Biogenic Sulfur Gases as Biosignatures on Temperate Sub-Neptune Waterworlds

The Kepler mission revealed a large fraction of discovered planets with radii between Earth and Neptune (Howard et al. 2012; Thompson et al. 2018; Bean et al. 2021). Observed masses and radii indicate a population of sub-Neptunes likely containing water-rich interiors, while evolution models also point to the existence of these waterworlds on the population scale (Zeng et al. 2019; Venturini et al. 2020; Luque & Pallé 2022; Rogers et al. 2023). In particular, several such planets orbiting M dwarf stars receive comparable instellation ⁷ to Earth, placing them in their planetary systems' habitable zones (e.g., Table 1 in Madhusudhan et al. 2021). These temperate sub-Neptunes have sparked great interest in atmospheric characterization and the assessment of habitability. Given suitable climate conditions (Innes et al. 2023; Pierrehumbert 2023), these water-rich worlds could host surface water oceans below hydrogen-rich atmospheres—recently referred to as "Hycean" (Hydrogen ocean) worlds (Madhusudhan et al. 2021; Nixon & Madhusudhan 2021). Promisingly, their hydrogen-rich envelopes are more favorable for atmospheric characterization in transmission observations due to large scale heights, compared to the higher molecular weight N₂- or CO₂-dominated atmospheres.

Since the water detection in the atmosphere of the temperate sub-Neptune K2-18 b (Benneke et al. 2019; Tsiaras et al. 2019), follow-up analyses and modeling efforts have sought to unveil the nature of K2-18 b and similar temperate sub-Neptunes. Madhusudhan et al. (2020) explored the bulk composition under different interior structures. Tsai et al. (2021b) and Yu et al. (2021) proposed using atmospheric compositional evolution to infer the presence of a shallow surface, whereas Hu et al. (2021) investigated the carbon inventories in a Hycean planet scenario. Recent JWST transit observations revealed a strong detection of carbon dioxide (CO₂) and methane (CH₄) on K2-18 b (Madhusudhan et al. 2023). Based on this basis and upper limits of carbon monoxide (CO) and ammonia (NH₃), Madhusudhan et al. (2023) argued that the atmospheric characteristics of K2-18 b are more consistent with a Hycean world scenario. However, several inconsistencies warrant consideration: (1) It is challenging to accumulate a percentage level of CH₄ without biological input or thermochemical recycling from the interior (Tsai et al. 2021b; Yu et al. 2021). (2) On Hycean planets, CO can still be efficiently produced to around 0.1%–1% level through photolysis of CO₂, while the quenched CO abundance is controlled by the interior temperature on Neptune-like planet with a thick (≳100 bar) H₂ atmosphere (Wogan et al. 2024). (3) The cross-correlation method may be required to identify CO in JWST NIRSpec data (Esparza-Borges et al. 2023), while current analysis based on a single transit observation might not be sufficient to conclusively rule out NH₃ before the upcoming MIRI and revisit observations (JWST Cycle 1, GO-2722, and GO-2372).

Intriguingly, Madhusudhan et al. (2023) also reported a tentative detection of dimethylsulfide (DMS), which is predominately produced by marine microbes on Earth and regarded as a biosignature gas, especially for anoxic biospheres (see Domagal-Goldman et al. 2011 and Schwieterman et al. 2018 for a review). On modern Earth, DMS is the main biological source of sulfur, about 1.8–3.5 × 10⁹ molecules cm⁻²s⁻¹ (Seinfeld & Pandis 2016; Cala et al. 2023). DMS and methanethiol (CH₃SH) are released from the degradation of dimethylsulfoniopropionate (DMSP), an organosulfur compound produced by marine phytoplankton. Microbial methylation and detoxification processes can also actively produce DMS from hydrogen sulfide (H₂S; Li et al. 2023), allowing hypothetical organisms to make use of the H₂S reservoir in a H₂-rich environment on Hycean worlds. In addition, decayed organic substances in the surface ocean can produce carbon disulfide (CS₂) and carbonyl sulfide (OCS) through photochemical processes. These biosulfur gases are not directly associated with energy generation but are products or byproducts of physiological responses, referred to as Type III biosignatures in Seager et al. (2013). On present-day Earth, these organic sulfur gases are readily destroyed through photolysis or oxidation by OH radicals (Kettle et al. 2001; Domagal-Goldman et al. 2011) and thus cannot accumulate to significant concentrations exceeding the ppm level required for remote detection.

