# Using SOFIA's EXES to search for C6H2 and C4N2 in Titan's atmosphere

Zachary C. Mcqueen, Conor A. Nixon, Curtis de Witt, Véronique Vuitton, Panayotis Lavvas, Juan Alday, Nicholas A. Teanby, Joseph Penn, Antoine Jolly, Patrick G. J. Irwin

<figure><img src="image_1.png" /></figure>

► To cite this version:

Zachary C. Mcqueen, Conor A. Nixon, Curtis de Witt, Véronique Vuitton, Panayotis Lavvas, et al. Using SOFIA's EXES to search for C6H2 and C4N2 in Titan's atmosphere. 2025. hal-05409485

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# Using SOFIA's EXES to search for C<sub>6</sub>H<sub>2</sub> and C<sub>4</sub>N<sub>2</sub> in Titan's atmosphere

ZACHARY C. MCQUEEN,<sup>1,2</sup> CONOR A. NIXON,<sup>1</sup> CURTIS DE WITT,<sup>3</sup> VÉRONIQUE VUITTON,<sup>4</sup> PANAYOTIS LAVVAS,<sup>5</sup>

JUAN ALDAY,<sup>6</sup> NICHOLAS A. TEANBY,<sup>7</sup> JOSEPH PENN,<sup>8</sup> ANTOINE JOLLY,<sup>9</sup> AND PATRICK G. J. IRWIN<sup>8</sup>

<sup>1</sup>NASA Goddard Space Flight Center, 8800 Greenbelt Rd, Greenbelt, MD 20771, USA

<sup>2</sup>Southeast Universities Research Association, 1201 New York Avenue, Suite 430, Washington, DC 20005, USA

<sup>3</sup>Space Science Institute, 4765 Walnut St STE B, Boulder, CO 80301, USA

<sup>4</sup>Univ. Grenoble Alpes, CNRS, IPAG, 38000 Grenoble, France

<sup>5</sup>GSMA UMR 7331, University Reims Champagne Ardenne, Reims, France

<sup>6</sup>Instituto de Astrofísica de Andalucía, CSIC, Granada, Spain

<sup>7</sup>University of Bristol, Queens Road Clifton, Bristol, BS8 1RJ, United Kingdom

<sup>8</sup>Oxford University, Clarendon Laboratory, Parks Rd, Oxford OX1 3PU, United Kingdom

<sup>9</sup>Université Paris Est Créteil and Université Paris Cité, Créteil, France

## ABSTRACT

In Titan's atmosphere, the chemistry of simple hydrocarbons (e.g. CH<sub>4</sub> and C<sub>2</sub>H<sub>2</sub>) and nitrogen bearing species (e.g. N<sub>2</sub> and CN) represent an important link between molecular species and the ubiquitous organic haze that gives Titan its characteristic orange hue. Here we present a new search for two previously undetected molecules, triacetylene (C<sub>6</sub>H<sub>2</sub>) and the gas phase dicyanoacetylene (C<sub>4</sub>N<sub>2</sub>), using the Echelon-Cross-Echelle Spectrograph (EXES) instrument aboard the SOFIA (Stratospheric Observatory For Infrared Astronomy) aircraft. We do not detect these two molecules but determine upper limits for their mixing ratios and column abundances. We find the 3σ upper limits on the uniform volume mixing ratio (VMR) above 100 km for C<sub>6</sub>H<sub>2</sub> to be 4.3 × 10<sup>-11</sup> which is lower than the photochemical model predictions. This new upper limit suggests that the growth of linear molecules is inhibited. We also put a strict upper limit on the uniform VMR for gas phase C<sub>4</sub>N<sub>2</sub> above 125 km to be 1.0 × 10<sup>-10</sup>. This upper limit is well below the saturation mixing ratio at this altitude for C<sub>4</sub>N<sub>2</sub> and greatly limits the feasibility of C<sub>4</sub>N<sub>2</sub> forming ice from condensation.

**Keywords:** Titan (2186), Natural satellite atmospheres (2214), Infrared spectroscopy (2285), Atmospheric composition (2120)

## 1. INTRODUCTION

Titan's major atmospheric components, N<sub>2</sub> (nitrogen) and CH<sub>4</sub> (methane), photodissociate and ionize in Titan's ionosphere, consequentially leading to the formation of other hydrocarbon and nitrile species (S. M. Hörst 2017; C. A. Nixon 2024). These minor components continue this photochemical process, leading to larger and more complex organic species and ultimately leading to the formation of Titan's characteristic haze (M. G. Trainer et al. 2006; J. H. Waite Jr. et al. 2007). Discovery of Titan's gaseous atmosphere came from early observations of Titan from Earth based astronomy, where G. P. Kuiper (1944) discovered the presence of CH<sub>4</sub>. The Voyager 1 flyby then confirmed the bulk of Titan's atmosphere was composed of N<sub>2</sub>, and infrared observations of Titan's atmosphere from both Voyager 1 and Voyager 2

