Aims. 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. Methods. 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. Results. The possible interior structures and correlations between structural parameters differ depending on data and data uncertainty. The strongest correlation is generally found between size of rocky interior and water mass fraction. Given the data, possible water mass fractions are high, even for most potentially rocky planets (HD 219134b, Kepler-93b, CoRoT-7b, and 55 Cnc e with estimates up to 35%, depending on the planet). Also, the interior of Kepler-10b is best constrained with possible interiors similar to Earth. Among all tested planets, only the data of Kepler-10b and Kepler-93b allow to put a higher probability on the planetary bulk Fe/Si to be stellar compared to extremely sub-stellar. Conclusions. 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.
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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.
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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. Methods. 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. Results. 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. Conclusions. 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.
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Context. A terrestrial planet is molten during formation and may remain molten due to intense insolation or tidal forces. Observations favour the detection and characterisation of hot planets, ...potentially with large outgassed atmospheres. Aims. We aim to determine the radius of hot Earth-like planets with large outgassing atmospheres. Our goal is to explore the differences between molten and solid silicate planets on the mass–radius relationship and transmission and emission spectra. Methods. An interior–atmosphere model was combined with static structure calculations to track the evolving radius of a hot rocky planet that outgasses CO2 and H2O. We generated synthetic emission and transmission spectra for CO2 and H2O dominated atmospheres. Results. Atmospheres dominated by CO2 suppress the outgassing of H2O to a greater extent than previously realised since previous studies applied an erroneous relationship between volatile mass and partial pressure. We therefore predict that more H2O can be retained by the interior during the later stages of magma ocean crystallisation. Formation of a surface lid can tie the outgassing of H2O to the efficiency of heat transport through the lid, rather than the radiative timescale of the atmosphere. Contraction of the mantle, as it cools from molten to solid, reduces the radius by around 5%, which can partly be offset by the addition of a relatively light species (e.g. H2O versus CO2) to the atmosphere. Conclusions. A molten silicate mantle can increase the radius of a terrestrial planet by around 5% compared to its solid counterpart, or equivalently account for a 13% decrease in bulk density. An outgassing atmosphere can perturb the total radius, according to its composition, notably the abundance of light versus heavy volatile species. Atmospheres of terrestrial planets around M-stars that are dominated by CO2 or H2O can be distinguished by observing facilities with extended wavelength coverage (e.g. JWST).
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The characterization of exoplanets relies on that of their host star. However, stellar evolution models cannot always be used to derive the mass and radius of individual stars, because many stellar ...internal parameters are poorly constrained. Here, we use the probability density functions (PDFs) of directly measured parameters to derive the joint PDF of the stellar and planetary mass and radius. Because combining the density and radius of the star is our most reliable way of determining its mass, we find that the stellar (respectively planetary) mass and radius are strongly (respectively moderately) correlated. We then use a generalized Bayesian inference analysis to characterize the possible interiors of 55 Cnc e. We quantify how our ability to constrain the interior improves by accounting for correlation. The information content of the mass-radius correlation is also compared with refractory element abundance constraints. We provide posterior distributions for all interior parameters of interest. Given all available data, we find that the radius of the gaseous envelope is . A stronger correlation between the planetary mass and radius (potentially provided by a better estimate of the transit depth) would significantly improve interior characterization and reduce drastically the uncertainty on the gas envelope properties.
The nature of the TRAPPIST-1 exoplanets Grimm, Simon L.; Demory, Brice-Olivier; Gillon, Michaël ...
Astronomy & astrophysics,
05/2018, Volume:
613
Journal Article, Web Resource
Peer reviewed
Open access
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 planet’s masses. Aims. The goal of this paper is to improve our knowledge of the TRAPPIST-1 planetary masses and densities using transit-timing variations (TTVs). 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%.
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Aims.
The secondary atmospheres of terrestrial planets form and evolve as a consequence of interaction with the interior over geological time. We aim to quantify the influence of planetary bulk ...composition on the interior–atmosphere evolution for Earth-sized terrestrial planets to aid in the interpretation of future observations of terrestrial exoplanet atmospheres.
Methods.
We used a geochemical model to determine the major-element composition of planetary interiors (MgO, FeO, and SiO
2
) following the crystallization of a magma ocean after planet formation, predicting a compositional profile of the interior as an initial condition for our long-term thermal evolution model. Our 1D evolution model predicts the pressure–temperature structure of the interior, which we used to evaluate near-surface melt production and subsequent volatile outgassing. Volatiles are exchanged between the interior and atmosphere according to mass conservation.
Results.
