Investigation of Titan's South Polar HCN Cloud during Southern Fall Using Microphysical Modeling

The southern 300 km cloud was first detected by multiple instruments on the Cassini spacecraft on 2012 May 6, or approximately L_s = 33° (Le Mouelic et al. 2012; West et al. 2013, 2016). The cloud was not detected in earlier (2011 September 11) Cassini measurements (West et al. 2016). Spectral data from VIMS shortly after the cloud appeared include two spectral peaks from solid HCN (de Kok et al. 2014). The cloud remains visible in ISS images until at least mid-2016 (see, e.g., ISS image W1848110699) and in VIMS imagery until the end of the mission (Le Mouélic et al. 2018). Subsequent measurements reveal the equatorward expansion of a spectral peak from HCN ice (Le Mouélic et al. 2018), indicating that the extent of the cloud increased from 75°S in 2013 to 58°S by 2017 April (L_s = 883). However, because radiative transfer analyses have not been performed, the altitude and microphysical properties of the condensate between 2013 and 2017 are not known (Anderson et al. 2018b).

Despite the abundant imagery of the cloud, there are few quantitative constraints on the cloud properties, and those that are available are only from a limited time period. Specifically, de Kok et al. (2014) and West et al. (2016) have placed quantitative constraints on four variables between 2012 May and 2013 July (L_s = 33°–45°): cloud-top altitude; effective particle radius, r_eff; cloud number mixing ratio, N_mr; and cloud vertical optical depth, τ_v . Available estimates place the cloud-top altitude at around 300 km, with de Kok et al. (2014) determining the top to be 300 ± 70 km (where the uncertainty is limited by the resolution of the VIMS imagery) and West et al. (2013, 2016) estimating top altitudes of 300 km, with uncertainty of ±10 to ±20 km, in ISS images along the limb from 2012 May 6 (L_s = 331) through 2013 April 16 (L_s = 440).

These studies also provided estimates of the effective radius and vertical optical thickness of the cloud. From radiative transfer retrievals of ISS and VIMS data, de Kok et al. (2014) constrain the cloud particle effective radius to 0.6–1.2 μm, while West et al. (2016) estimate an effective radius of 1–5 μm. The VIMS imagery analyzed by de Kok et al. (2014) captures the cloud on 2012 June 7 (L_s = 34°) from an oblique angle nearly tangent to Titan's surface at the south pole such that the cloud appears "detached" from the surface (see their Figure 2). West et al. (2016) show using ISS imagery that the cloud forms at the same location as the detached haze layer, leaving a similar gap between the cloud and the opaque lower-stratosphere haze in 2012 May (L_s = 33°; their Figure 2), 2012 June (L_s = 34°), and 2013 April (L_s = 44°; their Figure 5(c)). De Kok et al. (2014) derive a slanted-path optical thickness (0.09 ± 0.006 at 2.7 μm) from their measurement of the cloud's reflectance, and then they estimate the vertical optical thickness of 0.01–0.07 (at 0.9 μm) by assuming the depth of the cloud is "ten times smaller than the length of the slanted path." Using nadir ISS images of the cloud captured on 2012 June 26 (L_s = 347), West et al. (2016) estimate a larger vertical optical thickness of 0.6–2.6 (at 0.889 μm), and they also note that the cloud is thin enough that surface features can be seen through it in VIMS imagery. The cloud number mixing ratio, tied to the radius, optical thickness, and assumptions of the cloud's spatial extent, was only estimated by de Kok et al. (2014), who reported a range from 10⁷ to 10⁸ kg⁻¹.

The cloud parameters from de Kok et al. (2014) and West et al. (2016) are summarized in Table 1. These apply to cloud observations between 2012 May and 2013 July (L_s = 33°–45°). Radiative transfer modeling of later observations of the cloud have not been published, so there is no additional information regarding the microphysical or macrophysical properties of the condensed HCN over this time period.

