arXiv subjects

Tim Lichtenberg

Publications and source records attributed to Tim Lichtenberg.

At least 37 records · Page 2Linked to original sources

arXiv2026

The Goldilocks problem for detecting water in terrestrial planets: Constraining water abundances in the mid-IR with LIFE

We investigate how well the Large Interferometer for Exoplanets (LIFE) mission concept can detect habitable conditions on exoplanets through the presence of atmospheric water vapor as a proxy for surface oceans. We model the atmosphere of a pre-biotic Earth-like planet across a range of water concentrations, from water-poor to water-rich, with surface partial pressures from 10$^{-7}$ to 1 bar of H$_2$O. We simulate LIFE-like noise at spectral resolutions R = 50 and 100 using LIFEsim and perform Bayesian atmospheric retrievals to determine the technical requirements for LIFE to confirm habitability. We model three vertical water distributions: a vertically constant profile, a Manabe-Wetherald based Earth-like profile, and a diffusion and photochemistry profile to test how the assumed vertical structure influences the retrieved abundances. Clouds are not modeled. We find the ability for LIFE to detect water strongly depends on the vertical profile assumed. LIFE is unable to constrain the highest water cases and provides upper limits on low water planets. For the highest water abundances, absorption features saturate and reduce sensitivity to characterize precise H$_2$O levels. Water vapor is not detectable in any profile modeled for $\leq10^{-6}$ bar in surface water, comparable to Mars. For an Earth-like profile, LIFE could constrain H$_2$O concentrations from $\sim10^{-3}$ to 1 bar, spanning below and above present-day Earth concentrations of 10$^{-2}$ bar. Detectable atmospheric water may imply surface oceans, as water is highly reactive and rapidly removed by surface mineral reactions. Thus, LIFE can characterize water abundances indicative of habitable surface conditions.

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arXiv2026

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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arXiv2026

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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arXiv2026

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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arXiv2026

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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arXiv2026

Water enrichment of forming sub-Neptune envelopes limited by oxygen exhaustion

The interaction between a magma ocean and a primordial atmosphere is increasingly recognized as a key process in shaping planetary envelope compositions. This coupling should strongly influence gas accretion, yet its role during the disk-embedded stage remains poorly constrained. We develop a time-dependent model that couples solid accretion, nebular-gas accretion, and water enrichment and partitioning through magma-atmosphere interactions, along with post-disk thermal evolution and escape. We find that, for super-Earth-mass planets, water production is generally limited by the magma oxygen budget and typically ceases before disk dispersal. Subsequent nebular-gas accretion dilutes the envelope toward hydrogen-dominated compositions, largely independent of the initial magma redox state. This establishes an upper bound on the envelope water fraction -- the oxygen exhaustion limit -- primarily set by the reactive-oxygen inventory and the planet mass. After disk dispersal, degassing increases the water fraction only in Earth-mass planets undergoing strong escape, while super-Earths exhibit little change because surface pressures are hardly affected by escape. Magma-atmosphere coupling alone therefore cannot maintain water-rich envelopes in sub-Neptunes and produces a strong mass-composition relation imposed by the oxygen exhaustion limit. Highly enriched sub-Neptunes would therefore imply additional mechanisms such as late volatile delivery or post-disk giant impacts. The relation between planetary radius and envelope composition offers a means to infer magma properties, providing a pathway to connect present-day observables with early formation histories.

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arXiv2026

Magma ocean interactions can explain JWST observations of the sub-Neptune TOI-270 d

Sub-Neptunes with substantial atmospheres may possess magma oceans in contact with the overlying gas, with chemical interactions between the atmosphere and magma playing an important role in shaping atmospheric composition. Early JWST observations have found high abundances of carbon- and oxygen-bearing molecules in a number of sub-Neptune atmospheres, which may result from processes including accretion of icy material at formation or magma-atmosphere interactions. Previous work examining the effects of magma-atmosphere interactions on sub-Neptunes has mostly been limited to studying conditions at the atmosphere-mantle boundary, without considering implications for the upper atmosphere which is probed by spectroscopic observations. In this work, we present a modeling architecture to determine observable signatures of magma-atmosphere interactions. We combine an equilibrium chemistry code which models reactions between the core, mantle and atmosphere with a radiative-convective model that determines the composition and structure of the observable upper atmosphere. We examine how different conditions at the atmosphere-mantle boundary and different core and mantle compositions impact the upper atmospheric composition. We compare our models to JWST NIRISS+NIRSpec observations of the sub-Neptune TOI-270~d, finding that our models can provide a good fit to the observed transmission spectrum with little fine-tuning. This suggests that magma-atmosphere interactions may be sufficient to explain high abundances of molecules such as H$_2$O, CH$_4$ and CO$_2$ in sub-Neptune atmospheres, without additional accretion of icy material from the protoplanetary disk. Although other processes could lead to similar compositions, our work highlights the need to consider magma-atmosphere interactions when interpreting the observed atmospheric composition of a sub-Neptune.

