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Fly-by encounters between two planetary systems II: Exploring the interactions of diverse planetary system architectures

Planetary systems formed in clusters may be subject to stellar encounter flybys. Here we create a diverse range of representative planetary systems with different orbital scales and planets' masses and examine encounters between them in a typical open cluster. We first explore the close-in multi-super earth systems $\lesssim0.1$ au. They are resistant to flybys in that only ones inside a few au can destabilise a planet or break the resonance between such planets. But these systems may capture giant planets onto wide orbits from the intruding star during distant flybys. If so, the original close-in small planets' orbits may be tilted together through Kozai--Lidov mechanism, forming a ``cold'' system that is significantly inclined against the equator of the central host. Moving to the intermediately-placed planets around solar-like stars, we find that the planets' mass gradient governs the systems' long-term evolution post-encounter: more massive planets have better chances to survive. Also, a system's angular momentum deficit, a quantity describing how eccentric/inclined the orbits are, measured immediately after the encounter, closely relates to the longevity of the systems -- whether or not and when the systems turn unstable in the ensuing evolution millions of years post-encounter. We compare the orbits of the surviving planets in the unstable systems through (1) the immediate consequence of the stellar fly or (2) internal interplanetary scattering long post-encounter and find that those for the former are systematically colder. Finally, we show that massive wide-orbit multi-planet systems like that of HR 8799 can be easily disrupted and encounters at a few hundreds of au suffice.