IMPLICATION OF FORMATION MECHANISMS OF HC₅N IN TMC-1 AS STUDIED BY ¹³C ISOTOPIC FRACTIONATION

The spectra of the five ¹³C isotopologues of HC₅N were taken with signal-to-noise ratios of 12−20, as shown in Figure 1. We also obtained high quality data for the normal species. Since the spectra show a symmetric single peak structure, we fitted the spectra with a Gaussian profile and obtained the spectral line parameters, as summarized in Table 1. The line widths (${\rm{\Delta }}v$ [km s⁻¹]) in the 23 GHz region (∼0.8 km s⁻¹) are broader than those in the 42 GHz region (∼0.5 km s⁻¹). Although the origin of their difference is unclear, the following possibility can be considered. It is well known that the TMC-1 CP region has a complex velocity structure (Langer et al. 1995; Dickens et al. 2001). Since the telescope beam samples a wider area at 23 GHz than at 42 GHz, the line width could be larger at 23 GHz. However, this difference does not affect our discussion on the relative abundance ratios among the five ¹³C isotopologues seriously, and hence, we do not discuss the line width further. The values of V${}_{\mathrm{LSR}}$ are consistent with one another, and are in good agreement with the V${}_{\mathrm{LSR}}$ value reported for this source (5.85 km s⁻¹, Kaifu et al. 2004).

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The ratio of the integrated intensities ($\int {T}_{{\rm{A}}}^{*}{dv}$ [K km s⁻¹]) of the five ¹³C isotopologues is derived to be 1.00:0.95:0.97:1.01:1.16 (±0.16) (1σ) and 1.00:1.01:1.12:1.13:1.17 (±0.19) (1σ) for [H¹³CCCCCN]:[HC¹³CCCCN]:[HCC¹³CCCN]:[HCCC¹³CCN]:[HCCCC¹³CN] for the J = 9 − 8 and J = 16 − 15 lines, respectively. Although HCCCC¹³CN is slightly brighter than the other species, there are no significant differences in intensities among the five ${}^{13}{\rm{C}}$ isotopologues. The result contrasts with that for HC₃N, which shows clear differences in intensities of the three ¹³C isotopologues (Takano et al. 1998).

The rotational population of ${\mathrm{HC}}_{5}{\rm{N}}$ is not completely thermalized to the gas kinetic temperature, because the H₂ density of TMC-1 CP ($4\times {10}^{4}$ cm⁻³ (Hirahara et al. 1992)) is equal to or lower than the critical densities of the HC₅N lines. However, Takano et al. (1990) showed that the observed brightness temperatures of the HC₅N lines are well approximated by the rotation temperature of 6.5 K. Then, we calculated the column densities of the normal species and the five ¹³C isotopologues of HC₅N using the local thermodynamic equilibrium (LTE) as shown in the following formulae (Takano et al. 1998):

$$\begin{eqnarray}&&\tau =-\mathrm{ln}\left[1-\displaystyle \frac{{T}_{{\rm{A}}}^{*}}{f{\eta }_{{\rm{B}}}\{J({T}_{\mathrm{ex}})-J({T}_{\mathrm{bg}})\}}\right],\end{eqnarray} \tag{ 1 }$$

where

$$\begin{eqnarray}&&J(T)=\displaystyle \frac{h\nu }{k}{\left\{\mathrm{exp}\left(\displaystyle \frac{h\nu }{{kT}}\right)-1\right\}}^{-1},\end{eqnarray} \tag{ 2 }$$

and

$$\begin{eqnarray}N & = & \tau \displaystyle \frac{3h{\rm{\Delta }}v}{8{\pi }^{3}}\sqrt{\displaystyle \frac{\pi }{4\mathrm{ln}2}}Q\displaystyle \frac{1}{{\mu }^{2}}\displaystyle \frac{1}{{J}_{\mathrm{lower}}+1}\mathrm{exp}\left(\displaystyle \frac{{E}_{\mathrm{lower}}}{{{kT}}_{\mathrm{ex}}}\right)\\ & & \times {\left\{1-\mathrm{exp}\left(-\displaystyle \frac{h\nu }{{{kT}}_{\mathrm{ex}}}\right)\right\}}^{-1}.\end{eqnarray} \tag{ 3 }$$

