The Resonant Remains of Broken Chains from Major and Minor Mergers

Observations with the Transiting Exoplanet Survey Satellite and Kepler have revealed that practically all close-in sub-Neptunes form in mean-motion resonant chains, most of which unravel on timescales of 100 Myr. Using a series of N-body integrations, we study how planetary collisions resulting from the destabilization of resonant chains produce the distribution of orbital periods observed among mature systems, focusing on the resonant fine structures that remain post-instability. In their natal chains, planets near first-order resonances have period ratios just wide of perfect commensurability, driven there by disk migration and eccentricity damping. Sufficiently large resonant libration amplitudes (of unknown origin) are needed to trigger instability. Ensuing collisions between planets ("major mergers") erode but do not completely eliminate resonant pairs; survivors which avoid mergers show up as narrow "peaks" just wide of commensurability in the histogram of neighboring-planet period ratios. Merger products exhibit a broad range of period ratios, with each resonant peak in the histogram spawning a continuum of ratios wide of the given resonance. These continua may fill in period ratios between relatively closely separated resonances such as the 5:4, 4:3, and 3:2, but may fail to bridge the relatively wide gap between the 3:2 and the 2:1. Thus a "trough" manifests just short of the 2:1 resonance (and only the 2:1 resonance), as observed. Major mergers are not perfect, and generate collisional debris which undergoes "minor mergers" with planets, in many cases further widening resonant pairs. With all this dynamical activity, free eccentricities of resonant pairs, and by extension the phases of their transit timing variations (TTVs), are readily excited. Because non-resonant planets are merger products, they are predicted to have higher masses than resonant planets.