While great uncertainties persist regarding how biology could operate in an H₂-rich atmosphere, useful analogies can be drawn from anoxic environments on Earth. As early microbial life emerged, the Archean atmosphere was more reducing than the present-day atmosphere, with abundant CO₂ and CH₄ (e.g., Catling & Zahnle 2020). As indicated by genomic analysis, organic sulfur cycling could date back to the Proterozoic (Mateos et al. 2023), while sulfur-based metabolic pathways likely emerged in Earth's earliest biosphere in the Archean and may have been common for biological evolution (House et al. 2003; Pilcher 2003). On Archean Earth-like worlds, most biogenic sulfur gases are rapidly destroyed in the atmosphere similar to that of the present day, except with the major sink being the reaction with atomic O produced by photolysis (Domagal-Goldman et al. 2011). Curiously, the potential sulfur-based biosignatures and chemical pathways within a H₂-dominated atmosphere have not yet been fully explored with self-consistent photochemistry. Moreover, many close-in sub-Neptunes around M stars might be tidally locked. On the permanent nightside, such photochemical sinks of these organic sulfur gases do not exist. It is therefore essential to quantify whether the biogenic gases can build up on the terminators where transit observations probe.

In this Letter, we explore the global distribution and detectability of methane- and sulfur-based biosignature gases on Hycean planets through photochemical and climate modeling. While there is currently no robust evidence that K2-18 b is a Hycean planet, we adopt its properties as a paradigmatic example for Hycean exoplanets overall.

Here, we model the atmospheric composition of a Hycean planet under a range of biological surface emissions. Using the planetary parameters of K2-18 b as a fiducial example, we vary the surface flux of biosulfur gases and stellar UV flux to quantify the impacts on the global composition of Hycean planet atmospheres.

2.1. 1D Climate and Photochemical Models

2.2. 3D GCM 2D Photochemical Model

3.1. 1D: S_org Flux ≳20× Modern Earth Value Is Required to Accumulate ppm Levels of DMS

Figure 1 illustrates the average mixing ratios of several carbon-bearing and organic sulfur species in response to increases of biological production of sulfur gases. With modern Earth's S_org flux, surface DMS reaches abundances of around 1–30 ppb, before being destroyed above 0.01 bar in our Hycean K2-18 b model. The DMS concentrations on Hycean K2-18 b are slightly higher than modern and Archean Earth's values, which are around 0.01–1 ppb levels (Domagal-Goldman et al. 2011; Zhang et al. 2020). As the S_org flux continues increasing, there is an abrupt transition between 20 and 30 times S_org flux in our S_org-deposition-free setup. After this threshold, the atmosphere becomes rich in organic sulfur species and poor in CO, while CH₃SH, DMS, and DMDS jump from the sub-ppm level to above 0.1%. In the more conservative scenario where the ocean is not saturated, DMS is expected to be limited by the surface deposition and increased linearly with increasing S_org, as shown by the dashed line in Figure 1. Once S_org exceeds 20×–30× Earth's value, H₂S begins accumulating in the upper atmosphere, as a result of photochemistry reducing sulfur back to its thermochemically favored state. This occurs when CH₃SH builds up to sufficiently high abundances that its photodissociation becomes significant, producing H₂S via the following pathway:

$$\begin{eqnarray}&&\begin{array}{c}{\mathrm{CH}}_{3}\mathrm{SH}\mathop{\longrightarrow }\limits^{{\rm{h}}\nu }{\mathrm{CH}}_{3}+\mathrm{SH}\\ {\mathrm{CH}}_{3}+\mathrm{SH}\longrightarrow {\mathrm{CH}}_{4}+{\rm{S}}\\ {\rm{S}}+{{\rm{H}}}_{2}\mathop{\longrightarrow }\limits^{{\rm{M}}}+{{\rm{H}}}_{2}{\rm{S}}.\end{array}\end{eqnarray} \tag{ 1 }$$

