The sulphur species in hot rocky exoplanet atmospheres

The first JWST observations of hot Jupiters showed an unexpected detection of SO2 in their hydrogen-rich atmospheres. We investigate how much sulphur can be expected in the atmospheres of rocky exoplanets and which sulphur molecules can be expected to be most abundant and detectable by transmission spectroscopy. We run thermo-chemical equilibrium models at the crust-atmosphere interface, considering surface temperatures 500 to 5000 K, surface pressures 1 to 100 bar, and various sets of element abundances based on common rock compositions. Between 1000 K and 2000 K, we find gaseous sulphur concentrations of up to 25 percent above the rock in our models. SO2, SO, H2S and S2 are by far the most abundant sulphur molecules. SO2 shows potentially detectable features in transmission spectra at about 4 micron, between 7 and 8 micron, and beyond 15 micron. In contrast, the sometimes abundant H2S molecule is difficult to detect in these spectra, which are mostly dominated by H2O and CO2. Although the molecule PS only occurs with concentrations below 300 ppm, it can cause a strong absorption feature between 0.3 and 0.65 micron in some of our models for high surface pressures. The detection of sulphur molecules would enable a better characterisation of the planetary surface.


INTRODUCTION
In our Solar System, sulphur is the fifth most abundant volatile element Asplund, Grevesse, Sauval, and Scott (2009), Gao, Marley, Zahnle, Robinson, and Lewis (2017), Asplund, Amarsi, and Grevesse (2021), with a sulphur/hydrogen ratio of [S/H] = 10 −4.85 (Lodders, 2019).This is small compared to carbon [C/H] = 10 −3.53 , nitrogen [N/H] = 10 −4.15 , and oxygen [O/H] = 10 −3.29 .It is therefore remarkable that the sulphur carrying species SO 2 was among the first new molecules discovered by the James Webb Space Telescope (JWST) in an exoplanet atmosphere.Sulphur-dioxide SO 2 was observed in the gas giant WASP 39 b jointly with H 2 O, CO 2 , CO, and Na I (Rustamkulov et al., 2023).Tsai et al. (2023) suggest that the observed SO 2 is photochemically produced from H 2 S, which actually is the main sulphur carrier in this atmosphere, but remained undetected.Their model requires a large metallicity of 10× solar.Carone, Lewis, Samra, Schneider, and Helling (2023) argue that sulphur may be overabundant in the inner atmosphere in WASP 39 b compared to Mg, Si and Fe, making it a candidate for tracing planet formation.Crossfield (2023) elaborates this idea by considering gas-phase kinetics for C/N/O/H/S species without the feedback of condensation processes.Earlier studies by Zahnle, Marley, Morley, and Moses (2016) for 51 Eri b did not predict large amounts of SO 2 , but these authors used low metallicities and low irradiations in their exoplanet models.
Venus is known to contain about 150 ppm SO 2 in its CO 2rich atmosphere at ∼ 90 bar, with [S/H] ≈ 2, and H 2 SO 4 cloud particles at ∼ 1 bar (Rimmer et al., 2021, see references of previous modelling work on the Venusian atmosphere in this article).Visscher et al. (2006) modeled Jupiter's atmospheric conditions and found sulphur being predominantly present in the form of H 2 S. Photolysis of H 2 S could be a step in the chemical reaction chain towards sulphur hazes (Gao et al., 2017).These aerosols are expected to have a smoothing effect on infrared transit spectra of exoplanets (e.g.Dymont, Yu, Ohno, Zhang, & Fortney, 2021;Gao, Wakeford, Moran, & Parmentier, 2021).Both laboratory and space research have shown that sulphur can stimulate haze formation.He et al. (2020) conducted laboratory experiments and confirm this for warm, CO 2 -rich atmospheres.Haze particles can form, e.g. from S 8 -molecules (Zahnle et al., 2016), and act as a catalyser, triggering reactions of species such as NH 3 or CH 4 , which can change the optical appearance of the respective spectral features.
During the SL-9 impact on Jupiter, large amounts of CS, CS 2 , and OCS were detected in the impact region, but SO and SO 2 were not (Zahnle & Mac Low, 1994).The authors argue, that these detections are an indicator for a local carbon to oxygen ratio of C∕O > 1, in which case sulphur forms CS, CS 2 and OCS, whereas in the case C∕O < 1, sulphur would form SO and SO 2 .In protoplanetary disks, high CS and low SO and SO 2 abundances have been suggested as indicators for a high C/O ratio (Le Gal et al., 2021).
The simplest and most straightforward approach to model the near-crust composition of exoplanet atmospheres is to assume thermo-chemical equilibrium at the interface between planet crust and atmosphere.While the computation of gas phase equilibrium concentrations has been long established, for example by Tsuji (1973), Gail, Keller, and Sedlmayr (1984), Allard and Hauschildt (1995), Woitke and Helling (2004), it is the inclusion of solid and liquid species in phase equilibrium that allows us to discuss the composition of gases above silicate materials, for example Lodders and Fegley (2002), Hashimoto, Abe, and Sugita (2007), Schaefer, Lodders, and Fegley (2012), Ito et al. (2015), Woitke et al. (2018), Wood, Smythe, and Harrison (2019), Fegley, Lodders, and Jacobson (2020), Herbort, Woitke, Helling, and Zerkle (2020), and Fegley, Lodders, and Jacobson (2023).In particular, Fegley et al. (2016) have studied the solubility of rock in steam atmospheres.Schaefer et al. (2012) and Herbort et al. (2020) have calculated the chemical composition of the near-crust gas above common rock materials as function of surface temperature and pressure, showing a large variety of results for different element mixtures.Recently, Timmermann, Shan, Reiners, and Pack (2023) have developed an open-source python code for equilibrium condensation, and compared their results to those of GGCHEM (Woitke et al., 2018).Fegley, Lodders, and Jacobson (2023) have published an extensive study of 69 elements in thermo-chemical equilibrium, using dry and wet Bulk Silicate Earth (BSE) abundances.Considering temperature 1000 − 4500 K, they conclude that the silicate vapour behaves ideally at least up to 100 bars, and discuss the effects of treating the silicate melt as a non-ideal solution.
The validity of such an equilibrium approach can be questioned.For example, Hobbs, Rimmer, Shorttle, and Madhusudhan (2021) used a combination of LEVI, a photochemical kinetics code, and FastChem (Stock, Kitzmann, Patzer, & Sedlmayr, 2018), a thermo-chemical equilibrium solver to study the sulphur chemistry on hot Jupiters.The authors compared their modelling results to a model proposed by Wang, Miguel, and Lunine (2017) and showed that thermochemistry dominates in most parts -except for the uppermost layers -for the example of a  eq = 2000 K atmosphere with solar metallicity.Rimmer et al. (2021) showed that thermochemical equilibrium can simultaneously explain the crust composition and near-crust gas composition of Venus.
Arriving at similar conclusions, Shulyak D., Lara, L. M., Rengel, M., and Nèmec, N.-E.(2020) modeled hot Jupiter atmospheres around A0, F0, G2 and K0 stars for temperatures around 2000 K.They demonstrated that disequilibrium processes such as vertical mixing and stellar XUV radiation do not change the spectral results much at these temperatures.However, for lower temperatures around 1000 K the picture changes.Shulyak et al. predicted that the molecular mixing ratios in such UV-dominated atmospheres are strongly affected by disequilibrium processes, and possibly detectable with the James Webb Space Telescope (JWST).
The main JWST targets will be hot Jupiters and close in rocky exoplanets with equilibrium temperatures between about 900 K and 2200 K around stars of types FKGM (Kolecki & Wang, 2021;Stevenson et al., 2016).For these objects, an application of thermo-chemical models can at least provide a good starting point for the composition of their atmospheres.To classify the chemistry in these atmospheres, it is an important question whether sulphur molecules might be detectable.
The observable concentrations of sulphur molecules in the atmospheres of rocky exoplanets are linked to the sulphur abundance (and those of the other elements) in the crust, which is ultimately set by planet formation and evolution.These conditions include, among other factors, the temperature conditions and availability of elements during planet formation and the proximity to the star, for example Andrews et al. (2018), Kama et al. (2019), Khorshid, Min, Désert, Woitke, and Dominik (2021), Cevallos Soto, Tan, Hu, Hsu, and Walsh (2022), Speedie, Pudritz, Cridland, Meru, and Booth (2022) Depending on the element abundances present in the planet's crust and surface, the atmospheric conditions can vary from oxidising to reducing (Ortenzi et al., 2020), and evolve with time.Observational data for the atmospheres of rocky planets are still very sparse even if utilizing JWST (Greene et al., 2023;Wordsworth & Kreidberg, 2021).
In Sect.2, we run thermo-chemical equilibrium models to predict the abundances of sulphur molecules in the near-crust atmosphere, and determine which are the most abundant sulphur molecules to be expected in the atmosphere of hot rocky planets.In Sect.3, we run simple radiative transfer models based on hydrostatic model atmospheres with constant temperature and chemical composition to find out which sulphur molecules might be detectable.We use ARCiS (Min, Ormel, Chubb, Helling, & Kawashima, 2020) to generate transmission spectra, and then simulate JWST/NIRSpec and JWST/MIRI observations in Sect.4, to discuss which spectral fingerprints of sulphur molecules might be detectable.We conclude and discuss our findings in Sect. 5.

