Production, preservation, and biological processing of mass-independent sulfur isotope fractionation in the Archean surface environment

Abstract

Mass-independent fractionation of sulfur isotopes (S MIF) in Archean and Paleoproterozoic rocks provides strong evidence for an anoxic atmosphere before ∼2,400 Ma. However, the origin of this isotopic anomaly remains unclear, as does the identity of the molecules that carried it from the atmosphere to Earth’s surface. Irrespective of the origin of S MIF, processes in the biogeochemical sulfur cycle modify the primary signal and strongly influence the S MIF preserved and observed in the geological record. Here, a detailed model of the marine sulfur cycle is used to propagate and distribute atmospherically derived S MIF from its delivery to the ocean to its preservation in the sediment. Bulk pyrite in most sediments carries weak S MIF because of microbial reduction of most sulfur compounds to form isotopically homogeneous sulfide. Locally, differential incorporation of sulfur compounds into pyrite leads to preservation of S MIF, which is predicted to be most highly variable in nonmarine and shallow-water settings. The Archean ocean is efficient in diluting primary atmospheric S MIF in the marine pools of sulfate and elemental sulfur with inputs from SO₂ and H₂S, respectively. Preservation of S MIF with the observed range of magnitudes requires the S MIF production mechanism to be moderately fractionating (20–40‰). Constraints from the marine sulfur cycle allow that either elemental sulfur or organosulfur compounds (or both) carried S MIF to the surface, with opposite sign to S MIF in SO₂ and H₂SO₄. Optimal progress requires observations from nonmarine and shallow-water environments and experimental constraints on the reaction of photoexcited SO₂ with atmospheric hydrocarbons.

With few exceptions, the enrichment or depletion of the rare, stable isotopes of sulfur (³³S, ³⁴S, and ³⁶S) relative to the abundant isotope (³²S) scale as the mass difference between the isotopes (1). Sulfur isotope mass-independent fractionation (S MIF) is defined as a departure from these theoretically derived and empirically observed mass laws, and denoted S and S. S MIF is observed in modern atmospheric sulfate aerosols, as well as in sulfate-bearing layers hosted in glacial ice (2, 3), but is conspicuously absent from the sedimentary record of the last 2,400 My. In contrast, older rocks of the Archean and early Paleoproterozoic eons preserve large and variable S MIF (4, 5). On the basis of experimental SO₂ photolysis and atmospheric chemistry models, the prevailing hypothesis to explain this observation is that the absence of atmospheric oxygen before ∼2,400 Ma allowed both the photochemical production of S MIF and its delivery to the surface in the reduced and oxidized products of sulfur photochemistry (4–7). Thus, S MIF is considered strong geochemical evidence for an anoxic atmosphere before ∼2,400 Ma.

Although research converges on atmospheric processes as the source of S MIF, its production mechanism and the identity of its vectors to the surface remain unclear. A focus on photolysis experiments and measurements of SO₂ isotopologue (molecules of ^3xSO₂ with x = 2, 3, 4, 6) absorption cross-sections has led to significant progress in understanding the origin of S MIF (8–12). However, attempts to relate experimental results to geologic observations, or to use the observations to inform the experimental search for a mechanism, are unavoidably compounded by the myriad of oceanographic and sedimentologic processes that operate in the sulfur cycle (13). These processes control the degree of postatmospheric mixing among the various S MIF carriers and ultimately the magnitude and spatial distribution of the observable signal. Many of these processes may be quantified using independent knowledge of the sulfur cycle and low-temperature geochemistry. This allows a more complete and more refined use of the information encoded in the observable record, with the objective of better understanding the nature of the atmospheric signal. In this paper, a detailed, spatially resolved model for the coupled biogeochemical cycles of iron and sulfur is developed and used to constrain processes in the Archean sulfur cycle, the identity of atmospheric S MIF carriers, and the sign and magnitude of S in these carriers.