In fact, the ultimate fate of S_org species in a Hycean atmosphere is either photochemical oxidation into CH₃SO or reduction back to hydrocarbons and H₂S, where CH₃SO is mainly produced by DMDS reacting with atomic O. The path to H₂S becomes more dominant over CH₃SO as S_org flux increases and makes the atmosphere more reducing. Although SO₂ is also photochemically produced, it is highly soluble and deposition into the ocean limits abundances to insignificant levels.

Zoom In Zoom Out Reset image size

Notably, the atmosphere also becomes rich in hydrocarbons as S_org increases, as pointed out in Domagal-Goldman et al. (2011). CO follows an opposite trend to S_org, showing an abrupt decline after 20 times modern Earth's S_org flux. In this carbon-rich regime, the high abundances of haze precursors, such as C₄H₂ and C₆H₆ (Tsai et al. 2021), imply that the atmosphere would be covered by photochemical hazes (Arney et al. 2018). A main pathway to produce organic haze precursors in the upper atmosphere initiated by DMS photolysis is

$$\begin{eqnarray}&&\begin{array}{c}\mathrm{DMS}({\mathrm{CH}}_{3}{\mathrm{SCH}}_{3})\mathop{\longrightarrow }\limits^{{\rm{h}}\nu }{\mathrm{CH}}_{3}+{\mathrm{CH}}_{3}{\rm{S}}\\ {\mathrm{CH}}_{3}+{\mathrm{CH}}_{3}\mathop{\longrightarrow }\limits^{{\rm{M}}}{{\rm{C}}}_{2}{{\rm{H}}}_{6}\\ {{\rm{C}}}_{2}{{\rm{H}}}_{6}\mathop{\longrightarrow }\limits^{{\rm{M}}}{{\rm{C}}}_{2}{{\rm{H}}}_{4}+2{\rm{H}}\\ {{\rm{C}}}_{2}{{\rm{H}}}_{4}\mathop{\longrightarrow }\limits^{{\rm{h}}\nu }{{\rm{C}}}_{2}{{\rm{H}}}_{2}+2{\rm{H}}\\ {{\rm{C}}}_{2}{{\rm{H}}}_{2}\mathop{\longrightarrow }\limits^{{\rm{h}}\nu }{{\rm{C}}}_{2}{\rm{H}}+{\rm{H}}\\ {{\rm{C}}}_{2}{{\rm{H}}}_{2}+{{\rm{C}}}_{2}{\rm{H}}\longrightarrow {{\rm{C}}}_{4}{{\rm{H}}}_{2}+{\rm{H}}\\ {{\rm{C}}}_{4}{{\rm{H}}}_{2}+{\rm{H}}\mathop{\longrightarrow }\limits^{{\rm{M}}}{{\rm{C}}}_{4}{{\rm{H}}}_{3}\\ {{\rm{C}}}_{2}{{\rm{H}}}_{2}+{{\rm{C}}}_{4}{{\rm{H}}}_{3}\mathop{\longrightarrow }\limits^{{\rm{M}}}{{\rm{C}}}_{6}{{\rm{H}}}_{5}\\ {{\rm{C}}}_{6}{{\rm{H}}}_{5}+{{\rm{H}}}_{2}\longrightarrow {{\rm{C}}}_{6}{{\rm{H}}}_{6}+{\rm{H}}.\end{array}\end{eqnarray} \tag{ 2 }$$

