Caroline Dorn

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

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

Aims. We explore the possibility that the stellar relative abundances of di erent species can be used to constrain the bulk abundances of known transiting rocky planets. Methods. We use high resolution spectra to derive stellar parameters and chemical abundances for Fe, Si, Mg, O, and C in three stars hosting low mass, rocky planets: CoRoT-7, Kepler-10, and Kepler-93. These planets follow the same line along the mass-radius diagram, pointing toward a similar composition. The derived abundance ratios are compared with the solar values. With a simple stoichiometric model, we estimate the iron mass fraction in each planet, assuming stellar composition. Results. We show that in all cases, the iron mass fraction inferred from the mass-radius relationship seems to be in good agreement with the iron abundance derived from the host star’s photospheric composition. Conclusions. The results suggest that stellar abundances can be used to add constraints on the composition of orbiting rocky planets.

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

The main goal of this work is to study element ratios that are important for the formation of planets of different masses. We study potential correlations between the existence of planetary companions and the relative elemental abundances of their host stars. We use a large sample of FGK-type dwarf stars for which precise Mg, Si, and Fe abundances have been derived using HARPS high-resolution and high-quality data. A first analysis of the data suggests that low-mass planet host stars show higher [Mg/Si] ratios, while giant planet hosts present [Mg/Si] that is lower than field stars. However, we found that the [Mg/Si] ratio significantly depends on metallicity through Galactic chemical evolution. After removing the Galactic evolution trend only the difference in the [Mg/Si] elemental ratio between low-mass planet hosts and non-hosts was present in a significant way. These results suggests that low-mass planets are more prevalent around stars with high [Mg/Si]. Our results demonstrate the importance of Galactic chemical evolution and indicate that it may play an important role in the planetary internal structure and composition.

Bayesian analysis of interiors of HD 219134b, Kepler-10b, Kepler-93b, CoRoT-7b, 55 Cnc e, and HD 97658b using stellar abundance proxies

Using a generalized Bayesian inference method, we aim to explore the possible interior structures of six selected exoplanets for which planetary mass and radius measurements are available in addition to stellar host abundances: HD~219134b, Kepler-10b, Kepler-93b, CoRoT-7b, 55~Cnc~e, and HD~97658b. We aim to investigate the importance of stellar abundance proxies for the planetary bulk composition (namely Fe/Si and Mg/Si) on prediction of planetary interiors. We performed a full probabilistic Bayesian inference analysis to formally account for observational and model uncertainties while obtaining confidence regions of structural and compositional parameters of core, mantle, ice layer, ocean, and atmosphere. We determined how sensitive our parameter predictions depend on (1) different estimates of bulk abundance constraints and (2) different correlations of bulk abundances between planet and host star. [...] Although the possible ranges of interior structures are large, structural parameters and their correlations are constrained by the sparse data. The probability for the tested exoplanets to be Earth-like is generally very low. Furthermore, we conclude that different estimates of planet bulk abundance constraints mainly affect mantle composition and core size.

The nature of the TRAPPIST-1 exoplanets

Context. The TRAPPIST-1 system hosts seven Earth-sized, temperate exoplanets orbiting an ultra-cool dwarf star. As such, it represents a remarkable setting to study the formation and evolution of terrestrial planets that formed in the same protoplanetary disk. While the sizes of the TRAPPIST-1 planets are all known to better than 5% precision, their densities have significant uncertainties (between 28% and 95%) because of poor constraints on the planets masses. Aims.The goal of this paper is to improve our knowledge of the TRAPPIST-1 planetary masses and densities using transit-timing variations (TTV). The complexity of the TTV inversion problem is known to be particularly acute in multi-planetary systems (convergence issues, degeneracies and size of the parameter space), especially for resonant chain systems such as TRAPPIST-1. Methods. To overcome these challenges, we have used a novel method that employs a genetic algorithm coupled to a full N-body integrator that we applied to a set of 284 individual transit timings. This approach enables us to efficiently explore the parameter space and to derive reliable masses and densities from TTVs for all seven planets. Results. Our new masses result in a five- to eight-fold improvement on the planetary density uncertainties, with precisions ranging from 5% to 12%. These updated values provide new insights into the bulk structure of the TRAPPIST-1 planets. We find that TRAPPIST-1,c and e likely have largely rocky interiors, while planets b, d, f, g, and h require envelopes of volatiles in the form of thick atmospheres, oceans, or ice, in most cases with water mass fractions less than 5%.

