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

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 0.36 f for single-layer planets and by 0.30 f 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.