Modelling approach
We use the principle of minimisation of Gibbs free energy to determine both the chemical composition of the gas and the material composition of the crust at the surface of a rocky planet.We use the Fortran code GGCHEM (Woitke et al., 2018) in this work.Similar phase equilibrium models have been developed e.g. by Lodders and Fegley (2002), Schaefer et al. (2012), Ito et al. (2015), Fegley et al. (2016), Wood et al. (2019), and Timmermann et al. (2023).Our modelling approach is visualised by Fig. 1 in Herbort et al. (2020).A given set of total element abundances is considered in chemical and phase equilibrium at pressure  and temperature  , assuming an equilibrium between outgassing and deposition.The code determines which condensates are stable, how much of these condensates are deposited, and calculates the composition of the remaining gas phase in contact with them.The results include the chemical concentrations of all considered sulphur molecules.The resulting fractions of the condensed species are interpreted as the surface mineral composition of the rocky exoplanet.The GGCHEM model assumes a mixture of ideal gases, so we use partial pressures instead of the more general concept of fugacities.
Our model includes 18 elements (H, C, N, O, F, Na, Mg, Al, Si, P, S, Cl, K, Ca, Ti, Cr, Mn, and Fe).According to this selection of elements, GGCHEM finds 471 molecules (71 of them contain sulphur) and 208 liquid and solid condensates in its database.We do not include silicic acid as a gaseous species (as proposed by Fegley et al., 2016).Concerning the assumed total element abundances prior to condensation, we consider the following 10 datasets as described in Herbort et al. (2020) and Herbort, Woitke, Helling, and Zerkle (2022): Bulk Silicate Earth (BSE), Continental Crust (CC), CI chondrite (CI), Mid Oceanic Ridge Basalt (MORB), Archean, present Earth (see Appendix A in Herbort et al. 2022), and solar abundances.We also consider Polluted White Dwarf (PWD) compositions.The spectroscopic measurements of PWDs (e.g.Bonsor et al., 2020) do not allow for certain key element abundances to be determined, in particular hydrogen, but also nitrogen, flourine and chlorine, to mention a few.We therefore completed one basic PWD dataset of element mass fractions (Melis & Dufour, 2016) with the mass fractions of the missing elements from either BSE, CC or CI, see table 2 in Herbort et al. (2022) for more details.For example, the notation PWD-BSE means that we consider base PWD abundances, completed by BSE abundances.

Resulting gas compositions
Similar to Hashimoto et al. (2007), Schaefer et al. (2012) andFegley et al. (2016), we studied the gas phase composition above rocks in models for  = 1 bar and 100 bar.Table B3 lists our results for the 10 different sets of total element abundances in form of the main molecules and condensates that occur at different temperatures between 100 K and 5000 K for a constant surface pressure of  = 100 bar.This pressure is similar to Venus' surface pressure.We also list the sulphur concentrations that result to remain in the gas phase, i.e. in the atmosphere.
Figure 1 plots the same results as function of temperature.According to these results, rocky exoplanet atmospheres can contain up to 25% of gaseous sulphur.This maximum value is found at 3000 K and 100 bar in the PWD-BSE model.This gaseous elemental sulphur concentration is significantly higher, for example, than in our model with Earth-like element abundances, where it only reaches a maximum of about 1.7% at about 1000 K.
Both Tables B3 and B4 show that all models (except for the hydrogen-rich CI chondrite model) are featured by an N 2rich atmosphere at the lowest temperatures.As the hydrogen content in CI chondrite atmospheres is high, NH 3 replaces N 2 at these temperatures.Ammonia is further discussed in Hashimoto et al. (2007) and Schaefer and Fegley (2007).Figure 1 Sulphur abundances in the gas over rocky surfaces of different materials (labelled) as function of temperature. S gas is the element abundance of S in the gas phase and  tot gas the sum of all element abundances in the gas phase.Results are shown on a linear axis on the top, and on a logarithmic axis at the bottom.The left and right figures show the results for 100 bar and 1 bar, respectively.The material labels are explained in Sect.2.1.Similar to gas giants such compositions would be classified as an A-type atmosphere following the scheme of Woitke et al. (2020) based on H, C, N, O element abundances.We have extended this classification to include sulphur in APPENDIX A:.It provides a very helpful scheme to understand the very complex sulphur chemistry and the condensations that can occur therein (Table A2 ).The sulphur chemistry is not only characterised by the redox-state (see -axis in Fig. A1 ), but we have a two-dimensional problem, where a suitable second axis is found to be a relative carbon content in the gas (see axis in Fig. A1 ).The molecule CO 2 , which is predicted to be abundant in type B and type C atmospheres, cannot form in Atype atmospheres.And the molecule CH 4 , which is found to be abundant in type A and C atmospheres, cannot form in B-type atmospheres.
Figure 2 shows the results of one of our equilibrium condensation models in more detail.We selected the BSE model at  = 1 bar for this plot, see Table B4 for details.The relative sulphur abundance in the gas phase peaks around 1000 − 2000 K (green line, labeled S), reaching a maximum value of about 6.5%.At these temperatures, sulphur becomes the third most abundant element in the gas phase after hydrogen and oxygen, more abundant than carbon and nitrogen.The family names of condensates used in the upper part of Fig. 2 are explained in the appendix in Table B6 .