A generalized bayesian inference method for constraining the interiors of super Earths and sub-Neptunes

Aims. We aim to present a generalized Bayesian inference method for constraining interiors of super Earths and sub-Neptunes. Our methodology succeeds in quantifying the degeneracy and correlation of structural parameters for high dimensional parameter spaces. Specifically, we identify what constraints can be placed on composition and thickness of core, mantle, ice, ocean, and atmospheric layers given observations of mass, radius, and bulk refractory abundance constraints (Fe, Mg, Si) from observations of the host star’s photospheric composition. nMethods. We employed a full probabilistic Bayesian inference analysis that formally accounts for observational and model uncertainties. Using a Markov chain Monte Carlo technique, we computed joint and marginal posterior probability distributions for all structural parameters of interest. We included state-of-the-art structural models based on self-consistent thermodynamics of core, mantle, high-pressure ice, and liquid water. Furthermore, we tested and compared two different atmospheric models that are tailored for modeling thick and thin atmospheres, respectively. nResults. First, we validate our method against Neptune. Second, we apply it to synthetic exoplanets of fixed mass and determine the effect on interior structure and composition when (1) radius; (2) atmospheric model; (3) data uncertainties; (4) semi-major axes; (5) atmospheric composition (i.e., a priori assumption of enriched envelopes versus pure H/He envelopes); and (6) prior distributions are varied. nConclusions. Our main conclusions are: (1) given available data, the range of possible interior structures is large; quantification of the degeneracy of possible interiors is therefore indispensable for meaningful planet characterization. (2) Our method predicts models that agree with independent estimates of Neptune’s interior. (3) Increasing the precision in mass and radius leads to much improved constraints on ice mass fraction, size of rocky interior, but little improvement in the composition of the gas layer, whereas an increase in the precision of stellar abundances enables to better constrain mantle composition and relative core size; (4) for thick atmospheres, the choice of atmospheric model can have significant influence on interior predictions, including the rocky and icy interior. The preferred atmospheric model is determined by envelope mass. This study provides a methodology for rigorously analyzing general interior structures of exoplanets which may help to understand how exoplanet interior types are distributed among star systems. This study is relevant in the interpretation of future data from missions such as TESS, CHEOPS, and PLATO.

The language of exoplanet ranking metrics needs to change

We have found many Earth-sized worlds but we have no way of determining if their surfaces are Earth-like. This makes it impossible to quantitatively compare habitability, and pretending we can risks damaging the field.

Secondary Atmospheres on HD 219134 b and c

We analyze the interiors of HD~219134~b and c, which are among the coolest super Earths detected thus far. Without using spectroscopic measurements, we aim at constraining if the possible atmospheres are hydrogen-rich or hydrogen-poor. In a first step, we employ a full probabilistic Bayesian inference analysis in order to rigorously quantify the degeneracy of interior parameters given the data of mass, radius, refractory element abundances, semi-major axes, and stellar irradiation. We obtain constraints on structure and composition for core, mantle, ice layer, and atmosphere. In a second step, we aim to draw conclusions on the nature of possible atmospheres by considering atmospheric escape. Specifically, we compare the actual possible atmospheres to a threshold thickness above which a primordial (H

Constraining planet structure and composition from stellar chemistry: trends in different stellar populations

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Mass, Radius, and Composition of the Transiting Planet 55 Cnc e: Using Interferometry and Correlations—A Quick Update

-dominated) atmosphere can be retained against evaporation over the planets lifetime. The best constrained parameters are the individual layer thicknesses. The maximum radius fraction of possible atmospheres are 0.18 and 0.13