Two empirical regimes of the planetary mass-radius relation

¹ School of Geosciences, Tel-Aviv University, Tel-Aviv, Israel
² Center for Theoretical Astrophysics & Cosmology, Institute for Computational Science, University of Zurich, 8057 Zürich, Switzerland
e-mail: rhelled@physik.uzh.ch
³ Physics Institute, University of Bern, 3012 Bern, Switzerland

Received: 18 October 2016
Accepted: 25 January 2017

Abstract

Today, with the large number of detected exoplanets and improved measurements, we can reach the next step of planetary characterization. Classifying different populations of planets is not only important for our understanding of the demographics of various planetary types in the galaxy, but also for our understanding of planet formation. We explore the nature of two regimes in the planetary mass-radius (M-R) relation. We suggest that the transition between the two regimes of “small” and “large” planets occurs at a mass of 124 ± 7M_⊕ and a radius of 12.1 ± 0.5R_⊕. Furthermore, the M-R relation is R ∝ M^{0.55 ± 0.02} and R ∝ M^{0.01 ± 0.02} for small and large planets, respectively. We suggest that the location of the breakpoint is linked to the onset of electron degeneracy in hydrogen, and therefore to the planetary bulk composition. Specifically, it is the characteristic minimal mass of a planet that consists of mostly hydrogen and helium, and therefore its M-R relation is determined by the equation of state of these materials. We compare the M-R relation from observational data with the relation derived by population synthesis calculations and show that there is a good qualitative agreement between the two samples.