Why so much sulphur?
The peaking sulphur abundance as function of temperature is a consequence of condensation.From hot to cold temperatures, the relative sulphur abundance first increases, by about two orders of magnitude in the BSE model, as the first Ca-Al-Ti compounds form, as well as some of the most stable liquid silicates and iron-oxides, which drastically reduce the Mg, Si, Fe, Figure 2 Equilibrium condensation model at constant pressure  = 1 bar for Bulk Silicate Earth (BSE) total element abundances.The upper plot shows the condensate-to-gas mass ratio, i.e. the mass of families of condensed species with respect to the mass of the gas.The lower plot shows the relative element abundances in the gas phase on a log 10 axis.
Ca and Al abundances in the gas phase (see Fig. 2 ).At temperatures ≲ 1170 K in this model, sulphur starts to condense as well, here in form of FeS[s] (troilite), below which the sulphur abundance in the gas phase falls quickly.Thus, although sulphur is only the 12 th most abundant element at high temperatures, it becomes the 3 rd most abundant element in the gas between about 1000 K and 2000 K, due to condensation.
At 1500 K, the composition of the atmospheric gas (molar mixing ratios) is 66% H 2 O, 19% SO 2 , 11% CO 2 , 1.5% HCl, 0.64% NaCl, 0.43% HF, and 0.37% KCl, followed by H 2 , N 2 , CO and FeCl 2 , with all other molecules having concentrations < 100 ppm.We note that results like these depend on the completeness of molecular and condensed species included in the model.For example, Fegley et al. (2016) claim that silicic acids is among the species present in a hot steam atmosphere.
At  ≲ 650 K, phyllosilicates and graphite start to become stable in this model, which successively removes all remaining oxygen, hydrogen and carbon from the gas phase, leaving behind a pure N 2 atmosphere.A condensate to gas mass ratio of 10 6 is reached below about 600 K, which means that one gram of gas corresponds to one ton of condensates.
The first idea to explain the large range of gaseous sulphur concentrations is to consider the total sulphur (gas and condensed) mass fraction that we use as input.However, we do not see a clear correlation here, see Table B3 .For example, the model PWD-BSE with the highest gaseous sulphur abundance has an input sulphur mass fraction of 3.3%, whereas the Earth-model, which results in one of the lowest gaseous sulphur concentrations, uses 4.8%.
The amount of sulphur remaining in the gas phase is controlled by the thermal stability of the condensates.In fact, it is the determination of the stable condensates, not the amount of them, that sets the gas phase results.Each stable condensate provides one auxiliary condition to the solution of the gas phase equilibrium, namely that a certain combination of partial pressures must equal the given saturation pressure of that condensate.The amount of each stable condensate can hence be arbitrarily increased without changing the gas phase results, see Appendix B of Woitke et al. (2018).
The most frequent sulphur condensates are found to be FeS[l,s] (trolite), FeS 2 [s] (pyrite), CaSO 4 [s] (anhydrite) and MnS[s] (alabandite), see Table B3 .This would suggest that the gaseous S concentration should depend on the availability of Fe and Ca to form those sulphur compounds.The more Fe and Ca was available, the more sulphur condensates should form, which would consume more S and hence lower the S gas concentration.However, this idea also fails to explain our results.All PWD models, for example, use a large input Fe mass fraction of about 10%, whereas the MORB and BSE models use less, 7.3% and 6.3%, respectively; yet the PWD-BSE and PWD-CC models have more gaseous sulphur.
The best explanation we can provide is that it depends on the hierarchy of condensation, i.e. how well the most refractory elements, such as Si, Mg, Fe, Al and Ca, can be put together into highly refractory condensates, which depends on their element stoichiometry.If there is a leftover of Fe or Ca (or, precisely speaking, if it is necessary to put these leftovers into less stable condensates), then sulphur condensates start to form, and the S concentration in the gas phase drops.
More insight into the regulating processes can be obtained by studying the  -dependence shown in Fig. 1 .We can distinguish between two different cases.
(1) The PWD-BSE, PWD-CC and PWD-CI models show clear peaks of the sulphur concentration that remains in the gas phase as function of  , and a positive slope in the 1500 − 3000 K region at 1 bar (the peak value in the PWD-CI model is lower by about a factor of 2-4).At these temperatures, the models show a gradual transition from CO 2 to CO on a ≈ 40%-level (see Table B5 ), an about constant SO 2 concentration, a rising S 2 concentration, and a gradual evaporation of FeS[l] while the FeO[l] concentration rises with increasing temperature.Our conclusion is that the dissociation CO 2 → CO + O is followed by FeS (2) The MORB and BSE models show a constant gaseous sulphur abundance between about 1200 K and 2000 K at 1 bar.These models are featured by a steam atmosphere with high and about constant H 2 O-concentration (see Table B5 ), followed by constant SO 2 , CO 2 and O 2 concentrations.There are no stable sulphur condensates at these temperatures, and no CO 2 -dissociation, so the gaseous S abundance stays about constant.
Other models show a combination of these two patterns.For example, the CI model at 1 bar first follows the pattern of case (1) up to ∼ 1800 K, above which FeS[l] is no longer stable and the gaseous S concentration becomes constant.The CI model has more hydrogen, so H 2 O remains the most abundant molecule throughout, and H 2 is present as well.Thus, the release of oxygen as described in case (1) leads to a gradual change of the redox character, causing the H 2 S concentration to drop, whereas SO 2 increases, while S 2 is also present.Changing the gas pressure from 1 bar to 100 bar (see right and left parts of Fig. 1 ) does not change the qualitative behaviour of the mixture of gas and condensates.It mainly causes a shift of the thermal stability to higher temperatures such that the temperature thresholds, at which certain phase transitions occur are raised by a factor of roughly 1.3-1.4.
The CC model looses its last sulphur condensate CaSO 4 [s] at about 900 K at 1 bar, above which there is a constant steam atmosphere made of 44% H 2 O and 34% CO 2 with about 5% SO 2 , see Table B5 .The model with solar input abundances shows a straightforward behaviour, with FeS[s] as the main sulphur condensate up to about 650 K at 1 bar, above which there is a constant but low concentration of H 2 S which changes to HS at higher temperatures.Gas giants as investigated by Gao et al. (2017), Hobbs et al. (2021) and Helling et al. (2021) are relevant examples for such A-type atmospheres, see APPENDIX A:.However, the majority of our rocky exoplanet models favours the production of SO 2 , which is classified as BC1, BC2 or BC3-type atmospheres in APPENDIX A:.
In the PWD-CC and PWD-BSE models, the molecule S 2 (disulphur) also reaches concentrations of a few percent beside the molecule SO 2 .Tables B3 and B4 show that these high S 2 concentrations coincide with the peak of the gaseous sulphur abundance around 2500-3500 K shown in Fig. 1 .
Beside the expected SO 2 , H 2 S and S 2 molecules, we find smaller concentrations of the molecule PS (phosphorus sulfide) in some of our models, see Table 1 .In certain cases, this molecule shows a surprisingly strong absorption feature at optical wavelengths, see Sect.3.2.5.In the models using polluted white dwarf abundances, and in the Archean and CI models, the concentrations of PS are between about 1 and several 100 ppm at 2000 K and 100 bar.
In the following section, we explore whether it might be possible to detect sulphur molecules -in particular SO 2 , H 2 S and PS -by transmission spectroscopy using the James Webb Space Telescope (JWST), given the high sulphur abundances that we predict for hot rocky exoplanets.

