EXOA4

We investigate the efficiency of moon formation around giant planets with numerical N-body simulations and study the habitability of Earth-sized, newly formed moons. Our results show that by the end of the moon formation process the individual mass of moons is higher, if the planet is in a close orbit around the host star. We also find that the time-scale for moon formation is shorter around close-in planets than at larger distances from the star, however, a significant number of protomoons and satellitesimals escape from the planet, decreasing moon formation efficiency. To determine the habitability of these newly formed moons, we calculate the incident stellar radiation and the tidal heating flux that can arise in moons depending on their orbital and physical parameters. We found that some of the synthetic moons orbit in the circumplanetary habitable zone. Based on our calculations, half a hundred confirmed giant planets can harbour habitable moons beyond the outer edge of the circumstellar habitable zone.

How to cite: Dobos, V., Dencs, Z., and Regály, Z.: Moon formation and habitability in the circumplanetary habitable zone, Europlanet Science Congress 2022, Granada, Spain, 18–23 Sep 2022, EPSC2022-112, https://doi.org/10.5194/epsc2022-112, 2022.

Catastrophic events dominated the history of the early; the last Giant Impact was energetic enough to transform the proto-Earth and the impactor Theia into a protolonar disk or synestia. The Earth – Moon couple condensed upon cooling from this object. The first stage of the Earth condensation was into fully molten Magma Ocean.

Here we consider a six-component silicate melt whose composition reproduces dry pyrolite [1], the chemical and mineralogical model for the bulk silicate Earth (BSE). We explore the melts at the atomic scale, using ab initio molecular dynamics simulations. We monitor the behavior of a series of volatiles, like H2O, CO, and CO2, in the temperature and density ranges characteristic to the magma ocean.

We find that carbon is massively released in the first outgassing stage, mostly as CO2. The gas, with a strong greenhouse effect, contributed to maintaining a hot dense atmosphere through a long geological time. As such, water degassed only at a later stage, when the pressure and the temperature dropped significantly. The relative proportion of released CO2 increased with increasing oxidation state, decreasing density, and decreasing temperature [2].

The carbon fraction that remained in the melt formed oxo-carbon species in the upper parts of the magma ocean. In the deeper parts, carbon formed complex polymerized species, involving both Fe and Si [3].

Thus, our simulations offer a remarkable atomistic view in the mechanisms of magma outgassing and reactions with atmospheric gases. Our results can have extensive implications not only in understanding the chemistry of the atmosphere from the early Earth, but also in understanding volcano degassing and eruptions today.

This work was supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (grant agreement number 681818 IMPACT), by the Extreme Physics and Chemistry Directorate of the Deep Carbon Observatory, by the Research Council of Norway project HIDDEN, and through its Centres of Excellence funding scheme, project number 223272.

[1] McDonough & Sun (1995) Chemical Geology 120, 223-253.

[3] Solomatova & R. Caracas (2021) Science Advances 7, eabj0406.

[2] Solomatova & R. Caracas (2019) Nature Communications 10, 1-7.

How to cite: Caracas, R.: Condensation path of the protolunar disk and the Earth's first atmosphere, Europlanet Science Congress 2022, Granada, Spain, 18–23 Sep 2022, EPSC2022-1146, https://doi.org/10.5194/epsc2022-1146, 2022.

Context. In order to find life outside the Solar System we first need to understand how terrestrial planets form in different environments. Many terrestrial planets are formed by a conversion process, during which planets lose most of their H₂-rich (primordial) atmospheres. Primordial atmospheres are formed in the early, disk-embedded phase of planet formation, where a protoplanetary core can accumulate gas from the circumstellar disk into a planetary envelope.
Aim. The aim of this thesis is to simulate the formation process of primordial atmospheres and to analyse their formation as a function of core mass, disk lifetime, and orbital radius. In doing so, this study considers cores that have formed at the start of the embedded phase and do not change their mass during atmosphere formation, as well as cores that grow continuously during the embedded phase.
Methods. The formation of primordial atmospheres are described using the equations of radiation-hydrodynamics, which are solved numerically using the adaptive implicit RHD-code (TAPIR). The discretisation of the physical equations is based on finite volumes on a staggered mesh and advective flows are calculated using the second order van Leer flux limiter.
Results. The study considers primordial atmospheres for orbital radii between 0.387 and 1.524 au, and disk lifetimes in the range of 1 - 10 Myr. The atmospheres get more massive for larger orbital radii, larger core masses, and longer lifetimes of the surrounding disk. Atmospheres of cores more massive than a limitating mass M_c,limit at some point enter a runaway collapse, while atmospheres of less massive cores grow smoothly during their entire formation. The core mass limit M_c,limit shrinks with disk lifetime and orbital radius. The smallest value found is M_c,limit = 0.7 M_⊕.

How to cite: Sommeregger, A.: Formation of primordial atmospheres for growing protoplanetary cores, Europlanet Science Congress 2022, Granada, Spain, 18–23 Sep 2022, EPSC2022-866, https://doi.org/10.5194/epsc2022-866, 2022.

