Three experiments were conducted using a modified Dickson-type experimental setup that allows simulations of in-situ hydrothermal environment conditions (Dickson et al., 1963; Seyfried et al., 1987). Reactants (fluids and solids) reside within a collapsible container, which is sealed and mounted into a stainless-steal pressure vessel filled with distilled water (see Figure 2). Pressure of the water reservoir and the temperature of the vessel can be controlled independently (up to 400°C and 56.5 MPa). As the pressure is isostatically transferred to the contents of the collapsible cell, fluid sampling is enabled through a titanium access tube (featuring an in-line 0.2 µm mesh Ti-filter) and an attached custom fitted Ti-valve. Due to the reactivity of gold in H₂S-rich hydrothermal solutions we used a collapsible titanium foil cell (V_tot ∼ 60 mL) instead of the more widely used cells made of gold (Hayashi and Ohmoto, 1991; Wu et al., 2016). Prior to the experiments, the Ti-cells were thoroughly cleaned with hydrochloric acid and heated to 400°C in air to create a surface layer of titanium oxide that is sufficiently inert under the targeted experimental conditions.

All three experiments were designed to investigate the isotopic fractionation of SO₂, H₂S and S⁰, respectively, during the synproportionation reaction. The reactants sodium sulfide hydrate (Na₂S · 3 H₂O) and sodium sulfite (Na₂SO₃) were weighed and transferred into the titanium cell prefilled with ∼60 mL of O₂-free ultrapure water (thoroughly purged with N₂). The reactants were weight into the cell to set a 20 mmol/L sulfide and 10 mmol/L sulfite concentration within approximately 60 mL of fluid (see Table 1; Supplementary Table S1). The concentrations for sulfide and sulfite were chosen in the milli-molal range to reflect typical concentrations of dissolved sulfur gases in submarine magmatic-hydrothermal systems (e.g., Butterfield et al., 2011; de Ronde et al., 2011; Seewald et al., 2015). The H₂S:SO₂ ratio of 2:1 is the same used by Mizutani and Sugiura (1966). A neglectable amount of elemental sulfur (between 0.9 and <2.5 mg) was added as seed crystals to prevent kinetic inhibition that can occur with homogenous nucleation.

Upon dissolution under hydrothermal conditions, these reactants provide the naturally occurring sulfide and sulfite for the experiments: N a 2 S   ·   3   H 2 O + H 2 O = H S – + 2   N a + + O H – + 3   H 2 O (4) N a 2 S O 3 + H 2 O = H S O 3 – + 2   N a + + O H – (5)

The OH⁻ released by reaction (4) and (5) causes the starting solution to be highly alkaline, which prevents degassing of sulfide and sulfite. However, the natural hydrothermal fluids are acidic and the neutral species H₂S and SO₂ dominate. The pH was therefore adjusted to a pH of 1.2 by adding <1 mL of 25% HCl (see Supplementary Table S1) right before the Ti-foil cell was sealed within the pressure vessel. H S – + O H – + 2   H C l = H 2 S a q + 2   C l – + H 2 O (6) H S O 3 – + O H – + 2   H C l = S O 2 a q + 2   C l – + 2   H 2 O (7)

Thus, the starting fluid had 60 mmol/L of both Na⁺ and Cl⁻ dissolved. The setup was then heated to approximately 220°C for approximately 24 h, while the pressure was maintained between 20 and 30 MPa.

For the characterization of S⁰, H₂S and SO₄ ^2–, 10 mL of sample were drawn from the reactor cell with a gastight syringe at experimental conditions after 24 h.

The samples were transferred into a vacuumed septum vial and 1 mL of 85% H₃PO₄ was added to enable a quantitative extraction of H₂S by means of N₂ purging (20 min) through a gas wash bottle prefilled with 20 mL of 5% AgNO₃ solution. Sulfide precipitated as Ag₂S flakes and was collected on a pre-weighed polycarbonate filter enabling a subsequent gravimetrical quantification. Next, 5 mL of the N₂-purged, acidified solution were transferred to a second vacuumed vial and 300 µL of a 1M BaCl₂ solution were added to precipitate any potentially present sulfate. In experiment #3, 600 µL of the 1M BaCl₂ solution were just added to the 10 mL sample in order to maximize the sulfate yield for subsequent isotopic characterization. Total amount of dissolved sulfate previously precipitated as BaSO₄ was subsequently derived by weight.