TRANSMISSION SPECTRA OF SULPHUR-RICH EXOPLANETS
Current and future observational missions like JWST (Benz et al., 2021), LUVOIR, HabEx and HABITATS (Wang et al., 2020) can be expected to provide an unprecedented quality and variety of transit spectra of diverse rocky exoplanetary worlds.As shown in Tables B3 and B4 , our models suggest that some of the atmospheres of these rocky planets might be very rich in sulphur.Therefore, the question arises whether we can detect sulphur-molecules by transmission spectroscopy with present and future observational facilities also for rocky planets.We will not focus on any particular targets, but instead provide a first guidance of where to look for detectable spectroscopic signatures of sulphur-bearing molecules.

The model atmosphere
We use simple 1D hydrostatic models with an isothermal structure and constant molecular concentrations.The molecular concentrations are taken from the GGCHEM phase equilibrium models for the surface as described in Sect. 2. Constant molecular concentrations were previously adopted for atmospheres of magma planets, see e.g.Barth et al. (2021) and Graham, Table 2 Atoms and molecules that can be fairly abundant in our atmosphere models without opacity data in ARCiS (1)  Lichtenberg, Boukrouche, and Pierrehumbert (2021).Strong vertical mixing is expected to occur in such atmospheres, keeping the molecular mixing ratios sustained throughout.We neglect cloud formation.

The set of opacities in ARCiS
We used ARCiS (Min et al., 2020) (Bernath, 2020), ExoMol (Tennyson et al., 2016(Tennyson et al., , 2020) ) and NIST (Kramida, Ralchenko, & Reader, 2013).The ARCiS code has a list of molecules for which opacity data is available, which are:   et al. (2020).By setting the name of the planetary system, these values are automatically adopted by ARCiS.The models use 50 pressure layers for the hydrostatic atmospheric structure.The spectral resolution is set according to the resolution of the MIRI LRS spectrograph on JWST which is tailored to mid infrared spectroscopy.

Input parameters
The physical input parameters for the ARCiS models are listed in Table 3 .We use the hot Super Earth 55 Cnc e as a reference for the stellar and planetary parameters.55 Cnc e orbits a GV 8 star (Folsom et al., 2020;Tabernero et al., 2020;von Braun et al., 2011), has an equilibrium temperature of 2350 K and a surface pressure of 5−10 bar (Hammond & Pierrehumbert, 2017).
We set the surface pressure to 10 bar and the atmospheric temperature to 2000 K for these simple explorative models, except for those models where we investigate the dependencies on pressure and temperature.

Atmospheric composition and extent
The molecular concentrations, taken from the simulations of the near-crust atmospheric composition at  surf ,  surf (Sect.2), result in very different mean molecular weights, see Table B5 .which has an important impact on the observability of the spectral features, because large mean molecular weights translate into compact atmospheres with a small atmospheric extent.Some of the molecules and atoms, which are included in GGCHEM, are not implemented in ARCiS yet.These molecules are not passed to ARCiS for spectra generation, and are listed in Table 2 .Other species are implemented in ARCiS, but have no opacity data there, such as SO and S 2 .The absorption features of these molecules cannot be predicted.Ignoring some of the abundant molecules in the ARCiS simulations might have a small impact on the calculation of  3 .Nine models with different total element abundances are shown on the left and right.The transmission depths vary according to the different mean molecular weights .We note the different scaling of the -axis on the left and right.All spectra have been computed for a surface pressure of 10 bar and an isothermal atmosphere of 2000 K.The solar model is not shown here because its mean molecular weight  ≈ 2.05, see Table B5 , is so small that the transit depth is significantly larger than all other models.the mean molecular weight in ARCiS.However, as Table 2 shows, none of these molecules exceeds a concentration of 3%, and the molecules > 1% only occur in our hottest models  ≥ 2500 K or in the artificially sulphur-enriched models.Among these molecules is NaOH in the Archean and BSE models, for which opacity data has recently been published by Owens et al. ( 2021) like for the SO molecule.The impact of the mean molecular weight of our models is discussed further in Sect.3.2 and Sect.3.3.

Pressure broadening and CIA
In our models, the atmospheres of hot rocky exoplanets are mostly constituted of CO 2 , H 2 O, CO, H 2 , and SO 2 (see Tab. B5 ).These atmospheres are hence very different from the atmospheres of gas giants where H 2 and He dominate.The opacities we use in this work assume pressure broadening by H 2 and He.The available broadening data of HITRAN2020 (I. Gordon et al., 2021) for other species indicate that pressure broadening from H 2 O in particular is expected to be relevant.Works such as Gharib-Nezhad and Line (2019) and Anisman et al. (2022) illustrate the effect that self pressure broadening can have for H 2 O in steam atmospheres.However, even if we were able to take these pressure broadening effects into account, we do not expect them to affect the main conclusions of the present work.We compute our models considering only collision induced absorption (CIA) from H 2 -H 2 and H 2 -He.Future work will show whether updated CIA opacities have an influence on these results.

Resulting transmission spectra
The following sections show our calculated transmission spectra for 10 different rocky element mixtures and different atmospheric temperatures and surface pressures, see Fig. 3 for an overview.In each of these cases, we are looking out for observable spectral features of the various sulphur molecules.

Mean molecular weight and scale height
The pressure scale height   has a profound impact on the observability of spectral features in exoplanet transmission spectra.It is given by where   is the Boltzmann constant,  the temperature,  =  pl ∕ 2 pl the surface gravity of the planet, and  the mean molecular weight in units of the mass of hydrogen  H . ,  pl , and  pl are the gravitational constant, the mass and radius of the planet, respectively, which were adopted from 55 Cnc e (Table 3 ).In our isothermal models with constant molecular concentrations, we have  =  pl (temperature of the planet's surface and atmosphere), and   and  are constants.
Table B5 lists the results of a series of ten models with different element abundances at fixed  = 2000 K and fixed  3 .The four compositions which show the strongest SO 2 absorption features are selected: CC, BSE, MORB and PWD-BSE.The blue lines show the spectra when the SO 2 line opacity is omitted.
surface pressure  surf = 10 bar.Beside the resulting molecular compositions, we also list the mean molecular weights that varry between 9.2 and 61.6, where the abundant heavy SO 2 molecule can have a profound influence.
Figure 3 shows our predicted transmission spectra for nine of the ten models (solar model excluded), where we see a clear correlation between  and the transit depths.For example, the model with the largest transit depth is the PWD-CI composition.The main species in its atmosphere is H 2 with a mixing ratio of about 67%, followed by H 2 O (20%) and CO (8.5%), which results in a mean molecular weight of only  = 9.2 (Table B5 ).Larger mean molecular weights  lead to smaller scale heights   , making it more difficult to detect any molecular features by transmission spectroscopy.This effect limits our ability to find and spectroscopically characterise sulphur-rich exoplanets, which generally have large .

