Astronomical Detection of the Interstellar Anion C₁₀H⁻ toward TMC-1 from the GOTHAM Large Program on the Green Bank Telescope

It has now been more than 15 yr since the first reported molecular anion was detected in astronomical environments with the discovery of C₆H⁻ (McCarthy et al. 2006). This detection was the culmination of the early predictions that anions should be present under interstellar conditions (Herbst 1981). As summarized by Millar et al. (2017) molecular anions are critically important to the physics and evolution of astronomical objects—including building up structures in the early universe, dominating the visible opacity for stars like the Sun, being the possible carriers to the diffuse interstellar bands, and determining the physical and chemical environments of astrophysical regions including measuring the impact of interstellar radiation fields and other molecular cloud properties given their reactivity. As such, the detection of interstellar molecular anions are far beyond just an astrochemical curiosity.

The initial detection then sparked the search for new molecular anions and the identification of C₄H⁻ (Cernicharo et al. 2007; Agúndez et al. 2008), C₈H⁻ (Brünken et al. 2007; Gupta et al. 2007; Kentarou et al. 2007; Remijan et al. 2007), C₃N⁻ (Thaddeus et al. 2008), C₅N⁻ (Cernicharo et al. 2008, 2020), and ${\mathrm{CN}}^{-}$ (Agundez et al. 2010), observed primarily toward the dark cloud source TMC-1 and the evolved star IRC+10216. Since these initial detections, searches for C₆H⁻ have shown that this anion is abundant in a variety of sources, from quiescent dark clouds to active star-forming regions (Cordiner et al. 2013). These searches revealed a wide discrepancy in the anion-to-neutral column density ratios. The anion-to-neutral column density ratio for carbon chains varies markedly with the chain length and the astrophysical environment. In TMC-1, the C₆H⁻/C₆H ratio is ∼2.5%, whereas the C₄H⁻/C₄H ratio is only ∼0.0012% (Cordiner et al. 2013), increasing twentyfold to ∼0.024% toward IRC+10216 (Cernicharo et al. 2007). The enhanced anion fraction of longer chains is mirrored by the N-terminated species: C₅N⁻/C₅N ≈12.5% and C₃N⁻/C₃N ≈0.7% in TMC-1. (Cernicharo et al. 2020). These observations highlight that anion chemistry and the limit to which carbon-chain anions can grow in astronomical environments are still not well understood.

Recently, Siebert et al. (2022) reported the identification of the largest CH₃-terminated carbon-chain molecule CH₃C₇N toward TMC-1 and in that work, determined the column densities of several large carbon-chain families and made predictions for the column densities for those species yet to be detected. These predictions were made using the three-phase gas/grain chemical network model nautilus (v1.1; Ruaud et al. 2016). In addition, a linear extrapolation as a function of the chain length was made from the measured column densities of the smaller carbon chains. While the predicted and measured column density ratios can differ up to an order of magnitude, it served as motivation to conduct an astronomical search for the elusive, larger carbon-chain species that may already be contained within our existing TMC-1 data set.

As such, to follow on from the recent detections and surveys of molecular anions, an extensive search for the decapentaynyl radical (C₁₀H) and the decapentaynyl anion (C₁₀H⁻) was conducted toward the dark cloud TMC-1—the site of the first detection of interstellar anions—with the Green Bank Telescope (GBT) Observations of TMC-1: Hunting for Aromatic Molecules (GOTHAM) survey. The family of H-terminated carbon-chain radicals—C_2n H (where n >1) and their associated anions have been studied in various astronomical environments, and these species are believed to share common chemical formation pathways (Bettens & Herbst 1997; Walsh et al. 2009). To best constrain the column density ratios between the radical and anion species, we performed a complete reanalysis of the C₄H, C₆H, C₈H radicals and their associated anions taking advantage of the significantly improved signal-to-noise ratio (S/N) and spectral resolution of our data compared to their original detections. These observations provide the most rigorous measurement of the column densities of these species with which to compare to chemical formation and machine learning models. They have also set a new limit to the largest carbon-chain species detectable in astronomical environments as the first detection of C₁₀H⁻ and a tentative detection of C₁₀H are reported toward TMC-1. The observing parameters describing the search for these carbon-chain species are presented in Section 2. The new spectroscopic analyses for C₄H, C₆H, and C₁₀H⁻ are given in Section 3, which includes a discussion of how the astronomical detection of C₁₀H⁻ enabled the more accurate determination of its molecular constants. The observational analyses on how the physical parameters of TMC-1 are determined from these data are presented in Section 4. The results of the observational searches for C₁₀H and C₁₀H⁻ and the previously detected carbon-chain molecules are presented in Section 5. A comparison of the predicted-to-measured column density ratios for this family of carbon-chain molecules from both state-of-the-art gas/grain chemical models and from machine learning analyses are given in Section 6. Finally, our conclusions are highlighted in Section 7.

