arXiv subjects

Paolo A. Sossi

Publications and source records attributed to Paolo A. Sossi.

At least 19 recordsLinked to original sources

arXiv2026

Hydrodynamic escape from the proto-lunar disk and the origin of the Earth-Moon volatile dichotomy

Volatile elements - those that vaporize at low temperatures - are depleted in lunar rocks relative to terrestrial rocks. This systematic chemical depletion is evidence for vaporization and preferential removal of vapor from proto-lunar materials during the high-temperature processes accompanying lunar origin. Despite the robustness of these observations, the physical processes by which proto-lunar vapors were removed after the giant impact are not yet well-understood. Here, we show that toward the end of post-giant impact cooling history, Earth's atmosphere was dominated by carbon species (e.g., CO) and was spatially compact, behaving as a closed system retaining Earth's volatile inventory, whereas the proto-lunar disk atmosphere was dominated by H and H2 and was spatially extended, developing into a hydrodynamic outflow analogous to the solar wind. We find that equilibrium H2 recombination (2H->H2) in a partially-dissociated disk atmosphere produces a nearly isothermal structure, a feature known to activate outflows. The expected outflow was strong enough to propel proto-lunar volatiles from a Roche-interior (r < 3RE) disk out of Earth's gravity field and to establish a cometary tail composed of volatile elements transporting proto-lunar disk volatiles into interplanetary space. The proposed model suggests that the dichotomy in volatile element abundances between the silicate Earth and Moon is a natural outcome of the hydrodynamical behavior of magma ocean atmospheres and that lunar chemical and isotopic volatile abundances are diagnostic of the radial structure of the proto-lunar disk towards the end of its condensation.

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arXiv2026

Super-Earth Interiors Shrink by About 10% as They Crystallise

Super-Earth exoplanets are among the most abundant planets known, yet their bulk densities leave the interior state degenerate. The static structure models used to interpret them, and the interior retrievals built on them, typically describe the cold, solidified end state of an evolution that begins hot and molten. During this magma ocean stage the interior, the outgassed atmosphere, and the surface co-evolve and set the long-term climate and geophysics of super-Earths. We develop and validate a fully coupled model for the structural and thermal evolution of super-Earth exoplanets within the PROTEUS framework, including new and upgraded models of the interior structure, mantle energetics, and volatile outgassing. In volatile-poor super-Earths of 1 to 10 Earth masses, the silicate interior contracts by about 10 % of its molten radius through cooling and crystallisation, nearly independent of planet mass and driven by the thinning silicate shell alone. The solidified radius is set by planetary mass and core fraction, insensitive to the host star, irradiation, and initial thermal state. In contrast, volatile-rich super-Earths at and above about 5 Earth masses may not solidify: their thick outgassed atmospheres throttle the surface heat loss until the interior settles into a deep magma ocean, keeping the planet inflated and limiting the contraction to about half its volatile-poor value. Mantle contraction alone thus shapes the low-mass exoplanet transit population, motivating joint interpretation of atmospheric and geophysical signatures in upcoming exoplanet surveys.

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arXiv2026

Volatile-bearing mineral atmospheres of hot rocky exoplanets as probes of interior state and composition

The atmospheres of hot rocky exoplanets (HREs), should they persist, are products of interactions with underlying magma oceans. Spectra collected by the James Webb Space Telescope (JWST) hint at a CO/CO$_2$-rich atmosphere on the HRE 55 Cancri e, indicative of such a process. Here, we aim to identify diagnostic features that can be used to infer the composition and geochemical state of HREs. We construct a coupled atmosphere-interior model that computes the equilibrium gas speciation in the atmosphere in the system Si-Mg-Fe-O-C-H-S-N-He. The model accounts for both the equilibrium vaporisation of mineral gases and the partitioning of volatile species between the magma ocean and atmosphere. Using a fiducial planet with the properties of 55 Cancri e, we explore a parameter space that spans volatile mass fractions from 0.1 to 10 times that of the Earth, solar- to Earth-like metallicities, and 12 orders of magnitude in oxygen fugacity fO$_2$. We find fO$_2$ to be the major control of the shape of emission and transmission features. The presence of species such as SO$_2$ and the relative intensities of H$_2$O and CO$_2$ features allow to distinguish the origin of the gas, accreted or outgassed, while the atmospheric mass is more challenging to constrain. Inflated HREs, whose densities are compatible with a nebular atmosphere are rare, but a viable explanation for the planet TOI-1408 c. The majority of HREs, including 55 Cancri e, are too dense to be dominated by H$_2$-rich nebular gas yet too puffy for an Earth-like volatile budget, implying modest atmospheres of mixed heritage that are degenerate in fO$_2$, volatile mass and composition. The MIRI observation of 55 Cancri e disfavours oxidised Earth-like and reduced primoridal atmospheres alike, while the NIRCam data remain inconclusive. Future observations at wavelengths beyond 8 $μ$m are key to discerning between potential scenarios.

