CH₃-Terminated Carbon Chains in the GOTHAM Survey of TMC-1: Evidence of Interstellar CH₃C₇N

One of the most well-studied sites of cold, interstellar carbon chemistry is a pre-stellar core within the Taurus Molecular Cloud complex, commonly referred to as Taurus Molecular Cloud 1 (TMC-1) (Churchwell et al. 1978). The chemistry occurring in TMC-1 produces a suite of exotic molecules (by terrestrial standards) including unsaturated cyanopolyyne (HC_2n+1N; n = 1, 2, 3,...) and acetylenic (C_2n H₂) linear carbon chains. Among the variations on these abundant molecules are the symmetric top methylpolyynes (MPs) and methylcyanopolyynes (MCPs), which have the form CH₃C_2n H and CH₃C_2n-1N, respectively. These species have been known in the interstellar medium (ISM) since the discovery of methyl cyanide (CH₃CN) (Solomon et al. 1971) and methyl acetylene (CH₃CCH) (Irvine et al. 1981). Toward TMC-1, MPs and MCPs as large as CH₃C₆H and CH₃C₅N have been detected and characterized (Irvine et al. 1981; Matthews & Sears 1983; Broten et al. 1984; Loren et al. 1984; MacLeod et al. 1984; Walmsley et al. 1984; Remijan et al. 2006; Snyder et al. 2006).

Currently, the chemical formation of MPs and MCPs in TMC-1 is unconstrained. While it is possible that simple carbon-addition reactions occurring on the surfaces of dust grains may account for the growth of these species toward cold, dark clouds (Turner et al. 2000), it is also plausible that ion–molecule reaction pathways in the gas phase can account for their formation (Quan & Herbst 2007). Because molecules with C_3v symmetry have unique excitation properties that do not allow for easy interconversion between A and E symmetry states, the relative populations of their K-ladders can offer additional clues to their formation conditions (see e.g., Askne et al. 1984; Minh et al. 1993; Willacy et al. 1993; Mendoza et al. 2018), but, to date, analysis of these populations has only been done for the shortest MPs and MCPs. Furthermore, comparing the relative column densities of the similarly structured cyanopolyynes has proven to be a useful tool in testing chemical models and assessing the mechanisms through which carbon chain species grow in the ISM (Agúndez et al. 2017; Burkhardt et al. 2018; Loomis et al. 2021).

Obtaining a more complete understanding of their chemistry and setting constraints on the abundances and excitation conditions of the various methyl-terminated carbon chains requires exploring the extent to which these types of species can grow (i.e., how long of a carbon chain can form). Such observations would enable the direct comparison of measured abundances with both grain-surface and gas-phase reaction pathways, especially when combined with a fully self-consistent excitation analysis of MPs and MCPs in TMC-1. In addition, these studies will set the overall limit to the detectability of longer-chain MPs and MCPs based on both an improved understanding of the chemical formation pathway and on a new computational methodology to detect the weak signals coming from the larger carbon chain species.

The ongoing GBT Observations of TMC-1: Hunting for Aromatic Molecules survey (GOTHAM) along with a deep Q-band survey being conducted on the Yebes 40 m radio telescope (Cernicharo et al. 2020) have thus far proven to be very useful for rigorous studies of exotic molecules in TMC-1. With many new detections of various carbon-bearing molecules, their isomers, and cyclic/polycyclic species, these projects have effectively expanded our knowledge of the interstellar molecular carbon reservoir before star formation occurs (McGuire et al. 2018; McCarthy et al. 2021; McGuire et al. 2020; Xue et al. 2020; Cabezas et al. 2021; Cernicharo et al. 2021; Loomis et al. 2021; McGuire et al. 2021). In this work, we present a detailed analysis of CH₃-terminated carbon chains toward TMC-1 as well as the first detection of methylcyanotriacetylene (CH₃C₇N; Chen et al. 1998) using the second data release of GOTHAM. We also search for methyltetraacetylene (CH₃C₈H; Travers et al. 1998) in our data, but do not find significant emission and thus report upper limits on its abundance.

