Draft version December 26, 2019 Typeset using LATEX twocolumn style in AASTeX62

Sulfate Aerosol Hazes and SO2 Gas as Constraints on Rocky Exoplanets’ Surface Liquid Water

Kaitlyn Loftus,1 Robin D. Wordsworth,1, 2 and Caroline V. Morley3

1Department of Earth and Planetary Sciences, Harvard University, Cambridge, MA 02140, USA 2Harvard Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02140, USA 3Department of Astronomy, University of Texas at Austin, Austin, TX 78712, USA

ABSTRACT Despite surface liquid water’s importance to habitability, observationally diagnosing its presence or absence on exoplanets is still an open problem. Inspired within the Solar System by the differing sulfur cycles on Venus and Earth, we investigate thick sulfate (H2SO4 –H2O) aerosol haze and high trace mixing ratios of SO2 gas as observable atmospheric features whose sustained existence is linked to the near-absence of surface liquid water. We examine the fundamentals of the sulfur cycle on a rocky planet with an ocean and an atmosphere in which the dominant forms of sulfur are SO2 gas and H2SO4 –H2O aerosols (as on Earth and Venus). We build a simple but robust model of the wet, oxidized sulfur cycle to determine the critical amounts of sulfur in the atmosphere-ocean system required for detectable levels of SO2 and a detectable haze layer. We demonstrate that for physically realistic ocean pH values (pH & 6) and conservative assumptions on volcanic outgassing, chemistry, and aerosol microphysics, surface liquid water reservoirs with greater than 10−3 Earth oceans are incompatible with a sustained observable H2SO4 –H2O haze layer and sustained observable levels of SO2. Thus, we propose the observational detection of an H2SO4 –H2O haze layer and of SO2 gas as two new remote indicators that a planet does not host significant surface liquid water.

Keywords: exoplanet atmospheres — exoplanet surface characteristics — habitable planets

1. INTRODUCTION While these fundamental requirements can be reason- Surface liquid water is considered essential to Earth- ably evaluated from a planet’s density and received stel- like life (e.g., Scalo et al. 2007; Kasting 2012), so deter- lar flux, evaluating whether rocky, habitable-zone plan- mining whether a planet possesses liquid water is es- ets actually possess surface oceans will be a substantial sential to constraining its habitability. As exoplanet challenge, even for next-generation telescopes. While at- detection and characterization techniques improve, ob- mospheric spectra can identify water vapor in a planet’s servational constraints on the presence of surface water atmosphere (e.g., Deming et al. 2013; Huitson et al. in the form of oceans will be a precursor to building 2013; Fraine et al. 2014; Sing et al. 2016), such a de- an understanding of the occurrence rate of Earth-like tection says nothing conclusively about surface liquid planets and, ultimately, to building an understanding of water. Temporally resolved reflected light spectra can the occurrence rate of Earth-like life. For many plan- potentially identify the presence of liquid water via color ets, the absence of surface oceans can be determined variation due to dark ocean color (Cowan et al. 2009), from straightforward physical arguments. Oceans re- polarized light variation due to ocean smoothness (Zug- quire a surface temperature and pressure consistent with ger et al. 2010), and/or ocean glint due to ocean re- the stability of liquid water. These requirements limit flectivity (Robinson et al. 2010). However, these meth- possible ocean-hosting planet candidates to low-mass ods all involve some combination of caveats, including still-unresolved potential false positives, decades-away (M . 10M⊕) planets in the habitable zone (e.g., Kast- ing et al. 1993; Kopparapu et al. 2013). instrumentation, and a reliance on ideal planetary con- ditions (Cowan et al. 2012). To systematically probe the presence of surface oceans on exoplanets, additional Corresponding author: Kaitlyn Loftus methods will unquestionably be needed. Here, we pro- [email protected] pose two such methods. 2 Loftus, Wordsworth, & Morley

Though all existing ocean detection proposals exploit 2. THE SULFUR CYCLE ON WET, OXIDIZED liquid water’s radiative properties, other planetary-scale PLANETS implications of the presence of surface liquid water ex- In this paper, we model the sulfur cycle on wet, oxi- ist. A hydrosphere can substantially alter a planet’s dized planets. We take a wet planet to be a planet with chemistry, including—most notably here—its sulfur cy- a reservoir of surface liquid water and an active hydro- cle. Previous studies of the observability of sulfur in logical cycle. We define an oxidized planet based on the exoplanet atmospheres suggest that sulfur has the capa- atmospheric gas and aerosol sulfur species present, as bility to be observed in atmospheres in both aerosol and discussed in further detail below. gas species (Kaltenegger and Sasselov 2010; Kaltenegger Figure1 summarizes the sulfur cycle on a wet planet. et al. 2010; Hu et al. 2013; Misra et al. 2015; Lincowski Sulfur gas (SO2 or H2S) is outgassed from melt trans- et al. 2018). In this paper, we test whether the observa- ported from the interior via volcanism. In the ocean, tions of a permanent sulfate (H2SO4 –H2O) haze layer this gas dissolves, and the aqueous sulfur species are and atmospheric SO2 can diagnose the absence of signif- dynamically mixed; in the lower atmosphere, the gas is icant surface liquid water. (Note that we do not consider dynamically mixed. Some gas reaches the upper atmo- the inverse of this hypothesis—i.e., a lack of observable sphere where a series of photochemical reactions pro- atmospheric sulfur implies the presence of an ocean— duces sulfur gas that condenses into aerosols (H2SO4- which is not particularly tenable.) H2O or S8, depending on the atmospheric redox state). H2SO4 –H2O aerosols with sufficient optical depth These aerosols are transported from the upper atmo- could be detected in exoplanet atmospheric spectra in sphere to the lower atmosphere via gravitational set- the near future (Hu et al. 2013; Misra et al. 2015). tling or mixing on timescales that may depend on the Within the Solar System, Venus and Earth are examples size of the aerosol. Both sulfur gas and aerosols are re- of rocky planets with drastically different surface liquid moved from the lower atmosphere via their interactions water volumes and sulfur aerosol opacities. Venus has a with cloud-water and rainwater. Henry’s law dictates an global, optically thick H2SO4 –H2O aerosol layer (Knol- equilibrium between sulfur gas in the atmosphere and lenberg and Hunten 1980) and no surface liquid wa- aqueous dissolved sulfur species. Further reactions lead ter. Earth, in contrast, only briefly hosts H2SO4 –H2O to the formation of sulfur minerals, which precipitate aerosol layers of significant optical depth after large out of the ocean when they become saturated. These volcanic eruptions (McCormick et al. 1995). Earth’s sediments may eventually be recycled in the interior de- present inability to sustain an H2SO4 –H2O aerosol layer pending on the planet’s tectonic regime. in its atmosphere can be directly tied to the presence of Because sulfur can stably occupy a wide range of redox oceans, as we show in Section3. states (commonly -2, 0, +4, +6; or S(-II), S(0), S(IV), Beyond aerosols, SO2 gas also has the potential to be S(VI), respectively), the precise sulfur species involved detected at & 1 ppm mixing ratios (Kaltenegger and Sas- in a planet’s cycle depend on the oxidization state of selov 2010; Hu et al. 2013). Previous results have found its interior, atmosphere, and ocean (e.g., Kasting et al. that building up sulfur concentrations to this level with 1989; Pavlov and Kasting 2002; Johnston 2011; Hu et al. an Earth-like sulfur cycle requires implausibly high out- 2013). Generally, oxidized atmospheres have SO2 gas gassing rates (Kaltenegger et al. 2010; Hu et al. 2013). and form aerosols composed of H2SO4 and H2O, whereas We show in Section3 that the presence of surface liquid reduced atmospheres have H2S gas and aerosols made water represents a fundamental barrier to maintaining of S8 (Hu et al. 2013). A planetary system in a more high trace atmospheric sulfur gas levels in such circum- intermediate redox state will have both types of sulfur stances. species present, with ratios between them determined The structure of this paper is as follows. In Section by the precise oxidation level (Hu et al. 2013). 2, we define the range of planetary atmospheres we con- In this work, we focus on the oxidized sulfur cycle, sider. Section3 describes our model of the sulfur cycle as (1) it is much more tightly coupled to planetary wa- on a wet, oxidized world. Section4 presents the key ter inventory and (2) its aerosol photochemistry is bet- findings of our model on the incompatibility of observ- ter constrained by observations on Earth. We consider able H2SO4 –H2O aerosols and SO2 gas with abundant an oxidized atmosphere to be one in which most sul- surface liquid water. In Section5, we discuss the im- fur aerosols present are composed of H2SO4-H2O rather plications and limitations of this study and make some than S8. The issue of how oxidized and reduced sulfur suggestions for future work. Section6 summarizes our cycles can be distinguished observationally via transit conclusions. spectra is discussed in Section 5.2. Oceans & the Sulfur Cycle 3

GAS AEROSOLS UPPER photochemistry, microphysics ATMOSPHERE gravitational settling/ mixing

violent mixing mixing eruption

DISSOLVED SPECIES, water cloud GAS AEROSOLS

mixing LOWER rain outgassing ATMOSPHERE

atmosphere-ocean SURFACE equilibrium ROCK OCEAN DISSOLVED SPECIES outgassing precipitation MELT PRECIPITATED INTERIOR MINERALS, burial MELT INSOLUBLE SPECIES

Figure 1. Schematic of the major components of the sulfur cycle on a planet with an ocean and active hydrological cycle.

