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

Monthly Notices of the Royal Astronomical Society 541:3 (2025), pp. 2566–2584

Authors:

Harrison Nicholls, Claire Marie Guimond, Hamish C. F. C. Hay, Richard D. Chatterjee, Tim Lichtenberg, and Raymond T. Pierrehumbert

Abstract:

Rocky exoplanets accessible to characterization 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 time-scales. 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.

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

Monthly Notices of the Royal Astronomical Society Oxford University Press 541:3 (2025) 2566-2584

Authors:

Harrison Nicholls, Claire Marie Guimond, Hamish CFC Hay, Richard D Chatterjee, Tim Lichtenberg, Raymond T Pierrehumbert

Abstract:

Rocky exoplanets accessible to characterization 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 time-scales. 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.

A geochemical view on the ubiquity of CO2 on rocky exoplanets with atmospheres

Copernicus Publications (2025)

Authors:

Claire Marie Guimond, Oliver Shorttle, Raymond T Pierrehumbert

Abstract:

To aid the search for atmospheres on rocky exoplanets, we should know what to look for. An unofficial paradigm is to anticipate CO2 present in these atmospheres, through analogy to the solar system and through theoretical modelling. This CO2 would be outgassed from molten silicate rock produced in the planet’s mostly-solid interior—an ongoing self-cooling mechanism that should proceed, in general, so long as the planet has sufficient internal heat to lose.Outgassing of CO2 requires relatively oxidising conditions. Previous work has noted the importance of how oxidising the planet interior is (the oxygen fugacity), which depends strongly on its rock composition. Current models presume that redox reactions between iron species control oxygen fugacity. However, iron alone need not be the sole dictator of how oxidising a planet is. Indeed, carbon itself is a powerful redox element, with great potential to feed back upon the mantle redox state as it melts. Whilst Earth is carbon-poor, even a slightly-higher volatile endowment could trigger carbon-powered geochemistry.We offer a new framework for how carbon is transported from solid planetary interior to atmosphere. The model incorporates realistic carbon geochemistry constrained by recent experiments on CO2 solubility in molten silicate, as well as redox couplings between carbon and iron that have never before been applied to exoplanets. We also incorporate a coupled 1D energy- and mass-balance model to provide first-order predictions of the rate of volcanism.We show that carbon-iron redox coupling maintains interior oxygen fugacity in a narrow range: more reducing than Earth magma, but not reducing enough to destabilise CO2 gas. We predict that most secondary atmospheres, if present, should contain CO2, although the total pressure could be low. An atmospheric non-detection may indicate a planet either born astonishingly dry, or having shut off its internal heat engine.

Crustal Controls on Seafloor Weathering and Climate Regulation

(2025)

Abstract:

The upcoming generation of extremely large ground-based telescopes and space observatories promises to transform our understanding of rocky exoplanets within the habitable zones of their stars. Observations from the James Webb Space Telescope are already challenging current models of exoplanetary atmospheres and interiors (e.g., Foley 2024). Conventionally, a habitable zone exoplanet orbits within a circumstellar region where liquid water could potentially exist on its surface (e.g., Hart 1979; Kasting et al. 1993). It is generally assumed that silicate weathering regulates atmospheric carbon dioxide (CO2) to levels supporting liquid water, providing a stabilizing feedback on climate (Walker et al. 1981); otherwise, planetary habitability would be a matter of luck. This negative feedback underpins the concept of the circumstellar habitable zone (CHZ) and may play a critical role in climate regulation on water-bearing, tectonically active rocky exoplanets. Identifying evidence for a carbon cycle on exoplanets and verifying the validity of the habitable zone concept are key objectives for future research (e.g., Bean et al. 2017)—efforts that would benefit from a deeper understanding of the carbonate–silicate cycle. In particular, the interplay between global climate, atmospheric CO2, and silicate weathering rates is not fully understood. While the role of continental weathering in this negative feedback has been extensively studied, seafloor weathering has received comparatively less attention despite its potential to be equally significant. For instance, during the Late Mesozoic—known for its hothouse climate state—seafloor weathering fluxes were comparable in magnitude to those of continental weathering (e.g., Coogan & Gillis 2013). Here, I explore the factors controlling basalt dissolution by applying the more mechanistic weathering model of Maher and Chamberlain (2014) to both the modern and Late Mesozoic upper oceanic crust.The oceanic crust, through its formation, alteration, and subduction, is a key component of this geochemical cycle. Carbon is transferred from Earth’s mantle to surface reservoirs (e.g., the atmosphere and oceans) via volcanic outgassing. Concurrently, basalt dissolution and carbonate precipitation recapture dissolved carbon from seawater, storing it within the oceanic crust. Over geological timescales, subducted tectonic plates carry these carbonates back into the mantle reservoir, ultimately supplying carbon to volcanoes. Nonetheless, the primary controls on seafloor weathering rates remain debated. Most models have historically focused on the dependence of mineral dissolution kinetics on temperature and CO2 concentrations, yet observational data suggest that both kinetic and thermodynamic factors govern global weathering fluxes, underscoring the need for models that can incorporate this dual control. Kinetic weathering models (e.g., Walker et al. 1981) fail to account for the changes in Earth’s weatherability through time (e.g., West et al. 2005). To address this, Maher & Chamberlain (2014) developed a solute transport model that integrates hydrological and tectonic influences and imposes a thermodynamic limit on weathering rates. However, this model has only occasionally been applied to continental weathering in exoplanet climate studies (e.g., Graham & Pierrehumbert 2020, 2024), and its relevance to seafloor weathering remains largely unexplored (Hakim et al. 2021).In this work, I assessed the model’s sensitivity to key parameters by comparing its predictions with observed age-dependent carbon content in the upper oceanic crust (Gillis & Coogan 2011). I then extended the model into two dimensions to represent the evolving age distribution of Earth’s seafloor and examine its impact on global weathering fluxes. Simulations using this supply-limited seafloor weathering model successfully reproduce observed age-related trends in carbon content within Earth’s upper oceanic crust and provide further evidence that over 80% of carbonate formed within 20 Myr of crust formation (Gillis & Coogan, 2011; Albers et al. 2023). This model can also capture the higher CO2 concentrations in Late Mesozoic crust compared to Cenozoic crust. Our results indicate that crustal age, permeability, porosity and fluid flow strongly influence weathering rates. These findings challenge the prevailing view that elevated temperatures primarily drove enhanced carbon uptake during the Late Mesozoic, emphasizing further the importance of incorporating geologic and hydrologic processes into climate models. Consequently, seafloor weathering emerges as a necessary process not only for understanding Earth’s past climate but also for interpreting future observations of potentially habitable rocky exoplanets.

