>3,5</sub></td><td>0.35 (0.05)</td><td>22 (3)</td></tr><tr><td>224 876</td><td>—</td><td>1.98 (0.06)</td><td>17 (2)</td></tr><tr><td>250 807</td><td>—</td><td>0.15 (0.02)</td><td>8 (3)</td></tr><tr><td>252 256</td><td>—</td><td>0.20 (0.02)</td><td>19 (3)</td></tr><tr><td>252 531</td><td>—</td><td>0.45 (0.04)</td><td>15 (3)</td></tr><tr><td>254 677</td><td>—</td><td>0.34 (0.03)</td><td>25 (3)</td></tr><tr><td>263 452</td><td>—</td><td>0.12 (0.03)</td><td>4 (2)</td></tr><tr><td>271 968</td><td>—</td><td>0.44 (0.05)</td><td>7 (2)</td></tr><tr><td>306 192</td><td>AlO N, J, F = 8,15/2,8–7,15/2,7</td><td>0.64 (0.08)</td><td>22 (2)</td></tr></tbody></table>

**Notes.** Column 3: integrated intensity (in antenna temperature) of the line with its formal uncertainty; Col. 4: expansion velocity derived from the linewidth with its uncertainty which includes the width of half a channel (1 MHz) except for the lines with a low S/N where a full channel (2 MHz) is included. The uncertainties given (within parentheses) do not include additional uncertainties derived from the absolute flux calibration and baseline subtraction.
<table><caption>**Table B.2.** Artifacts identified in the spectra between 167 475–174 800 MHz.</caption><thead><tr><th>ν<sub>rest</sub><br>(MHz)</th><th>∫ T<sup>*</sup><sub>ant</sub> dv<br>(K km s<sup>-1</sup>)</th><th>ν<sub>exp</sub><br>(km s<sup>-1</sup>)</th></tr></thead><tbody><tr><td>168 422</td><td>0.007 (0.002)</td><td>9 (1)</td></tr><tr><td>169 104</td><td>0.008 (0.002)</td><td>23 (2)</td></tr><tr><td>169 729</td><td>0.012 (0.002)</td><td>6.1 (0.9)</td></tr><tr><td>170 407</td><td>0.008 (0.002)</td><td>4.0 (0.9)</td></tr><tr><td>171 000</td><td>0.005 (0.002)</td><td>22.8 (0.6)</td></tr><tr><td>171 145</td><td>0.037 (0.002)</td><td>10.9 (0.7)</td></tr><tr><td>171 174</td><td>0.010 (0.002)</td><td>20 (1)</td></tr><tr><td>171 393</td><td>0.032 (0.002)</td><td>26.0 (0.4)</td></tr><tr><td>171 591</td><td>0.009 (0.002)</td><td>13 (2)</td></tr><tr><td>171 638</td><td>0.044 (0.003)</td><td>17.8 (0.8)</td></tr><tr><td>171 758</td><td>0.016 (0.003)</td><td>23 (2)</td></tr><tr><td>171 874</td><td>0.013 (0.003)</td><td>4.6 (0.4)</td></tr><tr><td>172 605</td><td>0.063 (0.004)</td><td>8.13 (0.08)</td></tr><tr><td>172 725</td><td>0.049 (0.003)</td><td>3.9 (0.2)</td></tr><tr><td>172 799</td><td>0.010 (0.003)</td><td>21 (1)</td></tr><tr><td>173 242</td><td>0.015 (0.003)</td><td>3 (31)</td></tr><tr><td>173 444</td><td>0.048 (0.004)</td><td>24.9 (0.7)</td></tr><tr><td>173 562</td><td>0.122 (0.004)</td><td>18.7 (0.3)</td></tr><tr><td>173 812</td><td>0.135 (0.006)</td><td>18.8 (0.3)</td></tr><tr><td>173 933</td><td>0.051 (0.005)</td><td>22 (1)</td></tr><tr><td>174 267</td><td>0.014 (0.004)</td><td>7 (2)</td></tr></tbody></table>

<figure><img src="image_12.png" /><figcaption>**Fig. B.1.** Example of the artifacts (R) produced by the receivers (see Table B.2). Several symmetrical spurious replicas of the real SiO J = 4–3 line appear at both sides of it (equidistant). The intensities of the replicas decrease with the frequency distance to the real feature.</figcaption></figure>
Appendix C: IRAM-30 m survey of IK Tau