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arXiv2026

Low-spin ferrous iron suppresses mantle oxidation beyond Earth-like pressures

The Earth's mantle has elevated Fe$^{3+}$ relative to those of other rocky bodies, yet the oxidation- and electronic state of iron at extreme pressures is poorly known. We present in-situ energy-domain synchrotron Mössbauer spectra of $^{57}$Fe-enriched silicate glasses at 298 K from 1 bar to 174 GPa in a diamond anvil cell. Glasses were synthesised with Fe$^{3+}$/[Fe$^{3+}$ + Fe$^{2+}$] from 0.02 $\pm$ 0.02 to 1.00 $\pm$ 0.02, as determined by colourimetry. While pure Fe$^{3+}$-basaltic glass shows minimal changes up to 174 GPa, the spectra of Fe$^{2+}$-peridotitic and basaltic glasses are fit by two doublets, D$_1$ and D$_2$. At 1 bar, their relative intensities are $\sim$92 % and $\sim$8 %, respectively, but the integral area ratio, D$_2$/(D$_1$ + D$_2$), reaches 0.65 by 172 GPa. Because this transition is reversible with pressure and no metallic iron is detected, the D$_2$ feature is Fe$^{2+}$ low spin (LS), whereas D$_1$ is Fe$^{2+}$ high spin (HS). Consequently, the Fe$^{3+}$/[Fe$^{3+}$+Fe$^{2+}$] of planetary mantles reach a maximum near $\sim$40 GPa, before decreasing at higher pressures due to the stabilisation of Fe$^{2+}_{\mathrm{LS}}$. This peak coincides with estimated core-mantle equilibrium on Earth, implying that its uniquely oxidised mantle and habitable state may result from core formation within a Goldilocks pressure range. Secondary atmospheres are predicted to transition from H$_2$-rich for Moon-sized bodies, to CO-rich for Earth-like planets and H$_2$- and CH$_4$-bearing around super-Earths and sub-Neptunes.

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arXiv2026

Homogeneous accretion of the Earth in the inner Solar System

Meteorites are classified as either non-carbonaceous- (NC) or carbonaceous (CC), representing bodies that likely formed in the inner- or outer solar system, respectively. Despite its location in the inner solar system, the Earth is thought to contain either minor- (~6 %) or substantial amounts (~40 %) of outer solar system material. However, because neither interpretation leverages variations among multiple isotopic systems simultaneously, Earth's provenance remains equivocal. Here, we examine variations in 10 nucleosynthetic isotope anomalies among planetary- and meteorite parent bodies to show that the linear extension of an array defined by NC bodies in any two isotopic anomalies always intersects the observed isotopic composition of the bulk silicate Earth to within 1 standard deviation. The Earth therefore formed exclusively from inner solar system material whose composition did not vary over the course of accretion and was, on average, unlike that of any chondrite. Extension of the NC array yields isotopic compositions for Mercury and Venus that are more extreme than for Earth, implying a spatial or temporal gradient during the formation of the terrestrial planets.