Since the detection of the 300 km cloud, other ices have been identified at a range of altitudes in the south polar stratosphere. Vinatier et al. (2018) identify signs of benzene condensation in the south polar stratosphere in 2013 May (L_s = 445) at 300 km and 2015 March (L_s = 652) between 170 and 250 km using CIRS mid-IR spectra. Additionally, the "Haystack" 221 cm⁻¹ spectral signature, originally detected by Voyager I in the northern hemisphere (Anderson et al. 2014, 2018b), was first detected in the far-IR by CIRS in the south polar stratosphere by Jennings et al. (2012) on 2012 July 24 (L_s = 356). Anderson et al. (2018b) later locate the Haystack stratospheric ice cloud signature in CIRS far-IR observations from 2015 July (L_s = 690) at an altitude of 110 km at 79°S. In the same far-IR data set, Anderson et al. (2018b) also identify a stratospheric ice cloud with a far-IR spectral signature consistent with co-condensed HCN:C₆H₆ (with a 1:4 mixing ratio) near 210 km, though the microphysical properties of this condensate remain unknown.

The atmospheric temperature and HCN vapor pressure are critical for understanding the formation and evolution of the HCN cloud. Unfortunately, there is an incomplete observational record of the south polar temperature and HCN vapor abundance. In particular, there are no CIRS retrievals of temperature profiles or HCN abundance near 300 km coincident with the appearance of the cloud. Full vertical profiles in southern high latitudes are available only well before the cloud was detected and at later dates when the cloud-top altitude has not been constrained.

Radiative transfer retrievals from 2011 June (L_s = 23°) and 2012 February (L_s = 31°) near 80°S reveal a slowly changing temperature profile below 300 km with cooling at higher altitudes, such that the temperature at 450 km decreased from around 180 K on 2011 June 20 to less than 160 K on 2012 February 19 (Vinatier et al. 2015). Further retrievals covering the full depth of the south polar stratosphere are not available until 2015 March (L_s = 66°). These retrievals reveal that substantial cooling occurred over this period, with the 300 km temperature dropping from 175 K to around 145 K (Teanby et al. 2017; Mathé et al. 2020; Vinatier et al. 2020). Retrievals during the remainder of the Cassini mission show a reversal of this cooling; the temperature near 300 km increases to 160 K by 2016 February, about L_s = 76° (Teanby et al. 2017, 2019), and 170 K by 2017 May 25, or L_s = 90° (Vinatier et al. 2020).

While there are no south polar temperature retrievals around 300 km during the period when the cloud top is estimated to be around this altitude, Vinatier et al. (2018) construct partial temperature profiles for data from 2013 May (L_s = 44°). Restricted to altitudes below 250 km, they find a cold region centered near 200 km south of 80°S with a minimum temperature of about 115 K. (Their retrievals also reveal large latitudinal gradients, with temperature at 83°S around 20 K cooler at 78°S.) Using this as an a priori with similar observations from 2014 April (L_s = 55°), Vinatier et al. (2018) find the same cold region near 180 km at nearly the same temperature.

Taken together, the above observations show a dramatic cooling of the south polar region in early southern fall occurring first in the upper stratosphere (above 300 km) and then later at lower altitudes (at and below 300 km). This cooling results in stratospheric temperatures dropping below 120 K before increasing again by the winter solstice.

Retrievals of HCN vapor abundance are available for the same periods as the temperature retrievals. These reveal an HCN volume mixing ratio near the stratopause (∼0.003 hPa, 450 km) increasing from ∼10⁻⁷ in 2010 January (L_s = 5°) to nearly 2 × 10⁻⁵ by 2012 February (L_s = 30°; Vinatier et al. 2015). The HCN mixing ratio is similar at about 4 × 10⁻⁵ when measured again in 2015 March (L_s = 65°; Vinatier et al. 2020), but by 2016 February, it has decreased to 2 × 10⁻⁵ (Teanby et al. 2017; Vinatier et al. 2020). Retrievals by Mathé et al. (2020) show a similar trend but find that HCN at 400 km never exceeds 10⁻⁵. At lower altitudes, there is a similar increase in south polar HCN from ∼10⁻⁷ to >10⁻⁵ between 2010 January and mid-2015 (Vinatier et al. 2015; Teanby et al. 2017; Mathé et al. 2020; Vinatier et al. 2020). Based on these observations, we interpret the observed 400 km HCN mixing ratio at L_s = 30° as 10⁻⁵ ≤ q₄₀₀ < 10⁻⁴.