3. METHODS Our model considers three reservoirs for surface sul- As implied by Figure1, the sulfur cycle involves atmo- fur: (1) an isothermal upper atmosphere (stratosphere), spheric dynamics, photochemistry, microphysics, aque- (2) a moist adiabatic lower atmosphere (troposphere), ous chemistry, and interior dynamics. Here, we aim to and (3) a surface liquid water layer (ocean). This ba- combine these components into a model that maximizes sic atmospheric thermal structure arises from physical simplicity while retaining all of the most essential pro- principles that are expected to be a reasonable ap- cesses. Our emphasis on simplicity is driven by our focus proximation across a wide variety of planetary condi- on the implications of the sulfur cycle for the detection tions (e.g., Pierrehumbert 2010). The sulfur species of an ocean. Furthermore, as we discuss throughout this and phases that we include are H2SO4 (`) and SO2 (g) section, the large uncertainties associated with many in the stratosphere; SO2 (g) in the troposphere; and – 2– of these processes mean that more complicated mod- SO2 (aq), HSO3 (aq), and SO3 (aq)—S(IV) species— els would be unlikely to give significantly more accurate in the ocean. The planetary parameters required are results. surface pressure psurf, surface temperature Tsurf, strato- In our model, key parameters are constrained from ba- sphere temperature Tstrat, atmospheric composition, sic physical arguments and Solar System analogs. For planetary radius RP, planetary mass MP, and surface each parameter x, we consider both the best reasonable relative humidity (saturation of water vapor) RHsurf. estimate (xb) and the limiting scenario that promotes Our modeling approach begins with the critical SO2 conditions for observable sulfur (x`). The latter presents mixing ratio for detection of atmospheric SO2 or the the most challenging conditions for our hypothesis that critical aerosol optical depth for observational detection of a haze layer. Working backward, we then calculate oceans are incompatible with sustained observable SO2 the critical number of sulfur atoms in the atmosphere or H2SO4 –H2O haze and thus represents the most strin- gent test of our hypothesis. Table1 summarizes the two and ocean system necessary for detection. Finally, we sets of parameter values. compare this critical value to the expected number of surface sulfur atoms to evaluate whether observable SO2 4 Loftus, Wordsworth, & Morley buildup or observable haze formation is likely. In the fol- where g is the local surface gravity and µair is the average lowing subsections, we discuss the various components molar mass of the planet’s air. In Sections 3.2-3.6, we of our model in detail. calculate the corresponding critical p∗ for observ- SO2,surf able H SO –H O aerosols, before returning in Section 3.1. Critical Atmospheric Sulfur for Observable SO 2 4 2 2 3.7 to the implications of this critical p∗ for the SO2,surf SO2 gas is observable because it absorbs in character- sulfur budget of the ocean. istic bands in the infrared. In order to be observed, SO2 must be present in high-enough concentrations such that 3.2. Aerosol Extinction its absorption lines have sufficient width and strength H SO –H O aerosols are observable because they ex- to be identified. Kaltenegger and Sasselov(2010) find a 2 4 2 tinguish (scatter and absorb) light. This extinction of constant SO mixing ratio of 1-10 ppm observable via 2 light is most effective per unit mass of particle in the Mie transit spectroscopy in an Earth-like atmosphere. We ∗ scattering regime, where particles are the same order- thus set the critical SO2 mixing ratio for detection f SO2 of-magnitude size as the wavelength of light being scat- to f ∗b = 1 ppm in our reasonable case scenario and SO2 tered. The mass extinction coefficient κ characterizes conservatively to f ∗` = 0.01 ppm in our limiting case e SO2 how effectively light is extinguished per unit particle scenario. Hu et al.(2013) illustrate that photochemical mass as loss of SO2 can be a significant limiting factor in the life- 3 Q κ = e , (3) time of SO2 in the atmosphere and thus can prevent high e 4 rρaero SO2 buildup. Here, we ignore the photochemical loss of where r is the average particle radius, ρ is the av- SO2—again to conservatively estimate the minimum sul- aero fur required for detection. As shown in Section4, we can erage particle density, and Qe is the particle extinction efficiency (Pierrehumbert 2010). Physically, r and ρ draw strong conclusions even from this minimum SO2 aero value, so there is little need to complicate this portion are determined from the microphysics of H2SO4 –H2O of our model with photochemistry. We discuss the pho- aerosol formation. In contrast with water cloud forma- tion, H SO and H O can condense directly from the tochemistry of SO2 in the context of aerosol formation in 2 4 2 Section 3.4. Finally, conceivably there may be exoplanet gas phase to form liquid aerosol particles at physically realizable saturation levels (Seinfeld and Pandis 2012; UV-photon-limited regimes where SO2 is neither signif- icantly photodissociated nor destroyed from reactions M¨a¨att¨anenet al. 2018). with reactive photochemical products, in which case this The ratio of H2SO4 to H2O by mass in an aerosol w maximum estimate would be valid. depends on both temperature and the ambient num- ber densities of H SO and H O vapor (M¨a¨att¨anen To first order, the amount of SO2 in the light path, 2 4 2 et al. 2018). The ratio w controls both ρ (ρ = not SO2’s relative abundance in the atmosphere, is what aero aero wρ +(1−w)ρ ) and the index of refraction of the characterizes SO2’s spectroscopic influence (Pierrehum- H2SO4 H2O bert 2010); mixing ratio is a convenient and tradi- aerosol, which impacts Qe. Theoretically, more H2SO4 tional way of expressing abundance of trace gases, but gas is predicted to lead to aerosols with higher H2SO4 its relationship to observability in transmission spec- concentrations (M¨a¨att¨anenet al. 2018); however, ob- tra will vary with total atmospheric pressure. To make servational estimates for w from H2SO4 –H2O aerosols in Earth’s stratosphere (a sulfur-poor environment) and Kaltenegger and Sasselov(2010)’s SO 2 detection thresh- old more broadly applicable to non-Earth planetary con- Venus’ H2SO4 –H2O haze layer (a sulfur-rich environ- ment) both give w ≈ 0.75 (Turco et al. 1979; Russell ditions, we translate their critical mixing ratio of SO2 for detection in an Earth-like atmosphere to a critical et al. 1996; Seinfeld and Pandis 2012; Hansen and Hov- ∗ enier 1974; Ragent et al. 1985). We thus set w = 0.75 mass column (mass per unit area) of SO2 uSO : 2 for both limiting and best conditions. ∗ f psurf,⊕ µ u∗ = SO2 SO2 (1) Once nucleated, aerosols grow rapidly via condensa- SO2 g⊕ µair,⊕ tion if either H2SO4 or H2O gas is supersaturated (Turco where psurf,⊕ is the Earth’s surface pressure, g⊕ is the et al. 1979; Seinfeld and Pandis 2012). The aerosols additionally grow via coagulation: diffusion and turbu- Earth’s surface gravity, µSO2 is the molar mass of SO2, and µair,⊕ is the average molar mass of Earth air. Eval- lence lead to sticking collisions between aerosols, which uating Equation (1) yields u∗b = 2.3 × 10−2 kg m−2 increase particle size and decrease particle number (e.g., SO2 and u∗` = 2.3 × 10−4 kg m−2. We then set the critical Seinfeld and Pandis 2012). In both Earth’s and Venus’s SO2 ∗ atmospheres, H2SO4 –H2O aerosols tend to be relatively partial pressure of SO2 at the surface pSO ,surf as 2 mono-dispersed in size (Knollenberg and Hunten 1980; µ p∗ = u∗ g air (2) Seinfeld and Pandis 2012), so describing their size dis- SO2,surf SO2 µSO2 Oceans & the Sulfur Cycle 5

101 spectra. This procedure is described in Section 3.6 af- ter we finish outlining the structure of the rest of the atmosphere. From the definition of mass column u, we can calculate ∗ 100 the critical mass of H2SO4 MH SO as

] 2 4 [

e Q M ∗ = u∗w4πR2 (5) H2SO4 P

∗ Mie, Sun-like where RP is the radius of the planet. Putting u in Mie, M-dwarf ∗ 10 1 terms of δ and aerosol parameters with Equations (3) Rayleigh, Sun-like Rayleigh, M-dwarf and (4), we then calculate the critical number of H2SO4 10 1 100 molecules in aerosols needed to create an observable haze r [ m] layer as