For DMS at low concentrations below the ppm level, its primary sink is direct photodissociation. After the transition to where DMS has a high concentration, its photodissociation halts in the lower atmosphere due to shielding by DMDS, CH₃SH, and self-shielding. The reaction with atomic H becomes the main sink. This shielding effect from S_org also reduces the photolysis of CO₂ causing the drop of CO when the flux ≳20× S_org. The overall impact of shielding across this transition is evident in the top left panel of Figure 2, where DMS, DMDS, and CH₃SH significantly elevate the near-UV (NUV) photosphere and subsequently attenuate the NUV flux reaching the surface.

Zoom In Zoom Out Reset image size

For an equivalent solar flux, the same average abundances of hydrocarbon and sulfur gases as a function of biological sulfur flux are shown in the bottom of Figure 1. One major difference is that the stronger NUV irradiation generates atomic H down to the surface, which significantly suppresses DMS and other organic sulfur gases. DMS remains below 10 ppb level for S_org flux up to 200 times modern Earth's value. Moreover, the concentration of DMS is confined near the surface, whereas for an M dwarf host star, DMS can extend vertically above 0.01 bar. Since S_org never reaches significant abundances under a Sun-like star, shielding of CO₂ photolysis does not occur. Consequently, both CH₄ and CO progressively increase with S_org flux. Our model results with an active M star show qualitatively similar trends to those with the equivalent solar flux owing to its enhanced UV flux.

3.2. 2D: DMS Is Homogenized by Global Circulation

The temperature and wind structures simulated by our Hycean K2-18 b GCM can be found in Figure C1. The circulation exhibits an eastward zonal jet in the troposphere and day–night thermally driven cells in the stratosphere. In the upper atmosphere above 10⁻⁴ bar, the flow transitions to retrograde, likely due to vertical momentum transport (Tsai et al. 2014). The mean tropospheric zonal wind below 0.01 bar is about 20 m s⁻¹, consistent with the jet speed estimated from wave balance (Hammond et al. 2020). This zonal wind speed translates to a horizontal transport timescale of ∼10 days.

Figure 3 illustrates the equatorial distribution of DMS and DMDS for modern Earth S_org production. DMS exhibits a rather uniform abundance below 10⁻⁴ bar. As the zonal winds change to retrograde in the upper atmosphere, DMS extends to higher altitudes around the evening terminator due to the westward transport from the nightside. On the other hand, DMDS is photochemically produced by CH₃SH via

$$\begin{eqnarray}&&\begin{array}{c}{\mathrm{CH}}_{3}\mathrm{SH}\mathop{\longrightarrow }\limits^{{\rm{h}}\nu }{\mathrm{CH}}_{3}{\rm{S}}+{\mathrm{CH}}_{3}\\ {\mathrm{CH}}_{3}{\rm{S}}+{\mathrm{CH}}_{3}{\rm{S}}\longrightarrow \mathrm{DMDS}({\mathrm{CH}}_{3}{{\rm{S}}}_{2}{\mathrm{CH}}_{3})\end{array}\end{eqnarray} \tag{ 3 }$$

in the stratosphere between 10⁻²–10⁻⁴ bar and follows the thermally driven cells. This relatively uniform distribution of DMS can be understood by comparing relevant timescales. The photochemical lifetime of DMS on the dayside (${\tau }_{{DMS}}^{{day}}$) is determined by ${\tau }_{\mathrm{DMS}}^{\mathrm{day}}=1/{k}_{\mathrm{DMS}}$, where k_DMS is its photolysis rate. ${\tau }_{{DMS}}^{{day}}$ is ∼10⁸–10⁹ s in the troposphere below 10⁻² bar. On the nightside, the replenish timescale (${\tau }_{{DMS}}^{\mathrm{night}}$) is given by ∼$H/{K}_{\mathrm{zz}}^{2}$ ∼ 10⁸ s. Given that ${\tau }_{{DMS}}^{{day}}$ and ${\tau }_{{DMS}}^{\mathrm{night}}$ are comparable to each other and considerably longer than the horizontal transport timescale of ∼10⁶ s, the S_org species on the nightside is still constrained by the photochemical processes on the dayside through global transport. We note that our 2D model already assumes an optimistic scenario with a uniform S_org flux across the nightside. In reality, the nightside S_org flux might be much lower due to the lack of stellar energy input to power a (hypothetical) photosynthetic biosphere. Overall, the DMS abundance predicted by our 2D photochemical model is broadly consistent with that from 1D model, as indicated by the right panel in Figure 3.

