# Photochemically produced SO2 in the atmosphere of WASP-39b

Shangmin Tsai, Elspeth K.H. Lee, Diana K. Powell, Peter Gao, Xi Zhang, Julianne I. Moses, Éric Hébrard, Olivia Venot, Vivien Parmentier, Sean Jordan, et al.

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

## To cite this version:

Shangmin Tsai, Elspeth K.H. Lee, Diana K. Powell, Peter Gao, Xi Zhang, et al.. Photochemically produced SO2 in the atmosphere of WASP-39b. Nature, 2023, 617 (7961), pp.483-487. 10.1038/s41586-023-05902-2. hal-04233255

HAL Id: hal-04233255

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Submitted on 18 Oct 2023

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<figure><img src="image_2.png" /></figure>
Photochemically-produced SO₂ in the
atmosphere of WASP-39b

Shang-Min Tsai¹,²*, Elspeth K. H. Lee³, Diana Powell⁴, Peter Gao⁵, Xi

Zhang⁶, Julianne Moses⁷, Eric Hébrard⁸, Olivia Venot⁹, Vivien

Parmentier¹⁰, Sean Jordan¹¹, Renyu Hu¹²,¹³, Munazza K. Alam⁵, Lili

Alderson¹⁴, Natalie M. Batalha¹⁵, Jacob L. Bean¹⁶, Björn

Benneke¹⁷, Carver J. Bierson¹⁸, Ryan P. Brady¹⁹, Ludmila

Carone²⁰, Aarynn L. Carter¹⁵, Katy L. Chubb²¹, Julie

Inglis¹³,²², Jérémy Leconte²³, Michael Line¹⁸, Mercedes

López-Morales⁴, Yamila Miguel²⁴,²⁵, Karan Molaverdikhani²⁶,²⁷, Zafar

Rustamkulov²⁸, David K. Sing²⁸,²², Kevin B. Stevenson²⁹, Hannah R

Wakeford¹⁴, Jeehyun Yang¹², Keshav Aggarwal³⁰, Robin

Baeyens³¹, Saugata Barat³¹, Miguel de Val Borro³², Tansu

Daylan³³,³⁴, Jonathan J. Fortney¹⁵, Kevin France³⁵, Jayesh M

Goyal³⁶, David Grant¹⁴, James Kirk⁴,³⁷,³⁸, Laura Kreidberg³⁹, Amy

Louca²⁴, Sarah E. Moran⁴⁰, Sagnick Mukherjee¹⁵, Evert

Nasedkin³⁹, Kazumasa Ohno¹⁵, Benjamin V. Rackham⁴¹,⁴²,⁴³, Seth

Redfield⁴⁴, Jake Taylor¹,¹⁷, Pascal Tremblin⁴⁵, Channon

Visscher⁷,⁴⁶, Nicole L. Wallack⁵,¹³, Luis Welbanks¹⁸,⁴⁷, Allison

Youngblood⁴⁸, Eva-Maria Ahrer⁴⁹,⁵⁰, Natasha E. Batalha⁵¹, Patrick

Behr³⁵, Zachory K. Berta-Thompson⁵², Jasmina Blecic⁵³,⁵⁴, S.L.

Casewell⁵⁵, Ian J.M. Crossfield⁵⁶, Nicolas Crouzet²⁴, Patricio E.

Cubillos⁵⁷,²⁰, Leen Decin⁵⁸, Jean-Michel Désert³¹, Adina D.

Feinstein¹⁶,⁵⁹, Neale P. Gibson⁶⁰, Joseph Harrington⁶¹, Kevin

Heng²⁶,⁵⁰, Thomas Henning³⁹, Eliza M.-R. Kempton⁶², Jessica

Krick⁶³, Pierre-Olivier Lagage⁴⁵, Monika Lendl⁶⁴, Joshua D.

Lothringer⁶⁵, Megan Mansfield⁴⁷,⁶⁶, N. J. Mayne⁶⁷, Thomas

Mikal-Evans³⁹, Enric Palle⁶⁸, Everett Schlawin⁶⁶, Oliver

Shorttle¹¹, Peter J. Wheatley⁴⁹,⁵⁰ and Sergei N. Yurchenko¹⁹

*Corresponding author(s). E-mail(s): shang-min.tsai@physics.ox.ac.uk
All author affiliations are listed at the end of the paper.
Abstract

Photochemistry is a fundamental process of planetary atmospheres that regulates the atmospheric composition and stability [1]. However, no unambiguous photochemical products have been detected in exoplanet atmospheres to date. Recent observations from the JWST Transiting Exoplanet Early Release Science Program [2, 3] found a spectral absorption feature at 4.05 µm arising from SO₂ in the atmosphere of WASP-39b. WASP-39b is a 1.27-Jupiter-radii, Saturn-mass (0.28 M<sub>J</sub>) gas giant exoplanet orbiting a Sun-like star with an equilibrium temperature of ~1100 K [4]. The most plausible way of generating SO₂ in such an atmosphere is through photochemical processes [e.g., 5, 6]. Here we show that the SO₂ distribution computed by a suite of photochemical models robustly explains the 4.05 µm spectral feature identified by JWST transmission observations [7] with NIRSpec PRISM (2.7σ) [8] and G395H (4.5σ) [9]. SO₂ is produced by successive oxidation of sulphur radicals freed when hydrogen sulphide (H₂S) is destroyed. The sensitivity of the SO₂ feature to the enrichment of the atmosphere by heavy elements (metallicity) suggests that it can be used as a tracer of atmospheric properties, with WASP-39b exhibiting an inferred metallicity of ~10× solar. We further point out that SO₂ also shows observable features at ultraviolet and thermal infrared wavelengths not available from the existing observations.

JWST observed WASP-39b as part of its Transiting Exoplanet Early Release Science Program (ERS Program 1366), with the goal of elucidating its atmospheric composition [2, 3]. Data from the NIRSpec PRISM and NIRSpec G395H instrument modes revealed a distinct absorption feature between 4.0 and 4.2 µm, peaking at around 4.05 µm that atmospheric radiative-convective-thermochemical equilibrium models could not explain with metallicity and C/O values typically assumed of gas giant planets (1–100× Solar and 0.3–0.9, respectively; [8, 9]). After excluding instrument systematics and stellar variability, a thorough search for gases has revealed sulphur dioxide (SO₂) as a promising candidate with the best-fit absorption feature (see Methods), although ad-hoc spectra with injected SO₂ were used in the analysis.

Sulphur shares some chemical similarities to oxygen but uniquely forms various compounds with a wide range of oxidation states (-2 to +6; [10]). While SO₂ is ubiquitously outgassed and associated with volcanism on terrestrial worlds (e.g., Earth, Venus, and Jupiter's satellite Io), the source of SO₂ is fundamentally different on gas giants. Under thermochemical equilibrium, sulphur chiefly exists in the reduced form, such that hydrogen sulphide (H₂S) is the primary sulphur reservoir in a hydrogen/helium-dominated gas giant [11–14]. At the temperature of WASP-39b, the equilibrium mixing ratio of SO₂ in the observable part of the atmosphere is less than ~10⁻¹² for 10× solar
metallicity and less than ~10⁻⁹ for even 100× solar metallicity (see Extended Data Fig. 1). This equilibrium abundance of SO₂ is several orders of magnitude smaller than the values needed to produce the spectral feature observed by JWST (volume mixing ratios of 10⁻⁶–10⁻⁵) [8, 9]. In contrast, under UV irradiation, SO₂ can be oxidised from H₂S as a photochemical product. H and OH radicals, generated by photolysis processes, are key to liberating SH radicals and atomic S from H₂S and subsequently oxidising them to SO and SO₂. While previous photochemical modelling studies have shown that substantial SO₂ can be produced in hydrogen-rich exoplanet atmospheres in this way [5, 6, 13, 15, 16], the extent to which such a model could reproduce the current WASP-39b observations remained unverified.