Concentrations and absolute contents for H₂S, SO₄ ^2– and S⁰ given in Table 1 were derived by extrapolating the amounts retrieved from the respective sample volumes to the total fluid volume for each experiment.

An additional 1.75 mL of fluid were sampled into a gas tight syringe for the quantification of potentially formed H₂. Hydrogen was then quantified from about 0.25 mL gaseous headspace that unmixed from the fluid upon depressurization using an Agilent 7820 A gas chromatograph equipped with a 60/80 Molsieve column and a thermal conductivity detector.

For sulfur isotope measurements, ca. 50 μg of elemental sulfur or 300–400 µg of silver sulfide are mixed with 400–800 µg of V₂O₅ and homogenized within a tin cup. Isotope measurements were carried out via elemental analyzer isotope ratio mass spectrometry (EA-IRMS) using a Flash EA IsoLink attached to a Thermo Fisher Scientific Delta V Advantage mass spectrometer. The reproducibility determined by replicate measurements was usually better than 0.3‰ (1σ). Analytical performance was controlled with IAEA-S1, -S2, -S3 and NBS 127 as international reference materials and with laboratory internal standards.

Using the initial isotopic composition of the reactants, we constructed a Rayleigh fractionation model (cf. McDermott et al., 2015; Kleine et al., 2021; Kürzinger et al., 2022). With this fractionation model we were able to predict sulfur isotopic compositions for all potential formation pathways and classify the measured values accordingly. Further details of the calculations are given in the Supplementary Material. Note: The isotopic composition of the reactants does not reflect the isotopic composition of naturally occurring sulfur species in magmatic-hydrothermal systems. Thus, the experimental isotope values will not mirror those measured in natural samples, but the magnitude and direction of isotope fractionation between the different sulfur species at given pT-conditions will be comparable.

Gibbs energies of reaction under experimental conditions were calculated for the sulfur formation reactions (syn- and disproportionation) as well as for the dissociation reactions of all involved sulfur species using the SUPCRT92 code (Johnson et al., 1992). The reaction path computation with Geochemist’s Workbench (v. 12) makes use of a tailor-made database constructed for 25 MPa using SUPCRT92 and the OBIGT database (Dick, 2019). Equilibrium constants of all possible redox reactions (see Supplementary Figure S1) involving the four species H₂S, S⁰, SO₂ and HSO₄ ⁻ are included in the database. These were derived essentially from prior experimental studies of sulfur hydrolysis and redox reactions (e.g., Ellis and Giggenbach, 1971).

The model is not a traditional titration path but instead it has the full amounts of SO₂ and H₂S in the system initially. All possible redox reactions are then kinetically inhibited to the same extent to investigate how the reaction network is predicted to evolve as the system approaches equilibrium state.

Photographs of the experimental results as well as representative SEM images of elemental sulfur formed during the experiments are shown in Figures 3, 4.

For each experimental run, the individual steps were carried out as described above. During the first experiment (#1), precipitation of sulfur was not observed, although H₂S clearly had formed (strong characteristic smell) and the solution acquired a yellowish color. Sulfur precipitation only occurred following acidification with phosphoric acid for H₂S expulsion. Apparently, the synproportionation reaction does not proceed under alkaline conditions or kinetics are too sluggish for significant reaction turnover (previous pH ∼ 7.8, see Table 1).

Accordingly, the follow-up experiments (#2 and #3) were run at conditions energetically more favorable for the synproportionation reaction we suspect to take place at Toxic Castle in the Kemp Caldera hydrothermal system. The pH at Toxic Castle is likely lower than measured in 2019 (pH_25°C = 5.7) due to seawater entrainment during sampling (see Kürzinger et al. (2022) for details). We hence adjusted the starting pH_{25 °C} to 2 in experiments #2 and #3, and native sulfur did form under these acidic conditions. Abundant fine-crystalline sulfur could then be recovered from the open titanium cell after terminating both experiments (Figure 3). Small sulfur flakes were visible even in the fluid sample extracted prior to the termination of the experiment, indicating that the sulfur did not form during cooling. Sulfate, only present in dissolved form, could be precipitated as BaSO₄ for a subsequent quantification (0.3–0.6 mmol/L). In addition, small amounts of H₂ could be quantified (5–10 μmol/L).

