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A&A
Volume 683, March 2024
Article Number A62
Number of page(s) 9
Section Interstellar and circumstellar matter
DOI https://doi.org/10.1051/0004-6361/202348994
Published online 07 March 2024

© The Authors 2024

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

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1 Introduction

There are now more than 300 molecules detected in space (see, e.g., the webpages of the Astrochymist1 and the Cologne Database for Molecular Spectroscopy (CDMS2), also McGuire 2022). A few iconic objects have proven to be very prolific sources for detecting new interstellar molecules: Sgr B2, a giant molecular cloud close to the Galactic Center (see, e.g., Nummelin et al. 2000; Belloche et al. 2013; Neill et al. 2014), TMC 1, a cold dark cloud in the Taurus complex (see, e.g., Kaifu et al. 2004; Cernicharo et al. 2021, 2022a,b, 2023; Fuentetaja et al. 2022 for recent detections of some hydrocarbon species), L483, a dense core around a class 0 protostar (Agúndez et al. 2019, 2023), and, particularly, the circumstellar envelope around the evolved star CW Leo (also known as IRC+10216, see e.g., Cernicharo et al. 2000; Tenenbaum et al. 2010; Pardo et al. 2022).

Concerning extragalactic molecules, two objects stand out in molecule count: the nearby starburst galaxy NGC 253 (e.g., Martin et al. 2006, 2021), and the z = 0.89 molecular absorber toward the lensed quasar PKS 1830–211, for which more than 60 species have been reported to date (Muller et al. 2006, 2011, 2014a; Tercero et al. 2020). The latter presents a pure-absorption spectrum, where low-energy transitions are highly favored. As a result, the spectral line density is significantly lower than in rich molecular-emitting sources in closer proximity, which drastically limits line confusion and simplifies line identification. The z = 0.89 molecular absorber toward PKS 1830-211 provides us with a unique opportunity to investigate the interstellar medium and its chemistry in the disk of a distant galaxy (e.g., Muller et al. 2017). The absorber is a nearly face-on (i = 26°, Combes et al. 2021) spiral galaxy which acts as a gravitational lens, splitting the background quasar into two bright and compact images, separated by 1" (Subrahmanyan et al. 1990; Jauncey et al. 1991; Winn et al. 2002). Molecular absorption is seen against both lensed images (Wiklind & Combes 1998; Muller et al. 2006, 2014a). The line of sight to the southwestern (SW) image, notably, is the place of the numerous molecular detections. It intercepts the absorber’s disk at a projected galac-tocentric radius of 2.4 kpc, and has a large column density of H2, ~2 × 1022 cm-2, about one order of magnitude larger than the northeastern (NE) line of sight (Muller et al. 2014a).

Here, we report the identification of a new interstellar molecular ion, protonated acetylene (C2H3+)$${{\rm{C}}_2}{\rm{H}}_3^ + $$, in the absorber toward PKS 1830-211 SW. C2H3+$${{\rm{C}}_2}{\rm{H}}_3^ + $$ is the protonated form of acetylene (C2H2), the simplest alkyne, i.e., an hydrocarbon with one carbon-carbon triple bond. Due to its symmetry, acetylene does not have permitted dipole rotational transitions and it has to be observed through its infrared vibration-rotation spectrum. Within the Solar system, acetylene is found in planetary atmospheres (e.g., Ridgway 1974; Gillett 1975) and in comets (e.g., Brooke et al. 1996). Beyond, acetylene was first detected in IRC+10216 (Ridgway et al. 1976) and in infrared sources embedded in molecular clouds (Lacy et al. 1989). Its observations tend to be limited to warm environments associated with young stellar objects (e.g., Boonman et al. 2003; Sonnentrucker et al. 2007; Rangwala et al. 2018). The protonated form of acetylene has also been suspected to be present in the interstellar medium as well (e.g., Herbst et al. 1977; Glassgold et al. 1992), although it has eluded detection so far, probably due to its unfavorable millimeter-wave rotational spectrum for ground-based observations in local (z ~ 0) sources. Both acetylene and its protonated form are key building blocks of larger hydrocarbons and other complex molecules (e.g., Schiff & Bohme 1979; Oka et al. 2003; Chapman et al. 2009).

2 Observations

2.1 Ortho‐C2H3+$$Ortho - {C_2}H_3^ + $$

We obtained ALMA band 6 observations of PKS 1830-211 on 2022 October 11th. The array was composed of 44 antennas in the approximative configuration C-3, with projected baselines ranging from 15 to 500 m resulting in a synthesized beam of ~0.7″. The antenna primary beam (field of view ~20″) was much larger than the separation between the lensed images of PKS 1830-211. The amount of precipitable water vapor was between 0.4 and 0.5 mm during the observations. The total observing time on PKS 1830-211 was 36 min. Four spectral windows of 1.875 GHz-wide were used to cover various spectral lines. The spectral window of interest for this discovery was centered at 261.6 GHz and yields a velocity resolution of about 1.1 km s−1. It also contained the strong [C I] (3P1−3P0) line, redshifted to 260.98 GHz.