Figure 2. Extinction efficiency (Qe) of H2SO4 –H2O M ∗ 16π δ∗ w aerosols versus average particle radius (r). Solid lines are cal- N ∗ = H2SO4 = rρ R2 (6) H2SO4 aero P culated from Mie theory and dashed lines show the Rayleigh mH2SO4 3 Qe mH2SO4 limit (valid approximation for small particles). Values for a where m is the mass of a molecule of H SO . Sun-like star are in dark blue and those for an M dwarf in H2SO4 2 4 light blue. 3.3. Aerosol Sedimentation and Mixing Once in the troposphere, H SO -H O aerosols are tribution by a single average radius r is a valid approx- 2 4 2 ideal cloud condensation nuclei because of their high imation. affinity for water, and they are rapidly removed by pre- We estimate a reasonable r value from the H2SO4 –H2O cipitation (Seinfeld and Pandis 2012). For a mean res- aerosols that dominate Venus’ haze layer’s radiative idence time τ ,H SO remains in the stratosphere as properties as rb = 1 µm (Hansen and Hovenier 1974; life 2 4 an aerosol contributing to the optical depth of the sulfur Knollenberg and Hunten 1980). From the inverse de- haze. We only consider H2SO4 as radiatively relevant pendence of κe on r in Equation (3), smaller r values are until it is transported to the tropopause—the bound- more favorable for haze formation for a given number of ary between the isothermal stratosphere and convecting atmospheric sulfur atoms. However, particles too small troposphere—because of H SO ’s short lifetime in the will be observationally indistinguishable from Rayleigh 2 4 troposphere. scattering by gas molecules. We therefore set r` by The parameter τlife depends on the size of the aerosol. considering where Qe transitions from the Rayleigh If coagulation and condensation are effective and parti- scattering limit to the Mie scattering regime. cles grow large enough, they will gravitationally settle Qe is calculated with Mie theory from r, the compo- out of the upper atmosphere. Otherwise, small particles sition of the particle (within the H2SO4 –H2O system, will instead likely be removed by dynamic processes first specified by w), the index of refraction of this given due to their slow settling velocities. Thus, the average H2SO4 –H2O mixture (Palmer and Williams 1975), and lifetime of an H SO –H O aerosol in the stratosphere the wavelength of incident light (λ) being attenuated 2 4 2 is approximately (Bohren and Huffman 2008). We take λ to be the peak of the planet’s host star’s spectrum, which is easily cal- τlife = min{τfall, τmix} (7) culated from Wien’s displacement law given the star’s observed effective temperature. Figure2 shows Qe as a where τfall is the gravitational settling timescale and τmix function of r for both Sun-like (λ = 0.556 µm) and M- is the dynamic mixing timescale of exchange between the dwarf stars (for illustrative purposes, λ = 1 µm) with stratosphere and troposphere. the Rayleigh limit superimposed. Based on this calcu- We calculate τfall from the Stokes velocity of the falling lation, we set r` = 0.1 µm for a Sun-like star and r` = particle as 0.2 µm for an M dwarf. We calculate the aerosol layer vertical path optical zfall 9 zfallη τfall = = 2 . (8) depth δ as vStokes 2 r gρaeroCC δ = uκe (4) Here, g is planet surface gravity, η is the dynamic vis- where u is the mass column of aerosol particles. We cosity of air, and CC is the Cunningham-Stokes correc- estimate the critical minimum optical depth value for tion factor for drag on small particles (Seinfeld and Pan- ∗ an observable haze layer δ by simulating transmission dis 2012). zfall is the average distance a sulfur aerosol 6 Loftus, Wordsworth, & Morley must fall from its formation location to the tropopause. (Turco et al. 1979; Stockwell and Calvert 1983; Burkholder We conservatively estimate this parameter as the scale et al. 2015). For part 2, the proposed reaction is −1 height of the stratosphere (i.e., zfall = RTstrat(µairg) ). Calculating τmix from first principles is not possible SO3 + H2O −−→ H2SO4, (13) because a general theory of stratosphere-troposphere mixing timescales as a function of external parameters but it is unclear whether this reaction proceeds as a two- does not yet exist. However, insights can be gained body or three-body reaction kinetically (Seinfeld and from studying Earth. Today, Earth’s strong strato- Pandis 2012; Burkholder et al. 2015). Large uncertain- spheric temperature inversion inhibits this stratosphere- ties in reaction rates for these reactions are compounded troposphere exchange. Since radiatively generating an by the reaction kinetics’ sensitivity to photochemical upper atmospheric temperature inversion stronger than product (OH, O) concentrations, which require detailed knowledge of atmospheric composition for accurate re- Earth’s is difficult, Earth’s τmix is likely near an upper bound on stratosphere-troposphere mixing timescales. sults (Jacob 1999). On the most observable M-dwarf planets, permanent Despite these uncertainties, we can make simplifica- day-night sides of planets due to tidal effects are pred- tions because SO2,H2O, and stellar UV photons are es- icated to generate strong winds (e.g., Showman et al. sential for the conversion, regardless of the pathway. In 2010; Showman and Polvani 2011) that will almost cer- particular, because photochemistry is the rate limiting step except potentially in extremely dry atmospheres, tainly reduce τmix from Earth values. Therefore, from we can estimate a lower limit of τSO →H SO by con- Earth-based timescales, we estimate τmix = 1 year for 2 2 4 all cases (Warneck 1999). sidering how long it takes for the number of UV pho- tons necessary for the reaction to proceed to strike the 3.4. Aerosol Formation planet’s atmosphere. For photolysis-driven reactions, the lifetime τ of the The saturation vapor pressure of H SO at expected 2 4 photolyzed species can be described by terrestrial planet stratosphere temperatures is extremely low ( 10−6 Pa) (Kulmala and Laaksonen 1990), Z −1 1 τ = q(λ)σ(λ)φγ (λ)dλ (14) so all stratospheric H2SO4 is effectively found con- 4 densed in aerosols rather than as a gas. The sulfur λUV source for H SO –H O aerosols in oxidized atmo- 2 4 2 where λ is wavelength of light, q is the quantum yield or spheres is SO gas. Here, we define τ as 2 SO2→H2SO4 the probability that a photon will dissociate a molecule, the timescale required to convert stratospheric SO to 2 σ is the absorption cross section of the molecule, φ is H SO . τ is challenging to calculate precisely γ 2 4 SO2→H2SO4 the flux of photons to a planet’s atmosphere per unit because SO2 is oxidized to H2SO4 through a series of wavelength, and the factor of 1/4 accounts for day–night photochemical reactions that are poorly constrained and stellar zenith angle averaging (Jacob 1999; Cronin both in terms of reaction pathways and rates (Turco 2014). To represent the most rapid conversion rate et al. 1979; Stockwell and Calvert 1983; Yung and De- of SO to H SO , we set q = 1 for all wavelengths More 1998; Burkholder et al. 2015, etc.). The two main 2 2 4 (i.e., 100% probability that a photon will dissociate a stages of the conversion of SO to H SO are (1) SO is 2 2 4 2 molecule it strikes). At minimum, the SO to H SO converted to SO via a photochemical product and (2) 2 2 4 3 reaction requires one O or OH molecule. For weakly SO and H O react to form H SO (Burkholder et al. 3 2 2 4 to strongly oxidized terrestrial planet atmospheres, this 2015). For part 1 of the conversion, commonly proposed photochemical product will most likely be the result of reactions are the dissociation of H2O, O2, or CO2. (Ostensibly, pho- todissociated SO2 could also provide O, but at the sur- SO2 + O + M −−→ SO3 + M (9) face number densities of SO2 we consider here, SO2 is (Yung and DeMore 1998; Burkholder et al. 2015) or so optically thin that it cannot effectively absorb pho- tons (Manatt and Lane 1993; Hamdy et al. 1991).) At SO2 + OH + M −−→ HSO3 + M (10) each λ, we set σ(λ) as the maximum absorption cross section from these three molecules, using data given (Turco et al. 1979; Stockwell and Calvert 1983; Burkholder in Chan et al.(1993), Mota et al.(2005), Lu et al. et al. 2015) followed by either (2010), Yoshino et al.(1988), Kockarts(1976), Brion et al.(1979), and Huestis and Berkowitz(2010). HSO + O −−→ SO + HO (11) 3 2 3 2 To set the wavelength for the upper limit of integra- HSO3 + OH −−→ SO3 + H2O (12) tion, we take the smallest minimum bond dissociation Oceans & the Sulfur Cycle 7 energy of H2O, O2, and CO2 and convert it to a wave- Chameides 1985; Seinfeld and Pandis 2012; Hu et al. length (via Edis = Eγ = hν = hc/λ). A minimum 2013). The high effective solubility of SO2 means that −19 energy of 8.2 × 10 J(deB. Darwent 1970) yields a effectively all SO2 at and below the cloud deck is re- maximum wavelength of 240 nm. We begin the integra- moved every rainfall event (Giorgi and Chameides 1985). tion from λ = 0 nm for a maximum number of photons. This process of wet deposition greatly limits the lifetime In general, φγ will be determined from the host star’s of SO2 in the lower atmosphere and decreases the mix- spectrum and the distance of the planet from its host ing ratio of SO2 (fSO2 ≡ pSO2 /p) beyond the water cloud star. Here, we use the present-day flux of the Sun to layer in the upper atmosphere relative to the surface. Earth as measured by Thuillier et al.(2004) as a base- In our model, we take the mixing ratio of SO2 at the line φγ for a Sun-like star. The ratio of UV flux to stellar tropopause to be directly proportional to the mixing ra- bolometric flux declines as stellar mass declines (due to tio of SO2 at the surface, such that lower effective temperatures and thus higher wavelength pSO2,tropopause pSO2,surf Planck peaks) while the ratio of extreme UV (EUV) flux = α . (17) ptropopause psurf to bolometric flux tends to increase for M dwarfs rela- tive to Sun-like stars due to higher magnetic activity Here, p is the total atmospheric pressure, and α is the (Scalo et al. 2007; Shkolnik and Barman 2014; Schae- change of mixing ratio between the surface and the up- fer et al. 2016; Wordsworth et al. 2018). The precise per atmosphere due to the effects of wet deposition. We change in UV and EUV flux relative to bolometric flux do not yet know much about hydrological cycles on plan- for an M dwarf relative to the Sun will depend on the ets with less surface liquid water than Earth, so in the specific star and its age, but for illustrative purposes limiting case we completely ignore wet deposition and ` b here, we assume a 10× decrease in UV flux and a 10× set α = 1. For the reasonable case, we assume α = increase in EUV flux relative to the solar value. (Here, 0.1, based on comparison with SO2 vertical profiles mea- we define the EUV wavelength cutoff as λ = 91 nm, sured on Earth (Georgii 1978; Meixner 1984). following Wordsworth et al.(2018).) Plugging in val- We calculate a pressure-temperature profile from sur- ues to Equation (14) then leads to τ ` ≈ 3.4 face temperature Tsurf and pressure psurf assuming a dry SO2→H2SO4 days for a Sun-like star and τ ` ≈ 2.5 days for adiabat until water vapor becomes saturated and then a SO2→H2SO4 moist adiabat until a specified (isothermal) stratospheric an M dwarf. On modern Earth, τSO2→H2SO4 ≈ 30 days (Turco et al. 1979; Macdonald and Wordsworth 2017), temperature Tstrat is reached, following the derivation which we take as τ b . of Wordsworth and Pierrehumbert(2013). This calcula- SO2→H2SO4 tion requires an assumed mixing ratio of water fH O ≡ Once we have estimated the lifetimes of H2SO4 and 2 pH O/p at the surface. This mixing ratio is calculated SO2 in the stratosphere, we can directly relate the 2 from relative humidity at the surface RHsurf and Tsurf via steady-state NH2SO4 in aerosols to NSO2 in gas by as- fH O,surf = RHsurf ×psat,H O(Tsurf) where psat,H O(Tsurf) suming that the production rate of H2SO4 is equal to 2 2 2 its removal rate: is the saturation pressure of water at temperature Tsurf. b We set RHsurf = 0.77 like the Earth. Increasing fH2O N N H2SO4 = SO2 . (15) yields a higher tropopause, which results in a higher τlife τSO →H SO 2 2 4 pSO2,surf for a given pSO2,tropopause. Therefore, we set RH` = 0 (yielding a dry adiabat atmospheric struc- From Equation (15) and the definition of pressure as surf ture). force over area, N ∗ converted to a critical partial pres- SO2 sure of SO (p∗ ) at the tropopause is 2 SO2 3.6. Aerosol Observability gm τ Having reviewed the atmospheric conditions dictated p∗ = N ∗ SO2 SO2→H2SO4 (16) SO2,tropopause H2SO4 2 by the presence of an observable H2SO4 –H2O haze 4πRP τlife layer, we can now return to the problem of how to cal- ∗ where mSO2 is the mass of a molecule of SO2. culate the critical optical depth δ for observation. We simulate the transmission spectra expected of a planet 3.5. Lower Atmosphere Transport with a sulfur haze for a range of optical depths to de- On a wet, temperate planet, SO2 faces no signifi- termine at which δ-value the hazy spectrum becomes cant sinks below the photochemically active upper at- distinct from the clear spectrum. The appendices of mosphere until it encounters the water cloud layer in the Morley et al.(2015); Morley et al.(2017) provide the troposphere. Once SO2 encounters condensed water (as details of our model for simulating transmission spectra, either rain or cloud droplets), the SO2 dissolves and is which uses the matrix prescription presented in Robin- subsequently rained out of the atmosphere (Giorgi and son(2017). We calculate molecular cross sections as 8 Loftus, Wordsworth, & Morley

