Determining the stable phase of the binary rock-ice mixture at extreme conditions is crucial for structure and evolution models. Yet, research into rock-ice interactions at pressure and temperature conditions exceeding those found on Earth remains limited. The discovery of new exoplanets points to some of them having substantial water abundance, implying that the interaction between an overlying layer of ice and the underlying rock would occur under several megabar of pressure. We determine the solvus temperatures for magnesium silicates and water across pressures relevant to the deep interiors of super-Earth to sub-Neptune sized bodies by atomistic simulations. Using density functional theory molecular dynamics simulations, we investigate the miscibility of magnesium silicates (MgSiO₃ and MgO) and water ice (H₂O) up to 8000 K and from 0.3-2 Mbar, using a heat-until-it-mixes approach to determine liquidus conditions. Our findings reveal that MgSiO₃ becomes miscible in H₂O upon melting in the entire pressure range we explored. Surprisingly, we observe a significant depression in the melting point of MgO by over 2000 K in the presence of H₂O, highlighting complex interactions between rock and water at extreme conditions. These findings have implications for structure and evolution models, including those of the deep interiors of the ice giants, as well as for considerations ofplanet habitability.  

How to cite: Kovacevic, T., González-Cataldo, F., and Militzer, B.: Simulations of Rock-Ice Mixtures in the mantles of water-rich planets, Europlanet Science Congress 2024, Berlin, Germany, 8–13 Sep 2024, EPSC2024-97, https://doi.org/10.5194/epsc2024-97, 2024.

Water is expected to be abundant component in planetary interiors, particularly in sub-Neptune planets, whose radii suggest the presence of volatiles in their atmospheres. However, directly observing the precise water mass fraction and water distribution remains unfeasible. In our study, we employ an internal structure code to model planets with high water content and explore potential interior distributions. Departing from traditional assumptions of a layered structure, we determine water and rock distribution based on water-rock miscibility criteria. We model wet sub-Neptunes with an iron core and a homogeneous mixture of rock and water above it. At the outer regions of the planet, the pressure and temperature decrease below the rock-water miscibility point (the second critical point), causing the segregation of water and rock. Consequently, a shell of water is formed in the outermost layers, resulting in a subsequent manifestation as a gaseous water atmosphere. By considering the water-rock miscibility and the gaseous state of water, our approach holds significant implications for estimating the water mass fraction of detected exoplanets.

We model two extreme cases: a fully homogeneous mass-rock envelope surrounding an iron core, and a more traditional three-layer structure where water and rock are separated. In both cases, the outermost water layers form an atmosphere.

With various equilibrium temperatures and masses, assuming different structures, we calculate different radii for various scenarios. Planetary interiors are modeled using a modified version of the Magrahtea code (Huang et al., 2022). With these tools, we model the internal structure of a sample of exoplanets (L 98-59 d, TOI-1685 b, TOI-776 b, TOI-270 d, K2-146 b, K2-146 c).

How to cite: Lozovsky, M. and Vazan, A.: Internal structure of Water-rich planets, Europlanet Science Congress 2024, Berlin, Germany, 8–13 Sep 2024, EPSC2024-150, https://doi.org/10.5194/epsc2024-150, 2024.

The magma ocean (MO) phase typically describes the early stage of rocky planets, during which the entire planet is molten due to heat generated by accretion processes. In the case of short-period exoplanets inside the runaway greenhouse limit, this phase may last Gyrs, until the inventory of major greenhouse gasses, such as H2O and H2, is exhausted. The internal evolution of these planets is influenced by various factors, including the exchange of volatiles between the molten planetary interior and the atmosphere. This exchange significantly impacts planetary climate, exoplanet bulk densities, surface conditions , and long-term geodynamic activity by controlling greenhouse effects, surface water stability, and atmospheric composition. This research focuses on modeling this interaction under different redox conditions. Using a coupled computational framework of the planetary interior and atmosphere, we study the detailed evolution of the magma oceans phase, aiming to understand the crystallization sequence and the resulting internal structure of the planet. We investigate the impact of the cooling sequence and evolving climatic conditions on mantle differentiation, mineralogy, formation of crusts, and the consequent composition of the atmosphere.