In Equation (1), ${T}_{{\rm{A}}}^{*}$ denotes the antenna temperature, f the beam filling factor, ${\eta }_{{\rm{B}}}$ the main beam efficiency (see Section 2), and τ the optical depth. We used 0.8 and 1 for f in the 23 GHz and 42 GHz band data, respectively. We employed these f values, because a size of the emitting region of carbon-chain molecules in TMC-1 CP is approximately 25 according to the mapping observations by Hirahara et al. (1992). ${T}_{\mathrm{ex}}$ is the excitation temperature, ${T}_{\mathrm{bg}}$ is the cosmic microwave background temperature ($\approx 2.7$ K), and J(T) in Equation (2) is the Planck function. We derived ${T}_{\mathrm{ex}}$ and τ simultaneously from the observed intensities of the 23 and 42 GHz lines by using formula (1). In Equation (3), N is the column density, ${\rm{\Delta }}v$ is the line width (FWHM), Q is the partition function, μ is the permanent electric dipole moment of HC₅N ($4.33\times {10}^{-18}$ [esu cm] (Alexander et al. 1976)), and ${E}_{\mathrm{lower}}$ is the energy of the lower rotational energy level. In the energy level calculations, we used the rotational constants of the normal species and the ¹³C isotopologues (Alexander et al. 1976; Sanz et al. 2005).

The calculated column densities and the ¹²C/¹³C ratios are summarized in Table 2. For the normal species, the excitation temperature and the column density are determined to be 6.5 ± 0.2 K and (6.2 ± 0.3) × 10¹³ cm⁻², respectively, where the errors are estimated from the Gaussian fits and represent the confidence level of one standard deviation. The optical depths for the J = 9 − 8 and 16 − 15 lines are 1.084 ± 0.014 and 1.19 ± 0.03 (1σ), respectively. The obtained excitation temperature and column density of the normal species are consistent with the previous result (6.5 ± 0.2 K and (6.3 ± 0.6) × 10¹³ cm⁻²) (Takano et al. 1990) within the error ranges.

Table 2.  Column Densities and ¹²C/¹³C Ratios of HC₅N

Species	Column Densitya	12C/13Ca	Column Densityb	12C/13Cb
⋯	(×1011 cm−2)	Ratio	(×1011 cm−2)	Ratio
HC5N	(6.2 ± 0.3) $\times {10}^{2}$	⋯	⋯	⋯
H13CCCCCN	6.4 ± 0.9	98 ± 14	7.0 ± 1.0	89 ± 13
HC13CCCCN	6.2 ± 0.8	101 ± 14	6.8 ± 0.9	91 ± 12
HCC13CCCN	6.6 ± 0.8	95 ± 12	6.8 ± 0.9	91 ± 12
HCCC13CCN	6.7 ± 0.9	93 ± 13	6.9 ± 1.0	90 ± 13
HCCCC13CN	7.4 ± 0.9	85 ± 11	7.5 ± 1.0	83 ± 11

Notes. The error corresponds to one standard deviation.

^aThe values of ¹³C isotopologues were calculated by using ${T}_{\mathrm{ex}}=6.5$ K obtained from the normal species. ^bThe values were calculated by using the ${T}_{\mathrm{ex}}$ derived for each isotopologue.

