Vertical distribution of cyclopropenylidene and propadiene in the atmosphere of Titan

Titan's atmosphere is a natural laboratory for exploring the photochemical synthesis of organic molecules. Significant recent advances in the study of the atmosphere of Titan include: (a) detection of C$_3$ molecules: C$_3$H$_6$, CH$_2$CCH$_2$, c-C$_3$H$_2$, and (b) retrieval of C$_6$H$_6$, which is formed primarily via C$_3$ chemistry, from Cassini-UVIS data. The detection of $c$-C$_3$H$_2$ is of particular significance since ring molecules are of great astrobiological importance. Using the Caltech/JPL KINETICS code, along with the best available photochemical rate coefficients and parameterized vertical transport, we are able to account for the recent observations. It is significant that ion chemistry, reminiscent of that in the interstellar medium, plays a major role in the production of c-C$_3$H$_2$ above 1000 km.


INTRODUCTION
Titan's atmosphere comprises a rich hydrocarbon chemistry unlike anything seen elsewhere in the solar system outside of Earth. The conditions are likely similar to those found on the early Earth before the build-up of oxygen. They also share characteristics with the experiments of Miller & Urey (1959) who demonstrated that complex organics can be synthesised by the irradiation of mixtures of simple gases in a reducing environment. Titan therefore provides an ideal laboratory in which the chemistry and synthesis of complex organics and prebiotic molecules can be explored.
Our knowledge of the composition of Titan's atmosphere has been greatly enhanced by observations by Cassini and ALMA. In particular, several molecules with three carbon atoms have been observed in Titan's atmosphere, including CH 3 C 2 H, C 3 H 6 (Lombardo et al. 2019a;Nixon et al. 2013;Magee et al. 2009), and C 3 H 8 (Lombardo et al. 2019a;Nixon et al. 2013;Vinatier et al. 2010), and recently two more -cyclopropenylidene (c-C 3 H 2 ) (Nixon et al. 2020) and propadiene (CH 2 CCH 2 ) (Lombardo et al. 2019b) -have been added to the list. Additionally, ions with m/z corresponding to C 3 H + 3 and C 3 H + 5 have been observed by Cassini/INMS (Mandt et al. 2012). These observations provide good constraints on the modeling of the C 3 H n species which are important for controling the abundance of larger molecules such as benzene.
In this paper we focus on the chemistry of C 3 hydrocarbons. These have previously been modeled by Hébrard et al. (2013), Li et al. (2015) and Vuitton et al. (2019). In the light of the new detection of c-C 3 H 2 (Nixon et al. 2020) we revisit their chemistry and update our previous model (Li et al. 2015;Willacy et al. 2016) to include the isomers of C 3 H 2 and C 3 H, and ion-molecule chemistry. We discuss these updates in Section 2. We present our results and compare them to the observations in Section 3. Finally, we discuss the results and conclusions in Section 4.

MODELS 2
We use the Caltech/JPL coupled photochemical/transport model, KINETICS (Allen et al. 1981;Yung et al. 1984). The model solves the mass continuity equation from Titan's surface to 1500 km altitude where n i is the number density of species i and P i and L i are the production and loss rates respectively. φ i is the vertical flux of species i calculated from where D i and H i are the molecular diffusivity coefficient and the scale height of species i, H α is the atmospheric scale height, α i is the thermal diffusion coefficient of i, T is the temperature and K zz is the eddy diffusion coefficient. We use the values of K zz derived by Li et al. (2014): where z 1 = 120 km, z 2 = 300 km, z 3 = 500 km and z 4 = 1000 km. The atmospheric density and temperature profiles are also taken from Li et al. (2015), and are based on the T40 Cassini flyby (Westlake et al. 2011).
The aerosols in our model both absorb radiation and provide surfaces for condensation. Their mixing ratio and surface area as a function of altitude are taken from Lavvas et al. (2010). The properties were derived from a microphysical model validated against Cassini/Descent Imager Spectral Radiometer observations. To calculate the absorption of UV by dust we assume absorbing aerosols with extinction cross-sections that are independent of wavelength (Li et al. 2014(Li et al. , 2015. The chemical network has been extended to include the isomers of C 3 H and C 3 H 2 using the networks of Hébrard et al. (2013) and Loison et al. (2017). Additionally, ion-molecule chemistry has been added with reactions from Vuitton et al. (2019) and the astrochemical databases UMIST12 , and KIDA . The full list of species is given in Table 1 and the reaction network can be found in Appendix A.
The rate coefficients for photodissociation of the isomers of C 3 H, C 3 H 2 are taken from Hébrard et al. (2013). Rate coefficients for other photodissociation and photoionization processes are taken from the standard KINETICS database.