Photochemistry versus Escape in the Trappist-1 planets.

(2025)

Authors:

Sarah Blumenthal, Richard Chatterjee, Harrison Nicholls, Louis Amard, Shang-Min Tsai, Tad Komacek, Raymond Pierrehumbert

Abstract:

Survive or not survive, that is the question of the 500-hour JWST Rocky Worlds DDT Program. Whether a terrestrial planets’ atmosphere can suffer under the intense XUV of its host, or if it completely escapes, these are the questions we explore. Zahnle & Catling (2017) defined the Cosmic Shoreline, but recent observations from JWST reveal airless worlds around M-stars, calling for a refinement of this “receding” shoreline (Pass et al. 2025). M-stars spend a longer time in pre-main sequence, subjecting their orbiting worlds to some higher intensity XUV activity. This complicates our present understanding of this shoreline. Investigating chemical effects of planet-star interactions could be the key to a more complete picture of this shoreline.  We investigate the interplay between photochemistry, mixing, and escape of carbon dioxide atmospheres under intense and mild XUV fluxes as follow on work to both Johnstone et al. (2018) and Nakayama et al. (2022). We expand on this work by adopting thermal structure models from Nakayama et al. (2022) and apply them to identify key chemical pathways for escape. We create a reduced C-O chemical network including neutral and ionic species to identify these pathways. As photochemistry simulations take into account many reactions, these 1D calculations are too computationally expensive to be done in 3D. Although rudimentary at best, the mixing parameter– eddy diffusion term, K_zz, comprises the dynamical element of 1D photochemical simulations. Here, we consider the mixing of photochemical products in competition with escape to explore the chemical pathways of retention and loss. We compare the photochemical model results for active and inactive cases for the Trappist-1 system planets. Then, using the resulting composition-dependent heating and cooling rates for Trappist-1 planets, we assess their propensity for efficient atomic line cooling versus escape. We follow the work of Chatterjee & Pierrehumbert (2024) in this assessment.  Finally, using our pathway analysis, we find an analytical formula for calculating an energy-limited escape boundary for these planets based on composition.  It is important here to note the limitations of 1D work. First, there exists an exchange of rigor between modelling chemistry and dynamics. Insights from this work are ripe for implementation into 3D GCMs, especially in response to incorporating UV-driven processes for thermospheric modelling mentioned in Ding and Wordsworth (2019). Second, interaction with the interior is important in the early phase of planetary formation, i.e., the magma ocean phase. Due to exchange between atmosphere and magma early in the planet’s formation, incorporation with an interior-atmosphere model would better constrain higher pressure chemical abundances. Although this work focuses on the upper atmosphere, extrapolation to the surface environment is a key goal for understanding a planet.  Considering planet-star interaction is imperative for the selection of targets for observation. However, it is also important when considering anomalous detections of atmospheres around planets predicted to not have an atmosphere. This could be a first step in determining an atmosphere as non-primary and/or distinguishing between an airless planet and one with high altitude haze.