$^{13}$C isotopic ratios of HC$_3$N on Titan measured with ALMA

We present the first determination of the abundance ratios of $^{13}$C substitutions of cyanoacetylene (HC$_{3}$N), [H$^{13}$CCCN]:[HC$^{13}$CCN]:[HCC$^{13}$CN] in Titan's atmosphere measured using millimeter-wave spectra obtained by the Atacama Large Millimeter-submillimeter Array. To compare the line intensities precisely, datasets which include multiple molecular lines were extracted to suppress effects of Titan's environmental conditions and observation settings. The [HC$^{13}$CCN]:[HCC$^{13}$CN] and [H$^{13}$CCCN]:[HCC$^{13}$CN}] ratios were obtained from 12 and 1 selected datasets, respectively. As a result, nearly the uniform [H$^{13}$CCCN]:[HC$^{13}$CCN]:[HCC$^{13}$CN] abundance ratios as 1.17 ($\pm$0.20) : 1.09 ($\pm$0.25) : 1 (1$\sigma$) were derived, whereas previously reported ratios for interstellar medium (ISM) have shown large anomalies that may be caused by $^{13}$C concentrations in precursors. The result obtained here suggests that $^{13}$C concentration processes suggested in the ISM studies do not work effectively on precursors of HC$_{3}$N and HC$_{3}$N itself due to Titan's high atmospheric temperature and/or depletion of both $^{13}$C and $^{13}$C$^+$.


INTRODUCTION
The 13 C substituted species of cyanoacetylene (HC 3 N), namely, H 13 CCCN, HC 13 CCN and HCC 13 CN, have been discovered in various interstellar media (ISM), and are known to exhibit large isotopic anomalies that HCC 13 CN and/or H 13 CCCN show high 13 C concentrations (Takano et al. 1998;Taniguchi et al. 2016;Araki et al. 2016;Taniguchi et al. 2017). Such anomalies are considered to be due to the 13 C concentrations on the precursors of HC 3 N such as CN and C 2 H (Furuya et al. 2011;Taniguchi et al. 2019), and give us important information on the environments and possible chemical reactions in the ISM.
HC 3 N is also present on Saturn's largest moon, Titan, and was first detected in the atmosphere by the Voyager 1 spacecraft (Kunde et al. 1981). The main production pathway of HC 3 N was expected iino@nagoya-u.jp arXiv:2108.05019v1 [astro-ph.EP] 11 Aug 2021 as follows: C 2 H 2 + CN −−→ HC 3 N + H (1) Since then, a number of in-situ, ground-and space-based observations have been performed to illustrate the spatial and time variation of HC 3 N along with other nitriles and hydrocarbons (Hidayat et al. 1997;Coustenis et al. 1998Coustenis et al. , 2003Gurwell 2004;Coustenis et al. 2007Coustenis et al. , 2010Cordiner et al. 2014;Coustenis et al. 2016Coustenis et al. , 2018Thelen et al. 2019).
Adding to Reaction 1, a following reaction of C 2 H radical with HNC (Loison et al. 2015) possibly produces a portion of HC 3 N because HNC is present in the upper stratosphere (Moreno et al. 2011;Cordiner et al. 2014).
C 2 H + HNC −−→ HC 3 N + H In turn, due to the extremely high reaction barrier, the reaction of C 2 H with HCN, an isomer of HNC, does not work effectively. Thus, Reaction 2 is the only reaction to produce HC 3 N from C 2 H radical. Two precursor radicals of HC 3 N, namely CN and C 2 H, are important for the HC 3 N production along with the reaction counterparts, C 2 H 2 and HNC. They are easily produced by the photo-dissociation HCN and C 2 H 2 molecules, and their expected abundances are ∼10 ppb at 1000 km (Lavvas et al. 2008).
As for the ISM, 13 C substitutions of HC 3 N have also been detected on Titan. The first observational result was reported by Jennings et al. (2008) using infrared spectra obtained with the Composite Infrared Spectrometer on-board Cassini spacecraft. Spectral emissions of the three isotopologues were clearly detected, whereas the HC 13 CCN and HCC 13 CN lines were blended. Using the H 13 CCCN and HC 3 N lines, the 12 C/ 13 C ratio was measured to be 79±17, which is consistent with that measured in HCN (70-120: Hidayat et al. (1997), 132±25 or 108:±20: Gurwell (2004), 89.8±2.8: Molter et al. (2016) ) and C 2 H 2 (84.8±3.2: Nixon et al. (2012)). A recent submillimeter spectroscopy using ALMA succeeded in the detection of H 13 CCCN with a high S/N ratio along with HCCC 15 N (Cordiner et al. 2018), although the 12 C/ 13 C value was not determined for HC 3 N.
In this study, we report the first observational determination of the relative 13 C carbon isotopic ratios of three isotopologues of HC 3 N, namely [H 13