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arXiv2025

A Thick Volatile Atmosphere on the Ultrahot Super-Earth TOI-561 b

Ultrashort-period (USP) exoplanets -- with $R_p \leq 2~$R$_{\oplus}$ and periods $\leq$1 day -- are expected to be stripped of volatile atmospheres by intense host star irradiation, which is corroborated by their nominal bulk densities and previous eclipse observations consistent with bare rock surfaces. However, a few USP planets appear anomalously under-dense relative to an Earth-like composition, suggesting an exotic interior structure (e.g., core-less) or a volatile-rich secondary atmosphere increasing their apparent radius. Here we present the first dayside emission spectrum of the low-density (4.3$\pm$0.4 g~cm$^{-3}$) USP planet TOI-561 b, which orbits an iron-poor, alpha-rich, $\sim$10 Gyr old thick disk star. Our 3-5 $μ$m JWST/NIRSpec observations demonstrate the dayside of TOI-561 b is inconsistent with a bare-rock surface at high statistical significance, suggesting instead a thick volatile envelope that is cooling the dayside to well below the $\sim$3000 K expected in the bare-rock or thin-atmosphere case. These results reject the popular hypothesis of complete atmospheric desiccation for highly irradiated exoplanets and support predictions that planetary-scale magma oceans can retain substantial reservoirs of volatiles, opening the geophysical study of ultrahot super-Earths through the lenses of their atmospheres.

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arXiv2025

Constraining exoplanet interiors using observations of their atmospheres

Astronomical surveys have identified numerous exoplanets with bulk compositions that are unlike the planets of the Solar System, including rocky super-Earths and gas-enveloped sub-Neptunes. Observing the atmospheres of these objects provides information on the geological processes that influence their climates and surfaces. In this Review, we summarize the current understanding of these planets, including insights into the interaction between the atmosphere and interior based on observations made with the James Webb Space Telescope (JWST). We describe the expected climatic and interior planetary regimes for planets with different density and stellar flux and how those regimes might be observationally distinguished. We also identify the observational, experimental, and theoretical innovations that will be required to characterize Earth-like exoplanets.

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arXiv2025

Identifying rocky planets and water worlds among sub-Neptune-sized exoplanets with the Habitable Worlds Observatory

Astronomers are debating whether the plentiful "sub-Neptune" exoplanets -- worlds a bit larger than Earth but smaller than Neptune -- are predominantly rocky planets, water-rich "ocean worlds," or gas-enshrouded mini-Neptunes. This question is crucial because such sub-Neptune-sized planets are among the most common in our galaxy, yet we have no analog in our own solar system, making them a key to understanding planet formation and diversity. It also directly impacts the search for habitable worlds: larger-than-Earth planets with solid surfaces or oceans could support life, whereas gas-rich mini-Neptunes likely cannot. However, distinguishing these types using only a planet's mass and radius is very challenging, because different compositions can produce similar densities, leaving a world's nature ambiguous with current data. The proposed Habitable Worlds Observatory (HWO), a future NASA flagship telescope, offers a solution. HWO could directly image and spectroscopically analyze starlight reflected from 50~100 sub-Neptunes around nearby stars, aiming to reveal their atmospheric compositions and potential surfaces. Using visible and near-infrared spectroscopy along with sensitive polarimetry, HWO would detect atmospheric gases (such as water vapor, methane, and carbon dioxide) and search for telltale surface signatures, including rock absorption features and the characteristic reflectivity patterns of oceans. By analyzing these signals, we could determine whether sub-Neptunes are large rocky planets or water worlds rather than gas-dominated mini-Neptunes. Crucially, expanding the search beyond Earth-sized planets to include these abundant sub-Neptunes may uncover entirely new classes of potentially habitable worlds, directly advancing HWO's mission to identify and characterize planets that could support life.

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arXiv2025

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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arXiv2025

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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arXiv2025

A Terminology and Quantitative Framework for Assessing the Habitability of Solar System and Extraterrestrial Worlds

The search for extraterrestrial life in the Solar System and beyond is a key science driver in astrobiology, planetary science, and astrophysics. A critical step is the identification and characterization of potential habitats, both to guide the search and to interpret its results. However, a well-accepted, self-consistent, flexible, and quantitative terminology and method of assessment of habitability are lacking. Our paper fills this gap based on a three year-long study by the NExSS Quantitative Habitability Science Working Group. We reviewed past studies of habitability, but find that the lack of a universally valid definition of life prohibits a universally applicable definition of habitability. A more nuanced approach is needed. We introduce a quantitative habitability assessment framework (QHF) that enables self-consistent, probabilistic assessment of the compatibility of two models: First, a habitat model, which describes the probability distributions of key conditions in the habitat. Second, a viability model, which describes the probability that a metabolism is viable given a set of environmental conditions. We provide an open-source implementation of this framework and four examples as a proof of concept: (a) Comparison of two exoplanets for observational target prioritization; (b) Interpretation of atmospheric O2 detection in two exoplanets; (c) Subsurface habitability of Mars; and (d) Ocean habitability in Europa. These examples demonstrate that our framework can self-consistently inform astrobiology research over a broad range of questions. The proposed framework is modular so that future work can expand the range and complexity of models available, both for habitats and for metabolisms.

