# An intense thermospheric jet on Titan

E. Lellouch, M. Gurwell, R. Moreno, S. Vinatier, D. Strobel, A. Moullet, B.

Butler, L. Lara, T. Hidayat, E. Villard

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

## To cite this version:

E. Lellouch, M. Gurwell, R. Moreno, S. Vinatier, D. Strobel, et al. An intense thermospheric jet on Titan. Nature Astronomy, 2019, 3 (7), pp.614-619. 10.1038/s41550-019-0749-4. hal-03140289

HAL Id: hal-03140289

https://hal.science/hal-03140289v1

Submitted on 2 Oct 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_2.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
# An intense thermospheric jet on Titan

E. Lellouch<sup>1*</sup>, M. A. Gurwell<sup>2</sup>, R. Moreno<sup>1</sup>, S. Vinatier<sup>1</sup>, D. F. Strobel<sup>3,4</sup>, A. Moullet<sup>5</sup>, B. Butler<sup>6</sup>, L. Lara<sup>7</sup>, T. Hidayat<sup>8</sup> and E. Villard<sup>9</sup>

The presence of winds in Titan's lower and middle atmosphere has been determined by a variety of techniques, including direct measurements from the Huygens Probe<fnref n="1" /> over 0–150 km; Doppler shifts of molecular spectral lines in the optical, thermal infrared and millimetre ranges²⁻⁴, which together have probed the ~100–450 km altitude range; inferences from the thermal field over 10–0.001 mbar (that is, ~100–500 km)⁵,⁶; and inferences from central flashes in stellar occultation curves⁷⁻⁹. These measurements predominantly indicated strong prograde winds, reaching maximum speeds of ~150–200 m s⁻<fnref n="1" /> in the upper stratosphere, with important latitudinal and seasonal variations. However, these observations provided incomplete atmospheric sounding; in particular, the wind regime in Titan's upper mesosphere and thermosphere (500–1,200 km) has remained unconstrained so far. Here we report direct wind measurements based on Doppler shifts of six molecular species observed with the Atacama Large Millimeter/submillimeter Array (ALMA). We show that contrary to expectations, strong prograde winds extend up to the thermosphere, with the circulation progressively turning into an equatorial jet regime as the altitude increases, reaching ~340 m s⁻<fnref n="1" /> at 1,000 km. We suggest that these winds may represent the dynamical response of forcing by waves launched at upper stratospheric/mesospheric levels and/or of magnetospheric-ionospheric interaction. We also demonstrate that the distribution of the hydrogen isocyanide (HNC) molecule is restricted to Titan's thermosphere above ~870 km altitude.

Observations of Titan were conducted on 2016 July 22 and August 18/19 with ALMA. The period corresponded to Titan's northern late spring (solar longitude ~80°). Observations altogether covered a fraction of the 329–364 GHz range, by means of three scheduling blocks, each associated with a frequency set-up (see details in Supplementary Information). ALMA was at that time in a moderately extended configuration (C40-5), providing angular resolutions of ~0.16”–0.23” (‘natural weighting’), to be compared with an angular size of 1.0”–1.05” for Titan and its ~1,000-km-thick atmosphere. The spectra, taken at spectral resolutions of 1–2 MHz, include the rotational signatures of nine molecular species (CO, HCN, HNC, HC₃N, CH₃CN, C₂H₅CN, C₂H₃CN, CH₃CCH and C₃H₈, some of them with several isotopologues), mostly present in emission owing to their being formed in Titan's stratosphere. As expected from radiative-transfer model calculations, spectral signatures (see examples in Supplementary Fig. 2) are most apparent at the limb, owing to the gain in path and the decrease of the N₂ continuum. In addition, as already seen in previous ALMA and

other datasets<sup>4,10,11</sup>, most molecular emissions show non-uniform distributions across the disk. This results from the combined effects of latitudinal variations of temperature<sup>5,6</sup> and composition and of the observing geometry. Our data thus bear information on the 3D temperature and composition fields, complementing the Cassini results<sup>1,2,13</sup> for some of the molecules (CO, HCN, HC₃N, CH₃CCH) and providing new information for others.

Six molecules (HCN, DCN, HNC, HC₃N, CH₃CN and CH₃CCH) were further observed at a high spectral resolution of ~60 kHz (~280 kHz for CH₃CCH) to map their precise line-of-sight (LOS) central frequencies. As exemplified in Fig. 1 for HNC and CH₃CN, strong blueshifts (redshifts) are evident at beam positions centred on Titan's east (west) equatorial limbs at 425 km altitude. These shifts correspond to a beam-integrated limb-to-limb speed difference of ~490 m s⁻<fnref n="1" /> for HNC and ~400 m s⁻<fnref n="1" /> for CH₃CN. This is much larger than Titan's solid rotation (16 m s⁻<fnref n="1" /> at 1,000 km altitude) and implies very fast prograde winds. Maps of these Doppler winds are shown in Fig. 2 for all six species (including separate fits for the components of the HCN hyperfine triplet), based on Gaussian fits of the line central frequencies at all beam positions with sufficient line signal (see details in Supplementary Information). For most molecules, wind information is restricted to regions at or beyond the Titan limb, as emission features are too weak in nadir geometry. A prominent exception is CH₃CN, for which the strong extended emission and the availability of three lines enable LOS wind measurements over the entire disk with an accuracy of ~6–8 m s⁻<fnref n="1" />. For other molecules, LOS wind errors (at/beyond limb) are 6–8 m s⁻<fnref n="1" /> for HC₃N and HCN, 12–20 m s⁻<fnref n="1" /> for HNC, and 30–50 m s⁻<fnref n="1" /> for CH₃CCH and DCN which exhibit weaker and broader lines.