Observations for this study were obtained as part of the GOTHAM survey. GOTHAM is a large project on the 100 m Robert C. Byrd GBT currently managed by the Green Bank Observatory (GBO). The GOTHAM program is a dedicated spectral line observing program of TMC-1 covering almost 30 GHz of bandwidth at high sensitivity and spectral resolution. All data were taken with a uniform frequency resolution of 1.4 kHz (0.05–0.01 km s⁻¹ in velocity) and an rms noise of ∼2–20 mK across most of the observed frequency range with the rms gradually increasing toward higher frequency because of the shorter integration times. This work uses the fourth data reduction (DR4) of GOTHAM targeting the cyanopolyyne peak (CP) of TMC-1, centered at α_J2000 = 04^h41^m42.5^s., δ_J2000 = +25°41'268. Briefly, the spectra in these data cover the entirety of the X-, K-, and Ka-receiver bands with nearly continuous coverage from 7.9 to 11.6 GHz, 12.7 to 15.6 GHz, and 18.0 to 36.4 GHz (24.9 GHz of total bandwidth). Data reduction involved removal of radio frequency interference and artifacts, baseline continuum fitting, and flux calibration using complementary Very Large Array observations of the source J0530+1331. Uncertainty from this flux calibration is estimated at ∼20%, and is factored into our statistical analysis described below (McGuire et al. 2020). A full description of the fourth data reduction can be found in Sita et al. (2022), and the observing strategy and reduction pipeline is fully described in McGuire et al. (2020).

Upon comparison of the astronomical data and the fitted laboratory spectra found in the publicly available Cologne Database for Molecular Spectroscopy (CDMS; Endres et al. 2016), it was determined that a reanalysis of the measured and predicted frequencies was needed for C₄H and C₆H. The spectroscopic data available for the other radicals and associated anions very closely matched the observational spectrum and no reanalysis was required. The subsections below describe the process for how the catalogs for C₄H and C₆H were revised and how the catalog for C₁₀H⁻ was generated using the astronomically measured spectroscopic data.

3.1. C₄H

3.2. C₆H

3.3. C₁₀H⁻

To our knowledge, no laboratory spectra exist for C₁₀H⁻, and our own efforts to produce detectable quantities in our instruments have not yet been successful. Unlike C₄H and C₆H, however, C₁₀H⁻ is a closed-shell linear molecule, and as such, it is straightforward to predict its rotational spectrum, which presents as a series of lines spaced by ∼2B. Given a reliable prediction of the rotational constant, B, prior work has shown that it is possible to identify such species in interstellar spectra preceding their laboratory confirmation. Examples include C₃H⁺ (Pety et al. 2012) in the Horsehead photodissociation region and C₅H⁺ (Cernicharo et al. 2022), HC₅NH⁺ (Marcelino et al. 2020), and HC₇NH⁺ (Cabezas et al. 2022) in TMC-1, among others.

We began our search for C₁₀H⁻ by using a value of B = 299.882 MHz and D = 1 Hz, obtained by extrapolating and scaling from the shorter members of the family of anions. The B value specifically is in excellent agreement with that obtained from a quantum chemical calculation carried out at the M06-2X/6–31+G(d) level of theory and basis set using the Psi4 suite of programs (Smith et al. 2020) of B = 303.761 MHz. This level of theory and basis set has been previously shown to reliably produce rotational constants in excellent agreement with experiments (Lee & McCarthy 2020).

Using our estimated values of B and D, we produced a catalog of lines and performed a simulation, using a set of fiducial values for v_lsr, the column density ratios between velocity components, the excitation temperature (T_ex), and the line width (ΔV). These values are based on our prior detection and treatment of benzonitrile within the source, and have been shown to be excellent starting points for the analysis of other molecules in the GOTHAM data (see Supplementary Information of McGuire et al. 2021). No individual transitions were seen above the noise level of the observations. A spectral stack of the data using this first-pass estimated catalog, however, revealed a strong (>5σ) signal in the stacked spectra shifted by just over 10 km s⁻¹ from the expected central velocity (Figure 1).

