Dynamics and Origins of the Near-resonant Kepler Planets

Abstract

Short-period super-Earths and mini-Neptunes encircle more than ∼50% 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 multiplanetary systems and examine the near-resonant dynamics of over 100 planet pairs detected by 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 ≈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.

exoMMR: A New Python Package to Confirm and Characterize Mean Motion Resonances

“…In this work, we study 20 systems and 36 resonances that overlap with Goldberg & Batygin (2023). Of these systems, we confirm 40% of resonances that they also confirm.…”

“…There are numerous other ways to study and confirm MMRs, including verifying that the system lies within the separatrix of the system's phase space (Winter & Murray 1997). Our methods rely entirely on the libration of the resonant angles, and recent studies have suggested this technique might not be completely accurate; Goldberg & Batygin (2023) found that many TTV systems might show librating angles, even if the system is formally nonresonant because the Hamiltonian has no separatrix.…”

Enhanced Size Uniformity for Near-resonant Planets

“…However, as encountered in the case of the turbulent disk model, this formalism alone may not suffice as a global framework for the evolution of multiple-planet systems. The postnebular instabilities characteristic of this model are expected to occur efficiently and near-ubiquitously (Ghosh & Chatterjee 2023;Lammers et al 2023) such that only a few percent of systems would be expected to retain their initial resonant signatures (Goldberg & Batygin 2023), which lies in direct tension with the observed occurrence of near-resonant planetary configurations. While the achievement of nearresonant structures in such a formalism could thus occur primarily by chance following the epoch of instability (Goldberg & Batygin 2023), such near-resonant pairs would lose memory of their primoridal uniformity and lack any means of subsequent coordination in planetary size, disallowing the prospect of enhanced size uniformity altogether.…”

“…Recent work by Goldberg & Batygin (2023) has demonstrated that, of these various paradigms, the turbulent disk model is particularly amenable to reproducing the properties of observed planetary configurations, as it provides energy dissipation sufficient to reproduce the aforementioned degree of broadened spacing while simultaneously introducing stochastic forces that excite the mixed resonance angles into circulation, thereby successfully dislodging planets from MMR on both accounts. In consideration of planetary pairs within such a disk, we note that, since the provision of nearly equal masses constitutes a stable and energetically optimal configuration for a two-planet system (Adams et al 2020a(Adams et al , 2020b, it reasons that invariance to such stochastic perturbations may itself scale with planetary uniformity as well, such that highly uniform pairs may have a greater tendency to retain their orbital spacing while less uniform pairs may drift farther from MMR (Adams et al 2020b), where subsequent secular interactions between pairs significantly dislodged from MMR may further sculpt their orbital evolution.…”

“…Consequently, even in regimes where this dissolution is favorable, perturbations induced by disk turbulence may not be sufficiently disruptive to uniquely generate the nonresonant configurations that dominate the observed sample, indicating that such modal architectures may be the result of complementary or alternative mechanisms. Furthermore, while the degree of stochasticity afforded by turbulence may indeed disrupt idealized capture into MMR, it may be too greatly amenable to the narrowing of pair spacing (Goldberg & Batygin 2023;Choksi & Chiang 2023) in a manner that disfavors the well-characterized excess of pairs lying slightly wide of commensurability (Figure 1). It has been demonstrated that such asymmetries in the period ratio distribution may be preserved under a scheme with comparatively smoother migration torques, while mixed resonant angles for a given pair may still be excited into circulation via secular forcing from an external perturbing planet (Choksi & Chiang 2023).…”