flybys, allowed for the discovery of a wealth of new trace species (A. L. Broadfoot et al. 1981; R. Hanel et al. 1981; W. C. Maguire et al. 1981; R. E. Samuelson et al. 1983; B. Letourneur & A. Coustenis 1993). Space based observatories, like the Infrared Space Observatory, also contributed greatly to discovering new trace gases in Titan's atmosphere including water and benzene (A. Coustenis et al. 1998, 2003; T. Encrenaz 2003). The return to Titan with the Cassini-Huygens mission provided excellent spatial, temporal, and vertical coverage of Titan's atmosphere (A. Coustenis et al. 2010; C. A. Nixon et al. 2019), allowing for several detailed IR studies of Titan over several seasons (e.g. N. Teanby et al. (2008); S. Vinatier et al. (2015); N. A. Lombardo et al. (2019a); N. A. Teanby et al. (2019); S. Vinatier et al. (2020); L. Wright et al. (2025)). Following
<table><caption>**Table 1.** Description of EXES observations of Titan's atmosphere.</caption><thead><tr><th>Target, setting (cm<sup>-1</sup>)</th><th>Date (yyyy-mm-dd)</th><th>Altitude (ft)</th><th>Airmass</th><th>Distance (A.U.)</th><th>D<sub>v</sub> (km/s)</th><th>Integration time (s)</th></tr></thead><tbody><tr><td>Callisto, 621</td><td>2021-06-09</td><td>43000</td><td>1.84</td><td>-</td><td>-</td><td>1408</td></tr><tr><td>Titan, 621</td><td>2021-06-09</td><td>43000</td><td>1.68</td><td>9.321</td><td>-20.994</td><td>1504</td></tr><tr><td>Vesta, 472</td><td>2021-06-11</td><td>39000</td><td>1.68</td><td>-</td><td>-</td><td>1504</td></tr><tr><td>Titan, 472</td><td>2021-06-15</td><td>43000</td><td>1.84</td><td>9.264</td><td>-18.930</td><td>1600</td></tr><tr><td>Titan, 472</td><td>2021-06-17</td><td>43000</td><td>1.67</td><td>9.240</td><td>-22.499</td><td>2560</td></tr><tr><td>Titan, 472</td><td>2021-12-04</td><td>36000</td><td>2.00</td><td>10.424</td><td>+28.940</td><td>3392</td></tr></tbody></table>

the conclusion of the Cassini-Huyugens mission, Earth-based observations at infrared and sub-millimeter wavelengths have been a major contributor to searching for and detecting trace gases that are predicted to be present in Titan's atmosphere at low abundances (M. Y. Palmer et al. 2017; A. E. Thelen et al. 2019; N. A. Lom-bardo et al. 2019b; M. A. Cordiner et al. 2019; C. A. Nixon et al. 2020; M. A. Cordiner et al. 2020). Most recently, observations using the James Webb Space Tele-scope have allowed for the recent discovery of the CH$_3$ radical in Titan's atmosphere (C. A. Nixon et al. 2025), showing the importance of continued searches for trace gases that connect the many chemical mechanisms in Titan's atmosphere.

Polyynes or poly-acetylenes are linear chains of acetylene groups and bear the molecular formula C$_{2}$nH$_{2}$ where n ≥ 2. Polyynes represent one potential path-way to form macromolecules in Titan's atmosphere that bridge the gap between simple molecules and Titan's aerosols (E. Chassefière & M. Cabane 1995; S. Lebonnois et al. 2002). Polyynes form readily through the addition of the ethynyl radical (C$_2$H) to the precursor acetylene (C$_2$H$_2$) or poly-acetylene molecule i.e. diacetylene C$_4$H$_2$ (X. Gu et al. 2009). Although polyynes have been observed in the interstellar medium (J. Cernicharo et al. 2001b,a), and are predicted to form in Titan's atmo-sphere at observable abundances (X. Gu et al. 2009; V. Vuitton et al. 2019), C$_4$H$_2$ is the highest order polyyne that has been detected in Titan's atmosphere (V. G. Kunde et al. 1981; N. Teanby et al. 2009). Triacetylene (C$_6$H$_2$), which forms from C$_4$H$_2$, is predicted in photo-chemical models to have a stratospheric abundance of 0.6 ppb (V. Vuitton et al. 2019) yet, to this date the spectroscopic detection of C$_6$H$_2$ has eluded the community.

There have been two previous studies of Titan's C$_6$H$_2$ upper limits. The first upper limit of C$_6$H$_2$, reported by C. Delpech et al. (1994), was determined by comparing the expected signal intensity from the strongest vibrational mode of C$_6$H$_2$ to the observed emission features

of a reference compound and was found to be 0.6 ppb above 100 km. This study was in agreement with the photochemical model predictions at the time, but was limited by the low spectral resolution of Voyager's IRIS and the authors note that a higher resolution spectrometer may allow C$_6$H$_2$ to be detected. F. Shindo et al. (2003) updated measurements of the C$_6$H$_2$ IR spectrum and re-calculated the upper limits and lowered them to 0.44 ppb above 150 km using a similar method. Still, at these upper limits, C$_6$H$_2$ and higher order polyynes represent a potential pathway to the formation of large hydrocarbons in Titan's atmosphere. Therefore, an updated analysis of the upper limits for C$_6$H$_2$ at high spectral resolution will provide useful estimations of the potential for higher-order polyyne formation in Titan's atmosphere.

