Low Hesperian P_CO2 constrained from in situ mineralogical analysis at Gale Crater, Mars

Significance

Approximately 3.5-Ga sedimentary rocks surveyed by the Mars Science Laboratory rover in Gale Crater, Mars, contain secondary mineral phases indicating aqueous alteration and release of cations from mafic minerals during sediment deposition in lakes. However, carbonate phases are not detected, and our model calculations indicate atmospheric CO₂ levels at the time of sediment deposition 10s to 100s of times lower than those required by climate models to warm early Mars enough to maintain surficial water. Our results offer a ground-based reference point for the evolution of martian atmospheric CO₂ and imply that other mechanisms of warming Hesperian Mars, or processes that allowed for confined hydrological activity under cold conditions, must be sought.

Abstract

Carbon dioxide is an essential atmospheric component in martian climate models that attempt to reconcile a faint young sun with planetwide evidence of liquid water in the Noachian and Early Hesperian. In this study, we use mineral and contextual sedimentary environmental data measured by the Mars Science Laboratory (MSL) Rover Curiosity to estimate the atmospheric partial pressure of CO₂ (P_CO2) coinciding with a long-lived lake system in Gale Crater at ∼3.5 Ga. A reaction–transport model that simulates mineralogy observed within the Sheepbed member at Yellowknife Bay (YKB), by coupling mineral equilibria with carbonate precipitation kinetics and rates of sedimentation, indicates atmospheric P_CO2 levels in the 10s mbar range. At such low P_CO2 levels, existing climate models are unable to warm Hesperian Mars anywhere near the freezing point of water, and other gases are required to raise atmospheric pressure to prevent lake waters from being lost to the atmosphere. Thus, either lacustrine features of Gale formed in a cold environment by a mechanism yet to be determined, or the climate models still lack an essential component that would serve to elevate surface temperatures, at least locally, on Hesperian Mars. Our results also impose restrictions on the potential role of atmospheric CO₂ in inferred warmer conditions and valley network formation of the late Noachian.

More than four decades of orbital imaging of Mars provide geomorphological evidence of a more active hydrological cycle and larger inventory of water during the Noachian and Early Hesperian (1, 2). The widespread distribution of hydrous clay minerals in martian terrains of this age and their subsequent demise provide pivotal supporting evidence (3, 4), but the clay mineral-bearing deposits also present a paradox in that carbonate minerals, expected coprecipitates in surficial settings in communication with a CO₂-bearing atmosphere, are typically absent (5). Atmospheric reconstructions using carbon isotopic measurements and global inventories of martian carbon also indicate 100s mbar CO₂ levels (5, 6). This leads to the question of how the surface of ancient Mars, faintly heated by a young sun, was kept warm enough to allow an active hydrological cycle, without substantial amounts of a key greenhouse gas in the atmosphere. However, the breadth of available constraints on carbon sinks (6) and potential clay mineral formation in subsurface settings uninfluenced by the atmosphere (7) introduce uncertainties to estimates and the periods to which they apply. In this work we use mineralogical and sedimentological data from ∼3.5 Ga martian lake sediments to obtain a reference point for the evolution of martian P_CO2.

During its traverse to the lower slopes of Aeolis Mons (informally known as Mt. Sharp), the MSL team documented a ∼70 m sedimentary section of mudstones, siltstones, sandstones, and conglomerates deposited by lakes and rivers on the floor of Gale crater between 3.8 and 3.1 Ga (8). Sedimentary rocks analyzed by the CheMin X-ray diffraction (XRD) instrument during the traverse share many of the same components including (i) crystalline silicates including pigeonite, intermediate calcic plagioclase, and olivine from a basaltic source or sources; (ii) poorly crystalline clay minerals; (iii) various Fe oxides including magnetite; (iv) Ca–sulfate minerals, which mainly occur in cross-cutting fractures and veins; and (v) an X-ray amorphous component (9, 10). Thus far, carbonate minerals have not been definitively detected in Gale Crater sedimentary rocks. This is surprising given the reactivity of minerals making up sediments to carbonic acid.

