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Harrison Nicholls

Publications and source records attributed to Harrison Nicholls.

At least 19 recordsLinked to original sources

Evolutionary pathways toward survival of a thick CO2- or SO2-rich atmosphere on the lava world TOI-561 b

Rocky planets evolve through the exchange of volatiles between their interiors and atmospheres, an interplay still poorly constrained by observations. Remarkably, highly irradiated ultrashort-period (USP) exoplanets may offer a window into this exchange -- some retain low bulk densities compatible with volatile-rich envelopes surrounding rocky interiors, indicating possible secondary atmospheres. TOI-561 b is a prime example, with a bulk density of $4.3\pm0.4$ g cm$^{-3}$ and recent JWST observations favoring a thick volatile atmosphere overlying a dayside magma ocean. Here, we investigate the evolutionary pathways allowing TOI-561 b to retain a substantial atmosphere over gigayears using the PROTEUS coupled interior--atmosphere framework. We explore different core radius fractions, Bond albedos, atmospheric escape efficiencies, mantle redox states, and initial C--H--O--N--S volatile inventories, under in situ evolution and late inward migration. Over half of our simulations leave a bare interior too dense to match observations. Successful cases favor a volatile-rich origin ($\lesssim200$ Earth oceans of hydrogen, S/H $\le10$, and N/H $\le1$), an oxidized mantle ($f$O$_2 \gtrsim \mathrm{IW}+4$), a small iron core ($\le 0.40$ for the core radius fraction), and low escape efficiency ($\epsilon \lesssim 10^{-3}$) in the hydrodynamic escape regime. At present, TOI-561 b is consistent with a global magma ocean beneath a thick (surface pressure $\approx 10^{3}$--$10^{4}$ bar), high mean molecular weight atmosphere ($38$--$60$ g mol$^{-1}$). Two archetypes emerge, differentiated by bulk sulfur content: a CO$_2$-dominated and an SO$_2$-dominated atmosphere. Migration is viable but not required to reproduce the observations. Our study illustrates how interior--atmosphere coupling governs atmospheric retention on irradiated rocky planets.

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A Highly Reflective Atmosphere on the Lava World TOI-561b Revealed by JWST/NIRSpec Phase Curve

Ultra-short period (USP) rocky planets are expected to be depleted of any substantial gaseous envelope due to the intense irradiation they receive from their host star, making the recent detection of an atmosphere around TOI-561~b particularly surprising. That finding was based on the planet's bulk density and dayside emission spectrum, but full-orbit phase curve observations offer a more comprehensive way to constrain the presence and characteristics of a planet's atmosphere. In this paper, we map TOI-561~b's 3-5~$\mu$m emission using JWST/NIRSpec multi-orbit spectroscopic phase curves, explicitly accounting for the curvature of the out-of-eclipse baseline and possible hotspot offsets. From a simple energy balance argument as well as comparing to general circulation models, we find the phase curve observations are best explained with high Bond albedo and moderate global heat transfer. Our 37-hour continuous observation provides a long baseline that allows us to model stellar granulation, the planetary phase curve, and dayside emission simultaneously, effectively disentangling these signals and yielding a dayside emission spectrum that is more robust against stellar variability and consistent with previous eclipse-only fits. Using general circulation model outputs, we constrain where clouds can plausibly form and test candidate compositions, finding that silicate clouds, such as SiO$_2$ and MgSiO$_3$, can form on the dayside near the terminator and explain the observed albedo. Our findings confirm that TOI-561~b appears to have a global reflective atmosphere, suggesting exchange of volatiles with the interior to maintain it.