Dicyanoacetylene (C$_4$N$_2$) in the gas phase is predicted to form in Titan's atmosphere through the reaction of HC$_3$N with CN (V. Vuitton et al. 2019). This was recently shown to occur in crossed molecular beam experiments by E. V. F. d. de Aragão et al. (2025). Additionally, C$_4$N$_2$ can form through HCN reaction with C$_3$N and through hydrogen elimination of HC$_4$N$_2$, though HC$_4$N$_2$ is formed following C$_4$N$_2$ formation (J. Loison et al. 2015). C$_4$N$_2$ is unique in Titan's atmosphere because, although the gas phase species has not been detected, C$_4$N$_2$ ice has been reported in both Voyager's Infrared Interferometer Spectrometer and Radiometer (IRIS) spectra and Cassini's Composite Infrared Spectrometer (CIRS) spectra (R. Samuelson et al. 1997; C. M. Anderson et al. 2016). Following the Voyager flyby, an emission feature at 478 cm$^{-1}$ was assigned to the ice-phase $\nu_8$ vibrational mode of C$_4$N$_2$, however, the gas phase emission at 471 cm$^{-1}$ was not present. Some years later, the same anomalous feature at 478 cm$^{-1}$ arose in CIRS observations of Titan's atmosphere and was also assigned to C$_4$N$_2$ ice. Since then, there have been several studies attempting to understand why this ice feature is so strong but the gas is not present in detectable amounts. R. Samuelson et al. (1997) sug-
gested that the gas phase C₄N₂ is enriched during the winter, leading to condensation, and then photochemically consumed rapidly at the Spring Equinox while the condensate progressively builds up in the lower stratosphere. This however was suggested to not be feasible by R. de Kok et al. (2008), as their upper limit of 1×10⁸, before equinox, was too small to allow for ice formation even under the rapid depletion scenario.

The most recent hypothesis for C₄N₂ ice formation in Titan's atmosphere was presented in C. M. Anderson et al. (2016) where, rather than C₄N₂ ice forming directly from condensation, it is formed completely via solid-state photochemistry within HCN-HC₃N ice mixtures. This proposed mechanism, however, requires a column abundance of 10¹⁷ molecules/cm² to obtain a good spectral fit to the 478 cm⁻¹ emission feature. Such a high column abundance is larger than the simpler, but related molecule, cyanogen (C₂N₂), which has been detected in Titan's atmosphere (V. G. Kunde et al. 1981; J. Loison et al. 2015). Updated estimations of the upper limits on the gas phase abundance of C₄N₂ will help constrain the feasibility of C₄N₂ ice formation in Titan's atmosphere.

In the present study, we use high-resolution ($R \sim 90,000$) mid-IR spectroscopy with observations made by the Echelon-Cross-Echelle Spectrograph (EXES) aboard the SOFIA (Stratospheric Observatory Infrared Astronomy) aircraft at two spectral regions, 621 cm⁻¹ and 472 cm⁻¹, to search for C₆H₂ and C₄N₂ respectively. We perform radiative transfer models of the measured spectra to retrieve the atmospheric abundances of C₄H₂ and C₃H₄ and derive upper limits for the undetected species, C₆H₂ and C₄N₂. We then compare these upper limits to photochemical model predictions of the target species and discuss the implications these upper limits have on our understanding of Titan's atmospheric chemistry.

## 2. EXES OBSERVATIONS

Observations of Titan's atmospheric spectra were made using EXES aboard NASA's SOFIA (Stratospheric Observatory for Infrared Astronomy) aircraft (M. J. Richter et al. 2018). Details of the observations are listed in Table 1. Spectra were collected during flights 744 and 746 in June 2021. EXES was operated in a high-medium configuration to obtain high-resolution ($R \sim 75000-90000$) spectra centered at 472 cm⁻¹ and 621 cm⁻¹ to observe the emission features of C₄N₂ for the former and C₄H₂, C₆H₂, and C₃H₄ for the latter region. Targets were nodded along the slit in an ABAB pattern by 7-8" at intervals of 4 minutes to facilitate sky background subtraction.

The 2.65" slit width was used for the 621 cm⁻¹ setting. Even at SOFIA's altitude, the telluric spectrum at 621 cm⁻¹ has interference from densely spaced atmospheric lines of CO₂, O₃ and N₂O. To enable removal of these features, Callisto (the telluric calibrator) and Titan were observed on adjacent flight legs, at the same altitude and with an air mass difference of 0.16, ensuring the best possible match in telluric transmission. To accurately model the instrument line-shape, we derived the resolving power of the measurement by fitting synthetic transmission models to the Callisto spectrum which were generated by Planetary Spectrum Generator (PSG, G. L. Villanueva et al. (2018)). We found the resolving power at the 621 cm⁻¹ spectral setting to be $R = 90000 \pm 2500$.

The 472 cm⁻¹ observations were taken on 3 flights with a slit width 3.2". Due to the low density of telluric atmosphere features near 472 cm⁻¹, telluric interference was a minor issue that could be addressed by synthetic PSG atmosphere models and masking the regions containing features due to water. The telluric calibrator, Vesta was observed for this setting to mitigate risk, but it was only used to derive a resolving power for the 472 cm⁻¹ setting, $R = 75000 \pm 2500$.

All data were reduced with the EXES Redux pipeline (M. Clarke et al. 2015) version 3.0.1.dev.7 with the customary steps including spike removal, flat fielding, recertification of the cross-dispersed orders, coadding of nodpairs, and extraction to the 1-D using optimal PSF weighting. Following data reduction using the Redux pipeline, spectral data points were binned using Nyquist sampling to a $\Delta\bar{\nu} = 0.003$ in order to reduce the noise in the spectrum.