Boundary conditions
The lower boundary of our model is the surface of Titan and the upper boundary is at 1500 km. For H and H 2 the flux at the lower boundary is zero and at the top of the atmosphere these species are allowed to escape at their Jeans escape velocity of (2.5 × 10 4 cms −1 and 6.1 × 10 3 cms −1 respectively). For all other neutral gaseous species the concentration gradient at the lower boundary is assumed to be zero, while they have zero flux at the top boundary. Ions have a mixing ratio of zero at z = 0 km, and at the upper boundary their flux is zero.
The mixing ratio of N 2 is held fixed at 0.95 at all altitudes. The mixing ratio of CH 4 is fixed to the observed (super-saturated) values (Niemann et al. 2010) below the tropopause and allowed to vary above this.

C 3 H 2
C 3 H 2 can exist in three forms: c-C 3 H 2 , (cyclopropenylidene), l-C 3 H 2 (propadienylidene) and t-C 3 H 2 (propynylidene). The cyclic form, the most abundant isomer, was recently identified for the first time in Titan's atmosphere by Nixon et al. (2020). The molecule was detected by observations taken in 2016 and 2017 with column densities of 3-5 × 10 12 cm −2 and 1-2 × 10 12 cm −2 for the two epochs respectively. t-C 3 H 2 and l-C 3 H 2 remain undetected.
Our model includes all three structural isomers and their predicted mixing ratios are shown in Figure 1. The mixing ratio of c-C 3 H 2 is in excellent agreement with the best fit vertical abundance profile derived by Nixon et al. (2020). The model column density of this molecule (N(c-C 3 H 2 ) = 2.6 × 10 12 cm −2 ) is consistent with that observed. Similar column densities were predicted by the models of Vuitton et al. (2019) (for a single C 3 H 2 isomer) and Hébrard et al. (2013) (who considered the three isomers as separate species). The predicted column densities of the other two isomers are lower, with N(l-C 3 H 2 ) = 1.6 × 10 11 cm −2 and N(t-C 3 H 2 ) = 6.9 × 10 9 cm −2 . The main production and loss reactions for c-C 3 H 2 and their rates are shown in Figure 2. The important reactions vary with altitude, with electron recombination of c-C 3 H + 3 (R1159) and C 3 H + 5 (R1183) dominating above 1200 km and isomerization of l-C 3 H 2 (R22) and t-C 3 H 2 (R23) by reaction with H atoms below this. Photodissication of CH 2 CCH 2 is important at all altitudes. The reaction between CH and C 2 H 2 also forms c-C 3 H 2 above 500 km: Additional formation below 600 km is provided by Destruction above 600 km is by photodissociation forming c-C 3 H, l-C 3 H, and C 3 , and by reaction with CH 3 Photodissociation and reaction with CH 3 continue to be important below 600 km, but at these altitudes destruction also occurs via and For l-C 3 H 2 the formation processes are similar to c-C 3 H 2 , with recombination of C 3 H + 5 (R1184) important at high altitudes, along with photodissociation of CH 2 CCH 2 and CH 3 C 2 H (at all altitudes). Neutral-neutral reactions play a role below 1000 km (see Figure 3).
Destruction is dominated by reaction with hydrogen atoms forming c-C 3 H 2 at all altitudes. Below 400 km reaction with CH 3 and C 2 H 3 can also destroy l-C 3 H 2 (Figure 3) The chemistry of t-C 3 H 2 is different. It forms by with a major contribution from recombination of electrons with c-C 3 H + 3 and c-C 3 H + 5 above 800 km. Destruction at all altitudes is by reaction with H atoms to form c-C 3 H 2 . The production and loss rates are shown in Figure 4.
We will briefly discuss the peak structure seen in the abundance of c-C 3 H 2 and l-C 3 H 2 at 600 km in Figure 1. A major contributor to this feature is the reaction of C 3 and H 2 forming l-C 3 H and c-C 3 H which subsequently react with H 2 to form c-C 3 H 2 and l-C 3 H 2 at this altitude. The rate of this reaction is uncertain. Here we use an estimated value of 8.0 × 10 −12 e (−1420/T ) cm 3 s −1 from . Changes to this rate might reduce the size of the peak in the abundance of the C 3 H 2 isomers. In addition, there is a stagnant layer in the vertical transport, as manifest in a minimum in the value for K zz in Section 2 (see also the red line in Fig. 4 of Li et al. 2014). Both of these factors contribute to the increase in c-C 3 H 2 seen at this altitude.