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Constraining the lives and times of exoplanets through evolutionary Bayesian retrievals

Static retrieval frameworks are leading tools for interpreting exoplanet observations, yet time-independent modelling leaves them prone to degeneracy and unable to resolve exoplanets' histories. The compositions and structures of surveyed super-Earth and sub-Neptune sub-populations remain unclear, but are shaped by physics acting across Gyr timescales. Interpreting these planets as static non-evolving snapshots allows multiple degenerate scenarios to explain their observed properties. We develop a generalised parameter retrieval framework, built on asynchronous Bayesian optimisation to efficiently dispatch a multi-physics forward-model, resolving exoplanets' evolving properties from their initial magma ocean conditions to the present day. By building Bayesian retrievals into the PROTEUS framework, sensitive coupled interior-atmosphere interactions are naturally resolved and interpretations are constrained to physically permissible scenarios. We test evolutionary retrievals with three exoplanet prototypes: a young sub-Neptune, an older super-Earth, and a warm terrestrial planet - representative of the surveyed exoplanet population. Evolutionary retrieval jointly infers their mantle redox conditions, metallic core fractions, and early volatile inventories from spectroscopically accessible observables. Some scenarios remain subject to well-established degeneracies between core fractions and volatile budgets. Terrestrial-mass exoplanets benefit from strong observable-parameter correlations that lift these degeneracies; we recover post-formation volatile inventories with <20 percent error. Exoplanet science is primed for incoming JWST, PLATO, Roman, and ELT data - observations which necessitate careful interpretation. Adoption of time-evolved models lifts interpretive degeneracies, providing the means to understand the deep interiors and lifetime histories of worlds throughout our galaxy.

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Atmospheric evolution through outgassing and escape on young molten rocky exoplanets

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.

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Sulfur photochemistry observationally traces mantle redox states of rocky planets

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 um and at 7.3 / 8.7 um, 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.

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Reflation: redox-driven atmospheric inflation as tracer of super-Earth geochemistry

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 $\sim$60$\%$ 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 $\gtrsim$ 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.

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Coupled atmospHere Interior modeL Intercomparison (CHILI). I. Evolutionary Modelling -- Primordial Magma Oceans of Earth and Venus

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.

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Geophysical and atmospheric implications of $f$O$_{2}$-dependent melting on rocky exoplanets

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 H$_2$-CO-rich atmospheres; oxidized mantles favour thinner H$_2$O-CO$_2$ 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.

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Equifinality of Venus-like CO$_2$ Atmospheres

While Earth locks much of its carbon in its crust as carbonates, Venus retains a comparable carbon inventory almost entirely in its atmosphere as CO$_2$. On Earth, the geological carbon cycle that has produced this vast crustal carbonate inventory is regulated by biology, liquid water, and plate tectonics, which together have stabilised climate over geological timescales. Venus presently lacks all these processes. We test whether Venus's massive CO$_2$ atmosphere is diagnostic of a specific evolutionary pathway by quantifying three routes: primary magma-ocean outgassing, secondary volcanic degassing in a stagnant-lid regime, and remobilisation of crustal carbonates after climate destabilisation. Using a coupled climate--weathering framework, we find that a past habitable Venus could have stored $\sim$20 bar of CO$_2$ as crustal carbonates. Following transition to runaway conditions, crustal heating releases this reservoir over tens of Myr. In stagnant-lid secondary-degassing models with a MORB-like mantle, outgassing reaches only $\sim$25 bar CO$_2$, limited by progressive mantle volatile depletion. However, Venus-like inventories can be achieved through: (i) magmatic carbon enrichment, (ii) increased magmatic delivery to the surface (high extrusion or melt production), and (iii) the recycling of undegassed carbon back into the planet's interior. Primary magma-ocean outgassing can generate $>10^2$ bar CO$_2$, but the retained fraction after early escape remains uncertain. Ultimately, a Venus-like massive CO$_2$ atmosphere is an equifinal outcome and does not uniquely diagnose a temperate past.

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Beyond the mass-radius plane: Integrated radiative-convective and interior structure simulations of the exoplanet continuum