Of the phases present, smectitic clay minerals and magnetite provide a potential means of estimating ancient P_CO2 by constraining dissolved inorganic carbon (DIC) levels in the pore fluids of Gale Crater sediments. It is proposed that isochemical alteration during the deposition of lacustrine mudstone at YKB involved dissolution of Fe²⁺-bearing olivine (Fo₆₂) providing a source of Fe²⁺ and Mg²⁺ in pore waters for subsequent coeval precipitation of magnetite and Fe²⁺-bearing, ferrian saponite–type clay minerals (9, 11–14). The detection of these secondary phases indicates anoxic to poorly oxidizing conditions (13), and places lower limits on the pore water activity of Fe²⁺ and Mg²⁺ released from olivine. Therefore, the thermodynamic stability fields of ferrian saponite and magnetite with respect to Fe and Mg carbonates can be used as the basis of estimates of atmospheric P_CO2 at the time of Sheepbed deposition. Ferrian saponite and magnetite are thermodynamically unstable with respect to Fe and Mg carbonates, such as siderite and magnesite, between 10⁻⁵ to 10⁻² bar P_CO2 depending on assumed activity of silica and Al³⁺ of pore waters (Fig. 1).

Fig. 1.

Thermodynamic stability of secondary minerals (magnetite and Fe saponite) detected in the Sheepbed member, Yellowknife Bay with respect to siderite under varying pH and gaseous CO₂ levels. The threshold P_CO2 at which siderite is favored over ferrian saponite is dependent on aqueous silica and Al³⁺ activity. The threshold is higher when SiO_2(aq) is saturated with respect to amorphous silica (long dashed line) rather than quartz (short dashed line). In both cases Al³⁺ is set to saturation with respect to albite—reasonable given that the Sheepbed contains ∼20 wt % plagioclase feldspar (9). In drawing the stability boundaries for magnetite, redox state is set at the magnetite/hematite boundary, as detailed in the main text. All thermodynamic data come from the Lawrence Livermore National Laboratory dataset (15) with the exception of Fe saponite (Na_0.35Fe₃Al_0.35Si_3.65O₁₀OH₂) determined by Wilson et al. (16). Diagram produced using Geochemist Work Bench 9.

Estimates of P_CO2 on the Archean (>2.5 Ga) Earth, derived from paleosols and banded iron formations, also use the thermodynamic stability of clay minerals and magnetite (17–19), but are criticized because they rely on assumptions of mineral equilibrium and do not account for enhanced delivery of carbon and reducing power to sediments via biological activity (20, 21). Metamorphic overprinting of original mineral assemblages in terrestrial rocks this old is ubiquitous and complicates interpretations further (22).

In many ways, deriving P_CO2 estimates from Gale Crater sedimentary rocks is more straightforward than doing so in their terrestrial equivalents. Examination of ancient sediments at YKB shows that they, despite their age, have been subject to minimal burial diagenetic alteration and heated to no more than 70 °C (9, 12, 13) consistent with reconstructed burial history and estimates of ancient geothermal gradients (23). The observed persistence of smectite clay minerals, magnetite, levels of hematite at CheMin’s detection limit of ∼1 wt % and absence of cation leaching in YKB sediments revealed by bulk geochemistry (9, 11) is inconsistent with pervasive postdepositional chemical weathering or alteration that may have otherwise had the potential to dissolve authigenic carbonate minerals.

In addition, MSL has not detected signs of biological influence on the Gale Crater sediments. In particular, the organic molecules observed by the Sample Analysis at Mars (SAM) instrument suite are extremely localized and restricted to simple structures (e.g., C1-C4 alkyl and single-ring aromatic hydrocarbons and chlorohydrocarbons; ref. 24) that lack source information. As such, they may be derived from meteoritic, abiogenic, or geologically reworked biological inputs to the sediments.