<figure><img src="image_13.png" /><figcaption>Fig. C.1. Line identification of the IRAM-30 m line survey of IK Tau. We marked in red the unidentified lines (UIs) with the central frequency of the line. The lines which display time variability of their intensity are marked in blue. Image band and spurious feaures/artifacts have been blanked off (see Table B.2 and Fig. B.1)</figcaption></figure>
<figure><img src="image_14.png" /><figcaption>Fig. C.1. continued.</figcaption></figure>
<figure><img src="image_15.png" /><figcaption>Fig. C.1. continued.</figcaption></figure>
<figure><img src="image_16.png" /><figcaption>Fig. C.1. continued.</figcaption></figure>
<figure><img src="image_17.png" /><figcaption>Fig. C.1. continued.</figcaption></figure>
<figure><img src="image_18.png" /><figcaption>Fig. C.1. continued.</figcaption></figure>
<figure><img src="image_19.png" /><figcaption>Fig. C.1. continued.</figcaption></figure>
<figure><img src="image_20.png" /><figcaption>Fig. C.1. continued.</figcaption></figure>
<figure><img src="image_21.png" /><figcaption>Fig. C.1. continued.</figcaption></figure>
<figure><img src="image_22.png" /><figcaption>Fig. C.1. continued.</figcaption></figure>
<figure><img src="image_23.png" /><figcaption>Fig. C.1. continued.</figcaption></figure>
<figure><img src="image_24.png" /><figcaption>Fig. C.1. continued.</figcaption></figure>

Appendix D: Population diagrams

<figure><img src="image_25.png" /><figcaption>Fig. D.1. Population diagrams for CO and ¹³CO. The results from the fit (red dashed line) are shown in each box. The emission size adopted and the dipole moment of the molecule are shown in the bottom-left corner of each box. Error bars include the formal uncertainty of the measurement and a 25% uncertainty due to flux calibration or poor baseline subtraction.</figcaption></figure>
<figure><img src="image_26.png" /><figcaption>Fig. D.2. As in Fig. D.1 but for SiO isotopologues.</figcaption></figure>
<figure><img src="image_27.png" /><figcaption>Fig. D.3. As in Fig. D.1 but for HCN isotopologues.</figcaption></figure>

<figure><img src="image_28.png" /><figcaption>Fig. D.4. As in Fig. D.1 but for CS isotopologues.</figcaption></figure>
<figure><img src="image_29.png" /><figcaption>Fig. D.5. As in Fig. D.1 but for SiS isotopologues.</figcaption></figure>

<figure><img src="image_30.png" /><figcaption>Fig. D.6. As in Fig. D.1 but for NaCl.</figcaption></figure>

<figure><img src="image_31.png" /><figcaption>Fig. D.7. As in Fig. D.1 but for H₂S. We fitted simultaneously the ortho and para species adopting an ortho-to-para ratio of 3:1 (Decin et al. 2010a). The line o-H₂S J, *K*ₐ, *k* = 4₁,₄–3₂,₁ significantly outlies the fit probably owing to its low S/N, therefore, it has been excluded from the diagram.</figcaption></figure>

<figure><img src="image_32.png" /><figcaption>Fig. D.8. As in Fig. D.1 but for SO isotopologues.</figcaption></figure>
<figure><img src="image_33.png" /><figcaption>**Fig. D.9.** As in Fig. D.1 but for SO₂ isotopologues. The rotational diagram of SO₂ was separated in two different trends (see Sect. 5.2).</figcaption></figure>

<figure><img src="image_34.png" /><figcaption>**Fig. D.10.** As in Fig. D.1 but for CN.</figcaption></figure>

<figure><img src="image_35.png" /><figcaption>**Fig. D.11.** As in Fig. D.1 but for NS.</figcaption></figure>

<figure><img src="image_36.png" /><figcaption>**Fig. D.12.** As in Fig. D.1 but for P-bearing molecules. The PO line Ω = 1/2, e, J, F = (11/2, 5)–(9/2, 5) significantly outlies the fit probably owing to its low S/N, therefore, it has been excluded from the diagram.</figcaption></figure>

<figure><img src="image_37.png" /><figcaption>**Fig. D.13.** Population diagram for H₂CO. We show the results from the fits of the rotational ladders K_a = 0 (red), K_a = 1 (blue), and K_a = 2 (green). For the K_a = 3 (pink) we adopted as rotational temperature the average of the rotational temperatures of the K_a = 0, 1, and 2 ladders to estimate a rough value for the K_a = 3 column density.</figcaption></figure>
## Appendix E: SO₂ IOS calculations

Close coupling (CC) calculations based on a state-of-the-art potential-energy surface (PES) (Spielfiedel et al. 2009) have provided collisional para- and ortho-H₂ rate coefficients for temperatures ranging from 5 to 30 K for the 31 lowest SO₂ rotational levels (Cernicharo et al. 2011). However, an extension of these full CC calculations to a large number of SO₂ rotational levels and high temperatures would be prohibitive in terms of memory and CPU time, so the use of different approximate methods (coupled states (CS) and infinite order sudden (IOS)) is needed (Green 1976, 1979). Considering the high-J SO₂ levels observed in the present work, we used the IOS approximation which is expected to give reliable estimates of rate coefficients, except for low energies. State-to-state de-excitation rate coefficients between the 410 lowest levels (with energy up to 743.9 K) were calculated for energies up to 9000 cm⁻¹ (value limited by the validity domain of the PES) giving data for temperatures up to 1000 K Balança et al. (in prep.). The SO₂ energy levels and wave functions were obtained from spectroscopic constants describing the SO₂ Hamiltonian up to the fourth order and provided by the MADEX code (Cernicharo 2012). The results show a relatively flat temperature variation of the rates.