Very strong prograde winds are seen in all species, with maximum measured LOS winds of 250–350 m s⁻<fnref n="1" />, and even the less precise CH₃CCH and DCN winds confirm this picture. However, Fig. 2 reveals differences in the wind regime from the different species. HNC LOS speeds are strongest at the equator, forming a jet, with no hint of latitudinal asymmetry. In contrast, CH₃CN winds are enhanced in the southern (winter) hemisphere, as seen by the ‘widening’ of the iso-wind contours when moving from south to north. None of the studied molecules shows convincing evidence for meridional or day-to-night flows, with upper limits estimated to be 25–30 m s⁻<fnref n="1" />.

Assigning altitudes or pressure levels to these wind measurements relies on the ‘contribution functions’, themselves dependent on the local vertical distributions of temperature and abundances and the pointing geometry. Ultimately, this would require analysing our entire dataset in terms of the atmospheric thermal and composition

<footnote n="1">¹LESIA, Observatoire de Paris, Université PSL, CNRS, Sorbonne Université, Université Paris Diderot, Sorbonne Paris Cité, Meudon, France. ²Center for Astrophysics | Harvard & Smithsonian, Cambridge, MA, USA. ³Department of Earth and Planetary Sciences, Johns Hopkins University, Baltimore, MD, USA. ⁴Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD, USA. ⁵SOFIA/USRA, NASA Ames Research Center, Moffett Field, CA, USA. ⁶National Radio Astronomical Observatory, Socorro, NM, USA. ⁷Instituto de Astrofísica de Andalucía — CSIC, Glorieta de la Astronomía, Granada, Spain. ⁸Bandung Institute of Technology, Bandung, West Java, Indonesia. ⁹Joint ALMA Observatory, Alonso de Cordova, Vitacura, Santiago, Chile.
*e-mail: emmanuel.lellouch@obspm.fr</footnote>
<figure><img src="image_3.png" /><figcaption>**Fig. 1** | Evidence for zonal winds. **a,b,** Line profiles of CH₃CN (a) and HNC (b) at Titan east (+0.425°, 0″ from disk centre) and west (-0.425°, 0″ from disk centre) limbs, observed on 18 August 2016. These pointings correspond to a radial distance of ±3,000 km from disk centre (that is, a limb tangent altitude of 425 km above the surface). The reference zero frequencies are the rest frequencies of the CH₃CN *J*,*K* = 18,1 line (349.44699 GHz) and HNC (4–3) line (362.63030 GHz), respectively. Panel **a** also includes the CH₃CN *J*,*K* = 18,0 line at 349.45370 GHz. The limb-to-limb velocity difference is ~400 m s⁻¹ for CH₃CN and ~490 m s⁻¹ for HNC.</figcaption></figure>

3D field. For now, we have calculated typical contribution functions for equatorial nadir and limb conditions. Details of the procedure, involving inversion techniques for temperatures and abundances, are given in the Methods and Supplementary Information. Note that for species whose lines are mostly Doppler-broadened (HNC and HC₃N), the classical inversion technique based on line profile was complemented by the limb sounding capabilities offered by the data. This new approach provides us with a determination of the HNC profile in Titan's atmosphere, found to be essentially restricted to thermospheric levels above ~870 km altitude. This has important implications for models¹⁴; in particular, the lack of HNC in the stratosphere suggests that galactic cosmic rays play at most a minor role in Titan's HNC chemistry.

Equatorial profiles for all six species and the associated contribution functions are shown in Fig. 3. Together, the various molecules probe the entire atmosphere above 150 km, encompassing the mesosphere (300–800 km) and thermosphere (>800 km). The latter is best sounded by HNC, which probes 900–1,100 km, providing a direct zonal wind measurement in that part of Titan's atmosphere. CH₃CN, DCN and CH₃CCH sound the upper stratosphere/lower mesosphere at 150–400 km, while, owing to their steep slope and large thermospheric abundance, HCN (main line at 354.505 GHz) and HC₃N sound a broad region roughly centred at ~700 km and extending 200–300 km above and below, as detailed in the Methods. The difference in the sounded altitudes is consistent with the similarities and differences in the structure of the winds for the different molecules. Supplementary Fig. 6 shows LOS winds as a function of projected distance from Titan's rotation axis. Despite their larger uncertainties, winds inferred from DCN and CH₃CCH have a similar structure to those from CH₃CN. In contrast, HNC data show a distinct signature of high-speed winds at large projected distances from the polar axis, corresponding to the equatorial jet outlined above. Winds derived from HC₃N and HCN bear similar structures, which appear intermediate between the previous ones (that is, stronger winds than those from CH₃CN, but with a less prevalent jet than for HNC). Simple fits of the LOS winds that assume solid-body rotation indicate that winds increase with altitude, from ~200 m s⁻¹ equatorial at ~350 km to ~280–300 m s⁻¹ at 600 km and above. The Richardson number (Ri) associated with this wind profile remains comfortably above the Ri < ¼ limit for turbulence.

Assuming purely zonal flow, we used our forward model and a trial-and-error approach to de-convolve the LOS winds measured in CH₃CN, HNC and HC₃N in terms of latitudinal wind profiles at the associated altitudes (see Supplementary Information).