Data selection
Since Titan is often used as a calibrator of ALMA, a large amount of observation data of Titan is available in the ALMA archive. We calibrated and imaged all of the archived observational data of Titan that were available as of January 2020. The details of the calibration and imaging procedure were as described in our previous paper that analyzed nitrogen isotopic ratio of CH 3 CN on Titan (Iino et al. 2020).
Spectral lines of the isotopologues of HC 3 N are often observed by ALMA by chance because their pure rotational transitions appear every ∼10 GHz. To measure the line intensities precisely, we have chosen spectral windows (SPW) that observed multiple isotopologues simultaneously. The usage of the data in the same SPW suppresses the systematic uncertainties arising from the differences in the observation configurations such as the synthesized beam size and absolute flux calibration, and Titan's environmental conditions such as the horizontal and vertical distribution of HC 3 N and the atmospheric structure. To measure the line intensities that have a narrow (∼1.5 MHz) line-width, SPW that have a high frequency resolution of <2 MHz were chosen. The frequency difference between HC 13 CCN and HCC 13 CN that share the same rotational state J is no more than 20 MHz because they have a very similar rotational constant B. Thus, in most cases, they are observed in the same SPW. In turn, since the rotational constant of H 13 CCCN is ∼2% smaller than those of HC 13 CCN and HCC 13 CN, the number of SPW including three lines was smaller than that includes HC 13 CCN -HCC 13 CN pair.
As an important phenomenon, Titan's trace gases including HC 3 N and its precursors, C 2 H 2 and HCN, are known to exhibit large spatial and time variations. The analyzed period, from 2012 to 2015, is a season of northern summer, when increase and decrease of trace species have been observed by Cassini and ALMA for southern and northern hemispheres, respectively (Cordiner et al. 2015;Thelen et al. 2019;Cordiner et al. 2019;Coustenis et al. 2018).
To decrease the effect of such data-to-data variability of the HC 3 N spatial distribution, diskaveraged spectra were extracted from the imaged cube fits with a 0. 4 radius circle which is large enough to cover the entire disk of Titan for all of the analyzed datasets.
The baseline structure of the spectra was attempted to be removed using polynomial fitting method, while the effect was very limited. For the line intensity measurement, spectral intensities within a range of ±1 MHz from the line center were integrated. Noise level was measured in the line-free region and multiplied by √ n where n is the number of averaged channel. After extracting 29 SPW which include multiple emission lines, SPW that exhibit high S/N ratio as >4 were chosen for the intensity ratio measurement analysis.
The number of selected SPW including HC 13 CCN -HCC 13 CN and H 13 CCCN -HCC 13 CN pairs obtained with high S/N ratio were 12 and 1, respectively. Observation parameters of the selected SPW are summarized in Table 1. The rotational state transitions corresponding to 217, 226, 235, 244 and 271 GHz bands were J = 24-23, 25-24, 26-25, 27-26 and 30-29, respectively. For an selected H 13 CCCN -HCC 13 CN pair, they have different transition of J=35-34 and 34-33 for H 13 CCCN and HCC 13 CN, respectively. Most of the bands are of the ALMA Band 6, except for 308 GHz of the Band 7. The project code 2015.1.00512.S data has a long observation time by concatenating short observation time data to improve the S/N ratio. Figures 1 and 2 show the obtained spectra for each pair. The HC 13 CCN and HCC 13 CN lines are plotted in the same panels in Figure 1 due to small differences in frequency, while the lines for H 13 CCCN and HCC 13 CN are over-plotted in Figure 2. For H 13 CCCN including data, as shown in Figure 2, since the HC 13 CCN line was blended with a Ethyl Cyanide (C 2 H 5 CN(36 1,36 − 35 1,35 )) line, only the HCC 13 CN line was used for the intensity comparison. Note that the detection of C 2 H 5 CN with ALMA was reported previously (Cordiner et al. 2015).
In Titan's atmosphere, the chemical processes associated with HC 3 N vary with altitude, with ion chemistry being dominant at high altitudes and neutral chemistry at low altitudes. Previous ALMA observation study (Thelen et al. 2019) derived an altitude range where HC 3 N (J=35-34) is sensitive by the radiative transfer analysis of the disk averaged spectra. The optically thick line core region of ± 2 MHz from the line center probes at the ∼800 km high altitude region, whereas wings has sensitivity at 150 km, where HC 3 N shows abundance peaks in the high latitude regions. Because the obtained intensities of isotopomer lines analyzed in our study are quite weaker than that of HC 3 N line, we infer that the isotopomer lines have sensitivity at the lower stratosphere.

