Abstract
With more observations of terrestrial exoplanets becoming available every year, the importance of geodynamical studies focusing on exoplanets is increasing. We know from observations that stellar chemical abundances vary in the Solar neighbourhood, which is likely to result in terrestrial exoplanets with a similar chemical diversity. Bulk planet composition affects many properties of the interior directly (e.g., core size, mantle viscosity) or indirectly (e.g., thermal evolution, layering). This may extend to atmospheric properties, since terrestrial planet atmospheres form and evolve under continuous interaction with the interior. In order to better understand the variability of interior properties among terrestrial exoplanets, here we attempt to constrain the range of bulk compositions of terrestrial exoplanets in the Solar neighbourhood. We subsequently study the effects of this compositional spread on the planet interior evolution with a geodynamical model.
Introduction
Terrestrial exoplanets have interiors properties that may diverge from Earth's, and therefore may follow different evolutionary pathways as a result. It has been studied how interior properties, such as mantle viscosity, melting behaviour, core size, and planet radius affect interior evolution, dynamical behaviour of the lithosphere, and evolution of the atmosphere.However, bulk planet composition has not been considered in these studies so far. We know from observations that stellar chemical abundances vary in the Solar neighbourhood, and this is likely to result in terrestrial exoplanets with a similar chemical diversity, and can affect results of these models.
In our previous work (Spaargaren et al., in review), we established that interior composition affects the evolution of both the interior and the atmosphere of a planet. Bulk planet composition affects many properties of the interior directly (e.g., core size, mantle viscosity) or indirectly (e.g., thermal evolution, layering). This extends to atmospheric properties, since terrestrial planet atmospheres form and evolve under continuous interaction with the interior. Here, we aim to incorporate a more complex compositional model, where we constrain the range of possible bulk terrestrial exoplanet compositions with observations of stellar abundances. Additionally, we aim to investigate the effects of this range on interior evolution using a geodynamical model.
Constraining bulk composition
Since a planet forms from the same material as its host star, we can use stellar abundances to constrain bulk compositions of exoplanets. We use abundance data from the Hypatia catalog [1], which records abundances of stars in the Solar neighborhood (within 150 pc). To determine planetary compositions, we utilize the compositional trend between Earth and the Sun. This trend shows a growing depletion of elements in Earth with decreasing condensation temperature of the element. We apply this devolatilization trend from [2] to the stellar abundance data from the Hypatia catalog, to simulate compositions of hypothetical exoplanets with the same formational history as the Earth. We consider the elements Si, Fe, Mg, O, Al, Ca, Na, K, Ni, and S.
For this set of simulated bulk planet compositions, we simulate core-mantle differentiation by distributing oxygen among elements according to their tendency to stabilize oxides over metals. Metals are partitioned in the core, and oxides in the mantle. We include partitioning of light elements into the core, by including 6 wt\% Si and 2 wt\% O in the core. Thus, we obtain a proxy for bulk silicate compositions.
Interior modelling
From the obtained bulk terrestrial exoplanet compositions, we identify a small number of end-member bulk planet compositions. We recommend these end-member bulk planet compositions for use in modelling of terrestrial exoplanet interiors. To investigate the interior evolution of these planets, we first translate the obtained bulk silicate compositions to mineralogical mantle profiles, and prescribe the corresponding physical mantle properties in a geodynamical model. We determine mantle mineralogy and physical properties by using a Gibbs energy minimization algorithm, PerpleX [3], with a thermodynamic database which is valid for most of the pressure-temperature conditions found in the mantle [4]. Finally, we explore the effect of this variability in bulk composition on long-term evolution of the planetary interior using a 2D parametrized convection model [5].
Extension to atmospheric models
Future work will focus on extending these models to include atmospheric evolution, as the atmosphere controls surface conditions. This is an important constraint for considering habitability of a planet. Additionally, atmospheric observations of terrestrial exoplanets will be possible in the future, with upcoming missions (e.g., JWST, ARIEL, E-ELT) being able to place constraints on upper atmosphere chemistry of some of these planets. Since the atmosphere evolves under interaction with the interior, atmospheric observations may provide constraints on interior properties, including composition.
We found in our previous work that interior temperature and viscosity, which mainly depends on the Mg/Si-ratio of the mantle, has a strong effect on atmospheric evolution. A melting model based on a more complex chemistry can complement this previous result by establishing more links between interior composition and atmospheric evolution. Additionally, we found that the volatile exchange between the atmosphere and interior depends on the dynamic behaviour of the planets' lithosphere (i.e., whether plate tectonics is possible). It is therefore interesting to investigate whether mantle composition affects the likelihood of developing plate tectonics, as it would provide another strong effect of bulk composition on atmospheric evolution.
Bibliography
[1] 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.
[2] Wang, H.S., Liu, F., Ireland, T.R., et al. (2018). Enhanced constraints on the interior composition and structure of terrestrial exoplanets. Monthly Notices of the Royal Astronomical Society, 482(2), 2222-2233.
[3] 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.
[4] Stixrude, L., Lithgow-Bertelloni, C. (2011). Thermodynamics of mantle minerals - II. Phase equilibria. Geophysical Journal International, 184(3), 1180-1213.
[5] 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.