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We then performed a least-squares fit to determine what value of the rotational constant would be required to reproduce the observed signal at the expected central velocity. We derive a value of B = 299.87133 MHz, differing from the scaled prediction by 11 kHz or 0.004%. This derived value was then used to generate a final spectral line catalog for C₁₀H⁻ that was used for the remainder of the analysis described in this paper; a summary of the values of the B rotational constant determined by our methods are summarized in Table 1. As described in detail in McGuire et al. (2021), a fractional accuracy of better than 10⁻⁵ (and ideally better than 10⁻⁶) in the rotational constants of a molecule is required to recover any significant signal from our spectral stacking techniques. Thus, we can infer that our derived value of B is likely accurate to at least 3 kHz.

Table 1. Rotational Constant of C₁₀H⁻ from Quantum Chemistry, Scaled from Experimental Values of smaller Anions, and Determined in this Work from our Astronomical Observations

Parameter	M06-2X/6–31+G(d)	Scaled	This Work
B (MHz)	301.353	299.882	299.87133
D (Hz)	⋯	[1.0] a	[1.0] a

Note.

^a D was fixed to a value near that of C₈H⁻ (D = 4.3 Hz; Gupta et al. 2007), but no attempt was made to refine it further, given the limitations of the analysis.

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In order to derive physical parameters (column density [N_T ], excitation temperature [T_ex], line width [ΔV], and source size [^'']) for the target molecules in our observations, we used the same Markov Chain Monte Carlo (MCMC) model employed in prior GOTHAM analyses (see, e.g., Lee et al. 2021a; Siebert et al. 2022; Sita et al. 2022) and discussed in detail in Loomis et al. (2021). In short, the MCMC model calculates the probability distributions and covariances for these parameters that are used to describe the emission of molecules observed in our data. The resulting corner plots for the molecules analyzed here are shown in Figures A2, A3, B1, C1, D1, E1, F1, and G1.

We adopt the 50th percentile value of the posterior probability distributions as the representative value of each parameter for the molecule and use the 16th and 84th percentile values for the uncertainties. For probabilities that show a Gaussian distribution, these correspond to the 1σ uncertainty level. Many of our resulting probability distributions are indeed either Gaussian or nearly Gaussian, and thus these values are usually quite representative of the 1σ uncertainties. One of the advantages of the MCMC technique over a traditional least-squares fit approach is that far more of parameter space is explored. Correspondingly, a much larger exploration of the uncertainty space is performed as well, including highlighting parameters that may be highly covariant with one another. This manifests as nonseparable distributions in the corner plots.

To explore this parameter space with our MCMC approach, a model of the molecular emission is generated for each set of parameters using the molsim software package (Lee et al. 2021b) and following the conventions of Turner (1991) for a single excitation temperature and accounting for the effect of optical depth. Prior observations from GOTHAM (Xue et al. 2020) and others (Dobashi et al. 2018, 2019) have found that most emission seen at centimeter wavelengths in TMC-1 can be separated into contributions from four distinct velocity components within the larger structure, at approximately 5.4, 5.6, 5.8, and 6.0 km s⁻¹ (Loomis et al. 2021). In some cases, especially for less abundant species where there is not a clear detection in one of the velocity components, we find that a three-component model has performed better (McGuire et al. 2020).

To determine the statistical evidence that our model of the emission of these molecules is consistent with the data, we followed the procedures described in detail in Loomis et al. (2021) and performed a spectral stack and matched filtering analysis for C₁₀H and C₁₀H⁻. Briefly, a weighted average of the observational spectra in the velocity space and centered on each spectral line of a target molecule was performed. The weights were determined by the relative intensity of the expected emission (based on the MCMC-derived parameters) and the local rms noise of the observations. Considering the weak expected intensities for both C₁₀H⁻ and the C₁₀H isomers, any observational windows containing emission at >5σ were ignored in the analysis of those molecules.

Simulated spectra of the molecular emission using the same MCMC-derived parameters were then also generated and stacked using identical weights. This simulation was then used as a matched filter, which is passed through the observational signal. The resulting impulse response function represents the statistical evidence that our model of the emission from the molecule—and thus our derived parameters for the molecule—is consistent with the observations. In addition to the details of the methodology provided in Loomis et al. (2021), the appendices of McGuire et al. (2021) include an extensive analysis of the robustness of the methodology, including the improbability of spurious signals and the minimal impact of red noise on the procedure.

We also performed MCMC fits for the more abundant C₄H, C₄H⁻, C₆H, C₆H⁻, C₈H, and C₈H⁻ molecules. Given the low line density in our spectra, it is extremely improbable that interfering signals from other species would be present. Still, the spectral regions containing these transitions were manually inspected to ensure there were no interloping signals or other concerns. All strongly detected lines in our data are shown in the Appendix for C₄H (Figures B2–B4), C₄H⁻ (Figure C2), C₆H (Figures D2 and D3), C₆H⁻ (Figure E2), C₈H (Figure F2), and C₈H⁻ (Figure G2).