Abundance ratio calculation
To calculate the abundance ratios for the two pairs of isotopologues, as described methods below, we compared the measured integrated line intensities instead of retrieving the vertical abundance using radiative transfer method. Since they share similar vertical abundance, optical depth and the same temperature profile, their relative abundance can be derived with a proper consideration of the difference of the rotational transitions between the two isotopologues. In addition, optically thin molecular lines enable us to assume that the measured intensity is proportional to the optical depth. This method was also applied to the previous [H 13 CCCN]:[HCCC 15 N] measurement using ALMA observation result (Cordiner et al. 2018). Because we did not need to consider the effect of the difference of beam size, temperature profile and three-Dimensional distribution of HC 3 N, the only effect on the line intensity that was estimated and applied was the difference in spectroscopic parameters with respect to the stratospheric temperature. For the calculation of the parameters relating to opacity such as the partition function and population, the equations used were those listed in the appendix of Turner (1991) and Iino et al. (2014). Line parameters such as the Einstein coefficient A ul , the lower state energy E l and the rotational constant B, were obtained from the NASA JPL catalogue (Picket et al. 1998). The considered excitation temperatures were from 140 to 180 K under the assumption of the local temperature equilibrium condition.
For the HC 13 CCN -HCC 13 CN pair, the evaluation was simple because they share the same rotational state J. For the range of analyzed rotational transitions, the line intensity difference between HC 13 CCN and HCC 13 CN was estimated to be less than 0.02% for the modeled temperature range. The only exception was the J=24-23 transition, where HCC 13 CN has three hyperfine splitting lines. In this case, the line intensities of three transitions were simply integrated. As a result, the line intensity difference for the J=24-23 pair was determined to be ∼0.2%. Thus, considering the line intensity difference between two isotopologues and optically thin line intensities, for all the HC 13 CCN -HCC 13 CN pair, we used the integrated line intensity ratios as the abundance ratio.  (Takano et al. 1998;Araki et al. 2016;Taniguchi et al. 2016Taniguchi et al. , 2017. Assuming that no time variation of 12 C/ 13 C ratio is present since the previous observation, the result indicates that the 12 C/ 13 C ratios on three isotopologues are same as 79±17 that measured on H 13 CCCN (Jennings et al. 2008). Below, the derived results are discussed from two viewpoints: 13 C concentration on HCC 13 CN and H 13 CCCN. The obtained absence of carbon fractionation process on Titan is possibly explained by the environmental difference such as atmospheric temperature between Titan and the ISM, and may constrain chemical reactions present in Titan's middle and upper atmosphere.

HCC 13 CN concentration
Assuming the main HC 3 N production as Reaction 1, in case of HCC 13 CN concentration exists, 13 C concentrations on CN and/or its precursor are greater than that in reaction counterparts, C 2 H 2 , whose 12 C/ 13 C ratio was determined to be 84.8±3.2 using the infrared spectra obtained by the Cassini spacecraft . A main production pathway of CN is a photo-dissociation of HCN (Loison et al. 2015). The other pathway, a photo-dissociation of C 2 N 2 , is negligible because the abundance is below 1-0.1% of HCN. The most recent ALMA observation reported that no significant 13 C concentration in HCN (89.8±2.8: Molter et al. (2016)) in relative to C 2 H 2 . Thus, if exists, 13 C concentration on CN occurs after the photolysis of HCN.
An ion-molecule isotope exchange process between 13 C + and CN has been proposed for exothermic 13 CN concentration process for interstellar clouds as follows (Colzi et al. 2020): Reaction 3 likely causes HCC 13 CN enrichment in some ISM, especially in low-temperature conditions (∼ 10 K) (Takano et al. 1998). However, Reaction 3 does not seem to work effective on Titan's relatively higher atmospheric temperature (140 -180 K in the stratosphere) than interstellar, because the backward reaction of Reaction 3 can proceed and suppress the isotopic fractionation of CN in such high temperature environment. The other scenario is relating to abundance of 13 C + ion. Vuitton et al. (2007) calculated C + number density as 1.4×10 −2 cm −3 considering mas spectral measurement result. The calculated density is smaller than other major ions such as CH + 2 , CH + 3 , CH + 5 , N + and so on, thus the Reaction 3 may not work effective to concentrate 13 C on CN and subsequently HC 3 N.

