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