We have performed several independent, cloud-free 1D photochemical model calculations of WASP-39b using the ATMO, ARGO, KINETICS, and VULCAN codes (see Methods for model details). All models included sulphur kinetic chemical networks and were run using the same vertical temperature-pressure profiles of the morning and evening terminators adopted from a 3D WASP-39b atmospheric simulation with the Exo-FMS general circulation model (GCM; see Extended Fig 2) [17]. The nominal models assumed a metallicity of 10× solar [18] with a solar C/O ratio (C/O = 0.55) while we explored the sensitivity to atmospheric properties.

The peak mixing ratios of the major sulphur species produced by the different photochemical models are largely consistent with each other to within an order of magnitude, as shown in Figure 1. The SO₂ mixing ratio profiles are highly variable with altitude and strongly peaked at 0.01–1 mbar with a value of 10–100 ppm. SO₂ (along with CO₂) is more favoured at the cooler morning terminator where H₂S is less stable against reaction with atomic H at depth (with SO₂ abundance peak of 50–90 ppm at the morning terminator and 15–30 ppm at the evening terminator). While the peak SO₂ abundance from the photochemical models is greater than that estimated from fitting to the PRISM and G395H data, which assumed vertically constant mixing ratios of ≈1–10 ppm and ≈2.5–4.6 ppm, respectively, the column integrated number densities above 10 mbar are highly consistent (see Methods). Our models indicate that S, S₂, and SO, which are precursors of SO₂, also reach high abundances in the upper atmosphere above the pressure level where H₂S is destroyed. Nevertheless, they are not expected to manifest observable spectral features in the PRISM/G395H wavelength range.

The important pathways of sulphur kinetics in WASP-39b's atmosphere from our models are summarised in Figure 2. The photochemical production
<figure><img src="image_3.png" /><figcaption>Fig. 1: Simulated vertical distribution of sulphur species and CO₂</figcaption></figure>

The colour-shaded areas indicate the span (enclosed by the maximum and minimum values) of volume mixing ratios (VMR) of CO₂ (blue), SO₂ (pink with black borders), and other key sulphur species (H₂S: orange; S: yellow; S₂: grey; and SO: light blue) computed by an ensemble of photochemical models (ARGO, ATMO, KINETICS, and VULCAN) for the morning (a) and evening (b) terminators. The thermochemical equilibrium VMRs are indicated by the dotted lines, with SO₂ not within the x-axis range due to its very low abundance in thermochemical equilibrium. The range bar on the right represents the main pressure ranges of the atmosphere probed by JWST NIRSpec spectroscopy. Photochemistry produces SO₂ and other sulphur species above the 1 mbar level with abundances several orders of magnitude greater than those predicted by thermochemical equilibrium.

paths of SO₂ from H₂S around the SO₂ peak are as follows:

$$
\begin{align*}
& H_2O \xrightarrow{h\nu} OH + H \\
& H_2O + H \longrightarrow OH + H_2 \\
& H_2S + H \longrightarrow SH + H_2 \\
& SH + H \longrightarrow S + H_2 \tag{1} \\
& S + OH \longrightarrow SO + H \\
& \underline{SO + OH \longrightarrow SO_2 + H} \\
& \text{net: } H_2S + 2H_2O \longrightarrow SO_2 + 3H_2
\end{align*}
$$

Water photolysis in (1) is an important source of atomic H that initiates the pathway. The last step of oxidising SO into SO₂ is generally the rate-limiting step. The oxidisation of SO and photolysis of SO₂ account for the main sources and sinks of SO₂, which lead to altitude-varying distribution that peaks around 0.1 mbar (see Extended Data Fig. 4). At high pressures with less available OH, reactions involving S₂ become important in oxidising S (see Methods).
<figure><img src="image_4.png" /></figure>

**Fig. 2: A simplified schematic of the chemical pathways of sulphur species.** H₂S, which is the stable sulphur-bearing molecule at thermochemical equilibrium in an H₂ atmosphere, readily reacts with atomic H to form SH radicals and subsequently atomic S in the photochemical region (above ~ 0.1 mbar). Reaction of S with photochemically-generated OH then produces SO, which is further oxidized to SO₂. The thick arrows denote efficient reactions and M denotes any third body. Inefficient reactions and inactive paths in the temperature regime of WASP-39b are greyed out. The dark cyan arrows mark the main path from H₂S to SO₂ whereas the orange arrows mark the path important at higher pressures. Sulphur species are colour-coded by the oxidation states of S. Rectangles indicate stable molecules while ovals indicate free radicals.

The growth of elemental sulphur allotropes beyond S₂ effectively stops for temperatures higher than ~ 750 K [5, 6].

Figure 3 shows the morning/evening averaged transmission spectra resulting from the different photochemical models. All models are able to reproduce the strength and shape of the 4.05 µm SO₂ feature seen in the NIRSpec PRISM and G395H modes. The scatter in the model spectra is on par with the uncertainties of the data, and is attributed to the spread in the vertical VMR structure of SO₂ and CO₂ produced by each model (Fig. 1). Also shown in Fig. 3 are the predicted spectra in the MIRI LRS wavelength range (5–12 µm), which exhibit prominent SO₂ features around 7.5 µm and 8.8 µm as well as an upward slope redward of 12 µm due to CO₂. In addition, our models predict a strong UV (0.2–0.38 µm) transmission signal from the presence of S species: H₂S, S₂, SO₂, and SH produce a sharp opacity gradient shortward of 0.38 µm (Extended data Fig. 7), where the room-temperature UV cross sections are used except those at 800 K for SH. The discrepancy between the models and previous HST STIS and VLT FORS2 observations [20] (see Fig. 3) within 0.38–0.5 µm could be potentially due to enhanced UV opacities at high
<figure><img src="image_5.png" /></figure>

**Fig. 3: Terminator averaged theoretical transmission spectra.** We show the transmission spectra averaged over the morning and evening terminators generated from 1D photochemical model results. (a): Comparison to the NIRSpec PRISM FIREFly reduction [8]). (b): Comparison to the NIRSpec G395H weighted-mean reduction [9]). (c): Comparison to the current HST and VLT/FORS2 optical wavelength data [19, 20], the models show pronounced features at UV wavelengths due to sulphur species compared to the model without S bearing species (dashed blue line). (d): Predicted spectra across the MIRI LRS wavelength range, with SO₂ removed from the VULCAN output shown in grey to indicate its contribution. All of the spectral data show 1-σ error bars and the standard deviations averaged (unweighted) over all reductions are shown for the NIRSpec G395H data.

temperatures and/or aerosol particles. Further characterization of the sulphur species spectral features in the UV is promising with the scheduled HST/UVIS observation (Program 17162, PIs Rustamkulov & Sing).