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arXiv2025

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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arXiv2025

Bioverse: Potentially Observable Exoplanet Biosignature Patterns Under the UV Threshold Hypothesis for the Origin of Life

A wide variety of scenarios for the origin of life have been proposed, with many influencing the prevalence and distribution of biosignatures across exoplanet populations. This relationship suggests these scenarios can be tested by predicting biosignature distributions and comparing them with empirical data. Here, we demonstrate this approach by focusing on the cyanosulfidic origins-of-life scenario and investigating the hypothesis that a minimum near-ultraviolet (NUV) flux is necessary for abiogenesis. Using Bayesian modeling and the \bioverse\ survey simulator, we constrain the probability of obtaining strong evidence for or against this ``UV Threshold Hypothesis'' with future biosignature surveys. Our results indicate that a correlation between past NUV flux and current biosignature occurrence is testable for sample sizes of $\gtrsim$50 planets. The diagnostic power of such tests is critically sensitive to the intrinsic abiogenesis rate and host star properties, particularly maximum past NUV fluxes. Surveys targeting a wide range of fluxes, and planets orbiting M dwarfs enhance the chances of conclusive results, with sample sizes $\gtrsim$100 providing $\gtrsim$80\% likelihood of strong evidence if abiogenesis rates are high and the required NUV fluxes are moderate. For required fluxes exceeding a few hundred erg/s/cm$^2$, both the fraction of inhabited planets and the diagnostic power sharply decrease. Our findings demonstrate the potential of exoplanet surveys to test origins-of-life hypotheses. Beyond specific scenarios, this work underscores the broader value of realistic survey simulations for future observatories (e.g., HWO, LIFE, ELTs, Nautilus) in identifying testable science questions, optimizing mission strategies, and advancing theoretical and experimental studies of abiogenesis.

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arXiv2025

Geodynamics of super-Earth GJ 486b

Many super-Earths are on very short orbits around their host star and, therefore, more likely to be tidally locked. Because this locking can lead to a strong contrast between the dayside and nightside surface temperatures, these super-Earths could exhibit mantle convection patterns and tectonics that could differ significantly from those observed in the present-day solar system. The presence of an atmosphere, however, would allow transport of heat from the dayside towards the nightside and thereby reduce the surface temperature contrast between the two hemispheres. On rocky planets, atmospheric and geodynamic regimes are closely linked, which directly connects the question of atmospheric thickness to the potential interior dynamics of the planet. Here, we study the interior dynamics of super-Earth GJ 486b ($R=1.34$ $R_{\oplus}$, $M=3.0$ $M_{\oplus}$, T$_\mathrm{eq}\approx700$ K), which is one of the most suitable M-dwarf super-Earth candidates for retaining an atmosphere produced by degassing from the mantle and magma ocean. We investigate how the geodynamic regime of GJ 486b is influenced by different surface temperature contrasts by varying possible atmospheric circulation regimes. We also investigate how the strength of the lithosphere affects the convection pattern. We find that hemispheric tectonics, the surface expression of degree-1 convection with downwellings forming on one hemisphere and upwelling material rising on the opposite hemisphere, is a consequence of the strong lithosphere rather than surface temperature contrast. Anchored hemispheric tectonics, where downwellings und upwellings have a preferred (day/night) hemisphere, is favoured for strong temperature contrasts between the dayside and nightside and higher surface temperatures.

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arXiv2024

Reliable Detections of Atmospheres on Rocky Exoplanets with Photometric JWST Phase Curves

The prevalence of atmospheres on rocky planets is one of the major questions in exoplanet astronomy, but there are currently no published unambiguous detections of atmospheres on any rocky exoplanets. The MIRI instrument on JWST can measure thermal emission from tidally locked rocky exoplanets orbiting small, cool stars. This emission is a function of their surface and atmospheric properties, potentially allowing detections of atmospheres. One way to find atmospheres is to search for lower day-side emission than would be expected for a black body planet. Another technique is to measure phase curves of thermal emission to search for night-side emission due to atmospheric heat redistribution. Here, we compare strategies for detecting atmospheres on rocky exoplanets. We simulate secondary eclipse and phase curve observations in the MIRI F1500W and F1280W filters, for a range of surfaces (providing our open access albedo data) and atmospheres on thirty exoplanets selected for their F1500W signal-to-noise ratio. We show that secondary eclipse observations are more degenerate between surfaces and atmospheres than suggested in previous work, and that thick atmospheres can support emission consistent with a black body planet in these filters. These results make it difficult to unambiguously detect or rule out atmospheres using their photometric day-side emission alone. We suggest that an F1500W phase curve could instead be observed for a similar sample of planets. While phase curves are time-consuming and their instrumental systematics can be challenging, we suggest that they allow the only unambiguous detections of atmospheres by night-side thermal emission.

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arXiv2024

Convective shutdown in the atmospheres of lava worlds

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. Future work should consider how atmospheric escape and chemistry modulates the lifetime of magma oceans, and the role of tidal heating in sustaining atmospheric convection

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