Publications

Volatile outgassing from planetary interiors controls the composition of rocky exoplanets' secondary atmospheres. However, observations indicate that disequilibrium processes, such as photochemistry and vertical transport, can strongly alter the chemical structure of Hot Jupiters. Which process dominates under different types of rocky planets, and how outgassing and photochemistry jointly determine the atmospheric composition, remain open questions. Sulfur species are promising tracers of interior-atmosphere coupling because their atmospheric abundances are sensitive to both mantle redox state and stellar irradiation. The PROTEUS planetary interior-atmosphere evolution modelling framework is coupled to two chemical models, FastChem and VULCAN, for post-processed chemistry calculations. We run a grid of planetary evolution simulations spanning diverse mantle redox states, instellation fluxes, and Solar versus M-star host-star spectra. For each case, we compare atmospheric compositions under thermochemical equilibrium, only vertical transport, and vertical transport plus photochemistry. The bulk atmospheric composition remains controlled by the redox state of the mantle and outgassing history, even when disequilibrium chemistry is included. Reduced mantles produce atmospheres rich in H₂, and oxidised mantles are dominated by CO₂. Photochemistry affects the upper atmosphere, strongly depleting neutral volatiles and enhancing radicals, especially for highly irradiated cases. SO₂ is strongly enhanced at intermediate-to-oxidised redox states. Synthetic emission spectra show that photochemical SO₂ can generate absorption features at 4 μm and at 7.3 / 8.7 μm, reaching ~60 ppm and ~100 ppm, before sequentially returning to the outgassed signatures of ~30 ppm and ~50 ppm for the oxidised mantle redox state. These signatures are detectable with JWST, motivating targeted observational campaigns.

Earth and Venus represent two evolutionary outcomes arising from initially molten 'magma ocean' periods, followed by lifetimes of chemical and geophysical divergence. Their physics is common to all rocky planets and is accessible to simulations that adopt coupled interior-atmosphere modelling approaches. Our understanding of planet histories and interpretation of current states is dependent on this modelling, yet existing codes vary in their approximations. Here, we present the first results from the Coupled atmospHere Interior modeL Intercomparison (CHILI) project; benchmarking planetary evolution codes in the context of Earth and Venus to identify key model sensitivities. Our 'nominal' Earth models predict magma ocean solidification timescales within 4 Myr of thermal evolution, and are consistent with empirical constraints on Earth's early history. Venus scenarios exhibit more diverse behaviours where prolonged magma ocean stages can be conditionally sustained for 50 Myr. Cooling timescales correlate with initial hydrogen and carbon budgets, but model-specific treatments of volatile partitioning and vertical energy transport introduce substantial inter-model variance. Different parametrisations of mantle geodynamics, convection, melting curves, rheological properties, and radiative transfer give rise to divergent evolutionary behaviours. Discrepancies in atmospheres generated by magma ocean outgassing underscore these differences, although C-H-O compositions with surface pressures exceeding 100 bar are favoured. This intercomparison identifies critical sensitivities in volatile partitioning, escape processes, mantle viscosity, and melting. Validating these treatments is essential for enabling deep insight into the early histories of the Solar System's terrestrial planets, and for drawing meaningful interpretations from ongoing observational exoplanet campaigns.

The earliest rocky planet atmospheres are shaped by competition between initial volatile inventories and atmospheric escape. On young magma ocean planets, outgassing competes with atmospheric escape, controlling volatile retention and atmospheric evolution. We investigate how atmospheric escape and replenishment via outgassing during magma ocean crystallization shape rocky planet atmospheres. We extend a coupled interior-atmosphere model to simulate rocky planet evolution during the magma ocean era by incorporating an energy-limited atmospheric escape module. Comparing radiative-convective and prescribed-convective atmospheres, we quantify how atmospheric energy transport affects escape. We explore a wide range of orbital separations, escape efficiencies, oxidation states, and initial volatile inventories to identify regimes where sustained magma-ocean outgassing or escape dominates. We estimate atmospheric loss and compositions for young rocky planets around Sun-like and M-dwarf stars over geologic timescales. Atmospheric escape shortens magma ocean lifetimes by weakening greenhouse insulation. Radiative-convective atmospheres reduce solidification timescales compared to purely convective cases. Volatile dissolution into the magma ocean interacts with escape to chemically fractionate the planetary volatile budget over time by retaining more soluble species. For Earth-mass planets, atmospheres survive if loss rates remain moderate. Mantle redox state remains a key control on retained atmospheric composition: high oxygen fugacity (fO₂) yields heavier, H₂O- and CO₂-rich atmospheres, while low fO₂ produces light, H₂- or CO-dominated atmospheres, consistent with previous studies. Orbital separation, initial volatile inventory, and stellar type produce diverse evolutionary pathways, from bare rocky planets to magma oceans with thick atmospheres, ranging from H₂- to SO₂-dominated.