Summary

The local elemental abundances of Carbon, Hydrogen, Nitrogen, Oxygen and Sulfur (CHNOS) in icy dust grains in planet-forming disks are crucial to understand the initial volatile budgets of planetesimals and, by extension, planets. The evolution of the ice composition of local dust, however, is affected by disk processes such as dust settling, radial drift, turbulent stirring, collisional growth and fragmentation of dust grains, and the formation and evaporation of ice. Altogether the processes which affect the evolution of the ice composition of local dust can be coupled and non-local. 
We develop a model where we track the effects of these processes on a single tracer dust grain. We use our model to constrain the disk regions where dynamical, collisional and ice processing are fully coupled. In addition, we predict the resulting evolutionary trajectories of individual dust grains. These individual dust grain histories can subsequently be used to make inferences about the ice composition of local dust. We find that the locations of regions where disk processes are fully coupled depend on both the chemical species considered and the grain size. In addition, the evolutionary trajectories of initially fully identical dust grains can diverge significantly, both spatially and in terms of composition. Since different grain sizes are connect via collisional growth and fragmentation, our results imply that there is no region where the disk processes considered fully decouple. Therefore, our model highlights the importance a statistical analysis of many individual dust grains to predict the volatile CHNOS present on local dust and, by extension, available for planetesimal formation.

Background
CHNOS play a crucial role in the evolution and chemical habitability of rocky planets [1]. For example, CHNOS-bearing volatile molecules such as H₂O, CO₂, CH₄ or N₂ play a key role in the surface conditions and habitability via their abundance in the planet atmosphere [2]. In addition, the abundance of CHNOS in the planetary interior has profound effects on processes such as core formation [3] and volcanic outgassing [4].
In order to understand the evolution of a planet, the amount of CHNOS a planet accumulates during its formation needs to be constrained. The first stage of planet formation involves the growth of micron-sized dust grains into millimeter- to centimeter-sized aggregates through collisions [5]. Planetesimals can subsequently form either as a product of continuous coagulation with efficient sticking or through gravitational collapse triggered by e.g. the streaming instability [6].
In the colder regions of the disk, a considerable fraction of the solid-phase CHNOS mass budget exists as ices associated with volatile molecular species such as H₂O, CO, CO₂, CH₄, NH₃, H₂S and SO₂ [1]. The amount of volatile CHNOS present on a dust grain is thus set by a balance of molecule adsorption and desorption. However, the adsorption and desorption rates strongly depend on the local temperature, radiation field and composition of the gas phase [7]. Moreover, as dust grains grow into larger aggregates through collisions, dynamical processes such as vertical settling, radial drift and turbulent diffusion result in significant displacement of dust throughout the disk [8]. This dynamical transport exposes individual dust grains to a wide range of local conditions, which could have profound consequences on the ice composition. 
Although numerous models have been developed to describe one or several aspects of the interplay between local dust ice composition and non-local disk processes, a fully coupled, systematic approach which can be used to describe any set of volatile molecule is not available to date [9,10,11].

Methods, results and outlook
We develop a stochastic model where inferences about the ice composition of the local dust population can be made by tracking the behavior of individual small tracer particles called “monomers” embedded in a larger “home aggregate” (Figure 1). The size of the home aggregate may change over time due to collisions with other dust particles, while we trace the amount and composition of ice on the monomer. The monomer and home aggregate are allowed to interact with the background disk environment, which is informed from a thermo-chemical disk model (ProDiMo) [12].
We use our model to explore the importance of the interplay between turbulent diffusion, vertical settling, radial drift and collisions for the ice properties of individual monomers. Figure 2 depicts an example of a monomer whose CO and CH₄ ice is lost due to thermal desorption, which is in turn a consequence of the home aggregate drifting into a warmer disk region.
As a next step, we are quantifying the effect of these non-local disk processes on the ice composition of local dust populations by studying the statistical behaviour of a large group of monomers. Specifically, we aim to predict the ice composition of dust present in the midplane in order to derive implications for the volatile CHNOS abundance of the first generation of planetesimals.    

Figure 1: A monomer of radius s_m is embedded inside a home aggregate of effective radius s_a at some monomer depth z_m. Depending on the monomer depth, the monomer is exposed, which allows the interaction with impinging gas phase molecules (adsorption) and UV photons (photodesorption).

Figure 2: Example evolutionary trajectory of a monomer released from r=50 AU and z=0 AU inside a porous home aggregate with filling factor φ=10^-3. The quantities depicted from left to right are the radial and vertical position (r and z, respectively), the monomer depth z_m, and ice composition.

[1] Krijt et al. 2022, arXiv 2203.10056 [2] Kasting et al. 1993, Icarus 101, p.108-128 [3] Wood et al. 2014, Geochimica et Cosmochimica Acta 145, p.248-267 [4] Van Hoolst et al. Advances in Physics: X, 4 [5] Dominik & Tielens 1997, The Astrophysical Journal 480, p.647-673 [6] Johansen et al. 2014, Protostars and Planets VI, p.547 [7] Cuppen et al. 2017, Space Science Reviews 2012, p.1-58 [8] Armitage 2010, Astrophysics of Planet Formation [9] Krijt et al. 2020, The Astrophysicsl Journal 899, p.134 [10] Bergner & Ciesla 2021, The Astrophysical Journal 919, p.45 [11] Van Clepper et al. 2022, arXiv 2202.00524 [12] Woitke et al. 2009, Astronomy & Astrophysics 501, p.383-406

How to cite: Oosterloo, M., Kamp, I., and van Westrenen, W.: Tracking CHNOS during the first stages of planet formation, Europlanet Science Congress 2022, Granada, Spain, 18–23 Sep 2022, EPSC2022-964, https://doi.org/10.5194/epsc2022-964, 2022.