The sulfur recovered from experiments #2 and #3 had a very similar appearance compared to the sulfur samples from the Kemp Caldera (Figure 4). Some very fine-grained elemental sulfur (fitting through the 2 µm in-line Ti-filter) was removed from the cell into the syringe or precipitated from the solution upon rapid cooling and depressurization. This sulfur resembles the liquid S⁰ at Toxic Castle (Figure 4A). On the other hand, the sulfur from the cooled reaction cell is fine-crystalline as it is at Great Wall (Figure 4B).

The amounts of sulfate (as BaSO₄) and sulfide (as Ag₂S) obtained from the subsamples (ca. 5 or 10 mL) and the elemental sulfur retrieved from the much larger residual volume left in the Ti-cell, i.e., ∼45 or ∼35 mL were both extrapolated to match the initial 60 mL (see Table 1). The total amounts of the different sulfur compounds retrieved from the experiment and their relative proportions indicate which reactions must have dominated in the system. Elemental sulfur is by far the most abundant, H₂S is only a small fraction of the initial amount, and sulfate concentration is also low. The experimental design is not geared towards full recovery of all species and phases, and hence the final concentrations reported do not add up to the amount of sulfur present in system (30 mmol/L in total or 1.8 mmol in the 60 mL volume of the reaction cell). We suspect that the missing sulfur is mainly represented by a coating on the inner walls of the reaction cell, which could not be fully retrieved after the experiment was terminated. A small fraction of the H₂S may be sorbed to elemental sulfur (e.g., Bacon et al., 1943).

Our experimental results indicate that the largest fractionation of the sulfur formed during the experiments could not have been due to SO₂ disproportionation. This can easily be seen by the data presented in Table 1. First, less than 0.1 mmol of the original 1.2 mmol sulfide in the reaction cell remained unreacted. This shows that sulfide was not produced during SO₂ disproportionation (Eq. 1), but instead it was consumed (such as in reaction 3). Second, disproportionation should produce twice as much sulfate than sulfur (see Eq. 2). But in the observed reaction product the amount of sulfur is greater than the amount of sulfate. The development of abundant elemental sulfur in concert with the pronounced drop in sulfide concentration can only be explained if synproportionation (Eq. 3) occurred in the reactor.

Isotopic compositions for the reactants Na₂S · 3 H₂O, Na₂SO₃ and S⁰ (used as crystallization nucleus) were determined along with that of the S⁰, H₂S and SO₄ fractions formed during the experiments (Table 1). Isotopic compositions for H₂S were determined from precipitated Ag₂S. Elemental sulfur in experiment #1 was only precipitated during sample processing and is clearly different in morphology from that produced in experiments #2 and #3. The sulfur produced in those later experiments has δ³⁴S values close to 0‰ in both instances (Table 1). The sulfur isotopic composition of H₂S is only 1.1‰ higher than those of S⁰ which is consistent with an expected small equilibrium fractionation between native sulfur and H₂S (Ohmoto and Rye, 1979).

To further illuminate the sulfur formation process, we used the known initial isotopic composition of the reactants (Table 1) to construct a set of Rayleigh fractionation models for the different possible formation pathways (see Supplementary Material for details) and plotted the results together with the measured isotopic values of the sulfur recovered from the experiments (Figure 5). Another sulfur formation mechanism could be SO₄ reduction, but these values could not be calculated because we did not have an initial δ³⁴S_SO4 value due to no existing sulfate at the beginning of the experiment.

The calculated values for H₂S oxidation as well as SO₂ disproportionation fall outside the measured range because they are either far too negative or too positive (see Figure 5). Thus, these reactions can be excluded as a possible sulfur formation process. However, the calculation results suggest that δ³⁴S_S values resulting from SO₂–H₂S synproportionation are consistent with the measured sulfur isotope values (δ³⁴S = −0.3 to 0.4‰) of elemental sulfur retrieved from experiments #2 and #3.