Figure 2 shows the stacked data, the stacked MCMC model, as well as the matched filter response and the first detection of interstellar C₁₀H⁻ toward TMC-1. The stacked emission in the right panel of Figure 2 exhibits evidence at >9σ for the presence of this molecule. Figure A1 shows the individual spectral lines present in the survey. While no individual lines of C₁₀H⁻ are present above the current noise level of the survey at >3σ, there are spectral features seen in the corresponding passbands that show some emission above the noise (see, e.g., transitions at 10195.41, 13194.04, 14993.2, and 19191.26 MHz). Table 2 lists the measured physical values determined from the C₁₀H⁻ fits. In this case, three independent velocity components were detected, and a total C₁₀H⁻ column density of ${4.04}_{-2.23}^{+10.67}\times {10}^{11}$ cm⁻² was determined.

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Table 2. Summary Statistics of the Marginalized C₁₀H⁻ Posterior

vlsr	Size	NT	Tex	ΔV
(km s−1)	(arcsec)	(1011 cm−2)	(K)	(km s−1)
${5.624}_{-0.014}^{+0.012}$	${16}_{-7}^{+9}$	${3.68}_{-2.23}^{+10.67}$
${5.759}_{-0.020}^{+0.020}$	${27}_{-9}^{+10}$	${0.27}_{-0.12}^{+0.27}$
⋯	⋯	⋯	${4.00}_{-0.21}^{+0.21}$	${0.360}_{-0.025}^{+0.027}$
${6.040}_{-0.019}^{+0.019}$	${659}_{-274}^{+234}$	${0.09}_{-0.02}^{+0.02}$
NT (Total): ${4.04}_{-2.23}^{+10.67}\times {10}^{11}$ cm−2

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Figure 3 show the stacked observational data, the stacked MCMC model, as well as the matched filter response and a tentative detection of the C₁₀H radical toward TMC-1. The stacked molecular emission of C₁₀H in the right panel of Figure 3 exhibits evidence at ∼3.2σ for the presence of this molecule; no individual spectral lines were present. Table 3 lists the measured physical values determined from the C₁₀H fits. In this case, four independent velocity components were fit and a total C₁₀H column density of ${2.02}_{-0.82}^{+2.68}\times {10}^{11}$ cm⁻² was reported.

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Table 3. Summary Statistics of the Marginalized C₁₀H Posterior

vlsr	Size	NT	Tex	ΔV
(km s−1)	(arcsec)	(1011cm−2)	(K)	(km s−1)
${5.590}_{-0.009}^{+0.010}$	${24}_{-4}^{+4}$	${0.53}_{-0.16}^{+0.26}$
${5.726}_{-0.010}^{+0.015}$	${29}_{-4}^{+4}$	${0.29}_{-0.09}^{+0.13}$	${5.45}_{-0.29}^{+0.31}$	${0.102}_{-0.011}^{+0.019}$
${5.859}_{-0.010}^{+0.010}$	${13}_{-6}^{+12}$	${1.15}_{-0.80}^{+2.67}$
${6.036}_{-0.013}^{+0.015}$	${633}_{-256}^{+246}$	${0.05}_{-0.01}^{+0.01}$
NT (Total): ${2.02}_{-0.82}^{+2.68}\times {10}^{11}$ cm−2

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6.1. Chemical Modeling Predictions

Building on the modeling efforts of carbon-chain chemistry in Siebert et al. (2022), we utilized the nautilus v1.1 code (Ruaud et al. 2016) which has been used previously to successfully study the formation of carbon-chain molecules detected with GOTHAM data (Xue et al. 2020; McGuire et al. 2021; Shingledecker et al. 2021). The model's physical conditions are identical to those studies (T_gas = T_grain = 10 K, ${n}_{{{\rm{H}}}_{2}}$ = 2 × 10⁴ cm⁻³, A_V = 10, and ζ_CR = 1.3 × 10⁻¹⁷ s⁻¹; Hincelin et al. 2011) as are the elemental abundances (Loomis et al. 2021). Based originally off of the Kinetic Database for Astrochemistry network, our network already contained some formation routes to the C_n H family from n = 2 to n = 10 and the C_n H⁻ family from n = 4 to n = 10.

The simulated abundances are compared with those observed in TMC-1 and the machine learning predictions discussed in Section 6.2 assuming a TMC-1 hydrogen column density of ${N}_{{{\rm{H}}}_{2}}$ = 10²² cm⁻². For utility of comparison, we adopt the same source age as discussed in Siebert et al. (2022). However, it should be noted that the simulated time of peak abundance can vary between species, with heavier species and longer carbon chains typically requiring a longer time to form. This time dependence is shown in greater detail in Appendix I.

