Dynamical effects on the classical Kuiper Belt during the excited-Neptune model

The link between the dynamical evolution of the giant planets and the Kuiper Belt orbital structure can provide clues and insight about the dynamical history of the Solar System. The classical region of the Kuiper Belt has two populations (the cold and hot populations) with completely different physical and dynamical properties. These properties have been explained in the framework of a subset of the simulations of the Nice Model, in which Neptune remained on a low-eccentricity orbit (Neptune's eccentricity is never larger than 0.1) throughout the giant planet instability. However, recent simulations have showed that the remaining Nice model simulations, in which Neptune temporarily acquires a large-eccentricity orbit (larger than 0.1), are also consistent with the preservation of the cold population (inclination smaller than 4 degrees), if the latter formed in situ. However, the resulting a cold population showed in many of the simulations eccentricities larger than those observed for the real population. We focus on a short period of time which is characterized by Neptune's large eccentricity and a slow precession of Neptune's perihelion. We show that if self-gravity is considered in the disk, the precession rate of the particles longitude of perihelion is slowed down. This, combined with the effect of mutual scattering among the bodies, which spreads all orbital elements, allows some objects to return to low eccentricities. However, we show that if the cold population originally had a small total mass, this effect is negligible. Thus, we conclude that the only possibilities to keep at low eccentricity some cold-population objects during a high-eccentricity phase of Neptune are that (i) either Neptune's precession was rapid, as suggested by Batygin et al. (2011) or (ii) Neptune's slow precession phase was long enough to allow some particles to experience a full secular cycle.