In addition to supposing specific sulfur redox reactions and studying their isotopic consequences, we conducted an arbitrary kinetics reaction path model computation to examine the predicted sequence in a hypothetical network of ten reactions (between the considered four oxidation states of sulfur (−2, 0, +4 and +6) there are 4!/((4–2)!*2!) = 6 possible simple redox reactions with two reaction partners and 4!/((4–3)!*3!) = 4 possible syn-/disproportionation reactions with three reaction partners; Supplementary Figure S1). The model predicts which of these reactions is expected to contribute how much to the total reaction turn-over as the system approaches equilibrium (Figure 6). Starting with initial concentrations of 10 mM SO₂ and 20 mM H₂S in the reaction cell (t = 0), two reactions are predicted to dominate in the first time-segment: (1) SO₂–H₂S synproportionation and (2) SO₂ disproportionation to S⁰ and HSO₄ ⁻. As SO₂ is consumed and HSO₄ ⁻ is produced in these reactions, the Gibbs energies of the reactions change. The affinity for the SO₂–H₂S synproportionation will go down, while those for reactions with HSO₄ ⁻ will go up. The transition from the first to the second time-segment is reached when the SO₂ disproportionation turns endergonic and H₂S–HSO₄ ^– synproportionation turns exergonic. SO₂–H₂S synproportionation continues to create small amounts of S⁰. In reaching equilibrium, of the 30 mM total sulfur dissolved initially, 25 mM are predicted to have been converted to S⁰, of which 23 mM are due to synproportionation (roughly equal contributions from SO₂–H₂S and H₂S–HSO₄ ^–) and 2 mM are due to SO₂ disproportionation. Equilibrium concentrations of H₂S and HSO₄ ⁻ are 3.7 and 1.2 mM, respectively.

In addition to instantaneous equilibrium isotope partitioning, we used the sulfur species abundances from the GWB reaction path model to compute Rayleigh fractionation trends. Kleine et al. (2021) suggested that Rayleigh fractionation more reliably represents isotope fractionation in irreversible geochemical reactions in closed systems than the equilibrium partitioning supported by GWB. The evolution of isotopic composition of H₂S, S⁰, SO₂, and HSO₄ ⁻ is shown in Figure 7. The correspondence between the measured and predicted isotopic compositions is excellent for S⁰ and HSO₄ ⁻. The measured δ³⁴S value of the leftover H₂S is lower than the predicted one.

The stability of elemental sulfur in water-bearing systems is known from experimental studies of sulfur hydrolysis to H₂S and SO₂ as well as H₂S and HSO₄ ⁻ (e.g., Ellis and Giggenbach, 1971). These reactions are the reverse of synproportionation discussed in this work. Formation of native sulfur by SO₂–H₂S synproportionation was already considered by Mizutani and Sugiura (1966) and Giggenbach (1987) as potential sulfur forming reactions in gaseous subaerial fumarole systems. Subequal amounts of both compounds in a cooling system will create thermodynamic drive for the reaction to proceed. Some H₂S is expected to form when SO₂ reacts with FeO in the rock through which the fumarole gas flows and undergoes cooling (Giggenbach, 1987). Hence low-temperature fumaroles in many volcanoes have both gases present in subequal amounts, and hence elemental sulfur can form by synproportionation of SO₂ and H₂S in the gas phase. It was unclear what the energetics and kinetics of the reaction in aqueous solutions under hydrothermal conditions are.

The energetics of native sulfur formation in an aqueous environment by synproportionation was examined by Kürzinger et al. (2022) for the Kemp Caldera, but the thermodynamic computations presented in this earlier communication were subject to large uncertainties in pH and sulfite concentrations of the hydrothermal fluids. Based on the new tight experimental constraints, we here reevaluate the energetics of the syn- and disproportionation pathways of elemental sulfur formation. For the measured low pH_25°C of ∼1.2 in experiments #2 and #3, the dissociation equilibrium is predicted to lie entirely on the undissociated side with sulfite and sulfide being dominated entirely by SO₂ and H₂S, respectively (see Figure 14 in Kürzinger et al., 2022). Results for Δ_RG for the dis- and synproportionation reactions over a temperature range from 0 to 300°C are listed in Table 2. They were calculated using the concentrations and activity coefficients (γ) provided in the footnote of Table 2 and are shown in Figure 8.

At lower temperatures, both reactions are clearly exergonic, while the disproportionation reaction becomes endergonic at temperatures >210°C. Synproportionation, however, remains exergonic up to a temperature of about 275°C at the selected conditions (p = 30 MPa). From an energetic perspective, both reactions are likely to occur in the experiment. But even if the disproportionation reaction is endergonic at the target temperature of 220°C, this sulfur formation process cannot be entirely excluded. The experimentally produced elemental sulfur could have formed by disproportionation during the cooling phase as the system passed through the temperature range in which this reaction would be predicted to take place.