## 3. RADIATIVE TRANSFER MODELING

Spectra were modeled using the archNEMESIS (J. Alday et al. 2025) radiative transfer model, which is a Python implementation of the Non-linear Optimal Estimator for Multivariate Spectral Analysis (NEMESIS) (P. Irwin et al. 2008). NEMESIS has been used extensively to model Titan atmospheric spectra (C. A. Nixon et al. 2013; N. A. Teanby et al. 2019; L. Wright et al. 2024; N. A. Lombardo et al. 2019b; A. E. Thelen et al. 2019) and has been used for modeling observations of Titan with TEXES (Texas Echelon-Cross-Echelle Spectrometer), the sister instrument to EXES (N. A. Lombardo et al. 2019b). archNEMESIS allows for both multi-core processing and larger spectral datasets due to improved memory efficiency in Python.

For this study, archNEMESIS is employed in two different ways to model the target species. First, the spectra are inverted using the optimal estimation method
<figure><img src="image_2.png" /><figcaption>**Figure 1.** Reference profiles of the atmospheric gas composition (left panel), vertical temperature profile (right panel, solid black trace), and haze profiles (gray dashed trace). Temperature and gas profiles are from the photochemical model detailed in V. Vuitton et al. (2019).</figcaption></figure>

to retrieve the continuous atmospheric profiles of C₄H₂ and C₃H₄ (for the 621 cm⁻¹ spectral setting) as well as the scaling factor for Titan's haze profile (both spectral settings). We retrieved continuous profiles for the known gases (C₄H₂ and C₃H₄) and a scaling factor for the haze profile. We used an atmospheric model with 100 homogeneous layers equally spaced in log pressure to sufficiently sample the vertical profile of Titan's atmosphere. The a priori reference atmosphere used, shown in Figure 1, uses gas and temperature profiles described in the V. Vuitton et al. (2019) photochemical model. The photochemical model profiles for C₄H₂ and C₃H₄ were each scaled by 0.2 and 0.5, respectively, prior to retrieving the continuous profiles to ensure a good fit to the spectrum was achieved. To fit the continuum level, we retrieved a scaling factor for a uniform haze profile with an a priori concentration of 1.29 × 10⁷ particles/m³ above 50 km (Figure 1), using a uniform cross-section across the wavelength range for both spectra.

Since the EXES observations are of Titan's disk, we modeled these observations using a weighted average of emission rays from different emission angles of the solid body and emission rays from the limb. We followed a similar approach to N. Teanby et al. (2013) to both sufficiently sample Titan's radiance and calculate weights for each emission ray. In total, we used 55 emission rays from the disk center out to a limb height of 975 km.

### 3.1. Spectroscopic Data

Spectra were calculated in line-by-line mode using pre-tabulated line-by-line lookup tables calculated at 30 pressure and temperature levels between 5.6 × 10⁻⁹ - 2.5 bar and 70-250 K. Line data was then interpolated to the pressures and temperatures at each atmospheric layer in the atmospheric model. Spectra were also calculated using a Gaussian line shape at the resolving power of each spectral setting. The spectroscopic line lists for the known gas emission features at the 621 cm⁻¹ spectral setting, namely the ν₈ band of C₄H₂ and the ν₉ band of C₃H₄, were obtained from the HITRAN (I. Gordon et al. 2022) and GEISA (T. Delahaye et al. 2021) spectroscopic databases, respectively. All band intensities for the observed and targeted emission features are listed in Table 2, with the exception of the band intensity of the ν₉ band of C₃H₄, not reported in K. Pekkala (1990). Both target species for this study, C₆H₂ and C₄N₂, are less commonly measured in atmospheric spectra and are not available in the standard databases, however, their infrared spectra have been well characterized in laboratory settings. F. Shindo et al. (2003) measured the mid-infrared spectrum of C₆H₂ and is the most up-to-date line-list for the ν₁₁ band at ~ 622 cm⁻¹. This band is an intense, out-of-plane bending mode that is centered in a window ideal for being targeted by EXES. The ν₅
<figure><img src="image_3.png" /><figcaption>**Figure 2.** Model fit (red trace) to the measured spectrum (gray trace) for the 621 cm⁻¹ (A) and 472 cm⁻¹ (B) spectral settings. Bottom panels show the residual of the model fit to the measured spectra and a 1σ estimation of the instrument uncertainty in the blue shaded regions. Emission features from C₄H₂ and C₃H₄ are indicated by the respective markers in A. There are no known emission features in the 472 cm⁻¹ spectral setting and only the haze and CIA continuum levels were fit in the retrieval.</figcaption></figure>

band is more intense, but the Q-branch is centered at 3322 cm⁻¹ where the Titan spectra is opaque due to strong absorption from CH₄. Similarly, A. Jolly et al. (2015) obtained the line list for the ν₈ bending mode of C₄N₂ in a previous investigation of the upper limits of the gas phase species in Titan's atmosphere. This ν₈ is covered by the EXES spec-