+ – 2– described in Freedman et al.(2008, 2014), including an acid, which dissociates to H , HSO3 , and SO3 ions: updated water line list from Polyansky et al.(2018). − + As inputs to our model, we require aerosol size and SO2 (aq) + H2O )−−−−* HSO3 + H (19) − 2− + number densities, atmospheric gases number densities, HSO3 )−−−−* SO3 + H (20) and temperature as functions of pressure. From Equa- tion (15), we calculate an H2SO4 –H2O aerosol number (Neta and Huie 1985; Halevy et al. 2007). The ocean’s density profile, assuming exponential decay in aerosols pH (log of the concentration of H+ ions) controls the – from the tropopause until a parameterized cutoff height partitioning of sulfur between SO2(aq), HSO3 , and 2– (due to lack of photochemical H2SO4 production). We SO3 —species which are collectively known as S(IV) input atmospheric number densities assuming constant or sulfur in a +4 redox state. As we discuss in the next mixing ratios (except for H2O) for a given atmospheric section, however, the picture of aqueous sulfur chem- composition. The temperature-pressure profile follows istry given by Equations (18)-(20) is incomplete because a moist adiabat until it reaches an isothermal strato- S(IV) disproportionation is effective under a wide range sphere. The mixing ratio of H2O fH2O is determined by of conditions. We return to this point shortly. the moist adiabat. fH2O is set at the surface and is held The atmosphere is only in equilibrium with SO2(aq), constant until water vapor becomes saturated. Then, so when Equations (18)-(20) hold, the ocean’s pH reg- fH2O evolves according to water’s saturation pressure ulates its ability to store sulfur versus the atmosphere. until the tropopause, above which fH2O remains con- Ocean pH is treated as an independent variable in our stant. model because it has a strong influence on the sulfur Varying δ in these simulated transit spectra for an distribution and is difficult to estimate from first princi- Earth-like atmosphere (see Section 4.1 and Figure3) ples (e.g., Kempe and Degens 1985; Macleod et al. 1994; suggested that the critical minimum value for an ob- Sleep and Zahnle 2001; Halevy and Bachan 2017). Our servable haze layer is δ∗ ≈ 0.1. Different atmospheres model’s pH dependence is discussed further in Section will yield different δ∗ values, but likely not by orders of 4.4. magnitude. The precise shape of a hazy planet’s transit With the partial pressure of SO2 at the surface and an spectrum is also somewhat sensitive to the photochem- assumed pH, Equations (18)-(20) give the concentration ical haze cutoff height. Lower cutoff heights yield more of S(IV) species [S(IV)(aq)] in the ocean as traditionally haze-characteristic flat spectra (e.g., Kreid- − 2− berg et al. 2014), and higher, less physical cutoff heights [S(IV)(aq)] = [SO2(aq)] + [HSO3 ] + [SO3 ] yield more structured—though still smoothed relative p  K K K  = SO2,surf 1 + 1 + 1 2 . (21) + + 2 to a clear atmosphere—spectra; but the full range of KH [H ] [H ] possible haze cutoff values still yields spectra identifi- + −pH −1.86 −7.2 able as hazy. In the absence of a detailed photochemical Here [H ] = 10 , and K1 = 10 and K2 = 10 model, we choose to display results in Figure3 with are the first and second, respectively, acid dissociation a cutoff height of two stratospheric scale heights (11.7 constants of sulfurous acid (Neta and Huie 1985). These km), following Earth and Venus H2SO4 –H2O aerosol constants depend on salinity, pressure, and temperature profile observations (e.g., Sekiya et al. 2016; Knollen- in general, although we neglect this dependence here. berg and Hunten 1980). At this point, we incorporate the most significant vari- able in our model: the planet’s total mass of surface 3.7. Ocean Sulfur Storage liquid water Moc. Like pH, Moc is taken to be an in- When surface liquid water is present, convection and dependent variable because it is the unknown we are the hydrological cycle act to bring the lower atmo- interested in investigating. The total number of sul- spheric and dissolved sulfur in the ocean into equilib- fur atoms needed in the atmosphere-ocean system to ∗ rium rapidly. The partial pressure of SO2 at the surface achieve observable atmospheric sulfur NS is a function of [S(IV)(aq)], p , and M . It can be written as (pSO2,surf) is held in equilibrium with the concentration SO2,surf oc of dissolved, aqueous SO2 in the ocean [SO2 (aq)] via the sum of sulfur atoms required in the atmosphere and Henry’s law: the ocean:

∗ ∗ ∗ pSO2,surf = KH(T )[SO2 (aq)], (18) NS = NS,atm + NS(IV),oc. (22)