The bright quasar J 1924–2914 (~6.7 Jy at 260 GHz, at time of the observations) was used as bandpass and flux calibrator. The quasar J 1832–2039 (~0.3 Jy) was used for gain calibration. After the standard calibration by the ALMA pipeline (CASA version 6.4.1.12, The CASA Team 2022), the visibilities of PKS 1830–211 were self-calibrated, phase only, at the shortest integration time interval of 6 s.

The final spectra along the NE and SW images of PKS 1830–211 were extracted by visibility fitting using the Python-based tool UVMultiFit (Martí-Vidal et al. 2014) and a model of two point sources, for which the positions were fixed at the continuum locations and the amplitude per spectral channel left as free parameters. The spectra were then normalized to their corresponding continuum level (i.e., 1.3 and 1.0 Jy at 250 GHz for the NE and SW images, respectively). The rms sensitivity was 0.1 and 0.08% of the SW and NE continuum levels, respectively.

2.2 Para‐C2H3+$$Para - {C_2}H_3^ + $$

The data described above are complemented by ALMA archival data observed on 2014 March 8th. For these, the array was composed of 25 antennas, with projected baselines ranging between 15 and 420 m, resulting in a synthesized beam ~0.7″. The amount of precipitable water vapor was -2 mm. The total observing time on PKS 1830-211 was 1.5 h. The spectral window of interest here was 1.875 GHz wide, centered at 228.5 GHz, and was smoothed to a final velocity resolution of about 1.9 km s−1. The calibration was done using J 1733–1304 for the bandpass response of the antennas, Titan for the flux scale, and J 1923–210 for the antenna gains (CASA version 4.2). After self-calibration, the final spectra were extracted the same way as previously explained. The rms noise level was 0.3% and 0.2% for the SW and NE normalized spectra, respectively – at that epoch, the flux density of the NE and SW images at 230 GHz was ~0.5 Jy and 0.3 Jy, respectively.

thumbnail Fig. 1

ALMA spectra toward the SW and NE lines of sight to PKS 1830-211: (a) The 212–101 transition of Ortho-C2H3+$$Ortho - {C_2}H_3^ + $$ (rest frequency 494.034 GHz) observed in 2022. (b) The 111–000 transition of Para-C2H3+$$Para - {C_2}H_3^ + $$ (431.315 GHz, rest), observed in 2014. (c) For comparison, spectra of [C I] (3P1–3P0) taken from the same spectral window as observations of a). The best fits by a Gaussian line profile are indicated in red on top of the C2H3+$${{\rm{C}}_{\rm{2}}}{\rm{H}}_{\rm{3}}^{\rm{ + }}$$ lines. All spectra have been normalized to the continuum level of each lensed image. For clarity, the spectra along the NE line of sight have been shifted by –0.01 (except for [C I] which has optical depths multiplied by 20 and shifted by –0.5) and are shown in blue.

3 Results and discussion

3.1 Identification of C2H3+$${C_2}H_3^ + $$

We started with the serendipitous detection of the absorption feature in Fig. 1a, which at first we could not identify with any other known species toward PKS 1830–211. The feature is clear and seen only on the SW line of sight, where many other molecules have already been detected. There is no counterpart in the NE spectra at the same velocities, removing the possibility of spurious instrumental artifacts or of atmospheric lines. Because the two lensed images of PKS 1830-211 are only separated by 1″, the non-detection of signal on the NE spectra also indicates that the SW absorption feature does not arise from interstellar medium in the Milky Way. We thus have strong evidence that the lines arise in the z = 0.89 molecular absorber.

Given the shape and signal-to-noise ratio (S/N) of the line in Fig. 1a, we adopt a simple Gaussian profile to obtain a first estimate of its rest frequency, 49 4032 ± 1 MHz, assuming that the line profile is centered at z = 0.88582 in the heliocentric velocity frame. The total integrated opacity is (109 ± 8) × 10−3 km s−1 and the full-width at half maximum (FWHM) is 20 ± 2 km s−1. The linewidth is comparable to previous observations (e.g., Muller et al. 2011, 2014a) and to the FWHM of the [CI] absorption in Fig. 1c. Armed with this rest frequency estimate, we have searched for its line identification in the CDMS (Müller et al. 2005; Endres et al. 2016) and JPL (Pickett et al. 1998) molecular databases. As far as we can find exploring a range of ± 10 MHz around 494.032 GHz (i.e., a range slightly larger than the FWHM), there is only one transition with low energy: the 212–101 ground-state transition of C2H3+$${{\rm{C}}_{\rm{2}}}{\rm{H}}_{\rm{3}}^{\rm{ + }}$$ at rest frequency 49 4034.0653 ± 0.0633 MHz as reported in CDMS. Within the considered frequency range, the next transitions in increasing energy level already have Elow > 80 K, correspond to more complex molecules, and are unlikely to be detectable at all. For completeness, we also searched around 261.961 GHz (i.e., case where the absorption would occur at z = 0), and could not find any convincing candidate. The 212–101 transition of C2H3+$${{\rm{C}}_{\rm{2}}}{\rm{H}}_{\rm{3}}^{\rm{ + }}$$ thus appears as our unique alternative. By repeating the Gaussian fit with this new frequency, we find a velocity centroid v0 = 1.26 ± 0.68 km s−1 at the adopted redshift.