Existing Constraints

Systematic sampling of the Archean and Proterozoic rock record has shown that S in pyrite spans a range of approximately to (4, 14–16), that barite (BaSO₄ and, by inference, marine sulfate) carries S values around (4, 16, 17), and that the data form a loose array of S against S with a slope of approximately (14). Sulfide minerals with low S and some in Archean volcanogenic massive sulfide deposits also carry weak S 0 (7, 18, 19). Both are interpreted to have originated from seawater sulfate, the former through microbial reduction and the latter through mixing with volcanogenic sulfur, supporting S 0 in seawater sulfate. Sulfur isotope analyses of carbonate-associated sulfate (CAS) suggest instead that marine sulfate carried S 0 (20). However, carbonates that precipitated out of the sulfate-poor Archean ocean contain little sulfate, requiring dissolution of large volumes of rock for analysis and making it difficult to rule out contamination by trace pyrite or organic sulfur. Improvements in small-sample analysis promise to overcome these difficulties (21).

Experimental UV photolysis of SO₂ was found to produce large S MIF in H₂SO₄, in cyclic octa-atomic elemental sulfur (S₈), and in the residual SO₂ (4, 8–10). The magnitudes of S and S, as well as the S–S and S–S relationships vary with wavelength, with the photolysis column optical thickness, and with bath gas composition and pressure. Once produced, atmospheric models indicate that S MIF would reach the surface in the oxidized and reduced products of sulfur photochemistry only if atmospheric oxygen was below to present atmospheric levels, depending on the trace gas composition of the atmosphere (6, 7, 22, 23). Thermal sulfate reduction has been suggested as the source of Archean S MIF (24), but recent experiments yield only anomalous fractionation of ³³S (S 0), suggesting a magnetic isotope effect and in contrast to Archean S MIF (25).

The emerging picture is of photochemical pathways, which persisted over hundreds of millions of years, generating S 0 (S 0) in atmospheric SO₂ and H₂SO₄ and S 0 (S 0) in other products of sulfur photochemistry, taken to be S₈. Characteristic S–S and S–S relationships are thought to provide a fingerprint of these photochemical pathways, with modification of the former, but not the latter, by subsequent biogeochemical sulfur cycling (7).

S MIF Production Mechanism

The mechanism by which S MIF was generated remains unclear. Explanations divide broadly into two categories: effects related to different photoexcitation probabilities of the SO₂ isotopologues, and kinetic isotope effects associated with the relaxation or ultimate dissociation of photoexcited SO₂. Effects in the latter category have yet to be discussed in the literature for SO₂, but may be analogous to isotope-dependent relaxation rates of excited ozone or of state-to-state transformations of carbon monoxide, which lead to mass-independent oxygen isotope effects (26). Effects in the former category stem from subtle differences in the absorption cross-sections of the SO₂ isotopologues. Self-shielding occurs when the atmosphere is optically thick in one or more of the isotopologues. The radiation suitable for the photolysis of the abundant isotopologue is absorbed at altitude, whereas the radiation suitable for photolysis of the rare isotopologues penetrates deeper into the atmosphere. The proportions of sulfur isotopes in the photoproducts and residual SO₂ then deviate from mass dependence (27, 28). Calculations with absorption cross-sections at the highest currently available spectral resolution indicate that a significant component of S MIF generated in this way is inconsistent with geological observations (12). A second effect related to differences in absorption spectra occurs at any optical density of SO₂. Here, the subtle differences among the cross-sections lead to higher (lower) rates of photo-excitation of one or more of the isotopologues, depending on the spectrum of incident radiation (11–13, 29). The photoproducts then are mass-independently enriched (depleted) in this isotopologue relative to the residual SO₂.

The identity of the S MIF carriers other than SO₂ and H₂SO₄ also is uncertain. Photolysis experiments that produced S₈ involved high concentrations of SO₂, which favor oligomerization of elemental sulfur to form S₈ rings. Recent experiments with realistic abundances of SO₂ do not produce S₈, but in the presence of realistic methane concentrations, do generate methanesulfonic acid (MSA; CH₃SO₃H) (30). Experiments with other atmospherically relevant hydrocarbons generate additional organosulfur molecules (31). Unlike S₈, MSA is generated not from the UV dissociation of SO₂, but from the reaction of photoexcited SO₂ with methane. Calculations convolving SO₂ isotopologue absorption cross-sections with the solar spectrum at wavelengths that cause photoexcitation (λ 240 nm) yield S MIF with a S–S relationship consistent with the Archean record, but with S 0 in the residual SO₂ and S 0 in the photoexcitation products (32). A third possibility is that H₂SO₄ and SO₂ carried opposite signs of S MIF. Atmospheric H₂SO₄ formed from direct oxidation of SO₂ would carry the same sign S MIF as the SO₂, but H₂SO₄ formed from photoexcited SO₂ would carry S MIF of the opposite sign.

