New Perspectives on the Exoplanet Radius Gap from a Mathematica Tool and Visualized Water Equation of State

Abstract

Recent astronomical observations obtained with the Kepler and TESS missions and their related ground-based follow-ups revealed an abundance of exoplanets with a size intermediate between Earth and Neptune (1 R ⊕ ≤ R ≤ 4 R ⊕ ). A low occurrence rate of planets has been identified at around twice the size of Earth (2 × R ⊕ ), known as the exoplanet radius gap or radius valley. We explore the geometry of this gap in the mass–radius diagram, with the help of a Mathematica plotting tool developed with the capability of manipulating exoplanet data in multidimensional parameter space, and with the help of visualized water equations of state in the temperature–density (T–ρ) graph and the entropy–pressure (s–P) graph. We show that the radius valley can be explained by a compositional difference between smaller, predominantly rocky planets (<2 × R ⊕ ) and larger planets (>2 × R ⊕ ) that exhibit greater compositional diversity including cosmic ices (water, ammonia, methane, etc.) and gaseous envelopes. In particular, among the larger planets (>2 × R ⊕ ), when viewed from the perspective of planet equilibrium temperature (T eq ), the hot ones (T eq ≳ 900 K) are consistent with ice-dominated composition without significant gaseous envelopes, while the cold ones (T eq ≲ 900 K) have more diverse compositions, including various amounts of gaseous envelopes.