At this stage, we already consider C2H3+$${{\rm{C}}_{\rm{2}}}{\rm{H}}_{\rm{3}}^{\rm{ + }}$$ as the most likely molecule responsible for the absorption feature observed in the SW line of sight of PKS 1830–211. First, C2H3+$${{\rm{C}}_{\rm{2}}}{\rm{H}}_{\rm{3}}^{\rm{ + }}$$ is a relatively simple closed-shell molecule with an electric dipole moment of 1.14 D (Lee & Schaefer 1986), that has been suggested to be present in the interstellar medium (e.g., Herbst et al. 1977; Glassgold et al. 1992). Considering the molecular zoo toward PKS 1830–211, with more than 60 species already detected along the SW line of sight (e.g., Muller et al. 2011, 2014a; Tercero et al. 2020), the presence of C2H3+$${{\rm{C}}_{\rm{2}}}{\rm{H}}_{\rm{3}}^{\rm{ + }}$$ indeed appears highly plausible. In particular, many other hydrocarbons have already been found in the absorber: CH, CH+, C2H, l-C3H, l-C3H+, c-C3H2, l-C3H2, C4H, together with some other complex molecules such as HC3N, CH3CN, CH3CCH, and CH2CHCN.Next, the rest frequency of the transition matches well our best fit estimates within uncertainties. Moreover, the absorption technique favors observations of low-energy level transitions. Especially in the low-density medium (diffuse to translucent clouds), the molecular excitation is easily coupled with photons from the cosmic microwave background, with TCMB = 5.14 K at z = 0.89 (see Muller et al. 2013). Indeed, the millimeter-wave absorption spectrum toward PKS 1830–211 is completely dominated by ground-state or low-energy transitions. The fact that the transition at 494.034 GHz of C2H3+$${{\rm{C}}_{\rm{2}}}{\rm{H}}_{\rm{3}}^{\rm{ + }}$$ is directly connected to the ground-state energy level of the more abundant ortho form is therefore a strong asset for its identification. Finally, molecular databases such as the CDMS or JPL are fairly complete which leaves very little chance that they miss any detectable molecule in our distant absorber.

Taking the spectroscopy information from the CDMS (see Sect. 3.2), we list the transitions absorbed from the first levels of C2H3+$${{\rm{C}}_{\rm{2}}}{\rm{H}}_{\rm{3}}^{\rm{ + }}$$ in Table 1 where ortho and para forms are considered separately. We have searched in the ALMA archives and found observations of PKS 1830–211 from March 2014 covering the 111–000 line of para-C2H3+$${\rm{para - }}{{\rm{C}}_{\rm{2}}}{\rm{H}}_{\rm{3}}^{\rm{ + }}$$, as shown in Fig. 1b. The best fit values with a Gaussian profile are the following: v0 = 7.2 ± 0.8 km s−1, FWHM = 10.5 ± 2.9 km s−1, and an integrated opacity of (6.0 ± 1.1) × 10−2 km s−1. The spectra of the ortho and para lines are not exactly aligned in velocity centroids but clearly overlap in velocity. However, the system is known to have significant time variations of the absorption profiles which are due to structural changes in the background quasar (Muller et al. 2006, 2020, 2021, 2023). Since the spectra have been taken eight years apart, it is therefore possible that the quasar illumination changed between the two epochs.

Assuming local thermodynamic equilibrium (LTE) conditions, excitation at TCMB, and the line parameters as obtained from our Gaussian fittings above, we estimate column densities of 1.4 × 1012 cm−2 and 0.7 × 1012 cm−2 for the ortho and para forms of C2H3+$${{\rm{C}}_{\rm{2}}}{\rm{H}}_{\rm{3}}^{\rm{ + }}$$, respectively. Since the lines were observed with a large time interval, we cannot directly sum the column densities of the two forms to get the total column density of C2H3+$${{\rm{C}}_{\rm{2}}}{\rm{H}}_{\rm{3}}^{\rm{ + }}$$, neither measure the ortho-to-para ratio (OPR). However, the values are comparable. From our measurement of ortho-C2H3+$${\rm{ortho - }}{{\rm{C}}_{\rm{2}}}{\rm{H}}_{\rm{3}}^{\rm{ + }}$$, we derive a total column density of ~2 × 1012 cm−2 with an assumed ortho-to-para ratio (OPR) of three. This corresponds to an abundance of 10−10 relative to H2. C2H3+$${{\rm{H}}_{\rm{2}}}{\rm{.}}{{\rm{C}}_{\rm{2}}}{\rm{H}}_{\rm{3}}^{\rm{ + }}$$ is then ~600 and 60 times less abundant than C2H and C4H, respectively (Muller et al. 2011). We note, however, that those column densities could be affected by our simple assumption of LTE. More advanced considerations including formation pumping are discussed in Sect. 3.3.