Zoom In Zoom Out Reset image size

3.3. Transmission Spectra

We simulated synthetic transmission spectra of our cloud-/haze-free Hycean K2-18 b models using PLATON (Zhang et al. 2019, 2020), including opacity sources of CH₄, CO, CO₂, C₂H₂, H₂O, $\mathrm{HCN}$, NH₃, O₂, NO, C₂H₄, C₂H₆, H₂CO, N₂, NO₂, H₂S, $\mathrm{COS}$, SH, SO₂, (CIA) of H₂-H₂, and H₂-He. We further include cross sections of CH₃SH, DMS, and DMS from the Pacific Northwest National Laboratories (PNNL) database (Johnson et al. 2004), which are limited to 1 bar pressure and room temperature.

The transmission spectra for none, 1× and 20× modern Earth S_org flux are compared in Figure 4. For the JWST NIRISS and NIRSpec coverage below 5 μm, all of our Hycean K2-18 b models with methanogenic flux produce CH₄ absorption features between 1 and 4 μm that are broadly consistent with the JWST data. However, it is challenging to distinguish the DMS absorption contribution within the NIRSpec coverage, even with 20× S_org flux. The signal of DMS around 3.5 μm for 20× S_org flux does not exceed 10 ppm, smaller than NIRSpec's precision of 30–50 ppm at R ∼ 50 (Madhusudhan et al. 2023). The most promising diagnostics window of DMS is in the mid-infrared, as indicated in the right panel of Figure 4. For the 20× S_org case, DMS and the photochemical byproduct C₂H₄ contribute to an absorption of about 50 ppm at 9–11 μm, in addition to the C₂H₆ feature at 7 μm. The 7 μm feature of C₂H₆ also overlaps with CS₂, making it difficult to differentiate the contribution of CS₂. Our transmission spectra reveal no discernible H₂S spectral signatures. While H₂S can reach above ppm levels with outgassing and photochemical sources (e.g., Equation (1)), its broad opacities that overlap with several species make it challenging to detect.

Zoom In Zoom Out Reset image size

Since ethane (C₂H₆) is efficiently produced from CH₄ and has strong mid-infrared absorption bands, C₂H₆ shows a prominent feature at 7 and 11–13 μm with or without the presence of S_org flux. By constraining [CH₄]/[C₂H₆], one can potentially estimate the relative contribution of methanogenic CH₄ flux relative to S_org flux (Domagal-Goldman et al. 2011). Since our model likely overpredicts C₆H₆ in the gas phase due to the lack of conversion to higher-order hydrocarbons and particles, we did not include C₆H₆ opacities when generating the spectra in Figure 4. However, it is interesting to keep in mind that the presence (≳50 ppm) of C₆H₆ would exhibit detectable features within NIRSpec wavelength range, in addition to CH₄ and CO₂ (see Figure C3). For biogenic flux ≳30× Earth's S_org flux, the atmospheric mean molecular weight exceeds 8 amu in addition to the expected aerosols that would flatten transmission spectral features, making it immediately distinguishable for ≲20× cases. We summarize the identifiable biosignature features with 1×–20× S_org flux in Table 1.