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arXiv2026

A chemical perspective on planet formation in reduced systems

Relative abundances of refractory elements in planets are commonly assumed to reflect those of their host stars. However, because elements are classified according to their behaviour in the solar nebula, this implicitly assumes condensation is independent of nebular chemistry, despite evidence to the contrary in chemically reduced systems with high molar carbon-to-oxygen (C/O) ratios. We investigate how variations in stellar C/O ratio and disk pressure modify condensation chemistry and assess the reliability of mapping stellar compositions to planetary building blocks in reduced environments. For a sample of FGK stars with C/O ratios spanning 0.65-0.95 (solar = 0.50), we compute equilibrium phase stability using FactSage over 1900-400 K at total pressures of 1e-2, 1e-4, and 1e-6 bar. Bulk planetesimal compositions are derived using a stochastic accretion framework aggregating condensates from temperature-dependent feeding zones. We identify three distinct condensation regimes: (i) solar-like (C/O < 0.7), (ii) transitional (C/O ~0.7-0.91), and (iii) reduced (C/O > 0.92). Relative to solar sequences, oxygen-bearing silicates condense at lower temperatures in transitional and reduced regimes, while carbides, silicides, and sulfides appear. Bulk planetesimal Fe/Mg, Fe/Si, and Fe/O ratios deviate substantially from host stellar values, producing more diverse rocky building blocks within a single disk. Condensation sequences are not universal across stellar compositions. In reduced disks, elemental ratios commonly treated as refractory may not reliably trace planetary bulk composition, providing potential formation pathways for metal-enriched super-Mercury analogues and C- and S-rich rocky planets.

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arXiv2026

Silane-Methane Competition in Sub-Neptune Atmospheres as a Diagnostic of Metallicity and Magma Oceans

The James Webb Space Telescope is characterising the atmospheres of sub-Neptunes. The presence of magma oceans on sub-Neptunes is expected to strongly alter the chemistry of their envelopes and observable atmospheres. At the magma ocean-envelope boundary (MEB, $>$10 kbar), gas properties deviate from ideality, yet the effects of real gas behaviour on chemical equilibria remain underexplored. Here, we compute equilibrium between magma-gas and gas-gas reactions using real gas equations of state in the H-He-C-N-O-Si system for TOI-421b, a canonical hot sub-Neptune potentially hosting a magma ocean. We find that H and N are the most soluble in magma, followed by He and C. We fit real gas equations of state to experimental data on SiH$_4$, and show that, for a fully molten mantle, SiH$_4$ dominates at the MEB under accreted gas metallicity of 1$\times$ solar, but is supplanted by CH$_4$ at 100$\times$ solar. Lower mantle melt fractions lower both magma-derived Si abundances in the envelope and the solubility of H and He in magma, yielding H$_2$- and He-rich envelopes. Projecting equilibrium chemistry through the observable atmosphere (1 mbar-100 bar), we find that `clouds' of Si-bearing condensates strongly deplete Si-bearing gases, although SiH$_4$ remains key, especially when a solar gas is accreted. SiH$_4$/CH$_4$ and Si/C ratios increase with mantle melt fraction and decrease with accreted gas metallicity. The competition between SiH$_4$ and CH$_4$ is therefore diagnostic of metallicity and presence of magma oceans on sub-Neptunes with equilibrium temperatures below 1000 K. The corollary is that H$_2$- and He-rich, SiH$_4$-deficient and CH$_4$-bearing observable atmospheres may indicate a limited role or absence of magma oceans on sub-Neptunes.

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arXiv2025

Physicochemical Controls on the Compositions of the Earth and Planets

Despite the fact that the terrestrial planets formed from the protoplanetary disk, their compositions show marked departures from that of solar nebula condensates. Metallic cores fix oxygen fugacities ($f$O$_2$s) of the planets to 5 (Mercury) to 1 log units below the iron-wüstite (IW) buffer, orders of magnitude higher than the nebular gas. Their oxidised character is coupled with a lack of volatile elements with respect to the solar nebula. Condensates from a solar gas at different temperatures ($T_0$) have Fe/O (by mass) of 0.93 ($T_0$ = 1250 K) to 0.81 ($T_0$ = 400 K), far lower than that of Earth (1.06). Because the reaction Fe(s) + H2O(g) = FeO(s) + H2(g) proceeds <600 K, temperatures at which most moderately volatile elements (MVEs) have condensed, oxidised planets should be volatile-rich, and vice-versa. That this is not observed suggests that planets did not accrete from equilibrium nebular condensates and/or underwent additional volatile depletion/$f$O$_2$ changes. Indeed, MVEs in small telluric bodies (Moon, Vesta) indicate near equilibrium evaporation/condensation at IW-1 and 1400-1800 K. Volatile-depleted elemental yet near-chondritic isotopes of larger telluric bodies (Earth, Mars) reflect mixing of bodies of variable volatile depletion, overprinted by volatile-undepleted material. From the Cr- and Ti isotopes in the BSE, such undepleted matter has been proposed to be CI chondrites. 6% CI added late to an enstatite chondrite-like proto-Earth would match the Earth. However, because Earth is an end-member in isotopic anomalies of heavier elements, no combination of existing meteorites alone can account for its chemical- and isotopic composition. Instead, the Earth is made partially or essentially entirely from an NC-like missing component. If so, the oxidised-, yet volatile-poor nature of inner solar system bodies, including Earth and Mars, is intrinsic to the NC reservoir.