Results for CH₃CN, which pertain to 345<sup>+60</sup><sub>-140</sub> km (0.01–0.7 mbar with peak sensitivity at 0.035 mbar), indicate a maximum speed of 220 m s⁻¹ at 15° S with, as expected from qualitative data inspection, a much more gradual decline in the southern than in the northern hemisphere. This result agrees within error bars with pioneering measurements¹ using the same species (160 ± 60 m s⁻¹ equatorial at 300 ± 100 km, assuming solid-body rotation). The north/south asymmetry that is evident in our CH₃CN data also confirms the well-trusted but still indirect inferences based on temperature fields and the use of the thermal wind equation. Those consistently indicate a strong, broad mid-latitude (~20°–50°) jet in the winter hemisphere with peak velocities in excess of 190 m s⁻¹, extending over about one decade in pressure centred at 0.1 mbar, whereas significant winds (up to 100 m s⁻¹) are still present at mid-latitudes of the opposite hemisphere⁵,⁶. Note that the thermal wind approach is valid only outside an altitude-dependent (but typically ±(10°–30°)) equatorial band, a limitation that does not hold in direct wind measurements. Analyses of stellar occultation central flashes in 2001–2003 (northern winter solstice) also indicate maximum winds of ~200 m s⁻¹ at 250 km, but disagree on their latitudinal extent⁷⁻⁹.

For HC₃N and HNC, the de-convolved equatorial speeds are 310–345 m s⁻¹, rapidly decreasing with latitude in both hemispheres and with no clear latitudinal asymmetry. For HC₃N, results are sharply different from ref. ⁴, both in the estimate for the probed altitude (710<sup>+190</sup><sub>-260</sub> km here versus 450 ± 100 km in ref. ⁴) and in the wind velocities (310 m s⁻¹ equatorial here, versus 60 ± 20 m s⁻¹ in ref. ⁴). As the data from ref. ⁴ refer to 2003–2004 (solar longitude L = 268°–280°), the contradiction—if taken at face value—would imply a temporal variation of the mesospheric circulation, with winds decreasing (increasing) with altitude at southern (northern) summer solstice, or near perihelion (aphelion).

Based on data from Cassini's Ion and Neutral Mass Spectrometer (INMS) and Plasma Spectrometer/Ion Beam Spectrometer (CAPS/IBS), ion winds at 1,000–1,400 km in the range 30–260 m s⁻¹ (vector component along the spacecraft trajectory) were reported¹⁵. Above 1,200 km, ions and neutrals are collisionally coupled¹⁶, so these speeds represent neutral winds, but the measured range was broad and the other wind components unconstrained. Our HNC data reveal that the circulation regime over 900–1,100 km is characterized by a relatively broad (±(30°–35°) latitude extent at half maximum) equatorial jet with ~350 m s⁻¹ maximum speed, that is, ~1.4 times the speed of sound. Such a regime was previously unexpected. Pre-Cassini models¹⁷,¹⁸ predicted subsolar to anti-solar (SSAS) winds of ~50 m s⁻¹. Early Cassini/INMS density profiles were used¹⁹ to construct an empirical altitude–latitude temperature model; by solving the momentum equations, a circulation pattern with a zonal jet of ~50 m s⁻¹ and very strong meridional winds (~150 m s⁻¹) at 70° N latitude was inferred. A more complete analysis of 32 Cassini/INMS passes²⁰ indicated that while mean temperatures over 1,050–1,500 km vary in the range 112–175 K, there is a conspicuous lack of correlation between temperatures, latitude, longitude, local time and solar zenith angle, indicating that the thermospheric thermal structure and dynamics are not primarily controlled by the absorption of solar extreme ultraviolet radiation (EUV). Some correlations were found between atmospheric temperatures and the local plasma environment²⁰,²¹, but seem to be of ambiguous interpretation. An analysis of thermospheric energetics²² demonstrated that particle sources (magnetospheric ions, pick-up ions and auroral electron precipitation) and Joule heating contribute lower power than EUV input, typically by a factor of 10 below 1,100 km, and solar EUV also dominates ionospheric production²³. But Saturn's co-rotation electric field, which drives magnetospheric plasma convection past Titan at 120 km s⁻¹, probably also drives ion convection at ~1 km s⁻¹ in the ionosphere²⁴. Collisionally coupled ion/neutral winds of ~350 m s⁻¹ would seem sufficient to power perpendicular electric fields E<sub>⊥</sub> = -v × B of order 1.5 μV m⁻¹, as inferred²⁵.
<figure><img src="image_4.png" /><figcaption>**Fig. 2 | Doppler wind maps.** Line-of-sight Doppler shifts (m s⁻¹) measured in CH₃CN, CH₃CCH, DCN, HCN (main line of the hyperfine triplet at 354.5055 GHz, and satellite lines at 354.5039 and 354.5075 GHz), HC₃N and HNC. Right ascension (RA) and declination (Dec.) are shown in terms of Titan's apparent radius, R<sub>Titan</sub>. Ellipses show the synthesized beams. White areas correspond to regions where emission signals are too faint for reliable measurements to be performed. Only CH₃CN emission makes it possible to measure winds throughout the disk. Some measurements within the disk are also possible with the main HCN 354.5055 GHz line, which appears in absorption in nadir geometry (see Supplementary Fig. 2). Doppler shifts in the various species clearly indicate a prograde wind regime, but with different structure for CH₃CN versus HNC, HCN and HC₃N. Winds in CH₃CCH are mostly measurable outside the low-latitude regions. Winds are only marginally detected from DCN emission. See Supplementary Information for details.</figcaption></figure>