The accuracy of these data was studied by comparing the resulting rate coefficients with CC and CS values obtained for collisions with para and ortho-H₂ and all transitions involving the 31 lowest levels. Compared to CC and CS data, it is found that the IOS approach leads a systematic underestimation of para-H₂ rates, within a factor better than 50% in average, the agreement being better at high temperatures. However, the situation is not as good for collisions with ortho-H₂ as the IOS approximation describes collisions with para-H₂ (jH₂ = 0) and does take into account all the angular couplings involved in collisions with ortho-H₂. The comparison between ortho- and para-H₂ CS rate coefficients shows that ortho-H₂ rates are systematically larger than para-H₂ rates by a factor two in average, with larger differences (up to a factor eight) for a number of transitions mainly identified as ΔKₐ = 1 transitions.

<table><caption>**Table E.1.** Parameters of the energy levels used for SO₂ modelling.</caption><thead><tr><th>Identifier</th><th>J</th><th>K<sub>a</sub></th><th>K<sub>c</sub></th><th>E</th><th>g</th></tr><tr><th>-</th><th>-</th><th>-</th><th>-</th><th>K</th><th>-</th></tr></thead><tbody><tr><td>1</td><td>0</td><td>0</td><td>0</td><td>0.000000</td><td>1</td></tr><tr><td>2</td><td>2</td><td>0</td><td>2</td><td>2.751006</td><td>5</td></tr><tr><td>3</td><td>1</td><td>1</td><td>1</td><td>3.339254</td><td>3</td></tr><tr><td>4</td><td>2</td><td>1</td><td>1</td><td>5.320091</td><td>5</td></tr><tr><td>5</td><td>3</td><td>1</td><td>3</td><td>7.743834</td><td>7</td></tr><tr><td>6</td><td>4</td><td>0</td><td>4</td><td>9.151093</td><td>9</td></tr><tr><td>...</td><td></td><td></td><td></td><td></td><td></td></tr></tbody></table>

**Notes.** Table E.1, available at the CDS, contains the following information: Col. 1: identifier for the energy level used in Table E.2; Col. 2: quantum number *J*; Col. 3: quantum number *K*<sub>a</sub>; Col. 4: quantum number *K*<sub>c</sub>; Col. 5: energy of the level in Kelvin; Col. 6: degeneracy of the level.

The rate coefficients were implemented in MADEX fitting the logarithm of the rate coefficients to a sixth order polynomial as:

$$P(x) = \sum_{i=0}^{6} a_{i}x^{i}, \qquad (E.1)$$

where

$$x = T^{3/2}, \qquad (E.2)$$

which reproduces practically all the rates with a relative error below 30% for temperatures between 20 and 1000 K, 410 energy levels and a maximum E<sub>u</sub> = 744 K. We provide the energy levels involved in the calculations in Table E.1, as well as the polynomial coefficients of the fit in Table E.2. The level identifier used in Table E.2 can be consulted in Table E.1 to find the corresponding level.
<table><caption>**Table E.2.** Polynomial coefficients of the fit to the rate coefficients.</caption><thead><tr><th>Upper level id</th><th>Lower level id</th><th>a<sub>0</sub></th><th>a<sub>1</sub></th><th>a<sub>2</sub></th><th>a<sub>3</sub></th><th>a<sub>4</sub></th><th>a<sub>5</sub></th><th>a<sub>6</sub></th></tr></thead><tbody><tr><td>2</td><td>1</td><td>-9.48415</td><td>-29.3454</td><td>350.453</td><td>-2071.21</td><td>6590.82</td><td>-11012.6</td><td>7610.91</td></tr><tr><td>3</td><td>1</td><td>-9.58292</td><td>-35.9159</td><td>406.891</td><td>-2385.77</td><td>7513.84</td><td>-12378.6</td><td>8410.64</td></tr><tr><td>3</td><td>2</td><td>-9.99698</td><td>-14.3352</td><td>120.467</td><td>-442.266</td><td>635.155</td><td>52.7172</td><td>-657.401</td></tr><tr><td>4</td><td>1</td><td>0.00000</td><td>0.00000</td><td>0.00000</td><td>0.00000</td><td>0.00000</td><td>0.00000</td><td>0.00000</td></tr><tr><td>4</td><td>2</td><td>-9.53669</td><td>-26.9597</td><td>289.292</td><td>-1598.36</td><td>4761.52</td><td>-7413.75</td><td>4772.86</td></tr><tr><td>4</td><td>3</td><td>-9.09926</td><td>-29.6351</td><td>346.972</td><td>-2025.33</td><td>6401.05</td><td>-10614.5</td><td>7267.38</td></tr><tr><td>...</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr></tbody></table>

**Notes.** Table E.2, available at the CDS, contains the following information: Col. 1: identifier for the upper energy level described in Table E.1; Col. 2: identifier for the lower energy level described in Table E.1; Cols. 3–9: coefficients of the 6th order polynomial fit to the rate coefficients.