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arXiv2025

Diversity of low-mass planet atmospheres in the C-H-O-N-S-Cl system with interior dissolution, nonideality, and condensation: Application to TRAPPIST-1e and sub-Neptunes

A quantitative understanding of the nature and composition of low-mass rocky (exo)planet atmospheres during their evolution is needed to interpret observations. The magma ocean stage of terrestrial- and sub-Neptune planets permits mass exchange between their interiors and atmospheres, during which the mass and speciation of the atmosphere is dictated by the planet's volatile budget, chemical equilibria, and gas/fluid solubility in molten rock. As the atmosphere cools, it is modified by gas-phase reactions and condensation. We combine these processes into an open-source Python package built using JAX called Atmodeller, and perform calculations for planet sizes and conditions analogous to TRAPPIST-1e and K2-18b. For TRAPPIST-1e-like planets, our simulations indicate that CO-dominated atmospheres are prevalent during the magma ocean stage, which, upon isochemical cooling, predominantly evolve into CO2-rich atmospheres of a few hundred bar at 280 K. Around 40% of our simulations predict the coexistence of liquid water, graphite, alpha-sulfur, and ammonium chloride, which are key ingredients for surface habitability. For sub-Neptune gas dwarfs, pressures are sufficiently high (a few GPa) that gas fugacities deviate from ideality, thereby drastically enhancing solubilities. This buffers the total atmospheric pressure to lower values than for the ideal case. These effects conspire to produce CH4-rich sub-Neptune atmospheres for total pressures exceeding around 3.5 GPa, provided H/C is approximately 100x solar and fO2 moderately reducing (3 log10 units below the iron-wustite buffer). Otherwise, molecular hydrogen remains the predominant species at lower total pressures and/or higher H/C. For all planets at high temperature, solubility enriches C/H in the atmosphere relative to the initial composition.

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arXiv2025

Water solubility in silicate melts: The effects of melt composition under reducing conditions and implications for nebular ingassing on rocky planets

Rocky planet atmospheres form and evolve through interactions between the planet's surface and interior. If a growing rocky planet acquires enough mass prior to the dissipation of the nebular gas disk, it can gravitationally capture a `primary' atmosphere dominated by H2. At the same time, these young, rocky bodies are likely to have partial or global magma oceans as a result of the heat from accretion, core formation and radioactive decay of short-lived major element isotopes. During this magma ocean stage, the dissolution of volatile, life-essential elements, such as hydrogen in the form of water or H2, into the magma is critical in determining the extent to which a rocky planet can maintain these elements over time. However, our ability to quantify the amount of hydrogen dissolved in the magma oceans of rocky planets is limited by the lack of experimental constraints on H-bearing species' solubilities at relevant pressure and temperature conditions, including those expected for the early Earth. Here we experimentally determine the solubility of water in silicate melts of various compositions in the Ca-Mg-Al-Si-Fe-O system at a total pressure of 1 bar and temperatures from 1673-1823 K, synthesized in a H2-CO2 gas-mixing furnace. We use Bayesian parameter estimation to derive a robust water solubility law that includes the effects of melt composition and temperature. Using this solubility law, we estimate that ~100 ppm of hydrogen can dissolve into a 1 MEarth planet with a surface pressure of ~300 bars set by accretion of solar-like nebular gas. For rocky planets in general, ingassing of a primary atmosphere may be an important source and initial storage mechanism for hydrogen-bearing species in a planet's interior, provided it grew to a sufficient mass within the lifetime of the solar nebula.