TitanCARMA is a one-dimensional cloud microphysical and radiation model that has been used to simulate Titan clouds composed of a variety of different volatile species (Toon et al. 1992; Barth & Toon 2003, 2006; Barth 2017). The model can be used either in isolation or coupled to a dynamics model to simulate clouds and aerosol in two or three dimensions (Barth & Rafkin 2007, 2010; Barth 2010). For this work, we primarily use the microphysics module, but the radiation module is used to calculate particle extinction. TitanCARMA is described in detail by Barth (2017), so we provide a brief overview of the model here, focusing on aspects specific to this study.

In TitanCARMA, cloud and haze particles undergo coagulation and are transported vertically via gravity, eddy diffusion, and advection. The haze production rate is governed by a Gaussian function of altitude with a scaling factor, R (see Table 2). Cloud and haze particles are represented using an Eulerian bin scheme with 35 mass-doubling haze bins starting at a radius of 1.3 nm and 32 mass-doubling HCN bins with a minimum radius of 105 nm. HCN particles nucleate on haze particles via vapor deposition nucleation, and sublimating HCN particles return the haze nuclei to the haze distribution. A vertical velocity is imposed to represent the downwelling branch of the Hadley cell. The input parameter w sets the velocity value at 300 km, and velocities at other layers are scaled by the inverse of the air density.

Cloud particles nucleate heterogeneously on haze particles, according to the classical nucleation theory for vapor deposition (Pruppacher & Klett 2012), where the nucleation rate, J, follows an Arrhenius relationship:

$$\begin{eqnarray}&&J\sim {r}_{{\rm{H}}}^{2}\sqrt{{\rm{\Delta }}{F}_{g}}{e}^{\tfrac{-{\rm{\Delta }}{F}_{g}}{{k}_{b}T}}.\end{eqnarray} \tag{ 1 }$$

The energy term, ΔF_g (T, s, σ_IA, σ_IH), is the free energy of germ formation on a haze particle and a function of the temperature T, supersaturation s, and "nucleation parameter" m; r_H is the radius of the haze particle in question; and k_B is the Boltzmann constant. The nucleation parameter is the cosine of the contact angle θ and given by Young's relation,

$$\begin{eqnarray}&&m=\displaystyle \frac{{\sigma }_{\mathrm{AH}}-{\sigma }_{\mathrm{IH}}}{{\sigma }_{\mathrm{IA}}}=\cos \theta ,\end{eqnarray} \tag{ 2 }$$

where σ_AH is the surface free energy between air and haze, σ_IH between ice and haze, and σ_IA between ice and air. For a small contact angle, or m = 1, a thin layer of ice can condense onto a haze particle, lowering the nucleation energy barrier. On the other hand, in the case of a large contact angle, a larger volume of ice must condense to form a thermodynamically favorable nucleus. The free energy available for germ formation is related to the saturation ratio by ${\rm{\Delta }}F\propto \mathrm{ln}s$, meaning that for a given m, we can calculate a "critical" nucleation supersaturation, s_nuc, by setting J = 1 cm⁻² s⁻¹ and solving for s. While nucleation experiments have estimated s_nuc for methane, ethane, and butane ice on tholins (Curtis et al. 2005, 2008), there are no data available for HCN ice (Barth 2017). The saturation vapor pressure and latent sublimation enthalpy of HCN are calculated using the parameterizations from Fray & Schmitt (2009).

TitanCARMA solves the continuity equations for transport of vapor and particles based on the model boundary conditions and then iterates through the depth of the atmosphere calculating nucleation, growth, and sublimation of particle distributions at each level. Particles are restricted from crossing the model top, but they are allowed to exit the bottom of the model via transport by gravity, advection, or eddy diffusion. Vapor has a constant flux boundary condition, f, at the top of the model and a constant-concentration boundary condition at the bottom of the model. Every simulation uses the same vertical grid, with 230 layers 2 km thick from an altitude of 30 to 490 km, significantly higher than the observed cloud-top altitude. We choose a baseline value of s_nuc = 35% following Barth (2017), and we test the sensitivity to this parameter by running additional simulations with s_nuc = 5%. Similarly, we choose a nominal HCN flux f₀ of 10 times the flux used by Barth (2017), which was estimated from Huygens measurements near the equator, in order to reflect the enhanced vapor concentrations observed in the polar fall (e.g., Teanby et al. 2017). Extinctions are calculated for a wavelength of 0.889 μm using the visible refractive index of 1.3 from Moore et al. (2010) and an imaginary refractive index of 5 × 10⁻⁴ from West et al. (2016). Sensitivity testing is discussed further in Sections 4 and 5.3.