In Section 2, we outline the specifics of our observations and reduction methods. In Section 3 we describe our spectroscopic calculations for the targeted molecules and statistical analysis procedures. In Section 4 we present our results for all targeted molecules and discuss their relative column densities and excitation physics. Finally, in Section 5 we discuss how our results fit in to the current understanding of chemistry in TMC-1, and compare them with predictions of our chemical model.

The observations obtained in this study were collected as part of the GOTHAM Survey. GOTHAM is a large project on the 100 m Green Bank Telescope (GBT) currently carrying out dedicated spectral line observations of TMC-1 covering almost 30 GHz of radio bandwidth at high sensitivity and ultra-fine spectral resolution. This work uses the second data release (DR2) of GOTHAM, which includes over 600 hr of observations targeting the cyanopolyyne peak (CP) of TMC-1, centered at α_J2000 = 0441425, δ _J2000 = +25°41'268. A full description of the DR2 specifications and our reduction pipeline has been described (McGuire et al. 2020), but, put briefly, the spectra in this data set cover the entirety of the X-, K-, and Ka-receiver bands with nearly continuous coverage from 8.0 to 11.6 GHz and 18.0 to 33.5 GHz (25.6 GHz of total bandwidth). All spectra have 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, with the rms gradually increasing toward higher frequency because of the lower integration times. Data reduction involved removal of radiofrequency 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 in to our statistical analysis described below (McGuire et al. 2020).

3.1. Molecular Spectroscopy

All the MPs and MCPs are prolate symmetric top molecules with C_3v symmetry, meaning their rotational energy states are defined by the total angular momentum state J in addition to its projection along the unique axis of rotation, denoted by the quantum number K. Depending on the values of J and K, symmetric top molecules will either exhibit A or E symmetry due to the nuclear spin on the methyl group; and since radiative and collisional transitions between these symmetry states are strictly limited, their relative populations can be far from the expected thermal distribution. Because of this, we treat transitions from nondegenerate (A₁, A₂ symmetry) and doubly degenerate (E) levels separately by running independent MCMC fits. As such, we can compare the relative abundances of carbon chains in these energy states, similar to the separate treatment of the K = 0 and K = 1 components employed by Snyder et al. (2006) and Remijan et al. (2006).

For molecules with C_3v symmetry, the total statistical weight of the rotational energy levels is the product of the typical J degeneracy g_J = 2J + 1, the K-level degeneracy (g_k = 1 for K = 0 and g_k = 2 for K ≠ 0), and the nuclear spin degeneracy g_I (Gordy & Cook 1984). The reduced statistical weight contributed by the nuclear spin statistics of three identical hydrogen nuclei in a methyl group (each with spin I = 1/2) can be computed with the following:

After combining all degeneracies, the states with A symmetry are weighted 2:1 relative to those with E symmetry, except in the case of K = 0, which is weighted equally because of the lower factor of g_k . The rotational constants for the largest MCPs and MPs were measured by Chen et al. (1998) and Travers et al. (1998). To generate the spectroscopic data used for this work from these measurements, we used PGopher (Western 2017; Western & Billinghurst 2019), which is able to account for the necessary symmetry and statistical considerations. The input files and line lists for all six species are available on the Harvard DataVerse 10.7910/DVN/K9HRCK.

As an example, Table 1 summarizes the spectroscopic properties of the rotational transitions of CH₃C₇N in the X-band that were a part of this investigation. The transition quantum numbers, calculated rest frequencies (MHz), upper-state energy level (K), and transition line strengths S(J, K) are presented. In the case of the MCPs, the nuclear spin on the nitrogen nucleus contributes hyperfine splitting to each rotational energy level.

