Abstract
Context. Planetary mass and radius data suggest that low-mass exoplanets show a wide variety of densities. This includes sub-Neptunes, whose low densities can be explained with the presence of a volatile-rich layer. Water is one of the most abundant volatiles, which can be in the form of different phases depending on the planetary surface conditions. To constrain their composition and interior structure, models must be developed that accurately calculate the properties of water at its different phases. Aims. We present an interior structure model that includes a multiphase water layer with steam, supercritical, and condensed phases. We derive the constraints for planetary compositional parameters and their uncertainties, focusing on the multi-planetary system TRAPPIST-1, which presents both warm and temperate planets. Methods. We use a 1D steam atmosphere in radiative-convective equilibrium with an interior whose water layer is in supercritical phase self-consistently. For temperate surface conditions, we implement liquid and ice Ih to ice VII phases in the hydrosphere. We adopt a Markov chain Monte Carlo inversion scheme to derive the probability distributions of core and water compositional parameters. Results. We refine the composition of all planets and derive atmospheric parameters for planets ‘b’ and ‘c’. The latter would be in a post-runaway greenhouse state and could be extended enough to be probed by space missions such as JWST. Planets ‘d’ to ‘h’ present condensed ice phases, with maximum water mass fractions below 20%. Conclusions. The derived amounts of water for TRAPPIST-1 planets show a general increase with semi-major axis, with the exception of planet d. This deviation from the trend could be due to formation mechanisms, such as migration and an enrichment of water in the region where planet d formed, or an extended CO2-rich atmosphere.
Highlights
Ongoing space missions such as CHEOPS (Benz 2017) and TESS (Ricker et al 2015), and their follow-up with ground-based radial velocity telescopes, are confirming the existence of lowmass exoplanets with a wide range of densities
The surface conditions are determined by the greenhouse effect caused by atmospheric gases, making the modelling of radiative-convective equilibrium in atmospheres a key parameter to determine the phase in which water could be present on the surface
We find that a CO2-dominated atmosphere with 1% water vapour in planet d would be in radiative-convective equilibrium by computing the outgoing longwave radiation (OLR) and absorbed radiation, as we have for water-dominated atmospheres
Summary
Ongoing space missions such as CHEOPS (Benz 2017) and TESS (Ricker et al 2015), and their follow-up with ground-based radial velocity telescopes, are confirming the existence of lowmass exoplanets with a wide range of densities. For temperate planets, we have updated the interior model presented in Brugger et al (2016, 2017) to include ice phases Ih, II, III, V, and VI We introduce these models in a Markov chain Monte Carlo (MCMC) Bayesian analysis scheme adapted from Dorn et al (2015). This allows us to derive the water mass fraction (WMF) and core mass fraction (CMF) that reproduce the observed radius, mass, and stellar composition measurements We use this model to explore the possible water content of the TRAPPIST-1 system, an ultra-cool M dwarf that hosts seven low-mass planets in close-in orbits. All planets in TRAPPIST-1 system have masses and radii that are characteristic of rocky planets, their differences in density indicate that each planet has a different volatile content This makes this planetary system ideal for testing planet interior, atmospheric structure, and formation scenarios.
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