Title: Constraining the giant planets' initial configuration from their evolution: implications for the timing of the planetary instability,
Abstract: 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.