A Simple Analytical Model for Rocky Planet Interiors

Abstract

This work aims at exploring the scaling relations among rocky exoplanets. With the assumption of internal gravity increasing linearly in the core, and staying constant in the mantle, and tested against numerical simulations, a simple model is constructed, applicable to rocky exoplanets of core mass fraction (CMF) $\in 0.1\sim 0.4$ and mass $\in 0.1\sim 10M_{\oplus }$. Various scaling relations are derived: (1) core radius fraction $\mathrm{CRF}\approx \sqrt{\mathrm{CMF}}$, (2) Typical interior pressure $P_{\text{typical}}\sim g_{\mathrm{s}}^2$ (surface gravity squared), (3) core formation energy $E_{\mathrm{diff}}\sim \frac{1}{10}{E}_{\mathrm{grav}}$ (the total gravitational energy), (4) effective heat capacity of the mantle $C_{\mathrm{p}}\approx \left(\frac{M_{\mathrm{p}}}{M_{\oplus }}\right)\cdot 7\cdot 10^{27}$ J K${}^{-1}$, and (5) the moment of inertia $I\approx \frac{1}{3}\cdot M_{\mathrm{p}}\cdot R_{\mathrm{p}}^2$. These scaling relations, though approximate, are handy for quick use owing to their simplicity and lucidity, and provide insights into the interior structures of rocky exoplanets. As examples, this model is applied to several planets including Earth, GJ 1132b, Kepler-93b, and Kepler-20b, and made comparison with the numerical method.

accepted by ApJ

References in corpus (8)

• Mass-Radius Relationships for Solid Exoplanets
• Mass-Radius Relation for Rocky Planets based on PREM
• The Mass of Kepler-93b and The Composition of Terrestrial Planets
• A method for the direct determination of the surface gravities of transiting extrasolar planets
• Kepler-21b: A rocky planet around a V = 8.25 magnitude star
• A 1.9 Earth radius rocky planet and the discovery of a non-transiting planet in the Kepler-20 system
• Kepler-93b: A Terrestrial World Measured to within 120 km, and a Test Case for a New Spitzer Observing Mode
• Variational Principle for Planetary Interiors

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• Planetary Magnetism as a Parameter in Exoplanet Habitability
• A Reanalysis of the Composition of K2-106b: an Ultra-short Period Super-Mercury Candidate
• Blue marble, stagnant lid: Could dynamic topography avert a waterworld?
• A Geologically Robust Procedure For Observing Rocky Exoplanets to Ensure that Detection of Atmospheric Oxygen is an Earth-Like Biosignature
• Understanding and predicting cadence effects in the characterization of exoplanet transits
• Exploring the habitability and interior composition of exoplanets lying within the extended habitable zone
• The dynamical evolution of close-in binary systems formed by a super-Earth and its host star. Case of the Kepler-21 system