How Jupiter and Saturn’s secular architecture constrains their early orbital evolution

The orbital structure of the outer solar system is best reproduced in numerical simulations when, rather than migrating smoothly, the giant planets attain their modern orbits through a violent episode of dynamical instability. Among other qualities, this epoch of rapid evolution is thought to have excited Jupiter’s fifth eccentric mode (commonly quantified by its amplitude e₅₅). High values of e₅₅ are achieved relatively easily in simulations of the event if Jupiter experiences a close encounter with one of the other planets. However, it is noticeably difficult to simultaneously match Saturn’s semi-major axis and eccentricity in such a scenario. Within the parameter space of possible Jupiter-Saturn orbital spacings and e₅₅ values, the solar system outcome lies at the extreme limit of numerically generated configurations. However, it is supremely important for studies of the solar system’s early formation to exclusively consider simulation outcomes that properly excite e₅₅, as Jupiter’s eccentricity largely drives the secular evolution of the solar system as a whole. In this manner, we perform a robust dynamical analysis of the solar system’s instability using a variety of different primordial configurations for the giant planets. In contrast to previous similar studies, and motivated by hydrodynamical simulations of the giant planets’ evolution within the nebular gas phase, our work considers the possibility that Jupiter and Saturn emerged from the gas disk locked in a mutual 2:1 resonance with non-zero eccentricities. We find that, in such a scenario, the modern Jupiter-Saturn system represents a more typical simulation outcome. Furthermore, we show that Uranus and Neptune’s final orbits can be fine tuned to more closely resemble the real ones by adjusting the total mass of the primordial Kuiper belt, and that of the ejected ice giant.