As Figure 4 shows for the C_n H family, the chemical model agrees within within a factor of 5 and the log-linear trend is generally reproduced. One of the primary production pathways of this family comes from atomic reactions of the form

$$\begin{eqnarray}&&{\rm{C}}+{{\rm{C}}}_{n-1}{{\rm{H}}}_{2}\to {{\rm{C}}}_{n}{\rm{H}}+{\rm{H}}.\end{eqnarray} \tag{ 1 }$$

The rate coefficients of these reactions were estimated by Loison et al. (2014) through extrapolation of the calculations by Chastaing et al. (2001) and Chastaing et al. (2000) on C + alkenes, alkynes, dienes, and diynes. The other major formation routes involve atomic reactions with related anions:

$$\begin{eqnarray}&&{\rm{C}}+{{\rm{C}}}_{n-1}{{\rm{H}}}^{-}\to {{\rm{C}}}_{n}{\rm{H}}+{e}^{-},\end{eqnarray} \tag{ 2 }$$

$$\begin{eqnarray}&&{\rm{H}}+{{\rm{C}}}_{n}^{-}\to {{\rm{C}}}_{n}{\rm{H}}+{e}^{-}.\end{eqnarray} \tag{ 3 }$$

For C₁₀H, these reactions were studied theoretically in Harada & Herbst (2008) and experimentally in Eichelberger et al. (2007) and Barckholtz et al. (2001). The majority of the family is primarily destroyed through electron attachment, producing their carbon-chain length analogs among the C_n H⁻ family. These rates were also estimated by Harada & Herbst (2008).

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For the carbon-chain anions, C_n H⁻, the abundances agree within an order of magnitude for C₆H⁻ and longer. While the model predictions show the monotonically decreasing abundances found for the radical species, akin to the log-linear trend seen for the majority of long carbon chains, it is not able to reproduce the enhanced abundances found in C₆H⁻ and C₁₀H⁻ nor the relative positive correlation between C_n H⁻ abundance and carbon-chain length. Given the measured values, the C₁₀H⁻/C₁₀H column density ratio is $\sim {2.0}_{-1.6}^{+5.9}$—the highest value measured between an anion and neutral species to date. Such a high ratio is impossible for our model to reproduce, even if every electron collision with C₁₀H results in C₁₀H⁻ formation. As such, the predictions from the gas/grain chemical model illustrate that there is much still uncertain about the chemistry needed to form molecular anions in astronomical environments. The chemical network for these species originates from estimations done by Harada & Herbst (2008). The primary production route of the anions (80%–90%) is through radiative electron attachment

$$\begin{eqnarray}&&{{\rm{C}}}_{n}{\rm{H}}+{e}^{-}\to {{\rm{C}}}_{n}{{\rm{H}}}^{-}+\gamma .\end{eqnarray} \tag{ 4 }$$

Another minor production route is also present involving reactions between longer carbon-chain anions and atomic oxygen,

$$\begin{eqnarray}&&{{\rm{C}}}_{n+1}{{\rm{H}}}^{-}+{\rm{O}}\to {{\rm{C}}}_{n}{{\rm{H}}}^{-}+\mathrm{CO}.\end{eqnarray} \tag{ 5 }$$

There are two product channels suggested for the destruction reactions between carbon-chain anions and atomic hydrogen (Harada & Herbst 2008). We considered the pathway involving associative electron detachment,

$$\begin{eqnarray}&&{{\rm{C}}}_{n}{{\rm{H}}}^{-}+{\rm{H}}\to {{\rm{C}}}_{n}{{\rm{H}}}_{2}+{e}^{-},\end{eqnarray} \tag{ 6 }$$

for C_n H⁻ (n = 4, 6, 8, and 10). In contrast, the other pathway involves fragmentation and has only been considered for C₁₀H⁻,

$$\begin{eqnarray}&&{{\rm{C}}}_{10}{{\rm{H}}}^{-}+{\rm{H}}\to {{\rm{C}}}_{8}{{\rm{H}}}^{-}+{{\rm{C}}}_{2}{\rm{H}}.\end{eqnarray} \tag{ 7 }$$

Harada & Herbst (2008) originally estimated all rates for route 6 to be 1.0 × 10⁻⁹ cm³ s⁻¹. This was also the rate estimated for route 7. In order to keep the total C₁₀H⁻ + H rate consistent with the other analogous anion reactions in route 6, we modified the rates of both C₁₀H⁻+H reactions from routes 6 and 7 from 1.0 × 10⁻⁹ cm³ s⁻¹ to 5.0 × 10⁻¹⁰ cm³ s⁻¹. This resulted in a factor of ∼2 increase in the abundance of C₁₀H⁻ relative to simulations performed with the original rates.

