The role of dissipative evolution for three-planet, near-resonant extrasolar systems

Gabriele Pichierri,Konstantin Batygin,Alessandro Morbidelli

doi:10.1051/0004-6361/201935259

Abstract

Early dynamical evolution of close-in planetary systems is shaped by an intricate combination of planetary gravitational interactions, orbital migration, and dissipative effects. While the process of convergent orbital migration is expected to routinely yield resonant planetary systems, previous analyses have shown that the semi-major axes of initially resonant pairs of planets will gradually diverge under the influence of long-term energy damping, producing an overabundance of planetary period ratios in slight excess of exact commensurability. While this feature is clearly evident in the orbital distribution of close-in extrasolar planets, the existing theoretical picture is limited to the specific case of the planetary three-body problem. In this study, we generalise the framework of dissipative divergence of resonant orbits to multi-resonant chains, and apply our results to the current observational census of well-characterised three-planet systems. Focusing on the 2:1 and 3:2 commensurabilities, we identify three three-planet systems, whose current orbital architecture is consistent with an evolutionary history wherein convergent migration first locks the planets into a multi-resonant configuration and subsequent dissipation repels the orbits away from exact commensurability. Nevertheless, we find that the architecture of the overall sample of multi-planetary systems is incompatible with this simple scenario, suggesting that additional physical mechanisms must play a dominant role during the early stages of planetary systems’ dynamical evolution.

Highlights

The search for exoplanets in recent years has uncovered a multitude of planetary systems, the study of which is the key to an understanding of planetary formation and evolution
In this work, we have generalised the formalism of dissipative divergence of resonant orbits to multi-resonant chains
If the orbital architecture of a system is found near one of these equilibrium points, it is strongly suggestive that the envisioned scenario of slow convergent orbital migration leading to capture into resonance and subsequent orbital divergence due to dissipative evolution really occurred for the system

Summary

Introduction

The search for exoplanets in recent years has uncovered a multitude of planetary systems, the study of which is the key to an understanding of planetary formation and evolution. The exoplanet population is dominated by Kepler’s transit detections, making the planetary physical radii and orbital periods the better constrained parameters of the sample. Concerning the first aspect, much work has been done recently to understand how photoevaporation sculpts the physical radii of planets (Fulton et al 2017, and references therein). In this work we address the second, complementary problem of the orbital period distribution. One of the most notable aspects of the Kepler data is that the distribution of the period ratios of neighbouring planets in multi-planets systems shows two seemingly conflicting features: on the one hand, it appears relatively broad and smooth, without any single, unmistakably emerging feature; on the other hand, a slight preference for near-resonant configurations is evident upon close examination. It is often pointed out that there is a lack of planet pairs in correspondence with period ratios very close to low-integer ratios, and a definite excess just wide of these values, especially the 2:1 and 3:2, see Fig. 1

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