After the solidification of the magma ocean, outgassing from the interior is the prevailing volatile source of Earth´s atmosphere. Besides the well-studied extrusive degassing, this process also includes the often neglected intrusive volatile release. Although, intrusive magma production rates are assumed to be significantly higher compared to extrusive rates. This renders the investigation and quantification of possible volatile exsolution mechanisms from intrusive magma bodies crucial.

An emplaced magma body progressively crystallizes due to cooling. The precipitation of certain minerals fractionates the primitive mantle over time by incorporation of compatible elements and molecules into the crystal lattice. In contrast, incompatible elements and molecules, including volatiles like H₂O and CO₂ are precluded from the crystal lattice due to their unsuitable ion radius or charge. Thus, ongoing crystallization likely leads to an oversaturation of volatiles in the remaining melt and an enhanced exsolution.

In our study, we simulate the partitioning, solubility and release of H₂O and CO₂ from a magma body emplaced at different depths within the lithosphere. Additionally, we take the possibility of melt ascent and the formation of hydrous minerals into account. According to our simulations the release of H₂O and CO₂ from an intrusive magma body is possible to a depth of at least 100 km (~3 GPa, which is comparable to the average thickness of the Earth's lithosphere). However, the release strongly depends on the initial volatile budget, the formation of hydrous phases, the depth of the intrusion and the buoyancy of the melt. Considering all these factors, our model suggests that about 0 - 85 % H₂O and 100 % CO₂ can be released from mafic intrusions. This renders the incorporation of intrusive volatile release mandatory in order to determine the volatile fluxes and the composition of Earth's atmosphere.

How to cite: Vulpius, S. and Noack, L.: The significance of intrusive volatile release for the Earth´s atmosphere., Europlanet Science Congress 2022, Granada, Spain, 18–23 Sep 2022, EPSC2022-149, https://doi.org/10.5194/epsc2022-149, 2022.

Noble gases have the particularity that each one of them has at least one stable non-radiogenic isotope and at least one radiogenic isotope. The ratio of non-radiogenic and radiogenic isotopes of the noble gases arriving at the surface is essential to understand processes occurring on various timescale in the Earth interior.

The isotopic signature of the noble gases in the mid-ocean ridge basalts (MORB) is different than in the ocean island basalts (OIB) such as in Iceland, Hawaii, Galapagos, Réunion, or Samoa. One such example is the high ³He/⁴He ratio observed in OIB, which is explained as a signature of the core, which in this case becomes a hidden geochemical reservoir. Here, we determine the chemical behavior of helium in the magma ocean during the core formation. We employ molecular dynamics simulations based on the density functional theory as implemented in the VASP package. We perform the simulations at several temperatures and pressures that sample the magma ocean adiabat.

These calculations will enable us to derive some trends on the preference of helium in the silicate or iron melts. In the long term, they will confirm or inform the existence of a hidden reservoir deep inside the Earth.

We acknowledge support from the Research Council of Norway, project number 223272. RC acknowledges support from the European Research Council under EU Horizon 2020 research and innovation program (grant agreement 681818 – IMPACT) and access to supercomputing facilities via the eDARI gen6368 grants, the PRACE RA4947 grant, and the Uninet2 NN9697K grant.

How to cite: Ozgurel, O. and Caracas, R.: Helium partitioning between the mantle and the core at the early Earth, Europlanet Science Congress 2022, Granada, Spain, 18–23 Sep 2022, EPSC2022-1062, https://doi.org/10.5194/epsc2022-1062, 2022.

A balanced ratio of oceans to land is thought to be essential for the evolution of an Earth-like biosphere. Emerged continents provide direct access to solar energy while large oceans enhance rainfall and prevent an all-to-dry climate. When assessing the habitability of Earth-like planets, one may be tempted to assume similar geological properties. After all, considering e.g., the volume of the continental crust, the latter is determined by an equilibrium between continental production, by subduction-zone related volcanism and continental erosion. Assuming the interior thermal state of Earth-sized exoplanets to be similar to the Earth’s is a straightforward and reasonable assumption if a similar composition can be assumed and if the temperature- and volatile-dependence of mantle viscosity governs the heat transfer in their mantles as it does in Earth’s. In that case, one might expect a similar equilibrium between continental production and erosion to establish and, hence, a similar continental land fraction. We will show that this conjecture is not likely to be true and that the present-day Earth may rather be an exceptional planet: Positive feedback associated with the coupled mantle water - continental crust cycle enhanced by the role of sediments may lead to a bifurcation of possible outcomes of the evolution. One of these is a land planet with about 80% of its surface covered with continental crust, or about 70% land surface if continental shelves covered with water are accounted for. The other extreme is a planet covered by about 20% with continents or a land fraction of only about 10%, again accounting for shelve areas. Both equilibrium planets minimize their lengths of subduction zones in equilibrium. Of the two, the land planet has a substantially larger zone of attraction in the space of reasonable initial conditions. About 80% of randomly chosen sets of initial conditions evolve to end there. The ocean planet attracts about 20% of the cases. Only around a percent of the evolution models result in an Earth-like configuration for which the continental coverage is about 40% but for which the length of the subduction zones is maximized, suggesting that the equilibrium is unstable. We find this equilibrium fixed point to be a saddle point, stable with respect to mantle water but unstable with respect to continental coverage. Still, because the rates of change are small after some billion years of evolution, the unstable equilibrium – if attained - can be occupied for a long time.  It is interesting to note that the bifurcation develops only after the planet has cooled to an interior temperature within some tens of K from the Earth’s present mantle temperature. This suggests that the dependence of the viscosity on the water concentration in the mantle becomes competitive with the dependence on temperature and the sediments as carriers of water in subduction zones become increasingly important for the bifurcation to occur. On Earth, this occurs roughly near the end of the Archean, about 2 billion years ago. We further studied the role of thermal blanketing by continents enriched in radioactive elements and included the effect of transfer of these elements from the mantle. We found that blanketing may enhance the positive feedback leading to the bifurcation although most of the blanketing effect is compensated by the effective cooling of the mantle depletion in radiogenic elements.