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arXiv2025

Detectability of oxygen fugacity regimes in the magma ocean world 55 Cancri e at high spectral resolution

Ultra-short Period exoplanets (USPs) like 55 Cnc e, hosting dayside magma oceans, present unique opportunities to study surface-atmosphere interactions. The composition of a vaporised mineral atmosphere enveloping the dayside is dictated by that of the surface magma ocean, which in turn is sensitive to its oxygen fugacity ($f$O$_2$). Observability estimations and characterisation of the atmospheric emission of 55 Cnc e have mostly remained limited to low spectral resolution space-based studies. Here, we aim to examine ground-based high-resolution observabilities of a diverse set of mineral atmospheres produced across a grid of mantle $f$O$_2$s varying over 12 orders of magnitude. We assume a Bulk Silicate Earth mantle composition and a substellar dayside temperature of T = 2500K in the near infrared wavelength (NIR) region. This spectral range is often featureless for this class of atmospheres at low-resolution. Coupling our newly developed simulator for synthesising realistic observations from high-resolution ground-based spectrographs (Ratri) to a pre-developed high-resolution cross-correlation spectroscopy (HRCCS) analysis pipeline (Upamana), we find that this array of mineral atmospheres would all be detectable with 11 hours of observing time of the dayside of 55 Cnc e with CARMENES and each individual scenario can be correctly differentiated within 1$σ$. Our analysis is readily able to distinguish between a planet with an Earth-like redox state (with $f$O$_2$ $\sim$3.5 log$_{10}$ units above the iron-wüstite, IW buffer) from a Mercury-like planet ($f$O$_2$ $\sim$5 log$_{10}$ units below IW). We thus conclude that the HRCCS technique holds promise for cataloguing the diversity of redox states among the rocky exoplanetary population.

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arXiv2024

A general machine learning model of aluminosilicate melt viscosity and its application to the surface properties of dry lava planets

Ultra-short-period exoplanets like K2-141 b likely have magma oceans on their dayside, which play a critical role in redistributing heat within the planet. This could lead to a warm nightside surface, measurable by the James Webb Space Telescope, offering insights into the planet's structure. Accurate models of properties like viscosity, which can vary by orders of magnitude, are essential for such studies. We present a new model for predicting molten magma viscosity, applicable in diverse scenarios, including magma oceans on lava planets. Using a database of 28,898 viscosity measurements on phospho-alumino-silicate melts, spanning superliquidus to undercooled temperatures and pressures up to 30 GPa, we trained a greybox artificial neural network, refined by a Gaussian process. This model achieves high predictive accuracy (RMSE $\approx 0.4 \log_{10}$ Pa$\cdot$s) and can handle compositions from SiO$_2$ to multicomponent magmatic and industrial glasses, accounting for pressure effects up to 30 GPa for compositions such as peridotite. Applying this model, we calculated the viscosity of K2-141 b's magma ocean under different compositions. Phase diagram calculations suggest that the dayside is fully molten, with extreme temperatures primarily controlling viscosity. A tenuous atmosphere (0.1 bar) might exist around a 40° radius from the substellar point. At higher longitudes, atmospheric pressure drops, and by 90°, magma viscosity rapidly increases as solidification occurs. The nightside surface is likely solid, but previously estimated surface temperatures above 400 K imply a partly molten mantle, feeding geothermal flux through vertical convection.

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arXiv2024

Impact of oxygen fugacity on atmospheric structure and emission spectra of ultra hot rocky exoplanets

