Dynamics and Origins of the Near-Resonant Kepler Planets

TL;DR

This study analyzes the near-resonant orbital configurations of over 100 Kepler planet pairs, revealing insights into their formation and early evolution through transit timing variations and an integrable resonance model.

Contribution

It introduces a novel method for analyzing transit timing variations and applies it to a large sample, uncovering the transition from libration to circulation near resonance and proposing a stochastic stirring formation scenario.

Findings

Transition from libration to circulation at 0.6% period ratio from resonance.

Orbital properties indicate systems are far from resonant equilibrium.

Stochastic turbulence models better explain observed architectures.

Abstract

Short-period super-Earths and mini-Neptunes encircle more than $\sim50\%$ of Sun-like stars and are relatively amenable to direct observational characterization. Despite this, environments in which these planets accrete are difficult to probe directly. Nevertheless, pairs of planets that are close to orbital resonances provide a unique window into the inner regions of protoplanetary disks, as they preserve the conditions of their formation, as well as the early evolution of their orbital architectures. In this work, we present a novel approach toward quantifying transit timing variations within multi-planetary systems and examine the near-resonant dynamics of over 100 planet pairs detected by \textit{Kepler}. Using an integrable model for first-order resonances, we find a clear transition from libration to circulation of the resonant angle at a period ratio of $\approx 0.6\%$ wide of exact resonance. The orbital properties of these systems indicate that they systematically lie far away from the resonant forced equilibrium. Cumulatively our modeling indicates that while orbital architectures shaped by strong disk damping or tidal dissipation are inconsistent with observations, a scenario where stochastic stirring by turbulent eddies augments the dissipative effects of protoplanetary disks reproduces several features of the data.