We perform simulations using two configurations of TitanCARMA: a static temperature profile configuration and a seasonal configuration. Unlike the static configuration, the seasonal model configuration features a temperature profile that evolves with time to reflect seasonal changes on Titan. We discuss the details of these two configurations next.

Static model simulations are initialized with a temperature–pressure–altitude profile and a vapor flux through the top of the model. Environmental and boundary conditions are held constant, and the model is run until it converges. Since some simulations converge to an oscillatory state with periodic cloud formation and dissipation, as seen by Barth & Toon (2003; see their Figure 6), profile plots use the average output over a period of 3 Earth months. Most simulations are found to converge rapidly within 40 Earth yr (1.36 Titan yr). The parameters for the baseline simulation are listed in Table 2, and the temperature profiles and upper vapor flux are described in Section 4.

In order to simulate the seasonal cloud formation, we run TitanCARMA in a transient configuration, where the temperature profile is updated at each time step. These simulations take as input a series of temperature profiles paired with the time at which the atmosphere is to match each profile. At each time step, the temperature is set by linearly interpolating between successive temperature profiles. Although the temperatures at each altitude may change significantly in these simulations, the pressure at each altitude is kept constant. Profiles are chosen to represent the changing temperatures throughout a single Titan year (29.46 Earth yr), and the model loops through the series of profiles to simulate consecutive years with identical temperature evolution. The model converges after 1 yr, which we identify as little or no difference in the output at a given L_s between consecutive years. We analyze the output from the third or later simulated Titan year. The temperature profiles and upper boundary vapor fluxes used in the transient simulations are described in Section 5.

Having shown that the model can simulate the key observed features of the cloud at L_s = 30°, we now examine the seasonal evolution of the cloud. To simulate this seasonal evolution, we need to prescribe the evolution of the stratospheric temperatures over a Titan year. As discussed in Section 2, observations of polar temperatures are only available at certain times, so we form an estimate of the annual evolution based on a combination of these measurements and the modified temperature profile from Section 4. Polar stratospheric temperature observations are not available at L_s = 30°, when the 300 km cloud was observed, so we use the modified ΔT = 50 K profile described in Section 4, for which the steady-state model produced the observed cloud features. Temperature profiles at other times are based on observations. The profiles representing L_s = 0°, 10°, 85°, 150°, and 265° are taken from the interpolated retrieval data of Teanby et al. (2019), while for L_s = 65°, we use a temperature profile retrieved by Vinatier et al. (2020) from observations at L_s = 658 and 859S. This profile is nearly identical to the revised retrieval from 87°S in Dubois et al. (2021). Since both temperature profiles from polar latitudes at L_s = 65° include a cold layer between 150 and 200 km (Vinatier et al. 2020), we assume that the cold layer at 300 km simply descends throughout southern fall until it reaches the cold lower stratosphere. To simulate this descent, we fit the L_s = 30° and 65° temperature profiles using splines and construct several intermediate temperature profiles (dotted lines in Figure 2). As the simulation runs, TitanCARMA sets the instantaneous temperature profile by linearly interpolating the specified temperature profiles in time. Atmospheric cooling from the start of the year to L_s = 30° is nearly linear between about 250 and 350 km, with a maximum cooling rate near 300 km of about 0.11 K day⁻¹.

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The evolution of atmospheric and cloud variables for this simulation is shown in Figure 3, and profiles from select times are in Figure 4. A layer of lower-stratosphere HCN cloud persists throughout the year around 100 km (see Figure 3 at L_s = 15° and 0°), which is consistent with prior measurements (e.g., Samuelson et al. 2007; Anderson & Samuelson 2011) and microphysical modeling (Lavvas et al. 2011; Barth 2017). HCN first condenses just below 300 km at L_s = 221, where the temperature reaches 120 K, but the cloud remains relatively thin until about L_s = 26°, when temperatures drop below 110 K and the supersaturation grows large enough to efficiently nucleate HCN ice (see Figures 3(c), (f), and (g) and the L_s = 24° and 30° lines in Figure 4).