Since K2-18 b requires reflective clouds and hazes to sustain water oceans, we explore the potential UV shielding effects due to clouds and hazes in the bottom panel of Figure 2. Organic sulfur species only start to build up when the stellar UV is reduced to less than 20%. For K2-18 b specifically, Leconte et al. (2024) highlighted the observed methane features deeper than ∼100 ppm (their Figure 9) are not consistent with highly reflective clouds. We argue that our photochemical results should remain robust to UV attenuation by clouds and hazes, unless muted spectral features indicate scattering by high-altitude aerosols can significantly reduce stellar UV flux.

The predicted requirement of 20× S_org flux to be potentially detectable is equivalent to about 0.004 g m⁻² based on the DMS lab production rate (Seager et al. 2013), which is within the plausible range of surface biomass density. Our predictions for the biogenic sulfur gases in Hycean atmospheres are broadly consistent with previous studies of the Archean Earth Domagal-Goldman et al. (2011) and Archean-like atmospheres on Trappist-1 planets (Meadows et al. 2023). While Meadows et al. (2023) concluded CH₃SH to be the most prominent S_org feature in N₂-dominated atmospheres, we find efficient CH₃SH conversion into H₂S in a H₂ atmosphere. Consequently, DMS appears to constitute the most detectable organic sulfur molecule in the mid-infrared for Hycean worlds.

On modern Earth, the oxidation of DMS might participate in the sulfuric cloud formation (Charlson et al. 1987) and affect climate feedback. It has been suggested that this biologically driven feedbacks could help stabilize the Earth's climate (Lovelock 1989), although the precise pathways and quantified contributions from DMS to aerosols still remain elusive. Similarly, on a Hycean world with highly elevated S_org flux (≳30× modern Earth's value; see Figure 1), hydrocarbon and elemental sulfur hazes (S₈) are expected to form. We speculate a similar negative feedback loop can take place in a Hycean world, where photochemical hazes derived from organic sulfur flux can increase albedo and prevent a runaway state.

Lastly, we reiterate that constructing complete line lists for DMS, DMDS, and CH₃SH to correctly account for the pressure-broadening effects would improve the interpretation of spectral data. Future work extending the study encompassing the diversity of halomethanes, such as methyl chloride and methyl bromide (e.g., Leung et al. 2022), will expand our understanding of the biosignature gases on sub-Neptune waterworlds.

We find a biogenic sulfur flux of approximately 20 times higher than modern Earth's is required for DMS to reach detectable levels (i.e., above ∼ppm) on a K2-18 b–like Hycean world. At the terminators, our 2D photochemical model shows only minor abundance enhancements in DMS compared to 1D model predictions. On the other hand, JWST/MIRI could detect C₂H₆ around 7 μm and the broad feature at 9–13 μm contributed from DMS, C₂H₄, and C₂H₆ with 20× S_org flux, based on our fiducial Hycean model. However, identifying DMS signatures within NIRSpec's wavelength range is demonstrated to be challenging, despite DMS appearing as the most promising biogenic sulfur signature directly from the S_org source. The moderate threshold for biological production suggests that the search for biogenic sulfur gases as one class of potential biosignature is plausible for Hycean worlds.

The authors thank Michaela Leung for the useful comments on an early draft of this article. The authors also thank Stephen Klippenstein and Julie I. Moses for the illuminating discussion on H₂CO kinetics and for sharing the ab initio calculations. S.-M.T. thanks Eva-Maria Ahrer, Guangwei Fu, Jake Taylor, and Lili Alderson for helpful discussions on data resampling and feature identification. S.-M.T. and E.W.S. acknowledge support from National Aeronautics and Space Administration (NASA) through Exobiology grant No. 80NSSC20K1437 and Interdisciplinary Consortia for Astrobiology Research (ICAR) grant Nos. 80NSSC23K1399, 80NSSC21K0905, and 80NSSC23K1398. H.I. is funded by the European Union (ERC, DIVERSE, 101087755, and ERC, EXOCONDENSE, 740963). Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Research Council Executive Agency. Neither the European Union nor the granting authority can be held responsible for them. N.F.W. was supported by the NASA Postdoctoral Program.