There are limited experimental constraints on these pathways and the corresponding rate coefficients. In particular, major route 4 is very challenging to measure experimentally because of two reasons. First, anions are difficult to produce in a stable quantity. Second, it is difficult to observe the photoemission process due to competing collisional stabilization. In addition, anion–neutral reactions, for example, might also contribute to the C_n H⁻'s formation, but these need to be investigated further. Furthermore, while the current model mainly focuses on the gas chemistry of the C_n H⁻ species, electron attachment processes might occur on grains, allowing the superexcited anion intermediate to be stabilized efficiently rather than being dependent on radiative processes in the gas phase. Our understanding of molecular anions and carbon chains can be improved by constraining their grain chemistry.

6.2. Machine Learning Predictions

Using the GOTHAM data, we report the first astronomical detection of the C₁₀H⁻ anion toward the dark cloud TMC-1 with the GBT. In fact, the astronomical observations provided the necessary data to the refinement of the spectroscopic parameters of C₁₀H⁻ to enable the first astronomical detection. These new parameters will be essential for future studies of C₁₀H⁻ in the laboratory. From the velocity stacked data and the matched filter response, C₁₀H⁻ is detected at >9σ confidence interval. In addition, there is evidence for several individual lines of C₁₀H⁻ in the GOTHAM data though none above the current noise level of the survey beyond the >3σ limit. In this case, three independent velocity components were detected and a total C₁₀H⁻ column density of ${4.04}_{-2.23}^{+10.67}\times {10}^{11}$ cm⁻² was determined.

A dedicated search for the C₁₀H radical was also conducted toward TMC-1. The stacked molecular emission of C₁₀H was detected at a ∼3.2σ confidence interval. As such, the presence of this molecule is currently considered tentative. In addition, no individual spectral lines from this species were detected. The measured physical values determined from the C₁₀H fits include four independent velocity components, and a total C₁₀H column density of ${2.02}_{-0.82}^{+2.68}\times {10}^{11}$ cm⁻² was reported. Given the measured values, the C₁₀H⁻/C₁₀H column density ratio is ∼${2.0}_{-1.6}^{+5.9}$ - the highest value measured between an anion and neutral species to date. Such a high ratio is at odds with current theories for interstellar anion chemistry.

The full GOTHAM data set was also used to better characterize the physical parameters including the column density [N_T ], excitation temperature [T_ex], line width [ΔV], and source size [''] for the more abundant C₄H, C₄H⁻, C₆H, C₆H⁻, C₈H, and C₈H⁻ molecules. These data were compared to predicted abundances from both a gas/grain chemical formation model and from a machine learning analysis. For the radical species, both models reproduce the measured abundances found from the survey better than an order of magnitude (except for the C₄H predicted abundance from the machine learning analysis). However, the machine learning analysis matches the detected anion abundances much better than the gas/grain chemical model suggesting that the understanding of the formation chemistry of molecular anions is still highly questionable. Finally, using the machine learning analysis, it is possible to make a prediction for the larger species, namely, C₁₂H and C₁₂H⁻ and the smaller molecular anion CCH⁻. For CCH⁻, a model prediction of 2.3 × 10¹² cm⁻² shows that predicted column density of CCH⁻ is in stark contrast to the reported upper limit of <2.2 × 10¹¹ cm⁻². However, for the larger species C₁₂H and C₁₂H⁻, the predictions of 7.1 × 10¹¹ cm⁻² and 7.0 × 10¹¹ cm⁻², respectively, suggest they may be detected in TMC-1 once the spectroscopy of these species has been fully characterized for an astronomical search.

The authors would like to thank the anonymous referees who provided valuable insight and suggestions that greatly improved the manuscript. We gratefully acknowledge support from NSF grants AST-1908576 and AST-2205126. I.R.C. acknowledges support from the University of British Columbia and the Natural Sciences and Engineering Research Council of Canada (NSERC). E.H. thanks the National Science Foundation (US) for support of his research program in astrochemistry through grant AST 19-06489. M.A.C. and S.B.C. were supported by the Goddard Center for Astrobiology. H.G. acknowledges support from the National Science Foundation for participation in this work as part of his independent research and development plan. Any opinions, findings, and conclusions expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. The Green Bank Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc.

Figure A1 shows individual lines of C₁₀H⁻ covered in the GOTHAM data through 25 GHz. The data and simulations are displayed at a smoothed resolution of 5.6 kHz (versus the 1.4 kHz native resolution of the GOTHAM observations) to show the (very weak) potential signal from these individual lines particularly between 13.1 and 19.2 GHz. Lines up to 30 GHz were included in the analysis (and are included in the catalog provided in the Supplementary Information), but are not shown here as the noise level of that data is much higher than the predicted line intensities.