Vertically propagating waves seem capable of depositing energy fluxes comparable to solar ultraviolet²². Evidence for waves in Titan's mesosphere and thermosphere is abundantly present in stellar occultation profiles⁹, in the Huygens Atmosphere Structure Instrument (HASI) profile²⁶ above 500 km and in the INMS density/temperature profiles²²,²⁷, and maybe in vertical molecular profiles. Gravitational tides²⁸ are not promising for explaining the strong wind speeds that we measure, owing to their small phase velocities (0 and ±5.9 m s⁻¹ equatorial) and inability to penetrate regions where their phase speed equals the zonal velocity (that is, between 0–5 km and in the 70–80 km region of minimum wind¹). Above 300 km altitude where the radiative time constant becomes shorter than a Titan day²⁹ (16 Earth days),

other gravity waves, in particular thermal tides generated by solar heating, diurnal and especially semi-diurnal with large vertical wavelength³⁰,³¹, will propagate vertically. They can deposit eddy momentum fluxes by viscous dissipation, interact with the weak solar-induced SSAS thermospheric circulation and produce a strong equatorial flow. Solar forcing of tides will be complex, as a solar day for a parcel advecting with zonal winds is 16 Earth days at the surface, approximately 1 day at 350 km and ~3/4 day at 1,000 km. Detailed models are needed to assess the plausibility of the mechanism, but an analogy may hold with the upper atmosphere of Venus, where gravity waves are thought to be responsible for the variable retrograde super-rotating zonal flow that is superimposed on the strong SSAS regime³².
<figure><img src="image_5.png" /><figcaption>**Fig. 3** | Molecular abundance profiles and probed altitudes. **a**, Equatorial vertical profiles for the six species used for the wind measurements (solid lines, with error bars indicated in the altitude ranges where information is available). As explained in the Supplementary Information, uncertainties on HNC and on the upper part of the HC₃N distribution are best described by a vertical shift of their altitude profile (dashed lines). For HCN, HC₃N and CH₃CCH, characteristic profiles from Cassini/CIRS, UVIS and INMS, and from previous 2012–2015 ALMA observations³³ are indicated. See Methods and Supplementary Information for details. **b**, Wind contribution functions (WCFs) in limb (solid lines) and nadir (dashed lines) geometries. For HCN, WCFs are shown separately for the main line at 354.5055 GHz and for the satellite lines at 354.5039 and 354.5075 GHz (averaging the two). For HC₃N, to avoid the contribution from the nearby HCN (4–3) line, a WCF calculated with zero HC₃N has been subtracted from the WCF before plotting. For other species, the peak below 100 km is due to the continuum. See Methods for details.</figcaption></figure>

**Methods**

**Radiative-transfer models.** Spectral calculations were based on a home-made radiative-transfer model in full spherical geometry, inherited from refs. 4,34,35. Line opacities are calculated using spectroscopic parameters from the Cologne Database for Molecular Spectroscopy (https://cdms.astro.uni-koeln.de/). As a consequence of small particle size and sharply decreasing absorption coefficients beyond 100 µm (ref. 36), thermal emission and scattering by haze are neglected, as in all previous studies of Titan at millimetre or submillimetre wavelengths. Pencil-beam radiances are calculated on a grid of impact parameters (distance to Titan centre) ranging from 0 km to 4,120 km (1.6 Titan radius). For each beam position under study, LOS radiances as a function of impact parameter from Titan's centre are re-interpolated over the Titan + atmosphere disk, and integrated over portions of the disk intercepted by the ALMA synthesized beam. At this step, we took into account the beam's elliptical shape and its orientation, and the precise apparent radius of Titan for each individual observation. This resulted in synthetic spectra expressed in Jansky per beam which could then be directly compared to the data, after applying minor (<10%) model-based calibration corrections to the data fluxes whenever needed.

**Temperature and abundance retrievals.** Temperature profile information was derived from modelling of the CO (3–2) and HCN (4–3) lines and their isotopic variants, using a home-made inversion code³⁵ and based on optimal estimation methods principles²⁷,³⁹. For the purpose of this task, which is mainly to assign altitude levels to the wind measurements, we focused on the equatorial region, leaving the study of the thermal and compositional field for future work. For the a priori, we used an equatorial profile derived from Cassini's Composite Infrared Spectrometer (CIRS) measurements in May 2016 (T119 flyby), extended above 700 km at a 153 K temperature, typical of the upper atmosphere according to Cassini/INMS measurements, and shown in Supplementary Fig. 1 (black line). Whereas CO lines constrain atmospheric temperatures below ~350 km, HCN probes much higher altitudes (up to ~1,000 km), with the difficulty that the temperature profile and the HCN profile are poorly constrained above the top of the sensitivity range of CIRS (~520 km). To alleviate the ambiguity between abundance and temperature effects in the core of the HCN (4–3) line, we inverted simultaneously the equatorial HCN (4–3) and H¹³CN (4–3) lines near the central meridian and at the limb. The characteristic absorption/emission appearance of the HCN hyperfine structure in nadir/limb geometry provides complementary information on temperature and abundance sensitivity. In doing so, we used the HCN profile from ref. ³⁹ (extended above 400 km to reach HCN = 10⁻⁴ at 800 km and above) as a priori.

The best-fit equatorial thermal profile retrieved in this manner is shown in Supplementary Fig. 1 (blue line), and the associated fits of the CO, HCN and H¹³CN lines in nadir and limb geometry are shown in Supplementary Fig. 2. The temperature profile shows a marked mesopause at 140 K near 800 km. The occurrence of such a cold temperature somewhere above the stratopause is in fact directly implied by the depth of the main component of the HCN (4–3) hyperfine structure, with a brightness temperature of 143 K in the line core in nadir geometry. Note also that the best-fit temperature/HCN profile permits a good match of the

HCN v2=1 emission at 354.460 GHz (Supplementary Figs. 2 and 3). The retrieved profile is also warmer than the a priori (CIRS) profile by up to ~3 K at 250 km and colder by ~6 K at 400–600 km. Differences between CIRS- and ALMA CO-derived thermal profiles of up to 5 K below 300 K have already been noted⁸⁰.