Software: Exo-FMS (Lee et al. 2020, 2021), VULCAN (Tsai et al. 2017, 2021), Numpy (van der Walt et al. 2011).

Table A1 lists the input parameters for Hycean K2-18 b with the HELIOS radiative transfer model and the Exo-FMS general circulation model. HELIOS includes H₂O, CH₄, CO, CO₂, NH₃, HCN, C₂H₂, collision-induced absorption (CIA) of H₂-H₂ and H₂-He as opacity sources. We ignore the H₂O self continuum absorption and likely underestimate the tropospheric temperature. Exo-FMS uses double-gray opacities for its radiative transfer. The optical depth in the infrared (τ_IR) and shortwave (τ_SW) bands is given by

$$\begin{eqnarray}&&d{\tau }_{i}=({\kappa }_{i,d}(1-q)+{\kappa }_{{\rm{i}},{\rm{w}}}q)({f}_{i}+2(1-{f}_{i}))\left.\left(\displaystyle \frac{p}{{p}_{s}}\right)\right)\displaystyle \frac{{dp}}{g},\end{eqnarray} \tag{ A1 }$$

where the i subscript represents either the SW or IR band, p is the pressure, and p_s the surface pressure. The opacities κ_i,w and κ_i,d represent the opacities due to the water vapor component and dry component (all other gases) of the atmosphere respectively. The factor f_i accounts for pressure dependence of opacity, due to collision-induced absorption and pressure-broadening effects. To reproduce the inversion in the HELIOS calculations, a second band was added in the SW part of the spectrum, receiving a fraction α of the total incoming flux. The optical depth in this band was given by

$$\begin{eqnarray}&&{\tau }_{{SW},2}=\displaystyle \frac{{\kappa }_{\mathrm{SW},2}p}{g}.\end{eqnarray} \tag{ A2 }$$

The water mass concentration, q, used in this calculation is taken from the 1D HELIOS calculation and remains constant throughout the simulation (though in reality this should be spatially inhomogeneous and linked to the local saturation vapor pressure at a given temperature and pressure). The value of κ_IR,w was taken to match the runaway greenhouse OLR of ≈280 Wm⁻² (as in Innes et al. 2023). The other values were tuned to match the HELIOS temperature-pressure profile. The parameters used are shown in Table A2.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Formaldehyde (H₂CO) is one of the main intermediate species in CO₂-CO-CH₄ interconversion. Forming and breaking the double bond between C and O in H₂CO may facilitate an important step that controls the overall timescale (Tsai et al. 2018). There are two three-body reactions involving H₂CO that we adopt the thermal dissociation rate coefficients due to the lack of low-pressure rate limits for recombination:

$$\begin{eqnarray}&&{\mathrm{CH}}_{2}\mathrm{OH}\mathop{\longrightarrow }\limits^{{\rm{M}}}{\rm{H}}+{{\rm{H}}}_{2}\mathrm{CO}\end{eqnarray} \tag{ B1 }$$

and

$$\begin{eqnarray}&&{\mathrm{CH}}_{3}{\rm{O}}\mathop{\longrightarrow }\limits^{{\rm{M}}}{\rm{H}}+{{\rm{H}}}_{2}\mathrm{CO}.\end{eqnarray} \tag{ B2 }$$

The recombination rates are then reversed by thermochemical data. In the default chemical networks in VULCAN (e.g., NCHO_photo_network ⁸ ), the adopted rate coefficients either underestimate the activation energy or are only valid at high temperatures. As a result, these reversed rates tend to overpredict the CO₂–CH₄ conversion efficiency around room temperatures. In this study, we have adopted the low-pressure rate coefficients for Equations (B1) and (B2) from Tsang & Hampson (1986) and Tsang (1987), which are more consistent with the ab initio calculations conducted by S. J. Klippenstein (2023, private communication). The original and updated rate coefficients are summarized in Table B1. This update of H₂CO kinetics significantly lowers the CH₄ abundance in our lifeless case (without methanogenic flux; Figure B1) from ∼10⁻⁵ to ∼10⁻⁸, which is consistent with the calculations in Wogan et al. (2024).