Table 1. Spectroscopic Properties of Stacked CH₃C₇N Lines Covered by the GBT X-band Receiver

Transitions			Symm.	Frequency	Eup	Sij μ2
	K			(MHz)	(K)	(D2)
11 → 10	1	10 → 9	E	8243.824	9.92	355.325
		11 → 10	E	8243.824	9.92	389.482
		12 → 11	E	8243.836	9.92	426.877
	0	10 → 9	A	8243.851	2.37	358.286
		11 → 10	A	8243.859	2.37	392.727
		12 → 11	A	8243.865	2.37	430.435
12 → 11	1	11 → 10	E	8993.262	10.35	391.696
		12 → 11	E	8993.263	10.35	426.021
		13 → 12	E	8993.272	10.35	463.320
	0	11 → 10	A	8993.293	2.81	394.435
		12 → 11	A	8993.299	2.81	429.000
		13 → 12	A	8993.304	2.81	466.560
13 → 12	1	12 → 11	E	9742.699	10.82	428.012
		13 → 12	E	9742.700	10.82	462.478
		14 → 13	E	9742.708	10.82	499.692
	0	12 → 11	A	9742.733	3.27	430.560
		13 → 12	A	9742.739	3.27	465.231
		14 → 13	A	9742.743	3.27	502.666
14 → 13	1	13 → 12	E	10492.136	11.33	464.286
		14 → 13	E	10492.137	11.33	498.870
		15 → 14	E	10492.144	11.33	536.010
	0	13 → 12	A	10492.173	3.78	466.667
		14 → 13	A	10492.178	3.78	501.429
		15 → 14	A	10492.181	3.78	538.758
15 → 14	1	14 → 13	E	11241.572	11.86	500.524
		15 → 14	E	11241.573	11.86	535.211
		16 → 15	E	11241.579	11.86	572.284
	0	14 → 13	A	11241.612	4.32	502.759
		15 → 14	A	11241.616	4.32	537.600
		16 → 15	A	11241.619	4.32	574.839

Note. Only K = 0 and K = 1 are included here since they contribute the brightest transitions; however, we still considered states as high as K = 13 in our MCMC model and stacking procedure. Similarly, lines ranging from to are covered by the GBT K- and Ka-bands and included in our analysis, but not shown here. For the full list of transitions used for CH₃C₇N and all other methyl carbon chains treated in this work, please refer to the linked Dataverse repository: 10.7910/DVN/K9HRCK.

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Methyl acetylene (CH₃CCH) was not included in our analysis as it does not have any transitions covered by the GOTHAM survey. Similarly, although the fundamental transition of methyl cyanide (CH₃CN) is included in our spectra, a lack of additional lines prevents us from performing a full characterization of this molecule. For both CH₃CN and CH₃CCH, we refer to previous works studying these molecules in TMC-1 (e.g., Askne et al. 1984; Minh et al. 1993), and instead base our analysis on the longer species.

3.2. MCMC Modeling

3.3. Spectral Line Stacking and Matched Filter

4.1. Column Densities and Physical Characteristics

Figure 1 shows the stacked data, the stacked MCMC model, as well as the matched-filter response of all the methyl carbon chains considered in this work. We clearly detect CH₃C₃N, CH₃C₅N, CH₃C₄H, and CH₃C₆H at high significance, and the model is able to fit all components (both velocity and hyperfine) of these molecules. In the case of CH₃C₇N, though no individual lines are present above the current noise level of the survey, the stacked emission in the top-right of Figure 1 exhibits a noteworthy signal. Furthermore, its matched filter has a central peak at 4.6σ, indicating evidence that this molecule is present in our data, and that the MCMC model converged to a set of parameters that reproduce its emission. The matched-filter response is weaker than previous molecules that were found using this same method (Lee et al. 2021; Loomis et al. 2021; McGuire et al. 2021) and falls just below our desired 5.0σ threshold for a definitive discovery, but it is sufficient to consider a tentative detection and adopt the parameters of its fit in our analysis. For more information on this detection as it is indicated in the Bayesian fit to the spectra (prior to any stacking of emission lines), in Appendix A we present corner plots illustrating the full results of the MCMC model for both CH₃C₇N and CH₃C₈H, and discuss the posterior distributions and covariances in the parameter spaces for each. In contrast to CH₃C₇N, CH₃C₈H shows a much higher degree of uncertainty in its fit, in addition to no signal in the stack nor its matched-filter response (bottom-right panels of Figure 1), so we therefore place upper limits on its column density.