Assuming that sedimentary mineral assemblages were in thermodynamic equilibrium with the atmosphere remains problematic, however. Even with martian P_CO2 levels above thermodynamic thresholds for carbonate stability, notoriously slow precipitation kinetics of Fe and Mg carbonates may have been a barrier to producing detectable quantities in Gale Crater sediments before burial and isolation from an atmospheric carbon source. For example, magnesite requires temperatures greater than ∼70 °C for direct precipitation in the laboratory (25). Siderite forms under ambient laboratory conditions at rates ∼4 orders of magnitude slower than calcite (26).

Here we take a step beyond assuming mineral equilibrium and combine estimated sedimentation rates, afforded by detailed sedimentary facies analysis (8, 12), with carbonate precipitation kinetics and observed mineralogy to estimate ancient P_CO2 using a geochemical reaction–transport model.

Model Summary

Our models are constructed to determine threshold P_CO2 levels that would permit the precipitation of detectable amounts of siderite by CheMin. For samples bearing the mixture of phases observed within Sheepbed mudstone (9), CheMin has a detection limit of ∼1 wt % siderite. The SAM instrument detects release of CO₂ upon sample heating, which can, in part, be derived from decomposition of carbonate minerals. The results of SAM analyses of YKB sediments provide no clear indication of Fe carbonate, but the expected CO₂ signal for carbonates may be masked by other CO₂ sources thus permitting the presence of Fe carbonates at abundances below the CheMin detection limit (27).

Precipitation rates and therefore accumulation of carbonates depend on the saturation state of pore water with respect to a particular carbonate phase (Ω), given by

$${\mathrm{\Omega }}_{carbonate}=\frac{\left[M^{2+}\right]\left[C{O}_3^{2-}\right]}{\left[K_{sp}\right]},$$ [1]

where K_sp is the solubility product of the carbonate in question and M²⁺ represents the concentration of the metal cation in pore water.

Ω is linked to carbonate precipitation rate (R_carbprec) by the expression,

$$R_{carbprec}\hspace{0.17em}=\hspace{0.17em}\hspace{0.17em}{K}_{carbprec}{\left({\text{Ω}}_{carbonate}\hspace{0.17em}-\hspace{0.17em}1\right)}^n,$$ [2]

where K_carbprec is the rate constant and n is the order of the reaction.

Our models calculate [${\text{CO}}_3^{2-}$] by simulating advection, diffusion, and reaction of DIC species, including precipitation of carbonate, in a one-dimensional porous sedimentary profile subject to active sedimentary accumulation and burial (detailed in SI Text, Model Details). Diffusion and advection from the upper model boundary actively replenish DIC (including ${\text{CO}}_3^{2-}$) lost from pore waters during carbonate precipitation and transport and, thus, are of critical importance in modeling the total carbonate accumulation. Upper model boundary conditions are set to simulate a well-mixed lake in equilibrium with an assigned P_CO2 atmosphere. This is a valid representation given the absence of glaciogenic sedimentary features, such as dropstones, ice wedges, and glacial tills, in Gale lake deposits that would indicate ice cover, and the meter-scale thicknesses of delta deposits that indicate water depths of the same order (8).

We can make broad inferences about lake water chemistry at the time of YKB formation deposition. Salinity appears to have been low based on limited Cl and S concentration in the sedimentary matrix and the lack of detection of evaporative minerals in the mudstone (9, 11, 12). This is compatible with bulk geochemical evidence of limited chemical alteration of sediments during erosion and transport from the source area (11). The observed stability of clay minerals and magnetite in the sediments implies circum-neutral pH pore waters (Fig. 1) that were not overwhelmed by hypothesized surficial sources of acidity sometimes invoked for Mars aqueous environments (28, 29). Thus, DIC speciation and concentrations at the upper model boundary (representing lake water) are calculated over a range of assigned pHs and atmospheric P_CO2 levels, with the lowest pH of 5 corresponding to the lower stability field of magnetite (Fig. 1).