Why did C2H3+$${{\rm{C}}_{\rm{2}}}{\rm{H}}_{\rm{3}}^{\rm{ + }}$$ elude detection at z = 0 so far? First, the frequencies of the ground-state transitions are difficult or impossible to observe from the ground. The 110–101 transition at 368 GHz falls in a deep atmospheric line. The 111–000 (431 GHz) and 212–101 (494 GHz) transitions are better placed and are accessible in ALMA band 8. We recall that the HIFI receiver of the Herschel Space Observatory was operating above 480 GHz. However, the greatest challenge for the detection of C2H3+$${{\rm{C}}_{\rm{2}}}{\rm{H}}_{\rm{3}}^{\rm{ + }}$$ is most likely the required sensitivity since the deepest absorption lines toward PKS 1830–211 only reach an opacity of ~0.005 at LTE. In fact, our detection with ALMA could only be achieved because the quasar was in a phase of high flux density, almost a factor two above average measurements done over the last decade (see Fig. 2 by Muller et al. 2023). Given those challenges, it will be interesting to check whether C2H3+$${{\rm{C}}_{\rm{2}}}{\rm{H}}_{\rm{3}}^{\rm{ + }}$$ can be detected in other targets, including Galactic sources.

3.2 Spectroscopy of C2H3+$${{\rm{C}}_{\rm{2}}}{\rm{H}}_{\rm{3}}^{\rm{ + }}$$

Protonated acetylene offers an interesting study case for quantum chemists and spectroscopists alike. The structure of the molecule has long been controversial, but it is now well established that the non-classical planar-bridged (cyclic) structure is more stable than the ‘Y’-shaped classical structure (Crofton et al. 1989). Both structures are illustrated in Fig. A.1.

In the bridged form, the molecule can be approximated to first order by a rigid asymmetric rotor (described by the quantum numbers J, Ka, Kc) with two equivalent protons. Transitions are allowed between levels with ΔJ = 0, ± 1, ΔKa = ± 1, and ΔKc = ± 1, and can be labeled ortho (between even-odd odd-even levels for Ka, Kc) or para (even-even and odd-odd levels), with statistical weight 3:1, respectively. The energy level diagram of C2H3+$${{\rm{C}}_2}{\rm{H}}_3^ + $$ is shown in Fig. A.2.

The internal dynamics of the molecule is however complicated by the possible tunneling migration of the protons, interconverting the structure from non-classical to classical with a barrier of about 1600 cm−1, as discussed by Hougen (1987). When considering this tunneling migration, the three protons become equivalent and the even-odd and odd-even levels turn into doublets with a statistical weight of 2:1 with respect to the even-even and odd-odd levels.

Laboratory measurements of the millimeter and submillime-ter spectrum of C2H3+$${{\rm{C}}_2}{\rm{H}}_3^ + $$ were carried out by Bogey et al. (1992) between 195 and 470 GHz. They did not observe line tunneling splitting larger than ~l MHz. New measurements were done by Cordonnier & Coudert (1996) with improved experimental resolution, where they obtain splittings of the order of a few 100s of kHz, confirming the tunneling. In particular, the 110−101 transition has a splitting of almost 500 kHz. Toward PKS 1830–211, the splitting is compressed by the factor (1 + z) = 1.89, and it is much smaller than the absorption linewidth. We thus consider it is negligible in the interpretation of our data and we can safely use the CDMS predictions (see Table 1) where these additional splittings are neglected.

Table 1

Line properties for the low-energy level transitions of C2H3+$${{\rm{C}}_2}{\rm{H}}_3^ + $$.

3.3 Excitation of C2H3+$${{\rm{C}}_2}{\rm{H}}_3^ + $$

It is interesting to note that, as shown on Fig. A.2, several low lying levels are metastable. They lack dipole-allowed transitions to any lower states. This implies that they could potentially sustain anomalously large populations and associated lines might be brighter than expected from simple LTE estimates.

Even if the chemical source of C2H3+$${{\rm{C}}_2}{\rm{H}}_3^ + $$ remains uncertain, its rate of destruction by dissociative recombination can be estimated, D = n(e)kDR, where kDR=1.26×10−6(T/100)−0.84 cm3 s−1. ${k_{DR}} = 1.26 \times {10^{ - 6}}{(T/100)^{ - 0.84}}{\rm{c}}{{\rm{m}}^3}{{\rm{s}}^{ - 1}}{\rm{. }}$(1)