Static structure models, which map mass-radius constraints to bulk planet composition, are frequently used to categorise exoplanets due to their computational efficiency and the high-level insight they offer into planetary properties. However, static structure models typically have simplified atmospheric treatments, which may introduce systematic biases when interpreting the structures - and therefore the climates - of sub-Neptunes and super-Earths. We present a framework for recovering exoplanet properties using static structure models that accounts for necessary physical-chemical complexity in their atmospheres. We produce a comprehensive library of 504,000 exoplanet simulations that unify deep planetary interior structure with radiative-convective-chemical climate calculations. From these models we demonstrate that a planet's envelope mass fraction - a critical parameter to infer - is frequently degenerate with its instellation flux and atmospheric metallicity, and sensitive to the treatment of gravitational acceleration at the mbar level. Such uncertainties have significant implications for inferring planetary processes, as our modelling shows that habitable-zone sub-Neptunes readily host supercritical surfaces or deep magma oceans, despite their temperate irradiation regime. To marginalise over these uncertainties, we introduce a Bayesian retrieval tool that uses our library of self-consistent models. By applying this Bayesian approach to case-studies of pi Men c and TOI-421 b, we show that robust physical interpretations are achievable through whole-planet mass-radius retrievals. While new data from JWST, Ariel, and PLATO will expand our observational horizon, physically-consistent modelling provides the means to transition from categorical interpretations toward a comprehensive picture of the exoplanet continuum.

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Mantle Convection and Nightside Volcanism on Lava World K2-141 b

Ultra-short period lava worlds offer a unique window into the coupled evolution of planetary interior and atmospheres under extreme irradiation. In this study, we investigate the mantle dynamics, nightside volcanism, and volatile outgassing on lava world K2-141 b ($1.54 R_{\oplus}$, $5.31 M_{\oplus}$) using two-dimensional convection models with tracer-based volatile tracking. Our simulations explore a range of interior configurations, including models with and without plastic yielding, basal versus mixed heating, core cooling, and melt intrusion. In models without plastic yielding (i.e. with a strong lithosphere), we find that mantle upwellings form at the substellar and antistellar points, while downwellings form near the day-night terminators at the boundary between the magma ocean and cold, solid nightside. These downwellings facilitate the recycling of crustal material, representing a form of asymmetric, single-lid tectonics. The resulting magma ocean thickness varies from 200 to 300 km depending on the model parameters, corresponding to about 2-3% of the planet's radius. Continuous nightside volcanism produces a basaltic crust and gradually depletes the mantle of volatiles. We find that over a billion years, volcanic eruptions can outgas tens of bars of CO$_{2}$ and H$_{2}$O. We show that even relatively large volcanic eruptions on the nightside produce thermal emission signals of no more than 1 ppm, remaining below the current detectability threshold in thermal phase curves. However, for most models, outgassing rates are increased near the day-night terminators and future studies should assess whether such localised outgassing could lead to atmospheric signatures in transmission spectroscopy.

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Most Rocky Sub-Neptunes are Molten: Mapping the Solidification Shoreline for Gas Dwarf Exoplanets

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 H$_2$-dominated atmospheres ($\mu$<3.8 g mol$^{-1}$), 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 $T_{\rm eff}$) 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 $f{\rm O}_2$ and bulk volatile C/H ratio both influence magma ocean cooling, planets with oxidising mantles and carbon-rich atmospheres are likely to have high mean-molecular weight atmospheres ($\mu$>3.8 g mol$^{-1}$) and are thus outside the scope of this study. Therefore, most detected sub-Neptunes, if they are gas dwarfs, have permanent magma oceans. This result motivates further research into the interactions between molten interiors and overlying atmospheres, and campaigns to identify unambiguous signatures of these interactions.

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Coupled atmospHere Interior modeL Intercomparison (CHILI) Protocol Version 1.0: A CUISINES Intercomparison Project of Magma Ocean Models

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.

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Onset of habitable conditions on the Hadean Earth set by feedback between tides and greenhouse forcing

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 $\texttt{PROTEUS}$ 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 $\sim$30 Myr up to $\sim$500 Myr, sensitive to interior redox conditions. Global radiative equilibrium epochs commonly arise across this range, lasting from $\sim$2 to $\sim$320 Myr, and typically occur from 24 Myr after the Moon-forming impact. Under oxidizing conditions, late-stage H$_2$O degassing promotes melt retention and sustained heating due to its significant contribution to greenhouse forcing. Weak tides increase the atmospheric abundance of H$_2$S and NH$_3$ and deplete CO. Therefore, the feedback between tides and atmospheric forcing induces a disequilibrium signature in the magma ocean atmosphere.