H 13 CCCN concentration
Reaction 2 is the only pathway to produce HC 3 N from C 2 H radical. Because C 2 H 2 , a precursor of C 2 H, is a symmetric carbon molecule, an anomaly between H 13 CCCN and HC 13 CCN is caused by the abundance difference between C 13 CH and 13 CCH. In the ISM, the anomaly is possibly due to the isotope exchange reaction to achieve 13 C concentration on C 13 CH as follows (Furuya et al. 2011): Similar to the case of Reaction 3, forward reaction of Reaction 4 is considered to be active only in low temperature environment such as the starless cores. In case of Titan, Reaction 4 is not expected to work for concentration of C 13 CH due to the high temperature condition. In addition, because of low HNC abundance (Moreno et al. 2011;Cordiner et al. 2014), contribution of the Reaction 2 for HC 3 N production may be negligible.

SUMMARY AND FUTURE PROSPECT
We have detected the presence of all three 13 C substituted species of HC 3 N, namely, H 13 CCCN, HC 13 CCN and HCC 13 CN, in Titan's atmosphere using observational data from ALMA archive. The statistically derived [HC 13 CCN]/[HCC 13 CN] value was determined to be 1.09±0.25, whereas that of measured in starless dark clouds and low-mass star forming regions were previously reported to excess the present error. Additionally, [H 13 CCCN]/[HCC 13 CN] was found to be 1.17±0.20, although this result is less reliable than that for [HC 13 CCN]/[HCC 13 CN] because of a single pair detection. For both cases, no significant 13 C concentration in HC 3 N was detected, which differs from most of the ISM cases.
The large environmental difference with ISM is the high atmospheric temperature environment of Titan. A recent ALMA temperature measurement revealed that the measured stratospheric temperature above 100 km is at least 130 K, and reaches 180 K at 300 km (Thelen et al. 2018). These temperatures are quite higher than that expected in the ISM as 10 K (Taniguchi et al. 2019). In such a cold region with temperatures around 10 K, the barrierless and exothermic isotopic exchange reactions, Reactions 3 and 4, which have been considered to cause fractionation on HC 3 N, are driven by the differences in the zero point energy. On the other hand, in a high temperature environment, such as Titan's stratosphere and mesosphere, the backward reactions of Reactions 3 and 4 can proceed to suppress the isotopic fractionation in the precursors of HC 3 N and HC 3 N itself.
Recently, similar to the case of Titan, Taniguchi et al. (2021) reported uniform carbon isotopic ratios of HC 3 N around a massive young star objects. They proposed that HC 3 N is mainly produced via HC 3 NH + ion, which has complicated formation pathway, which introduces more complicated pathways of HC 3 N formation pathways and thus the entire HC 3 N isotopic ratios would be affected by other reactions than Reactions 3 and 4. In addition to Reactions 1 and 2, a recent study suggested that the photo-dissociation of C 2 H 3 CN and H-atom addition to HC 4 N 2 may produce HC 3 N (Vuitton et al. 2019). For the total understanding of Titan's isotopic fractionation processes, such ion-relating reactions and newly proposed neutral reactions should be investigated. Similar to Reaction 3, new exchange reactions of 13 C and 13 C + with C-bearing species are proposed by recent publications (Colzi et al. 2020;Loison et al. 2020). These newly proposed reactions may induce 13 C concentrations in C-bearing species, in particular if 13 C and 13 C + are abundant which is unlikely in Titan atmosphere. Our result, together with the previously reported non-concentration of 13 C in C-bearing species on Titan such as CH 4 , C 2 H 2 , HCN, HC 3 N and CO, may be interpreted as the consequence of 13 C and 13 C + depletion.
This study makes use of the ALMA data listed in the table 1. 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 work was supported by grants from the Telecommunications Advancement Foundation (TI), the Japan Society for the Promotion of Science (JSPS) Kakenhi (17K14420, 19K14782, 20K14523, 20K04046 and 20K04017) Figure 1. Spectra of HC 13 CCN(red marker) and HCC 13 CN(blue marker). X and Y axes are for rest frequency (GHz) and intensity (Jy/beam), respectively. Order of panel is corresponding to Table 1