We demonstrate that the redox-sensitivity of mantle outgassing can trigger transient episodes of atmospheric re-inflation in highly irradiated and geochemically-reduced super-Earths, a mechanism we term reflation. Mantle redox governs the outgassing and speciation of CHONS volatiles, setting the background secondary atmospheric composition during extended photoevaporation at highly irradiated conditions. Using simulations of the coupled atmosphere-interior evolution of irradiated super-Earths, we illustrate that reduced mantles close to the iron-wustite buffer initially produce CO-dominated atmospheres. Hydrodynamic escape continuously removes volatiles while outgassing from the melt replenishes the atmosphere with H₂, converted from H₂O dissolved in the underlying magma ocean. This leads to a late-stage transition from C- to H-dominated gas that transiently re-inflates super-Earth atmospheres and decreases their bulk densities by up to ~60% between several hundreds of Myr to Gyr after their formation, prior to complete atmospheric erosion by photoevaporation. In contrast, oxidised mantles, closer to Earth-like geochemistry, strongly buffer their atmospheric composition while exposed to hydrodynamic escape, producing monotonic radius deflation. Reflation events are triggered by geochemically-reduced mantles, intermediate escape efficiencies, high irradiation, and initial water inventories ≳ 5 Earth oceans. This redox-dependent evolutionary divergence hinges on the sensitive feedback between interior and atmospheric evolution serving as a potential tracer of historical geochemical state. Population-level reflation signatures of close-in super-Earths may thus serve as tracers of interior geochemistry and formation conditions.

The geochemical evolution of long-lived magma oceans is strongly regulated by volatile exchange between the molten mantle and the atmosphere. For planets inside the runaway-greenhouse limit, this coupled evolution can persist for billions of years. However, most existing studies assume Earth-like (oxidized) conditions and neglect the influence of redox state on melt thermodynamics and volatile release. We quantified how experimentally derived, oxygen-fugacity-dependent melting curves implemented within the coupled interior-atmosphere framework PROTEUS propagate into the thermal structure, melt fraction, and rheological evolution of rocky exoplanet interiors, applying this to the short-period super-Earth GJ 1132 b. We found strongly non-linear thermal responses to variations in melting curves. In volatile-poor systems, reduced melting curves promote earlier deep-mantle crystallisation relative to oxidised and Earth-like cases, favouring late-stage surface magma oceans sustained by greenhouse warming, while oxidized melting curves maintain higher melt fractions and a vertically extended magma ocean. Reduced mantles produce massive H₂-CO-rich atmospheres; oxidized mantles favour thinner H₂O-CO₂ envelopes. In volatile-rich systems, the interior reaches radiative equilibrium at high melt fractions, sustaining a steady-state global magma ocean in which melting curve variations do not significantly influence solidification timing. This indicates a hierarchical control: volatile inventory and surface oxygen fugacity act as the primary regulators of thermal state, while oxygen-fugacity-dependent melting relations provide a secondary modulation. These contrasting regimes produce distinct atmospheric compositions and formation timescales, offering testable spectral predictions for close-in rocky exoplanets evaluable with forthcoming JWST observations.

Sub-Neptunes are the most common type of detected exoplanet, yet their observed masses and radii are degenerate with several interior structures. One possibility is that sub-Neptunes have silicate/iron interiors and H₂-dominated atmospheres, i.e., they are 'gas dwarfs'. If gas dwarfs have molten interiors, interactions between their magma oceans and atmospheres will produce distinct observational signatures. These signatures may break the degeneracy in interior structure, while providing insight into their interior processes, history, and population trends. We expect all such planets are born molten, but under what conditions do they remain molten today? We use the coupled interior-climate evolution model, PROTEUS, to estimate the 'solidification shoreline': the instellation flux boundary (as a function of stellar T_eff) that separates molten gas dwarfs from solidified ones. Our results show that 98% of detected sub-Neptunes occupy a region of parameter space consistent with their having permanent magma oceans, if they are gas dwarfs. While mantle fO₂ and bulk volatile C/H ratio both influence magma ocean lifetimes, planets with oxidising mantles and carbon-rich atmospheres are unlikely to have radii consistent with the sub-Neptune classification. Therefore, most detected sub-Neptunes (if they are gas dwarfs) have permanent magma oceans.