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Volatile-rich evolution of molten super-Earth L 98-59 d

Small low-density exoplanets are sculpted by strong stellar irradiation, but their primordial compositions and subsequent evolution are still unknown. Two often-considered scenarios hold that they formed with rocky interiors and H$_2$-He atmospheres ('gas-dwarfs'), or alternatively with bulk compositions dominated by H$_2$O phases ('water-worlds'). Here, we constrain the possible range of evolutionary histories linking the birth conditions of low-density super-Earth L 98-59 d to recent observations using a coupled atmosphere-interior evolutionary model. We find that the observations can be explained by in-situ photochemical production of SO$_2$ in an H$_2$ background, indicative of a chemically-reducing mantle and substantial (1.8 mass pct.) early sulfur and hydrogen content, inconsistent with both the gas-dwarf and water-world scenarios. L 98-59 d's interior comprises a permanent magma ocean, allowing long-term retention of volatiles within its mantle over billions of years, consistent with California-Kepler Survey trends. Our analysis reveals an evolutionary pathway in which planets host volatile-rich atmospheres sustained by long-term magma ocean degassing, shaped by secular cooling, atmospheric erosion and photochemistry. Internal and environmental processes contribute to the observed diversity of super-Earth and sub-Neptune exoplanets.

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AGNI: A radiative-convective model for lava planet atmospheres

It is important that we are able to accurately model the atmospheres of (exo)planets. This is because atmospheres play a central role in setting a planet's thermochemical environment at a given point in time, and also in regulating how it evolves over geological timescales. Additionally, it is primarily by observation of their atmospheres that we are able to characterise exoplanets. There is particular demand for accurate models in the context of so-called lava worlds: planets with molten interiors (or `magma oceans'). AGNI is a Julia program designed to solve for the temperature and radiation environment within the atmospheres of rocky (exo)planets. It leverages a well established FORTRAN code to calculate radiative fluxes from a given atmospheric temperature structure and composition, which -- alongside representations of convection and other processes -- enables an energy-conserving numerical solution for the atmospheric conditions. In contrast to most other numerical atmosphere models, AGNI uses a Newton-Raphson optimisation method to obtain its solution, which enables improved performance and scalability. Our model was specifically developed for use alongside planetary interior models within a coupled simulation framework. However, it can also be applied to scientific problems standalone when used as an executable program; it reads TOML configuration files and outputs figures and NetCDF datasets. AGNI can also function as a software library; it is used in this sense within the Jupyter notebook tutorials of our GitHub repository (https://nichollsh.github.io/AGNI/dev/)

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Absence of a Runaway Greenhouse Limit on Lava Planets

Climate transitions on exoplanets offer valuable insights into the atmospheric processes governing planetary habitability. Previous pure-steam atmospheric models show a thermal limit in outgoing long-wave radiation, which has been used to define the inner edge of the classical habitable zone and guide exoplanet surveys aiming to identify and characterize potentially habitable worlds. We expand upon previous modelling by treating (i) the dissolution of volatiles into a magma ocean underneath the atmosphere, (ii) a broader volatile range of the atmospheric composition including H2O, CO2, CO, H2, CH4 and N2, and (iii) a surface temperature- and mantle redox-dependent equilibrium chemistry. We find that multi-component atmospheres of outgassed composition located above partially or fully-molten mantles do not exhibit the characteristic thermal radiation limit that arises from pure-steam models, thereby undermining the canonical concept of a runaway greenhouse limit, and hence challenging the conventional approach of using it to define an irradiation-based habitable zone. Our results show that atmospheric heat loss to space is strongly dependent on the oxidation and melting state of the underlying planetary mantle, through their significant influence on the atmosphere's equilibrium composition. This suggests an evolutionary hysteresis in climate scenarios: initially molten and cooling planets do not converge to the same climate regime as solidified planets that heat up by external irradiation. Steady-state models cannot recover evolutionary climate transitions, which instead require self-consistent models of the temporal evolution of the coupled feedback processes between interior and atmosphere over geologic time.

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Self-limited tidal heating and prolonged magma oceans in the L 98-59 system

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.

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