A variety of approaches to estimate the activity of metal cations required to calculate the saturation states and accumulation rates of carbonates are possible (Eqs. 1 and 2). For example, in a full kinetic model, metal cation activities are calculated as a function of competing mineral dissolution and precipitation reactions, and in the case of Fe²⁺, the redox state of pore waters. Although this approach provides the most mathematically complete model of a given system, the assigned kinetic parameters are subject to significant uncertainty. For instance, the rate laws governing saponite precipitation are unknown and must be guessed through comparison with other clay minerals that differ in terms of chemistry and crystal structure (e.g., ref. 30). Moreover, order-of-magnitude differences between kinetic rate laws determined in the laboratory and observed in natural systems are a well-documented challenge for reaction–transport models.

Alternatively, if the goal of the model is to obtain an absolute upper threshold of P_CO2 consistent with nondetection of carbonates at Gale Crater, then our preferred hybrid kinetic model formulation becomes suitable. Calculating an upper P_CO2 threshold requires a minimum bound on the activity of metal cations in solution. For the sediments at YKB, where evidence of magnetite and saponite precipitation at the time of deposition is documented, a minimum bound can be placed on Fe²⁺ activity in pore water by assuming that both magnetite and ferrian saponite are at or above saturation levels. Fig. S1 shows that with expected activities of silica and Al³⁺, ferrian saponite is always supersatured when [Fe²⁺] is at saturation with respect to magnetite. Thus, [Fe²⁺] is calculated in the model assuming that pore waters are saturated with respect to magnetite. We note that in a full kinetic model [Fe²⁺] would approach magnetite saturation in a situation where precipitation of magnetite and saponite outcompeted siderite for [Fe²⁺].

Fig. S1.

Thermodynamic stability diagram showing the Fe²⁺ concentration required to be in equilibrium with various minerals and silica activities ranging from quartz to amorphous silica, as a function of pH. Lines show saturation values at 10 °C and a salinity of 10 g/kg. Minerals are supersaturated above their respective equilibrium lines. All thermodynamic data come from ref. 53 with the exception of Fe saponite (Na_0.35Fe₃Al_0.35Si_3.65O₁₀OH₂) determined in ref. 16. In drawing the stability boundaries for magnetite, redox state is set at the magnetite/hematite boundary, as detailed in the main text. In defining equilibrium lines for ferrian saponite, Al³⁺ is set to saturation with respect to albite, which is reasonable given that the Sheepbed contains ∼20 wt % plagioclase feldspar (9).

To calculate pore water [Fe²⁺] based on magnetite saturation requires a redox constraint. Redox is assigned to the magnetite/hematite boundary, again minimizing [Fe²⁺] in the model profile, in keeping with the goal of obtaining an upper P_CO2 threshold (Fig. S2). Formulating the model in this way is also consistent with detection of small amounts of hematite in YKB sediments (9). This state is represented by the following chemical reaction:

$$\text{Magnetite}\hspace{0.17em}+\hspace{0.17em}2\left[{\text{H}}^{+}\right]\hspace{0.17em}=\hspace{0.17em}\left[{\text{Fe}}^{2+}\right]\hspace{0.17em}+\hspace{0.17em}\left[{\text{H}}_2\text{O}\right]\hspace{0.17em}+\hspace{0.17em}\text{Hematite}.$$ [3]

Fig. S2.

Thermodynamic stability diagram showing the relation between Fe²⁺ activity (red line) and pH with redox state at the magnetite/hematite boundary. Note that in more oxidizing conditions magnetite is unstable. Under more reducing conditions Fe²⁺ activity is higher and thus the resulting P_CO2 threshold estimated using the reaction–transport model is reduced. The figure was generated using Geochemist’s Workbench for illustrative purposes. In the model [Fe²⁺] was calculated at a given pH, temperature and salinity using SUPCRT, as described in SI Text, Model Details.