Error bars on the retrieved HCN/temperature retrievals are a combination of uncertainties due to measurement noise and uncertainties due to the a priori profiles used in the inversion process. Noise-related uncertainties were calculated using the formalism described in ref. ³⁷ (their equations (23) and (24)). The associated temperature errors are formally very small (0.2–0.3 K) in relation to the high signal to noise ratio and high spectral resolution of the data. Uncertainties due to the a priori profiles were evaluated by repeating the temperature/HCN inversion process using several a priori temperature and HCN profiles, as detailed in Supplementary Information. These modelling variants yielded a suite of solution profiles, whose dispersion is a good indicator on the actual error bars on the retrieved temperature and HCN profile (Supplementary Fig. 4). Beyond the well-known characteristics of Titan's middle atmosphere thermal structure such as the stratopause near 270 km, robust new features of all retrieved profiles are the existence of a quasi-isothermal region over 450–600 km (already apparent in the CIRS-based a priori profile) and the existence of a ~140 K mesopause, located at 800 ± 50 km altitude depending on the a priori. Error bars on the retrieved temperatures remain below 2–3 K up to 800 km; above this level, they increase with the progressive lack of sensitivity of the measurements to ultimately reflect the a priori errors. The HCN profile (Fig. 3) is also very well defined (to within ~10–20%) over 100–850 km, before error bars progressively increase. The nominal HCN mixing profile that we determine reaches a 6.3 × 10⁻⁴ mixing ratio at 1,000 km, in agreement with results from both Cassini/INMS⁴¹ and Cassini's Ultraviolet Imaging Spectrograph (UVIS)⁴², respectively above and below 950 km (see Fig. 3).

The retrieved thermal profile shows a quasi-isothermal part at 156 K over 450–600 km and a 140 K minimum near 800 km. Although the resulting oscillatory structure may be reminiscent of the temperature perturbations seen in the Huygens/HASI data³⁸, its attribution to a wave is doubtful because (1) our data sample broad regions (beam size ~1,000 km), and nadir and limb data inverted simultaneously are separated by ~2,500 km; (2) the resulting wave amplitude and vertical wavelength would be ~5–10 K and ~300 km, respectively smaller and larger than in the HASI data (~10–20 K and ~100 km). Instead, the temperature profile, and in particular the 800 km temperature minimum, may be mostly radiatively controlled. A pioneering non-local thermodynamic equilibrium model¹³ of Titan's upper atmosphere predicted a 135–140 K mesopause (but at 600 km), primarily due to C₂H₆ cooling. Revising such a model in the light of new distributions derived from Cassini and the present work (especially for HCN, C₂H₆, HC₃N and CH₃CCH) and with updated spectroscopic databases would shed further light on this issue.

The retrieved thermal profile was then used to derive the other molecular profiles, again for the equatorial region. The DCN profile was taken as the retrieved HCN profile, multiplied by a constant DCN/HCN ratio of (2.5 ± 0.2) × 10⁻⁴ (ref. ⁴⁴), that is, assuming that the DCN profile follows that of HCN at all altitudes. CH₃CN and CH₃CCH were inverted using a priori profiles respectively based on ground-based data³⁶ (extended to 10⁻⁵ at 1,000 km and above) and CIRS observations¹⁵. For these three species, best fits of the (west) limb equatorial emission are presented in
Supplementary Fig. 3. Error bars on CH₃CN and CH₃CCH reflect the combined effects of noise, temperature profile uncertainty and a priori errors.

The Doppler-limited line-shape of HN C J = 4–3 line (Supplementary Fig. 5) contains limited information on the HNC vertical profile, except for the fact that this precludes HNC to be present at too deep atmospheric levels. Based on HNC J = 6–5, ref. 34 found that for constant mixing profiles above some level, the cut-off altitude cannot be lower than 300 km. Using HNC data averaged over a concentric ring 2,000–3,350 km from Titan centre, and testing photochemical profiles¹⁴ for HNC, we found that several of these HNC profiles overestimate the amount of HNC in the lower stratosphere. In contrast, the model in which the production of HNC by galactic cosmic-ray impact is omitted is essentially in agreement with the observed spectrum. Although this line-shape-based approach does not constrain the distribution of HNC at altitudes above the pressure-broadening levels, the latter can be determined from the observed variation of the line-integrated intensities with radial distance. Comparing the latter with model calculations for constant HNC profiles above some cut-off altitudes, we found that the bulk of HNC is located above 870 ± 40 km altitude, implying that HNC is mostly a thermospheric species. The photochemical model from ref. 14 without galactic cosmic rays also provides the correct radial dependence for the HNC emission, and was adopted as the nominal profile, allowing for a vertical shift of ±40 km in its altitude scale.

The situation is similar for the HC₃N J = 39–38 emission at 354.697 GHz, which—except in the high-northern and southern latitude regions where it is strongly enhanced—does not show Lorentzian wings. We performed the same study as for HNC on the radial distance variation of the HC₃N emission (using the slightly stronger J = 38–37 line at 345.609 GHz observed along with CO (3–2)), restricting ourselves to low-latitude regions. Considering piecewise profiles, this approach yielded a best-fit cut-off altitude of 630 ± 30 km (Supplementary Fig. 5), implying that HC₃N too is mostly present in Titan's upper atmosphere, albeit less so than HNC. This is not surprising given that HC₃N as measured by CIRS¹²,¹³ also has a measurable abundance in Titan's stratosphere and lower mesosphere, with mixing ratios increasing from 6 × 10⁻¹¹ to 1 × 10⁻⁷ over 150–450 km. Initializing the HC₃N profile at these values and a large abundance at altitude z > 800 km, we determined an equatorial HC₃N profile fitting both the shape of the J = 39–38 line and the radial variation of the J = 38–37 lines fluxes. In contrast, the nominal HC₃N profile from ref. 14 does not fit either of the two observables, indicating that this profile is overabundant at lower altitudes and underabundant in the upper atmosphere. Our HC₃N solution profile has a 1,000 km abundance as high as ~5 × 10⁻⁵. This agrees fairly well with the global value reported from Cassini/INMS¹⁶ and with the Cassini/UVIS HC₃N abundance over 850–950 km (ref. ¹²). We reiterate that our conclusions pertain to the equatorial HC₃N profile only.