In steady state, n(C2H3+)D$$n\left( {{{\rm{C}}_2}{\rm{H}}_3^ + } \right)D$$ can be equated with a total formation rate F (cm3 s−1). If we further assume that the formation process populates nascent states of C2H3+$${{\rm{C}}_2}{\rm{H}}_3^ + $$ with a Boltzmann distribution at some formation temperature Tform, then Tform is a parameter that governs the OPR, provided that the destruction rate can be assumed to be the same for all states. In this way, source and sink terms can be incorporated into the system of rate equations that controls the populations of all rotational levels (van der Tak et al. 2007). Crude estimates of inelastic collision rates have been made with a characteristic downward rate coefficient of 2 × 10−10 cm3 s−1 for H2 collisions. Inelastic collisions with electrons should also play a role but are neglected for simplicity. In any case, the details are not very important because the populations of the most important states are controlled by the formation process and by the radiative transitions in the 5.14 K black-body radiation field at z = 0.89. For example, at T = 100 K, n(H2) = 1000 cm−3, and n(e−) = 0.75 cm−3 with a formation temperature of Tform = 300 K, we find that the metastable 303, 404, and 505 states have anomalously high populations. Indeed, the 505 state is the most highly populated state of all in these conditions, and is depopulated most rapidly by absorption of CMB radiation in the 514−505 and 616 − 505 transitions at 388.9 and 730.8 GHz, respectively. These transitions are calculated to have higher optical depths than the 212−101 transition at 494 GHz observed by us. Because the metastable states add significantly to the total density, the total column density in this calculation needs to be 7.5 × 1012 cm−2 (rather than 2 × 1012 cm−2 in LTE at 5.14 K) in order to produce the observed integrated optical depth at 494 GHz. Moreover, the 414 −505 line at 25.2 GHz appears to be refrigerated well below the CMB temperature in this calculation. Given the adopted destruction rate and formation temperature, the OPR is calculated to be 3.125 – it is not assumed.

In short, although we do not know in detail the state-specific chemical processes or state-to-state collisional rates for C2H3+$${{\rm{C}}_2}{\rm{H}}_3^ + $$, it is likely that its formation and destruction processes play an important role in its excitation, with the possibility that excited metastable states will yield detectable absorption lines.

3.4 Chemistry of C2H3+$${{\rm{C}}_2}{\rm{H}}_3^ + $$

We here discuss the possible gas-phase formation channels of C2H3+$${{\rm{C}}_2}{\rm{H}}_3^ + $$, which is observed with an abundance ⋍10⋍10 relative to H2 toward PKS 1830–211 SW. First, C2H3+$${{\rm{C}}_2}{\rm{H}}_3^ + $$ does not react with H2 and is rapidly destroyed by dissociative recombination with electrons via the two dominant channels 1,2 in Table 2 (with branching ratios of 59 and 29%, respectively, Kalhori et al. 2002). The total destruction rate coefficient is ke ~ (9−1) × 10−6 cm3 s−1 at 10–100 K, respectively. Assuming steady-state kinetics and that the main formation route to C2H3+$${{\rm{C}}_2}{\rm{H}}_3^ + $$ involves parent species A+ and B(A++B→C2H3++products)$${\rm{B}}\left( {{{\rm{A}}^ + } + {\rm{B}} \to {{\rm{C}}_2}{\rm{H}}_3^ + + {\rm{products}}} \right)$$, with a typical formation rate kf ~ 10−9 cm3 s−1, we then can write: [ C2H3+ ]=kfke[ A+ ][B][ e− ].$\left[ {{{\rm{C}}_2}{\rm{H}}_3^ + } \right] = {{{k_f}} \over {{k_e}}}{{\left[ {{{\rm{A}}^ + }} \right][{\rm{B}}]} \over {\left[ {{{\rm{e}}^ - }} \right]}}.$(2)

Since [A+] < [e−], we get [ C2H3+ ]$$\left[ {{{\rm{C}}_2}{\rm{H}}_3^ + } \right]$$ < [B]/100. In PKS 1830–211 SW, we would thus require [B] > 10−8 relative to H2.

Hereafter, we discuss the cases where B=C2H2 and CH4, from the reaction list in Table 2.

3.4.1 The route of acetylene

Both acetylene and its protonated ion are key species involved in the rich hydrocarbon chemistry of the interstellar medium (e.g., Schiff & Bohme 1979; Herbst & Leung 1989; Oka et al. 2003).

Protonated forms MH+ of symmetric molecules M without dipole moment are interesting observational proxies of these unobservable species at radio wavelengths (e.g., Herbst et al. 1977), provided M and MH+ are clearly chemically connected (i.e., proton exchange reaction: M + XH+ → MH+ + X).

Proton donors to acetylene can be, e.g., the H3+$${\rm{H}}_3^ + $$, HCO+, and N2H+ ions (Reactions 4, 5, 6 from Table 2), with typical rates ~10−9 cm3 s−1. Adopting Eq.(2) for example with B=HCO+ (reaction 5 in Table 2), we would get: [ C2H2 ][ C2H3+ ]=7×103−7×107${{\left[ {{{\rm{C}}_2}{{\rm{H}}_2}} \right]} \over {\left[ {{{\rm{C}}_2}{\rm{H}}_3^ + } \right]}} = 7 \times {10^3} - 7 \times {10^7}.$(3)

with [HCO+]/[H2] = 9 × 10−9 (as measured toward PKS 1830–211 SW, Muller et al. 2011, 2014a) and [e−]/[H2] = 10−8−10−4, respectively, depending on the environment.

