Constraining the Giant Planets’ Initial Configuration from Their Evolution: Implications for the Timing of the Planetary Instability

Recent works on planetary migration show that the orbital structure of the Kuiper belt can be very well reproduced if before the onset of the planetary instability Neptune underwent a long-range planetesimal-driven migration up to $\sim$28 au. However, considering that all giant planets should have been captured in mean motion resonances among themselves during the gas-disk phase, it is not clear whether such a very specific evolution for Neptune is possible, nor whether the instability could have happened at late times. Here, we first investigate which initial resonant configuration of the giant planets can be compatible with Neptune being extracted from the resonant chain and migrating to $\sim$28 au before that the planetary instability happened. We address the late instability issue by investigating the conditions where the planets can stay in resonance for about 400 My. Our results indicate that this can happen only in the case where the planetesimal disk is beyond a specific minimum distance $\delta_{stab}$ from Neptune. Then, if there is a sufficient amount of dust produced in the planetesimal disk, that drifts inwards, Neptune can enter in a slow dust-driven migration phase for hundreds of Mys until it reaches a critical distance $\delta_{mig}$ from the disk. From that point, faster planetesimal-driven migration takes over and Neptune continues migrating outward until the instability happens. We conclude that, although an early instability reproduces more easily the evolution of Neptune required to explain the structure of the Kuiper belt, such evolution is also compatible with a late instability.