Lunar and Terrestrial Planet Formation in the Grand Tack Scenario

TL;DR

This study uses N-body simulations within the Grand Tack model to explore how initial disc conditions influence terrestrial planet formation, concluding that Mars-sized embryos dominated the early disc and the Moon formed 60-130 million years after solids first appeared.

Contribution

It provides new insights into the initial conditions of planet formation by coupling giant planet migration with terrestrial accretion in the Grand Tack scenario.

Findings

The timing of the last giant impact depends on the embryo-to-planetesimal mass ratio.

The size of the lunar impactor is linked to the initial embryo mass.

The Moon-forming event likely occurred 60-130 million years after initial solids.

Abstract

We present conclusions from a large number of N-body simulations of the giant impact phase of terrestrial planet formation. We focus on new results obtained from the recently proposed Grand Tack model, which couples the gas-driven migration of giant planets to the accretion of the terrestrial planets. The giant impact phase follows the oligarchic growth phase, which builds a bi-modal mass distribution within the disc of embryos and planetesimals. By varying the ratio of the total mass in the embryo population to the total mass in the planetesimal population and the mass of the individual embryos, we explore how different disc conditions control the final planets. The total mass ratio of embryos to planetesimals controls the timing of the last giant (Moon forming) impact and its violence. The initial embryo mass sets the size of the lunar impactor and the growth rate of Mars. After comparing our simulated outcomes with the actual orbits of the terrestrial planets (angular momentum deficit, mass concentration) and taking into account independent geochemical constraints on the mass accreted by the Earth after the Moon forming event and on the timescale for the growth of Mars, we conclude that the protoplanetary disc at the beginning of the giant impact phase must have had most of its mass in Mars-sized embryos and only a small fraction of the total disc mass in the planetesimal population. From this, we infer that the Moon forming event occurred between $\sim$60 and $\sim$130 My after the formation of the first solids, and was caused most likely by an object with a mass similar to that of Mars.