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A summary of parameters derived from the posterior distributions is provided in Table 2. Here, we note that the excitation temperatures of the MPs (4.3–7.2 K) are systematically higher than those of the MCPs (3.4–3.9 K), which is in agreement with previous studies of these species in TMC-1 (Askne et al. 1984; Broten et al. 1984; Snyder et al. 2006). However, one exception to this is seen for the E state of CH₃C₃N, which has T_ex ∼ 5.7 K. At all derived excitation temperatures, we find that less than 4% of the total integrated line flux is contributed by transitions with K > 1. Furthermore, the population of the K = 2 state at these low temperatures is less than 1% for all detected chains, which is well within the uncertainty of our measured column densities. In that sense, although states up to K = 13 were considered, the column densities of the A and E components reported in Table 2 can be treated as equivalent to the column densities of the K = 0 and K = 1 components, respectively.

Table 2. MCMC Model Results for All Observed CH₃-terminated Carbon Chains

Molecule	NT	NA	NE	Tex (A sym.)	Tex (E sym.)	Source Size	A/E Ratio
⋯	(1011 cm−2)	(1011 cm−2)	(1011 cm−2)	(K)	(K)	''	⋯
CH3C3N	8.66 (.46)	5.00 (.40)	3.66 (.24)	3.36 (.40)	5.70 (.26)	481.0 (8.7) a	1.37 (.15)
CH3C5N	2.86 (.30)	2.01 (.29)	0.85 (.07)	3.48 (.34)	3.97 (.48)	128.7 (4.9) b	2.40 (.40)
CH3C7N	0.86 (.19)	0.69 (.18)	0.17 (.06)	3.82 (.25)	3.90 (.44)	53.9 (1.0) c	4.20 (1.8)
CH3C4H	100.8 (5.7)	60.0 (5.0)	40.8 (2.8)	4.31 (.84)	5.50 (.37)	481.0 (8.6) a	1.46 (.15)
CH3C6H	10.4 (.72)	6.10 (.60)	4.30 (.40)	7.19 (1.2)	6.41 (1.1)	128.3 (4.8) b	1.41 (.20)
CH3C8H	<0.98	<0.8	<0.18	⋯	⋯	⋯	⋯

Notes. Uncertainties are listed as the 95% confidence level.

^a HC₃N source size adopted as prior. See Loomis et al. (2021) for more details. ^b HC₅N source size adopted as prior. ^c HC₇N source size adopted as prior.

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The total column densities (combining both A and E symmetries, leftmost column of Table 2) decrease with increasing carbon chain length, much like the similar linear cyanopolyynes (Loomis et al. 2021). This is shown pictorially in Figure 2, with a comparison to the column densities found by Remijan et al. (2006). There is small but notable disagreement (less than a factor of four) between the column densities we find and those derived in Remijan et al. (2006). We attribute this discrepancy to the intrinsic line strengths (S_ij ) adopted from our numerical treatment of these molecules (see Section 3.1) as they are factors of two to three larger than the analytic values employed in Remijan et al. (2006) and Snyder et al. (2006). Another important factor is that the column densities we derive take in to account decreasing source sizes, whereas previous studies of TMC-1 assume no effects due to beam dilution.

