Pairwise Tidal Equilibrium States and the Architecture of Extrasolar Planetary Systems

Abstract

Current observations indicate that the planet formation process often produces multiple planet systems with nearly circular orbits, regular spacing, a narrow range of inclination angles, and similar planetary masses of order $m_{\mathrm{p}}\sim 10M_{\oplus }$. Motivated by the observational sample, this paper determines the tidal equilibrium states for this class of extrasolar planetary systems. We start by considering two planet systems with fixed orbital spacing and variable mass ratios. The basic conjecture explored in this paper is that the planet formation process will act to distribute planetary masses in order to achieve a minimum energy state. The resulting minimum energy configuration --- subject to the constraint of constant angular momentum --- corresponds to circular orbits confined to a plane, with nearly equal planetary masses (as observed). We then generalize the treatment to include multiple planet systems, where each adjacent pair of planets attains its (local) tidal equilibrium state. The properties of observed planetary systems are close to those expected from this pairwise equilibrium configuration. In contrast, observed systems do not reside in a global minimum energy state. Both the equilibrium states of this paper and observed multi-planet systems, with planets of nearly equal mass on regularly spaced orbits, have an effective surface density of the form $\sigma \propto r^{-2}$, much steeper than most disk models.

18 pages, 5 figures, accepted to MNRAS

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Cited by in corpus (15)

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• A framework for the architecture of exoplanetary systems. I. Four classes of planetary system architecture
• Inner Planetary System Gap Complexity is a Predictor of Outer Giant Planets
• Intra-system uniformity: a natural outcome of dynamical sculpting
• Edge-of-the-Multis: Evidence for a Transition in the Outer Architectures of Compact Multi-Planet Systems
• A framework for the architecture of exoplanetary systems. II. Nature versus nurture: Emergent formation pathways of architecture classes
• Orbital Architectures of Kepler Multis From Dynamical Instabilities
• Confirming the 3:2 Resonance Chain of K2-138
• Architecture Classification for Extrasolar Planetary Systems
• On the Degree of Dynamical Packing in the Kepler Multi-planet Systems
• Earth-like planets hosting systems: Architecture and properties
• Diversities and similarities exhibited by multi-planetary systems and their architectures: I. Orbital spacings
• Biases from Missing a Small Planet in High Multiplicity Systems
• Split Peas in a Pod: Intra-System Uniformity of Super-Earths and Sub-Neptunes
• A Multi-Planet System's Sole Super-Puff: Exploring Allowable Physical Parameters for the Cold Super-Puff HIP 41378 f