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Figures A2 and A3 show the corner plots from the MCMC analysis of C₁₀H⁻ and C₁₀H, respectively.

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A.1. Jacknife Analysis

To further ensure that the signal attributed to C₁₀H⁻ is molecular in origin, we performed a jacknife analysis similar to that described in detail in McGuire et al. (2021). The catalog for C₁₀H⁻ was divided in half, with every other line assigned to one of two different catalogs. A spectral stack and matched filter was then performed on each catalog separately. Assuming the signal is indeed molecular and coming from C₁₀H⁻, the resulting impulse response functions should, when added in quadrature, closely reproduce the signal from the full catalog. The results of the analysis are shown in Figure A4, and we find impulse response functions of 5.3σ and 7.8σ. When added in quadrature, this results in a total of 9.2σ, in very good agreement with the value determined from the entire catalog and shown in Figure 2 of 9.3σ. As discussed in McGuire et al. (2021), the small mismatch is almost certainly due to minor contributions of red noise in the data at the level of, in this case, 0.1σ.

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The best-fit parameters from the MCMC fit for C₄H are shown in Table B1. The corner plot from the analysis is shown in Figure B1. Figures B2, B3, and B4 show the individual lines of C₄H detected in the GOTHAM observations.

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Table B1. C₄H Values

vlsr	Size	NT a	Tex	ΔV
(km s−1)	(arcsec)	(1013cm−2)	(K)	(km s−1)
${5.657}_{-0.009}^{+0.008}$	${570}_{-300}^{+289}$	${6.95}_{-0.94}^{+0.85}$
${5.754}_{-0.030}^{+0.029}$	${29}_{-5}^{+5}$	${6.52}_{-1.83}^{+2.24}$	${5.10}_{-0.42}^{+0.46}$	${0.178}_{-0.010}^{+0.013}$
${5.864}_{-0.032}^{+0.045}$	${543}_{-332}^{+311}$	${1.42}_{-0.68}^{+0.75}$
${6.047}_{-0.025}^{+0.019}$	${453}_{-292}^{+369}$	${1.33}_{-0.26}^{+0.30}$
NT (Total): b ${1.62}_{-0.22}^{+0.25}\times {10}^{14}$ cm−2

Notes. The quoted uncertainties represent the 16th and 84th percentile (1σ for a Gaussian distribution) uncertainties.

^a Column density values are highly covariant with the derived source sizes. ^b Uncertainties derived by adding the uncertainties of the individual components in quadrature.

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The best-fit parameters from the MCMC fit for C₄H⁻ are shown in Table C1. The corner plot from the analysis is shown in Figure C1. Figure C2 shows the individual lines of C₄H⁻ detected in the GOTHAM observations.

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Table C1. C₄H⁻ Values

vlsr	Size	NT	Tex	ΔV
(km s−1)	(arcsec)	(1010cm−2)	(K)	(km s−1)
${5.652}_{-0.032}^{+0.013}$	${40}_{-4}^{+4}$	${2.51}_{-1.07}^{+0.62}$
${5.740}_{-0.034}^{+0.047}$	${31}_{-4}^{+4}$	${0.95}_{-0.68}^{+1.32}$	${5.13}_{-0.47}^{+0.48}$	${0.181}_{-0.018}^{+0.014}$
${5.916}_{-0.047}^{+0.040}$	${29}_{-5}^{+5}$	${0.44}_{-0.39}^{+0.62}$
${6.018}_{-0.035}^{+0.058}$	${10}_{-3}^{+4}$	${2.89}_{-2.22}^{+4.41}$
NT (Total): ${6.79}_{-2.59}^{+4.68}\times {10}^{10}$ cm−2

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The best-fit parameters from the MCMC fit for C₆H are shown in Table D1. The corner plot from the analysis is shown in Figure D1. Figures D2 and D3 show the individual lines of C₆H detected in the GOTHAM observations.