Chemistry of C 3 H 4 -propadiene and methylacetylene
Both propadiene (CH 2 CCH 2 ; also known as allene) and methylactyelene (CH 3 C 2 H) have been observed in Titan's stratosphere (Lombardo et al. 2019a,b;Nixon et al. 2013;Vinatier et al. 2010). In addition, CH 3 C 2 H 2 was observed using Cassini/UVIS (UltraViolet Imaging Spectrometer) (Cui et al. 2009;Magee et al. 2009). The models over predict the abundances of these two molecules by a factor of a few ( Figure 5) in the lower atmosphere.
Since there is only a small difference in enthalpy between CH 3 C 2 H and CH 2 CCH 2 (∼ 1 kcal mol −1 ; Rogers and McIafferty 1995) their formation and loss rates are expected to be similar. Their main formation route is with other important reactions being Yung et al. (1984) suggested isomerization as a way to convert CH 2 CCH 2 into CH 3 C 2 H and this is the major route to CH 3 C 2 H throughout much of the atmosphere: Additionally, CH 3 C 2 H is also formed above 800 km by electron recombination of C 3 H + 5 and below 500 km by CH 2 CCH 2 is also formed by photodissociation of C 3 H 5 . The formation reactions of CH 3 C 2 H and CH 2 CCH 2 are summarized in Figure 6. Destruction of both molecules (Figure 7) is by photodissociation at high altitudes, forming c-C 3 H 2 and l-C 3 H 2 . In this region both molecules are also destroyed by reaction with HCNH + Below 600 km both molecules are destroyed by reaction with H atoms, with CH 2 CCH 2 undergoing isomerization, and (in a three-body reaction) both molecules forming C 3 H 5 :  Propylene (C 3 H 6 ) has been observed by Lombardo et al. (2019a), Nixon et al. (2013) and Magee et al. (2009). The model produces fractional abundances in good agreement wih the observations both in the lower atmosphere (below 400 km) and at ∼ 1000 km ( Figure 8).
The main production and destruction reactions are shown in Figure 9. Below 400 km production is dominated by Between 400 and 600 km the main production route is by photodissociation of C 3 H 8 , and above this reactions with CH and C 3 H + 7 dominate: CH + C 2 H 6 −→ C 3 H 6 + H (R88) At high altitudes (> 800km) destruction is by reaction with HCNH + forming HCN, and by Photodissociation forming C 2 H 2 , C 2 H 3 and C 3 H 5 is important at most altitudes. Below 400 km the main loss processes are .
The predicted abundance distribution of C 3 H 8 is in excellent agreement with the observations of Vinatier et al. (2010); Lombardo et al. (2019a) and Nixon et al. (2013) (Figure 10). In the upper atmosphere the models are in agreement with the INMS upper limits (Cui et al. 2009;Magee et al. 2009). The main production and loss reactions of propane are shown in Figure 11. Production is by and while destruction is mainly by photodissociation with an additional contribution from reaction with H atoms forming C 3 H 7 . Below 400 km C 3 H 8 reacts with NH 2 to form NH 3 and C 3 H 7 (R291).
3.5. C 3 H 3 and C 6 H 6 Although not observed the propargyl radical plays a crucial role in the formation of benzene ( Figure 12). Its peak abundance is 2.5 × 10 −6 at 1050 km and it is produced by the photodissociation of CH 2 CCH 2 , CH 3 C 2 H, 1-C 4 H 6 , 1,2-C 4 H 6 and 1,3-C 4 H 6 at all altitudes ( Figure 13). These are supplemented by the recombination of C 3 H + 5 with electrons at altitudes above 1000 km as well as Below 800 km it can also form by reaction of H and c-C 3 H 2 .
Above 1000 km reactions with N dominate Benzene is formed from neutral-neutral reactions involving C 3 H 3 , and this is the main formation route throughout much of the atmosphere below 1000 km. The abundance of benzene therefore provides a test of the model predictions of the C 3 H 3 radical. Figure 14 shows the predicted benzene abundance with the measured abundances retrieved from UVIS observations (Fan et al. 2019). The model provides a good fit to the observations at all altitudes, suggesting that our model also correctly describes the chemistry of the propargyl radical.
Above 1000 km ion chemistry is important for benzene formation through the recombination of C 6 H + 7 with electrons.
Destruction of benzene is by photodissociation forming C 6 H 5 , C 2 H 2 and C 3 H 3 . The major reactions involved in the benzene chemistry predicted by this model are consistent with the models of Vuitton et al. (2008) and Lavvas et al. (2008a,b).