How to cite: Sastre, M., Lichtenberg, T., Nicholls, H., Bower, D., and Kamp, I.: Interior Evolution of Magma Oceans Exoplanets, Europlanet Science Congress 2024, Berlin, Germany, 8–13 Sep 2024, EPSC2024-459, https://doi.org/10.5194/epsc2024-459, 2024.

Studying planetary habitability has become a major emerging research area, with critical implications for future exoplanet exploration and ambitious ground- and space-based telescopes. Efforts to design and optimize these missions have been focusing on maximizing the planet yield – the number of exoplanets a survey will be able to characterize – which is not necessarily equivalent to science return. We present Bioverse, a framework to quantify the diagnostic power of nextgeneration exoplanet surveys Bioverse allows to assess the detectability of population-level trends injected in simulated planet populations. Here, we apply Bioverse to explore the requirements for a mission to probe and characterize the inner edge of the habitable zone. We show that, through probing a discontinuity in the distribution of planetary radii and bulk densities caused by the runaway greenhouse transition, the PLATO mission will likely be able to constrain this demographic feature. This will constitute the first empirical test of the habitable zone concept.

We further use Bioverse to demonstrate how contextual information about a planet with a biosignature detection, such as its orbit or properties of its host star, lend or take away credibility from competing models of abiogenesis. We demonstrate that planet sample sizes ≥100 enable a strong test of a predicted correlation between past received nearultraviolet flux and the occurrence of biosignatures in the cyanosulfidic scenario for the origin of life.
Probabilistic assessments that take into account the population context will be critical for an effective search for extraterrestrial life in the Universe and to constrain the origin of life.

Figure 1. Detection of the Habitable Zone Inner Edge Discontinuity. We fit a population-level runaway greenhouse model (red posterior draws) to simulated radius measurements and test this hypothesis against the null hypothesis of an irradiation-independent distribution. In a large (N = 500) planet sample, the discontinuity is detected with high confidence.

References:
Bixel, A., & Apai, D. 2021, The Astronomical Journal, 161, 228, doi: 10.3847/1538-3881/abe042
Dorn, C., & Lichtenberg, T. 2021, ApJL, 922, L4, doi: 10.3847/2041-8213/ac33af
Ranjan, S., Wordsworth, R., & Sasselov, D. D. 2017, Astrobiology, 17, 687, doi: 10.1089/ast.2016.1596
Schlecker, M., Apai, D., Lichtenberg, T., et al., The Planetary Journal, in press. [arXiv:2309.04518]
Turbet, M., Bolmont, E., Chaverot, G., et al. 2021, Nature, 598, 276, doi: 10.1038/s41586-021-03873-w

How to cite: Schlecker, M., Apai, D., Lichtenberg, T., Bergsten, G., Salvador, A., Hardegree-Ullman, K., Affholder, A., Ranjan, S., Ferriere, R., Mazevet, S., and Heng, K.: Bioverse: Probing the Habitable Zone Inner Edge Discontinuity and the Origins of Life, Europlanet Science Congress 2024, Berlin, Germany, 8–13 Sep 2024, EPSC2024-1374, https://doi.org/10.5194/epsc2024-1374, 2024.

How to cite: Koll, D. D. B. and Lyu, X.: Characterizing rocky exoplanets without atmospheres, Europlanet Science Congress 2024, Berlin, Germany, 8–13 Sep 2024, EPSC2024-700, https://doi.org/10.5194/epsc2024-700, 2024.