tral bandwidth, however is less intense than the ν₉ vibrational mode, centered at 107 cm⁻¹ (A. Jolly et al. 2015), which is outside of the EXES spectral window. Additionally, the emission features for both target species were targeted during the SOFIA mission specifically because the 621 cm⁻¹ and 472 cm⁻¹ spectral windows are
<table><caption>**Table 2.** Literature values for the infrared band intensities of the molecules investigated.</caption><thead><tr><th>Molecule</th><th>Band</th><th>Position (cm<sup>-1</sup>)</th><th>Absolute Intensity (atm<sup>-1</sup>cm<sup>-2</sup>)</th><th>Reference</th></tr></thead><tbody><tr><td>C<sub>6</sub>H<sub>2</sub></td><td>ν<sub>11</sub></td><td>622</td><td>428±25</td><td>F. Shindo et al. (2003)</td></tr><tr><td>C<sub>4</sub>H<sub>2</sub></td><td>ν<sub>8</sub></td><td>628</td><td>563±23</td><td>A. Jolly et al. (2014)</td></tr><tr><td>C<sub>3</sub>H<sub>4</sub></td><td>ν<sub>9</sub></td><td>638</td><td>-</td><td>K. Pekkala (1990)</td></tr><tr><td>C<sub>4</sub>N<sub>2</sub></td><td>ν<sub>8</sub></td><td>471.6</td><td>52±1.5</td><td>A. Jolly et al. (2015)</td></tr></tbody></table>

blocked from the surface due to CO₂ and H₂O absorption in the Earth's atmosphere. Data for collision-induced absorption was obtained from the 2025 HITRAN database update (J. Terragni et al. 2025).

## 3.2. Determining Upper Limits

Following the spectral fit, we determine the upper limits to the C₆H₂ and C₄N₂ abundance. We determine the goodness-of-fit for the modeled spectrum by summing the ratio of the square residual of the fit to the squared uncertainty of the measurement, described in Equation 1.

$$ \chi^2 = \frac{\Delta\bar{\nu}_{\text{obs}}}{\Delta\bar{\nu}_{\text{res}}} \sum_{i=1}^{M} \frac{(I_m(\bar{\nu}_i) - I_r(\bar{\nu}_i))^2}{\sigma_i^2} \quad (1) $$

Where I_m and I_r are the spectral radiance for the measurement and retrieved spectrum, respectively, at wavenumber $\bar{\nu}_i$, and $\sigma_i$ is the wavenumber dependent uncertainty. Once the emission features of the spectral region are well fit, the remaining residual will be due to instrument noise and any unfit gas emission features that were not included in the retrieval. The vertical profile of the target species is then set to be uniform volume mixing ratio (VMR) above a condensation altitude and we iterate over a range of VMR values, calculating a forward model of the spectrum at each abundance and determine the change in the $\chi^2$, $\Delta\chi^2$, with increased abundance of the target species. If the gas is present in detectable amounts, $\Delta\chi^2$ will decrease significantly, indicating the spectral fit is improved with the inclusion of the target species. Alternatively, when $\Delta\chi^2$ increases, the upper limits can be determined at $\Delta\chi^2 = +1, +4$, and +9 for $1\sigma, 2\sigma$, and $3\sigma$ upper limits, respectively. This method has been used in several previous studies of Titan's atmospheric trace constituents for detections and upper limits (C. A. Nixon et al. 2010; N. Teanby et al. 2009; A. Jolly et al. 2015).

## 4. RESULTS

### 4.1. Abundance Retrievals for C₄H₂ and C₃H₄

To fit the measured spectra, we used the optimal estimation method for retrieving the vertical profiles of the gases, C₄H₂ and C₃H₄, known to have emission features

in the 621 cm⁻¹ spectral setting and a scaling factor for a uniform haze vertical profile at both spectral settings. The model fit to both spectra are shown in Figure 2. We obtained a good fit ($\chi^2/N = 0.999$) to the measured 621 cm⁻¹ spectrum by fitting to the gas emission features of C₄H₂ and C₃H₄. The residual of the fit to the measurement is shown in the lower panel and is within the $1\sigma$ estimation of the instrument noise. At lower wavenumbers, some of the emission features are slightly over fit and at longer wavenumbers the radiance of the stronger emission features are not fully captured, however the overall fit is good. C₄H₂ exhibits the strongest peaks, indicated by the blue vertical lines, with emission features originating from the P-branch of the $\nu_8$ vibrational mode. The emission features of C₃H₄, originating from the $\nu_9$ vibrational mode, are less intense, but tightly bunched and often near emission features from C₄H₂. Previously, these individual emission lines would not have been resolved with lower resolution spectrometers. At the 472 cm⁻¹ spectral setting, we only modeled the continuum level of the spectrum as no clear emission features were present. Without fitting any gas emission features, the model produced a $\chi^2/N = 1.01$, indicating the spectrum does not contain any significant features that are not being fit by the model.