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CH₃C₇N has a total best-fit column density of 8.60 ± 1.9 × 10¹⁰ cm⁻², which matches well with the log-linear slope set by CH₃C₃N and CH₃C₅N (Figure 2). Furthermore, this slope is very similar to that observed for the cyanopolyynes, and would imply the next chain (CH₃C₉N) to have a column density of about 3 × 10¹⁰ cm⁻². To detect stacked emission from this molecule at such an abundance, the rms noise of the survey would need to be reduced by at least a factor of five. This would require several hundred more hours of integration time, primarily at lower frequencies (e.g., the GBT X-band receiver) because the brightest transitions of this molecule are simulated to be present in the 8–10 GHz range.

In contrast to the cyanopolyynes and MCPs, the MPs decrease in abundance at a much faster rate than the other carbon chains in TMC-1 (about 1 dex for each subsequent species). Furthermore, the upper limit we place on CH₃C₈H appears to break the trend seen in the shorter MPs. A linear extrapolation on the column densities of CH₃C₄H and CH₃C₆H (the blue points in Figure 2) would imply the next chain length has a column density ∼2 × 10¹¹ cm⁻², but in this case we would have detected emission from CH₃C₈H at the sensitivity of our survey. Instead, it appears that the MPs experience a sharp drop-off in column density after CH₃C₆H, which indicates that the production of these carbon chains is severely hindered for these longer species.

A comparison to analogous linear species in TMC-1 is more difficult for the MPs, because the acetylene chains H₂C_2n have no dipole moment, and thus no rotational transition lines with which we could apply a similar analysis. However, the hydrocarbon radicals (C_2n H) do exhibit transitions in the radio/sub-mm range and have been characterized in TMC-1 up to a chain length of eight by Brünken et al. (2007) (green points in Figure 2). Here, it is apparent that those species also exhibit a nonlinear decrease in column density after a chain length of six carbon atoms. In other words, a similar ratio of to what is observed for would be in agreement with the upper limits we set in this work. This may suggest that similar chemical routes govern the abundances of both the MPs and the hydrocarbon radicals. However, since our upper limit on CH₃C₈H is still very close to the log-linear extrapolated column density, it will be imperative to continue studying this molecule with future, more sensitive data releases from the GOTHAM survey to identify how steep this drop-off is, and how similar it is to the relative column density of C₈H.

4.2.  A/E Symmetry State Populations

Askne et al. (1984) found that in TMC-1 methyl acetylene (CH₃CCH) has about equal abundances of A and E symmetry states, which is not expected under LTE conditions and could indicate this molecule formed at a higher temperature. A similar result was found for CH₃C₄H by Walmsley et al. (1984). In contrast, Minh et al. (1993) found that for CH₃CN in TMC-1, N_E /N_A = 0.76 ± 0.09, which suggests that these states are equilibrated to the kinetic temperature. With the sensitivity and bandwidth of GOTHAM DR2, we are able to revisit some of these population studies with a larger data set and expand them to the longer molecules CH₃C₆H, CH₃C₃N, CH₃C₅N, and CH₃C₇N. Because we performed separate MCMC analyses for the A and E states of each symmetric top carbon chain, their ratios can be computed directly and are shown in the last column of Table 2.

Figure 3 shows a comparison of all A/E ratios derived in this work plotted alongside the expected ratio in a thermalized distribution for a range of excitation temperatures. The gas-phase kinetic temperature at the CP of TMC-1 has recently been placed at 11 ± 1.0 K by Fehér et al. (2016), so methyl chains with A/E ≈ 1.75 can be considered as having equilibrated to this temperature.

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For the MCPs (left plot in Figure 3), we note that the A/E ratio increases for longer chain lengths, starting at a superthermal value of 1.33 for CH₃CN (as measured by Minh et al. 1993) and reaching 4.2 ± 1.8 for CH₃C₇N, which corresponds to an excitation temperature of 6.1 ± 2 K, much lower than the kinetic temperature in TMC-1. In contrast, the MPs (right plot in Figure 3) have nearly constant A/E ratios between 1.4 and 1.5. While this is only slightly smaller than the equilibrium value of 1.75, it is indicative that all MPs studied here have slightly larger E symmetry populations than what is expected given the physical conditions in TMC-1.