Including CO₂ outgassing in the model and the long-term carbonate-silicate cycle, we found that the land planet and the ocean planet differed by only about 5K in average surface temperature. Still, we would expect that the land planet has a substantially dryer, colder and harsher climate possibly with extended cold deserts in comparison with the ocean planet and with the present-day Earth. These planets would all be considered habitable but their fauna and flora may be quite different. The Earth in its geologic history has experienced climates that could resemble the one expected for the land planet (e.g., the Pleistocene) and for the ocean planet (e.g., the Paleocene).

How to cite: Spohn, T. and Hoening, D.: Land/Ocean Surface Diversity on Earth-like (Exo)planets: Implications for Habitability, Europlanet Science Congress 2022, Granada, Spain, 18–23 Sep 2022, EPSC2022-506, https://doi.org/10.5194/epsc2022-506, 2022.

Accurate measurements of a planet's mass, radius and age (provided for example by the PLATO mission and follow-up measurements) together with compositional constraints from the stellar spectrum can help us to deduce potential evolutionary pathways that rocky planets can evolve along, and allow us to predict the range of likely atmospheric properties that can then be compared to observations (from ground or space, i.e. with JWST or in the more distant future with direct imaging such as proposed by the LIFE initiative).

However, for the evolution of composition and mass of an atmosphere, a large degeneracy exists due to several planetary and exterior factors and processes, making it very difficult to link the interior (and hence outgassing processes) of a planet to its atmosphere. The community therefore thrives now to identify the key factors that impact an atmosphere, and that may lead to distinguishable traces in planetary, secondary outgassed atmospheres. Such key factors are for example the planetary mass (impacting atmospheric erosion processes) or surface temperature (impacting atmospheric chemistry, weathering and interior-atmosphere interactions).

Here we investigate the signature that a planet evolving into plate tectonics leaves in its atmophere due to its impact on volcanic outgassing fluxes and volatile releases to the atmosphere - leading possibly to distinguishable sets of atmospheric compositions for stagnant-lid planets and plate tectonics planets. These outgassing fluxes further strongly depend on the evolution of the atmosphere, including atmosphere losses to space or by condensation or weathering. 

How to cite: Noack, L. and Brachmann, C.: Variation in outgassing efficiency for plate-tectonics vs. stagnant-lid planets under different evolving atmospheric conditions, Europlanet Science Congress 2022, Granada, Spain, 18–23 Sep 2022, EPSC2022-129, https://doi.org/10.5194/epsc2022-129, 2022.

From the White Paper series within the ESA “Voyage 2050” process [1] and the US Astro 2020 Decadal [2], it is clear that the astronomical community is going to focus on investigating temperate, terrestrial exoplanets to understand their potential habitability and search for atmospheric signatures of biospheres. 

Various concepts for future space missions have been proposed, from a large IR/O/UV (LUVOIR/HabEx-like) space mission for studies in reflected light [3, 4], to the mid-infrared nulling interferometer LIFE (Large Interferometer for Exoplanets), to characterize the thermal portion of the planetary spectrum [5, 6]. Their goal is to constrain the bulk parameters, atmospheric structure and composition, and the surface conditions of dozens of terrestrial exoplanets. Atmospheric retrieval studies are essential to define the potential of future missions, determine the technical requirements, as well as to validate the analysis pipelines. It is also relevant at this stage to quantify any synergy among the various instruments, in order to identify compelling science cases whose characterization would be enhanced by observation in multiple wavelength ranges.

Bayesian retrieval routines are the key to a statistically robust analysis of a measured atmospheric spectrum. The Bayesian retrieval method builds on iteratively fitting a parametric model for the planet spectrum to the observed spectrum to get estimates on the composition of the planet’s atmosphere and its structure. Such a method can be useful to quantify the amount of information that can be extracted from an observed spectrum, depending on its quality (in terms of resolution, signal-to-noise ratio, observing time, and wavelength range).

Retrieval studies are currently being performed in order to determine the requirements for the upcoming missions. In this talk, I will summarize the main results of the latest atmospheric retrieval studies that were performed during the studies of some future space mission concepts. 

References:

[1] https://www.cosmos.esa.int/web/voyage-2050

[2] National Academies of Sciences, Engineering, and Medicine. 2021, Pathways to Discovery in Astronomy and Astrophysics for the 2020s (Washington, DC: The National Academies Press)

[3] Gaudi, B. S., et al. 2020, arXiv e-prints,arXiv:2001.06683

[4] Peterson, B. M., Fischer, D., & LUVOIR Science and Technology Definition Team. 2017, in American Astronomical Society Meeting Abstracts, Vol. 229, 405.04

[5] Quanz, S. P., et al., 2018, Proc. SPIE, 107011I

[6] Quanz, S. P., et al. 2021, arXiv e-prints,arXiv:2101.07500

How to cite: Alei, E., Konrad, B. S., Angerhausen, D., and Quanz, S. P. and the LIFE collaboration: Atmospheric retrievals of terrestrial planets with future space missions, Europlanet Science Congress 2022, Granada, Spain, 18–23 Sep 2022, EPSC2022-674, https://doi.org/10.5194/epsc2022-674, 2022.

