Classification and Nomenclature of Planets in the Mass-Radius Plane

TL;DR

This work introduces the Fundamental Planetary Plane (FPP), a three-parameter framework using mass, radius, and the moment of inertia to classify celestial bodies and distinguish planets from non-planetary objects. It employs a self-gravitating, polytropic model with $P = K \rho^{1+1/n}$ and Lane--Emden analysis to derive the $R$–$M$ relation and $I = k_n M R^2$, situating diverse Solar System bodies and exoplanets within the plane. The study proposes a physical planet window from $10^{23}$ kg ($0.02\mathrm{EU}$) to $2.5\times10^{28}$ kg ($13\mathrm{JU}$) and identifies distinct turn-offs separating rocky planets, gas giants, brown dwarfs, and low-mass stars, while showing Pluto does not occupy the planetary regime. An additional radius–density diagnostic corroborates the FPP boundaries, offering an independent structural perspective on planetary taxonomy. The framework aims to standardize planet definition across Solar System, exoplanet, and free-floating contexts, with practical implications for catalogs and classification schemes.

Abstract

6500+ exoplanets have been detected using various techniques. This prompted the emergence of many recent works on the taxonomy, or classification, of exoplanets. However, there is still no basic, fundamental definition of 'What is a planet?'. IAU has forwarded a definition in 2006, which however, raised more questions than it solved. The first task here is to establish if there are limits on the size/mass of planets. The lower mass limit may be assumed as of Mimas (0.03 EU) - approximately minimum mass required to attain a nearly spherical hydrostatic equilibrium shape. The upper mass limit may be easier - there is a natural lower limit to what constitutes a star: 0.08 SU. But then there are brown dwarfs: IAU has defined brown dwarfs as objects exceeding the deuterium burning limit (~13 JU), and giant exoplanets generally have masses of 0.3 to 60 JU. The resolution requires assembling the basic physical parameters that define planets quantitatively. Mass and radius are the two fundamental properties, and we propose to use a third correlated parameter: the moment of inertia. Based on this, we create the parametric Fundamental Planetary Plane where the two parameters are correlated with the third. The fundamental planetary plane (FPP) with turn-off point diagrams is constructed for visual representation. We propose an alternate potential description of a planet definition as 'A celestial spherical object, bound to a star or unbound, that lies on the fundamental planetary plane, within a mass range between 0.02 EU to 13 JU'. This definition is intended to complement existing taxonomies by providing a quantitative, structure-based criterion applicable to both Solar System planets, exoplanets and free-floating planets. These turn-off point diagrams serve as an alternative to the Hertzsprung-Russell (HR) diagram, but for planets.

Figures (9)

• Figure 1: Mass-Radius plot of asteroids, moons, planets, brown dwarfs and low-mass stars. From nearly 5600 exoplanets listed in the PHL-HWC database, 1504 are categorized as terrestrial worlds (orange dots), 2609 as Neptunian worlds (green dots), 1355 as Jovian worlds (purple dots), and 115 as brown dwarfs (brown dots).
• Figure 2: Turn-off for rocky planets. The moment of inertia increases exponentially with mass for rocky planets, but is relatively constant for small-sized objects.
• Figure 3: Rocky Planet Plane: Red diamonds overlapping with brown dots which represent rocky planets in the Solar System. The black cross near the magenta triangle markers for moons corresponds to Pluto. Red diamonds located above the rocky exoplanets indicate giant planets of the Solar System. Blue stars represent IAU candidate objects under consideration for planetary status. Blue triangles denote asteroids.
• Figure 4: Pluto turn-off in the moons plane: the magenta and blue colored triangles represent the moons and asteroids of the Solar System, respectively, while the blue stars denote IAU planetary candidates.
• Figure 5: Turn-off for gas giants: The gas giants of the Solar System can be identified by the red diamonds above the turn-off point, while the rocky planets and the ice giants lie below it.