Figure 3 summarizes the retrieved profiles for all six molecules used to probe the winds. Error bars are indicated in the range where information is available. For HNC and HC₃N, uncertainties are best expressed as a vertical shift of ±40 km and ±30 km in the profiles, for reasons explained above. These profiles are compared to characteristic profiles locally derived from Cassini/UVIS at 6°S (T41I, ref. ¹⁴), INMS¹⁴,¹⁶ and CIRS. For the latter, we show HNC and CH₃CCH profiles at 9°S from May 2016 (T119, ref. ⁴⁵); for HC₃N, not clearly detected in the latter observations, we use instead a 5°N profile from January 2007 (T23, ref. ¹⁷). Also shown in Fig. 3 are disk-averaged HCN and HC₃N profiles derived from 2012–2015 ALMA observations (ref. ³³, their Figure 10). Figure 3 highlights the overall agreement between these profiles, in particular giving great confidence in our HCN and HC₃N profiles in the middle/upper atmosphere. A noteworthy difference is that 'local' molecular profiles (from Cassini CIRS and UVIS) show small-scale vertical variations (see for example Figures 3 and 4 of ref. ⁴⁷, and Figure 26 of ref. ¹²), not predicted in photochemical models¹⁴ and presumably of dynamical origin; those are particularly visible in Fig. 3 for the HCN and HC₃N profiles derived from UVIS.

**Contribution functions and wind altitudes.** The retrieved profiles for all six molecules used to probe the winds are shown in Fig. 3a. Based on these profiles, 'wind contribution functions' (WCFs) were calculated to estimate the range of altitudes probed by the wind measurements in each molecule. For this, we first calculated 'traditional' contribution functions $B(T) \propto \exp(-\tau)/d\ln(p)$ (where T is temperature, p is pressure, τ is optical depth and B is the Planck function) both monochromatically (over a spectral interval matching the one used for the wind measurements), and for every pencil-beam LOS. At each frequency, these contributions functions were then convolved with the synthesized beam associated to each observation. To estimate how the probed altitude may vary with the observing geometry, these spatially convolved—but still monochromatic—contribution functions were calculated both in nadir view (that is, pointing to Titan's disk centre) and in limb view, defined here as a position distant from Titan's centre by 1.3 Titan radius (that is, 772.5 km above the solid planet limb). This corresponds typically to the distance where we measure strongest winds before signals become too faint. Finally, these spatially convolved contribution functions were spectrally convolved, using a weight proportional to the local spectral slope of the synthetic spectrum¹⁴⁸. For each species, these WCFs for the nadir and limb geometries are shown in Fig. 3b. For HCN, we show separately the WCF for the main line at 354.5055 GHz and for the two satellite lines at 354.5039GHz and 354.5075 GHz (averaging their two very similar WCF).

WCFs highlight three regions: a narrow (900–1,100 km) thermospheric region probed by HNC; another relatively narrow region, encompassing the upper stratosphere/lower mesosphere (200–400 km) probed by CH₃CN, CH₃CCH and DCN; and a much broader zone, straddling from ~400 km to ~1000 km (in limb geometry), probed by HCN and HC₃N. In limb geometry, the mean probed altitudes (that is, the WCF-weighted mean altitudes) are: 345±⁶⁰/¹⁴⁰ km for CH₃CN; 315±⁹⁰/¹⁶⁰ km for CH₃CCH; 340±⁹⁰/¹⁵⁵ km for DCN; 745±³⁶⁰/³²⁰ km for the main HCN line; 540±¹²⁰/¹⁸⁵ km for the HCN satellite lines; 710±¹⁹⁰/²⁶⁰ km for HC₃N; and 990±¹⁰⁰/¹²⁰ km for HNC, where the 'error bars' mark the vertical extent of each WCF, that is the range in which it exceeds half of its maximum value. The impacts of the thermal profile and abundance uncertainties (see Supplementary Information) on the WCF are small. Specifically, the mean probed altitude, as defined above, shifts by ±45 km for HNC, ±20 km for HC₃N, ±25 km (±15 km) for the main (the satellite) HCN line and ±10 km for CH₃CN, CH₃CCH and DCN. Thus, except to some degree for HNC, the associated error bar appears dwarfed by the broad vertical extent of the WCF, from which we conclude that the vertical scale associated with our wind measurements is robust.

WCFs calculated by ref. 4 for Plateau de Bure interferometer observations of CH₃CN and HC₃N lines at 220 GHz indicated sounding altitudes of 300 ± 150 km for CH₃CN and 450 ± 100 km for HC₃N, which compares well with our computation for CH₃CN but is rather different for HC₃N. This stems from the combination of three factors, all of which are 'pushing' the HC₃N contribution function to higher levels in our case: (i) a higher HC₃N abundance in the upper atmosphere compared to the profile³⁰ adopted in ref. 4; (ii) the fact that we calculated the WCF for pointing towards a distance of 1.3 Titan radius (versus 1.0 Titan radius in ref. 4), and (iii) the ~3 times smaller synthesized beam in our observations (~0.2" versus 0.6"), which enhances the contribution of limb with respect to nadir, thereby tending to probe higher altitudes.