How to cite: Wang, H., Quanz, S., Yong, D., Liu, F., Seidler, F., Acuna, L., and Mojzsis, S.: The interior diversity of terrestrial-type exoplanets: constrained with devolatilized stellar abundances and mass-radius measurements, Europlanet Science Congress 2022, Granada, Spain, 18–23 Sep 2022, EPSC2022-283, https://doi.org/10.5194/epsc2022-283, 2022.

Introduction
The catalog of known exoplanets has increased vastly since the first detection in 1995. In the era of JWST, this catalog is expected to grow even further, and especially the fraction of terrestrial exoplanets will grow due to the enhanced capabilities of next-generation instruments compared to its predecessors. Due to limited observation time with instruments such as JWST, target selection is an important process, especially for the difficult-to-observe terrestrial planets. This process can be improved by using readily available data, stellar abundances, by considering that a planet and its host star originate from material with the same composition.

The composition of a terrestrial planet modulates many properties, including core size, mantle rheology, and mantle melting behaviour. This will determine whether the planet has a mobile surface, with plate tectonics-like behaviour, or an immobile surface, with e.g. stagnant-lid-like behaviour. Further, interaction between the interior and the atmosphere depends on interior properties, and interior composition may therefore leave its mark on the planet’s atmosphere. Finally, these compositional effects may have an influence on whether the surface is capable of forming and sustaining life-forms [1]. However, the full effect of compositional influence on terrestrial planet evolution has only recently reached a level of maturity that it can now be applied to planets orbiting other stars.

Bulk compositions of terrestrial exoplanets can to some extent be estimated by considering them as devolatized stars. By applying devolatilization factors [2], we have determined the range of bulk terrestrial exoplanet compositions in the Solar neighbourhood (Spaargaren et al., in preparation) based on stellar abundances from the Hypatia catalog [3]. In this work, we identified 20 end-member bulk planet compositions that span the full range of compositional diversity. Here, we study these end-members in more detail, to investigate how compositional effects alter the evolutionary pathway of terrestrial planets.

Compositions
We study 20 planets of one Earth mass, with the previously established end-member bulk compositions, in more detail. Bulk composition is given in terms of the most common elements in rocky planets: Fe, Mg, Si, O, Ca, Al, Na, Ni, and S, where the latter two exclusively appear in the metallic iron core. The structure (i.e., relative sizes of the metallic iron core and silicate mantle) is determined by considering bulk iron, nickel, and sulphur abundances, assuming constant bulk planet oxygen fugacity. Core composition is subtracted from the bulk to determine mantle composition.

To calculate mantle physical properties from bulk mantle composition, we employ the Gibbs energy minimization algorithm Perple_X [4]. This algorithm calculates mineralogy, based on a new thermodynamic database by Stixrude and Lithgow-Bertelloni (2022; [5]) and related physical properties for each of the 20 cases. 

Interior Modelling
We explore the effects of bulk planet composition on long-term interior evolution using a geodynamical model, StagYY [6]. We run this model for five billion years, to analyze the thermal evolution of our planetary test-cases. Adjustments are made to the melting calculation scheme based on the basalt fraction and iron abundance in the mantle, where the latter can change solidus temperature by up to 36 K per wt% FeO. Further, we explore the effects of yield stress for each of our compositional end-members, to determine the propensity of each planet towards plate tectonics-like behaviour, stagnant lid-like behaviour, or behaviour that falls under a different dynamic regime.

In general, Earth tends to have an average composition for most elements, except for iron, which it is relatively rich in, and therefore it has an above average core size. Our preliminary results show that core size (and thus iron abundance) affects convective vigor, and thus thermal evolution of the interior. Interesting to note is that on average, due to galactic chemical evolution, the iron abundance and thus exoplanet core sizes tends to increase (e.g., [7]). Therefore, Earth will tend more towards being average in younger populations. 

We further find major differences for planets with different ratios of Mg-silicates, as these minerals control mantle viscosity, and thereby thermal evolution. Planets with lower Mg/Si than Earth will have a significantly stronger mantle, impeding cooling on planetary lifetimes, while planets with much higher Mg/Si have weaker upper mantles, impacting surface mobility. Stellar Mg/Si is a good indicator of the relative abundances of these minerals, and can be an important source of information. Therefore, the host stellar abundances seem to be an indicator of rocky planet properties, and can be used in the target selection for future missions.

 [1] Mojzsis, S.J. (2021). Geoastronomy: Rocky planets as the Lavosier-Lomonosov Bridge from the non-living to the living world. in Royal Society of Chemistry, Prebiotic Chemistry and the Origin of Life. arXiv:2112.04309

[2] Wang, H.S., Lineweaver, C.H., Ireland, T.R. (2019). The volatility trend of protosolar and terrestrial elemental abundances. Icarus, 328, 287-305.

[3] Hinkel, N., Timmes, F., Young, P., et al. (2014). Stellar abundances in the Solar neighbourhood: the Hypatia Catalog. The Astronomical Journal, 148(3), 33 pp.