Model of the Archean Sulfur Cycle

Independent constraints on the carriers of S MIF and on the characteristics of S MIF in those carriers might valuably inform theoretical and experimental work. Given current uncertainty, the approach here is not to directly calculate S MIF generation, but to prescribe S MIF-bearing fluxes from the atmosphere to the ocean and to model in detail the marine processes that distribute, mix, and ultimately bury the isotopic anomaly in seafloor sediments. The premise of the approach is that with the marine biogeochemistry of the various S MIF carriers accounted for in the model, prescribed atmospheric fluxes of these carriers will have diagnostic outcomes in the preserved magnitude, sign, and spatial distribution of S MIF.

The model is described in detail in the Materials and Methods, SI Materials and Methods, and Tables S1–S5. The major ocean boxes (Fig. 1) were chosen to capture large-scale effects of global, density-driven circulation on ocean chemistry. Additional boxes represent specific physical environments, which are sampled by observations (e.g., continental shelf sediments, hydrothermal mounds). S MIF in these environments is expected to reflect the local sources of sulfur and the locally dominant biogeochemical processes. The model tracks the concentrations of seven sulfur species: sulfate , sulfite , polythionates , thiosulfate , elemental sulfur particles (S₈), sulfide (), and organic sulfur (MSA and similar molecules); and three iron species: dissolved and (and their complexes in seawater) and particulate Fe(OH)₃. The concentrations of polysulfides are not tracked dynamically but calculated in equilibrium with sulfide and S₈. Coupled, nonlinear mass-balance equations for the 10 model species in each box include natural source terms (rivers, atmospheric deposition, hydrothermal activity, etc.), ultimate sinks (mineral precipitation, loss to sediments and hydrothermal circulation), transport between model boxes (advection, particle settling, etc.), and biogeochemical transfer of material among the various species (chemical reaction, biological utilization, etc.). The preservation of S MIF suggests that water-column biological activity did not cycle sulfur between its oxidation states enough to strongly attenuate atmospherically generated S MIF (13). Therefore, here biological sulfur cycling is taken to occur within the sediments.

Fig. 1.

Model geometry. Seawater boxes are white and sediment boxes are gray. Dotted black arrows denote atmospheric fluxes. Thin black bidirectional arrows denote diffuse exchange between model boxes. Thicker colored arrows denote directional flow (blue, thermohaline circulation; red, coastal upwelling; orange, riverine influx and evaporative outflux). Values of geometric and transport parameters are in Tables S1 and S2.

The atmospheric influxes to the surface boxes are based on the results of photochemical modeling studies (6, 7, 22). Proportions of atmospherically deposited species vary among the models (Table 1) as a result of differences in the trace-gas composition of the atmosphere, the oxidation state of volcanic emissions, and the included chemical reactions and their rates. As discussed below, this leads to variability both in the concentrations of marine sulfur-bearing compounds and in their S MIF composition. Using atmospheric fluxes from the photochemical models and the dynamics described above, the equations are solved numerically for the steady-state concentrations of the model species. The steady-state concentrations and fluxes, together with specified values of S in the atmospheric influxes, then are used to solve for the S MIF composition of the marine and sedimentary reservoirs. Empirical knowledge and isotopic mass balance guide the values of S carried in the atmospheric vectors (Fig. 2 and Materials and Methods).

Table 1.

Approximate proportions of atmospheric species in total flux to the surface

Model	H2SO4	SO2	S8	H2S*	Sorg
(A) Pavlov and Kasting (6)	0.07	0.24	0.33	0.36	0.00
(B) Ono et al. (7)	0.16	0.11	0.63	0.10	0.00
(C) Zahnle et al. (22)	0.56	0.18	0.26	0.00	0.00
(D) Sorg	0.05	0.45	0.00	0.45	0.05

*Including HS.