SO 2 and H 2 S in transmission spectroscopy
Table B5 shows that the most abundant gaseous sulphur species in any of our models is either SO 2 or H 2 S. Both molecules are non-linear and polar, with a bent structure similar to H 2 O. Whereas SO 2 is more dominant in the BSE, MORB, CC, present Earth, PWD-BSE and PWD-CC compositions, H 2 S dominates in the solar, Archean, CI and PWD-CI models.
Figures 4 and 5 show the simulated transmission spectra for 2000 K and 10 bar for different total element abundances.From our sample of 10 different rocky element compositions, we have selected the spectra with the most distinct absorption features of SO 2 and H 2 S. See APPENDIX C: for all other spectra.
Besides the full spectra based on all included opacities (orange), the figures also show spectra for which the opacities of SO 2 and H 2 S have been artificially set to zero (blue).Thus, these molecules are still included in the calculation of the mean  3 .The two compositions with visible H 2 S features are selected here: CI and PWD-CI.The blue line shows the spectrum when the H 2 S line opacity is omitted.molecular weight in ARCiS.The following spectral features of SO 2 and H 2 S occur: • a box-like absorption feature at 7 − 8 m with a right shoulder extending to ∼ 10 m ⇒ SO 2 , • a left shoulder on the main CO 2 absorption band at 4.5 m ⇒ SO 2 , this is the feature that was recently detected by (Rustamkulov et al., 2023) in WASP 39 b, • increased absorption longward of 15 m ⇒ SO 2 .
None of our models predicts strong spectral features of H 2 S. Whether H 2 S or SO 2 dominates in the gas depends on the O/H ratio in the atmosphere.Our classification scheme for temperatures below 600 K (APPENDIX A:) indicates no coexistence of H 2 S and SO 2 .However, at larger temperatures, Table B5 shows that both molecules are important in the CI model at 2000 K and 10 bar, indicating a smooth transition from one molecule to the other.At 100 bar, Table B3 indicates that in the CI model, H 2 S is abundant below 1700 K and SO 2 at higher temperatures.

Distinct SO 2 absorption features
SO 2 gives rise to some very distinct spectral features as shown in Figs. 4 , 5 , C3 and C5 .These absorption features are particularly strong in the models for MORB, BSE and PWD-BSE compositions.These are particularly rich in gaseous sulphur as illustrated by Figure 1 .The PWD-BSE model provides the sulphur richest atmosphere, with a sulphur concentration of ∼ 15% in the gas phase at 2000 K and 1 bar surface pressure, see Fig. 1 ), which also shows the strongest spectral features due to SO 2 absorption.However, even though the overall gaseous sulphur abundance is the highest there, the SO 2 abundance is not the highest in the PWD-BSE model.It's atmosphere reaches a SO 2 concentration of ∼ 14% at 2000 K and 10 bar surface pressure, whereas it is by 4 − 5% higher for the atmospheres of the BSE and MORB compositions respectively, see Table B5 .This puzzling behaviour of the SO 2 absorption features can be explained by looking at the dominant molecular species in the three different atmospheres.Whilst the dominating molecule in the PWD-BSE atmosphere is CO 2 , the BSE and MORB atmospheres are mainly composed of H 2 O. Water produces very strong absorption features all the way between 2 and 10 m, such that the SO 2 features become undetectable.

H 2 S absorption features
Using ARCiS, we find only weak H 2 S absorption features.These features are just about visible in the PWD-CI and the CI models, see Fig. 5 .CI chondrites found on Earth date back to the time of the evolutionary formation stages of the solar system (Herbort et al., 2020) and are particularly rich in carbon.Besides a high C/O ratio, CI chondrites also have a high H/O ratio.This shows to have a strong impact on the formation of H 2 S rather than SO 2 .In the CI model, H 2 S is the major gaseous sulphur species below 2400 K at 100 bar surface pressure.Above 2400 K, SO 2 becomes the dominant sulphur species even in the CI atmosphere.
The gaseous sulphur concentration in the CI and PWD-CI models is low in comparison to other models such as the BSE composition (see Fig. 1 ), even though the total sulphur abundance for both hydrogen-rich models is high.Therefore, the mixing ratios of all sulphur containing species is relatively low in these two models.The H 2 S content reaches 3.6% in the CI model, compared to 19% for SO 2 in the MORB model, which is the model with the largest SO 2 concentration.This is one of the reasons for the shallowness of the H 2 S features in Fig. 5 .
In addition, the H 2 S features are located at wavelengths where the H 2 O molecule is dominant.The overlap with H 2 O opacity is stronger for H 2 S than it is for SO 2 , such that the water, which dominates in all atmospheres with high H 2 S concentrations, masks their features.

The strong absorption feature of PS
Table 1 shows that all PWD models, the Archean model, and the CI model contain 1 − 260 ppm of the PS molecule at 2000 K and 10 bar surface pressure.We discovered that this molecule causes a surprisingly strong and broad absorption feature between 0.3 and 0.8 m, see Fig. 6 .This figure shows the transmission spectrum of the PWD-CI model, which has the largest PS concentration among all models (260 ppm).The transmission spectra of all other models producing the PS absorption feature are shown in APPENDIX C:.This unexpected result raises the question about the reliability of the thermo-chemical data used to calculate the PS concentrations.A comparison of different data sources for the Gibbs free energies of PS (Worters, Millard, Hunter, Helling, & Woitke, 2017) shows deviations of about 5 kJ/mol, which is a typical uncertainty, so this suspicion can be rejected.According to the NIST database, PS is energetically favored over P 2 and S 2 by about 15 − 20 kJ/mole at about 1500 K. 5% 1% 0.1% 0.027% 0.01% 0.001%

Figure 7
Transmission spectra for a Bulk Silicate Earth composition with artificially varied total sulphur element mass fraction (gas and condensates).The spectra have been computed for a surface pressure of 10 bar and an isothermal atmosphere of 2000 K.The numbers next to the graphs indicate the corresponding sulphur mass fraction for each modeled spectrum.

Dependence on total sulphur abundance
Considering the BSE composition as an example, we have investigated how the transmission spectrum changes if we arbitrarily vary the total sulphur element abundance in the model.Figure 7 shows spectra for sulphur mass fractions of 0.001, 0.01, 0.027 (unaltered BSE model), 0.1, 0.993 (∼ 1.0), and 4.77 (∼ 5.0) 1 .A larger total element abundance of sulphur allows for more SO 2 and S 2 to form in the gas phase, see Table B5 .As both are very heavy molecules, the mean molecular weight of the atmosphere increases, leading to a drop in scale height   and therefore to a flattening of all features.This is illustrated in Fig. 7 .The box-like feature around 7 − 8 m of SO 2 is strongest for a total sulphur mass fraction of 0.027%.For smaller values, the SO 2 concentration in the atmosphere drops quickly.For larger values, the radial extent of the atmosphere shrinks substantially, see Table B5 .

