Diverse Carbonates in Exoplanet Oceans Promote the Carbon Cycle

Carbonate precipitation in oceans is essential for the carbonate-silicate cycle (inorganic carbon cycle) to maintain temperate climates. By considering the thermodynamics of carbonate chemistry, we demonstrate that the ocean pH decreases by approximately 0.5 for a factor of 10 increase in the atmospheric carbon dioxide content. The upper and lower limits of ocean pH are within 1–4 of each other, where the upper limit is buffered by carbonate precipitation and defines the ocean pH when the carbon cycle operates. If the carbonate compensation depth (CCD) resides above the ocean floor, then carbonate precipitation and the carbon cycle cease to operate. The CCD is deep (>40 km) for high ocean temperature and high atmospheric carbon dioxide content. Key divalent carbonates of magnesium, calcium and iron produce an increasingly wider parameter space of deep CCDs, suggesting that chemical diversity promotes the carbon cycle. The search for life from exoplanets will benefit by including chemically more diverse targets than Earth twins.


INTRODUCTION
The carbonate-silicate cycle, also known as the inorganic carbon cycle, is a negative climate feedback mechanism that stabilises the surface temperature via the greenhouse effect of carbon dioxide in response to changes in volcanism rates, stellar luminosity, atmospheric composition and opacity, planetary orbital movements and spin axis tilt (Berner 2004;Catling & Kasting 2017).Continental silicate rocks and atmospheric carbon dioxide react with water in a process known as silicate weathering to produce carbonateforming ions that precipitate as carbonates onto the ocean floor (Walker et al. 1981).The carbon cycle is completed when carbonates are transferred into the mantle for deep storage or carbon is eventually released back into the atmosphere by volcanism (Holland 1978;Sleep & Zahnle 2001), although the degassing efficiency is debated (Kelemen & Manning 2015;Foley 2015).Silicate weathering and carbonate precipitation are traditionally represented by the net chemical reaction (Walker et al. 1981), where wollastonite (CaSiO 3 ), which serves as a proxy for silicate rocks, is converted into calcite (CaCO 3 ).Calcium thus plays a crucial role in silicate weathering and carbonate precipitation and is present as Ca 2+ cations in oceans (Sect.2).The existence of habitable zones assumes that the carbon cycle operates on Earth analogues to stabilise their atmospheric carbon dioxide content (Kasting et al. 1993).Implicitly, this assumes not only that silicate weathering operates, but that ocean floor precipitation and deep storage of carbonates also occur.There exists a critical ocean depth known as the carbonate compensation depth (CCD), below which carbonates are unable to exist in their solid form because carbonate solubility increases with pressure in the ocean (Zeebe & Westbroek 2003, see also Sect.2.3, Figure 1).In modern Earth oceans, the CCD is located between 4-5 km, below the average ocean depth of about 3.8 km (Zeebe 2012).If the CCD resides at a depth above the ocean floor, then carbonates are unable to settle.This leads to the disruption of the carbon cycle-at least, as it is understood to operate on Earth.Moreover, there are currently no theoretical constraints on exoplanet ocean chemistry.We investigate the interplay between atmospheric carbon dioxide content, ocean acidity (pH) and carbonate precipitation.We then calculate the CCD over a broad range of physical conditions.

Ca system
Ocean chemistry is modelled by considering thermochemical equilibrium for pure Ca, Mg, or Fe systems.The CO 2 partial pressure P CO2 , ocean-surface temperature T and local ocean pressure P oc are control parameters (Figure 1, Table 1).In the Ca system, there are 13 unknowns, the number density n of H (2) The chemical dissolution or dissociation of CO 2 in ocean water leads to the production of HCO − 3 and H + ions and thereby increases the ocean acidity (and decreases ocean pH = − log 10 (n H + /n 0 ), where the standard number density n 0 = 1 m −3 ) by the following reaction: To maintain the charge balance in ocean water, the addition of Ca 2+ to oceans decreases the number density of H + and hence increases the ocean pH.The charge balance equation is given by: where CO 2− 3 is produced due to the bicarbonate dissociation reaction: and where OH − is produced due to the water dissociation reaction: The mass conservation of H is given by Ca tot partitions into Ca 2+ , calcite and wollastonite which is accounted for by mass conservation: Calcite precipitation occurs when n Ca 2+ is saturated to a certain value determined by the equilibrium constant of the calcite precipitation reaction and the abundance of n CO 2− 3 : SiO 2,tot partitions into aqueous silica SiO 2 (aq), quartz SiO 2 (s) and wollastonite CaSiO 3 (s).The mass conservation for SiO 2 is given by: The quartz precipitation reaction is: The reaction of wollastonite precipitation is given by: These equilibrium chemistry calculations are performed using Reaktoro v2 (Leal 2015), a multi-phase (aqueous, gas and solid mineral phases) chemistry software.This software implements the extended law of mass action including the determination of stable and unstable species for a given set of species in the system (Leal et al. 2017).We use the SUPCRTBL database for thermodynamic data (Johnson et al. 1992;Zimmer et al. 2016), the Peng-Robinson activity model for gases (Peng & Robinson 1976), the HKF activity model for water (Helgeson et al. 1981) and the Drummond activity model for CO 2 (aq) (Drummond 1981).