“Water worlds” - planets with rocky cores overlain by water-rich envelopes - may make up a significant proportion of the sub-Neptune population and their atmospheric characterisation with JWST can offer insights into planetary formation and migration (e.g., Benneke et al. 2024). Whereas colder water worlds may be able to form liquid water oceans and have hydrogen-rich upper atmospheres, warmer planets would contain water in a supercritical state. In this case, hydrogen in the envelope mixes with the supercritical water and the observable upper atmosphere would have a high mean molecular weight with a smaller scale height. In intermediate regimes, a supercritical water layer will lie below a condensing cloud deck and hydrogen-dominated upper atmosphere. In this work, we aim to define the boundary between these three regimes using a 1D radiative-convective model. Our model uses the SOCRATES radiative transfer code coupled to a radiative-convective driver to solve for equilibrium temperature-pressure profiles in a water world atmosphere. We account for the effects of convective inhibition in the condensing layers and the non-idealness of supercritical water at high temperatures and pressures, both of which can dramatically affect the structure of the atmosphere. The resulting framework allows us to demarcate the transition between ocean worlds and sub-Neptunes with a mixed envelope as a function of instellation, interior flux and envelope composition. In the case where water is supercritical, the level at which condensation occurs (and the cold-trapping of water vapour) determines whether the observable atmosphere is hydrogen or water-dominated. We discuss whether the change in composition of the upper atmosphere accompanied by this transition would be observable. 

How to cite: Innes, H. and Pierrehumbert, R.: Mapping the transition from liquid to supercritical water on sub-Neptunes, Europlanet Science Congress 2024, Berlin, Germany, 8–13 Sep 2024, EPSC2024-723, https://doi.org/10.5194/epsc2024-723, 2024.

Characterizing the interior structure of exoplanets, that is, the size and mass of their main compositional reservoirs, is an essential part in understanding the diversity of observed exoplanets and the processes that govern their formation and evolution. However, the interior of an exoplanet is inaccessible to observations, and can only be investigated via numerical structure models. This poses an inverse problem, where the structure models need to conform to observed parameters. Unlike the planets in the Solar System, for which a wealth of observational data is available, mass and radius often remain the only parameters which can be determined for an exoplanet. Since the relative proportions of iron, silicates, water ice, and volatile elements inside the planet are not known, this poses a highly non-unique problem, where even with accurate radius and mass measurements many different solutions for the internal structure can be found.

Probabilistic inference methods, such as Markov chain Monte Carlo sampling, are a common tool to solve this inverse problem and obtain a comprehensive picture of possible planetary interiors, while also taking into account observational uncertainties. However, these typically require the calculation of hundreds of thousands of interior structures per investigated planet, which makes the characterization of exoplanets a computationally expensive and time-consuming process.

We explore an alternative approach to interior characterization utilizing machine learning. The application of machine learning methods has seen an extensive growth in the geodynamics and planetary science community in recent years, primarily driven by the need to address increasingly complex and computationally and data intensive problems that traditional methods of modeling and analysis struggle to solve. In particular, machine learning offers the opportunity to speed up time-consuming numerical simulations.

We present here ExoMDN, a stand-alone machine-learning model based on mixture density networks (MDNs) that is capable of providing a full probabilistic inference of exoplanet interiors in under a second, without the need for extensive modeling of each exoplanet's interior or even a dedicated interior model. ExoMDN is trained on a large database of 5.6 million precomputed, synthetic interior structures of low mass exoplanets.

The fast prediction times allow investigations into planetary interiors which were not feasible before. We demonstrate how ExoMDN can be leveraged to perform large-scale interior characterizations across the entire population of low-mass exoplanets. We can show how ExoMDN can be used to comprehensively quantify the effect of measurement uncertainties on the ability to constrain the interior of a planet, and to which accuracy these parameters need to be measured to well characterize a planet’s interior.

Training the model on different (potentially) observable parameters allows us to search for parameters which can better constrain the interior. Among these, the inclusion of the fluid Love number k₂ helps to significantly reduce the degeneracy of interior structures.

ExoMDN is freely accessible on GitHub at https://github.com/philippbaumeister/ExoMDN

How to cite: Baumeister, P. and Tosi, N.: ExoMDN: Rapid characterization of exoplanets interiors with machine learning, Europlanet Science Congress 2024, Berlin, Germany, 8–13 Sep 2024, EPSC2024-493, https://doi.org/10.5194/epsc2024-493, 2024.