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Initial cloud formation is marked by nucleation of a small number of particles that grow rapidly, resulting in effective radii greater than 10 μm. These particles soon fall out of the cold layer, encounter warmer temperatures, and rapidly sublimate, effectively transporting vapor to lower altitudes (see vapor mixing ratio, q_mr, in Figure 4) and leaving the cloud separated or "detached" from the lower-stratospheric cloud by a 150 km deep layer of low extinction (see Figures 3(f) and 4). A similar low-extinction layer appears in imagery from both VIMS (de Kok et al. 2014, their Figure 2; from 2012 June, L_s = 34°) and ISS (West et al. 2016, their Figures 2 and 5(b); with images from 2012 June and 2013 April, L_s = 44°). While the timing of the low-extinction layer in the simulation does not match the observations, these results demonstrate that a cold layer in the upper stratosphere can produce detached cloud consistent with observations. The cloud remains detached until about L_s = 26°, when the stratosphere below 200 km becomes saturated. Once the below-cloud temperature drops beneath the freezing point, cloud particles no longer sublimate but instead fall all the way to the troposphere. Since there is abundant vapor below the cloud, the first particles to reach lower altitudes grow very large, with effective radii >20 μm by the time these particles reach the troposphere (see r_eff at L_s = 30° in Figure 4). This population of particles produces a local maximum extinction near 150 km at about L_s = 30°, or about 2.5 yr into the simulation (see Figure 3, panel (c) for N_mr and panel (e) for extinction). When stratospheric cooling ceases at L_s = 30°, there is less excess vapor available, and particle sizes at the tropopause steadily decrease.

The temperature minimum near 300 km and L_s = 30° produces a second population of particles nucleated primarily between 300 and about 330 km, where the temperature drops below 120 K. This nucleation event produces many more particles than the initial nucleation, but the increased competition for vapor results in the particles remaining small, with effective radii of <3 μm (Figures 3(d) and 4). These particles fall more slowly, producing the extinction maximum just above 200 km after L_s = 30° (Figures 3(e) and 4). Particles continue to nucleate near 120 K as the low-temperature region descends, but the effective radii stay below 5 μm throughout the upper half of the cloud's depth. Although the temperature below the cloud top continues to decrease, the remaining vapor is insufficient to produce large particles after the initial population precipitates into the troposphere. The simulated 0.889 μm optical thickness of the cloud peaks at about 0.15 at L_s = 30° (the maximum optical thickness at 2.7 μm is about 0.17 at the same time). This is between the estimates by de Kok et al. (2014) and West et al. (2016; see Table 1), which differ by a factor of 100.

The HCN column mass (see Figure 5) increases during the beginning of the year until cloud formation, reaching a maximum of 1.27 g m⁻² about 1 Earth yr into the simulation, or L_s = 12°, and shortly after, the temperature begins decreasing throughout the stratosphere (see Figure 2). Cloud condensation and subsequent precipitation result in the rapid removal of HCN from the stratosphere, illustrated in Figure 5, which culminates in the minimum total HCN column mass of 0.225 g m⁻², less than a quarter of the maximum, at about 5.7 Earth yr, or L_s = 67°. Nearly half of the annual precipitation out of the stratosphere occurs during the initial cooling period between L_s = 10° and 30°, as the precipitation rate decreases once the stratosphere begins to warm. The HCN column minimum occurs just after the cold layer begins to rapidly warm (L_s = 65° profile in Figure 2). By the winter solstice (L_s = 90°, 7.8 Earth yr), the cold layer becomes indistinguishable from the steep temperature inversion in the lower stratosphere, and HCN condensation is restricted to altitudes at or below 120 km, though the optical thickness of HCN remains >10⁻² until nearly L_s = 130° (not shown). This is consistent with earlier observations by Samuelson et al. (2007), who found HCN cloud below 160 km during north polar winter (2005 March 31, equivalent to L_s = 123° in the southern hemisphere). Furthermore, Mathé et al. (2020, their Figure 12) find that HCN vapor above 200 km is depleted in early northern winter but gradually replenishes between 2005 (L_s = 301°) and 2011 (L_s = 28° of the next year), consistent with the simulated total HCN vapor column (Figure 5). In summary, the HCN column increases until cloud formation begins in early fall, at which point precipitation rapidly removes the majority of the HCN. Precipitation effectively ceases by about L_s = 65°, and by L_s = 90°, the HCN cloud is restricted to the lower stratosphere, allowing HCN vapor at higher altitudes to replenish throughout the rest of the year.