**Data availability**

The data that support the plots within this paper and other findings of this study are available from the ALMA archive (http://almacscience.nrao.edu/aq/; Cycle 3 programme 2015.1.01023.S (PI M. Gurwell)) and from the corresponding author upon reasonable request.

**Code availability**

Novel methods developed for this research and not available from previous studies are available from the corresponding author upon reasonable request.

Received: 23 October 2018; Accepted: 8 March 2019;

Published online: 15 April 2019

**References**

1. Folkner, W. M. et al. Winds from Titan from ground-based tracking of the Huygens probe. *J. Geophys. Res.* **111**, E07S02 (2006).

2. Luz, D. et al. Characterization of the zonal winds in Titan's stratosphere of Titan with UVES. 2. Observations coordinated with the Huygens Probe entry. *J. Geophys. Res.* **111**, E08S90 (2006).

3. Kostiuk, T. et al. High spectral resolution infrared studies of Titan: winds, temperature and composition. *Planet. Space Sci.* **58**, 1715–1723 (2010).

4. Moreno, R., Marten, A. & Hidayat, T. Interferometric measurements of zonal winds on Titan. *Astron. Astrophys.* **437**, 319–328 (2005).

5. Achterberg, R. K. et al. Titan's middle atmospheric temperatures and dynamics observed by the Cassini Composite Infrared Spectrometer. *Icarus* **194**, 263–277 (2008).

6. Achterberg, R. K. et al. Temporal variations of Titan's middle atmospheric temperatures from 2004 to 2009 observed by the Cassini/CIRS. *Icarus* **211**, 686–698 (2011).

7. Hubbard, W. B. et al. The occultation of 28Sgr by Titan. *Astron. Astrophys.* **269**, 541–563 (2005).

8. Bouchez, A. H. *Seasonal Trends in Titan's Atmosphere: Haze, Winds, and Clouds*. PhD thesis, California Institute of Technology (2004).

9. Sicardy, B. et al. The two Titan stellar occultations of 14 November 2003. *J. Geophys. Res.* **111**, E11S91 (2006).

10. Cordiner, M. et al. ALMA measurements of the HNC and HC₃N distributions in Titan's atmosphere. *Astrophys. J. Lett.* **795**, L30 (2014).

11. Lai, J. C.-Y. et al. Mapping vinyl cyanide and other nitriles in Titan's atmosphere using ALMA. *Astron. J.* **154**, L206 (2017).

12. Vinatier, S. et al. Vertical abundance profiles of hydrocarbons in Titan's atmosphere at 15°S and 80°N retrieved from Cassini/CIRS spectra. *Icarus* **188**, 120–138 (2007).

13. Teanby, N. et al. Vertical profiles of HCN, HC₃N and C₃H₄ in Titan's atmosphere derived from Cassini/CIRS data. *Icarus* **186**, 364–384 (2007).

14. Dobrijevic, M., Loison, J.-C., Hickson, K. M. & Gronoff, G. 1D-coupled photochemical model of neutrals, cations and anions in the atmosphere of Titan. *Icarus* **268**, 313–339 (2016).
15. Crary, F. J. et al. Heavy ions, temperatures and winds in Titan's ionosphere: combined Cassini CAPS and INMS observations. *Planet. Space Sci.* **57**, 1847–1856 (2009).

16. Cravens, T. et al. Dynamical and magnetic field time constants for Titan's ionosphere: empirical estimates and comparisons with Venus. *J. Geophys. Res.* **115**, A08319 (2010).

17. Rishbeth, H., Yelle, R. V. & Mendillo, M. Dynamics of Titan's thermosphere. *Planet. Space Sci.* **48**, 51–58 (2000).

18. Müller-Wodarg, I. C. F., Yelle, R. V., Mendillo, M. & Aylward, A. D. On the global distribution of neutral gases in Titan's upper atmosphere and its effect on the thermal structure. *J. Geophys. Res.* **108**, 1453 (2003).

19. Müller-Wodarg, I. C. F., Yelle, R. V., Cui, J. & Waite, J. H. Horizontal structures and dynamics of Titan's thermosphere. *J. Geophys. Res.* **113**, E10005 (2008).

20. Snowden, D. et al. The thermal structure of Titan's upper atmosphere. I: Temperature profiles from Cassini INMS observations. *Icarus* **226**, 552–582 (2013).

21. Westlake, J. H. et al. Titan's thermospheric response to various plasma environments. *J. Geophys. Res.* **116**, A03318 (2011).

22. Snowden, D. & Yelle, R. V. The thermal structure of Titan's upper atmosphere. II: Energetics. *Icarus* **228**, 64–77 (2014).

23. Ågren, K. et al. On the ionospheric structure of Titan. *Planet. Space Sci.* **57**, 1821–1827 (2009).

24. Ulusen, D. et al. Comparisons of Cassini flybys of the Titan magnetospheric interaction with an MHD model: evidence for organized behavior at high altitudes. *Icarus* **217**, 43–54 (2012).

25. Ågren, K. et al. Detection of currents and associated electric fields in Titan's ionosphere from Cassini data. *J. Geophys. Res.* **116**, A04313 (2011).

26. Aboudan, A., Colombatti, G., Ferri, F. & Angrilli, F. Huygens probe entry trajectory and attitude estimated simultaneously with Titan's atmospheric structure by Kalman filtering. *Planet. Space Sci.* **56**, 573–585 (2008).