Spectroscopic characterization of rocky exoplanets with the James Webb Space Telescope has brought the origin and evolution of their atmospheres into the focus of exoplanet science. Time-evolved models of the feedback between interior and atmosphere are critical to predict and interpret these observations and link them to the Solar System terrestrial planets. However, models differ in methodologies and input data, which can lead to significant differences in interpretation. In this paper, we present the experimental protocol of the Coupled atmospHere Interior modeL Intercomparison (CHILI) project. CHILI is an (exo-)planet model intercomparison project within the Climates Using Interactive Suites of Intercomparisons Nested for Exoplanet Studies (CUISINES) framework, which aims to support a diverse set of multi-model intercomparison projects in the exoplanet community. The present protocol includes the initial set of participating magma ocean models, divided into evolutionary and static models, and two types of test categories, one focused on Solar System planets (Earth & Venus) and the other on exoplanets orbiting low-mass M-dwarfs. Both test categories aim to quantify the evolution of key markers of the links between planetary atmospheres and interiors over geological timescales. The proposed tests would allow us to quantify and compare the differences between coupled atmosphere-interior models used by the exoplanet and planetary science communities. Results from the proposed tests will be published in dedicated follow-up papers. To encourage the community to join this comparison effort and as an example, we present initial test results for the early Earth and TRAPPIST-1 b, conducted with models differing in the treatment of energy transport in the planetary interior and atmosphere, surface boundary layer, geochemistry, and the in- and outgassing of volatile compounds.

In the aftermath of the Moon-forming giant impact, the Hadean Earth's mantle and surface crystallized from a global magma ocean blanketed by a dense volatile-rich atmosphere. While prior studies have explored the thermal evolution of such early Earth scenarios under idealized, oxidizing conditions, the potential feedback between tidal heating driven by Earth-Moon orbital forcing and variable redox scenarios have not yet been explored in detail. We investigate whether tidal heating could have prolonged this early magma ocean phase and supported quasi-steady state epochs of global radiative equilibrium: periods of thermal balance between outgoing radiation and interior heat flux. Using the PROTEUS simulation framework, we simulate Earth's early evolution under a range of plausible tidal power densities, oxygen fugacities, and volatile inventories. Our results suggest that feedback between tidal heating and atmospheric forcing can induce substantial variation in magma ocean lifetimes, from ~30 Myr up to ~500 Myr, sensitive to interior redox conditions. Global radiative equilibrium epochs commonly arise across this range, lasting from ~2 to ~320 Myr, and typically occur from 24 Myr after the Moon-forming impact. Under oxidizing conditions, late-stage H₂O degassing promotes melt retention and sustained heating due to its significant contribution to greenhouse forcing.

Small low-density exoplanets are sculpted by strong stellar irradiation but their origin is unknown. Two competing scenarios are that they formed either with rocky interiors and H₂-He atmospheres ('gas-dwarfs'), or instead with bulk compositions dominated by H₂O phases ('water-worlds'). Observations of L 98-59 d have revealed its unusually low density and spectral characteristics, opening a window for disentangling its origin. We constrain the possible range of evolutionary histories linking L 98-59 d's birth conditions to these observations, using a coupled atmosphere-interior modelling framework. Observations are explained by a chemically-reducing mantle and early substantial (>1.8 mass%) sulfur and hydrogen content, inconsistent with both the gas-dwarf and water-world origin scenarios. Observed spectral features are explained by in-situ photochemical production of SO₂ in an H₂ background. L 98-59 d's interior comprises a permanent magma ocean, allowing long-term retention of volatiles within its interior over billions of years. In breaking with the supposed gas-dwarf/water-world dichotomy, we reveal an evolutionary pathway defined by high-molar-mass atmospheres overlying magma oceans, and invite a more nuanced taxonomy of small exoplanets.

