# Two Empirical Regimes of the Planetary Mass-Radius Relation

## TL;DR

This paper identifies two distinct regimes in the planetary mass-radius relation, linked to planetary composition and electron degeneracy, with implications for understanding planet formation and classification.

## Contribution

It reveals a transition point in the M-R relation at 124 Earth masses and 12.1 Earth radii, connecting it to the onset of electron degeneracy in hydrogen.

## Key findings

- Two regimes in M-R relation with different power laws.
- Transition point linked to hydrogen electron degeneracy.
- Good agreement between observational data and models.

## 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 \pm 7, M_Earth and a radius of 12.1 \pm 0.5, R_Earth. Furthermore, the M-R relation is R \propto M^{0.55\pm 0.02} and R \propto M^{0.01\pm0.02} 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 which 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 one derived by population synthesis calculations and show that there is a good qualitative agreement between the two samples.