Based on stellar compositions reported in the Hypatia catalog, we predict that about half of rocky exoplanets have a mantle that convects as a single layer (whole-mantle convection), and the other half exhibit double-layered convection due to the presence of a mid-mantle compositional boundary. Double-layered convection is more likely for planets with high bulk planetary Fe-content and low Mg/Si-ratio. We find that planets with low Mg/Si-ratio tend to cool slowly because their mantle viscosity is high. Accordingly, low-Mg/Si planets also tend to lose volatiles swiftly through extensive melting. Moreover, the dynamic regime of the lithosphere (plate tectonics vs. stagnant lid) has a first-order influence on the thermal evolution and volatile cycling. These results suggest that the composition of terrestrial exoplanetary atmospheres can provide information on the dynamic regime of the lithosphere and the thermo-chemical evolution of the interior.
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We have collected transit times for the TRAPPIST-1 system with the Spitzer Space Telescope over four years. We add to these ground-based, HST, and K2 transit-time measurements, and revisit an N-body ...dynamical analysis of the seven-planet system using our complete set of times from which we refine the mass ratios of the planets to the star. We next carry out a photodynamical analysis of the Spitzer light curves to derive the density of the host star and the planet densities. We find that all seven planets' densities may be described with a single rocky mass-radius relation which is depleted in iron relative to Earth, with Fe 21 wt% versus 32 wt% for Earth, and otherwise Earth-like in composition. Alternatively, the planets may have an Earth-like composition but enhanced in light elements, such as a surface water layer or a core-free structure with oxidized iron in the mantle. We measure planet masses to a precision of 3%-5%, equivalent to a radial-velocity (RV) precision of 2.5 cm s−1, or two orders of magnitude more precise than current RV capabilities. We find the eccentricities of the planets are very small, the orbits are extremely coplanar, and the system is stable on 10 Myr timescales. We find evidence of infrequent timing outliers, which we cannot explain with an eighth planet; we instead account for the outliers using a robust likelihood function. We forecast JWST timing observations and speculate on possible implications of the planet densities for the formation, migration, and evolution of the planet system.
Abstract
We demonstrate that the deep volatile storage capacity of magma oceans has significant implications for the bulk composition, interior, and climate state inferred from exoplanet mass and ...radius data. Experimental petrology provides the fundamental properties of the ability of water and melt to mix. So far, these data have been largely neglected for exoplanet mass–radius modeling. Here we present an advanced interior model for water-rich rocky exoplanets. The new model allows us to test the effects of rock melting and the redistribution of water between magma ocean and atmosphere on calculated planet radii. Models with and without rock melting and water partitioning lead to deviations in planet radius of up to 16% for a fixed bulk composition and planet mass. This is within the current accuracy limits for individual systems and statistically testable on a population level. Unrecognized mantle melting and volatile redistribution in retrievals may thus underestimate the inferred planetary bulk water content by up to 1 order of magnitude.
Context. The Transiting Exoplanet Survey Satellite (TESS) is revolutionising the search for planets orbiting bright and nearby stars. In sectors 3 and 4, TESS observed TOI-402 (TIC-120896927), a ...bright V = 9.1 K1 dwarf also known as HD 15337, and found two transiting signals with periods of 4.76 and 17.18 days and radii of 1.90 and 2.21 R⊕, respectively. This star was observed prior to the TESS detection as part of the radial-velocity (RV) search for planets using the HARPS spectrometer, and 85 precise RV measurements were obtained before the launch of TESS over a period of 14 yr. Aims. In this paper, we analyse the HARPS RV measurements in hand to confirm the planetary nature of these two signals. Methods. HD 15337 happens to present a stellar activity level similar to the Sun, with a magnetic cycle of similar amplitude and RV measurements that are affected by stellar activity. By modelling this stellar activity in the HARPS radial velocities using a linear dependence with the calcium activity index log(RHK′) $\log(R^{\prime}_{\textrm{HK}})$ log(RHK′) , we are able, with a periodogram approach, to confirm the periods and the planetary nature of TOI-402.01 and TOI-402.02. We then derive robust estimates from the HARPS RVs for the orbital parameters of these two planets by modelling stellar activity with a Gaussian process and using the marginalised posterior probability density functions obtained from our analysis of TESS photometry for the orbital period and time of transit. Results. By modelling TESS photometry and the stellar host characteristics, we find that TOI-402.01 and TOI-402.02 have periods of 4.75642 ± 0.00021 and 17.1784 ± 0.0016 days and radii of 1.70 ± 0.06 and 2.52 ± 0.11 R⊕ (precision 3.6 and 4.2%), respectively. By analysing the HARPS RV measurements, we find that those planets are both super-Earths with masses of 7.20 ± 0.81 and 8.79 ± 1.68 M⊕ (precision 11.3 and 19.1%), and small eccentricities compatible with zero at 2σ. Conclusions. Although having rather similar masses, the radii of these two planets are very different, putting them on different sides of the radius gap. By studying the temporal evolution under X-ray and UV (XUV) driven atmospheric escape of the TOI-402 planetary system, we confirm, under the given assumptions, that photo-evaporation is a plausible explanation for this radius difference. Those two planets, being in the same system and therefore being in the same irradiation environment are therefore extremely useful for comparative exoplanetology across the evaporation valley and thus bring constraints on the mechanisms responsible for the radius gap.
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