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The previous subsection shows that the simulated cloud is consistent with measurements given the following parameters: ΔT = 50 K, f = f₀, s_nuc = 35%, w₃₀₀ = 0 m s⁻¹, and K_diff = K_T92 (see Table 2). In order to test the sensitivity of the model to changes in these parameters, we ran further simulations using different combinations of these additional values: ΔT = 40 or 30 K, f = 0.1 × f₀ or 10 × f₀, s_nuc = 5%, w₃₀₀ = −2 or −0.2 mm s⁻¹, and K_diff = 5 × K_T92 or 0.2 × K_T92 (all simulations relevant to this publication are tabulated in Table 3). All simulations were run for 4 or more Titan yr, and we use the last year for analysis. These additional simulations show that the primary conclusions from Section 5.2 are insensitive to these parameters; the cloud always forms by L_s = 30° and descends, following the cold layer, until it reaches the lower stratosphere around L_s = 60°, and precipitation always removes over half of the total column mass of HCN during the fall season. The output for the f = 0.1 × f₀ simulation is shown in Figures 6 and 7 as an example. Versions of Figures 3, 4, and 5 for each simulation are archived along with the simulation output in the Johns Hopkins data repository.

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5.3.1. Cold Layer Temperature

5.3.2. Vapor Flux

The rate and timing of the maximum precipitation intensity, the duration of the detached period, and the vertical optical thickness all depend on the vapor flux (see Figure 8(b)). Lower f corresponds with a delay in the peak precipitation from 2.3 Earth yr (L_s = 28°; see Figure 8) to 3–4 Earth yr (L_s = 36°–48°), while with f = 10 × f₀, the peak precipitation occurs earlier, between 1.7 and 2 Earth yr (L_s = 21°–24°). Similarly, lower f causes delayed cloud formation and extends the detached period from less than half an Earth year (see Figure 3(f)) to close to a full Earth year (Figure 6(f)), though with smaller vertical optical thickness.

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5.3.3. Nucleation Efficiency

5.3.4. Subsidence

5.3.5. Eddy Diffusivity

5.3.6. Comparison with Observations

As predicted by de Kok et al. (2014), we find that the formation of the 300 km south polar cloud requires temperatures far colder than contemporaneous measurements and that these conditions result in the majority of the vapor being rapidly removed from the stratosphere. We model the observed cloud by introducing a cold layer at 300 km, which then descends to the lower stratosphere. Although HCN condensation begins at higher temperatures, the observed cloud particle number mixing ratio, effective radius, and optical depth only occur at temperatures around T₃₀₀ = 97–107 K, which is 40–50 K lower than the minimum temperature observed at 300 km and about 15 K lower than the temperature estimated by de Kok et al. (2014). Using synthetic temperature profiles, measurements by Teanby et al. (2019), and temperature profiles retrieved by Vinatier et al. (2020) at 86°S and L_s = 658, we model the descent of a cold layer from its initiation at L_s = 30° until it reaches the cold lower stratosphere at L_s = 85°. The cloud is initially detached from the lower stratosphere by a deep low-extinction layer, where particles sublimate as they precipitate out of the supersaturated region. This low-extinction layer persists for a few Earth months before stratospheric cooling halts the sublimation of precipitating particles. Once precipitation from the cloud reaches the condensation in the lower stratosphere (L_s = 30° in Figures 3 and 4 and L_s = 36° in Figures 6 and 7), we find that precipitation from the ∼300 km deep cloud results in the rapid removal of the majority of the HCN in the stratosphere (see same times in Figures 5 and 8). By the winter solstice, HCN condensates exist only in the lower stratosphere, and HCN vapor is already being replenished throughout the rest of the stratosphere.