The effect of temperature
The temperature affects (i) the equilibrium chemistry in the gas phase, (ii) the phase equilibrium at the planetary surface, and (iii) the shape of the spectral features as more and more high-excitation lines show up with increasing temperature.As 1 When we set the total element abundance of each individual element (crust and atmosphere) in percentage mass fraction, they do not sum up to exactly 100%.Before computing the equilibrium chemistry, GGCHEM renormalises to 100%.shown in APPENDIX A:, the mixing ratios in a cold atmosphere without condensation are constant up to about 600 K (Woitke et al., 2020).At higher temperatures, the diversity of gaseous species increases such that other sulphur bearing species occur, for example COS or SO, in addition to SO 2 or H 2 S, see Table B5 .But most importantly, the amount of sulphur in the gas is controlled by condensation at the surface, which changes the sulphur content radically.
Figure 8 shows spectra for the BSE model at 1000 K, 2000 K and 2500 K.As in Fig. C3 , the influence of SO 2 is highlighted.At a temperature of 1000 K, the spectral features of SO 2 become almost invisible, which appear clearly in the high- spectra.This agrees with the predictions in Fig. 1 , which shows a drastic drop in the gaseous sulphur concentration below ∼ 1300 K for the BSE composition with a surface pressure of 100 bar.Less SO 2 can form below this temperature as the condensate FeS builds up.
The overall transit depth, shape and distinctiveness of the absorption features are affected as well.As the temperature is increased from 1000 K to 2000 K, the SO 2 features appear in the IR wavelength regime, as discussed.At shorter wavelengths, an optical feature of OH at ∼ 0.3 − 0.4 m is present at 2000 K but not at 1000 K.A further increase in temperature from 2000 K to 2500 K mainly affects these shorter wavelengths, see Fig. 8 .The OH peak becomes more distinct and two new peaks appear as shown in Fig. 9 .These additional features are due to K (potassium) at ∼ 0.8 m and MgO (Magnesium Oxide) between ∼ 0.45 − 0.8 m.
The MgO feature at 2500 K is particularly strong.Magnesium (Mg) is a highly refractory element which predominantly occurs in condensates.However, as the temperature is increased above ∼ 2000 K in the 10 bar model, Mg evaporates to form MgO and MgH.

Dependence on surface pressure
Figure 10 shows spectra of the BSE model at 2000 K for four different surface pressures between 0.01 and 100 bar.The main effect is a change in the total radial extent of the atmosphere, which increases the overall transit depth.The shape and magnitude of the features is not much affected by the surface pressure between 1−100 bar.For much lower pressures, however, other molecular features appear, in particular at shorter wavelengths.The additional peaks in the 0.01 bar spectrum are due to higher concentrations of MgO and K in the gas.This effect is similar to a temperature increase from 2000 K to 2500 K at 10 bar surface pressure as discussed in section 3.2.7.

OBSERVABILITY WITH JWST
In order to investigate the detectability of sulphurous molecules, we use the modelling tool PandExo (Batalha et al., 2017).This allows us to predict the size of the error bars of James Webb telescope (JWST) measurements for atmospheres of rocky planets.We looked at the NIR regime which will be covered by the MIRI LRS and NIRCam spectrographs of JWST as well as the MIR regime covered by MIRI MRS.

Observability of SO 2 and H 2 S
Figures C3 , C4 and C5 predict that the atmospheric compositions originating from PWD-BSE crust models show the strongest SO 2 features of all our investigated compositions.Therefore we choose this model to check the observability of SO 2 with JWST.
Figure 11 shows predicted SO 2 observational signatures of this composition assuming a hot equilibrium chemistry atmosphere of 55 Cnc e.The ∼ 5 ppm strong SO 2 signal is in principle observable with JWST using NIRSpec/G395M (left) and MIRI/LRS (right) combining 30 and 40 transits, respectively.However, in these calculations 'perfect' performance without systematic noise was assumed.In general, H 2 S is found to show much weaker absorption lines than SO 2 such that it appears quite unlikely that present and future missions such as JWST, Ariel, or the Habitable World Observatory (HWO) (Dick et al., 2019;Martin et al., 2020;Ygouf et al., 2020) will be able to detect H 2 S in an atmosphere like the one we modeled.The strongest H 2 S feature we found is located at long wavelengths in the MIR regime between 20 − 30 m.

Observability of PS
Our ARCiS spectral models show that the molecule PS may cause a broad absorption feature between 0.3 and 0.65 m that is surprisingly strong (up to ∼ 40 ppm in the PWD-CI chondrite model), despite being based on gaseous PS concentrations of only a few ppm to a few 100 ppm, see Fig. C7 .The feature's wavelength interval is at the edge of the observable range with JWST.Only NIRSPEC Prism covers the longer wavelength part of this PS feature between 0.6 − 0.65 m, where it reaches 8 ppm at maximum.Towards shorter wavelengths the feature strength would increase as predicted in Sect.3.2.5, but this is completely out of the detectable range of JWST.In addition, the instrument mode NIRSPEC Prism is only usable for faint stars (  ≥ 10.5).For such targets, the PS feature won't be detectable in any of the compositions according to PandExo predictions as demonstrated in Fig. 12 .However, future space telescopes operating at optical wavelengths (0.3 − 0.6 m), such as LUVOIR-B, could certainly observe a 40 ppm strong PS feature.Finding PS in a rocky planet atmosphere could also be an interesting science case for ground-based instruments.

Dependence on atmospheric structure
We ran a number of additional verification tests where we used more realistic temperature structures for 55 Cancri e.These studies included atmospheric profiles where the temperature is monotonously decreasing with height, similar to Fig. 2 of Jindal et al. (2020), and profiles with a temperature inversion, similar to Fig. 1 in Zilinskas, Miguel, Lyu, and Bax (2021).In these models, we used GGCHEM to adjust the molecular concentrations to chemical equilibrium at each atmospheric height to the local temperature and pressure, without condensation.While the transition depth and spectral shape of the various absorption features can change substantially in these models, we found that our general conclusions about the detectability of SO 2 and PS in warm and hot rocky exoplanet atmospheres, and the non-detectability of H 2 S, remain the same.