[4] Connolly, J.A. (2005). Computation of phase equilibria by linear programming: a tool for geodynamic modeling and its application to subduction zone decarbonation. Earth and Planetary Science Letters, 236(1-2), 524-541.

[5] Stixrude, L., Lithgow-Bertelloni, C. (2022). Thermal expansivity, heat capacity and bulk modulus of the mantle. Geophysical Journal International, 228(2), 1119-1149.

[6] Tackley, P.J. (2008). Modelling compressible mantle convection with large viscosity contrasts in a three-dimensional spherical shell using the yin-yang grid. Physics of the Earth and Planetary Interiors, 171(1-4), 7-18.

[7] Matteuci, F., Greggio, L. (1986). Relative roles of type I and II supernovae in the chemical enrichment of the interstellar gas. Astronomy & Astrophysics, 154, 279-287.

How to cite: Spaargaren, R., Ballmer, M., Mojzsis, S., and Tackley, P.: Exploring the effects of terrestrial exoplanet bulk composition on long-term planetary evolution, Europlanet Science Congress 2022, Granada, Spain, 18–23 Sep 2022, EPSC2022-1017, https://doi.org/10.5194/epsc2022-1017, 2022.

Exoplanets in the mass range between Earth and Saturn show a large spread in radii/densities for a given planetary mass. The most approaches to explain this spread and the distribution of planetary properties therein can be split into two groups. The first considers the planetary formation paths as the primary mechanism shaping this distribution, and the second group considers the radius spread as a consequence of the atmospheric evolution driven by the atmospheric mass loss. The majority of the latter studies, however, consider only the observed radius spread with some theoretical underlying mass distribution, as for most of the Kepler planets the mass is unknown.
In this study, we examine the mass-radius distribution of the observed planets with masses between 1 and 108 Earth masses with the aim to understand to which extent it can be explained by the evolution of planetary atmospheres driven by thermal contraction and the hydrodynamic escape, and in which regions of the parameters state the initial parameters of planets set up by specific formation processes are critical for the final (gygayears old) state.
Our modeling framework accounts simultaneously for the realistic atmospheric mass loss by interpolating within the grid of upper atmosphere models and for the thermal evolution of planets by means of the MESA code. As the atmospheric mass loss on the long timescales is strongly affected by high energy stellar radiation, we also account for the whole range of different possible stellar evolution histories as represented by the Mors code. 
We consider the grid of model planets in the mass range given above evolving at different orbital separations (corresponding to the equilibrium temperatures of ~500-1700 K) around the solar mass star. As initial parameters for our atmosphere evolution models, we adopt the predictions of the analytical approximations based on formation models (Mordasini 2020) and consider the two possible scenarios: planets formed in the inner disk (relatively small initial atmospheres) and beyond the snow line (large initial atmospheres) with consequent inward migration at the early phase of the planetary system evolution.
The whole radius spread predicted using this approach outlines well the observed distribution (including about 240 planets with mass and radius uncertainties below 45% and 15% respectively), except for a group of very close in (within ~0.1 AU) massive (~70-110 Mearth) planets with radii comparable to the Jupiter radius. The radii of these planets can not be reproduced by our models even by assuming the atmospheric mass fractions above 80% without some additional heating source. A strong correlation of the radii with equilibrium temperature (Rpl~Teq^0.7) suggests that the inflation mechanism is similar to that of the so-called "inflated Jupiters", where a range of possible explanations was suggested including the tidal interaction with the host star, vertical heat transport towards the deep atmospheric levels or the Ohmic dissipation.
The more detailed analysis shows that the low-mass end of the mass-radius distribution (below 10-15 Earth masses) is dominated by the effect of the atmospheric mass loss (and thus extremely dependent on the activity evolution history of the host star) and weakly depend on the initial parameters, and thus, on the specific formation mechanism of the exoplanets. For more massive planets, though some of them can be significantly affected by the atmospheric mass loss, the initial conditions become important and the variability in the possible stellar histories can only explain about one fourth of the whole spread. Thus, for explaining the upper boundary of the spread above ~20 Mearth one needs to consider the voluminous initial atmospheres which can be explained by the formation at the large distance from the host star. However, the activity history of the host star can be theoretically resolved using the present-day radii of the companion planets for the significant fraction of planets with masses up to ~60 Mearth.
Finally, the detailed comparison between the model predictions and the observations within different Teq intervals reveals a relatively small (~6%) but a presumably systematic group of the outliers with radii considerably smaller than the lower boundary predicted by our models for Teq<~800 K. Assuming the hydrogen dominated atmospheres surrounding rocky cores, these planets would not have more than ~1% of their mass in the envelope, while for their masses (>10 Mearth) the accretion models predict the initial atmospheric mass fraction order of 10%, and the total atmospheric mass loss throughout the evolution according to our models is insufficient to remove this much of the atmospheric material. This suggests, that the formation mechanisms and structures of these planets are considerably different from our assumption of the hydrogen-dominated atmospheres accreted onto the rocky core.

How to cite: Kubyshkina, D. and Fossati, L.: Mass-radius relation of intermediate-mass planets outlined by the hydrodynamic escape of planetary atmospheres and formation, Europlanet Science Congress 2022, Granada, Spain, 18–23 Sep 2022, EPSC2022-1089, https://doi.org/10.5194/epsc2022-1089, 2022.