These conclusions are largely insensitive to changes in most model parameters. More efficient HCN nucleation (s_nuc = 5%) results in cloud formation at higher 300 km temperatures, though only the T₃₀₀ = 107 K (ΔT = 40 K) case is consistent with observations, as T₃₀₀ = 97 K (ΔT = 50 K) produces too many particles, and T₃₀₀ = 115 K (ΔT = 30 K) produces too few particles. Finally, weak downward motion of w₃₀₀ = −0.2 mm s⁻¹ can be offset with decreased HCN flux (f = 0.1 × f₀) for simulations to remain consistent with observations if we relax the lower constraint on the 400 km HCN vapor abundance, q₄₀₀. Thus, we conclude that our primary results are robust to the significant uncertainties in the temperature profile and microphysical properties of HCN and Titan's haze.

The rapid precipitation that we see in mid-fall may lead to HCN on the surface being concentrated in polar regions while also seeding tropospheric methane and ethane clouds and potentially enhancing precipitation that could contribute to the lakes and seas found in Titan's polar regions. Smaller HCN particles with slower fall speeds are less likely to serve as ice nuclei and may circulate throughout the troposphere before they reach the surface. Precipitation from clouds in the upper stratosphere expedites the transport of HCN vapor from the upper atmosphere to the surface and may prevent its circulation and condensation throughout the rest of the stratosphere. Although we focused on HCN, it is possible that other volatile species could be similarly affected by precipitation, which complicates the use of volatiles as tracers during polar winter. A scarcity of polar CIRS observations between 2012 and 2017 limits our understanding of how the abundances of these gases evolve throughout the season, but observations just before the end of the Cassini mission in 2017 reveal dramatic decreases in the stratospheric abundances of several volatile species (Coustenis et al. 2020; Vinatier et al. 2020). Precipitation may explain better than chemical lifetime or circulation patterns why the stratospheric HCN concentration increases less than concentrations of other trace gases during polar fall (see, e.g., Teanby et al. 2019; Sharkey et al. 2021, their Figures 4(n) and 15, respectively). Since concentration gradients in volatiles such as HCN and HC₃N are frequently used to infer atmospheric circulation patterns (e.g., Teanby et al. 2019; Coustenis et al. 2020; Vinatier et al. 2020), a better understanding of precipitation in polar winter is critical for understanding polar vortex dynamics.

Several areas deserve further study, including observational verification of the simulated cloud evolution, model and laboratory studies of the impact of simultaneous condensation of multiple species, and cloud microphysical simulations that include other atmospheric processes like radiation and convection. While Le Mouélic et al. (2018) catalog several VIMS multispectral images of the cloudy south polar region during southern fall and show HCN ice signatures, no radiative transfer analysis of these images revealing macro- or microphysical cloud properties has been published to date. Analysis of these VIMS data between 2014 and 2017 could reveal the optical thickness, cloud-top altitude, and microphysical properties of the HCN cloud and potentially other condensates. Additional details regarding the evolution of the cloud in south polar fall are necessary to better understand the impact of the cloud on the radiative and volatile budgets, as well as the polar circulation. In addition to HCN, there is evidence of condensed C₆H₆, HC₃N, and C₄N₂, as well as ice composed of multiple co-condensed compounds, in polar fall and winter clouds (Coustenis et al. 1999; Anderson & Samuelson 2011; Anderson et al. 2014, 2018a, 2018b; Vinatier et al. 2018). Stratospheric microphysical cloud models up to now have only included the condensation of individual volatile species (Barth 2017; Dubois et al. 2021), entirely neglecting potential interspecies interactions. Future modeling work should explore the implications of simultaneous condensation of multiple species, as well as co-condensation as mixed crystals. Finally, despite evidence of significant radiative cooling (e.g., Teanby et al. 2017) and convective motions (West et al. 2013, 2016), the present work excludes cloud radiative, convective, and dynamic interactions. Integration of condensation into dynamical models, including Titan global circulation models, will be critical for understanding the role of clouds and condensation in Titan's polar stratosphere.