Figure 3 shows the retrieved continuous profiles of each fit species in the altitude region where the Jacobian is peaked. For each species, the model was most sensitive in the stratosphere and lower mesosphere between 80 and 275 km, where the majority of the gas abundance is found, peaking at ~130 km (~5 × 10⁻³ bar) for each species. Overall, the shape of the vertical profiles was retained in the retrieval, however, the retrieved profile for C₄H₂ is significantly lower than the V. Vuitton et al. (2019) photochemical model. This lower abundance is in better agreement with the J. Loison et al. (2019) predicted profile, however the J. Loison et al. (2019) model under-predicts the abundance below 150 km in the stratosphere. Also shown in Figure 3 is the retrieved vertical profile from S. Vinatier et al.
<figure><img src="image_4.png" /><figcaption>**Figure 3.** Retrieved stratospheric profiles (colored trace) of C₄H₂ (A) and C₃H₄ (B) and the photochemical model predictions from V. Vuitton et al. (2019) (solid black trace) and J. Loison et al. (2015) (dot-dot-dash trace). The scaled profile from V. Vuitton et al. (2019), used as the a priori reference profile is shown in the solid gray trace. The retrieved profile from S. Vinatier et al. (2007) is also shown for comparison (gray points and dot-dash trace). Each panel also shows the Jacobian at $\bar{\nu}_{max}$ for each molecule to indicate the altitude range the model is sensitive to.</figcaption></figure>

(2007), who retrieved the vertical profiles of several trace species from infrared spectra of Titan's limb collected by CIRS. The retrieval from the present work agrees well with S. Vinatier et al. (2007) at the probed altitudes. The retrieved profile for C₃H₄ was in better agreement with the V. Vuitton et al. (2019) prediction than that of C₄H₂. The retrieval was slightly lower than

the prediction in the upper stratosphere (near 250 km), but a slight enhancement in the profile at the lower stratosphere brought the retrieval closer to the photochemical model prediction. This retrieved profile was also in good agreement with that of S. Vinatier et al. (2007), though, the S. Vinatier et al. (2007) profile shows the consistent VMR of ~ 5 × 10⁻⁹ goes deeper in the atmosphere. The J. Loison et al. (2019) prediction agrees within the error estimation near 200 km, but under predicts the C₃H₄ abundance below ~ 150 km.

## 4.2. Upper limits for C₆H₂ and C₄N₂

Following the retrievals, we determine the upper limits of C₆H₂ and C₄N₂ by simulating multiple spectra with increasing abundance of the target species while keeping the retrieved profiles of the known gases and haze fixed. The difference between the $\chi^2$ of the updated spectrum and the retrieved spectrum ($\Delta\chi^2$) is calculated at each abundance or scale factor. If the target species is present, the $\Delta\chi^2$ value will decrease significantly, indicating the spectrum is better fit. A rejection of the detection occurs when the $\Delta\chi^2$ increases sharply with increased abundance. Figure 4 shows the $\Delta\chi^2$ with increased VMR for C₆H₂ (A) and C₄N₂ (C). The cutoff altitude for C₆H₂ was set to 100 km, based on the condensation altitude reported in F. Shindo et al. (2003), who also performed an upper limits study of C₆H₂ using a similar profile. The $\Delta\chi^2$ dips slightly below zero with increased abundance of C₆H₂, but is nowhere near a significance level to indicate detection, and increases sharply as the VMR increases above $10^{-11}$. The upper limit values for both C₆H₂ and C₄N₂ are reported in Table 3. We find a $3\sigma$ upper limit on the uniform abundance of $4.29 \times 10^{-11}$ for C₆H₂. Figure 4(B) shows the corresponding spectra from each abundance at $1\sigma$, $2\sigma$, and $3\sigma$ upper limits. There is a clear growth in the radiance due to the $\nu_{11}$ vibrational mode of C₆H₂, indicated by the black triangle markers. The three main emission features in this spectra lie near strong emission features from C₄H₂, highlighting the importance of using the high-resolution capabilities of EXES. These emission features from C₆H₂ would have been smoothed together with emission features from C₄H₂ with lower resolution spectrometers such as CIRS or IRIS, requiring a much higher abundance of C₆H₂ to deviate significantly from the measurement and consequently leading to higher upper limits.

A uniform vertical profile above 125 km was used to determine the upper limits to the abundance of gas phase C₄N₂ based on the saturation vapor pressure
<figure><img src="image_5.png" /><figcaption>**Figure 4.** (A) The $\Delta\chi^2$ plotted as a function of the VMR for the uniform profile of C$_6$H$_2$ and (B) the corresponding simulated spectra for the 1$\sigma$, 2$\sigma$, and 3$\sigma$ upper limits with C$_6$H$_2$ peaks indicated by the black triangle markers. (C-D) The $\Delta\chi^2$ and corresponding spectra for the upper limits of C$_4$N$_2$. All emission features in (D) are due to C$_4$N$_2$.</figcaption></figure>

<table><caption>**Table 3.** Upper limits for C$_6$H$_2$ and C$_4$N$_2$.</caption><thead><tr><th rowspan="2">Species</th><th rowspan="2">1σNESR (nW cm<sup>-2</sup> sr<sup>-1</sup>/cm<sup>-1</sup>)</th><th colspan="3">Volume Mixing Ratio</th><th>Column Density (m<sup>-2</sup>)</th></tr><tr><th>1σ</th><th>2σ</th><th>3σ</th><th>3σ</th></tr></thead><tbody><tr><td>C<sub>6</sub>H<sub>2</sub></td><td>1.028</td><td>&lt; 2.30 &times; 10<sup>-11</sup></td><td>&lt; 3.24 &times; 10<sup>-11</sup></td><td>&lt; 4.29 &times; 10<sup>-11</sup></td><td>&lt; 1.69 &times; 10<sup>14</sup></td></tr><tr><td>C<sub>4</sub>N<sub>2</sub></td><td>1.003</td><td>&lt; 1.80 &times; 10<sup>-11</sup></td><td>&lt; 5.58 &times; 10<sup>-11</sup></td><td>&lt; 9.96 &times; 10<sup>-11</sup></td><td>&lt; 1.94 &times; 10<sup>14</sup></td></tr></tbody></table>