By calculating the equilibrium constant K_mag/hem for reaction 3 at given temperature and salinity values and assuming H₂O activity of 1 a pH-dependent expression for [Fe²⁺] is obtained.

$$\left[{\text{Fe}}^{2+}\right]\hspace{0.17em}={\hspace{0.17em}\text{K}}_{\text{mag}/\text{hem}}\hspace{0.17em}.\hspace{0.17em}{\left[{\text{H}}^{+}\right]}^2.$$ [4]

[Fe²⁺] is calculated in the model profile at each time step based on pH using Eq. 4 allowing the saturation state with respect to siderite to be determined. Combining calculated Ω_siderite with the slowest kinetic rate law governing siderite precipitation available in the literature (Table S1), we determine the upper threshold of atmospheric P_CO2 that would result in siderite being undetectable by CheMin in the YKB formation. Note that in configuring the model in this way it is assumed that siderite precipitation kinetics limit carbonate production; Fe²⁺ supplied by the dissolution of olivine does not. Fig. S3 shows this assumption is valid. Typical equilibrium outputs of a model run are shown in Fig. S4.

Table S1.

Rate constants for siderite precipitation

Rate constant (mmol·kg−1·y−1)	Refs.
0.050	47
0.053	48
12.623	49

Fig. S3.

Comparison of olivine dissolution rates over a range of pH values with siderite precipitation rates at various values of Ω. SI Text, Comparison of Olivine Dissolution and Siderite Precipitation Kinetics describes details of how rates were derived.

Fig. S4.

Typical reaction–transport model output. The four panels show calculated changes in pH, DIC, siderite content and saturation with respect to siderite with depth below sediment/water interface. In this simulation, porosity within the model profile is 0.6, sediment accumulation rate is 1 cm/y, temperature is 10 °C and salinity is 10 g/kg. Carbonate speciation and concentrations at the upper model boundary, representing lake waters, are set to be in equilibrium at pH 5.5 with an atmospheric P_CO2 of 63 mbars.

Results and Discussion

Fig. 2A shows upper P_CO2 thresholds for siderite detection over a range of assigned water column pH and at various sediment accumulation rates. Water column pH has limited influence on rates of siderite production between values of 5 and 7 in our model. This is because siderite precipitation rate is determined by Ω_siderite = [Fe²⁺][CO₃^2-], where at low pH small carbonate anion concentrations are compensated for by higher [Fe²⁺] required to maintain magnetite saturation (Fig. S2). Above pH 7, P_CO2 thresholds decrease (Fig. 2A). To maintain high pH within a water column in equilibrium with the range of atmospheric P_CO2 values investigated here requires elevated carbonate alkalinity and thus DIC. High DIC levels make diffusion and carbonate precipitation in the lower parts of modeled sedimentary profiles more efficient, lowering P_CO2 thresholds. Because we aim to determine an upper constraint on P_CO2 we focus our discussion on the P_CO2 thresholds obtained assuming pH of lake waters between 5 and 7—the lowest values compatible with saponite and magnetite precipitation (Fig. 1).

Fig. 2.

(A) P_CO2 required to produce 1 wt % siderite within model sedimentary profiles at various sediment accumulation rates, sediment porosities, and water column pH values. [Fe²⁺] is set to be saturated with respect to magnetite under redox conditions corresponding to the magnetite/hematite boundary. (B) Sensitivity of P_CO2 thresholds to salinity and temperature with a burial rate of 1 cm/y and sedimentary porosity of 0.6.

Sedimentary porosity influences the rates of siderite production by controlling the quantity of pore water DIC available for reaction with Fe²⁺ released from olivine and rates of chemical diffusion within sediments, both of which generally increase with porosity. On Earth, mud deposits typically have initial porosities of between 60 and 80% (31). We have assigned a porosity value of 60% in our model profiles to obtain upper P_CO2 thresholds (Fig. 2A). No significant sedimentary compaction is expected within ∼1.5–3 m model interval where carbonates form.