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We calculated the column densities of the five ¹³C isotopologues using Equation (3) and the excitation temperature derived for the normal species (6.5 K). The calculated column densities of the normal species and the five ¹³C isotopologues, and the ¹²C/¹³C ratios are summarized in Table 2. For the five ¹³C isotopologues, the column densities were derived to be (6.4 ± 0.9) × 10¹¹, (6.2 ± 0.8) × 10¹¹, (6.6 ± 0.8) × 10¹¹, (6.7 ± 0.9) × 10¹¹, and (7.4 ± 0.9) ×10¹¹ cm⁻², for H¹³CCCCCN, HC¹³CCCCN, HCC¹³CCCN, HCCC¹³CCN, and HCCCC¹³CN, respectively. The abundance ratio of the ¹³C isotopologues of HC₅N is then 1.00:0.97:1.03:1.05:1.16 (±0.19) (1σ) for [H¹³CCCCCN]:[HC¹³CCCCN]:[HCC¹³CCCN]:[HCCC¹³CCN]:[HCCCC¹³CN]. This result agrees with those obtained from integrated intensities. The averaged ¹²C/¹³C ratio of HC₅N is 94 ± 6 (1σ), which is slightly higher than the elemental ratio of 60−70 in the local interstellar medium (e.g., Langer & Penzias 1990, 1993; Savage et al. 2002; Milam et al. 2005). The intensities are also affected by the calibration errors (main beam efficiency and filling factor). However, we obtained the data of the normal species and the five ¹³C isotopologues simultaneously. Then, these calibration errors do not affect the ¹²C/¹³C ratios. We discuss these ratios in Section 4.2.

We investigated the sensitivities of the assumed ${T}_{{\rm{ex}}}$ values on the column densities and the ¹²C/¹³C ratios. We calculated the column densities of the normal species and the five ¹³C isotopologues using ${T}_{\mathrm{ex}}$ of 5.9 and 7.1 K, which are the lowest and highest values in the 3σ error range of the excitation temperature. We derived the column densities of the normal species to be (7.0 ± 0.5) × 10¹³ cm⁻² and (4.7 ± 0.2) ×10¹³ cm⁻² for 5.9 K and 7.1 K, respectively. The column densities of the ¹³C isotopologues were not significantly affected by the change of the excitation temperature. The ¹²C/¹³C ratios averaged for the five isotopologues are 125 ± 6 (1σ) and 89 ± 5 (1σ) for 5.9 K and 7.1 K, respectively. Although the ¹²C/¹³C ratios slightly depend on the excitation temperature, the ¹²C/¹³C ratio of HC₅N is still higher than that of the elemental ratio in the local interstellar medium.

We also evaluated the ratio by using the excitation temperature derived for each ¹³C isotopologue. We derived ${T}_{\mathrm{ex}}$ to be 6.2 ± 0.6, 6.2 ± 0.6, 6.3 ± 0.5, 6.3 ± 0.6, and 6.3 ± 0.5 K (1σ) for H¹³CCCCCN, HC¹³CCCCN, HCC¹³CCCN, HCCC¹³CCN, and HCCCC¹³CN, respectively, from the intensities of the observed two rotational transitions. These results are consistent with the value obtained from the normal species (6.5 K) within the errors, which implies that we can neglect the effect of self-trapping for the normal species. We then calculated the column densities using ${T}_{\mathrm{ex}}$ obtained for each ¹³C isotopologue. The ¹³C isotopic fractionation is not affected by the changes in ${T}_{\mathrm{ex}}$, and the ¹²C/¹³C ratios are also not affected within the errors. The results are also shown in Table 2.

We here consider possible reactions leading to cyanopolyynes, using the UMIST Database for Astrochemistry 2012 (McElroy et al. 2013). By focusing on the rate constants, activation energies, abundances, and formation pathways of precursors, we can sketch formation pathways of cyanopolyynes, as shown in Figure 2. Three types of formation pathways are possible as follows.

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Pathway 1: the reactions of ${{\rm{C}}}_{2n}$ H₂ + CN,

Pathway 2: the growth of the cyanopolyyne carbon chains via ${{\rm{C}}}_{2}{{\rm{H}}}_{2}^{+}+{\mathrm{HC}}_{2n+1}$ N, and

Pathway 3: the reactions between hydrocarbon ions and nitrogen atoms followed by electron recombination reactions.