Mg and Fe systems
In the Mg system, Ca is replaced by Mg, calcite by magnesite MgCO 3 (s) and wollastonite by enstatite Mg 2 Si 2 O 6 (s).This includes replacing equilibrium constants of all reactions including Mg.Similarly, in the Fe system, Ca is replaced by Fe, calcite by siderite FeCO 3 (s) and wollastonite by fayalite Fe 2 SiO 4 (s).We limit our calculations to Fe 2+ although its oxidation has inhibited the formation of siderite during Earth's history, particularly since the great oxidation event (Rye et al. 1995).

Weathering model
The introduction of carbonate-producing divalent cations in oceans is dictated by silicate weathering.Silicate weathering and therefore the total number density of divalent cations D 2+ (D = Ca, Mg or Fe) must depend on the CO 2 partial pressure P CO2 and surface temperature T (Walker et al. 1981;Hakim et al. 2021), where '0' represents the Earth reference values (Table 1), T e = 13.7 K is the e-folding temperature and β = 0.3 is the weathering power-law exponent (Walker et al. 1981).
However, not all added Ca (or Mg, Fe) in oceans remains in the form of divalent cations, a fraction of it precipitates as carbonates on the ocean floor and another fraction as silicates.For this reason, we perform partitioning calculations of Ca (or Mg, Fe) in different phases following the ocean chemistry model (Sect.2.1).

CCD model
Carbonates are deposited onto the ocean floor as part of sediments.The transition from calcite-rich to calcitefree sediments is gradual.The carbonate compensation depth (CCD) for the Earth ocean is normally defined as the depth at which the dissolution flux of calcite balances the precipitation flux (Zeebe 2012).The depth at which the rapid dissolution of calcite-rich sediments begins is known as the lysocline, which is a sediment property (Zeebe & Westbroek 2003).The lysocline and CCD serve as bounds on the transition zone (∼0.5 km) between calcite-rich and calcite-free sediments.Other definitions for the CCD exist (Berger et al. 1976 We consider the CCD to be the depth d CCD (equivalent to the ocean pressure where P oc = P CCD ) at which 99.9% of near-surface (P oc = P surf ) Ca, Mg or Fe-carbonates dissolve, Our calculations of CCD are performed up to d CCD = 45 km because of the availability of thermodynamic data up to the pressure of 5000 bar (Zimmer et al. 2016).This limitation does not affect our conclusions.

Analytical solution of ocean pH
Upper limit of ocean pH.For calcite precipitation, all reactions in Section 2 need to be satisfied.However, two of these reactions can be used to analytically constrain ocean pH: Equations 9 and 16 where Equation 16 is a combination of Equations 3 and 5, The ocean pH can be written as a function of P CO2 , n Ca 2+ and equilibrium constants of Equations 9 and 16 (Appendix A): This equation demonstrates the reason for the slope of approximately −0.5 for the upper limit of ocean pH as a function of the logarithm (base 10) of P CO2 .Because K 9 and K 16 are constants at a fixed T and P , pH becomes a function of only P CO2 and n Ca 2+ in Equation 17.As a function of P CO2 , n Ca 2+ at the limit of carbonate saturation varies between ∼0.1 m −3 (at P CO2 = 0.01 µbar) and ∼6 m −3 (at P CO2 = 0.3 bar).This additional increase in n Ca 2+ of less than two orders of magnitude over seven orders of magnitude increase in P CO2 , makes the slope of ocean pH slightly steeper than −0.5 (see Fig. A1).
Using n Ca 2+ from the numerical solution in Equation 17results in a semi-analytical solution matching with the numerical solution until P CO2 = 0.1 bar, beyond which non-ideal effects accounted in the numerical solution exhibit a small deviation from the analytical equation.
Lower limit of ocean pH.In the absence of divalent cations in ocean, the ocean pH is largely governed by the conversion of CO 2 to protons (Equation 3).For P CO2 > 1 µbar, the ocean is acidic, where the number density of H + is larger than that of OH − and the number density of HCO − 3 is larger than CO 2− 3 (bicarbonate-carbonatewater equilibria, Wolf-Gladrow et al. 2007).Therefore, the charge balance equation can be approximated as In terms of the equilibrium constant of Equation 3, this leads to (Appendix A) At a fixed T and P , K 3 is constant and thus the ocean pH exhibits a slope of −0.5 for P CO2 > 1 µbar (Fig. A1).For P CO2 < 1 µbar, the analytical solution does not hold because the number density of OH − is significant enough to make the charge balance approximation in Equation 18 invalid.The lower limit of ocean pH is independent of the Ca, Mg or Fe systems considered.