Calculated P_CO2 thresholds are also highly sensitive to sediment accumulation rates, with faster rates permitting higher threshold atmospheric P_CO2 levels (Fig. 2). We have no direct constraints on the rates of deposition of the YKB formation, but given the similarity of the sedimentary architecture with terrestrial fluvial–lacustrine deposits (8) we use compilations of thousands of lacustrine accumulation rates observed on Earth to obtain an upper limit for the YKB formation (31). Terrestrial lacustrine sedimentation rates span several orders of magnitude, with a dependence on the time span of accumulation (32). With accumulation times of 100s to 10,000 y estimated for the 1.5-m-thick Sheepbed member (12), accumulation rates as high as 5 cm/y are possible, with an average rate ∼0.1 cm/y (32). Lacustrine deposits with sedimentation rates >1cm/y make up <1% of available records. The highest rates are not sustainable for periods of more than ∼100 y, thus we use an upper sedimentation rate of 1 cm/y in calculating P_CO2 estimates. We find that temperature and pore water salinity have a minor influence on P_CO2 thresholds (Fig. 2B; SI Text, Sensitivity Tests).

At 10 °C and a salinity of 10 g/kg, an accumulation rate of 1 cm/y and sedimentary porosity of 60% the upper limit on P_CO2 levels where siderite production remains below XRD detection limits in the Sheepbed member is 70 mbar. This falls to 10 mbar at average sedimentation rates of ∼0.1 cm/y. Our P_CO2 estimates are orders of magnitude above those based on thermodynamic stability of magnetite with respect to siderite (Fig. 1), but remain well below the 1000s mbar CO₂ levels required by the most optimistic climate simulations to keep the average temperature of early Mars above 273 K for long periods (33); for example, Ramirez et al. (34) model clement conditions at 1.3 bars CO₂, with 20% H₂ as an additional greenhouse gas.

As discussed above, our models and choice of input parameters are designed to provide an absolute upper limit P_CO2 based on observed mineralogy and sedimentology at YKB. However, there are various reasons to believe that [Fe²⁺] was higher in pore waters and P_CO2 may have been lower than the thresholds shown in Fig. 2. First, it is possible that magnetite and hematite detected in YKB sediments (9) are detrital phases that do not place bounds on pore water [Fe²⁺] or act as a sink for Fe. This would allow for more reducing conditions, higher [Fe²⁺] (Fig. S2) and lower P_CO2 thresholds. Second, if the supply of [Fe²⁺] from olivine outstripped removal by secondary phases (i.e., olivine dissolution kinetics >> precipitation of secondary phases), [Fe²⁺] would also be higher than in our upper threshold P_CO2 simulations. In both these cases [Fe²⁺] would tend toward approaching levels of olivine saturation, thus providing a reduced P_CO2 threshold limit for a given sedimentation rate, porosity, salinity, and temperatures. Model [Fe²⁺] for this lower P_CO2 threshold based on olivine saturation requires an assumption about [SiO_2(aq)] of pore waters to be made, but in natural near-surface pore waters [SiO_2(aq)] is typically between saturation with respect to quartz or amorphous silica. Both these situations can be used to obtain a pH-dependent expression to determine [Fe²⁺]:

$$\text{Fayalite}\hspace{0.17em}+\hspace{0.17em}4\left[{\text{H}}^{+}\right]\hspace{0.17em}=\hspace{0.17em}2\left[{\text{Fe}}^{2+}\right]\hspace{0.17em}+\hspace{0.17em}\text{Quartz}\hspace{0.17em}+\hspace{0.17em}2\left[{\text{H}}_2\text{O}\right],$$ [5]

or

$$\text{Fayalite}\hspace{0.17em}+\hspace{0.17em}4\hspace{0.17em}\left[{\text{H}}^{+}\right]\hspace{0.17em}=\hspace{0.17em}2\left[{\text{Fe}}^{2+}\right]\hspace{0.17em}+\hspace{0.17em}\text{Amorphous}\hspace{0.17em}\text{silica}\hspace{0.17em}+\hspace{0.17em}2\left[{\text{H}}_2\text{O}\right],$$ [6]

$$\left[F{e}^{2+}\right]=\sqrt{K_{reaction}\hspace{0.17em}.}{\left[H^{+}\right]}^4,$$ [7]

where K_reaction is the reaction constant of either Eq. 5 or 6. The resulting P_CO2 thresholds are shown in Fig. 3. With comparable porosity and burial rates P_CO2 thresholds are approximately half the values calculated assuming pore water [Fe²⁺] at magnetite saturation. This reinforces our estimates that the martian atmosphere contained 10s mbar levels at the time of deposition of YKB sediments.