Fig. 2.

Conceptual model for distribution of S MIF in products of sulfur photochemistry. Arrows may represent complex, multistep reaction pathways rather than single reactions. S MIF in the photoproducts and in the residual SO₂ are shown in red. At wavelengths less than ∼220 nm, SO₂ dissociates and photoproducts are fractionated by a factor, E^D. Photoexcitation at wavelengths greater than ∼260 nm and subsequent reaction of the excited SO₂ may lead to a variety of final products. These photoproducts are fractionated by a different factor, E*. SO₃ (and subsequently H₂SO₄) may form by direct oxidation of SO₂, in which case the oxidation products will carry S MIF similar to the SO₂. The fractions of H₂SO₄ and S₈ formed by reaction of photoexcited SO₂ are denoted and , respectively.

Results and Discussion

Steady-state concentrations (Fig. 3) and isotopic compositions (Fig. 4) of the marine species are presented for four cases. In cases A through C, inorganic sulfur compounds (S₈ or H₂SO₄) are the S MIF carrier (in addition to SO₂). In case D, organic sulfur compounds (S_org) carry S MIF, and this is the only case in which marine concentrations of S_org are nonzero. Cases A through C cover a range of atmospheric deposition fluxes from photochemical models (Table 1).

Fig. 3.

Sulfur species concentrations (bars) and their proportions in fluxes to the sediment (pie charts). Sulfite, polythionates, and thiosulfate, which derive almost exclusively from deposited atmospheric SO₂ and exchange sulfur rapidly with one another, carry identical S MIF and therefore are plotted together. Their combined concentration is dominated by thiosulfate, with the other two species at least four orders of magnitude less abundant. The vertical extent of the bars reflects the range of concentrations obtained with different atmospheric deposition fluxes (Table 1, cases A–D) and with variable values for uncertain reaction rate constants (see text). Labels on the leftmost pie charts correspond to the model cases (B, fluxes from ref. 7; C, fluxes from ref. 22; D, carrier with fluxes in Table 1).

Fig. 4.

S in marine sulfur species for five scenarios (S₈ carrier in cases B and C, H₂SO₄ carrier in cases B and C, and carrier in case D) in the deep-ocean and estuarine boxes. Values of , , , and are below each of the scenario S results. The shaded region brackets the observed range of Archean S.

Sulfur Chemistry in the Archean Ocean.

Species’ concentrations are high near their sources and low near their sinks. For example, sulfide concentrations are higher in the sediments, where sulfide is produced by microbial reduction of more oxidized forms of sulfur, and lower in surface boxes, where sulfide is scavenged by photooxidation. Sulfur exits the ocean primarily as pyrite, with sulfate evaporite and barite formation accounting for 5–9% of outfluxes, consistent with suggestions that pyrite burial accounted for essentially all the sulfur exiting the oceans over much of the Precambrian (33).

A qualitative difference between the seawater and sediment boxes arises as the result of microbial activity within the sediments. In seawater boxes, several species reach high concentrations, notably sulfate (∼20–60 μM), thiosulfate (∼2–10 μM), and S_org in case D (∼20 μM). These concentrations are in agreement with recent estimates of Archean seawater sulfate concentrations from multiple sulfur isotopes in volcanogenic massive sulfide deposits (19). By contrast, concentrations of sulfite, polythionates, sulfide, and S₈ are subnanomolar. Despite low concentrations, some of these species react rapidly with the more abundant species, facilitating isotopic exchange between sulfur compounds of different oxidation states (e.g., polythionate lengthening and shortening reactions involve exchange of sulfur among polythionates, thiosulfate, and sulfite). Although atmospheric fluxes to the ocean contain large proportions of SO₂, S₈, and H₂S, the total concentration of sulfur species in the ocean is heavily dominated by sulfate and thiosulfate. The reason for this is that the atmospherically deposited species react or settle rapidly once in the ocean. Sulfate and thiosulfate, on the other hand, are produced rapidly from less stable species, but are only slowly removed by microbial reduction within the sediments (SI Materials and Methods). This concentration of sulfoxy anions (70 μM) is high enough that isotopic fractionation associated with microbial reduction should be large, as suggested by sulfur isotope ratios in Lake Matano, where sulfate concentrations in surface waters are 25 μM yet large fractionations are observed (21). However, the geologic record of S in bulk pyrite shows clear evidence for strong fractionation of sulfur isotopes between sulfate and sulfide starting only ∼2,500 Ma (14). The model suggests that this is not because low sulfate levels limited isotopic fractionation (34), but because quantitative reduction of oxidized sulfur species followed by rapid pyrite formation prevented influence of microbial reduction on the isotopic composition of seawater sulfate. This is consistent with large variability in S within single samples, indicating that microbial reduction resulted in strong fractionation as early as 3,450 Ma (35).

