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Fig. 2

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Stable resonant capture of a two-planet system with convergent migration. The planet and disk parameters are mi=1 M, mo=10 M, τm=2 × 105 yr and τm/τe = 1200. The planets get trapped in a 2:1 MMR at t≃104 yr exciting the inner planet’s eccentricity to 0.02. The resonant angle φi shifts from 0 to 2τ/3 as the system transitions into the resonant state. It gradually decreases as convergent migration strengthens the resonant interaction, causing the libration center to drift slowly. In phase space, the trajectory converges toward the resonant equilibrium and co-evolves with it. We refer to this resonant capture at a stationary equilibrium as a stable trap. See https://github.com/llh-astro/resonance/raw/main/gif/stable_trap.gif

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