sures reported in N. Fray & B. Schmitt (2009), which were extrapolated to Titan's stratospheric temperatures. This cutoff altitude is similar to the upper limit study by A. Jolly et al. (2015), who applied a similar method for determining the cutoff altitude for the uniform profile. Figure 4 (C) shows the $\Delta\chi^2$ increases sharply with VMR. We determine a 3$\sigma$ upper limit on the abundance of $9.96 \times 10^{-11}$. Figure 4(D) shows the many emission

features originating from the $\nu_8$ bending mode of C$_4$N$_2$ which is very dense with many emission lines. This high density of emission features provides strong statistical evidence for the rejection of C$_4$N$_2$ presence in the measurement, as each peak in the simulated spectra contributes to the total $\chi^2$ of the model.
<figure><img src="image_6.png" /><figcaption>**Figure 5.** The 3σ upper limits found for this study (gray squares) for C₆H₂ (A) and C₄N₂ (B) along with previous studies of the upper limits. Also included are the photochemical model vertical profiles of each species (red and blue traces), the uniform profiles used for the upper limits (gray solid trace), and the scaling factor for the V. Vuitton et al. (2019) C₆H₂ profile (gray dashed trace). The gray dotted line in panel (B) is the saturation altitude calculated using the V. Vuitton et al. (2019) temperature profile and equation for the saturation vapor pressures in N. Fray & B. Schmitt (2009).</figcaption></figure>

## 5. DISCUSSION

### 5.1. C₆H₂

Previous attempts at detecting C₆H₂ in Titan's atmosphere have ultimately led to non-detection and upper limit determinations of the abundance. Figure 5 shows the upper limits determined from this study in comparison with those from C. Delpech et al. (1994) and F. Shindo et al. (2003). The new upper limits improve upon the previous ones by over an order of magnitude. This can be attributed to the high-resolution of EXES which can resolve individual emission features in a small wavenumber range that may have previously been blended together at lower resolutions. Figure 5 also compares the present results with photochemical model predictions of the vertical C₆H₂ profile. Comparing to the V. Vuitton et al. (2019) profile of the C₆H₂ abundance, these upper limits are significantly lower than the predicted stratospheric abundance. We derived a scale factor of the V. Vuitton et al. (2019) profile of 0.093.

Included in Figure 5 is a vertical profile from an updated photochemical model for both C₆H₂ and C₄N₂ shared in private communication by Panayotis Lavvas (Lavvas, 2025) in Figure 5). These profiles are the results of a model similar to that presented in V. Vuitton et al. (2019), which is a 1D photochemical model of Titan's atmosphere including neutral and ionic chemical processes (P. Lavvas et al. 2008a, 2021). In addition to the model described in P. Lavvas et al. (2008a), the model includes high-resolution description of the energy deposition in Titan's upper atmosphere through solar photons (P. Lavvas et al. 2011), and the contribution of

the photochemical haze opacity in the radiation transfer in Titan's atmosphere based on measurements made by the Huygens Descent Imager/Spectral Radiometer (P. Lavvas et al. 2010). The photochemical model also accounts for the escape of atomic and molecular hydrogen according to the Jean escape rate and methane is allowed to escape at a fixed velocity of 100 cm/s to match the observed profiles of methane and argon in the upper atmosphere based on measurements made by the Ion Neutral Mass Spectrometer during the Cassini-Huygens mission (R. V. Yelle et al. 2008; P. Lavvas et al. 2008b).

The low upper limit for C₆H₂ in this work, combined with a lower retrieved abundance of its precursor, C₄H₂ suggests that loss mechanisms for C₄H₂ are not being fully represented in V. Vuitton et al. (2019). C₄H₂ can be lost in Titan's atmosphere through combination with atomic hydrogen (H + C₄H₂) (V. Vuitton et al. 2012, 2019). The Lavvas (2025) model prediction presented here does not include a heterogeneous loss mechanism of H to haze particle surfaces, described in Y. Sekine et al. (2008), enriching the H abundance and decreasing the C₄H₂ abundance compared to V. Vuitton et al. (2019). Consequentially, this leads to a lower predicted C₆H₂ abundance as shown in Figure 5, which is in closer agreement with the present upper limits. Furthermore, additional loss of C₄H₂ could occur through the reaction with 1,3-butadiene (C₄H₆ isomer). I. A. Medvedkov et al. (2025) recently showed through crossed molecular beam experiments that the C₄H radical can add directly to 1,3-butadiene or 2-methyl-1,3-butadiene followed by isomerization to form aromatic rings. Additionally, C₂H₂ has been shown to react with HCO⁺ to initiate a cascade
of chemical reactions ultimately leading to the formation of benzene (E. O. Pentsak et al. 2024). HCO+ has not been detected in Titan's atmosphere but is present in models of Titan's oxygen cycle (S. M. Hörst et al. 2008; M. Dobrijevic et al. 2016). Such reactions that form aromatics from C₂H₂ and C₄H₂, have not been well studied under Titan relevant conditions, but represent other potential loss mechanisms for the precursors to polyyne propagation in Titan's atmosphere. This suggests that polyyne propagation is not a suitable pathway to larger hydrocarbons or organic aerosols in Titan's atmosphere.