SO₂ has recently been suggested as a promising tracer of metallicity in giant exoplanet atmospheres [16]. To test this and reveal trends in atmospheric properties, we have conducted sensitivity analysis on metallicity as well as temperature and vertical mixing using VULCAN (see Methods for details and
<figure><img src="image_6.png" /></figure>

**Fig. 4:** The metallicity trends and synthetic spectra with varying metallicity. Panel (a) shows the averaged VMR of H₂O, CO₂, and SO₂ in the atmosphere between 10 and 0.01 mbar probed by transmission spectroscopy as a function of atmospheric metallicity. The nominal model is shown in solid lines, whereas the eddy diffusion coefficient (Kzz) scaled by 0.1 and 10 are shown in dashed and dashed-dotted lines, respectively. The models with the whole temperature increased and decreased by 50 K are indicated by the upward and downward facing triangles connected by dotted lines respectively. Panel (b) displays the morning and evening terminator-averaged theoretical transmission spectra with different metallicities (relative to solar value) compared with the NIRSpec observation.

further tests on C/O and stellar UV flux). Figure 4 (a) summarises these results for SO₂, along with H₂O and CO₂, which are more commonly used as proxies for atmospheric metallicity [13, 21–23]. Overall, the average abundance of SO₂ in the pressure region relevant for such observation is not strongly sensitive to temperature or vertical mixing once SO₂ has reached observable ppm levels and is mildly sensitive to C/O (see Extended Fig. 5). In contrast, SO₂ shows an either similar or stronger dependence on metallicity, compared to H₂O and CO₂. This sensitivity to metallicity can be understood from the net reaction (1), where it takes one molecule of H₂S and two molecules of H₂O to make one SO₂. While SO₂ can be further oxidised into SO₃, which requires additional oxygen, SO₃ is rarely produced to an observable level in an H₂-dominated atmosphere. Therefore, SO₂ can be an ideal tracer of heavy element enrichment for giant planets, with given constraints on the temperature and stellar FUV flux. The applicability of SO₂ as a tracer of metallicity is further shown in Figure 4 (b), where the increase in the SO₂ feature amplitude between 5× and 20× solar metallicity is much greater than that of CO₂ and H₂O. As such, retrieval analyses seeking to evaluate the atmospheric metallicity of warm giant exoplanets can substantially benefit from both CO₂ and SO₂ measurements.

Our results demonstrate the importance of considering photochemistry— and sulphur chemistry in particular—in warm exoplanet atmospheres when
interpreting exoplanet atmospheric observations. Exoplanet photochemistry has been investigated using numerical models since the detection of an atmosphere on a transiting exoplanet [24, 25], followed by a diverse set of subsequent studies elucidated the interplay of carbon, oxygen, nitrogen, hydrogen, and sulphur (e.g., see [26] for a review). It has been further pointed out that sulphur can impact other nonsulphur species, such as atomic H, CH₄, and NH₃ ([6, 15]; also see Extended Fig. 6). Temperature trends in the photochemical production of sulphur species (Extended Fig. 10) in exoplanet atmospheres are potentially observable with features in the UV and infrared (Fig. 3 and Extended Fig. 7). At temperatures higher than that of WASP-39b, SH and SO may become relatively more abundant than SO₂ [6, 13, 15]. Observing these compositional variations with temperature in H₂-dominated atmospheres, modulated by the atmospheric metallicity, could substantially improve our understanding of high-temperature chemical networks and atmospheric properties. The observational effort should also be complemented by a more accurate determination of key chemical reaction rate constants and UV cross sections at the relevant temperatures [e.g., 27, 28] as well as photochemical modelling developed beyond 1D that includes horizontal transport [e.g., 29–31].

The accessibility of sulphur species in exoplanet atmospheres through the aid of photochemistry allows for a new window into planet formation processes, whereas in the Solar System gas giants, the temperature is sufficiently low that sulphur is condensed out as either H₂S clouds or together with NH₃ as ammonium hydrosulphide (NH₄SH) clouds [32] making it more difficult to observe. Sulphur has been detected in protoplanetary discs [33] where it may be primarily in refractory form [34], making it a reference element revealing the metallicity contributions of accreted solid and gas [35–37]. Such efforts for warm giant exoplanets are now a possibility thanks to the observability of photochemically produced SO₂. Thus, the detection of SO₂ offers valuable insights into further atmospheric characterisation and planet formation.

**Data Availability.** The data used in this paper are associated with JWST program ERS #1366 and are available from the Mikulski Archive for Space Telescopes (https://mast.stsci.edu), which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-03127 for JWST. The chemical networks and abundance output of the photochemical models (ARGO, ATMO, KINETICS, and VULCAN) presented in this study are available at https://doi.org/10.5281/zenodo.7542781.

**Code Availability.**

The codes VULCAN and gCMCRT used in this work to simulate composition and produce synthetic spectra are publicly available:

VULCAN[6, 38] (https://github.com/exoclime/VULCAN)

gCMCRT[39] (https://github.com/ELeeAstro/gCMCRT)

**Acknowledgments.** This work is based on observations made with the NASA/ESA/CSA JWST. The working groups are associated with program
JWST-ERS-01366. The initial manuscript was improved by the constructive comments from Luigi Mancini, João Mendonça, Arianna Saba, and Xianyu Tan. S.-M.T. is supported by the European community through the ERC advanced grant EXOCONDENSE (#740963; PI: R.T. Pierrehumbert). E.K.H.L. is supported by the SNSF Ambizione Fellowship grant (#193448). X.Z. is supported by NASA Exoplanet Research grant 80NSSC22K0236. O.V. acknowledges funding from the ANR project ‘EXACT’ (ANR-21-CE49-0008-01), from the Centre National d'Études Spatiales (CNES), and from the CNRS/INSU Programme National de Planétologie (PNP). LD acknowledges support from the European Union H2020-MSCA-ITN-2109 under Grant no. 860470 (CHAMELEON) and the KU Leuven IDN/19/028 grant Escher. This work benefited from the 2022 Exoplanet Summer Program in the Other Worlds Laboratory (OWL) at the University of California, Santa Cruz, a program funded by the Heising-Simons Foundation.

**Author Contribution.** All authors played a significant role in the JWST Transiting Exoplanet Community Early Release Science Program, including the original proposal, preparatory work, tool development, and coordinating meetings, etc. Some specific contributions are listed as follows. SMT, PG, DP, XZ, EL, and VP designed the project and drafted the article. EL and LC performed 3D GCMs. SMT, JM, EH, OV, SJ, RH, JY, KM, RB, CJB, and AL development and/or performed photochemical models. SMT, JM, EH, OV, SJ, RH, KO, and PT contributed significantly to model comparisons and chemical analysis. KC and SMT compiled the sulphur opacities and EL computed the synthetic spectra. ZR, DS, JK, EvSc, EM, AC reduced and analysed the NIR-Spec PRISM data. LA, HRW, MKA, SB, DG, JI, TME, and NW reduced and analysed the NIRSpec G395 data, with additional contributions from JB and TD. BR, JF, SEM, SR, YM, KC, and LD provided significant feedback, with EH coordinated comments from all other authors, to improve the manuscript.

