Constructing the secular architecture of the solar system II: The terrestrial planets

TL;DR

This paper studies how the migration of giant planets affected the orbital evolution of terrestrial planets, identifying resonance crossings that could disrupt their current configuration and proposing solutions to avoid such instabilities.

Contribution

It introduces new insights into how giant planet migration influenced terrestrial planet orbits, especially through secular resonance crossings and potential mitigation scenarios.

Findings

Resonance crossings g5=g4 and g5=g3 are not problematic with fast migration.

Resonances g5=g2 and g5=g1 threaten terrestrial system stability.

Jumping Jupiter scenario can avoid harmful resonance crossings.

Abstract

We investigate the dynamical evolution of the terrestrial planets during the planetesimal-driven migration of the giant planets. A basic assumption of this work is that giant planet migration occurred after the completion of terrestrial planet formation, such as in the models that link the former to the origin of the Late Heavy Bombardment. The divergent migration of Jupiter and Saturn causes the g5 eigenfrequency to cross resonances of the form g5=gk with k ranging from 1 to 4. Consequently these secular resonances cause large-amplitude responses in the eccentricities of the terrestrial planets. We show that the resonances g5=g_4 and g5=g3 do not pose a problem if Jupiter and Saturn have a fast approach and departure from their mutual 2:1 mean motion resonance. On the other hand, the resonance crossings g5=g2 and g5=g1 are more of a concern as they tend to yield a terrestrial system incompatible with the current one. We offer two solutions to this problem. The first uses the fact that a secular resonance crossing can also damp the amplitude of a Fourier mode if the latter is large originally. A second scenario involves a 'jumping Jupiter' in which encounters between an ice giant and Jupiter, without ejection of the former, cause the latter to migrate away from Saturn much faster than if migration is driven solely by encounters with planetesimals. In this case, the g5=g2 and g5=g1 resonances can be jumped over, or occur very briefly.