Testing such simple chemical considerations with more elaborated gas-phase models of dark-cloud chemistry, Agúndez et al. (2015) found a good empirical correlation between the abundance ratio of a molecule M and its protonated form MH+ and the proton affinity of M. Considering the proton affinity of acetylene (~150 kcalmol−1), their correlation would yield a ratio [ C2H2 ]/[ C2H3+ ]∼104$$\left[ {{{\rm{C}}_2}{{\rm{H}}_2}} \right]/\left[ {{{\rm{C}}_2}{\rm{H}}_3^ + } \right] \sim {10^4}$$. Agúndez et al. (2022) updated their diagram of [MH+]/[M] abundance ratio versus proton affinity with observations of new protonated-neutral pairs and confirmed the trend. Basically, they argue that if the proton affinity of molecule M is lower than that of CO, then the main proton donor forming MH+ would be H3+$${\rm{H}}_3^ + $$. If the proton affinity is higher, then the main donor would be HCO+. Since the later is relatively abundant in cold dense clouds, the formation of MH+ could then be enhanced by orders of magnitude, moving the [M]/[MH+] ratio from a typical range 104−106 down to values of 10–103.

It is worth noticing that the [MH+]/[M] ratio is in principle sensitive to the degree of ionization, and thus, in particular to the cosmic-ray ionization rate, ζ. From OH+ and H2O+ absorption, Muller et al. (2016) did estimate a value ζ ~ 2 × 10−14 s−1 in the SW line of sight through the absorber. This value is comparable to values derived in our Galactic Center, but significantly higher (by about 1–2 orders of magnitude) than in the Galactic disk. The abundance of C2H3+$${{\rm{C}}_2}{\rm{H}}_3^ + $$ in the z = 0.89 absorber (SW line of sight) could then be enhanced by the elevated ζ.

Perhaps 1-C3H+, recently identified toward PKS 1830–211 by Tercero et al. (2020), is a better indirect tracer of acetylene than C2H3+$${{\rm{C}}_2}{\rm{H}}_3^ + $$, if its main source is C+ + C2H2 → C3H+ + H. Although 1-C3H+ reacts with H2, the rate coefficient is low, 5.2 × 10−12 cm3 s−1, so that it is likely to be destroyed mainly by dissociative recombination. In that case, and if PDR conditions prevail, [C+] ≈ [e−], then [C2H2]/[l-C3H+] ≈ 200 at T = 100 K. Given the column density found by Tercero et al. (2020), N(C3H+) = 1.2 × 1012 cm−2, the implied abundance of acetylene is ~10−8 relative to H2. If this is correct, then the abundance of C2H2 in PKS 1830–211 SW is likely too small for it to be the main parent of the observed C2H3+$${{\rm{C}}_2}{\rm{H}}_3^ + $$.

3.4.2 The route of methane

Other channels to the formation of C2H3+$${{\rm{C}}_2}{\rm{H}}_3^ + $$ involve reactions of CH4 with C+ or CH+ as parent molecules (reactions 7, 8 in Table 2). These reactions may indeed be particularly efficient in diffuse and translucent clouds where the abundance of C+ and CH+ is high. Direct observations of interstellar methane were first made by Lacy et al. (1991), who found CH4/CO ≈ 10−3 in the gaseous phase toward several IR-bright protostars. Subsequently Boogert et al. (1998) found CH4/H2 ≈4 × 10−7 in warm, dense gas toward protostars. Most recently, Nickerson et al. (2023) analyzed high-resolution SOFIA/EXES mid-infrared spectra of several species including CH4 and C2H2 toward Orion IRc2. Based on the measurements at 7.6 µm wavelength, CH4/H2 ≈ 1.5 × 10−6 and CH4/C2H2 = 1.5 there. These hot-core or protostellar sources may have such a large CH4 abundance owing to evaporation of ices from dust surfaces.

In PDR conditions where n(C+) ≈ n(e), the C+ + CH4 source of C2H3+$${{\rm{C}}_2}{\rm{H}}_3^ + $$ can maintain an abundance [ C2H3+ ]/[ H2 ]=1×10−10([ CH4 ]/1.3×10−7)$$\left[ {{{\rm{C}}_2}{\rm{H}}_3^ + } \right]/\left[ {{{\rm{H}}_2}} \right] = 1 \times {10^{ - 10}}\left( {\left[ {{\rm{C}}{{\rm{H}}_4}} \right]/1.3 \times {{10}^{ - 7}}} \right)$$. In other words, the estimated abundance of C2H3+$${{\rm{C}}_2}{\rm{H}}_3^ + $$ toward PKS 1830–211 SW can be explained by PDR conditions if methane is present at 1/10 of the abundance that it exhibits in hot core regions of the Milky Way like the material toward Orion IRc2. On the other hand, C2H2 is not a viable source of C2H3+$${{\rm{C}}_2}{\rm{H}}_3^ + $$ even when its abundance is as high as observed toward Orion IRc2, because the reactant ions (H3+$${\rm{H}}_3^ + $$ and HCO+) have much lower abundances than C+ in PDR conditions.