## 5.2. C₄N₂

The assignment of the emission feature at 478 cm⁻¹ to ice-phase C₄N₂ in both Voyager's IRIS data (R. Samuelson et al. 1997) and CIRS data (C. M. Anderson et al. 2016) has led to many studies attempting to understand the lack of gas phase C₄N₂ in spectra of Titan's atmosphere. Several upper-limits have been determined, including the most stringent ones from A. Jolly et al. (2015) where a 3σ upper limit on the stratospheric abundance of 1.5 × 10⁻⁹ using both nadir and limb observations of Titan's atmosphere using CIRS. Figure 5B shows the 3σ upper limit presented in this study (gray square) in comparison with previous estimations of the C₄N₂ gas phase upper limits (gray points). The upper limits of this study lower the upper limits of the gas phase C₄N₂ abundance by an order of magnitude. This improvement largely stems from the high-resolution of EXES where the individual emission features of the C₄N₂ ν₈ vibrational mode can be resolved. In previous studies of the upper limits, the lower resolution of CIRS and IRIS smooth the entire band into one peak, dampening the contribution of each line to the Δχ². Figure 5B also compares the upper limits here to the photochemical model of V. Vuitton et al. (2019) and the aforementioned Lavvas (2025) model. The photochemical models predict an abundance of C₄N₂ gas in the stratosphere between ~10⁻¹³ – 10⁻¹² which is substantially lower than the upper limits presented here.

Also present in Figure 5B are the altitudes at which C₄N₂ gas should condense (gray dotted line) based on the saturation vapor pressure temperatures presented in N. Fray & B. Schmitt (2009). We calculated the saturation mixing ratios based on the temperature profile used in this study (V. Vuitton et al. 2019) based on the empirical determination of the saturation vapor pressure of C₄N₂ gas in N. Fray & B. Schmitt (2009). Because the temperature changes dramatically with altitude in the stratosphere, the saturation mixing ratio also increases rapidly with altitude, hence the flat nature of the trace. We find that the upper limits presented here, calculated

at 125 km, are below the saturation mixing ratio of C₄N₂ at this altitude which suggests that ice nucleation is not likely.

This updated value for the upper limit, however, was determined from a disk averaged measurement, which is more sensitive to changes in the abundance at the equator where trace gas concentrations in Titan's atmosphere tend to be diminished (N. A. Teanby et al. 2008; S. Vinatier et al. 2020). If C₄N₂ is present in lower abundances, it is possible, still that it could be enriched in the polar regions of Titan during winter seasons. Titan's winter poles, however, are not visible from Earth, restricting the opportunities for improving searches for C₄N₂ gas by observing in regions where it may be enriched. The current proposed mechanism of C₄N₂ formation is that C₄N₂ ice is formed totally in the solid-state through UV induced photochemistry (C. M. Anderson et al. 2016). Based on this mechanism, C. M. Anderson et al. (2016) requires a C₄N₂ column abundance of 10¹⁷ molecules/cm² for C₄N₂ which is substantially larger than the present value of ~2 × 10¹⁴. This would suggest that the C₄N₂ ice is highly out of equilibrium with the gas phase and would need to be retained completely in the closed shell. Laboratory experiments studying more closely the gas and ice phase partitioning of C₄N₂ ice formed in closed shells would be needed to better understand the feasibility of this disequilibrium.

## 6. CONCLUSIONS

This study presents spectra collected in the mid-infrared of Titan's atmosphere using EXES during the SOFIA mission. These spectra represent the lone study of Titan's atmosphere during the SOFIA mission but display the value of using high-resolution infrared spectroscopy for atmospheric studies. The spectra presented in this study showed spectral signatures for C₄H₂ and C₃H₄, which allowed for their continuous stratospheric profiles to be retrieved. We showed the C₃H₄ profile to be similar to that of V. Vuitton et al. (2019), but the C₄H₂ profile was lower than the photochemical model prediction. The target species, C₆H₂ and C₄N₂ were not detected; instead, we performed an upper limits study to the atmospheric abundances of the target species. The C₆H₂ upper limit, which has not been assessed since the Voyager mission (C. Delpech et al. 1994), was found to be lower than previous studies of C. Delpech et al. (1994) and F. Shindo et al. (2003) and constrains the photochemical model in V. Vuitton et al. (2019). We show that C₄H₂ is over predicted in the V. Vuitton et al. (2019) model and ultimately leads to the over prediction of the C₆H₂ stratospheric abundance. This strict up-
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per limit shows the potential for C₆H₂ formation and large polyyne propagation is low and the precursors are likely lost to other chemical processes.

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Additionally we lower the upper limit for C₄N₂ gas in Titan's atmosphere by an order of magnitude. This new value for the C₄N₂ upper limit shows that ice nucleation is unlikely to occur in Titan's atmosphere directly. The formation of C₄N₂ ice through solid-state photochemistry is still possible, **though**, the ice would

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be substantially out of equilibrium with the gas phase. Further work would be needed to better understand the gas-solid phase partitioning of C₄N₂ ice formed in an enclosed shell.

ACKNOWLEDGMENTS

The material is based upon work supported by NASA under award number 80GSFC24M0006. NAT is supported by UK Science and Technology Facilities Council grant ST/Y000676/1.

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