The elevated sulfate concentrations measured indicate that sulfate was formed by disproportionation reactions that took place subordinated to synproportionation. The reaction path model predicts that sulfate is formed by disproportionation alongside native sulfur early on in the reaction sequence. The predicted quantities are 2 mM of S⁰ and 4 mM of sulfate. As SO₂ gets depleted and sulfate is enriched in solution, the energetics changes such that the synproportionation of sulfate and H₂S becomes exergonic, while sulfite-sulfide synproportionation continues with a small reaction turnover.

The formation of H₂ in the experiment, although in very small amounts of 5–10 μmol/L, indicates that another, subordinate reaction must have taken place in addition to the dominant synproportionation. A possible origin of the detected H₂ can be the partial oxidation of SO₂ with water as oxidant (Eq. 8). S O 2 a q + 2   H 2 O = H S O 4 – + H + + H 2   a q (8)

Using the concentrations and activity coefficients from Table 1 and 2 in concert with a calculated equilibrium constant (Log K_{220 °C} = 7.3) for Eq. 8, the measured H₂ concentrations correspond with the amount of H₂ predicted for equilibrium state in a pH 1.4 solution with 10 mM SO₂ and 2–6 mmol sulfate at 220°C. The reaction path model results suggest equilibrium concentrations of H₂ (4 µM) that are very close to the measured concentrations (Table 1). These results hence indicate that sulfate and SO₂ did indeed equilibrate in the hydrothermal apparatus. The formation of sulfuric acid plus H₂ by partial SO₂ oxidation could also explain why low pH may develop in systems in which SO₂ disproportionation is subordinate to SO₂–H₂S synproportionation.

In the conducted experiments, native sulfur was the most abundant sulfur species (4.6–6.75 mmol/L) and >10 times more abundant than sulfate (0.31–0.56 mmol/L) and sulfide (0.11–0.24 mmol/L). While the mass balance indicates that sulfur formation by synproportionation was dominant, the experimental setup was not optimized for allowing full retrieval of all sulfur species. It is hence not unexpected that the sum of the retrieved sulfur species does not add up to 30 mmol/L (the total sulfur concentration in the system). In the model, of the 25 mM S⁰ produced, 2 mM are from SO₂ disproportionation and roughly 11.5 mM each are due to synproportionation of SO₂–H₂S and H₂S–HSO₄ ^–, respectively.

The predicted isotopic composition of the native sulfur (0‰) is also in agreement with the measured δ³⁴S values (cf. Table 1; Figure 5). The predicted δ³⁴S value of sulfate is in the range of 23‰ at 220 °C and very close to the measured value of 23.6‰. We hence suggest that the sulfate produced in the experiments has been formed by disproportionation and (to a lesser extent) by partial oxidation of the residual SO₂ (Eq. 8). As SO₂ is highly soluble in water and because of its intermediate oxidation state, it can act as reducing and oxidizing agent.

The residual H₂S has measured δ³⁴S values that are 1.1‰ higher than that of the S⁰. The Rayleigh model predicts a higher δ³⁴S value (6.3‰) for H₂S than the 0.8‰–1.5‰ measured. Experimental data for H₂S–S⁰ fractionation (Ohmoto and Rye, 1979) suggest that, in equilibrium, H₂S is 0.7‰ lighter than S⁰. The measured difference of 1.1‰ is closer to the expected equilibrium value than the difference of the difference of 6.3‰ predicted by the Rayleigh model. This result may indicate that the small amount of H₂S left over in the experiment was close to equilibrium with the abundant S⁰ that had formed primarily by synproportionation.

Disproportionation of magmatic SO₂ in arc/back-arc magmatic-hydrothermal systems forms acid-sulfate type fluids with pH-values <3 (Gamo et al., 1997; Kim et al., 2009; de Ronde et al., 2011; Seewald et al., 2019). SO₂ degassing is common in these environments due to the oxidized nature of magma produced above a subducting slab (Wallace, 2005). Experimental and empirical studies (cf. Kusakabe et al., 2000; McDermott et al., 2015; Peters et al., 2021) have shown that the disproportionation-derived sulfate is enriched in ³⁴S, whereas the reduced counterparts (S⁰ and H₂S) are depleted in ³⁴S relative to the isotopic composition of the influxing SO₂, which ranges between 4 and 10‰ in δ³⁴S (Hannington et al., 2005). The temperature-dependent equilibrium isotope fractionation between aqueous SO₂, SO₄, S⁰ and H₂S has been established (Ohmoto and Rye, 1979; Ohmoto and Lasaga, 1982; Kusakabe et al., 2000) and these constraints were used to compute the isotopic evolution of SO₂ and the products of the disproportionation reactions in hydrothermal fluids (McDermott et al., 2015; Kleine et al., 2021; Peters et al., 2021). The results from these studies suggest that the δ³⁴S values of elemental sulfur are typically <0‰ and those of the associated sulfate are commonly <21‰. The equilibrium isotope fractionation between native sulfur and H₂S is very small (Ohmoto and Rye, 1979), hence sulfides in arc/back-arc vent settings are usually also characterized by δ³⁴S values <0‰. Often, the δ³⁴S value of S⁰ is lower than that of the dissolved H₂S (e.g., Peters et al., 2021), which may indicate that the S⁰ formed at lower temperatures than the H₂S.