**Competing interests.** The authors declare no conflict of interests.

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# Methods

## 4.05 µm Feature

A list of gas species that have been compared to the 4.05 µm absorption feature in the transit observation of WASP-39b can be found in [8]. In particular, species with absorption features at similar wavelengths but are ruled out include H₂S, HCN, HBr, PH3, SiO, and SiO₂. H₂S and HCN absorb shortward of the feature at 4.05 µm while SiO₂ absorb longward of that, whereas HBr, SiO, and PH₃ have wider absorption bands than the observed feature. Chemically, SiO and SiO₂ are also expected to rain out at the temperature of WASP-39b and the solar elemental abundances have little bromine (Br/H ~ 4×10⁻¹⁰). Ultimately, the injection tests of SO₂ provide 2.7σ detection with NIRSpec PRISM [8] and 4.8σ with G395H [9].

## The Temperature-Pressure and Eddy Diffusion Coefficient Profiles Derived from the Exo-FMS GCM

To provide inputs to the 1D photochemical models, a cloud-free WASP-39b General Circulation Model (GCM) was run using the Exo-FMS GCM model [17]. We computed the transmission spectra derived from our photochemical model results using gCMCRT [39] and the ExoAmes high-temperature SO₂ line list [40]. System parameters were taken from [7]. We assume a 10× solar metallicity atmosphere in thermochemical equilibrium and use two-stream, correlated-k radiative-transfer without optical and UV wavelength absorbers such as TiO, VO and Fe, which are assumed to have rained out from the atmosphere given the atmospheric temperatures of WASP-39b. The assumption about thermochemical equilibrium in radiative transfer calculations will be discussed in the next section.

Although the temperatures of WASP-39b cross several condensation curves of sulfide clouds, such as Na₂S and ZnS, the gas composition is not expected to be significantly affected. The elemental abundances of Na and Zn are less abundant than S (Na/S ≈ 0.13, Zn/S ≈ 0.0029), which would at most reduce ≈ 20% of the total sulphur, similar to how oxygen being sequestered in silicates and metals [41]. Furthermore, this full condensation is unlikely since sulfide condensates generally have high surface energies [42, 43] that inhibit efficient nucleation, consistent with the detection of gaseous sodium on WASP-39b [8].

WASP-39b's radius is inflated significantly and we assume an internal temperature of 358 K, taken from the relationship between irradiated flux and internal temperature found in [44]. Extended Data Fig. 2 (a) shows the latitude-longitude map of the temperature at a pressure level of 10 mbar. The input to the photochemical models are the temperature-pressure profiles at the morning and evening limbs (Extended Data Fig. 2), which we compute by taking the average of the profiles over all latitudes and ± 10° (as estimated from the opening angle calculations from [45]) of the morning (western) and evening (eastern) terminators (i.e., the region between the grey curves in Extended
Data Fig 2 (a). The cooler morning terminator as a result of the horizontal heat transport facilitated by the global circulation can be seen in the figure.

Vertical mixing in 1D chemical models is commonly parameterised by eddy diffusion. For exoplanets, the eddy diffusion coefficient ($K_{zz}$) is in general a useful but loosely constrained parameter. For the 1D photochemical models used in this work, we assume $K_{zz}$ follows an inverse square-root dependence with pressure in the stratosphere [e.g., 30] as

$$K_{zz}(\mathrm{cm}^2 \mathrm{s}^{-1}) = 5 \times 10^7 \left( \frac{5\mathrm{bar}}{P} \right)^{0.5} \qquad (2)$$

and held constant below the 5-bar level in the convective zone. The eddy diffusion profile generally fits the root-mean-squared vertical wind multiplied by 0.1 scale height as the characteristic length scale from the GCM. The resulting $K_{zz}$ profile is presented in Extended Data Fig. 2.

## Radiative Feedback of Disequilibrium Composition

The temperature profiles adopted from the GCM assume chemical equilibrium abundances. To evaluate the radiative feedback from disequilibrium chemical abundances, we first performed self-consistent 1D calculations, coupling the radiative-transfer and photochemical kinetics models using HELIOS[47] and VULCAN[6], where the opacity sources in HELIOS include H₂O, CH₄, CO, CO₂, NH₃, HCN, C₂H₂, SH, H₂S, SO₂, Na, K, H⁻, ClA H₂–H₂ and H₂–He (see references in [47]). Yet we found negligible differences between the temperature profile computed from equilibrium abundances and that from disequilibrium abundances. This is likely because water, as the predominant infrared opacity source, remains unaffected by disequilibrium processes. Meanwhile, a few opacities are missing in our radiative-transfer calculation. In particular, the opacity of SO₂ [49] does not extend into the visible and UV wavelength range. Previous works [13] and [50] indicated that SH and S₂ have strong absorption in the UV-visible and can potentially impact the thermal structure. To quantify the radiative effect of these sulphur species, we calculated the shortwave heating rate with

$$c_P \frac{dT}{dt} = \frac{F \kappa_i \Delta m_i}{\Delta m_{\text{air}}} \qquad (3)$$

where $c_P$ is the specific heat capacity of the air, F is the stellar flux associated with the direct beam, and $\Delta m_i$, $\Delta m_{\text{air}}$ are the column mass of species i and air of an atmospheric layer, respectively. Extended Data Fig. 3 illustrates the shortwave heating due to SH and S₂, and SO₂. Our estimate shows that SO₂ contributed the most in our WASP-39b model, rather than SH and S₂ being the main shortwave absorbers for atmospheres with solar-like metallicity [13][50]. The peak of heating due to SO₂ is comparable to a grey opacity of 0.05 cm²/g over 220–800 nm and could potentially raise the temperatures around 0.1 mbar (the visible grey opacity for WASP-39b’s irradiation is about 0.005 cm²/g [51]). Nevertheless, this heating effect does not change our main conclusions about
photochemically forming SO₂ on WASP-39b. As long as temperatures do not fall below ~750 K where sulphur allotrope formation starts to take over, SO₂ is not too sensitive to temperature increases up to 100 K.

## The Stellar Spectrum of WASP-39

We require the high-energy spectral energy distribution (SED) of the WASP-39 host star as input to drive our set of photochemical models. However, as an inactive mid G-type star ($T_{eff} = 5485 \pm 50$ K; [52]) at a distance of 215 pc (Gaia DR3), WASP-39 is too faint for high-S/N ultraviolet spectroscopy with HST. In order to approximate the stellar radiation incident on WASP-39b, we created a custom stellar SED that combines direct spectroscopy of WASP-39 in the optical (with HST/STIS G430L and G750L modes; GO 12473, PI - D. Sing) with representative spectra from analogous stars at shorter wavelengths.

