Impact of Cold Jupiter Scattering on the Mean-Motion Resonance of Inner Small Planets

TL;DR

This study explores how scattering of cold Jupiters can disrupt mean-motion resonances in inner super-Earth systems, explaining observed period ratio distributions.

Contribution

It demonstrates that even limited CJ scattering can significantly perturb inner planet resonances, providing a new dynamical pathway for system architecture evolution.

Findings

Single pericenter passage of eccentric CJ can disrupt inner resonances.

Deep penetration of CJs into inner systems is rare (<20%).

Scattering history of CJs can drive resonance disruption in most systems.

Abstract

A key feature of close-in, multiple super-Earth (SE) systems is the tendency for adjacent planet pairs to lie just wide of low-order mean-motion resonances (MMR). This period ratio distribution has motivated numerous theoretical studies, particularly those invoking post-disk processes that perturb initially resonant architectures. We investigate whether orbital instability among cold Jupiters (CJs) can perturb inner SE systems initially in MMR. We show that a single pericenter passage of a highly eccentric CJ can disrupt inner resonances once a critical perturbation strength is exceeded, increasing the libration amplitude of the resonant angles. However, N-body simulations show that deep penetration of CJs into the inner system is uncommon, with $\lesssim 10-20\%$ of cases reaching $\lesssim 10\%$ of the initial semi-major axis of the innermost CJ. Motivated by these results, we use secular perturbation theory to quantify the impact of time-dependent forcing from scattering CJs on the eccentricity and resonant-angle evolution of inner SEs. We find that for typical systems (e.g., with SEs at $\sim 0.1$ au and CJs at a few au), such forcing can efficiently disrupt resonances, driving resonance-angle circulation in most systems ($\gtrsim 60\%$ for 2:1 and $\sim 85\%$ for 3:2 configurations). Thus, even when the "final" CJ has little effect on the "current" SEs, its earlier scattering history can leave significant imprints on the system architecture. This mechanism, and similar ones involving more abundant cold Neptunes, provide a natural source of dynamical "kicks" and offer a pathway for producing the observed trough-peak structure in the period ratio distribution of Kepler multi-planet systems.