As noted in Section 3.1, both radiative and collisional interconversion between the A and E symmetry states are forbidden for both the MCPs and MPs (unless proton-exchange collisions are nonnegligible). Willacy et al. (1993) investigated the possibility that E → A conversion of CH₃CN occurs through E-state species adsorbing to and subsequently desorbing from grain surfaces in TMC-1. They found that this is an efficient process so long as the desorption rate is high enough. This may suggest that an important distinction may be happening in TMC-1. Highly exothermic reactions in the gas phase (e.g., dissociative recombination) may drive the formation of the MPs, forcing them into superthermal A/E distributions, whereas the largest MCPs may preferentially form on (or stick to) the surfaces of dust grains. The nonthermal desorption of large complex molecules like the MCPs in TMC-1 has been a topic of numerous recent computation efforts (Herbst & Cuppen 2006; Garrod et al. 2007; Minissale et al. 2016; Hoang & Tung 2019; Shingledecker et al. 2021), but it is still difficult to say exactly how efficient this process is for the species explored here. The investigation of the potential bifurcation of the formation pathways between the MPs and the MCPs using astrochemical models might shed further light on this intriguing situation.

To further explore the chemistry of methyl-terminated carbon chains in TMC-1, we utilized the adapted three-phase gas–grain chemical network model nautilus v1.1 code (Ruaud et al. 2016) discussed in previous analysis of GOTHAM data, which has previously been used to successfully study the formation of carbon chain molecules (McGuire et al. 2020; Xue et al. 2020; Shingledecker et al. 2021). The physical conditions of the model are equal to what has been previously used with this network (T_gas = T_grain = 10 K, 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 (KIDA) network, the network already contained the formation of MCPs up to n = 7 and MPs up to n = 6. Here, we expanded on this to include the formation of CH₃C₈H, as well as additional reaction to better constrain the formation of the smaller members of this family.

To simulate the formation and destruction of CH₃C₈H, we utilized the analogous pathways for the existing network of CH₃C₆H, whose primary formation routes are from the dissociate recombination of . As such, we expanded out the formation of from ion-neutral reactions with semi-saturated carbon chains, whose rates were estimated using the Langevin formula (Woon & Herbst 2009). It should be noted that the rates for and CH₃C₆H are calculated using the modified Arrhenius formula, which may result in some potential discrepancies between this and CH₃C₈H. As a source of destruction of , we adapted existing dissociate recombination of similar cations. The rates and branching ratios and were estimated and updated, respectively, based on the dissociate recombination of , whose rates are taken from Herbst & Leung (1989) and branching ratios are discussed in detail on the KIDA website. ⁶ In addition to dissociative recombination, C_n ions present in KIDA were also destroyed by reactions with anions. As such, the rates of the anion destruction of were based off analogous rates estimated for by Harada & Herbst (2008). Due to a lack of robust isomerization for large molecules within existing chemical networks, we only consider the and isomers with KIDA entries (i.e., ).

The analogous destruction of CH₃C₆H was also adapted for CH₃C₈H. This included (1) dissociation due to photons and cosmic rays, (2) ion-neutral reactions with abundant ions (i.e., H⁺, , C⁺, HCO⁺, and He⁺), which were estimated with Langevin formula, and (3) reaction with elemental carbon to form C₁₀H₂ and H₂. To properly study , we also added in several neutral-neutral reactions to better account for the formation of C₅H₃, a precursor, which were obtained originally from Hébrard et al. (2009). Finally, we included an additional formation pathway for the MPs by reactions of the C_2n H family with methane based on work by Quan & Herbst (2007) and formation of CH₃C₄H from CH₃CHCH₂ by Berteloite et al. (2010).

For the MCPs, no additional reactions or rates were added from the KIDA network beyond the related adaptations from other recent molecular detections, e.g., the expanded semi-saturated carbon chain networks for HC₄NC (Xue et al. 2020), C₆H₅CN (Burkhardt et al. 2021a), H₂CCCHC₃N (Shingledecker et al. 2021), and indene (Burkhardt et al. 2021b).

