Intruder Alert: Breaking Resonant Chains with Planetesimal Flybys

TL;DR

This work addresses why many compact exoplanet systems lack resonant chains by proposing a planetesimal-driven mechanism in which intermittent flybys from an external reservoir slowly diffuse resonant mode amplitudes until resonances break. A pendulum-like Hamiltonian framework accompanies N-body scattering experiments to quantify how the break probability scales with the root-cumulative mass $RCM = m_p\sqrt{N_{\rm flyby}}$, predicting a threshold reservoir mass of order $\sim 0.04\,M_{\oplus}$ for disruption and showing that systems disrupted by this process frequently become dynamically unstable within $\sim 100$ Myr. The results imply an intrinsic anti-correlation between inner resonant architectures and outer dynamical activity, consistent with age-dependent resonant fractions in Kepler-like systems and with outer debris disks that indicate substantial planetesimal reservoirs. By connecting outer small-body populations to inner planetary dynamics, the study provides a concrete avenue to test resonant-chain breaking through observations of debris disks, outer companions, and stellar-age demographics, offering new constraints on early planetary system evolution.

Abstract

The orbital architectures of compact exoplanet systems record their complicated dynamical histories. Recent research supports the ``breaking-the-chains'' hypothesis, which proposes that compact systems typically form in chains of mean-motion resonances (MMRs) but subsequently break out on a $\sim 100$Myr timescale. We investigate a scenario for breaking the chains through intermittent flybys of planetesimals originating from a distant reservoir. Using $N$-body simulations and semi-analytical calculations, we characterize the disruption of MMRs through these flybys. We find a planetesimal reservoir of total mass $\gtrsim 0.04 M_{\oplus}$ is required to disrupt MMR chains, depending on the mass distribution and the typical number of flybys executed by each planetesimal. We verify that systems disrupted in this way are frequently unstable to close encounters within $\sim 100$Myr of the final flyby. This mechanism operates in systems with both a sufficiently massive reservoir and an efficient mechanism for planetesimal injection. Consequently, we predict an anti-correlation between resonant inner systems and dynamically active outer configurations.

Figures (7)

• Figure 1: Cartoon illustration of the breaking of compact resonant chains through planetesimal scattering. The arrow of time proceeds clockwise, starting from the upper left.
• Figure 2: Example evolution of systems with 3:2-4:3 MMR chain perturbed by independent planetesimal flybys. Each systems receive $N$ flybys by planetesimals with mass $m_{\rm p}$ at a rate of 1 flyby per 1.5 years. Each column shows the result with different $N$ and $m_{\rm p}$. Top: time evolution for changes of planetary semi-major axes ($\Delta a = a-a_{\rm init}$). The faint lines show the measurement of $\Delta a/a$ after each flyby, while the solid curves show the average values from 200 uniformly spaced time bins. Middle: same as the top row, except showing the evolution of planetary eccentricities. Bottom: measurement of the MMR angles $\theta_{12}$ and $\theta_{23}$, defined as in Equations \ref{['eq:theta12']} and \ref{['eq:theta23']}, after each flyby.
• Figure 3: Time evolution of $\theta_{12}$ and $\theta_{23}$ in the 50 years after the last flyby is over, from the same simulations as in Figure \ref{['fig:theta_examples_aet']}. The gray lines show the sinusoidal fit to the time evolution (Equations \ref{['eq:theta12_sin']} and \ref{['eq:theta23_sin']}), while the shade regions represent the ranges of the sine curves.
• Figure 4: Probability of different resonance perturbation outcomes as a function of the root-cumulative perturber mass, ${\rm RCM} \equiv m_p\sqrt{N_{\rm flyby}}$ with $m_p$ as the mass of the planetesimal. The upper panel shows systems perturbed by independent flybys, while the lower panel shows results for recurring flybys of a single planetesimal. The solid, dashed-dotted, and dotted lines are the results from simulations with $N_{\rm flybys}=64$, $16$, and $4$, respectively.
• Figure 5: Critical total injected planetesimal mass $M_{\rm total} = m_{\rm p} N_{\rm object}$ required to perturb the resonant chain. When $N_{\rm object}$ planetesimals of individual mass $m_{\rm p}$ are injected into the inner planetary system, the MMR chain breaks if $(m_{\rm p},M_{\rm total})$ lies above the blue line. Similar thresholds for other outcomes are shown by different colors. The shaded region corresponds to the unphysical regime where the $m_{\rm p}>M_{\rm total}$.