Ions
The ion chemistry is initial by photoionization of N 2 and CH 4 forming N + 2 , N + and CH + 4 . Reactions of these ions drive the ion chemistry. The formation of ions involved in the C 3 H n chemistry is shown in Figure 15.
Ion observations are available in the upper atmosphere Cassini/INMS (Mandt et al. 2012). This provides the total number density of ions of a particular mass/charge ratio, but cannot distinguish between ions of a given mass. Figure 16 shows the predicted and observed number densities of ions with m/z = 14 (N + and CH + 2 ), 28 (N + 2 , HCNH + and C 2 H + 4 ), 39 (l-C 3 H + 3 , and c-C 3 H + 3 ) and 41 (C 3 H + 5 ). The observations cannot distinguish between different ions of the same mass, but the figure shows that the total abundance of ions with each mass is in good agreement with the observations.

DISCUSSION AND CONCLUSIONS
It is a tribute to the recent advances in remote sensing that we are now able to detect species such as cyclopropenylidene with mixing ratios on the order of parts per billion by volume (10 −9 ) in the mesosphere of Titan, or column densities on the order of 10 12 molecules cm −2 . Multiple in-situ and remote sensing techniques contribute to the detection of benzene. At the top of the atmosphere, in the thermosphere and ionosphere, we have measurements from Cassini-Ion and Neutral Mass Spectrometer (INMS) (Waite et al. 2007). In the mesosphere, we have Cassini-UVIS remote sensing of benzene (Fan et al. 2019). In the stratosphere we have mid-infrared data from Cassini Composite Infrared Spectrometer (CIRS) (Flasar et al. 2005;Coustenis et al. 2007;Vinatier et al. 2010). Finally, we have Cassini-Huygens Gas Chromatograph Mass Spectrometer (GCMS) measurements at the surface from the probe (Niemann et al. 2005).
Our model provides excellent agreement with the available data for the abundances of the C 3 hydrocarbons. It reproduces the column density of c-C 3 H 2 to within a factor of 3, as well as its extracted distribution with altitude. The abundances of C 3 H 6 and C 3 H 8 are also well-matched, although the models over predict the abundances of propadiene and methylacetylene in the lower atmosphere by factors of a few. The abundance of benzene is also in good agreement with the abundances derived from the UVIS observations. Since benzene forms mainly from reactions of C 3 H 3 this suggests that the model predictions of this (unobserved) precursor molecule are also reasonable. The possibility that the detection of benzene at the surface of Titan may require a new production mechanism that is different from the  ion chemistry and C 3 H 3 chemistry studied in this paper was suggested by (Zhou et al. 2010). These authors propose a solid-phase chemistry driven by cosmic rays, which effectively convert acetylene to benzene However we notice from Figure 14 that the standard gas phase mechanism is capable of generating a benzene mixing ratio of 10 −9 . A definitive value of benzene from the GCMS experiment is needed to confirm whether this additional cosmic ray driven mechanism is justified. The successful modeling of benzene opens up the exciting possibility of forming polycyclic aromatic hydrocarbons (PAHs) in planetary atmospheres. This possibility was first suggested by Wong et al. (2000Wong et al. ( , 2003 for the polar region of Jupiter. This type of chemistry could eventually lead to the production of dark aerosols (Zhang et al. 2013). Recent advances in experimental and theoretical studies of the formation of multi-ringed species (Yang et al. 2021) confirmed our earlier speculations, opening up new avenues of investigation for the planets in our Solar System and early Earth (Berry et al. 2019).