Depending on the proportion of H₂SO₄ in atmospheric fluxes to the ocean, up to 80% of the sulfate in the ocean is produced by oxidation and disproportionation of aqueous sulfite species, and essentially all the thiosulfate is produced by sulfite disproportionation. The model, therefore, is sensitive to the rate of this reaction, which is unknown at environmental temperatures, as discussed below. When H₂S proportions in fluxes from the atmosphere are high, another reaction of importance is aqueous-phase photooxidation of H₂S to form S₈, which may replace atmospheric deposition as the main source of marine S₈. In this case, the S₈ concentration is governed by a balance between H₂S photooxidation and settling of S₈ particles. Importantly, S MIF in the marine S₈ pool is variably diluted relative to S MIF in atmospheric S₈ by contributions from H₂S, which carries no S MIF.

Fluxes of sulfur to the sediment are dominated by sulfate, thiosulfate, and particles of S₈ (Fig. 3 pie charts). The proportions of these species in the flux to the sediment show a dependence on their proportions in atmospheric deposition fluxes, but are variably altered by their production and consumption in the ocean. For example, the proportion of S₈ in fluxes to the sediment is high even when its atmospheric deposition is modest as the result of S₈ production in the water column. In the sediment boxes, microbial reduction generates sulfide (∼10–60 μM) and depresses the concentration of sulfur oxyanions and S_org. Relatively high concentrations of S₈ (∼0.01–5 μM) are maintained in the sediments by rapid settling of particles and by partial reoxidation of sulfide by particles. Rapid reaction between H₂S and dissolved S₈ generates polysulfides, which promote isotopic mixing between these sulfur pools, although mixing with S₈ may be limited by the kinetics of S₈ particle dissolution. The confluence of sulfur from all oxidation states into porewater sulfide affects the minor isotopic composition of pyrite but not of the ocean, because pyrite formation rapidly scavenges most of the reduced sulfur.

Controls on Preserved S MIF.

Microbial reduction of all sulfur species to sulfide in the sediments leads to near-zero S in bulk pyrite. However, the species that together contribute to this value each carry appreciable S MIF (Fig. 4). If pyrite precipitation rapidly follows microbial production of sulfide, then S MIF in the different sulfur species may avoid homogenization and get preserved. This is in agreement with observations of highly variable S in finely disseminated pyrite and relatively constant S in co-occurring nodular pyrite (18), with the former possibly representing a small-scale contribution from single sulfur species and the latter representing the bulk sulfide produced by microbial reduction. Correlation between iron content and S magnitude in some rocks (36) also supports the idea that rapid pyrite formation relative to microbial sulfide production favors the preservation of a range of S MIF values. Locally within the sediment, therefore, the full range of S MIF compositions in the species delivered from the water column may get preserved and may account for the large S MIF variability in Archean sulfide minerals. Furthermore, observations of low S magnitudes in Mesoarchean rocks (37) may be the result of local homogenization of S MIF in the sampled paleoenvironments rather than decreased S MIF production, as also suggested by recent observations, which significantly stretch the envelope of Mesoarchean S MIF (16).