Our approach to estimating the ultraviolet stellar SED was based on two factors: 1) in the NUV (2300 – 2950 Å), where the flux is dominated by the photosphere, we chose a proxy with a similar spectral type to WASP-39, and 2) in the XUV and FUV (1 – 2300 Å), where the stellar flux is dominated by chromospheric, transition region, and coronal emission lines, we chose a proxy star with similar chromospheric activity indicators and used spectral type as a secondary consideration. In the NUV, we used HST/STIS E230M spectra of HD 203244, a relatively active (Ca II log($R'_{HK}$) = -4.4 [53]), nearby (i.e., unreddened, $d = 20.8$ pc; Gaia DR2), G5 V star ($T_{eff}=5480$ K; [54]) from the STARCat archive [55]. While HD 203244 is a suitable proxy at photospheric wavelengths, WASP-39 is a relatively old (~7 Gyr) star with low chromospheric activity (log $R'_{HK}$ = -4.97 ± 0.06) and a long rotation period ($P_{rot}$ = 42.1 ± 2.6 days; [52]), suggesting significantly lower high-energy flux than HD 203244. Therefore, we elected to use a lower-activity G-type star, the Sun, at wavelengths shorter than 2300 Å. The Sun has high-quality archival data available across the UV and X-rays and similar chromospheric activity to WASP-39 (the average solar Ca II log($R'_{HK}$) value is -4.902 ± 0.063, and ranges from approximately -4.8 to -5.0 from solar maximum to solar minimum [56, 57]). With the components in hand, we first corrected the observed STIS spectra of WASP-39 for interstellar dust extinction of $E(B - V) = 0.079$ [58] using a standard $R_V = 3.1$ interstellar reddening curve [59], then interpolated all spectra onto a 0.5 Å pixel⁻¹ grid. The NUV spectrum of HD 203244 was scaled to the reddening-corrected WASP-39 observations in the overlap region between 2900 and 3000 Å, and the XUV+FUV spectrum of the quiet Sun [60] was scaled to the blue end of the combined SED. The flux scaling between two spectral components is defined as $((F_{ref} - \alpha \times F_{proxy}) / \sigma_{ref})^2$ in the overlap region, where “proxy” is the spectrum being scaled, “ref” is the spectrum to which we are scaling, and $\alpha$ is the scale factor applied to the proxy spectrum. $\alpha$ is varied until the above quantity is minimized ($\alpha = 2.04 \times 10^{-16}$ and $7.58 \times 10^{-3}$ for the FUV and NUV component, respectively.). The final combined spectrum was convolved with a 2 Å FWHM Gaussian kernel, and wavelengths longer than 7000 Å were removed to avoid the near-IR fringing
in the STIS G750L mode. We show the stellar spectrum at the surface of the
star used for our photochemical models in Extended Data Fig. 2.

We compared our estimated SED for WASP-39 against archival *GALEX* observations from [61], who find the NUV (1771–2831 Å) flux density to be 168.89 µJy, or an average NUV spectral flux of $F_\lambda = 9.8 \times 10^{-16}$ erg cm$^{-2}$ s$^{-1}$ Å$^{-1}$ at 2271 Å. Correcting this value by the average extinction correction in the *GALEX* NUV bandpass, a factor of 1.79, and comparing it to the average flux of our estimated SED over the same spectral range (1.66 × $10^{-15}$ erg cm$^{-2}$ s$^{-1}$ Å$^{-1}$), we find the agreement between the *GALEX* measurement of WASP-39 and our stellar proxy to be better than 6%.

Simulated Transmission Spectra from gCMCRT

To post-process the 1D photochemical model output and produce transmission spectra, we use the 3D Monte Carlo radiative-transfer code gCMCRT [39].

For processing 1D columns, gCMCRT uses 3D spherical geometry but with a constant vertical profile across the globe in latitude and longitude. In this way, spectra from 1D outputs can be computed. We process each photochemical model's morning and evening terminator vertical 1D chemical profiles separately, taking the average result of the two transmission spectra to produce the final spectra that are compared to the observational data.

In the transmission spectra model, we use opacities generated from the following line lists: H₂O [63], OH [64] CO [65], CO₂ [66], CH₄ [67], CH₃ [68], HCN [69], C₂H₂ [70], C₂H₄ [71], C₂H₆ [72], C₄H₂ [72], C₂ [73], CN [74], CH [75], SO₂ [40], SH [49], SO [76], H₂S [77], NO [78], N₂O [78], NO₂ [78], HCl [72], Na [79], K [79].

Description of Photochemical Models

We use the following 1D thermo-photochemical models to produce the steady-
state chemical abundance profiles for the terminators of WASP-39b. All models
assume cloud-free conditions and adopt the same temperature profiles, stellar
UV flux, eddy diffusion coefficient profile (Extended Data Fig. 2), and zero-
flux (closed) boundary conditions. A zenith angle of 83 degrees (an effective
zenith angle that matches the terminator-region-mean actinic flux for near-
unity optical depth) is assumed for the terminator photochemical modelling.

VULCAN

The 1D kinetics model VULCAN treats thermochemical [38] and photochem-
ical [6] reactions. VULCAN solves the Eulerian continuity equations including
chemical sources/sinks, diffusion and advection transport, and condensa-
tion. We applied the C–H–N–O–S network (https://github.com/exoclime/
VULCAN/blob/master/thermo/SNCHOPhoto_network.txt) for reduced
atmospheres containing 89 neutral C-, H-, O-, N-, and S-bearing species and
1028 total thermochemical reactions (i.e., 514 forward-backward pairs) and
60 photolysis reactions. The sulphur allotropes are simplified into a system
of S, S₂, S₃, S₄, and S₈. The sulphur kinetics data is drawn from the NIST and KIDA databases, as well as modelling [80][5] and ab-initio calculations published in the literature [e.g., 81]. For simplicity and cleaner model comparison, the temperature-dependent UV cross sections [6] are not used in this work. The pathfinding algorithm described in [82] is utilised to identify the important chemical pathways. We note that the paths presented in this study are mainly based on VULCAN output (see Extended Data Table 1). While detailed reactions might differ between different photochemical models, the major paths remain robust.

## KINETICS

The “KINETICS” 1D thermo-photochemical transport model [41] uses the Caltech/JPL KINETICS model [83, 84] to solve the coupled 1D continuity equations describing the chemical production, loss, and vertical transport of atmospheric constituents of WASP-39 b. The model contains 150 neutral C-, H-, O-, N-, S-, and Cl-bearing species that interact with each other through 2350 total reactions (i.e., 1175 forward-reverse reaction pairs). These reactions have all been fully reversed through the thermodynamic principle of microscopic reversibility [85], such that the model would reproduce thermochemical equilibrium in the absence of transport and external energy sources, given sufficient integration time. The chemical reaction list involving C-, H-, O-, and N-bearing species is taken directly from [23]. Included for the first time here are 41 sulphur and chlorine species: S, S(1D), S₂, S₃, S₄, S₈, SH, H₂S, HS₂, H₂S₂, CS, CS₂, HCS, H₂CS, CH₃S, CH₃SH, SO, SO₂, SO₃, S₂O, HOSO₂, H₂SO₄ (gas and condensed), OCS, NS, NCS, HNCS, Cl, Cl₂, HCl, ClO, HOCl, ClCO, ClCO₃, CIS, ClS₂, Cl₂S, ClSH, OSCl, ClSO₂, and SO₂Cl₂. The thermodynamic data of several chlorine- and sulphur-bearing species are not available in previous literature, and we performed ab initio calculations for these species. We first carried out electronic structure calculations at the CBS-QB3 level of theory using Gaussian 09 ([86]) to determine geometric conformations, energies, and vibrational frequencies of the target molecules. Then the thermodynamic properties of these molecules were calculated by Arkane ([87]), a package included in the open-source software RMG v3.1.0 ([88, 89]), with atomic energy corrections, bond corrections, and spin-orbit corrections, based on the CBS-QB3 level of theory as the model chemistry. The reaction rate coefficients and photolysis cross sections for these S and Cl species are derived from Venus studies [90–95], interstellar medium studies [96], Io photochemical models [97, 98], Jupiter cometary-impact models [99, 100], the combustion-chemistry literature [101–104], terrestrial stratospheric compilations [105, 106], and numerous individual laboratory or computational kinetics studies [e.g., 107–111].
## ARGO

The 1D thermochemical and photochemical kinetics code, ARGO, originally [112, 113] utilised the Stand2019 network for neutral hydrogen, carbon, nitrogen and oxygen chemistry. ARGO solves the coupled 1D continuity equation including thermochemical-photochemical reactions and vertical transport. The Stand2019 network was expanded by Ref [114] by updating several reactions, incorporating the sulphur network developed by Ref [15], and supplementing it with reactions from Ref [116] and Ref [94], to produce the Stand2020 network. The Stand2020 network includes 2901 reversible reactions and 537 irreversible reactions, involving 480 species composed of H, C, N, O, S, Cl and other elements.