Short-period, low-mass planets have been found to often display inflated atmospheres [1]. Here, we investigate the interior structure of such planets with a moderate water budget using a fully self-consistent planet interior model [2, 3], where water can exist in supercritical state. This has been done by increasing the working range of an existing interior model, allowing us to explore the 0.2-2.3 Earth mass range. We consider planets with water mass fractions (WMF) ranging from 0.01% to 5% and irradiation temperatures between 500 and 2000K. Moreover, we consider three possible internal compositions; a pure rocky interior, an Earth-like core mass fraction (0.325) and a Mercury-like core mass fraction (0.7).

Figure 1: Computed planetary radii Rp at the transiting depth of 20mbar as a function of planetary mass and irradiation temperature. Columns correspond to different core mass fractions (0, 0.325, 0.7, from left to right) while rows correspond to different water mass fractions (5%, 1%, 0.01%, from top to bottom). Any missing data correspond to cases where the atmosphere is hydrostatically unstable.

We find that at higher masses, the planet radius increases with the planet mass, and the radii for planets with supercritical water are greater than if water was in a condensed phase. An important mass of water can also result in a notable compression of the refractory layers (up to 0.1 Earth radius for a WMF of 5%). At lower masses, we find that the steam atmosphere inflates, and becomes gravitationally unstable when the scale height of the atmosphere exceeds ~0.1 times the planetary radius. We propose to use this H/Rp ratio as a stability criterion for steam atmospheres. 

Our data can be used to estimate the maximum WMF that can be retained by a planet given its mass, irradiation temperature and interior composition. For a given mass and temperature, a large part of the planets considered here can be stable even if constituted of 100% water. As the temperature increases or as the mass decreases, the surface gravity of a 100% water planet becomes too weak to retain the steam atmosphere. It is then possible to estimate the maximum WMF under which the atmosphere is stable.

Our results show that planets under 0.9 Earth masses should typically present unstable hydrospheres.  We also find that a sharp transition exists between a planet able to hold a 100% water atmosphere and an unstable one, as the H/Rp stability criterion exceeds 0.1. Additionally, we note that this class of planets is a viable explanation of the current Super-Puff category without invoking instrumental limitations, as the mass of water molecules induces a more inflated atmosphere than H/He planets.

References:

[1] Turbet, M., Bolmont, E., Ehrenreich, D., et al. 2020, A&A, 638, A41

[2] Aguichine, A., Mousis, O., Deleuil, M., et al. 2021, ApJ, 914, 84

[3] Vivien, H.G., Aguichine, A., Mousis, O., et al. 2022, ApJ

How to cite: Vivien, H., Aguichine, A., Mousis, O., Deleuil, M., and Marcq, E.: Constraints on the existence of low-mass planets with supercritical hydrospheres, Europlanet Science Congress 2022, Granada, Spain, 18–23 Sep 2022, EPSC2022-418, https://doi.org/10.5194/epsc2022-418, 2022.

The high number of discovered close-in planets motivates the improvement of tidal modeling.Among the five thousand exoplanets discovered up to now, half of them have an orbital period of less than 10 days and therefore experience some form of tidal evolution. Besides, the habitable zone of ultra-cool dwarfs is located close-in (e.g. TRAPPIST-1, Gillon et al. 2017), so planets in the habitable zone of these dwarfs are expected to undergo tidal evolution. By impacting the orbital and rotational dynamics of close-in planets, tides have an impact on their habitability. Indeed, tides drive the spin evolution of planets, influence their thermal state by internal friction (Henning & Hurford 2014, Bolmont et al. 2020), and drive their orbital evolution by exchange of angular momentum. This leads to the migration of the planets, their eccentricity and obliquity damping, and the precession of their orbits ( e.g Hut 1981, Bolmont et al. 2011, 2012, Ragozzine & Wolf 2009).

Solid planetary tides also act to synchronize the spin of planets on circular orbits with their orbital motion. It is generally assumed that close-in planets (i.e. experiencing strong tidal interactions) have reached this state of synchronization, also called the 1:1 spin-orbit resonance (hereafter SOR). However, in the case of an eccentric or inclined orbit, tides can trap the spin in higher rotation rates, e.g. in the 3:2 or the 2:1 SOR. If a planet has an atmosphere, another tidal mechanism should be taken into account: the thermal tide, which is caused by the differential heating between day and night sides (Correia & Laskar 2001, Auclair-Desrotour 2017a). In the case of thick atmospheres such as that of Venus, the thermal tides acting on the atmosphere can be as strong as the gravitational tides acting on the solid core (Auclair-Desrotour et al. 2017b) and can both de-synchronize the planet and increase the spin inclination. The competition between the two tides, solid and thermal can be seen in figure [1].

Figure [1]:

The two tidal contributions, gravitational and thermal, acting in opposition to each other. The solide tide drives the spin to synchronization, while the thermal tide drives it away from it.

Tidal model

To understand the evolution of exoplanets, we need a consistent tidal model which encapsulates the complex response of rocky planets to stress. Most models assume that planets are made of weakly viscous fluid (e.g. Hut 1981, Goldreich & Soter 1966) even for rocky planets. However, it has been shown that they do not reproduce the correct behavior for highly viscous solid bodies (Henning et al. 2009; Efroimsky & Makarov 2013). In contrast, we use here a model which accounts for more realistic anelastic behavior for the rocks (such as the Andrade rheology) for a Venus-like planet (Dumoulin et al. 2017). We choose here an approach developed by Kaula (1964), which consists in using a decomposition of the tidal potential into Fourier harmonic modes. For the thermal tide, we use the analytical formulation of Leconte et al (2015), which aims at reproducing Venus today. Our developments were added to the ESPEM code (Benbakoura et al. 2019) to compute the orbital and rotational evolution of a Venus-like planet around a Sun-like star.