4 −1 where KH = 6.96 × 10 Pa L mol is the Henry’s law To avoid having to prescribe an fSO2 profile, we make constant for SO2 (Pierrehumbert 2010). Once dissolved, the simplifying assumption that SO2 is always well ∗ SO2 reacts with the ambient water to form sulfurous mixed in calculating NS,atm. For an observable level Oceans & the Sulfur Cycle 9 of SO2, the critical number of sulfur atoms in the atmo- (Karchmer 1970; Guekezian et al. 1997; Ryabinina and ∗ sphere NS,atm is Oshman 1972). These disproportionation reactions are thermodynam- 4πR2 N N ∗ = P p∗ A (23) ically favored based on their calculated Gibbs free en- S,atm g SO2,surf µ SO2 ergy changes (Guekezian et al. 1997). However, the pre- where µ is the molar mass of SO and p∗ is cise pathways by which S(IV) decay proceeds and their SO2 2 SO2,surf given by Equation (2); whereas for an observable haze respective reaction rates are unclear, even in environ- layer ments of well-known pH, [O2(aq)], and T (Ermakov and Purmal 2001). Nonetheless, experiments suggest across 4πR2 N N ∗ = P p∗ A + N ∗ (24) wide pH, [O (aq)], and T ranges that HSO – and SO 2– S,atm g SO2,surf µ H2SO4 2 3 3 SO2 are unstable on rapid timescales of seconds to weeks (Er- where p∗ is given by Equation (17) and N ∗ by SO2,surf H2SO4 makov and Purmal 2001; Avrahami and Golding 1968; Equation (6). For both observable atmospheric sulfur Guekezian et al. 1997; Suzuki 1999; Zopfi et al. 2004). – 2– products, the critical number of S(IV) sulfur atoms in Indeed, in Earth’s modern oceans, [HSO3 ] and [SO3 ] ∗ 2– the ocean NS(IV),oc is concentrations are close to zero, with SO4 ions (S(VI)) being the only major dissolved sulfur constituent, de- M N ∗ = [S(IV)(aq)]∗ oc 1000 L m−3
N (25) spite the fact that SO is the dominant sulfur outgassing S(IV),oc ρ A 2 H2O product (Schlesinger and Bernhardt 2013). For Earth’s where N is Avogadro’s number, [S(IV)(aq)]∗ is given 2– A pH and average surface pSO2 , the expected [SO3 ] con- by Equation (21), and the factor of 1000 L m−3 converts centration levels in the ocean in the absence of dispro- the moles per L of [S(IV)(aq)]∗ to SI units. portionation or oxidation are of order 0.01-0.001 mol L−1. Measurements of [SO 2– ] are of order 1×10−6 mol 3.8. Expected Sulfur in Surface Reservoir 3 L−1 or less (Goldhaber 2003). We now need to calculate the number of sulfur atoms After the oxidation or disproportionation of S(IV), expected in the atmosphere and ocean to compare to both possible sulfur products S(0) and S(VI) are lost the critical value given by Equation (22) to determine to the reservoir of sulfur in equilibrium with the atmo- whether observable SO2 buildup or haze formation is sphere until they have been reprocessed by the interior. reasonable. This calculation is simplified because aque- S(0) is insoluble (Boulegue 1978), so its formation re- – 2– ous HSO3 and/or SO3 are not thermodynamically moves that sulfur from the aqueous reservoir. S(IV) stable (Karchmer 1970; Hayon et al. 1972; Brimble- is soluble, but there are no known abiotic pathways to combe and Lein 1989; Guekezian et al. 1997; Jacobson reduce S(VI) back to S(IV) (Brimblecombe and Lein et al. 2000; Ermakov and Purmal 2001; Halevy 2013). 1989). We discuss the implications of the presence of Spontaneous or easily catalyzed disproportionation and sulfur-consuming life on the sulfur cycle in Section 5.4, oxidation reactions convert sulfur from S(IV) to S(VI) but it is not expected to substantially alter this picture. and/or S(0) (Karchmer 1970; Guekezian et al. 1997; Theoretically, aqueous S(VI) could be a source of Johnston 2011; Halevy 2013), the former even in the ab- H2SO4 gas from Henry’s law. However, because H2SO4 sence of dissolved oxygen (Guekezian et al. 1997; Zopfi is an extremely strong acid, dissolved H2SO4 will not be et al. 2004). The proposed stoichiometric oxidation re- present as H2SO4(aq). Significant H2SO4(aq) requires action is physically impossible water pHs . -3 (Jacobson et al. 2− 2− 2000). Thus, dissolved S(VI) species cannot contribute 2 SO3 + O2 −−→ 2 SO4 (26) to atmospheric H2SO4 either. though the chain of reactions from which this reaction As neither S(0) nor S(VI) is in equilibrium with atmo- proceeds is poorly understood (Ermakov and Purmal spheric SO2, aqueous chemistry can act as a pump for 2001; Halevy 2013). Proposed stoichiometric dispropor- rapidly removing SO2 from the atmosphere, and there is tionation reactions in anoxic waters include: essentially no potential for significant atmospheric sul- fur gas buildup over geologic time on planets with sur- 3 H2SO3 −−→ 2 H2SO4 + S + H2O (27) 2− 2− 2− − face liquid water (e.g., Kasting et al. 1989). A central 7 SO3 + 3 H2O −−→ S4O6 + 3 SO4 + 6 OH outcome of our analysis is, therefore, that the sulfur out- (28) gassing flux must continuously counterbalance aqueous 2− 2− 2− − 4 SO3 + H2O −−→ 2 SO4 + S2O3 + 2 OH S(IV) decay if significant SO2 is to be present in an at- (29) mosphere. 2− + 3 SO2 + 2 H2O −−→ 2 SO4 + S + 4 H (30) 10 Loftus, Wordsworth, & Morley

To see whether the buildup of observable SO2 or the rather than availability of ambient interior sulfur. Ex- formation of an observable haze layer is reasonable, we perimentally, the sulfur melt saturation limit is most can compare the critical number of sulfur atoms in the strongly controlled by melt oxidation state and then ∗ atmosphere and ocean required for observation (NS ) temperature with smaller effects from melt composition with the expected total number of sulfur atoms in the and pressure (Jugo et al. 2005; Jugo 2009; Righter et al. planet’s ocean and atmosphere (NS). As the sulfur must 2009). be supplied by recent outgassing, we estimate NS as Sulfur directly dissolved in melt is further in equilib- rium with a volatile vapor phase also held within the ˙ NS = NSτS(IV) (31) melt (e.g., Zajacz et al. 2012). This vapor phase is what outgasses. The partitioning of sulfur between melt ˙ where NS is the global outgassing rate of sulfur (number and vapor is a function of temperature, pressure, ox- of S atoms outgassed per unit time) and τS(IV) is the idation state, and melt composition (Shinohara 2008; timescale for S(IV) to decay in the ocean. In order for Zajacz et al. 2012). Recent experimental studies sug- a sulfur haze layer to be observed, we must have gest that the dependence on melt oxidation state of this vapor-melt partitioning and of dissolved melt sul- ∗ NS/NS ≥ 1. (32) fur saturation counteract each other such that the total gaseous sulfur available for outgassing is essentially in- To determine the most favorable conditions for atmo- dependent of interior oxidation state (Jugo et al. 2005; spheric sulfur buildup, we must evaluate a maximum Zajacz et al. 2012). The coupling of other dependencies sulfur outgassing rate N˙ . This estimation is hampered S between vapor-melt partitioning and melt saturation is by the lack of a clear path to placing a reasonable up- less clear, but qualitatively these dependencies tend to per bound given large uncertainties in the quantitative (like oxidation state) act in opposition—muting, rather chemistry that governs the transport of sulfur from the than amplifying, the effect of a given state variable on planetary interior to the surface as well as a large plan- total sulfur outgassing potential. etary parameter space; we make a good faith effort to Melts tend to outgas at the surface because decreas- estimate this maximum value but highlight this calcula- ing pressure increases the partitioning of sulfur into va- tion as a clear region for future study. We do note that, por relative to the melt. Traditionally it has been as- given our interest in an equilibrium state, we are con- sumed that initial sulfur vapor content at melt forma- sidering here maximum time-averaged outgassing rates tion (high pressure) is zero, and all sulfur ultimately rather than an instantaneous values from transient ex- outgassed originates from direct dissolution into melt at treme events. formation; however, more recent observations call into The precise frequency and magnitude of the out- question this latter assumption (see Oppenheimer et al. gassing events that determine N˙ will be a function of a S 2011, and references therein). Sulfur budget allocating planet’s tectonic regime, which at present is extremely estimates from larger explosive eruptions with satellite- poorly constrained for exoplanets, given conflicting re- quantifiable gas plumes suggest that an ambient vapor sults from interior dynamics models (e.g., O’Neill and reservoir can interact with the melt during its ascent and Lenardic 2007; Valencia et al. 2007; Stamenkovi´cet al. contribute more sulfur (e.g., Wallace and Gerlach 1994; 2012). Nonetheless, Kite et al.(2009) estimate theo- Gerlach et al. 1996; Shinohara 2008; Oppenheimer et al. retical upper bounds on terrestrial planet outgassing for 2011). The origins of this ambient vapor reservoir are both plate tectonics and stagnant lid regimes. They find not well understood (Oppenheimer et al. 2011). How- outgassing rate is a strong decreasing function of planet ever, proposed hypotheses seem to require either (1) an age after ∼1 Gyr and roughly constant across bodies older planet with a buildup of sulfur-rich sediments from of different sizes when normalized per unit planet mass. the surface having been transported deeper into the in- In their model, outgassing peaks at about 20× modern- terior, suggesting that the contributions of this ambient Earth outgassing levels. vapor reservoir should be muted for young planets with To translate an upper bound on total outgassing rate the highest outgassing fluxes or (2) a long-suppressed re- into an upper bound on sulfur outgassing rate, we as- gional eruption, suggesting limited influence over a time- sume that outgassing rate is proportional to melt pro- averaged outgassing rate (Oppenheimer et al. 2011). duction rate, following Kite et al.(2009). For near (or From these considerations, we believe assuming that above) Earth-like bulk sulfur contents, sulfur directly modern Earth’s average sulfur outgassing per unit melt dissolved in melt is largely limited by the saturation is within an order of magnitude of an upper bound is limit of the sulfur-bearing species in the melt (e.g., An- a reasonable assumption. The conclusion seems consis- derson 1974; Mathez 1976; Edmonds and Mather 2017) Oceans & the Sulfur Cycle 11 tent with Earth history: models of the Archean sulfur vertical optical depths in Figure3. The slant angle cycle suggest that, in order to reproduce observed sul- geometry of transit spectroscopy means that the haze fur isotope fractionations, the Archean sulfur outgassing layer causes significant differences to the transit spec- rate was a fraction of the modern rate despite elevated trum for δ values as low as 0.01 (Fortney 2005). These total volcanism relative to present day (e.g., Harman results informed our choice of the critical amount of et al. 2018b). From the average current Earth sulfur aerosols needed for observable haze detection in Sec- outgassing rate (N˙ S,⊕), we can then estimate our lim- tion3. Clearly, the presence of the optically thick haze iting value for this sulfur outgassing rate parameter as produces a distinct spectrum from a clear terrestrial- type atmosphere. For the Earth-like atmosphere mod- ˙ ` ˙ Mp eled here, the differences are strongest in 3-5 µm and NS = 10 × 20NS,⊕ (33) M⊕ 7.5-15 µm bands. In general, which bands have the 35 −1 strongest difference between hazy and clear conditions where N˙ S,⊕ = 1.89 × 10 atoms S yr (Schlesinger will vary with atmospheric composition. The height and Bernhardt 2013; Halmer et al. 2002), Mp is planet of the signals—and thus their detectability—will also mass, M⊕ is Earth’s mass, the factor of 20 is from Kite et al.(2009)’s calculations to account for the potential vary strongly with planetary size relative to stellar size for increased total outgassing, and the additional factor and atmospheric scale height. We discuss distinguish- of 10 is to account for the potential for higher sulfur con- ing H2SO4 –H2O from other spectra-flattening agents tent in melts than modern mass-averaged Earth values in Section 5.3. (e.g., from higher melt formation temperatures, greater influence of an at-depth vapor reservoir). We set the 4.2. Sulfur in the Atmosphere reasonable scenario from the modern-Earth outgassing We translated our observable sulfur criteria into a crit- value with ical amount of sulfur in the atmosphere from Equations Mp N˙ b = N˙ . (34) (23) and (24). For modern-Earth-like planetary condi- S S,⊕ M ⊕ tions and reasonable model parameters given in Table 37 The remaining key parameter in our model is the 1, we calculated that observable SO2 requires 4.9 × 10 S(IV) aqueous decay timescale τS(IV). As we have dis- S atoms = 2.6×1012 kg S in the atmosphere (the equiv- cussed, current understanding of the kinetics of aqueous alent of 1 ppm = 1000 ppb SO2 in an Earth-like atmo- S(IV) instability is still quite limited. Therefore, we sphere). Using the limiting model parameters given in ∗ 10 solve directly for the critical τS(IV) for observable sulfur Table1 instead gives 1% of this value (2 .6 × 10 kg S). buildup from a simplification of the condition for obser- For Earth-like conditions and reasonable model parame- vation given by Equation (32): ters, a sustained observable haze layer requires 2.5×1036 S atoms = 1.3×1011 kg S in the atmosphere (the equiv- ∗ ∗ τ = N /N˙ S. (35) S(IV) S(IV),oc alent of 50 ppb SO2 in an Earth-like atmosphere). Con- sidering limiting conditions yields 8.5% of this value for As τ relates only to the destruction rate of aque- S(IV) a Sun-like star (1.1×1010 kg S) and 13% for an M dwarf ous S(IV), we make this conservative assumption—to (1.7 × 1010 kg S). For context, Earth’s atmosphere cur- neglect the direct contribution of atmospheric sulfur to rently contains about 108 kg of sulfur in SO (equiva- the critical amount of sulfur necessary for atmospheric 2 lent to 0.04 ppb SO —if SO were well-mixed) (Brimble- observation—in lieu of adding the exchange rate of S(IV) 2 2 combe and Lein 1989), in an environment where anthro- between the ocean and atmosphere to our equilibrium pogenic emissions are about 10 times natural volcanic model. This simplification is favorable to atmospheric sources (Schlesinger and Bernhardt 2013). sulfur buildup, underestimating critical sulfur required The total number of sulfur atoms required in a plan- for observation in water-poor, low-pH regimes where etary atmosphere for observable SO buildup or a haze N  N . As we will show, the variation in 2 S(IV),oc S,atm layer is relatively insensitive to surface temperature τ ∗ value as a function of pH and ocean volume is so S(IV) T , stratospheric temperature T , surface pres- large that we are able to reach strong conclusions, even surf strat sure p , planetary radius R , atmospheric compo- given the uncertainties. surf P sition, and relative humidity of water at the surface 4. RESULTS RHsurf as shown in Figure4. We tested plausible values for these conditions for a terrestrial planet thought 4.1. Detecting a Haze Layer to potentially host water: Tsurf ∈ [250 K, 400 K], −2 2 We simulated the transmission spectra for an Earth- Tstrat ∈ [150 K, 225 K], psurf ∈ [10 atm, 10 atm], −1 −1 like planet with H2SO4-H2O hazes for a large range of RP ∈ [0.25 R⊕, 1.6 R⊕], µ ∈ [28 g mol , 44 g mol ], 12 Loftus, Wordsworth, & Morley

