Born eccentric: constraints on Jupiter and Saturn's pre-instability orbits

An episode of dynamical instability is thought to have sculpted the orbital structure of the outer Solar System. When modeling this instability, a key constraint comes from Jupiter's fifth eccentric mode (quantified by its amplitude e₅₅), which is a key driver of the Solar System's secular evolution. Starting from commonly-assumed near-circular orbits, the present-day giant planets lie at the extreme limit of numerically generated systems, and e₅₅ is rarely excited to its true value. Here we perform a robust dynamical analysis of the instability and test a variety of configurations for the giant planets' primordial orbits. In addition to more standard setups, and motivated by hydrodynamical simulations, we consider the possibility that Jupiter and Saturn emerged from the gaseous disk locked in 2:1 resonance with non-zero eccentricities. We show that, in such a scenario, the modern Jupiter-Saturn system represents a typical simulation outcome, and e₅₅ is commonly matched. Furthermore, we show that Uranus and Neptune's final orbits are determined by a combination of the mass in the primordial Kuiper belt and that of an ejected ice giant.