SUMMARY AND DISCUSSION
We have investigated how much sulphur can be expected in the atmospheres of warm and hot rocky exoplanets, which sulphur molecules are most abundant, and whether these molecules might be detectable with JWST.A large chemical diversity in planetary environments is expected.We considered various sets of total element abundances, i.e. before condensation, as found in common types of rocks (Herbort et al., 2020;Herbort et al., 2022) and assumed chemical and phase equilibrium at the planetary surface to calculate the chemical composition of the atmospheric gas.
For surface temperatures between about 1000 K and 3000 K, we found typical sulphur concentrations in the gas of a few percent, depending on total element abundances assumed.The most abundant sulphur molecule in the atmosphere, reflecting its redox state, is normally either SO 2 or H 2 S.However, in a few cases, both molecules can coexist beside S 2 .Other, less abundant sulphur molecules of interest are SO, SO 3 , COS, HS, S 2 O, Na 2 SO 4 and PS, all of which can occur with concentrations > 100 ppm.
The abundance of sulphur in these atmospheres is controlled by condensation at the surface-atmosphere interface in our models.As sulphur is among the more volatile elements, its gas abundance above 3000 K first increases with falling temperature, as more of the abundant refractory elements like Ca, Al, Ti, Si, Fe, Mn and Cr condense at the surface.Below about 1000 K to 2000 K, dependent on pressure, sulphur starts to form condensates as well, in particular FeS[s], FeS 2 [s], CaSO 4 [s], MnS[s] and Na 2 S[s], causing the S abundance in the gas phase to drop quickly.However, at intermediate temperatures, the ability of sulphur to condense, and hence the amount of sulphur left in the gas phase is controlled by the availability of metals such as Fe, Mn, Ca and Na, which depends on the assumed total element abundances in complicated ways.
In order to determine whether or not the various sulphur molecules might be detectable by transmission spectroscopy, we utilise simple 1D isothermal hydrostatic model with constant molecular concentrations and without clouds.We used the ARCIS modelling platform (Min et al., 2020) to predict such transmission spectra with star-planet system parameters adopted from 55 Cancri e.Based on these models, it seems most promising to search for SO 2 in the atmospheres of hot (≈ 2000 K) rocky exoplanets.SO 2 produces a left shoulder on one of the main CO 2 absorption features at 4.5 m, a distinct absorption feature at 7 − 8 m, and a broad absorption feature at 15 − 25 m.These features are most prominent for rocky element abundances derived from polluted white dwarf observations.Quick simulations with PandExo (Batalha et al., 2017) showed that SO 2 might be detectable with JWST in sources like 55 Cnc e, when about 30-40 transits can be observed.In comparison, the molecule H 2 S is more difficult to detect.Interestingly, the atmospheres containing lots of sulphur also have large mean molecular weights, and are hence less extended, which limits our ability to detect these molecules in the sulphur-richest atmospheres.
Among all other sulphur species included in our ARCiS models, only the molecule PS is found to be possibly detectable via a strong, broad spectral absorption feature around 0.3 − 0.65 m.This could be a case for optical ground-based instruments or LUVOIR, because of JWST's limited possibilities to observe the UV and optical.The NIRspec spectrograph, which we used for our detectability verifications, is only sensitive down to 0.6 micron and designed for faint sources only.
Beside the sulphur molecules SO 2 and PS, we also find detectable absorption features by TiO and MgH in the solar abundance model, and by MgO, OH and the K resonance line in our hot rocky exoplanet transmission spectra between 0.3 and 0.8 m, which are otherwise mostly dominated by H 2 O and CO 2 absorption.MgO, and K are visible only for surface temperatures ≳ 2000 K and the OH features becomes more distinct as the temperature rises from 2000 K to 2500 K.We note that ground-based instruments, which can observe highresolution spectra of exoplanet atmospheres, might allow for the detection of some of these species.
Since the sulphur content in rocky exoplanet atmospheres depends critically on the properties of the planet surface (surface pressure, surface temperature, surface bulk composition), an observational constraint on the SO 2 mixing ratio would be an important step towards a better characterisation of the chemical conditions on the planet's surface and habitability.Woitke et al. (2020) have classified the chemical composition of cold ( < 600 K) atmospheres which consist only of the four most abundant elements (C, H, N, and O).This resulted in three distinct atmospheric types.Hydrogen-rich type A atmospheres are characterised by the presence of CH 4 , H 2 O, NH 3 and (H 2 or N 2 ).Oxygen-rich type B atmospheres show the presence of O 2 , CO 2 , H 2 O and N 2 , and type C atmospheres show the coexistence of CH 4 , CO 2 , H 2 O, and N 2 .All other molecules have only trace concentrations in chemical equilibrium at low temperatures.In this appendix, we build upon this model and extend this characterisation to additionally include sulphur.In the low temperature limit, the bulk of the atmosphere is consisting of exactly the same number of molecules as the numbers of elements, so for C, H, N, O, S we expect five abundant molecules in all cases.The element abundances are then sufficient to determine the atmospheric type.With increasing temperatures, other molecules gain importance due to the entropy term in the Gibbs free energy.

APPENDIX A: CHEMICAL CLASSIFICATION OF THE CHNOS SYSTEM
Similarly to Woitke et al. (2020), we find different atmospheric types for the gas phase compositions of the CHNOS system.In Fig. A1 the number densities of the most dominant gas phase molecules for a sulphur abundance of S∕(C + H + O + S) = 0.1 are shown.Hereby, the nitrogen abundance is not taken into account as it does not interfere with the chemistry of the other elements but mainly forms N 2 .The emerging atmospheric types are described in the following as well as in Table A1 .
Type A: The hydrogen dominated atmospheric, subtypes A1 (with NH 3 and H 2 ) and A2 (with NH 3 and N 2 ).These types are the same as in Woitke et al. (2020) A1 .Thus, the subtypes BC1 to BC4 are forming a sequence in redox potential.
As in Woitke et al. (2020), additional atmospheric types occur in principle for very large carbon abundances, where graphite is supersaturated.This includes the new peculiar subtype CG, which is like type C except that water is replaced by the allotrope S 8 .For smaller sulphur abundances, see Fig. A2 , the parameter space occupied by the new subtypes is shrinking, and in the limiting case of very low sulphur element abundance, the original types A, B and C are again revealed.

A.1 Boundaries between two atmospheric types
Here, we show how the boundaries of the different atmospheric sub-types are derived.As nitrogen does not interfere with the chemistry of the other elements, we omit it for the calculation of the boundaries of the atmospheric types.
At each of these boundaries the element abundances are such that two molecules replace each other in the adjacent atmospheric types.The other present molecules remain unaltered.The location of the boundary is determined by the condition that   > 0. (A1) Here,   is the molecular partial pressure of a molecule , which is present in the investigated atmospheric types.
In the following, we show the derivation of the boundary conditions for atmospheric types on the example of the type C atmosphere, which consists only of the molecules CH 4 , CO 2 , H 2 O, H 2 S, and N 2 .The fictitious atomic pressure  atom of the gas mixture can be written as The considered species are the molecules dominating the atmosphere due to equilibrium at low temperatures.At each black line, which is one of the above mentioned boundaries, the element ratios become such that two molecules replace each other.

A.2 Condensation at low temperatures
In the low temperature limit, it is sub-type specific which condensates can form.(Woitke et al., 2020).However, not enough about the atmospheric chemistry of Venus is known in order to determine its exact type.Since gaseous water is Table A1 Classification of atmospheric types including sulphur (1) . type (1) In the low-temperature limit, only five molecules coexist in chemical equilibrium with mixing ratios exceeding trace abundances.The three main types are A for hydrogen-rich, B for oxygen-rich, and C for atmospheres where H 2 O, CH 4 , CO 2 and N 2 can coexist Woitke et al. (2020).By including sulphur, four new sub-types occur between B and C, the BC sub-types, and a fifth sub-type between C type and the graphite condensation zone, named the CG sub-type.certainly present in Venus' atmosphere, it is not type BC1.
If gaseous H 2 SO 4 occurs beside SO 2 , Venus would be type BC2.If gaseous S 2 or S 8 occur beside SO 2 it would be type BC3.The gas giants in our solar system have more reduced atmospheres.Jupiter's atmospheric type is known as an A-type with the corresponding sulphur condensate being NH 4 SH[s].
Predicting models for formation of the latter in Jupiter's atmosphere exist (Visscher et al., 2006), however it has never been confirmed by observations (Sromovsky & Fry, 2018). (1): The total (gas and condensate) sulphur abundances    Like Tab.B3 but for a surface pressure of 1 bar.

APPENDIX B: TABLES OF RESULTING GAS PHASE ABUNDANCES
(1) : where the sulphur abundance is at 1 2 of its maximum.
Table B5 Molecular composition of the atmospheric gas in our rocky exoplanet models with varying element composition, surface temperature and pressure.Sulphur molecules are highlighted in bold face.3 .On the left, the blue line shows the spectrum when the SO 2 line opacity is omitted.On the right, the blue line shows the spectrum when the H 2 S line opacity is omitted.3 .