Table 1. Model inputs

parameter limiting value - Sun-like (M dwarf) best estimate detection method ∗ −2 −4 −2 uSO2,surf [kg m ] 2.3 × 10 2.3 × 10 gas ravg [µm] 0.1 (0.2) 1 aerosol −1 wH2SO4 [kg kg ] 0.75 0.75 aerosol

τSO2→H2SO4 [day] 3.4 (2.5) 30 aerosol

τmix [yr] 1 1 aerosol

fSO2,tropopause/fSO2,surf [ ] 1 0.1 aerosol −1 MP MP N˙ S [kg S yr ] 200N˙ S,⊕ 1N˙ S,⊕ aerosol & gas M⊕ M⊕ Parameters for which we plot results in Section4.

85.0

84.8

=1 84.6 =0.1 =0.01 =0.001 84.4 =0.0001 clear transit depth [ppm] 84.2

84.0

0.5 1 5 10 50 wavelength [ m]

Figure 3. Simulated transmission spectra for atmospheres with varying amounts of H2SO4-H2O aerosols, as measured by their vertical path optical depth δ. The atmospheric composition and other planetary parameters are Earth-like. Size of transit depth signal will vary as relative star-to-planet size varies.

−5 and RHsurf ∈ [10 , 1]. Most plausible planetary condi- 4.3. Sulfur in the Atmosphere versus Ocean tions relative to modern-Earth values actually increase We next translated our observable sulfur criteria into the critical amount of atmospheric sulfur required for a critical amount of sulfur in the ocean-atmosphere sys- observation, which makes our hypothesis of the incom- tem. We calculated the distribution of sulfur in an patibility of the observable sulfur stronger. Given the – ocean between aqueous S(IV) species (SO2(aq), HSO3 , lack of sensitivity to planetary conditions, we plot the 2– SO3 ) as a function of pH, assuming S(IV) saturation, remaining results assuming Earth-like conditions (i.e., in Figure5. The fraction of S(IV) stored as SO 2— psurf = 101325 Pa, Tsurf = 288 K, Tstrat = 200 K, the only dissolved S(IV) species in direct equilibrium RP = R⊕, composition of air, and RHsurf = 0.77). with the atmosphere via Equation (18)—exponentially declines as pH increases. For a modern-Earth ocean pH Oceans & the Sulfur Cycle 13

Tsurf psurf 102

101 , S 0 N

/ 10 S N 10 1

10 2 250 300 350 400 103 104 105 106 107

Tsurf [K] psurf [Pa]

Tstrat composition 102

101 , S 0 N

/ 10 S N 10 1

10 2 160 180 200 30 35 40

Tstrat [K] [g/mol]

RP RHsurf 102

101 , S 0 N

/ 10 S N 10 1

10 2 0.5 1.0 1.5 10 6 10 4 10 2

RP [R ] RHsurf

aerosol gas Earth-like value < 10% NS /NS,

∗ Figure 4. Sensitivity of critical number of atmospheric sulfur atoms (NS ) required for observation for both SO2 gas (blue) H2SO4 –H2O aerosols (orange) to planetary conditions of surface pressure (psurf), surface temperature (Tsurf), stratospheric temperature (Tstrat), planetary radius (RP), atmospheric composition, and relative humidity of water vapor at the surface (RHsurf). Modern-Earth-like conditions are marked by a dashed gray vertical line for reference. Solid red boxes indicate regions of high sensitivity (<10% of Earth condition sulfur) to varying planetary parameters. No parameters fall into this regime. Sensitivity to varying atmospheric composition is tested considering only N2 and CO2 in the atmosphere and varying relative abundances between them. The resulting average molar mass (µ) is plotted on the x-axis. In testing sensitivity to RP, we set 0.27 the mass of the planet MP from Valencia et al.(2007)’s scaling relation RP ∝ MP and include effects from varying surface gravities and outgassing rates.

−6 = 8.14, 5.3×10 % of dissolved S(IV) is SO2(aq), 10.3% over the atmosphere as a function of pH with varying – 2– is HSO3 , and 89.7% is SO3 . total ocean mass. The storage capacity of the ocean From the distribution of S(IV) species, we then calcu- linearly increases with increasing ocean mass and expo- lated the expected ratio of S(IV) sulfur in the atmo- nentially increases with increasing ocean pH. For Earth sphere (SO2) to S(IV) sulfur in the ocean (SO2(aq), ocean pH and mass, the ratio of atmospheric to oceanic – 2– −9 HSO3 , SO3 ), again assuming saturation of aque- S(IV) is 2.13 × 10 . (Note that this ratio is not actu- ous S(IV) and atmosphere-ocean equilibrium. Figure ally observed in the modern ocean as the assumption of 6 shows the preferential storage of S(IV) in the ocean 14 Loftus, Wordsworth, & Morley

100 pHs and total masses below this line, observable atmo- spheric sulfur is possible. Above this line, observable sulfur grows increasingly unlikely.