## ATMO

The C-H-N-O chemical kinetics scheme from Ref [117] is implemented by Ref [118] in the standard 1D atmosphere model ATMO, which solves for the chemical disequilibrium steady state. As of the time of writing of this article, the sulphur kinetic scheme of ATMO, derived from applied combustion models, is still at the development and validation stage. Hence, for WASP-39b, we performed ATMO with the C-H-N-O-S thermochemical network from VULCAN [6] along with the photochemical scheme from Ref [119] (an update of the native photochemical scheme from Ref [117]), with the additional 71 photolysis reactions of H₂S, S₂, S₂O, SO, SO₂, CH₃SH, SH, H₂SO, and COS.

## Sensitivity Tests

We examine the sensitivity of our chemical outcomes to essential atmospheric properties using VULCAN. For models with various metallicity and C/O ratios, we explore the sensitivity to temperature and vertical mixing by systematically varying the temperature-pressure and eddy diffusion coefficient profiles. Specifically, the temperature throughout the atmosphere is shifted by 50 K and the eddy diffusion coefficients are multiplied/divided by 10. These variations span a range comparable to the temperature differences among radiative transfer models [47] and the uncertainties in parameterising vertical mixing with eddy diffusion coefficients [120, 121]. Regarding our choice of internal heat, we have further conducted tests with different internal temperatures and found the compositions above 1 bar are not sensitive to internal temperature, because the quench levels of the main species are at higher levels given the adopted eddy diffusion coefficient. We have also verified that the temperature above the top boundary of the GCM (~5 × 10⁻⁵ bar; Extended Data Fig. 2) does not impact the composition below.

Sensitivity to C/O is summarised in Extended Data Fig. 5 where the nominal model has a C/O ratio of 0.55 as in the main text. The averaged abundance of both SO₂ and H₂O in the pressure region relevant for transmission spectrum observations show similar dependencies on C/O, decreasing by a few factors as the C/O increased from sub-solar (0.25) to super-solar (0.75) values. The
averaged abundance of SO₂ is not too sensitive to temperature and vertical mixing either, except for C/O = 0.75 where the SO₂ concentration is ~ ppm level, similar to what is found in Figure 4.

Finally, we performed sensitivity tests to the UV irradiation – the ultimate energy source of photochemistry. We first tested the sensitivity to the assumed stellar spectra by performing the same models with the solar spectrum (close to WASP-39) and found negligible differences in the photochemical results. Since the UV spectrum shortward of 295 nm is constructed from stellar proxies rather than directly measured, we then focused on varying the stellar flux in the FUV (1–230 nm) and NUV (230–295) separately. Extended Fig. 8 shows that the resulting sulphur species abundances are almost identical when the UV flux is reduced by a factor of 10, broadly consistent with what [5] suggested that the photochemical destruction of H₂S only becomes photon limited when the stellar UV flux is reduced by about two orders of magnitude (for a directly imaged gas giant). On the other hand, while SO and SO₂ are not sensitive to increased NUV, they are significantly depleted with increased FUV. This is owing to that the photodissociation of SO and SO₂ mainly operates in the FUV, and the enhanced FUV can destroy SO and SO₂, even with the same amount of available OH radicals.

## Spectral Effects of Assuming a Vertically Uniform SO₂ Distribution

Minor species commonly have VMR varying with altitude in the observable region of the atmosphere, especially those produced or destroyed by photo-chemistry. Extended Fig. 9 demonstrates that assuming a vertically-constant VMR of SO₂ can lead to underestimating its abundances by about an order of magnitude. This is verified by comparing the column-integrated number density from the pressure level relevant for transmission spectroscopy. For example, the terminator-averaged column-integrated number density of SO₂ above 10 mbar by VULCAN is about 1.4 × 10¹⁹ molecules/cm², which is equal to a vertically uniform SO₂ with a concentration around 4 ppm. Hence modelling frameworks that assume vertically uniform composition should be treated with caution and would benefit from comparisons with photochemical models, especially for photochemical active species that can exhibit large vertical gradients.

## Opacities of Sulphur Species

The opacities of sulphur species illustrated in extended data Fig. 7 are compiled from UV cross sections and IR line lists. The room-temperature UV cross sections are taken from the Leiden Observatory database [122](http://home.strw.leidenuniv.nl/~ewine/photo). The IR opacities include SO₂[123], H₂S[124], [125], CS[126], and a newly computed high-temperature line list for SO[127]. The opacity from OCS[128] is currently only available up to room temperature, hence its coverage is likely incomplete in our region of interest.
Alternative SO₂ production pathways

S₂ formation can compete with SO₂ production, as we will explore in detail in the next section. On WASP-39b, reactions involving S₂ are found to be important in oxidising S at high pressures where less OH is available. S and SH would first react to form S₂ by SH + S → H + S₂ before getting oxidised through S₂ + OH → SO + SH. The scheme is similar to (1) except SH and S₂ play the role of catalyst to oxidise S into SO while SO can also self-react to form SO₂ in this regime (references of important reactions are listed in Extended Data Table 1).

Implications of Observing Sulphur Photochemistry

The temperature of WASP-39b resides within the sweet spot of producing SO₂[16]. Previous photochemical modelling works suggested that at lower temperatures, sulphur allotropes would be favoured over SO₂ while SH can prevail at higher temperatures[5, 6]. Here, we briefly elucidate the general temperature trends of sulphur photochemical products.

After S is liberated from H₂S, sulphur can either follow the oxidisation or chain polymerisation paths, as illustrated in Fig. 2. The competing of the two paths is essentially controlled by the abundance of the oxidising radical OH relative to atomic H. We can estimate the OH to H ratio by assuming OH is in quasi-equilibrium with H₂O, i.e. k<sub>H₂O</sub>[H₂O][H] = k'<sub>H₂O</sub>[OH][H₂], where k<sub>H₂O</sub> and k'<sub>H₂O</sub> are the forward and backward rate constants of H₂O + H → OH + H₂, respectively. Then [OH]/[H] ~ 2 (k<sub>H₂O</sub>/k'<sub>H₂O</sub>) × O/H, since most of the O is in H₂O. Extended Data Fig. 10 (a) shows that the [OH]/[H] ratio strongly depends on temperature. When the temperature drops below ~750 K, the scarcity of OH makes S preferably react with SH to form S₂. SO and SO₂ could only be produced at higher altitudes where more OH is available from water photolysis [e.g., 5, 6].

