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When two planets are born in a protoplanetary disk, they may enter into amean-motion resonance as a consequence of the convergent planetary migration.The formation of mean-motion resonances is important for understanding how theplanetary systems are shaped in the disk environments. Motivated by recentprogress in the comprehension of the migration of partial gap-opening planets,we have investigated the orbital evolution of the planet pairs in a wide rangeof masses and disk properties with the aim to find out when the resonancecapture is likely to happen. Using the formula for the migration timescale of agap-opening planet developed in our previous work, we have derived a simplecriterion that allows us to predict when the migration will be convergent(divergent). Further, we have verified the criterion using two-dimensionalhydrodynamic simulations. We have found that the resonant pair of planetsformed at the early phase of evolution can depart from the resonance at latertimes because the migration speed of the outer planet slows down due to the gapformation. Moreover, adopting our formula of the migration timescale, we havealso carried out three-body simulations, which confirm the results ofhydrodynamic simulations. Finally, we have compared our predictions with theobservations, selecting a sample of known two-planet systems.

Radial migration of gap-opening planets in protoplanetary disks. II. The case of a planet pair