Can we constrain the interior structure of rocky exoplanets from mass and radius measurements?

Abstract

Aims. We present an inversion method based on Bayesian analysis to constrain the interior structure of terrestrial exoplanets, in the form of chemical composition of the mantle and core size. Specifically, we identify what parts of the interior structure of terrestrial exoplanets can be determined from observations of mass, radius, and stellar elemental abundances. Methods. We perform a full probabilistic inverse analysis to formally account for observational and model uncertainties and obtain confidence regions of interior structure models. This enables us to characterize how model variability depends on data and associated uncertainties. Results. We test our method on terrestrial solar system planets and find that our model predictions are consistent with independent estimates. Furthermore, we apply our method to synthetic exoplanets up to 10 Earth masses and up to 1.7 Earth radii, and to exoplanet Kepler-36b. Importantly, the inversion strategy proposed here provides a framework for understanding the level of precision required to characterize the interior of exoplanets. Conclusions. Our main conclusions are (1) observations of mass and radius are sufficient to constrain core size; (2) stellar elemental abundances (Fe, Si, Mg) are principal constraints to reduce degeneracy in interior structure models and to constrain mantle composition; (3) the inherent degeneracy in determining interior structure from mass and radius observations does not only depend on measurement accuracies, but also on the actual size and density of the exoplanet. We argue that precise observations of stellar elemental abundances are central in order to place constraints on planetary bulk composition and to reduce model degeneracy. We provide a general methodology of analyzing interior structures of exoplanets that may help to understand how interior models are distributed among star systems. The methodology we propose is sufficiently general to allow its future extension to more complex internal structures including hydrogen-and water-rich exoplanets.

Constraining planet structure from stellar chemistry: the cases of CoRoT-7, Kepler-10, and Kepler-93

“…In the solar system the Sun's photospheric relative Fe-abundance can Article published by EDP Sciences L13, page 1 of 5 thus be used as a proxy for the iron mass fraction for three out of four terrestrial planets. This fraction is in turn a key quantity for the characterization of exoplanets: from measurement of mass and radius alone, the interior composition can only be weakly constrained owing to model degeneracies (Dorn et al 2015). It is thus interesting to see whether for the planets analyzed by Dressing et al (2015), a compositional correlation between the host stars and their planets is possible, suggesting that it may not be restricted to the solar system case.…”

ζ2Reticuli, its debris disk, and its lonely stellar companionζ1Ret

“…The achieved high precision in chemical abundances allowed observers to study the chemical abundances of stars with and without planets in detail (e.g., Gilli et al 2006;Robinson et al 2006;Delgado Mena et al 2014Kang et al 2011;Adibekyan et al 2012aAdibekyan et al ,b, 2015c. These studies are very important since the chemical abundances of stars with planets provide a huge wealth of information about the planet formation process (e.g., Bond et al 2010;Delgado Mena et al 2010), composition of planets (e.g., Thiabaud et al 2014;Dorn et al 2015;Santos et al 2015), and Based on data obtained from the ESO Science Archive Facility under request number vadibekyan204818, vadibekyan204820, and vadibekyan185979.…”

From stellar to planetary composition: Galactic chemical evolution of Mg/Si mineralogical ratio

“…Grasset et al 2009;Bond et al 2010;Delgado Mena et al 2010;Rogers & Seager 2010;Thiabaud et al 2014Thiabaud et al , 2015Dorn et al 2015). Among the most important mineralogical ratios are the Mg/Si, Fe/Si, and C/O ratios that can be used to constrain the chemical composition of terrestrial planets (e.g.…”

“…Among the most important mineralogical ratios are the Mg/Si, Fe/Si, and C/O ratios that can be used to constrain the chemical composition of terrestrial planets (e.g. Bond et al 2010;Thiabaud et al 2015;Dorn et al 2015). Recently, Dressing et al (2015) showed that all the terrestrial planets in their sample with masses lower than 6 M ⊕ lie in the same mass-radius area as Earth and Venus.…”