The Formation of Multi-planetary Systems in Chain Resonance

Chain resonance configuration is a common architecture in exoplanetary systems. Investigating the formation and evolution of multi-planet systems with chain resonances can provide new clues to the understanding of exoplanet formation. By selecting multi-planet systems whose period ratios match chain resonance configurations and analyzing the distribution of period ratios between adjacent planet pairs, we find that planet pairs are more frequently located near the 3:2 mean motion resonance (MMR) and less near the 2:1 MMR, indicating that chain resonance systems tend to have more compact orbital architectures. Numerical simulations are used to study the formation of such resonant chains. A basic model with two-planet system is established in which the pair is captured into 2:1 MMR. By adding a third planet beyond the orbit of the reference pair and varying its mass and location, we show that the outermost planet can drive the inner planet pair to migrate from 2:1 MMR to 3:2 MMR. Increasing the mass of the outermost planet raises the probability that both the inner and outer pairs are captured into 3:2 MMR. When the outermost planet is more massive, reducing its initial semimajor axis increases the chance for the inner pair to enter 3:2 MMR, while this effect is weak for lower masses. A fourth planet at the outermost orbit shows that its migration has little influence on the configuration of the inner three planets if it migrates slowly. The sequence in which planet pair enters resonance may be a key factor leading to different system architectures. The simulation results are consistent with the observed period ratio distribution in chain resonance systems and offer an explanation for their compact orbital architecture.