3.4.3 Other reactions

For completeness, we briefly list some other reactions involving C2H3+$${{\rm{C}}_2}{\rm{H}}_3^ + $$. First, the slightly endothermic hydrogenation reaction of C2H3+$${{\rm{C}}_2}{\rm{H}}_2^ + $$ (reaction 10 of Table 2, see, e.g., discussion by Oka et al. 2003 and Smith et al. 1993) may take place in regions where excess energy is present (e.g., being radiative, or due to shock or turbulence dissipation). C2H3+$${{\rm{C}}_2}{\rm{H}}_3^ + $$ may also interact either with other neutrals (HCN, NH3, H2O) to form back acetylene or with simple hydrocarbons to produce more complex hydrocarbon ions (Schiff & Bohme 1979; Chapman et al. 2009), e.g.: C2H3++CH4→C3H5++H2$$${{\rm{C}}_2}{\rm{H}}_3^ + + {\rm{C}}{{\rm{H}}_4} \to {{\rm{C}}_3}{\rm{H}}_5^ + + {{\rm{H}}_2}$$$(4) C2H3++C2H2→C4H3++H2,${{\rm{C}}_2}{\rm{H}}_3^ + + {{\rm{C}}_2}{{\rm{H}}_2} \to {{\rm{C}}_4}{\rm{H}}_3^ + + {{\rm{H}}_2},$(5) C2H3++HCn+1 N→H2Cn+3 N++H2.${{\rm{C}}_2}{\rm{H}}_3^ + + {\rm{H}}{{\rm{C}}_{{\rm{n}} + 1}}{\rm{N}} \to {{\rm{H}}_2}{{\rm{C}}_{{\rm{n}} + 3}}{{\rm{N}}^ + } + {{\rm{H}}_2}.$(6)

On the other hand, C2H3+$${{\rm{C}}_2}{\rm{H}}_3^ + $$ could be the product of top-down chemistry, e.g., C3H3++O→C2H3++CO,${{\rm{C}}_3}{\rm{H}}_3^ + + {\rm{O}} \to {{\rm{C}}_2}{\rm{H}}_3^ + + {\rm{CO}}$(7)

or even PAH photo-degradation (Allain et al. 1996) that produces acetylene, which can further be protonated as previously described.

Let us here finally recall that long carbon chains remain important candidates for the unknown carriers of the diffuse interstellar bands (Douglas 1977; Cox & Cami 2014), including perhaps protonated forms such as HC2nH2+$${\rm{H}}{{\rm{C}}_{2n}}{\rm{H}}_2^ + $$.

Table 2

Main chemical reactions involving C2H3+$${{\rm{C}}_2}{\rm{H}}_3^ + $$ in the interstellar medium (taken from KIDA, Wakelam et al. 2012).

3.5 Nature of the C2H3+$${{\rm{C}}_2}{\rm{H}}_3^ + $$ absorbing gas toward PKS 1830–211

There is evidence for a multi-phase medium in the absorbing column toward the SW image of PKS 1830–211. A component with low molecular hydrogen fraction (less than or about a few percent) is traced by hydrides such as ArH+ (Müller et al. 2015), OH+ and H2O+ (Muller et al. 2016), CH+ (Muller et al. 2017), and H2Cl+ (Muller et al. 2014b), which all have broad absorption profiles. In contrast, absorptions from CH and H218O$${\rm{H}}_2^{18}{\rm{O}}$$ (Muller et al. 2023) show a narrower profile, with a higher H2 -fraction (10-100%). More complex molecules like CH3OH, HC3N, CH3NH2 have their line barycenter offset compared to the bulk of other species (Muller et al. 2011), suggesting further chemical segregation. Finally, the time variability of the absorption profiles, caused by structural changes in the quasar’s morphology (Muller & Guélin 2008), has highlighted at least one velocity component that shows similarities with Galactic dark clouds, both in physical conditions and chemical composition (Muller etal. 2021,2023).

With the limited signal-to-noise ratio of the C2H3+$${{\rm{C}}_2}{\rm{H}}_3^ + $$ spectrum in Figs. 1a,b and the time variability of the system, it is difficult to conclude on the nature of the C2H3+$${{\rm{C}}_2}{\rm{H}}_3^ + $$ absorbing gas by comparing its line profile to previous observations. However, observations of future variations may reveal a correlation between C2H3+$${{\rm{C}}_2}{\rm{H}}_3^ + $$ and other species, giving us clues on its origin.

Finally, we note that the simultaneous detection of both the ortho and para forms would allow us to measure the actual OPR of C2H3+$${{\rm{C}}_2}{\rm{H}}_3^ + $$. This ratio could deviate from the statistical value of three and thus possibly help us to discriminate among the formation processes discussed above (see, e.g., Faure et al. 2013 for a discussion on “anomalous” OPR).

4 Summary and conclusions

We report the detection of protonated acetylene (C2H3+)$${\rm{(}}{{\rm{C}}_2}{\rm{H}}_3^ + )$$ in ALMA absorption spectra toward the southwestern image of the lensed quasar PKS 1830–211. This constitutes the first detection of C2H3+$${{\rm{C}}_2}{\rm{H}}_3^ + $$ in space, quite remarkably in a source at z = 0.89. Assuming LTE equilibrium with CMB and an OPR of three, we estimate a total C2H3+$${{\rm{C}}_2}{\rm{H}}_3^ + $$ column density of 2 × 1012 cm−2, corresponding to an abundance of 10−10 relative to H2. This makes the species quite challenging to detect, with small line opacities ≲0.005 toward PKS 1830–211 SW. However, we argue that formation pumping could increase the population of metastable states, resulting in more easily detectable absorption lines.