Fig. 3.

P_CO2 required to produce 1 wt % siderite within model sedimentary profiles at various sediment accumulation rates, sediment porosities, and water column pH values. [Fe²⁺] is set at equilibrium with fayalite with silica saturation in equilibrium with quartz (black lines) and amorphous silica (blue lines). Sedimentary porosity is set at 0.6 in all simulations.

Fluvial–lacustrine sediments in Gale Crater represent one of the youngest known instances of habitable surficial aqueous conditions on Mars, on the tail end of a period of rapid atmospheric degradation and loss (6, 12, 33). Thus, our P_CO2 estimate serves as a reference point at a critical juncture in martian atmospheric evolution. Combining ∼10s mbar estimates of P_CO2 derived from Gale Crater with upper estimates of the amount of CO₂ lost through sequestration as carbonate minerals in the martian crust (up to ∼500 mbar CO₂; ref. 35) and CO₂ lost to space (<100 mbar; ref. 36) limits atmospheric CO₂ during the Noachian and Early Hesperian to 100s mbar. This is well below threshold levels required to keep the average temperature of early Mars above 273 K for long periods in climate models, therefore either lacustrine features of Gale formed in a cold environment (37) or the problem of reconciling Mars' early climate with geological record of an active hydrosphere remains. Our results imply that the overall lack of carbonates found in the geological record of Mars (5, 6, 28, 35) is a direct reflection of the composition of the ancient atmosphere.

SI Text

Model Details.

The reaction–transport model was developed in R—an open source statistical computing environment (38). ReacTran, a package of functions, routines, and solvers for reactive–transport modeling, was used (39). In addition, functions in packages seacarb and marelec are used to calculate initial carbonate speciation in the water column based on specified P_CO2 and pH, as well as equilibrium constants and diffusion coefficients of chemical species under the specified physical and chemical conditions (40, 41).

The model finds a numerical solution to a set of three ordinary differential equations describing the temporal change in total dissolved inorganic carbon (DIC), pH, and siderite concentration in a one-dimensional porous sedimentary profile subject to diffusion and advection (transport) associated with sedimentary accumulation, and chemical reactions. The model equations were formulated using the direct substitution approach (42). Tracking temporal changes in the pH and DIC of the model domain allows calculation of the concentration of any species of inorganic carbon (e.g., ref. 43).

Exchange with lake water, assumed to behave as an infinite reservoir and represented by the upper boundary condition imposed on the model domain, occurs by diffusion only. As described in the main text and shown in Figs. 2 and 3, simulations are run with a range of lake water chemistries constrained to be in equilibrium with prescribed atmospheric CO₂ levels and lake water pH.

The rate of siderite precipitation follows the general scheme described in the main text and depends on the saturation state of pore waters with respect to siderite (Ω), given by

$${\mathrm{\Omega }}_{FeC{O}_3}=\frac{\left[F{e}^{2+}\right]\left[C{O}_3^{2-}\right]}{K_{sp}},$$ [S1]

where K_sp is the solubility product of siderite calculated with the formulation of ref. 44 and adjusted with salinity following ref. 45.

[CO₃^2-] is calculated at each time step from DIC and pH. As justified in the main text, [Fe²⁺] is set to be saturated with respect to either magnetite or fayalite as represented by reactions S2–S4. In the case of reaction S2 O₂(aq) activity is set to equal the magnetite/hematite boundary.

$$\text{Magnetite}+2\left[{\text{H}}^{+}\right]=\left[{\text{Fe}}^{2+}\right]+\left[{\text{H}}_2\text{O}\right]+\text{Hematite},$$ [S2]

$$\text{Fayalite}+4\left[{\text{H}}^{+}\right]=2\left[{\text{Fe}}^{2+}\right]+\text{Quartz}+2\left[{\text{H}}_2\text{O}\right],$$ [S3]

or

$$\text{Fayalite}+4\left[{\text{H}}^{+}\right]=2\left[{\text{Fe}}^{2+}\right]+\text{Amorphous}\hspace{0.17em}\text{silica}+2\left[{\text{H}}_2\text{O}\right].$$ [S4]

SUPCRT, implemented in the R package CHNOSZ (46), was used to calculate equilibrium constant of these reactions at given temperature and salinity values. [Fe²⁺] is calculated within the model profile at each time step based on pH and provides a lower limit on [Fe²⁺].