10 1 Low pH is most favorable for observable atmospheric sulfur in our results, but cations from surface weathering can act to buffer pH and likely maintain a pH near neu- tral (Grotzinger and Kasting 1993), particularly in low 2 10 water content regimes with lots of exposed land. Empir- Fraction Total Ocean S(IV)

SO2(aq) ically, paleo-pH estimates for both Earth and Mars seem

HSO3 2 to favor such a near-neutral regime (e.g., Halevy 2013; SO3 10 3 Grotzinger et al. 2014). From these considerations, we 2 4 6 8 10 12 14 pH choose pH = 6 to report characteristic ocean sizes lead- ∗ ing to observable atmospheric sulfur, given τS(IV) = 0.1 Figure 5. Distribution of aqueous S(IV) species SO2(aq) – 2– years. We also choose, somewhat arbitrarily, to de- (dark blue), HSO3 (medium blue), and SO3 (light blue) −3 as a function of pH from the reactions (19)-(20). Only fine significant surface liquid water as 10 Earth ocean SO2(aq) is directly in equilibrium with the atmosphere. masses or a global equivalent ocean layer of 2.75 m on an Earth-sized planet. For context, on Earth today, this amount of water is equivalent to about one third of the 102 Mocean = 0.001 M ocean Mediterranean Sea (Eakins and Sharman 2010). Mocean = 1 M ocean 10 1 Figure7 shows τ ∗ versus ocean parameters for ob- Mocean = 1000 M ocean S(IV) 10 4 serving SO2 with our best-guess parameter values. For −3 10 7 surface liquid water content greater than 10 Earth

10 10 ocean masses, observable SO2 with reasonable model pa- rameters requires τ ∗ 10 years for even the lowest 10 13 S(IV) & ∗ pHs most favorable for SO2 buildup and τ > 10,000 10 16 S(IV) Atmosphere S / Ocean years for pH > 6. Such long decay times are incompat- 19 10 ible with present highest quoted values for decay in the 10 22 literature, which are on the order of years (Ranjan et al. ∗ 2 4 6 8 10 12 14 2018). At pH = 6 and τS(IV) = 0.1 years, observable pH −9 SO2 requires an “ocean” of less than 1 × 10 Earth’s

Figure 6. The ratio of S in SO2 in the atmosphere compared ocean mass or a global equivalent layer of less than 3 to S in S(IV) in the ocean from NS(IV),oc and NS,atm given µm. in Equations (25) and (23), respectively, versus ocean pH. ∗ Figure8 shows τS(IV) versus ocean parameters for observing an H2SO4 –H2O haze layer with our best S(IV) saturation is violated because of the instability of guess parameter values. For surface liquid water content aqueous S(IV).) greater than 10−3 Earth ocean masses, observable haze formation with reasonable model parameters requires ∗ ∗ 4.4. Observable Sulfur versus Ocean Parameters τS(IV) & 1 year for all pHs and, again, τS(IV) >10,000 years for pH> 6. Again, these timescales are much, Finally, we look at how the presence and character- much longer than any τ ∗ estimates currently present istics of an ocean shape sulfur observability. First, we S(IV) in the literature. At pH = 6 and τ ∗ = 0.1 years, ob- calculated conditions for atmospheric sulfur observabil- S(IV) −8 ity for a range of ocean pHs and masses using the best- servable haze requires an ocean of less than 2.5 × 10 guess model parameters given in Table1. Then, we cal- Earth’s ocean mass or a global equivalent layer of less culated these conditions using the limiting parameters. than 68 µm. ∗ For all inputs, we plot contours of the critical timescale Figures9 and 10 show τS(IV) versus ocean parameters ∗ for observing SO2 and observing a haze layer, respec- for S(IV) decay (τS(IV)) necessary to have enough sulfur in the atmosphere-ocean system to sustain observable tively, with our limiting parameter values. At pH = 6 ∗ and τ = 0.1 years, observable SO2 with these most SO2 or an observable H2SO4 –H2O aerosol layer versus S(IV) ocean parameters of pH and mass. From present aque- stringent parameters still requires an ocean of less than −5 ous redox sulfur chemistry experimental results, we set 2 × 10 Earth’s ocean mass or a global equivalent layer τ ∗ = 0.1 years ≈ 1 month (white contour) as a rea- less than 5.5 cm. We calculate that at pH = 6 and S(IV) ∗ sonable timescale for aqueous S(IV) decay. For ocean τS(IV) = 0.1 years, an observable haze layer for a planet Oceans & the Sulfur Cycle 15

100 modern Earth ocean 103

10 2 1

] 10 n a e c o

M 4

[ 10 1 s 10 n a e c observable SO o 2 6

h 10 increasingly unlikely t r 10 3 a E

#

10 8 10 5 global equivalent ocean layer [m] observable SO2 possible 10 10 2 4 6 8 10 12 14 pH

2 1 0 1 2 4 10

log10( S(IV) [yr])

Figure 7. Contours of the critical lifetime of aqueous S(IV) (sulfur in redox state +4, in equilibrium with atmosphere) τS(IV)∗ for observable mixing ratios of SO2 versus ocean pH and mass (in Earth ocean masses). Model results are shown for the best-guess model parameters described in the text. The white contour indicates a reasonable timescale for aqueous S(IV) decay. The dashed gray lines indicate ocean parameters of interest (from a reasonable pH limit of 6 and a low-liquid-water threshold of 0.001 M⊕ocean). around an M-dwarf star requires an ocean of less than input, often physically inconsistent with each other (e.g., 1.3 × 10−3 Earth’s ocean mass or a global equivalent extremely high sulfur outgassing levels would not be con- layer of 3.6 m; around a Sun-like star gives an ocean sistent with extremely small aerosol particles microphys- of less than 1.5 × 10−3 Earth’s ocean mass or a global ically). These limiting parameters are intended to push equivalent layer of 4.1 m. our model to its limits given the breadth of our unknown parameters, rather than just presenting likely values in- 5. DISCUSSION formed by predominantly Earth-based Solar System in- 5.1. Model Uncertainties formation. The incompatibility of observable SO2 to be- low our threshold of significant liquid water by almost Robustly establishing sustained high trace mixing ra- two orders of magnitude and the incompatibility of ob- tios of SO2 and H2SO4 –H2O haze as indicators of lim- servable H2SO4 –H2O aerosols to very near our thresh- ited surface liquid water will require experimental con- old of significant liquid water for these limiting condi- straints on S(IV) decay pathways and kinetics. Bet- tions place the extremely strong constraints on surface ter theoretical constraints on the upper bounds of sul- liquid water for our best-guess model parameters into fur outgassing rates and lower bounds of ocean pHs in a larger context. Further, many of these model param- water-limited regimes will also improve the robustness of eters will be more constrainable for individual systems these newly proposed observational constraints on sur- with observations. Stellar spectrum observations would face liquid water. help constrain the timescale of SO2 to H2SO4 conversion However, in accounting for these poorly constrained τSO →H SO , and observable stellar properties like rota- inputs, we have concocted a worst-case scenario for each 2 2 4 16 Loftus, Wordsworth, & Morley

100 modern Earth ocean 103 10 1 102 10 2

] 1 n 10 a e

c 3

o 10 100 M [ 4 s 10 n 1 a 10 e

c 5

o 10 2 h 10 t r

a 10 6 observable H SO -H O

E 2 4 2 haze increasingly unlikely 10 3 # 7 10 observable

4 global equivalent ocean layer [m] H2SO4-H2O 10 10 8 haze possible 10 5 10 9 2 4 6 8 10 12 14 pH

2 1 0 1 2 4 10

log10( S(IV) [yr])

Figure 8. Contours of the critical lifetime of aqueous S(IV) τS(IV)∗ for the formation of an observable H2SO4 –H2O haze layer versus ocean pH and mass (in Earth oceans). Model results are shown for the best-guess model parameters described in the text. tion rate would help constrain stellar age, which would Sun-like stars to evolve toward more oxidized atmo- help place limits on the evolution of outgassing flux N˙S. spheric conditions, given M-stars’ extended high EUV Though in this paper we have emphasized the bene- and UV flux period for their first gigayear of main se- fits of using a simple model for our immediate hypoth- quence life (Shkolnik and Barman 2014) and the conse- esis test, in the future a hierarchy of models of vary- quent higher potential for H2O dissociation, H2 escape, ing complexities will be useful. Future work employing and O2 buildup (Luger and Barnes 2015; Tian and Ida more complicated photochemistry, microphysics, aque- 2015; Wordsworth et al. 2018). Depending on plane- ous chemistry, and interior dynamics models will allow tary age and thermal evolution, this O2 may be simply for more detailed evaluations of the constrainability of maintained in the atmosphere, or it may be absorbed surface liquid water from oxidized atmospheric sulfur into the mantle during a magma ocean phase and in- observations in specific planetary scenarios. Such work fluence the oxidation state of the secondary outgassed would be particularly useful if it were combined with im- atmosphere, but either way the planet is driven toward proved experimental constraints on key reaction rates in a more oxidized1 atmosphere (Wordsworth et al. 2018). the atmosphere and ocean. (Planets with Sun-like host stars can also undergo this process, although in this case its effectiveness is likely 5.2. Oxidation State of the Atmosphere

Currently, the proposed atmospheric sulfur anti-ocean 1 We specify that we are referring here to bulk changes in atmo- signatures are limited in scope to oxidized atmospheres. spheric redox state as opposed to purely photochemical production Theoretical predictions of the redox evolution of planets of O2 (e.g., Tian et al. 2014; Domagal-Goldman et al. 2014), which has been demonstrated to be unlikely given physically motivated orbiting M dwarfs (our most observable targets) sug- planetary conditions (Harman et al. 2018a). gest such planets are more likely than those orbiting Oceans & the Sulfur Cycle 17

100 modern Earth ocean 103

10 1 2

] 10 n a e

c 2 o 10

M 1 [

10 s n

a 10 3 e c observable SO o 2 0 10

h increasingly unlikely t r

a 10 4 E

# 10 1

10 5 global equivalent ocean layer [m] observable SO2 possible 10 2

10 6 2 4 6 8 10 12 14 pH

2 1 0 1 2 4 10

log10( S(IV) [yr])

Figure 9. Contours of the critical lifetime of aqueous S(IV) τS(IV)∗ for the formation of an observable H2SO4 –H2O haze layer versus ocean pH and mass (in Earth oceans). Model results are shown for the limiting set of model parameters described in the text.