27. Müller-Wodarg, I. C. F., Yelle, R. V., Borggren, N. & Waite, J. H. Waves and horizontal structures and dynamics of Titan's thermosphere. *J. Geophys. Res.* **111**, A12, id A12315 (2006).

28. Strobel, D. F. Gravitational tidal waves in Titan's upper atmosphere. *Icarus* **182**, 251–258 (2006).

29. Bézard, B., Vinatier, S. & Achterberg, R. Seasonal radiative transfer modeling of Titan's stratospheric temperatures at low latitudes. *Icarus* **302**, 437–450 (2018).

30. Fels, S. B. & Lindzen, R. S. The interaction of thermally excited gravity waves with mean flows. *Geophys. Fluid Dyn.* **6**, 149–191 (1974).

31. Zhu, X. Maintenance of equatorial superrotation in the atmosphere of Venus and Titan. *Planet. Space Sci.* **54**, 761–773 (2006).

32. Hoshino, N., Fujiwara, H., Takagi, M. & Kasaba, Y. Effects of gravity waves on the day-night difference of the general circulation in the Venusian lower thermosphere. *J. Geophys. Res. Planets* **118**, 2004–2015 (2013).

33. Thelen, A. et al. Abundance measurements of Titan's stratospheric HCN, HC₃N, C₃H₄ and CH₃CN from ALMA observations. *Icarus* **319**, 417–432 (2019).

34. Moreno, R. et al. First detection of hydrogen isocyanide (HNC) in Titan's atmosphere. *Astron. Astrophys.* **536**, L12 (2011).

35. Lellouch, E. et al. Detection of CO and HCN in Pluto's atmosphere with ALMA. *Icarus* **286**, 289–307 (2017).

36. Anderson, C. M. & Samuelson, R. E. Titan's aerosol and stratospheric ice opacities between 18 and 500 µm: vertical and spectral characteristics from Cassini CIRS. *Icarus* **212**, 762–778 (2011).

37. Conrath, B. J., Gierasch, P. J. & Ustinov, E. A. Thermal structure and para hydrogen fraction on the outer planets from Voyager IRIS measurements. *Icarus* **135**, 501–517 (1998).

38. Rodgers, C. D. *Inverse Methods for Atmospheric Sounding: Theory and Practice* (World Scientific, 2000).

39. Marten, A., Hidayat, T., Biraud, Y. & Moreno, R. New millimeter heterodyne observations of Titan: vertical distributions of nitriles: HCN, HC₃N, CH₃CN, and the isotopic ratio ¹⁵N/¹⁴N in its atmosphere. *Icarus* **158**, 532–544 (2002).

40. Thelen, A. E. et al. Spatial variations in Titan's atmospheric temperature: ALMA and Cassini comparisons from 2012 to 2015. *Icarus* **307**, 380–390 (2018).

41. Cui, J., Cao, Y.-T., Lavvas, P. P. & Koskinen, T. T. The variability of HCN in Titan's upper atmosphere as implied by the Cassini Ion-Neutral Mass Spectrometer measurements. *Astrophys. J. Lett.* **826**, L5 (2016).

42. Koskinen, T. T. et al. The mesosphere and lower thermosphere of Titan revealed by Cassini/UVIS stellar occultations. *Icarus* **207**, 511–534 (2011).

43. Yelle, R. V. Non-LTE models of Titan's upper atmosphere. *Astrophys. J.* **383**, 380–400 (1991).

44. Molter, E. M. et al. ALMA observations of HCN and its isotopologues on Titan. *Astron. J.* **152**, 42 (2016).

45. Vinatier, S. et al. Seasonal variations in Titan's stratosphere observed with Cassini/CIRS during northern spring. In *American Astronomical Society DPS Meeting 49* 304.03 (AAS, 2017).

46. Cui, J. et al. Analysis of Titan's neutral upper atmosphere from Cassini ion neutral mass spectrometer measurements. *Icarus* **200**, 581–615 (2009).

47. Vinatier, S. et al. Analysis of Cassini/CIRS limb spectra of Titan acquired during the nominal mission. I. Hydrocarbons, nitriles and CO₂ vertical mixing ratio profiles. *Icarus* **205**, 559–570 (2010).

48. Lellouch, E., Goldstein, J. J., Rosenqvist, J., Bougher, S. W. & Paubert, G. Global circulation, thermal structure, and carbon monoxide distribution in Venus' mesosphere in 1991. *Icarus* **110**, 315–339 (1994).

## Acknowledgements

E.L., R.M. and S.V. acknowledge support from the Programme National de Planétologie (PNP-INSU). This paper makes use of the following ALMA data: ADS/JAO.ALMA#2015.1.1023.S. 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. The paper is dedicated to the memory of Daniel Lellouch, deceased on 13 February 2019.

## Author contributions

M.A.G. wrote the ALMA proposal. M.A.G. and R.M. reduced the ALMA data. E.L. analysed and modelled the data (with contribution from R.M.) and wrote most of the manuscript. S.V. provided initial thermal profiles as well as insight in the general science context. D.F.S. led the interpretative part. All authors discussed the manuscript.

## Competing interests

The authors declare no competing interests.

## Additional information

*Supplementary information* is available for this paper at https://doi.org/10.1038/s41550-019-0749-4.

*Reprints and permissions information* is available at www.nature.com/reprints.

*Correspondence and requests for materials* should be addressed to E.L.

*Journal peer review information:* Nature Astronomy thanks Agustín Sanchez-Lavega and Jan-Erik Wahlund for their contribution to the peer review of this work.

*Publisher's note:* Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

© The Author(s), under exclusive licence to Springer Nature Limited 2019