Pushing out the Kuiper Belt

Given the difficulties of the collisional grinding scenario for the cold Kuiper belt, a dynamical way to solve the mass depletion problem has been proposed in [112]. In this scenario, the primordial edge of the massive proto-planetary disk was somewhere around 30-35 AU and the entire Kuiper belt population - not only the hot component as in [60] - formed within this limit and was transported to its current location during Neptune's migration. The transport process for the cold population had to be different from the one found in [60] for the hot population (but still work in parallel with it), because the inclinations of the hot population were excited, while those of the cold population were not.

In the framework of the classical migration scenario [119] [62], the mechanism proposed in [112] was the following: the cold population bodies were initially trapped in the 1:2 resonance with Neptune; then, as they were transported outward by the resonance, they were progressively released because of the non-smoothness of the planetary migration. In the standard adiabatic migration scenario [119], there would be a resulting correlation between the eccentricity and the semi-major axis of the released bodies. However, this correlation was broken by a secular resonance embedded in the 1:2 mean-motion resonance. This secular resonance was generated because the precession rate of Neptune's orbit was modified by the torque exerted by the massive proto-planetary disk that drove the migration.

Simulations of this process can match the observed (a, e) distribution of the cold population fairly well (see Fig. 30), while the initially small inclinations are only very moderately perturbed. In this scenario, the small mass of the current cold population is simply because only a small fraction of the massive disk population was initially trapped in the 1:2 resonance and then released on stable non-resonant orbits. The preservation of the binary objects would not be a problem because these objects were moved out of the massive disk in which they formed by a gentle dynamical process. The final position of Neptune would simply reflect the primitive truncation of the proto-planetary disk, as in [62]. Most important, this model explains why the current edge of the Kuiper belt is at the 1:2 mean-motion resonance with Neptune, although none of the mechanisms proposed for the truncation of the planetesimal disk involves Neptune in a direct way (see Sect. 4.3). The location of the edge was modified by the migration of Neptune by the migration of its 1:2 resonance.

On the flip side, the model in [112] re-opens the problem of the origin of the different physical properties of the cold and hot populations, because both would have originated within 35 AU, although in somewhat different parts of the disk.

Fig. 30. Left: the observed semi-major axis vs. eccentricity distribution of the cold population. Only bodies with multi-opposition orbits and i < 4° are taken into account. Right: the resulting orbital distribution in the scenario proposed in [112]

I stress, however, that the strength of [112] is in the idea that pushing out the cold Kuiper belt could solve both the problems related to mass deficit and edge location. The specific mechanism for pushing out the cold belt depends on the particular model of giant planet evolution that is adopted. The classical planet migration scenario used in [112] might not reflect the real evolution of the system (see Sect. 5). In this case, alternative push-out mechanisms should be investigated. Whatever the preferred mechanism, it will have to give a predominant role to the 1:2 mean-motion resonance with Neptune to explain the current location of the Kuiper belt edge.

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