Can a jumping-Jupiter trigger the Moon's formation impact?

We investigate the possibility that the Moon's formation impact was triggered by an early dynamical instability of the giant planets. We consider the well-studied "jumping Jupiter" hypothesis for the solar system's instability, where Jupiter and Saturn's semi-major axes evolve in step-wise manner from their primordially compact architecture to their present locations. Moreover, we test multiple different configurations for the primordial system of terrestrial planets and the Moon-forming projectile, with particular focus on the almost equal masses impact. We find that the instability/migration of the giant planets excites the orbits of the terrestrial planets through dynamical perturbations, thus allowing collisions between them. About 10% of the simulations lead to a collision with the proto-Earth which resulted in a final configuration of the terrestrial system that reproduces, to some extent, its present architecture. Most of these collisions occur in the hit-and-run domain, but about 15% occur in the partial accretion regime, with the right conditions for a Moon-forming impact. In most of the simulations, there is a delay of more than ~20 My between the time of the instability and the Moon-forming impact. This supports the occurrence of an early instability (< 10 My} after dissipation of the gas in the proto-planetary disk), compatible with the time of the Moon-forming impact (30-60 My) inferred from cosmochemical constraints. In general, the final states of the inner solar system in our simulations show an excess of Angular Momentum Deficit, mostly attributed to the over-excitation of Mercury's eccentricity and inclination.