We further perform photochemical calculations using VULCAN with a grid of temperature profiles across planetary equilibrium temperatures 600–2000 K, adopted from the 1D radiative-convective equilibrium models applied in [130], where an internal temperature of 100 K with perfect heat redistribution and gravity g = 1000 cm/s² are assumed. Apart from the thermal profiles, we keep the rest of the planetary parameters the same as the WASP-39b model in this work, including stellar UV irradiation. Extended Data Fig. 10 (b) sheds light on observing sulphur photochemistry on other irradiated exoplanets, summarising the averaged abundances of the key sulphur molecules produced by photochemistry as a function of equilibrium temperature. For 10 × solar metallicity, the sweet spot temperature for producing observable SO₂ is 1000 K ~ Tₐ₉ ≲ 1600 K. For Tₐ₉ ≲ 1000 K, SO₂ production below the 0.01 mbar level ceased and Sₓ (sulphur allotropes; mainly S₂ and S₈ here) is more favoured. For Tₐ₉ ≳ 1600 K, SH becomes the predominant sulphur-bearing molecular (apart from atomic S) around mbar levels. While observing SH is challenging in the infrared, it can potentially be identified in the Near-UV (300–400 nm) [131].
Extended Data

<figure><img src="image_7.png" /></figure>

**Extended Data Fig. 1:** Chemical equilibrium abundances in the atmosphere of WASP-39b. The volume mixing ratio profiles of H₂O (blue), CO₂ (orange), H₂S (green), and SO₂ (red), as computed by FastChem [132] based on the morning terminator temperature profile, are given for 10 × (solid) and 100 × (dashed) solar metallicity.
<figure><img src="image_8.png" /></figure>

(a)

<figure><img src="image_9.png" /></figure>

(b)

<figure><img src="image_10.png" /></figure>

(c)

**Extended Data Fig. 2:** The temperature-wind map of the WASP-39b Exo-FMS GCM and input for 1D photochemical models. (a): The colour scale represents temperature across the planet and arrows denote the wind direction and magnitude at 10 mbar. The ± 10° longitudinal regions with respect to the morning and evening terminators are indicated with solid grey lines. The '+' symbol denotes the sub-stellar point. (b): 1D Temperature-Pressure profiles adopted from the morning and evening terminators averaging all latitudes and ± 10° longitudes (grey-line enclosed regions in panel (a)) and the $K_{zz}$ profile (Equation (2)) and held constant below the 5-bar level) overlaying the root-mean-squared vertical wind multiplied by 0.1 scale height from the GCM (grey). The temperatures are kept isothermal from those at the top boundary of the GCM around $5 \times 10^{-5}$ bar when extending to lower pressures ($\sim 10^{-8}$ bar) for photochemical models. (c): Input WASP-39 stellar flux at the surface of the star. The pink shaded region indicates the optical wavelength range where the stellar spectrum is directly measured, whereas the blue and green shaded regions are those constructed from the Sun and HD 20324, respectively.
<figure><img src="image_11.png" /></figure>

**Extended Data Fig. 3:** Shortwave radiative heating of sulphur species. Radiative heating rates (erg s⁻¹ g⁻¹) of SO₂, SH, and H₂S to demonstrate their potential impact on the temperature structure. Heating due to a vertically constant grey opacity of 0.05 cm² g⁻¹ is shown for comparison. All heating rates are integrated over 220–800 nm.
<figure><img src="image_12.png" /><figcaption>Extended Data Fig. 4: The main source and sink profiles of SO₂ in our WASP-39b model. The reaction rates of the main sources and sinks of SO₂ in the VULCAN morning-terminator model for WASP-39b. The dashed lines of the same colour are the corresponding reverse reactions and the black dotted line indicates the distribution profile (arbitrarily scaled) of SO₂.</figcaption></figure>
<figure><img src="image_13.png" /><figcaption>**Extended Data Fig. 5: The C/O trends and synthetic spectra.** Same as Fig. 4 but as a function of a function of C/O ratio at 10× solar metallicity. Panel (a) shows the averaged VMR of H₂O, CO₂, and SO₂ between 10 and 0.01 mbar as a function of C/O ratio, where the solar C/O is 0.55. The nominal model is shown in solid lines, whereas the eddy diffusion coefficient (*K*<sub>zz</sub>) scaled by 0.1 and 10 are shown in dashed and dashed-dotted lines, respectively. The model for which the whole temperature increased and decreased by 50 K are indicated by the upward and downward facing triangles connected by dotted lines respectively. Panel (b) displays the morning and evening terminator-averaged theoretical transmission spectra with different C/O ratios compared with the NIRSpec PRISM observation. The error bars show 1-σ standard deviations.</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>**Extended Data Fig. 6: The impact of sulphur on other nonsulphur species.** Volume mixing ratio profiles of some species in our WASP-39b model that exhibit differences from VULCAN including sulphur kinetics (solid) and without sulphur kinetics (dashed).</figcaption></figure>
<figure><img src="image_15.png" /><figcaption>Extended Data Fig. 7: The opacities of several sulphur species. Opacities of several sulphur species at 1000 K and 1mbar, except that those in the UV and of OCS are at room temperature. The opacities in the infrared are binned down to R ~ 1000 for clarity.</figcaption></figure>
<figure><img src="image_16.png" /></figure>

**Extended Data Fig. 8:** The main sulphur species abundances with reduced and enhanced UV irradiation. Volume mixing ratio profiles of the main sulphur species in the VULCAN morning-terminator model with 0.1× (Panel (a)) and 10× (Panel (b)) UV. Our nominal model is shown in solid lines for comparison, while the model with varying FUV (1–230 nm) is shown in dashed line and that with varying NUV (230–295 nm) is shown in dashed-dotted line.

<table><caption>**Extended Data Table 1:** Important reactions for SO₂ Production.
Selected list of reactions relevant for SO₂ Production in the VULCAN model of WASP-39b.</caption><thead><tr><th>Reaction</th><th>Rate Coefficient<br>(cm<sup>3</sup> molecules<sup>-1</sup> s<sup>-1</sup>)</th><th>Valid Temperature<br>(K)</th><th>Ref.</th></tr></thead><tbody><tr><td>H<sub>2</sub>S + H → SH + H<sub>2</sub></td><td>5.8 × 10<sup>-17</sup> T<sup>1.94</sup> exp(-455/T)</td><td>190–2237</td><td>[109]</td></tr><tr><td>SH + H → S + H<sub>2</sub></td><td>2.16 × 10<sup>-11</sup></td><td>295</td><td>[133]</td></tr><tr><td>S + OH → SO + H</td><td>6.59 × 10<sup>-11</sup></td><td>298</td><td>[107]</td></tr><tr><td>SO + OH → SO<sub>2</sub> + H</td><td>1.79 × 10<sup>-7</sup> T<sup>-1.35</sup></td><td>295–703</td><td>[134]</td></tr><tr><td>S + SH → S<sub>2</sub> + H</td><td>4 × 10<sup>-11</sup></td><td>295</td><td>[135]</td></tr><tr><td>SO + SH → S<sub>2</sub> + OH</td><td>1 × 10<sup>-13</sup> exp(-2300/T)</td><td></td><td>Est.[102]</td></tr><tr><td>SO + SO → SO<sub>2</sub> + S</td><td>3.5 × 10<sup>-15</sup></td><td>298</td><td>[136]</td></tr></tbody></table>

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<figure><img src="image_17.png" /><figcaption>Extended Data Fig. 9: The effects of assuming a vertically uniform distribution of SO₂. Terminator-averaged theoretical transmission spectra generated from abundance distribution computed by photochemical model VULCAN compared to assuming constant 1, 5, 10 ppm of SO₂. As before, the NIRSpec PRISM observation is displayed with 1-σ error bars.</figcaption></figure>