Although both sulfur and sulfide typically have negative values of δ³⁴S, positive values for S⁰ and H₂S have also been documented in various hydrothermal systems. For instance, hydrothermal fluids at Niuatahi volcano (NE Lau Basin) display positive δ³⁴S_H2S values ranging from 0.2 to 4.5‰ (Peters et al., 2021). Other examples include the Macauley and Brothers hydrothermal system, both hosted in submarine caldera volcanoes the Kermadec arc. The Macauley white smoker vent field is close to the summit of a dacitic cone near the SE caldera wall. Here, S⁰ with a δ³⁴S value of −3.4‰ precipitates from highly acidic fluids with δ³⁴S_H2S values between 1.6 and 2.9‰ (Kleint et al., 2019; Peters et al., 2021). Brothers volcano hosts several chemically distinct active hydrothermal sites (e.g., de Ronde et al., 2005; de Ronde et al., 2011). Whereas the NW Caldera and Upper Caldera sites are dominated by black smoker-type fluids and Cu-Fe-rich sulfide chimneys, the Upper and Lower Cone vent fields are characterized by white smoker venting and the occurrence of elemental sulfur. Fluids of Brothers Upper Caldera show δ³⁴S values between 3.0 and 4.6‰ for dissolved sulfide (Kleint et al., 2019; Peters et al., 2021), while the Cone vent fluids are negative (δ³⁴S_H2S = −8.0 to −4.8‰; de Ronde et al., 2011). Niua, a volcano located in the northernmost Tonga arc, hosts two active vent sites (δ³⁴S_H2S = 2.6 to 4.5‰; Peters et al., 2021), but positive S⁰ was only found at Niua North, exhibiting a δ³⁴S value of 3.1‰ (Peters et al., 2021). Even higher isotope values for elemental sulfur in the range from 5 to 6‰ from active vents in the Kemp Caldera (South Sandwich arc) were reported by Kürzinger et al. (2022). The very large range in the isotopic composition of sulfur and sulfide in arc/back-arc hydrothermal systems could be an indication of multiple pathways of sulfur formation mechanisms due to essential differences in redox, which allows for variable proportions of SO₂ and H₂S to be added to the hydrothermal system (cf. Kusakabe et al., 2000).

Kürzinger et al. (2022) proposed that the high δ³⁴S_S values observed in the Kemp Caldera are inconsistent with disproportionation of SO₂ and instead suggested that the S⁰ is formed by SO₂–H₂S synproportionation. The experimental findings presented here provide irrefutable evidences that this novel S⁰ formation pathway does indeed take place if energetically favorable conditions prevail. Our experimental results clearly show that the synproportionation of SO₂ and H₂S is a feasible process given that SO₂ and H₂S are both abundantly present. An essential requirement for the reaction to take place in nature is the simultaneous degassing of both SO₂ and H₂S. Work on fumarolic gases at convergent margin volcanoes (Giggenbach, 1987; Symonds et al., 1994; Moretti et al., 2013) has shown that the ratios of SO₂ and H₂S can be highly variable and that both gases can be abundant, in particular in low-temperature fumaroles.

If H₂S does not degas coevally with SO₂, disproportionation would then dominate in the reaction network controlling the sulfur speciation and isotopic fractionation. The common occurrence of isotopically light sulfur in submarine arc/back-arc hydrothermal systems suggests that SO₂ is frequently the dominant sulfur species added to hydrothermal systems by magma degassing. The observations of isotopically heavy sulfur in places like Niua North and the Kemp Caldera, however, are inconsistent with SO₂ disproportionation as formation process. Our work shows that synproportionation can be invoked to explain seafloor hydrothermal S⁰ with such positive δ³⁴S values.