Rocky exoplanets accessible to characterisation often lie on close-in orbits where tidal heating within their interiors is significant, with the L 98-59 planetary system being a prime example. As a long-term energy source for ongoing mantle melting and outgassing, tidal heating has been considered as a way to replenish lost atmospheres on rocky planets around active M-dwarfs. We simulate the early evolution of L 98-59 b, c and d using a time-evolved interior-atmosphere modelling framework, with a self-consistent implementation of tidal heating and redox-controlled outgassing. Emerging from our calculations is a novel self-limiting mechanism between radiative cooling, tidal heating, and mantle rheology, which we term the 'radiation-tide-rheology feedback'. Our coupled modelling yields self-limiting tidal heating estimates that are up to two orders of magnitude lower than previous calculations, and yet are still large enough to enable the extension of primordial magma oceans to Gyr timescales. Comparisons with a semi-analytic model demonstrate that this negative feedback is a robust mechanism which can probe a given planet's initial conditions, atmospheric composition, and interior structure. The orbit and instellation of the sub-Venus L 98-59 b likely place it in a regime where tidal heating has kept the planet molten up to the present day, even if it were to have lost its atmosphere. For c and d, a long-lived magma ocean can be induced by tides only with additional atmospheric regulation of energy transport.

Atmospheric energy transport is central to the cooling of primordial magma oceans. Theoretical studies of atmospheres on lava planets have assumed that convection is the only process involved in setting the atmospheric temperature structure. This significantly influences the ability for a magma ocean to cool. It has been suggested that convective stability in these atmospheres could preclude permanent magma oceans. We develop a new 1D radiative-convective model in order to investigate when the atmospheres overlying magma oceans are convectively stable. Using a coupled interior-atmosphere framework, we simulate the early evolution of two terrestrial-mass exoplanets: TRAPPIST-1 c and HD 63433 d. Our simulations suggest that the atmosphere of HD 63433 d exhibits deep isothermal layers which are convectively stable. However, it is able to maintain a permanent magma ocean and an atmosphere depleted in H₂O. It is possible to maintain permanent magma oceans underneath atmospheres without convection. Absorption features of CO₂ and SO₂ within synthetic emission spectra are associated with mantle redox state, meaning that future observations of HD 63433 d may provide constraints on the geochemical properties of a magma ocean analogous with the early Earth. Simulations of TRAPPIST-1 c indicate that it is expected to have solidified within 100 Myr, outgassing a thick atmosphere in the process. Cool isothermal stratospheres generated by low molecular-weight atmospheres can mimic the emission of an atmosphere-less body.

Interactions between magma oceans and overlying atmospheres on young rocky planets leads to an evolving feedback of outgassing, greenhouse forcing, and mantle melt fraction. Previous studies have predominantly focused on the solidification of oxidized Earth-similar planets, but the diversity in mean density and irradiation observed in the low-mass exoplanet census motivate exploration of strongly varying geochemical scenarios. We aim to explore how variable redox properties alter the duration of magma ocean solidification, the equilibrium thermodynamic state, melt fraction of the mantle, and atmospheric composition. We develop a 1D coupled interior-atmosphere model that can simulate the time-evolution of lava planets. This is applied across a grid of fixed redox states, orbital separations, hydrogen endowments, and C/H ratios around a Sun-like star. The composition of these atmospheres is highly variable before and during solidification. The evolutionary path of an Earth-like planet at 1 AU ranges between permanent magma ocean states and solidification within 1 Myr. Recently solidified planets typically host H₂O- or H₂-dominated atmospheres in the absence of escape. Orbital separation is the primary factor determining magma ocean evolution, followed by the total hydrogen endowment, mantle oxygen fugacity, and finally the planet's C/H ratio. Collisional absorption by H₂ induces a greenhouse effect which can prevent or stall magma ocean solidification.

The earliest atmospheres of rocky planets originate from extensive volatile release during magma ocean epochs that occur during assembly of the planet. These establish the initial distribution of the major volatile elements between different chemical reservoirs that subsequently evolve via geological cycles. Current theoretical techniques are limited in exploring the anticipated range of compositional and thermal scenarios of early planetary evolution, even though these are of prime importance to aid astronomical inferences on the environmental context and geological history of extrasolar planets. Here, we present a coupled numerical framework that links an evolutionary, vertically-resolved model of the planetary silicate mantle with a radiative-convective model of the atmosphere. Using this method we investigate the early evolution of idealized Earth-sized rocky planets with end-member, clear-sky atmospheres dominated by either H₂, H₂O, CO₂, CH₄, CO, O₂, or N₂. We find central metrics of early planetary evolution, such as energy gradient, sequence of mantle solidification, surface pressure, or vertical stratification of the atmosphere, to be intimately controlled by the dominant volatile and outgassing history of the planet. Thermal sequences fall into three general classes with increasing cooling timescale: CO, N₂, and O₂ with minimal effect, H₂O, CO₂, and CH₄ with intermediate influence, and H₂ with several orders of magnitude increase in solidification time and atmosphere vertical stratification.