The results of this model can be seen in Figure 4 at a time of 2.5 × 10⁵ yr, assuming a TMC-1 hydrogen column density of cm⁻². At this time in the model, the simulated abundances of all studied species are within an order of magnitude of their observed values. For the MCPs (solid red line in Figure 4), the abundance of CH₃C₃N is higher than the observed value, while the remainder of the family are somewhat below their observed value. As such, the log-linear trend is less well constrained here. The relative trend line was also fairly independent of time, with a slight increase of the longer chains at later times, as seen in Figure A3. This is expected, as longer chains typically have their peak abundance several 10⁵ yr after similar smaller chains, as seen by the cyanopolyynes (Loomis et al. 2021). The dominant formation pathways for the MCPs are the dissociative recombination of the C_n+1H₄N⁺ ion family, which are in turn primarily produced by reactions between the cyanopolyynes and , with minor contributions from C_n+1H₃N⁺ and N + C_n+1 after several 10⁵ yr. In particular, CH₃C₃N has an additional production from H₃C₄N⁺ + H₂ that may account for its deviation from the trend line of the rest of the MCP family. The MCPs are primarily destroyed by ion-neutral reactions with abundant ions (i.e., H⁺, , C⁺, HCO⁺, and He⁺). The dependence on the cyanopolyynes (solid pink line in Figure 4) is consistent with the similar observed abundance trends seen in Figure 2.

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For the MPs (solid blue line in Figure 4), the relative abundance trends of both the simulated and observed values are in good agreement at this time. This slope of this trend is also very consistent with the simulated abundance trend of the C_n H family (solid green line in Figure 4). Within the general uncertainties of the source age of TMC-1 (∼2–5 × 10⁵ yr), the abundance of CH₃C₄H was found to be consistently in worst agreement with the observed values but improving at later times by a ∼60% abundance increase, while the longer chains increased up to nearly an order of magnitude (see Figure A3). As a result, the trend line was less consistently in agreement with the observed trend at later times, while reproducing the observed abundances better. Due to the overall depletion of CH₃C₄H, we have chosen this as a representative time as the simulated abundances are still within typical uncertainties for kinetic chemical models, and we suspect the trend at this model time would remain consistent if a more efficient production is found either through new proposed pathways or improved reaction rate measurement/calculations. More generally, this strong dependence on the source age contrasts with other carbon chain families such as the cyanopolyynes and MCPs, whose observed trends are fairly consistent across the possible source ages of TMC-1.

The dominant formation route for the MPs is from the dissociative recombination of the C_n+1 family, with a significant contribution from C_n H reactions with methane after ∼10⁵ yr. The C_n+1 family are produced by various ion-neutral reactions, notably C_n with methane and C_n+1 H₂ with (<10⁵ yr). These dominant pathways provide strength for the observed relation between the MPs and C_n H families. There is also an increased importance after 10⁵ yr of + methane for CH₃C₄H and C₃H₃ + C₄H₂ for CH₃C₆H. MPs are mostly destroyed by ion-neutral reactions and reactions with carbon atoms.

Overall, the predictions of these chemical models are within an order of magnitude of agreement with the observed values of TMC-1, indicating that carbon chain chemistry can be fairly well understood. In addition, the observed MP trend line can be reproduced well and is also analogous to what is observed for C_n H. The estimated branching ratios and reaction rates still remain a major source of uncertainties in the models, which provide a strong motivation for further laboratory and theoretical studies. As discussed in Burkhardt et al. (2021b), detailed study of increasingly larger molecules (e.g., molecules with 7+ heavy atoms and/or aromatic rings) will likely require a rigorous study of the formation of semi-saturated carbon chains that have historically been performed piecewise. The recent expanded inventory of known carbon chains in TMC-1 will provide key constraints in this study.