M-dwarf Sun-like 0 10 10 modern Earth ocean modern Earth ocean

4 ] n a e c

o 1 10 2 ) ] r M y [ [

) s V n observable I ( a 1 S

e H2SO4-H2O haze (

c observable 0

o increasingly 1 H2SO4-H2O haze g h unlikely t

increasingly o r 2 0 l a 10 unlikely E

# observable observable H2SO4-H2O 1 haze H2SO4-H2O haze possible possible 2 10 3 2 4 6 8 10 12 14 2 4 6 8 10 12 14 pH pH

Figure 10. Contours of the critical lifetime of aqueous S(IV) τS(IV)∗ for the formation of an observable H2SO4 –H2O haze layer versus ocean pH and mass (in Earth oceans) for a planet around an M dwarf (left) and Sun-like star (right). Model results are shown for the limiting set of model parameters described in the text. 18 Loftus, Wordsworth, & Morley more dependent on the composition of the planet’s at- We tested the ability to distinguish both low-lying wa- mosphere (Catling et al. 2001; Wordsworth and Pierre- ter clouds and higher ice clouds (with Earth-like char- humbert 2013; Wordsworth and Pierrehumbert 2014).) acteristics) from an H2SO4 –H2O haze layer, but even We can reasonably expect to encounter the oxidized at our assumed 100% cloud coverage, the H2SO4 –H2O planets that these methods apply to. Regardless, the haze is clearly distinguishable from H2O clouds; the study of the compatibility of buildup of sulfur gas and transit spectrum is probing higher optical depths than sulfur aerosol formation with liquid water could be ex- expected lower cloud peak heights, and even the higher tended to reduced atmospheres (featuring H2S gas and ice clouds are too low to significantly flatten the transit S8 aerosols) after better experimental characterization spectrum. The latter two alternative spectra-flattening of the photochemical reactions that produce S8 and the candidates—S8 and photochemical haze—require reduc- removal rates of associated dissolved products of H2S. ing atmospheres to form. Identification of an atmo- Observationally determining the general oxidation sphere as oxidizing, as described in the preceding sec- state of a planet’s atmosphere will be possible from tion, strongly disfavors these species’ formation. Dis- transit spectra in many cases. H2-dominated atmo- tinguishing H2SO4-H2O aerosols from S8 aerosols that spheres, which are strongly reducing, are identifiable form in reduced atmospheres could also be possible from from their extremely high scale heights due to low av- a distinct spectral feature: S8 aerosols’ radiative proper- erage molecular mass. CO2 and CH4 both have strong ties transition sharply between 0.3 µm and 0.5 µm from spectral features and have the potential to be identified dominantly attenuating light via absorption to scatter- even when not dominant atmospheric gases (Lincowski ing (Hu et al. 2013); H2SO4 –H2O aerosols do not ex- et al. 2018). While these carbon-bearing species can co- hibit this feature. exist to some extent, in terrestrial atmospheres, CO2 is Organic photochemical hazes are an active research the dominant carbon molecule in oxidized atmospheres topic (e.g., H¨orstet al. 2018), but many studies sug- and CH4 or CO in reduced atmospheres (Hu et al. 2012). gest that they require CH4/CO2 ratios & 0.1 (DeWitt Measuring CO2-to-CH4 (or CO) ratios can thus help to et al. 2009). Spectra indicating significant CO2 and constrain an atmosphere’s redox state. the absence of substantial mixing ratios of CH4 would therefore further disfavor organic photochemical haze as the spectra-flattening agent. Additionally, organic photochemical hazes form as fractal aggregates (Bar- 5.3. Identifying Haze as H2SO4 –H2O Nun et al. 1988) while H SO -H O aerosols are spher- Identifying haze particles as H SO –H O aerosols is 2 4 2 2 4 2 ical (Knollenberg and Hunten 1980). These distinct challenging but tractable. While we leave explicit mod- shapes have different radiative properties (Wolf and eling of haze composition retrieval with stellar noise and Toon 2010), which also have the potential to be recov- specific instrument systematics to future work, we dis- ered via inverse modeling (Ackerman and Marley 2001). cuss the basic logistics of H2SO4 –H2O identification here. 5.4. Life’s Impact on the Sulfur Cycle H2SO4-H2O aerosols are only weakly absorbing at vis- ible wavelengths, so Mie scattering dominates their spec- We have neglected the influence of life on the sulfur tral effects. They therefore tend to lack distinctively cycle throughout this paper. Of course, constraining characteristic spectral fingerprints (Hu et al. 2013). Our liquid water abundance is in the pursuit of finding life simulated transit spectra tests of aerosol cutoff height beyond Earth, so we would be remiss not to address sensitivity suggest that if the aerosols were to extend life’s influence on the sulfur cycle as we have presented it throughout much of the otherwise optically thin upper here. The most important direct effect would be sulfur- atmosphere (& 5 scale heights), H2SO4 –H2O features consuming life’s capacity to exchange redox states of could become identifiable. Such high extents would aqueous sulfur not expected from basic redox reactions seem to be disfavored from H2SO4 photochemical pro- (Johnston 2011; Kharecha et al. 2005). The thermody- duction and SO2 vertical transport considerations, but namic instability of aqueous S(IV) species makes them more detailed photochemical modeling and simulated re- an attractive microbial food source, so even if S(IV) is trievals are required to determine whether this direct the waste product of one organism’s metabolism, it is identification possibility is actually feasible. Regardless, likely to be rapidly consumed again and converted back H2SO4-H2O aerosols still have distinct radiative and for- to another redox state. The largest concern for our pic- mation properties when compared to other key spectra- ture is the potential for metabolic chains to produce flattening candidates: water clouds, organic photochem- dissolved H2S species, which will be in equilibrium with ical hazes, and elemental sulfur hazes. atmospheric H2S via Henry’s law, that could be oxidized Oceans & the Sulfur Cycle 19 to SO2 in the atmosphere and thus yield a new, unac- planet’s ability to sustain an optically thick H2SO4 –H2O counted source of SO2. However, this process would haze layer or a high trace mixing ratio of SO2 gas. De- serve as an effective recycling term of sulfur that would tectable levels of both H2SO4 –H2O aerosols and SO2 be a fraction of outgassing. As a less than order of gas require SO2 in the upper atmosphere, but the pres- magnitude effect, this recycling is not likely to impact ence of an ocean restricts the availability of SO2 in the the conclusions of our study, and thus we do not expect atmosphere. For expected ocean pHs, exponentially these proposed liquid water constraining methods to be more SO2 is stored in the ocean than in the atmosphere invalidated by the presence of life. We also neglect the because of basic chemical properties of aqueous SO2. possibility of intelligent life modifying its environment Within the ocean, the dissolved products of SO2 are via sulfur products (e.g., Caldeira et al. 2013); we leave thermodynamically unstable and thus short-lived. Re- coupled ecosystem-sulfur cycle studies as an intriguing cent outgassing must supply both the SO2 present in topic for future investigation. the atmosphere necessary for observation and the ac- companying amount of aqueous sulfur implied by the 5.5. Extensions to Observational Techniques beyond size of the ocean. Transmission Spectroscopy Via a quantitative model of this wet, oxidized sul- fur cycle, we have shown that neither observable Finally, we have focused our efforts in this paper on H SO –H O haze layers nor observable levels of SO observations of the sulfur cycle via transmission spec- 2 4 2 2 are likely compatible with significant surface liquid wa- troscopy; however, our analysis could easily be extended ter ( 10−3 Earth ocean masses). Despite the uncer- to other observational techniques, notably reflected light & tainties involved in modeling exoplanet processes, this spectroscopy given our interest in temperate planets. incompatibility seems to persist even in the most ex- The impact of different observational techniques is in treme physical conditions to promote SO buildup and estimating the critical atmospheric sulfur mass that be- 2 haze formation. Thus, we propose the observational comes observable. The technique of interest supplies detection of H SO –H O haze and SO gas as two new a critical mass path u∗ or a critical aerosol optical 2 4 2 2 ∗ constraints on surface liquid water. depth δ at which SO2 or H2SO4 –H2O aerosols, re- spectively, become observable. Once this calculation is The code for our sulfur cycle model is available at https: complete, evaluating the feasibility of atmospheric sulfur //github.com/kaitlyn-loftus/alien-sulfur-cycles. This buildup for a given amount of surface liquid water will work was supported by NASA grants 80NSSC18K0829 be straightforward using our open-source sulfur model. and NNX16AR86G. KL thanks Matthew Brennan, Jun- jie Dong, David Johnston, and Itay Halevy for helpful 6. CONCLUSION discussions on various aspects of sulfur chemistry. The The presence of liquid water on an oxidized planet authors also thank James Kasting for a productive re- strongly influences its sulfur cycle—particularly the view.

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