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Table D1. C₆H Values

vlsr	Size	NT	Tex	ΔV
(km s−1)	(arcsec)	(1012 cm−2)	(K)	(km s−1)
${5.600}_{-0.005}^{+0.012}$	${356}_{-110}^{+99}$	${1.15}_{-0.07}^{+0.15}$
${5.744}_{-0.008}^{+0.020}$	${35}_{-5}^{+55}$	${3.06}_{-1.78}^{+0.58}$	${5.12}_{-0.06}^{+0.13}$	${0.154}_{-0.008}^{+0.025}$
${5.882}_{-0.019}^{+0.021}$	${339}_{-136}^{+111}$	${0.50}_{-0.42}^{+0.08}$
${6.016}_{-0.023}^{+0.014}$	${284}_{-121}^{+144}$	${0.46}_{-0.07}^{+0.14}$
NT (Total): ${5.17}_{-1.83}^{+0.62}\times {10}^{12}$ cm−2

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The best-fit parameters from the MCMC fit for C₆H⁻ are shown in Table E1. The corner plot from the analysis is shown in Figure E1. Figure E2 shows the individual lines of C₆H⁻ detected in the GOTHAM observations.

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Table E1. C₆H⁻ Values

vlsr	Size	NT	Tex	ΔV
(km s−1)	(arcsec)	(1010cm−2)	(K)	(km s−1)
${5.646}_{-0.009}^{+0.009}$	${91}_{-13}^{+19}$	${8.76}_{-1.27}^{+1.49}$
${5.784}_{-0.018}^{+0.017}$	${32}_{-4}^{+4}$	${9.94}_{-2.24}^{+2.52}$	${4.32}_{-0.18}^{+0.22}$	${0.177}_{-0.012}^{+0.013}$
${5.905}_{-0.031}^{+0.024}$	${18}_{-4}^{+4}$	${6.66}_{-3.53}^{+4.95}$
${5.991}_{-0.010}^{+0.011}$	${636}_{-274}^{+249}$	${3.08}_{-0.43}^{+0.41}$
NT (Total): ${2.84}_{-0.44}^{+0.58}\times {10}^{11}$ cm−2

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The best-fit parameters from the MCMC fit for C₈H are shown in Table F1. The corner plot from the analysis is shown in Figure F1. Figure F2 shows the individual lines of C₈H detected in the GOTHAM observations.

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Table F1. C₈H Values

vlsr	Size	NT	Tex	ΔV
(km s−1)	(arcsec)	(1011cm−2)	(K)	(km s−1)
${5.632}_{-0.004}^{+0.004}$	${696}_{-253}^{+209}$	${1.35}_{-0.07}^{+0.06}$
${5.775}_{-0.008}^{+0.007}$	${20}_{-3}^{+4}$	${5.00}_{-1.22}^{+2.05}$	${7.15}_{-0.18}^{+0.18}$	${0.159}_{-0.008}^{+0.010}$
${5.897}_{-0.043}^{+0.031}$	${654}_{-265}^{+237}$	${0.47}_{-0.14}^{+0.10}$
${6.010}_{-0.021}^{+0.027}$	${672}_{-267}^{+227}$	${0.44}_{-0.15}^{+0.15}$
NT (Total): ${7.25}_{-1.23}^{+2.06}\times {10}^{11}$ cm−2

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The best-fit parameters from the MCMC fit for C₈H⁻ are shown in Table G1. The corner plot from the analysis is shown in Figure G1. Figure G2 shows the individual lines of C₈H⁻ detected in the GOTHAM observations.

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Table G1. C₈H⁻ Values

vlsr	Size	NT	Tex	ΔV
(km s−1)	(arcsec)	(1010cm−2)	(K)	(km s−1)
${5.646}_{-0.004}^{+0.004}$	${87}_{-27}^{+51}$	${0.70}_{-0.10}^{+0.17}$
${5.812}_{-0.009}^{+0.005}$	${29}_{-4}^{+4}$	${2.20}_{-0.55}^{+0.74}$	${6.17}_{-0.29}^{+0.30}$	${0.115}_{-0.005}^{+0.005}$
${5.896}_{-0.030}^{+0.037}$	${18}_{-4}^{+5}$	${0.51}_{-0.38}^{+1.05}$
${6.021}_{-0.005}^{+0.005}$	${12}_{-5}^{+7}$	${4.59}_{-2.50}^{+7.68}$
NT (Total): ${8.00}_{-2.59}^{+7.79}\times {10}^{10}$ cm−2

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The sources of the spectroscopic catalogs used for the analysis, as well as the literature references from which those catalogs were created, are provided in Table H1. The rotational partition function values for each of the molecules analyzed here are provided in Table H2 at the standard set of temperatures from SPFIT/SPCAT.

Figure I1 shows the time dependence of the simulated abundances within the nautilus chemical models in relation to the observed values, shown as hashed horizontal boxes. As it can be seen, the relative trend lines of these species can be quite time dependent, the time of peak abundance is strongly dependent on the carbon-chain length. For ease of comparison to previous studies of carbon chains in TMC-1, we adopt the same source age as Siebert et al. (2022) of 2.5 × 10⁵ yr, as also shown in Figure I1.

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