We explore possible gas-phase routes to the formation of interstellar C2H3+$$\eqalign{ & {{\rm{C}}_2}{\rm{H}}_3^ + \cr & \cr} $$. The ion mainly connects either to acetylene or methane, ironically both symmetric and lacking dipole moment hence unobservable at radio wavelengths. The methane route is shown to be likely more efficient in PDR conditions.

The discovery of C2H3+$${{\rm{C}}_2}{\rm{H}}_3^ + $$ (and recently of H2NC, Cabezas et al. 2021) toward PKS 1830–211 highlights the potentials of absorption spectroscopy against this quasar to search for, and potentially find other “missing” interstellar molecules, taking advantage of (i) the greatly reduced line confusion in the absorption spectrum, (ii) the red-shifting of the lines into potentially more favorable frequencies for ground-based observations, and (iii) periods when the quasar is bursting in millimeter waves for augmented line-detection sensitivity.

Acknowledgements

We thank the referee and language editor for their help improving the clarity of the manuscript. This paper makes use of the following ALMA data: ADS/JAO.ALMA#2022.1.01634.S (ortho-C2H3+$${{\rm{C}}_2}{\rm{H}}_3^ + $$ and [C I]) and ADS/JAO.ALMA#2012.1.00581.S (para-C2H3+$${{\rm{C}}_2}{\rm{H}}_3^ + $$). ALMA is a partnership of ESO (representing its member states), NSF (USA) and NINS (Japan), together with NRC (Canada), MOST and ASIAA (Taiwan), and KASI (Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO and NAOJ. This research has made use of the NASA’s Astrophysics Data System, the Cologne Database for Molecular Spectroscopy (CDMS, https://cdms.astro.uni-koeln.de/classic/molecules, Müller et al. 2005; Endres et al. 2016), the JPL Molecular Spectroscopy database (https://spec.jpl.nasa.gov, Pickett et al. 1998), and of the Kinetic Database for Astronomy (KIDA, https://kida. astrochem-tools.org, Wakelam et al. 2012).

Appendix A Complementary material

The possible structures of C2H3+$${{\rm{C}}_2}{\rm{H}}_3^ + $$ are illustrated in Fig. A.1. A diagram of energy levels of C2H3+$${{\rm{C}}_2}{\rm{H}}_3^ + $$ for levels below 100 K is shown in Fig. A.2.

thumbnail Fig. A.1

Illustration showing the possible structures of C2H3+$${{\rm{C}}_2}{\rm{H}}_3^ + $$. Up: classical ‘Y’-shaped. Down: non-classical planar-bridged cyclic. The lab data support the bridged structure over the classical one (Crofton et al. 1989; Cordonnier & Coudert 1996).
thumbnail Fig. A.2

Diagram of the energy levels of C2H3+$${{\rm{C}}_2}{\rm{H}}_3^ + $$ for levels below 100 K. The labels correspond to the JKaKc$${J_{{K_a}{K_c}}}$$ quantum numbers. The blue lines indicate the allowed rotational transitions, with frequencies given (in GHz), if below 1 THz. The lines observed in this work are shown in magenta.

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All Tables

Table 1

Line properties for the low-energy level transitions of C2H3+$${{\rm{C}}_2}{\rm{H}}_3^ + $$.

In the text
Table 2

Main chemical reactions involving C2H3+$${{\rm{C}}_2}{\rm{H}}_3^ + $$ in the interstellar medium (taken from KIDA, Wakelam et al. 2012).

In the text

All Figures

thumbnail Fig. 1

ALMA spectra toward the SW and NE lines of sight to PKS 1830-211: (a) The 212–101 transition of Ortho-C2H3+$$Ortho - {C_2}H_3^ + $$ (rest frequency 494.034 GHz) observed in 2022. (b) The 111–000 transition of Para-C2H3+$$Para - {C_2}H_3^ + $$ (431.315 GHz, rest), observed in 2014. (c) For comparison, spectra of [C I] (3P1–3P0) taken from the same spectral window as observations of a). The best fits by a Gaussian line profile are indicated in red on top of the C2H3+$${{\rm{C}}_{\rm{2}}}{\rm{H}}_{\rm{3}}^{\rm{ + }}$$ lines. All spectra have been normalized to the continuum level of each lensed image. For clarity, the spectra along the NE line of sight have been shifted by –0.01 (except for [C I] which has optical depths multiplied by 20 and shifted by –0.5) and are shown in blue.
In the text
thumbnail Fig. A.1

Illustration showing the possible structures of C2H3+$${{\rm{C}}_2}{\rm{H}}_3^ + $$. Up: classical ‘Y’-shaped. Down: non-classical planar-bridged cyclic. The lab data support the bridged structure over the classical one (Crofton et al. 1989; Cordonnier & Coudert 1996).
In the text
thumbnail Fig. A.2

Diagram of the energy levels of C2H3+$${{\rm{C}}_2}{\rm{H}}_3^ + $$ for levels below 100 K. The labels correspond to the JKaKc$${J_{{K_a}{K_c}}}$$ quantum numbers. The blue lines indicate the allowed rotational transitions, with frequencies given (in GHz), if below 1 THz. The lines observed in this work are shown in magenta.
In the text

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