Revised mass-radius relationships for water-rich rocky planets more irradiated than the runaway greenhouse limit

TL;DR

This paper develops new mass-radius relationships for water-rich rocky planets with thick atmospheres due to high irradiation, correcting overestimations from traditional models assuming condensed water.

Contribution

It introduces climate-model-based mass-radius relationships for highly irradiated water-rich planets, accounting for steam atmospheres and reducing bulk water content estimates.

Findings

Traditional models overestimate water content by orders of magnitude.

New relationships better match observed densities of planets like TRAPPIST-1 b, c, d.

Empirical formula for steam atmosphere thickness provided.

Abstract

Mass-radius relationships for water-rich rocky planets are usually calculated assuming most water is present in condensed (either liquid or solid) form. Planet density estimates are then compared to these mass-radius relationships, even when these planets are more irradiated than the runaway greenhouse irradiation limit (around 1.1~times the insolation at Earth for planets orbiting a Sun-like star), for which water has been shown to be unstable in condensed form and would instead form a thick H2O-dominated atmosphere. Here we use the LMD Generic numerical climate model to derive new mass-radius relationships appropriate for water-rich rocky planets that are more irradiated than the runaway greenhouse irradiation limit, meaning planets endowed with a steam, water-dominated atmosphere. For a given water-to-rock mass ratio, these new mass-radius relationships lead to planet bulk densities much lower than calculated when water is assumed to be in condensed form. In other words, using traditional mass-radius relationships for planets that are more irradiated than the runaway greenhouse irradiation limit tends to dramatically overestimate -- possibly by several orders of magnitude -- their bulk water content. In particular, this result applies to TRAPPIST-1 b, c, and d, which can accommodate a water mass fraction of at most 2, 0.3 and 0.08 %, respectively, assuming planetary core with a terrestrial composition. In addition, we show that significant changes of mass-radius relationships (between planets less and more irradiated than the runaway greenhouse limit) can be used to remove bulk composition degeneracies in multiplanetary systems such as TRAPPIST-1. Finally, we provide an empirical formula for the H2O steam atmosphere thickness which can be used to construct mass-radius relationships for any water-rich, rocky planet more irradiated than the runaway greenhouse irradiation threshold.