RESULTS AND DISCUSSION
We consider the ocean pH to be determined by the chemical dissolution of atmospheric carbon dioxide in a well-mixed ocean, which occurs at the atmosphereocean interface.The chemical dissolution of CO 2 is governed by the reaction between water and CO 2 to produce H + , HCO − 3 and CO 2− 3 ions (Sect.2).As P CO2 increases, the ocean becomes more acidic.We consider an atmospheric surface pressure of 1 bar, but allow the atmospheric carbon dioxide content to vary via P CO2 .Atmospheric surface pressures up to 100 bar have a negligible effect on our results and those between 100-1000 bar exhibit a small effect (Fig. A2a).
For a given value of P CO2 , the ocean pH is bounded between two limits (Fig. 2a).The ocean pH is restricted to a narrow range between 7-11 at P CO2 = 0.01 µbar and 4-7 for P CO2 = 0.1 bar.These ocean pH ranges are consistent with the inferences for Earth's history, transitioning from an acidic ocean during the Archean at high P CO2 to an alkaline ocean at present-day P CO2 (Halevy & Bachan 2017;Krissansen-Totton et al. 2018).The lower limit corresponds to the complete absence of divalent cations and thus it is independent of the carbonate system under investigation (Sect.2).The upper limit corresponds to the saturation of calcium cations in ocean water such that more weathering does not produce further changes in pH and simply produces more calcite.This upper limit is buffered by the precipitation of carbonates and hence it results in one solution of ocean pH when the carbon cycle is operational for a given carbonate system and P CO2 .Both upper and lower limits of ocean pH follow a slope of approximately -0.5 as a function of P CO2 (see Sect. 2.4).Between these two limits, the number density of calcium cations is below the threshold to precipitate carbonates onto the ocean floor; thus, the carbon cycle is not operational.
Due to their high condensation temperatures, the relative abundances of refractory elements observed in the photosphere of stars are expected to be mirrored in the rocky exoplanets they host (Bond et al. 2010;Thiabaud et al. 2015).For example, the calcium-tomagnesium ratio of the solar photosphere and Earth are 0.062 and 0.066, respectively (Lodders 2003;Elser et al. 2012).The relative abundances of Ca, Mg and Fe, measured from the spectra of stars, vary by up to an order of magnitude.For example, Ca/Mg=0.02-0.2 and Ca/Fe=0.04-0.2 in the Hypatia catalogue of more than 7000 stars (Hinkel et al. 2014).Furthermore, carbonates involving Mg and Fe are known to have formed during Earth's history: e.g., magnesite (MgCO 3 ) and siderite (FeCO 3 ); these carbonates have dissolution properties that differ from those of calcite.Siderite could have 10 8 10 7 10 6 10 5 10 4 10 3 10 2 10 1  played a key role in locking up CO 2 in carbonates on Earth during the Archean (Rye et al. 1995;Sverjensky & Lee 2010).We calculate ocean pH for the pure Mg and Fe systems in addition to the Ca system (Fig. 2b,c).The upper limit of ocean pH for a given P CO2 varies when considering systems with purely Ca, Mg or Fe as the source of weathering cations.The upper limit of ocean pH for the Mg system is only 0.2 higher than for the Ca system, whereas it is more than unity lower for the Fe system.For P CO2 < 10 µbar, ocean chemistry and hence the CCD is sensitive to the addition of aqueous silica (SiO 2 ) in the ocean (Fig. 3).Silica is another product of silicate weathering, which enables the locking up of cations in silicate minerals instead of carbonate minerals (Walker et al. 1981;Hakim et al. 2021).For instance, for T > 300 K and P CO2 < 0.1 µbar in the Ca system in the presence of aqueous silica, silicates impinge on the stability of calcite (Fig. 4a) and prevent carbonate precipitation at all depths (Fig. 3a).In contrast, when no silica is present in the ocean for T > 300 K and P CO2 < 0.1 µbar, calcite is stable (Fig. B2a) and deep CCDs are produced (Fig. B1a), thereby increasing the parameter-space where the carbon cycle is stable.Similarly, in the Mg and Fe systems, silicates are more stable than carbonates for P CO2 < 10 µbar (Fig. 4b,c).P CO2 > 10 µbar favours the thermodynamic stability of carbonates over silicates.
Carbon cycle box models of exoplanets often omit selfconsistent modelling of ocean chemistry and precipitation of carbonates.Carbonate precipitation is implicitly assumed to persist and is not expected to be a bottleneck for carbon cycling.Our ocean chemistry model can be incorporated directly into carbon cycle box models for exoplanets, which can couple via key parameters, P CO2 , T , and the carbonate chemistry.Thermochemical equilibrium calculations of our ocean model can be used to determine the carbon fluxes into or out of the near-surface reservoirs.The carbon cycle box models can also be informed of the effect of ocean chemistry and ocean depth on the efficiency of carbon degassing and recycling.
Upcoming observations of terrestrial exoplanets from the James Webb Space Telescope, Atmospheric Remotesensing Infrared Exoplanet Large-survey and Extremely Large Telescopes will put constraints on their atmospheric composition, for instance, the volume mixing ratio of atmospheric carbon dioxide (P CO2 /P ).Determining the partial pressure of carbon dioxide (P CO2 ) requires the atmospheric surface pressure (P ) which is not easily constrained.Nonetheless, our thermodynamic calculations provide strong constraints on ocean chem-istry in the presence or absence of magnesium, calcium or iron carbonates; the relative abundances of these carbonate-forming elements in planetary systems can be deduced from observations of stellar photospheres.Our results suggest that the carbon cycle will operate robustly on chemically-diverse terrestrial exoplanets exhibiting silicate weathering.This implies that the search for life from exoplanets with temperate climates or biospheres will benefit by broadening the target list to planets that are more chemically diverse than Earth.10 8 10 7 10 6 10 5 10 4 10 3 10 2 10 1 P CO 2 [bar]

