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

¹ University of Bordeaux, CNRS, LAB, UMR 5804, 33600 Pessac, France
² LPC2E, OSUC, Univ Orleans, CNRS, CNES, Observatoire de Paris, 45071 Orleans, France

^★ Corresponding author: jean-marc.hure@u-bordeaux.fr

Received: 12 February 2025
Accepted: 30 June 2025

Abstract

We analyze the effects of rotation on mass–radius relationships for single-layer and two-layer planets with a core and an envelope made of pure materials that includes iron, perovskite, and water in solid phase. The numerical surveys we adopted employ the DROP code updated with a modified polytropic equation of state (EoS). We investigated the flattening parameters, f, up to 0.2. In the mass range of 0.1 M_⊕ ≲ M ≲ 10 M_⊕, we find that the 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 0.55 f for two-layer planets (depending on the core size fraction, q, and the 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 established a multivariate fit of the form R_eq(M, f, q), which enables a fast characterisation 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 (i.e. circular or oblate). A simple application to the recently characterised super-Earth candidate LHS 1140 b is discussed in this work.