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A number of protoplanetary disks observed with ALMA potentially providedirect examples of initial conditions for planetary systems. In particular, theHL Tau disk has been intensively studied, and its rings/gaps are conventionallyinterpreted to be a result of unseen massive planets embedded in the gaps.Based on this interpretation, we carried out N-body simulations to investigateorbital evolution of planets within the protoplanetary disk and after the diskdispersal. Before the disk dispersal, our N-body simulations include bothmigration and mass-growth of the planet coupled with evolution of the disk. Byvarying the disk parameters, we produce a variety of widely-separated planetarysystems consisting of three super-Jupiters at the end of disk dispersal. Wefound the outer planet is more massive than the inner one, and the migration ofthe innermost planet is inefficient due to the accretion of outer planet(s). Wealso showed how the final configuration and the final planetary mass depend ondisk parameters. The migration is found to be convergent and no planet-pair hasa period ratio less than 2. After the disk dispersal, we switch to puregravitational N-body simulations and integrate the orbits up to 10 Gyr. Mostsimulated systems remain stable for at least 10 Gyr. We discuss implications ofour result in terms of the observed widely-separated planetary systems HR 8799and PDS 70.

Architecture of three-planet systems predicted from the observed protoplanetary disk of HL Tau