Ω_FeCO3 is linked to carbonate precipitation rates by the expression:

$$R_{sidprec}=k_{sidprec}{\left({\mathrm{\Omega }}_{FeC{O}_3}-1\right)}^n.$$ [S5]

Here, k_sidprec is the kinetic constant for siderite precipitation and n is the order of the reaction. We use the lowest value of k_sidprec (0.05 mmol·kg⁻¹·y⁻¹ at 25 °C) available from the literature (Table S1) because the aim is to obtain an upper bound on atmospheric P_CO2. k_sidprec varies with temperature (k_sidprecT) according to

$$K_{sidprecT}=K_{sidprec25}\hspace{0.17em}.\hspace{0.17em}{e}^{\frac{-Ea}{R}}\left(\frac{1}{T}-\frac{1}{298.15\hspace{0.17em}\text{K}}\right).$$ [S6]

An activation energy (Ea) of 54 kJ/mol was used based on the experimental work of Johnson (50). Siderite precipitation shows a first-order dependence on saturation state thus n = 1 (48).

Simulations are initiated with DIC, pH, and siderite content set to zero throughout the model sediment column. When the model is run, siderite precipitates and is buried, a process that consumes DIC. The depth of the model domain is manually adjusted through trial and error to ensure negligible carbonate is being added at the base of the model profile. Model profiles are typically ∼1.5 m deep and split into 45 layers. Model results are collected after equilibrium is assured, an interval of 250 y. Typical equilibrium outputs of a model run are shown in Fig. S4.

Comparison of Olivine Dissolution and Siderite Precipitation Kinetics.

As discussed in the main text, the model formulation implemented assumes that siderite precipitation kinetics limit carbonate production rather than Fe²⁺ supplied by the dissolution of olivine. Fig. S3 compares olivine dissolution rates from pH 5–10 with siderite precipitation rates for a range of siderite saturation states observed in model simulations (Ω). Olivine dissolution rate calculations follow the formulation of ref. 51 and a specific surface area of 5 m²/g, measured on olivine powder with similar grain size as the Sheepbed mudstone at YKB (52). Olivine dissolution always outpaces siderite precipitation.

Sensitivity Tests.

Fig. 2 shows results of model sensitivity analysis of P_CO2 thresholds to sedimentary porosity, temperature, and salinity, respectively.

Sedimentary porosity.

Terrestrial muds deposits that have not been buried typically have porosities of 0.6–0.8 (31). Fig. 2A shows the influence on P_CO2 thresholds of increasing sedimentary porosity values up to 0.8, from the value of 0.6 used in model runs discussed in the main text. The result is a ∼threefold decrease in P_CO2 threshold, regardless of burial rate. This confirms that using a porosity value of 0.6 provides an upper threshold on P_CO2.

Temperature.

Fig. 2B shows that as temperature increases the upper threshold on P_CO2 also increases. However, the increase is insignificant (∼10s mbar in the model scenario with a sedimentary porosity of 0.6 and burial rate of 1 cm/y), compared with the amounts of CO₂ needed in climate models to push martian climate to these higher temperatures.

Salinity.

P_CO2 thresholds are higher when water is either fresh or saline (Fig. 2B). In the model scenario presented in Fig. 2B, P_CO2 thresholds vary by as much as ∼30 mbar at 5 °C with the highest thresholds (100 mbar) obtained when waters are fresh. As discussed in the text, salinity appears to have been low at the time of deposition of YKB sediments, based on limited Cl and S concentration in the sedimentary matrix and the lack of detection of evaporative minerals in the mudstone (12). Uncertainty in the exact salinity of pore waters does not impact the conclusions drawn from our work.