  Close-in giant planets are thought to have formed in the cold outer regions
of planetary systems and migrated inward, passing through the orbital parameter
space occupied by the terrestrial planets in our own Solar System. We present
dynamical simulations of the effects of a migrating giant planet on a disk of
protoplanetary material and the subsequent evolution of the planetary system.
We numerically investigate the dynamics of post-migration planetary systems
over 200 million years using models with a single migrating giant planet, one
migrating and one non-migrating giant planet, and excluding the effects of a
gas disk. Material that is shepherded in front of the migrating giant planet by
moving mean motion resonances accretes into "hot Earths", but survival of these
bodies is strongly dependent on dynamical damping. Furthermore, a significant
amount of material scattered outward by the giant planet survives in highly
excited orbits; the orbits of these scattered bodies are then damped by gas
drag and dynamical friction over the remaining accretion time. In all
simulations Earth-mass planets accrete on approximately 100 Myr timescales,
often with orbits in the Habitable Zone. These planets range in mass and water
content, with both quantities increasing with the presence of a gas disk and
decreasing with the presence of an outer giant planet. We use scaling arguments
and previous results to derive a simple recipe that constrains which giant
planet systems are able to form and harbor Earth-like planets in the Habitable
Zone, demonstrating that roughly one third of the known planetary systems are
potentially habitable.
