Magnitude and timing of the giant planet instability: A reassessment from the perspective of the asteroid belt

It is generally accepted today that our solar system has undergone a phase during which the orbits of the giant planets became very unstable. In recent years, many studies have identified traces of this event and have provided reasonable justification for this occurrence. The magnitude (in terms of orbital variation) and the timing of the instability though (early or late with respect to the dispersal of the gas disk) still remains an open debate. The terrestrial planets seem to set a strict constraint: either the giant planet instability happened early, while the terrestrial planets were still forming, or the orbits of Jupiter and Saturn had to separate from each other impulsively, with a large enough "jump" in semimajor axis for the terrestrial planets to remain stable. Because a large orbital jump is a low probability event, the early instability hypothesis seems to be favored, however, the asteroid belt would also evolve in a different way, assuming different instability amplitudes. These two constraints need to match each other in order to favor one scenario over the other. Considering an initially dynamically cold disk of asteroids, previous studies concluded that a comparably large jump is needed to reconstruct the current asteroid belt. Here we confirm the same conclusion, but considering an asteroid population already strongly excited in eccentricity, such as that produced in the Grand Tack scenario. Because the asteroids existed since the time of removal of the gas disk, unlike the terrestrial planets, this constraint on the width of the giant planet jump is valid regardless of whether the instability happened early or late. Hence, at this stage, assuming an early instability does not appear to provide any advantage in terms of the probabilistic reconstruction of the solar system structure.