Constraining the primordial orbits of the terrestrial planets

Evidence in the Solar system suggests that the giant planets underwent an epoch of radial migration that was very rapid, with an e-folding time-scale shorter than 1 Myr. It is probable that the cause of this migration was that the giant planets experienced an orbital instability that caused them to encounter each other, resulting in radial migration. A promising and heavily studied way to accomplish such a fast migration is for Jupiter to have scattered one of the ice giants outwards; this event has been called the `jumping Jupiter' scenario. Several works suggest that this dynamical instability occurred `late', long after all the planets had formed and the solar nebula had dissipated. Assuming that the terrestrial planets had already formed, then their orbits would have been affected by the migration of the giant planets as many powerful resonances would sweep through the terrestrial planet region. This raises two questions. First, what is the expected increase in dynamical excitement of the terrestrial planet orbits caused by late and very fast giant planet migration? And secondly, assuming that the migration occurred late, can we use this migration of the giant planets to obtain information on the primordial orbits of the terrestrial planets? In this work, we attempt to answer both of these questions using numerical simulations. We directly model a large number of terrestrial planet systems and their response to the smooth migration of Jupiter and Saturn, and also two jumping Jupiter simulations. We study the total dynamical excitement of the terrestrial planet system with the angular momentum deficit (AMD) value, including the way it is shared among the planets. We conclude that to reproduce the current AMD with a reasonable probability (∼20 per cent) after late rapid giant planet migration and a favourable jumping Jupiter evolution, the primordial AMD should have been lower than ∼70 per cent of the current value, but higher than 10 per cent. We find that a late giant planet migration scenario that initially had five giant planets rather than four had a higher probability of satisfying the orbital constraints of the terrestrial planets. Assuming late migration, we predict that Mars was initially on an eccentric and inclined orbit while the orbits of Mercury, Venus and Earth were more circular and coplanar. The lower primordial dynamical excitement and the peculiar partitioning between planets impose new constraints for terrestrial planet formation simulations.