We performed a rigorous, self-consistent study of MPs and MCPs in TMC-1 using the second data release of the GOTHAM survey. Through MCMC modeling and matched-filter analysis of stacked-emission lines, we derived column densities, excitation temperatures, and A/E symmetry ratios for all previously found species, and discovered evidence for a new interstellar symmetric top, methylcyanotriacetylene (CH₃C₇N), at a confidence level of 4.6σ. We also searched for methyltetraacetylene (CH₃C₈H) in our spectra and place upper limits on its column density in TMC-1.

In our analysis, we found two important divisions between the different families of molecules explored in this work:

• 1.  
  The column densities of MCPs decrease in a log-linear manner with increasing carbon chain length, and the slope of this trend is similar to the cyanopolyynes. In contrast, the MPs experience a drop-off in column density for species larger than CH₃C₆H that is not consistent with the trend set by the smaller species.
• 2.  
  The A/E ratios of MCPs increase with carbon chain length, and are subthermal for the larger species. The detected MPs have systematically smaller A/E ratios that are not equilibrated to the kinetic temperature in TMC-1.

Given the structural similarity of the two classes of molecules, these dichotomies are striking and point to separate formation and carbon chain growth mechanisms in TMC-1. Whether these differences exist between the analogous cyanopolyynes (HC_2n+1N) and the pure hydrocarbon polyynes (H₂C_2n ) is unclear, as the latter have no dipole moment. To understand this, future infrared observations of vibrational bands from these molecules toward TMC-1 would be instrumental in constraining their abundances and understanding their formation chemistry.

Finally, utilizing a gas–grain chemical network, we modeled the formation and destruction of CH₃-terminated carbon chains in TMC-1. The model is able to reproduce our observed column densities to within an order of magnitude, and we see very similar trends in the exponentially decreasing abundances with carbon chain length. However, we are not able to predict the observed drop-off in column density for CH₃C₈H or C₈H using this model.

The results of this analysis offer important insights in to the formation of carbon chain molecules in cold, pre-stellar conditions, but it is important to note that many other families of unsaturated carbon chain species are known to form in TMC-1 (e.g., C_n O, C_n S, HC_n O). Similar in-depth analyses of these groups of molecules would be instrumental in improving our understanding of the extent and efficiency of carbon chemistry in TMC-1.

Figures A1 and A2 show the MCMC posterior distributions for CH₃C₇N and CH₃C₈H, respectively. Based on the off-diagonal heatmaps, we see that the majority of modeling parameters do not demonstrate significant covariance; those that do typically pertain to radial velocities and column densities of each velocity component, often those adjacent to one another in velocity and within the same symmetry group (i.e., the E-state column densities in neighboring velocity components). We do not expect significant covariance between the A/E states for both species, as they are by and large spectroscopically separate.

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Regarding the treatment of source sizes, we observe quite different posteriors in comparison to the earlier work done by Loomis et al. (2021), which highlighted significant covariance between source sizes and column densities. We do not observe this for CH₃C₇N, most likely due to an overly constrained prior placed on the source size, and we likely underestimate its uncertainty and covariance. In the case of CH₃C₈H, we fixed the mean value of HC₇N (Loomis et al. 2021), as we were interested in estimating upper limits to the column densities, and thus source sizes are not shown in Figure A2.

Comparison of the posterior distributions for the column densities between CH₃C₇N and CH₃C₈H provides a margin for detection and nondetection cases. In the former, the matched filter response in Figure 1 indicates a 4.6σ likelihood for CH₃C₇N, corroborating with smaller uncertainties in the column densities in comparison to CH₃C₈H, particularly for the first velocity component. We interpret this as a smaller range of column density values provide evidential support for the tentative detection of CH₃C₇N: even with the absence of individual lines, the likelihood-based sampling is able to place relatively large constraints on the possible values.

Figure B1 shows the time dependence of the simulated abundances within the nautilus chemical models in relation to the observed values. As 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.

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