For HC₃N, Pathway 1 is suggested to play a dominant role in its production: Takano et al. (1998) reported that the main formation pathway of HC₃N is the reaction of C₂H₂ + CN on the basis of their observational results of ¹³C isotopic fractionation. Fractionation of ¹³C in CN proceeds through the following reaction (Kaiser et al. 1991):

$$\begin{eqnarray}&&{}^{13}{{\rm{C}}}^{+}+\mathrm{CN}\to {{\rm{C}}}^{+}+{}^{13}\mathrm{CN}+{\rm{\Delta }}E\ (34\ {\rm{K}}).\end{eqnarray} \tag{ 4 }$$

This reaction is exothermic with an energy of 34 K due to decreasing the zero-point vibrational energy. Hence, its backward reaction is not effective in cold dark clouds, where the typical temperature is approximately 10 K (e.g., Benson & Myers 1989). As a result, the ¹²C/¹³C ratio for CN decreases in comparison with those for hydrocarbons such as C₂H₂ and C₄H₂, because similar fractionation processes of ¹³C do not occur in hydrocarbons (Watson et al. 1976).

If HC₅N is mainly formed by Pathways 1 and/or 2, at least one carbon atom in HC₅N, possibly that adjacent to the nitrogen atom, is not equivalent to the others. Assuming that HC₅N is mainly formed by Pathway 2, the ¹³C isotopic fractionation of HC₅N should be x:y:1.0:1.0:1.4, where x and y are arbitrary values, for [H¹³CCCCCN]:[HC¹³CCCCN]:[HCC¹³CCCN]:[HCCC¹³CCN]:[HCCCC¹³CN], unless scrambling of the carbon atoms is efficient. However, our observed abundances are roughly equal for all the ¹³C isotopologues. It is not likely that Pathway 1 and 2 are the main formation pathways of HC₅N.

On the basis of the above consideration, we propose that Pathway 3 should significantly contribute to the formation of HC₅N. In Pathway 3, all carbon atoms in ${\mathrm{HC}}_{5}{\rm{N}}$ originate from the hydrocarbon ions. If all the carbon atoms in the mother hydrocarbon ion have the similar ¹²C/¹³C ratio, the observational result can be explained. This seems indeed possible for a large hydrocarbon ion, because it is generally produced through various processes. This pathway is similar to the chemical model calculation by Markwick et al. (2000), where HC₅N can be produced through the reaction between a hydrocarbon ion (C₅${{\rm{H}}}_{3}^{+}$) and a nitrogen atom. Thus, we propose that Pathway 3 overwhelms Pathways 1 and 2, resulting in almost equivalent abundances of the ¹³C isotopologues of HC₅N.

Based on the above discussion on HC₅N, we also propose that the longer cyanopolyynes may be formed by a mechanism similar to that of ${\mathrm{HC}}_{5}{\rm{N}}$, namely the reactions between hydrocarbon ions and nitrogen atoms. However, it is difficult to confirm our suggestion by observations of ¹³C isotopic fractionation at the present. Langston & Turner (2007) tentatively detected the ¹³C isotopologues of HC₇N using the J = 11 − 10 and 12 − 11 transitions for the first time in the interstellar medium. They calculated the averaged ¹²C/¹³C ratio of HC₇N, but they could not study its ¹³C isotopic fractionation as they only derived upper limits for each of the seven ${}^{13}{\rm{C}}$ isotopologues. Hence, more sensitive observations are needed to confirm the flat ¹³C abundance over the seven ¹³C isotopologues of HC₇N. In the theoretical model by Markwick et al. (2000), the pathways leading to HC₇N and HC₉N via reactions between hydrocarbon ions (C₇${{\rm{H}}}_{3}^{+}$ and C₉${{\rm{H}}}_{3}^{+}$, respectively) and nitrogen atoms followed by the electron recombination reactions are presented. The most interesting point to emerge from our analysis is that cyanopolyynes longer than HC₅N are mainly produced by the reactions between hydrocarbon ions and nitrogen atoms, whereas HC₃N is mainly produced by the neutral–neutral reaction between C₂H₂ and CN. One possible reason is the high abundance of C₂H₂ (Markwick et al. 2000).

