Formation and Disruption of Resonant Chains of Super-Earths: Secular Perturbations from Outer Eccentric Embryos

Abstract Recent observations have revealed the distribution of orbital period ratios of adjacent planets in multiple super-Earth systems and how these distributions change with time. The aim of this study is to clarify under what conditions the observed features of orbital period ratios of super-Earths can be explained, and to identify what causes the dynamical instability of super-Earths captured into resonant chains. We perform N -body simulations for 100 Myr that follow the formation and orbital evolution of super-Earths originating from a ring of planetary embryos at 1 au from the star. The simulations show that super-Earths undergo inward migration in the disk and are captured into mean-motion resonances with their neighbors. As a result, several resonant pairs form a resonant chain. After disk dispersal, some of these chains become dynamically unstable. In such cases, the final distribution of orbital period ratios and their time evolution can be consistent with recent observations. The instabilities of resonant chains are likely triggered by secular perturbations from embryos that remain on outer orbits beyond 1 au, indicating that not only giant planets but also small embryos can disrupt the resonances among inner super-Earths. We therefore further investigate the secular perturbations from outer embryos using analytic formulas and additional orbital calculations. We discuss the conditions required to excite the eccentricities of inner super-Earths on a timescale of about 100 Myr. These conditions include the need for large eccentricities of the outer embryos, as well as constraints on their masses and semimajor axes.