The model predicts differences in sulfur species fluxes to the various sedimentary environments (Fig. 3, pie charts), with the implication that the sign and range of S preserved in sedimentary pyrite should vary among these environments. For example, S₈ particles comprise more than 90% of the sulfur delivered to deep ocean sediments. Pyrite formed in deep-water sediments therefore likely preserves a relatively narrow range of S values, similar to those in marine S₈. This is consistent with S 0 in fluvial and proximal marine facies and S 0 in distal marine facies of a Mesoarchean foreland basin (Witwatersrand Supergroup, South Africa) (15). The model prediction, that S₈ should be the predominant component of the flux to the sediment in the deep ocean, is consistent with the view that S₈ carried positive S to these distal settings. In contrast, in shallow-water settings (continental shelves and estuaries), the fractions of sulfate, thiosulfate, S₈, and S_org in fluxes to the sediment are of comparable magnitude, and the potential exists for local preservation of a larger range of S values. This is consistent with the largest observed range of S MIF in shallow-water volcaniclastic units of the Paleoarchean Fig Tree Group (16), and with observations of larger S magnitude and variability in the more proximal of two drill cores into the Neoarchean Transvaal Supergroup in South Africa (36).

Sulfate minerals, in contrast to pyrite, form exclusively from the marine sulfate pool, which the model suggests is large enough to be chemically and isotopically well mixed throughout the ocean (Fig. 3). This may be the reason for the relatively homogeneous S MIF in Archean barite (17). However, S MIF in barite or CAS should not be interpreted as directly representing atmospheric H₂SO₄, because marine sulfate carries a mixture of S MIF signatures from the atmospheric fluxes of both H₂SO₄ and SO₂ (through aqueous oxidation and disproportionation of sulfite). Depending on the S MIF production mechanism (Fig. 2), these two signatures may or may not be similar. This uncertainty may be resolved by future observations of S MIF preserved in nonmarine environments, which more likely represent unaltered atmospheric signatures.

A small number of aqueous reactions turn out to govern the concentrations and S of the sulfur species, but some of the rates of these reactions are poorly constrained. Notable among these is sulfite disproportionation to form sulfate and thiosulfate (38, 39). The rate of this reaction is not well known at seawater temperatures but is critical in determining the concentration of marine sulfoxy anions and in delivering S MIF from atmospheric SO₂ to these sulfur species. A second example is the rate of thiosulfate acid decomposition to form sulfite and S₈. The pH-dependent reaction rate has been determined experimentally around a pH of 2 (40), much lower than that expected in the Archean ocean (∼7; SI Materials and Methods). If the pH dependence determined under acidic conditions is valid at neutral pH, then this reaction provides an avenue for spreading S MIF from atmospheric SO₂ to thiosulfate and from it to S₈, thereby mixing S of opposite signs.

Identity of S MIF Carriers.

With variable values of the S MIF factors ( and ) and the fractions of atmospheric H₂SO₄ and S_org generated from photoexcited SO₂ ( and ), the model can preserve S MIF with the full range of S observed in Archean pyrite. This is possible when S MIF in SO₂ is balanced primarily by S MIF of opposite sign in H₂SO₄, S₈, or S_org. Several successful parameter combinations are shown in Fig. 4 for cases B through D. All these scenarios are plausible in terms of the required values of and ( to ), which are similar in approximate absolute magnitude to values obtained in experiments of broadband UV SO₂ photolysis (9–11). Their plausibility as explanations for the Archean record of S MIF may be tested further by the values of they require and by the sign of the S in the marine reservoirs.

First, a possibility not previously suggested is that H₂SO₄ and SO₂ were the only major S MIF carriers. Sulfate derived exclusively from oxidation of atmospheric and marine SO₂ (0) will have S similar in sign and magnitude to the SO₂. In contrast, when atmospheric sulfate comes from reaction of photoexcited SO₂ (1), S in sulfate and SO₂ diverge and may have opposite sign (e.g., Fig. 4, cases B and C with an H₂SO₄ carrier). In the ocean, sulfite oxidation and disproportionation deliver S MIF from SO₂ to marine sulfate, but delivery from sulfate to sulfite is negligibly small. Thus, two distinct fluxes of S MIF of opposite sign may reach the sediment without the requirement for atmospheric production of S₈ or S_org. This possibility appears unlikely for two reasons. First, it requires high values of , which are unlikely because most H₂SO₄ in the Archean atmosphere would have formed by direct oxidation of SO₂. Second, microbial reduction of both sulfate and sulfite–polythionate–thiosulfate within the sediments tend to homogenize and erase the isotopic anomaly.

