2026ApJ...996...12K

Type I disk migration can form a chain of planets engaged in first-order mean-motion resonances (MMRs) parked at the disk inner edge. However, while second- or even third-order resonances were deemed unlikely due to their weaker strength, they have been observed in some planetary systems, e.g., TOI-178 bc (5:3), TOI-1136 ef (7:5), and TRAPPIST-1 bcd (8:5-5:3). We performed >6000 Type I simulations of multiplanet systems that mimic the observed Kepler sample in terms of stellar mass, planet size, multiplicity, and intra-system uniformity over a parameter space encompassing transitional and truncated disks. We found that Type I migration coupled with a disk inner edge can indeed produce second- and third-order resonances (in a state of libration) in ∼10% and 2% of resonant-chain systems, respectively. Moreover, the relative occurrence of first- and second-order MMRs in our simulations is consistent with observations (e.g., 3:2 is more common than 2:1; while second-order 5:3 is more common than 7:5). The formation of higher-order MMRs favors slower disk migration and a smaller outer planet mass. Higher-order resonances do not have to form with the help of a Laplace-like three-body resonance, as was proposed for TRAPPIST-1. Instead, the formation of higher-order resonances is assisted by breaking a preexisting first-order resonance, which generates small but nonzero initial eccentricities (e ≈ 10^–3 to 10^–2). We predict that (1) librating higher-order resonances have higher equilibrium e (∼0.1), (2) are more likely found as an isolated pair in an otherwise first-order chain, and (3) more likely emerge in the inner pairs of a chain.