Close-in compact super-Earth systems emerging from resonant chains: slow destabilization by unseen remnants of formation

TL;DR

This work tests whether slow, post-disk dynamical diffusion of resonant planetary chains can reproduce mature, non-resonant Kepler-like populations. By performing long-duration N-body simulations with planet growth, Type I migration, and disk dispersal, the authors show that most resonant chains exit the gas disk in resonance but slowly diffuse, producing instabilities on tens to hundreds of Myr that break resonances and yield dynamically warmer, non-resonant systems. Instability timing follows a Weibull distribution with a common shape parameter, enabling extrapolation to Gyr ages; synthetic transit observations reveal that mature demographics, including the Kepler dichotomy and near-resonant fractions, can be reproduced, particularly for certain disk profiles and masses. The results support the breaking-the-chains scenario as a robust explanation for the observed evolution of compact planetary systems and highlight the importance of long-term dynamical evolution in interpreting exoplanet demographics.

Abstract

Planet formation simulations consistently predict compact systems of numerous small planets in chains of mean motion resonances formed by planet-disk interaction, but transiting planet surveys have found most systems to be non-resonant and somewhat dynamically excited. A scenario in which nearly all of the primordial resonant chains undergo dynamical instabilities and collisions has previously been found to closely match many features of the observed planet sample. However, existing models have not been tested against new observations that show a steep decline in the resonant fraction as a function of stellar age on a timescale of ~100 Myr. We construct a simplified model incorporating Type I migration, growth from embryos, and N-body integrations continued to 500 Myr and use it to generate a synthetic planet population. Nearly all systems exit the disk phase in a resonant configuration but begin slowly diffusing away from the center of the resonance. Dynamical instabilities can arise on timescales of tens or hundreds of Myr, especially when systems formed in disks with a convergent migration trap. In this case, a secondary chain of smaller planets that remained at their birth location eventually breaks, destabilizing the inner resonant chain. We also show that the instability statistics are well modeled by a Weibull distribution, and use this to extrapolate our population to Gyr ages. The close match of our modeled systems to the observed population implies that the high resonance fraction predicted by this class of models is in fact consistent with the data, and the previously-reported overabundance of resonant systems was a consequence of comparing simulations of early evolution to mature Gyr-old systems. This result also suggests that instabilities triggered by disk dissipation or other very early mechanisms are unlikely to be consistent with observed young systems.

Figures (19)

• Figure 1: Evolution of a typical simulation from the 20flat suite, which includes a migration trap at 1 au. Embryos accrete from a ring (top left panel) and grow until they saturate the corotation torque (top right, zero torque locations in gray), then migrate inwards in resonant convoys. At the end of the disk phase (bottom left), there is an inner resonant chain and an outer, less massive, and more compact one. By the end of the simulation (bottom right), the system has experienced a dynamical instability, breaking the resonances and merging planets.
• Figure 2: Migration map of the three disk profiles used (Eq. \ref{['eq:disk']}) at $t=0$ including the repulsive inner edge. Positive values of $\tau_a^{-1}$ indicate outward migration. For the flat and steep disks, there is a migration trap near the pressure bump at 1 au that suppresses migration until planets reach $\sim \qty{2}{M_\oplus}$, at which point they saturate the corotation torque and migrate inwards.
• Figure 3: Summary population statistics for the 40 synthetic planetary systems in the simulation suite 20flat at the end of the $\qty{500}{Myr}$ integration. Orange and cyan curves show planets in systems that did and did not undergo a dynamical instability after the dissipation of the protoplanetary disk, respectively. Only planets with orbital periods $<\qty{100}{d}$ are included.
• Figure 4: Same as Fig. \ref{['fig:20flatpopstats']} for run 40steep.
• Figure 5: Same as Fig. \ref{['fig:20flatpopstats']} for run 10straight.