When S₈ is the S MIF carrier, it delivers large S to the sediments only when the proportions of both S₈ and H₂S in atmospheric deposition fluxes are small. The former arises from the requirement for isotopic mass balance in the chain of reactions that generated S MIF, and the latter arises from the requirement for minimal dilution by H₂S photooxidation in the ocean. Case C satisfies both these requirements and displays large S 0 in S₈ and small S 0 in the combined sulfoxy anion pool, in accordance with the prevailing view of S MIF delivery to the Archean ocean. Cases B and D fail to meet one of the requirements, resulting in the inability of S₈ to support large S MIF magnitudes for reasonable values of and . In case B, the requirement for a small proportion of H₂S in atmospheric deposition fluxes is satisfied, but most (63%) of the sulfur is delivered to the ocean as S₈. Isotopic mass balance then requires atmospheric S₈ to carry smaller S than the residual SO₂. Consequently, although case B displays S values bracketing the observed range, large S is found in the combined sulfoxy anion pool, not in S₈. In case D, the proportion of H₂S in atmospheric deposition fluxes is much higher than that of S₈, resulting in dilution of strong S MIF in atmospheric S₈ by mass-dependent compositions in S₈ generated by aqueous H₂S photooxidation. In both cases B and D, if S₈ carries S 0, as in the prevailing view, the sense of asymmetry around S of zero is reverse to that in the Archean record of S MIF.

The sulfoxy anion pool is less susceptible to dilution of the S MIF signal, because production of these species from other aqueous sulfur compounds is negligible at low temperature and in the absence of dissolved oxygen. As such, this pool retains an undiluted S value very close to the atmospheric input of SO₂. In environments in which this pool contributes substantially to the flux to the sediments (e.g., estuaries in Fig. 3), the potential exists for preservation of S MIF very close to the primary atmospheric value. If, as in some atmospheric models (e.g., cases B and C), the fractional deposition of SO₂ is small, then this SO₂ will carry large magnitudes of S to the surface, again as a result of the constraints of isotopic mass balance in the S MIF-forming reactions. Conversely, high fractional deposition of SO₂ will lead to lower S magnitudes in this SO₂. Thus, relatively small and negative S in atmospheric SO₂ (and H₂SO₄), as in the prevailing view, implies that oxidized sulfur compounds comprised a large fraction of the atmospheric flux to the surface.

When organosulfur molecules carry S MIF, the most extreme values of S are in the S_org pool (Fig. 4, case D). This is because production of mass-dependent MSA by gas-phase and aqueous oxidation of more reduced organosulfur compounds, such as dimethyl sulfide (41), likely was minor in the oxidant-poor Archean ocean atmosphere. As a result, S MIF in MSA remains undiluted, and high positive S, such as that observed in the late Archean, can be reached with modest broadband values of the S MIF factor (∼13‰). However, the value of required to generate a second reservoir with smaller S of opposite sign also depends on the proportions of H₂SO₄, SO₂, and S_org in atmospheric deposition fluxes, as well as on the fractions of H₂SO₄ and S_org generated by reaction of photoexcited SO₂ ( and ). For the atmospheric fluxes specified in case D (Table 1), the value of required to bracket the range of the late Archean S record is ∼40‰. Propagation of S MIF in MSA and similar compounds to other marine sulfur reservoirs is expected to be minor because aqueous MSA is relatively unreactive, except with OH radicals (41), which likely were scarce in the Archean ocean. Therefore, dilution of the S of opposite sign in the sulfoxy anion pool is expected to be minor. Although no anaerobic bacteria are known to degrade MSA (42), this likely reflects an incomplete survey of existing microbial metabolisms and not the true absence of such organisms. Once in the sediments, MSA likely would undergo microbial reduction and end up in pyrite. A caveat to this statement, suggesting fertile ground for future research, is that anoxic aqueous chemistry of MSA and similar molecules is poorly characterized.