We compile ¹²C/¹³C ratios of some carbon-chain molecules at TMC-1 CP in Table 3. The ¹²C/¹³C ratios of carbon-chain molecules show more or less higher than that of the local interstellar elemental ratio (60–70) (e.g., Langer & Penzias 1990, 1993; Savage et al. 2002; Milam et al. 2005). This can be explained by the following reaction, which should be effective under low-temperature conditions (e.g., Watson et al. 1976; Langer et al. 1984),

$$\begin{eqnarray}&&{}^{13}{{\rm{C}}}^{+}+\mathrm{CO}\to {{\rm{C}}}^{+}+{}^{13}\mathrm{CO}+{\rm{\Delta }}E\ (35\ {\rm{K}}).\end{eqnarray} \tag{ 5 }$$

The reaction leads to a reduction in ${}^{13}{{\rm{C}}}^{+}$. Consequently, ¹³C isotopologues of carbon-chain molecules are also reduced, because ${{\rm{C}}}^{+}$ and C are important raw materials of carbon-chain molecules.

Table 3.  The ¹²C/¹³C Ratios in Various Carbon-chain Molecules toward TMC-1 CP

Species	12C/13C Ratio	References
HC3N/H13CCCN	79 ± 11 (1σ)	(1)
HC3N/HC13CCN	75 ± 10 (1σ)	(1)
HC3N/HCC13CN	55 ± 7 (1σ)	(1)
HC5N/H13CCCCCN	98 ± 14 (1σ)	(2)
HC5N/HC13CCCCN	101 ± 14 (1σ)	(2)
HC5N/HCC13CCCN	95 ± 12 (1σ)	(2)
HC5N/HCCC13CCN	93 ± 13 (1σ)	(2)
HC5N/HCCCC13CN	85 ± 11 (1σ)	(2)
HC7N/average 13C isotopologues	87 ${}_{-19}^{+35}$ (1σ)	(3)
CCH/13CCH	>250	(4)
CCH/C13CH	>170	(4)
C4H/13CCCCH	141 ± 44 (3σ)	(5)
C4H/C13CCCH	97 ± 27 (3σ)	(5)
C4H/CC13CCH	82 ± 15 (3σ)	(5)
C4H/CCC13CH	118 ± 23 (3σ)	(5)
CCS/13CCS	230 ± 130 (3σ)	(6)
CCS/C13CS	54 ± 5 (3σ)	(6)
C3S/13CCCS	>206 (3σ)	(5)
C3S/C13CCS	48 ± 15 (3σ)	(5)
C3S/CC13CS	30–206	(5)

References. (1) Takano et al. (1998), (2) This work, (3) Langston & Turner (2007), (4) Sakai et al. (2010), (5) Sakai et al. (2013), (6) Sakai et al. (2007).

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We derived the five ¹²C/¹³C ratios of HC₅N, and they are slightly higher than those of HC₃N (see Table 3). Langston & Turner (2007) were able to detect the ¹³C isotopologues only by combining the observations of all seven isotopologues of HC₇N into one spectrum. They derived the averaged ¹²C/¹³C ratio of HC₇N by the combination of multiple lines of the seven ¹³C isotopologues of HC₇N. These ratios indicate that the ¹³C species of the cyanopolyynes are less diluted than other carbon-chain molecules. For example, for HC₃N and HC₅N, the ¹²C/¹³C ratios coincide among their ¹³C isotopologues within about 20% and 10%, respectively. On the other hand, for CCS, ¹²C/¹³C of ¹³CCS is about four times larger than that of C¹³CS. In other words, an interesting characteristic of the ¹²C/¹³C ratios of the two cyanopolyynes is that their differences appear to be small among the ¹³C isotopologues of each cyanopolyyne, compared to other carbon-chain molecules. The reason why the ¹³C species of the cyanopolyynes are not significantly diluted is unclear. Mechanisms of the dilution of the ¹³C species are still controversial and are left for future studies.