N-Body Dynamics as a Mechanism for Mean Motion Resonance Formation in the Post-Gas Era

Abstract: Mean motion resonances (MMRs) are traditionally thought to form during the gas-rich phase of protoplanetary disks via disk-driven migration. Whether MMRs can form solely through collisional damping after disk dispersal has not been systematically investigated. To study MMR formation in the post-gas-disk era, we perform a large suite of N-body simulations, each containing 10,000 planetesimals around an M-dwarf star and evolving over 10 Myr. We compare two groups of simulations that differ only in their initial mass distributions. Each group consists of 10 runs with statistically identical initial planetesimal orbital distributions, generated using different random seeds. One group adopts a uniform planetesimal mass distribution, whereas the other features a bimodal distribution with massive embryos embedded in a swarm of smaller planetesimals. At 1 Myr, 40% of systems (8/20) exhibit near-resonant period ratios, but this fraction drops to 25% (5/20) by 10 Myr as higher-order commensurabilities dissolve. Resonant-angle tracking shows that all persistent systems have circulating resonant angles at 10 Myr, although one system undergoes a transient libration phase between about 2 and 7 Myr before returning to circulation. These results demonstrate that collisional merging can drive MMR formation even without a gas disk, although in this scenario near-resonant configurations are strongly favored over true resonances. Furthermore, this mechanism produces similar MMR fractions in both groups, suggesting that MMR formation is insensitive to the initial mass distribution, although the latter may modulate the formation pathway to a limited extent.