Conclusions

A model of the coupled sulfur and iron cycles constrains atmospheric S MIF production and delivery to the ocean. Either S₈ or S_org (or both) might have carried S MIF, generated by a moderately fractionating process ( and between 17‰ and 40‰). S MIF with an asymmetry similar to observations (strong positive and weak negative S) is preserved when (i) S 0 occurs in S₈ and both the fractional fluxes of S₈ and H₂S from the atmosphere to the ocean are small, (ii) S 0 occurs in the combined sulfite–polythionate–thiosulfate pool (derived from atmospheric SO₂) and S 0 is in marine S₈ (derived from atmospheric S₈ with high negative S and strongly diluted by inputs from H₂S oxidation), and (iii) S 0 occurs in S_org (derived from atmospheric MSA and similar molecules) and S 0 occurs in the combined sulfite–polythionate–thiosulfate pool. Options i and iii are consistent with existing observations of negative S in marine barite (17) and with a transition from negative S to positive S accompanying a traverse from proximal to distal marine environments (15). As mentioned above, option i constrains a large fraction of atmospherically deposited sulfur to be in oxidized forms (SO₂ and H₂SO₄).

The model predicts a spatial dependence of S MIF variability due to differential incorporation of the various marine sulfur species, which is consistent with observations of the dependence of preserved S MIF on sedimentary facies (15, 36). To further constrain the characteristics of atmospheric S MIF and inform its production mechanism, future observations from nonmarine environments would be optimal. In marine rocks, the best-preserved primary atmospheric signal likely represents the combined sulfite–polythionate–thiosulfate pool or S_org, both of which are undiluted by inputs from other marine sulfur species. Such a signal most likely will be found in pyrites from shallow-water environments hosting strong S gradients. Barite and carbonate-associated sulfate carry mixed S MIF, derived both from atmospheric H₂SO₄ and from oxidation and disproportionation of marine sulfite. These phases still may provide a good window into S MIF in atmospheric SO₂, as most atmospheric H₂SO₄ and marine sulfate are derived from gas-phase and aqueous reaction of SO₂ and should carry S MIF similar to SO₂.

Materials and Methods

The geochemical model is described fully in SI Materials and Methods.

Described here is the parameterization of S MIF in atmospheric fluxes. Internally consistent fluxes of S MIF-bearing material were calculated on the basis of photolysis experiments, SO₂ cross-section measurements, and isotopic mass balance (Fig. 2). Photodissociation of SO₂ at wavelengths 220 nm was taken to generate products that are fractionated relative to the residual SO₂ by an S MIF factor, . Oxidation of SO₂ to SO₃ and subsequent hydration do not generate additional S MIF, and the H₂SO₄ carries S MIF similar to the residual SO₂. Photoexcitation of SO₂ at wavelengths between 260 nm and 340 nm and the subsequent collision of photoexcited SO₂ with other gases results in quenching or reaction. Possible reactions include oxidation to ultimately form H₂SO₄, reduction to ultimately form S, or collision with hydrocarbon molecules to form CH₃SO₃H and other organosulfur molecules. These products were taken to be fractionated relative to the residual SO₂ by a second S MIF factor, . The ultimate magnitude and sign of S MIF in the carriers depends on the relative proportions of the carriers generated by photodissociation and photoexcitation and by the factors and . Within this framework, isotopic mass balance dictates that the total flux of S MIF carriers to the surface has a weighted average S MIF of exactly zero:

J denotes fluxes to the surface; denotes the fraction of the flux from photoexcited SO₂, with the rest produced by photodissociation in the case of S₈ and by direct oxidation in the case of H₂SO₄; denotes mass-independent isotopic compositions; and the SO₂, SO₄, and OTH subscripts denote values associated with the fluxes of SO₂, H₂SO₄, and the third carrier (S₈ or S), respectively. For S₈, = 0.6% was calculated using SO₂ absorption cross-section and the solar spectrum (SI Materials and Methods and Fig. S1). The remaining parameters (, , , ) were varied over a range of values.