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<figure><img src="image_18.png" /><figcaption>Extended Data Fig. 10: The OH to H ratio and the temperature trends for sulphur molecules produced by photochemistry. Panel (a) shows $k_{H_2O}/k'_{H_2O} \times O/H$ as a proxy of OH to H ratio at $10 \times$ solar metallicity, where $k_{H_2O}$ and $k'_{H_2O}$ are the forward and backward rate constants of $H_2O + H \rightarrow OH + H_2$, respectively. When OH becomes scarce relative to H as temperature decreases, the chain-forming path (not required OH) is favoured over the oxidisation path (required OH). Panel (b) presents the average VMR between 10 and 0.01 mbar as a function of planetary equilibrium temperature with temperature profiles adopted from [130] (see text for the setup). The grey dotted line marks approximately the required $SO_2$ concentration to be detectable with WASP-39b parameters. $S_x$ denotes the allotropes $S_2$ and $S_8$ and $SO_x$ denotes the oxidised species SO and $SO_2$.</figcaption></figure>

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## Author Affiliations
¹Atmospheric, Oceanic and Planetary Physics, Department of Physics, University of Oxford, Oxford, UK.

²Department of Earth Sciences, University of California, Riverside, California, USA.

³Center for Space and Habitability, University of Bern, Bern, Switzerland.

⁴Center for Astrophysics | Harvard & Smithsonian, Cambridge, USA.

⁵Earth and Planets Laboratory, Carnegie Institution for Science, Washington, DC, USA.

⁶Department of Earth and Planetary Sciences, University of California Santa Cruz, Santa Cruz, CA, USA.

⁷Space Science Institute, Boulder, CO, USA.

⁸University of Exeter, Exeter, UK.

⁹Université de Paris Cité and Univ Paris Est Creteil, CNRS, LISA, F-75013 Paris, France.

¹⁰Université Côte d'Azur, Observatoire de la Côte d'Azur, CNRS, Laboratoire Lagrange, Nice, France.

¹¹Institute of Astronomy, University of Cambridge, Cambridge, UK.

¹²Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA.

¹³Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, CA, USA.

¹⁴School of Physics, University of Bristol, Bristol, UK.

¹⁵Department of Astronomy & Astrophysics, University of California, Santa Cruz, Santa Cruz, CA, USA.

¹⁶Department of Astronomy & Astrophysics, University of Chicago, Chicago, IL, USA.

¹⁷Department of Physics and Institute for Research on Exoplanets, Université de Montréal, Montreal, QC, Canada.

¹⁸School of Earth and Space Exploration, Arizona State University, Tempe, AZ, USA.

¹⁹Department of Physics and Astronomy, University College London, United Kingdom.

²⁰Space Research Institute, Austrian Academy of Sciences, Graz, Austria.

²¹Centre for Exoplanet Science, University of St Andrews, St Andrews, UK.

²²Department of Physics & Astronomy, Johns Hopkins University, Baltimore, MD, USA.

²³Laboratoire d'Astrophysique de Bordeaux, Université de Bordeaux, Pessac, France.

²⁴Leiden Observatory, University of Leiden, Leiden, The Netherlands.

²⁵SRON Netherlands Institute for Space Research, Leiden, the Netherlands.

²⁶Universitäts-Sternwarte, Ludwig-Maximilians-Universität München, München, Germany.

²⁷Exzellenzcluster Origins, München, Germany.
<sup>28</sup>Department of Earth and Planetary Sciences, Johns Hopkins University, Baltimore, MD, USA.

<sup>29</sup>Johns Hopkins APL, Laurel, MD, USA.

<sup>30</sup>Indian Institute of Technology, Indore, India.

<sup>31</sup>Anton Pannekoek Institute for Astronomy, University of Amsterdam, Amsterdam, The Netherlands.

<sup>32</sup>Planetary Science Institute, Tucson, AZ, USA.

<sup>33</sup>Department of Astrophysical Sciences, Princeton University, Princeton, NJ, USA.

<sup>34</sup>LSSTC Catalyst Fellow.

<sup>35</sup>Laboratory for Atmospheric and Space Physics, University of Colorado Boulder, Boulder, CO, USA.

<sup>36</sup>School of Earth and Planetary Sciences (SEPS), National Institute of Science Education and Research (NISER), HBNI, Odisha, India.

<sup>37</sup>Department of Physics, Imperial College London, London, UK.

<sup>38</sup>Imperial College Research Fellow.

<sup>39</sup>Max Planck Institute for Astronomy, Heidelberg, Germany.

<sup>40</sup>Lunar and Planetary Laboratory, University of Arizona, Tucson, AZ, USA.

<sup>41</sup>Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA, USA.

<sup>42</sup>Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, Cambridge, MA, USA.

<sup>43</sup>51 Pegasi b Fellow.

<sup>44</sup>Astronomy Department and Van Vleck Observatory, Wesleyan University, Middletown, CT, USA.

<sup>45</sup>Maison de la Simulation, CEA, CNRS, Univ. Paris-Sud, UVSQ, Université Paris-Saclay, Gif-sur-Yvette, France.

<sup>45</sup>Université Paris-Saclay, Université Paris-Cité, CEA, CNRS, AIM, Gif-sur-Yvette, France.

<sup>46</sup>Chemistry and Planetary Sciences, Dordt University, Sioux Center, Iowa, USA.

<sup>47</sup>NHFP Sagan Fellow.

<sup>48</sup>NASA Goddard Space Flight Center, Greenbelt, MD, USA.

<sup>49</sup>Centre for Exoplanets and Habitability, University of Warwick, Coventry, UK.

<sup>50</sup>Department of Physics, University of Warwick, Coventry, UK.

<sup>51</sup>NASA Ames Research Center, Moffett Field, CA, USA.

<sup>52</sup>Department of Astrophysical and Planetary Sciences, University of Colorado, Boulder, CO, USA.

<sup>53</sup>Department of Physics, New York University Abu Dhabi, Abu Dhabi, UAE.

<sup>54</sup>Center for Astro, Particle and Planetary Physics (CAP3), New York University Abu Dhabi, Abu Dhabi, UAE.

<sup>55</sup>School of Physics and Astronomy, University of Leicester, Leicester.
⁵⁶Department of Physics and Astronomy, University of Kansas, Lawrence, KS, USA.

⁵⁷INAF - Turin Astrophysical Observatory, Pino Torinese, Italy.

⁵⁸Institute of Astronomy, Department of Physics and Astronomy, KU Leuven, Leuven, Belgium.

⁵⁹NSF Graduate Research Fellow.

⁶⁰School of Physics, Trinity College Dublin, Dublin, Ireland.

⁶¹Planetary Sciences Group, Department of Physics and Florida Space Institute, University of Central Florida, Orlando, Florida, USA.

⁶²Department of Astronomy, University of Maryland, College Park, MD, USA.

⁶³California Institute of Technology, IPAC, Pasadena, CA, USA.

⁶⁴Département d'Astronomie, Université de Genève, Sauverny, Switzerland.

⁶⁵Department of Physics, Utah Valley University, Orem, UT, USA.

⁶⁶Steward Observatory, University of Arizona, Tucson, AZ, USA.

⁶⁷Department of Physics and Astronomy, Faculty of Environment Science and Economy, University of Exeter, UK.

⁶⁸Instituto de Astrofísica de Canarias (IAC), Tenerife, Spain.