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Close-in giant planets are thought to have formed in the cold outer regionsof planetary systems and migrated inward, passing through the orbital parameterspace occupied by the terrestrial planets in our own Solar System. We presentdynamical simulations of the effects of a migrating giant planet on a disk ofprotoplanetary material and the subsequent evolution of the planetary system.We numerically investigate the dynamics of post-migration planetary systemsover 200 million years using models with a single migrating giant planet, onemigrating and one non-migrating giant planet, and excluding the effects of agas disk. Material that is shepherded in front of the migrating giant planet bymoving mean motion resonances accretes into "hot Earths", but survival of thesebodies is strongly dependent on dynamical damping. Furthermore, a significantamount of material scattered outward by the giant planet survives in highlyexcited orbits; the orbits of these scattered bodies are then damped by gasdrag and dynamical friction over the remaining accretion time. In allsimulations Earth-mass planets accrete on approximately 100 Myr timescales,often with orbits in the Habitable Zone. These planets range in mass and watercontent, with both quantities increasing with the presence of a gas disk anddecreasing with the presence of an outer giant planet. We use scaling argumentsand previous results to derive a simple recipe that constrains which giantplanet systems are able to form and harbor Earth-like planets in the HabitableZone, demonstrating that roughly one third of the known planetary systems arepotentially habitable.Comment: Submitted to ApJ, accepted pending revision

Formation of Earth‐like Planets During and After Giant Planet Migration