B. CCD WITHOUT SILICATE PRECIPITATION
When no silicates are allowed to precipitate, CCDs for the Ca, Mg and Fe systems become deeper for P CO2 < 1 µbar (Fig. B1).This is reflected in the phase stability plots in Fig. B2.

Figure 2 .
Figure 2. Sensitivity of ocean pH to PCO 2 at T = 288 K for pure (a) Ca, (b) Mg, (c) Fe systems.Upper and lower bounds of ocean pH are represented by the blue shaded region.Pink shaded regions are forbidden.

Figure 3 .Figure 4 .
Figure 3. Carbonate compensation depth (CCD) as a function of PCO 2 and T (Patm = 1 bar) for (a) Ca, (b) Mg and (c) Fe systems.Gray contours represent the weatheringdependent cation number density as a function of PCO 2 and T (Eq.13).Gray disc denotes modern Earth PCO 2 and T .

Figure A1 .
Figure A1.Numerical, analytical and semi-analytical solutions of the upper and lower limits of ocean pH in the Ca system.

n
Figure A2.The sensitivity of ocean pH to (a) P and (b) T in the Ca-system.
Model parameters, nD tot where D = Ca, Mg or Fe, nSiO 2,tot , PCO 2 , Patm, Poc and T .See Sect. 2 and Table 1 for a full list of output quantities and description.

Table 1 .
SiO 2 (aq), quartz SiO 2 (s), wollastonite CaSiO 3 (s) and calcite CaCO 3 (s).Out of the 13 unknowns, 2 are continental silicate weathering products, n Catot and n SiO2,tot , that depend on P CO2 and T (Sect.2.2).There are 11 remaining unknowns.We solve for 3 mass conservation equations (for H, Ca and SiO 2 ), 1 charge balance equation, and 7 equations from 7 chemical reactions providing relations between equilibrium constants (that depend on P oc and T ), reactants and products.Parameters and output quantities.