Figure 3
Figure3Transmission spectra calculated with ARCiS for input parameters listed in Table3.Nine models with different total element abundances are shown on the left and right.The transmission depths vary according to the different mean molecular weights .We note the different scaling of the -axis on the left and right.All spectra have been computed for a surface pressure of 10 bar and an isothermal atmosphere of 2000 K.The solar model is not shown here because its mean molecular weight  ≈ 2.05, see TableB5, is so small that the transit depth is significantly larger than all other models.

Figure 4
Figure 4 Impact of SO 2 on the transmission spectra generated with ARCiS for isothermal atmospheres with  = 2000 K and surface pressure  surf = 10 bar.The model input parameters are listed in Table3.The four compositions which show the strongest SO 2 absorption features are selected: CC, BSE, MORB and PWD-BSE.The blue lines show the spectra when the SO 2 line opacity is omitted.

Figure 5
Figure5Impact of H 2 S on the transmission spectra generated with ARCiS for isothermal atmospheres with  = 2000 K and  surf = 10 bar.The model input parameters are listed in Table3.The two compositions with visible H 2 S features are selected here: CI and PWD-CI.The blue line shows the spectrum when the H 2 S line opacity is omitted.

Figure 6
Figure 6Transmission spectrum obtained with ARCiS for PWD-CI abundances at 2000 K and 10 bar.The orange curve shows the complete results including PS, whilst the blue curve is the spectrum obtained with zero PS opacity.

Figure 8 Figure 9
Figure8Effect of temperature on the spectral appearance of SO 2 in transmission spectra of isothermal atmospheres calculated for BSE total element abundances and a surface pressure of 10 bar.

Figure 10
Figure 10 Effect of surface pressure on transmission spectra of rocky planets for the BSE model with  = 2000 K.The surface pressures are annotated.

Figure 11
Figure 11 Simulated transmission spectra for the PWD-BSE model with SO 2 (green line) and without SO 2 (orange line).Predicted JWST observations are based on combining 30 and 40 transits, respectively, using PandExo (Batalha et al., 2017) for NIRSpec/G395M in the top and for MIRI/LRS in the bottom panel.For clarity, the data was binned down to  ∼ 30 in their respective wavelength range for both simulated observations.

Figure 12
Figure 12 Simulated transmission spectrum for the PWD-CI composition with PS (green line) and without PS (orange line).Predicted JWST observations are based on combining 40 transits using PandExo (Batalha et al., 2017).The predictions are for NIRspec/Prism for a system similar to 55 Cnc e with a star of maximal allowed brightness in the J-band of 10.5 mag.A detection of PS does not seem possible.Note the different scaling of the y-axis compared to Fig. 11 .
CO 2 exists in the atmosphere b) no H 2 O exists in the atmosphere c) no CH 4 exists in the atmosphere Beyond each of these boundaries, a new type of atmosphere will occur.Figure A1 illustrates these boundaries in the C-H-O plane for a constant value of S. Each sub-figure shows the occurrence of one particular molecule as a function of (O-H)/(O+H) and carbon fraction (C/(C+H+O+S)) in the gas phase.

Figure A1
Figure A1 Number densities of different molecules for various abundances in the CHNOS system.The N2 abundance is subtracted, as it does only interfere for the type A atmospheres.The solid lines are derived from theoretical calculations as discussed in Sect.A.1.The coloured number densities are a result of equilibrium chemistry calculations with GGCHEM for 300 K and 1 bar.The element abundances of C, H, and O set according to the axis of the plots, while a fixed S abundance is investigated (S/(C+O+H+S)=0.1).Every subplot shows one distinct molecule.
gas+cond S(input) are listed in mass fraction percentages (% mf).The sulphur element abundances in the gas phase  ) are given in molar fractions, i.e. number of S-nuclei divided by the sum of the numbers of nuclei of all elements.(1): where  gas S is at least 1 2 of its maximum (2) : the atmospheric type of the model, see Appendix A1

Figure C3
Figure C3Impact of SO 2 and H 2 S on the transmission spectra generated with ARCiS for isothermal atmospheres with  = 2000 K and  surf = 10 bar.The model input parameters are listed in Table3.On the left, the blue line shows the spectrum when the SO 2 line opacity is omitted.On the right, the blue line shows the spectrum when the H 2 S line opacity is omitted.

Figure C5
Figure C5 Same as Fig. C3 but for element abundances derived from polluted white dwarfs.

Figure C6 Figure C7
Figure C6Same as Fig.C3but for solar element abundances, only showing the effect of SO 2 , and H 2 S. Both do not give rise to any strong spectral features.The towering absorption features at optical wavelengths are mainly due to TiO in between 0.38−1.03m with a sharp MgH feature between 0.47−0.61m.
. : Maximum gas particle concentrations  =  mol ∕ tot of atoms and molecules across all our atmospheric models with no opacity data in ARCiS, ordered by concentration.We note that KOH and NaOH line lists are now available from Owens,Tennyson, and Yurchenko  (2021).

Table 3
Input parameters for our ARCiS spectral models(1).: Stellar temperature and radius, as well as planetary radius and mass, are taken from estimates for 55 Cnc e, see Table1 in Tabernero . Sulphur is present in form of H 2 S. The oxygen dominated atmospheric types are characterised by the presence of O 2 , CO 2 and N 2 in all cases.Subtype B2 has H 2 SO 4 and H 2 O in addition, whereas the new subtype B1 has no water but H 2 SO 4 and SO 3 in addition.Subtype B1 occurs for high S/H ratios.The coexistence regime of CH 4 , CO 2 , H 2 O, and N 2 is completed by the presence of H 2 S as the major sulphur carrying species.With increasing sulphur abundance, four new subtypes emerge between type B and C atmospheres, called BC1 to BC4.All of these subtypes show the presence of CO 2 and N 2 .None of them contains CH 4 , NH 3 , O 2 or H 2 .Sulphur is present in form of certain combinations of H 2 S, S 8 , SO 2 , SO 3 and H 2 SO 4 , see Table

Table A2
Condensates occurring in the various atmospheric types of the CHNOS system at low temperatures.Type H 2 O[l,s] H 2 SO 4 [l,s] S[l,s],S 2 [s],S 8 [s] NH 4

: TRANSMISSION SPECTRA C.1 SO 2 and H 2 S
TableB3lists the major molecules and maximum sulphur fractions in the gas over different rock materials at 100 bar, together with some specifics about the temperature dependencies.TableB4does the same for 1 bar.TableB5shows the major molecules with concentrations > 1% and trace species with concentrations > 0.1%, > 100 ppm, and > 10 ppm, respectively, for different rock materials, temperatures and pressures.TableB6explains the condensate families used in Fig.2as a reference.Fig.C7compares the PS absorption features of the Polluted White Dwarf compositions.Whilst for the PWD-CI composition the absorption feature around 0.3−0.8m reaches 40 ppm, the feature strength reaches 5 ppm at most in the other compositions.Apart form the low oxygen abundance in the PWD-CI model, it is to note, that the scale height in this composition is particularly large, which could be one of the causes for this result.No PS feature can be observed in the solar like composition at all.
APPENDIX C

Table B3
Results of our chemical and phase equilibrium models for different element compositions at 100 bar(1).

Table B4
Results of our chemical and phase equilibrium models for different element compositions at 1 bar(1).

Table B6
Condensate families occuring in Fig.2