Impact of rotation on synthetic mass-radius relationships of two-layer rocky planets and water worlds

TL;DR

This study investigates how rotation influences the mass-radius relationships of rocky planets and water worlds, revealing that rotation causes significant radius increases comparable to observational uncertainties and EOS variations.

Contribution

It provides a new multivariate fit for planetary radius considering mass, rotation, and core size, aiding in interpreting observational data of exoplanets.

Findings

Rotation increases planetary radius by ~0.3f to 0.55f depending on parameters.

Rotation effects are comparable to current observational uncertainties.

A multivariate fit model enables quick characterization of planetary structure.

Abstract

We have analyzed the effects of rotation on mass-radius relationships for single-layer and two-layer planets having a core and an envelope made of pure materials among iron, perovskite and water in solid phase. The numerical surveys use the DROP code updated with a modified polytropic equation-of-state (EOS) and investigate flattening parameters $f$ up to $0.2$. In the mass range $0.1 M_\oplus < M < 10 M_\oplus$, we find that rotation systematically shifts the curves of composition towards larger radii and/or smaller masses. Relative to the spherical case, the equatorial radius $R_{eq}$ is increased by about $0.36f$ for single-layer planets, and by $0.30f$ to $0.55f$ for two-layer planets (depending on the core size fraction $q$ and planet mass $M$). Rotation is an additional source of confusion in deriving planetary structures, as the radius alterations are of the same order as i) current observational uncertainties for super-Earths, and ii) EOS variations. We have established a multivariate fit of the form $R_{eq}(M,f,q)$, which enables a fast characterization of the core size and rotational state of rocky planets and ocean worlds. We discuss how the observational data must be shifted in the diagrams to self-consistently account for an eventual planet spin, depending on the geometry of the transit (circular/oblate). A simple application to the recently characterized super-Earth candidate LHS1140b is discussed.