Atmospheres above lava-ocean planets (LOPs) hold clues as to the properties of their interiors, owing to the expectation that the two reservoirs are in chemical equilibrium. Here we consider `mineral' atmospheres produced in equilibrium with silicate liquids. We treat oxygen fugacity ($f$O$_2$) as an independent variable, together with temperature ($T$) and composition ($X$), to compute equilibrium partial pressures ($p$) of stable gas species at the liquid-gas interface. Above this boundary, the atmospheric speciation and the pressure-temperature structure are computed self-consistently to yield emission spectra. We explore a wide array of plausible compositions, oxygen fugacities (between 6 log$_{10}$ units below- and above the iron-wüstite buffer, IW) and irradiation temperatures (2000, 2500, 3000 and 3500 K) relevant to LOPs. We find that SiO(g), Fe(g) and Mg(g) are the major species below $\sim$IW, ceding to O$_2$(g) and O(g) in more oxidised atmospheres. The transition between the two regimes demarcates a minimum in total pressure ($P$). Because $p$ scales linearly with $X$, emission spectra are only modest functions of composition. By contrast, $f$O$_2$ can vary over orders of magnitude, thus causing commensurate changes in $p$. Reducing atmospheres show intense SiO emission, creating a temperature inversion in the upper atmosphere. Conversely, oxidised atmospheres have lower $p$SiO and lack thermal inversions, with resulting emission spectra that mimic that of a black body. Consequently, the intensity of SiO emission relative to the background, generated by MgO(g), can be used to quantify the $f$O$_2$ of the atmosphere. Depending on the emission spectroscopy metric of the target, deriving the $f$O$_2$ of known nearby LOPs is possible with a few secondary occultations observed by JWST.

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arXiv2024

Composition, Structure and Origin of the Moon

Here we critically examine the geophysical and geochemical properties of the Moon in order to identify the extent to which dynamical scenarios satisfy these observations. New joint inversions of existing lunar geophysical data (mean mass, moment of inertia, and tidal response) assuming a laterally- and vertically homogeneous lunar mantle show that, in all cases, a core with a radius of 300$\pm$20 km ($\sim$0.8 to 1.5 % the mass of the Moon) is required. However, an Earth-like Mg# (0.89) in the lunar mantle results in core densities (7800$\pm$100 kg/m$^3$) consistent with that of Fe-Ni alloy, whereas FeO-rich compositions (Mg# = 0.80--0.84) require lower densities (6100$\pm$800 kg/m$^3$). Geochemically, we use new data on mare basalts to reassess the bulk composition of the Moon for 70 elements, and show that the lunar core likely formed near 5 GPa, 2100 K and $\sim$1 log unit below the iron-wüstite buffer. Moreover, the Moon is depleted relative to the Earth's mantle in elements with volatilities higher than that of Li, with this volatile loss likely having occurred at low temperatures (1400$\pm$100 K), consistent with mass-dependent stable isotope fractionation of moderately volatile elements (e.g., Zn, K, Rb). The identical nucleosynthetic (O, Cr, Ti) and radiogenic (W) isotope compositions of the lunar and terrestrial mantles, strongly suggest the two bodies were made from the same material, rather than from an Earth-like impactor. Rb-Sr in FANs and Lu-Hf and Pb-Pb zircon ages point Moon formation close to $\sim$4500 Ma. Taken together, there is no unambiguous geochemical or isotopic evidence for the role of an impactor in the formation of the Moon, implying perfect equilibration between the proto-Earth and Moon-forming material or alternative scenarios for its genesis.

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arXiv2024

Interior Controls on the Habitability of Rocky Planets

No matter how fascinating and exotic other terrestrial planets are revealed to be, nothing generates more excitement than announcements regarding their habitability. From the observation of Mars to present-day efforts toward Venus and the characterization of exoplanets, the search for life, or at least environments that could accommodate life, has been a major drive for space exploration. So far, we have found no other unquestionably habitable world besides Earth. The conditions of the habitability of terrestrial planets have proved elusive, as surface conditions depend on the complex interplay of many processes throughout the evolution of a planet. Here, we review how the interior of a rocky planet can drive the evolution of surface conditions and the atmosphere. Instead of listing criteria assumed to be critical for life, we discuss how the bulk-silicate planet can affect the onset, continuation and cessation of habitability. We then consider how it can be observed and current efforts towards this end.

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arXiv2022

VapoRock: Thermodynamics of vaporized silicate melts for modeling volcanic outgassing and magma ocean atmospheres