2) A complex rotational evolution:

Figure [2] shows the evolution of a Venus-like planet, with and without an atmosphere, orbiting a Sun-like planet with an initial obliquity of 50 degrees and a rotation of about 100 days and on a circular orbit. 

No atmosphere (red curve):

When the planet does not have an atmosphere, the rotation spins down to synchronization in 100 million years. Interestingly and despite the absence of an eccentricity, Figure [2] shows that the obliquity of the planet allows the presence of the 2:0 spin-orbit resonance in which the planet spends a few 10 million years. The planet leaves this resonance when the obliquity becomes too low to maintain this configuration stable.

With atmosphere (blue curve):

The blue curve of Fig. [2] shows the effect of a strong CO2 atmosphere on the evolution of the spin and the obliquity. The evolution here is more complex. First, the combination of the two tides damps the spin toward the 2:1 SOR while increasing the obliquity. When the obliquity becomes high enough, the thermal torque begins to counter-balance the solid torque. The thermal tides continue to increase the obliquity and the spin of the planet until an equilibrium state between the solid and thermal tides is found.

Depending on the atmospheric parameters, the evolutions we obtain are complex, with spin-orbit resonances, coming either from the eccentricity or from the obliquity of the planet. I will show the variety of different spin evolutions of a Venus-like planet, and how it depends on the presence of an eccentricity or obliquity and the presence or not of a thick atmosphere.

Figure [2]

Simulation of a Venus-like planet orbiting a Sun-like star, without an atmosphere (in red) and with an atmosphere (in blue). Top panel: evolution of the ratio of the planetary spin Ω and the mean motion n. Bottom panel: evolution of the obliquity of the planet (defined as the angle between the equatorial plane and the orbital plane).

How to cite: Revol, A., Bolmont, É., Tobie, G., Dumoulin, C., Musseau, Y., Mathis, S., Strugarek, A., and Brun, A. S.: Improving tidal modeling for rocky worlds, Europlanet Science Congress 2022, Granada, Spain, 18–23 Sep 2022, EPSC2022-1007, https://doi.org/10.5194/epsc2022-1007, 2022.

How to cite: Acuna Aguirre, L., Deleuil, M., and Mousis, O.: Interior-atmosphere modelling of JWST rocky planets, Europlanet Science Congress 2022, Granada, Spain, 18–23 Sep 2022, EPSC2022-380, https://doi.org/10.5194/epsc2022-380, 2022.

Without aerobic life, the simultaneous presence of N₂ and O₂ in the Earth's atmosphere, as on any other planet, would be chemically incompatible over geologic timescales. The existence of an N₂-O₂-dominated atmosphere on an exoplanet would, hence, not only constitute a strong biosignature of aerobic life. It would also have to meet certain astro- and geophysical conditions to originate, evolve and to sustain.

Our definition of Eta-Earth (η_Earth), therefore, builds on the concept of a so-called Earth-like Habitat (EH), i.e., a planet within the complex habitable zone for life, at which N₂ and O₂ are simultaneously present as the dominant species while CO₂ only comprises a minor constituent in its atmosphere. By our present scientific knowledge, certain criteria must be fulfilled to allow the existence of such an Earth-like atmosphere. These can be subsumed within a new probabilistic formula for estimating a maximum number of EHs which we will present within this talk. Some of these criteria, such as the initial mass function, the bolometric luminosity and XUV flux evolution of a star, or the distribution of rocky exoplanets within the habitable zones of different stellar spectral types, are already rather well studied and can be tested through further observations. Other important criteria, like the prevalence of working carbon-silicate and nitrogen cycles, or the origin of life are by now poorly, or entirely un-constrained. Further factors, like the presence of a large moon or the importance of an intrinsic magnetic field, are not only poorly constrained but its importance for the evolution and stability of an Earth-like Habitat are even debated. While our new formula for estimating the maximum number of EHs can in principle incorporate all these factors as well as unknowns, we by now must restrict ourselves to the ones that are either well understood or can at least be tested soon. Based on our current knowledge, this approach only allows us to probabilistically estimate a maximum number of exoplanets on which an Earth-like Habitat can in principle evolve. The real number of EHs might, therefore, be significantly lower than our current best estimate but additional criteria should be verifiable in near future by upcoming ground- and space-based instrumentation such as PLATO, the E-ELT, or by the kinds of the proposed space-based observatory LUVOIR.

By considering all the factors that are presently scientifically quantifiable to at least some extent, we will present our current best estimate for the maximum number of EHs that might exist within the galaxy. If we redefine η_Earth, the mean number per star of rocky planets within the habitable zone, to only account for the mean number of EHs per star, η_EH, we end up with a number much smaller than current best estimates for η_Earth. It is, therefore, scientifically not justified to presume the astrobiological Copernican assumption that all potential habitats inside a habitable zone for complex life will evolve similar to Earth.

How to cite: Scherf, M., Lammer, H., and Sproß, L.: Eta Earth Revisited: How many Earth-like Habitats might there be in the Milky Way?, Europlanet Science Congress 2022, Granada, Spain, 18–23 Sep 2022, EPSC2022-1032, https://doi.org/10.5194/epsc2022-1032, 2022.