Table B1. Updated H₂CO Reaction Rate Coefficients

Reactions	Rate Coefficients a	Reference
Original
${\mathrm{CH}}_{2}\mathrm{OH}\mathop{\longrightarrow }\limits^{{\rm{M}}}{\rm{H}}+{{\rm{H}}}_{2}\mathrm{CO}$	${k}_{0}=1.66\times {10}^{-10}\exp (-12630/T)$ ${k}_{\infty }=3\times {10}^{9}\exp (-14640/T)$	Tsuboi et al. (1981), Cribb et al. (1992)
${\mathrm{CH}}_{3}{\rm{O}}\mathop{\longrightarrow }\limits^{{\rm{M}}}{\rm{H}}+{{\rm{H}}}_{2}\mathrm{CO}$	${k}_{0}=9\times {10}^{-11}\exp (-6790/T)$ ${k}_{\infty }=1.56\times {10}^{15}{T}^{-0.39}\exp (-13300/T)$	Baulch et al. (1994), Curran (2006)
Updated
${\mathrm{CH}}_{2}\mathrm{OH}\mathop{\longrightarrow }\limits^{{\rm{M}}}{\rm{H}}+{{\rm{H}}}_{2}\mathrm{CO}$	${k}_{0}=7.48\times {10}^{1}{T}^{-2.5}\exp (-17200/T)$ ${k}_{\infty }=4.53\times {10}^{34}{T}^{-7.11}\exp (-22200/T)$	Tsang (1987) Xu et al. (2015)
${\mathrm{CH}}_{3}{\rm{O}}\mathop{\longrightarrow }\limits^{{\rm{M}}}{\rm{H}}+{{\rm{H}}}_{2}\mathrm{CO}$	${k}_{0}=6.51\times {10}^{13}{T}^{-6.65}\exp (-16700/T)$ ${k}_{\infty }=3.17\times {10}^{24}{T}^{-4.25}\exp (-13100/T)$	Tsang & Hampson (1986) Xu et al. (2015)

Note.

^a In low pressure rate coefficient, k₀ (cm⁶ molecules⁻² s⁻¹), and high pressure rate coefficient, k_∞ (cm³ molecules⁻¹ s⁻¹).

Download table as:  ASCIITypeset image

The lower boundary conditions for our inhabited Hycean model are listed in Table C1. Figure C1 presents the output of the Exo-FMS model, while Figure C2 summarizes the abundance profiles from the Hycean K2-18b 1D photochemical models. Additionally, Figure C3 demonstrates the spectral feature of C₆H₆.

Table C1. Lower-boundary Conditions for Photochemical Modeling of Inhabited Hycean K2-18 b

Species	Surface Emission	Vdep
	(molecules cm−2 s−1)	(cm s−1)
CH4 a	7 × 1010	0
CH3SH a	8.3 × 108	0
DMS a	4.2 × 109	0 d
CS2 a	1.4 × 107	0
H2S b	2 × 108	0.015
SO2 b	9 × 109	1
$\mathrm{COS}$ b	5.4 × 107	0.003
H2O2 c	0	1
CH3S a	0	0.01
HSO a	0	1
S a	0	1
SO a	0	0.0003

Notes.

^a Domagal-Goldman et al. (2011). ^b Seinfeld & Pandis (2016). ^c Hauglustaine et al. (1994). ^d For the scenario that the surface layer of the ocean is saturated. The measured deposition velocity of DMS on land is 0.064–0.28 cm s⁻¹ (Judeikis & Wren 1977).

Download table as:  ASCIITypeset image