Silicate vapors play a key role in planetary evolution, especially dominating early stages of rocky planet formation through outgassed magma ocean atmospheres. Our open-source thermodynamic modeling software "VapoRock" combines the MELTS liquid model (Ghiorso et al., 1995) with gas-species properties from multiple thermochemistry tables (e.g., Chase et al., 1998). VapoRock calculates the partial pressures of 34 gaseous species in equilibrium with magmatic liquid in the system Si-Mg-Fe-Al-Ca-Na-K-Ti-Cr-O at desired temperatures and oxygen fugacities (fO2, or partial pressure of O2). Comparison with experiments shows that pressures and melt-oxide activities (which vary over many orders of magnitude) are reproduced to within a factor of ~3, consistent with measurement uncertainties. We also benchmark the model against a wide selection of igneous rock compositions including bulk silicate Earth, predicting elemental vapor abundances that are comparable (Na, Ca, & Al) or more realistic (K, Si, Mg, Fe, & Ti) than those of the closed-source MAGMA code (with maximum deviations by factors of 10-300 for K & Si). Vapor abundances depend critically on the activities of liquid components. The MELTS model underpinning VapoRock was calibrated and extensively tested on natural igneous liquids. In contrast, MAGMA's liquid model assumes ideal mixtures of a limited set of chemically simplified pseudo-species, which only roughly approximates the non-ideal compositional interactions typical of many-component natural silicate melts. Finally, we explore how relative abundances of SiO and SiO2 provide a spectroscopically measurable proxy for oxygen fugacity in devolatilized exoplanetary atmospheres, potentially constraining fO2 in outgassed exoplanetary mantles.

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arXiv2022

Solubility of water in peridotite liquids and the prevalence of steam atmospheres on rocky planets

Atmospheres are products of time-integrated mass exchange between the surface of a planet and its interior. On Earth and other planetary bodies, magma oceans likely marked significant atmosphere-forming events, during which both steam- and carbon-rich atmospheres may have been generated. However, the nature of Earth's early atmosphere, and those around other rocky planets, remains unclear for lack of constraints on the solubility of water in liquids of appropriate composition. Here we determine water solubility in 14 peridotite liquids, representative of Earth's mantle, synthesised in a laser-heated aerodynamic levitation furnace. We explore oxygen fugacities (fO$_2$) between -1.9 and +6.0 log units relative to the iron-wüstite buffer at constant temperature (2173$\pm$50 K) and total pressure (1 bar). The resulting fH$_2$O ranged from 0 to 0.027 bar and fH$_2$ from 0 to 0.064 bar. Total H$_2$O contents were determined by transmission FTIR spectroscopy from the absorption band at 3550cm$^{-1}$ and applying the Beer-Lambert law. The mole fraction of water in the liquid is $\propto$ (fH$_2$O)$^{0.5}$, attesting to its dissolution as OH. The data are fit by a solubility coefficient of 524$\pm$16 ppmw/bar$^{0.5}$, for a molar absorption coefficient, $ε_{3550}$, of 6.3$\pm$0.3 m$^2$/mol in basaltic glasses or 647$\pm$25 ppmw/bar$^{0.5}$, with $ε_{3550}$ = 5.1$\pm$0.3m$^2$/mol for peridotitic glasses. These solubility constants are 10-25 % lower than those for basaltic liquids at 1623 K and 1 bar. Higher temperature lowers water solubility, offsetting the greater depolymerisation of peridotite melts that would otherwise increase H$_2$O solubility relative to basaltic liquids. Because the solubility of water remains high relative to that of CO$_2$, steam atmospheres are rare, although they may form under oxidising conditions on telluric bodies, provided high H/C ratios prevail.

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arXiv2022

Stochastic accretion of the Earth

Earth is depleted in volatile elements relative to chondritic meteorites, its possible building blocks. The extent of this depletion increases with decreasing condensation temperature, and is approximated by a cumulative normal distribution, unlike that in any chondrite. However, moderately volatile elements, occupying the mid-range of the distribution, have chondritic isotope ratios, contrary to that expected from loss by partial vaporisation/condensation. Here we reconcile these observations by showing, using N-body simulations, that Earth accreted stochastically from many precursor bodies whose variable compositions reflect the temperatures at which they formed. Impact-induced atmospheric loss was efficient only when the proto-Earth was small, and elements that accreted thereafter retain near-chondritic isotope ratios. Earth's composition is reproduced when initial temperatures of planetesimal- to embryo-sized bodies are set by disk accretion rates of (1.08 $\pm$ 0.17) $\times$ 10$^{-7}$ solar masses/yr, although they may be perturbed by $^{26}$Al heating on bodies formed at different times. The model implies a heliocentric gradient in composition and rapid planetesimal formation within $\sim$ 1 Myr, in accord with radiometric volatile depletion ages of Earth.

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