Several models have been suggested in the past to describe the dynamical formation of hot Kuiper Belt objects (hereafter Hot Classicals or HCs for short). Here, we discuss a dynamical mechanism that allows orbits to evolve from the primordial planetesimal disk at 35?AU to reach the orbital region now occupied by HCs. We performed three different sets of numerical simulations to illustrate this mechanism. Two of these simulations were based on modern theories for the early evolution of the solar system (the Nice and jumping-Jupiter models). The third simulation was performed with the purpose of increasing the resolution at 41-46?AU. The common aspect of these simulations is that Neptune scatters planetesimals from 35?AU to 40?AU and then undergoes a long phase of slow residual migration. Our results show that to reach an HC orbit, a scattered planetesimal needs to be captured in a mean motion resonance (MMR) with Neptune where the perihelion distance rises due to the Kozai resonance (which occurs in MMRs even for moderate inclinations). Finally, while Neptune is still migrating, the planetesimal is released from the MMR on a stable HC orbit. We show that the orbital distribution of HCs expected from this process provides a reasonable match to observations. The capture efficiency and the mass deposited into the HC region appears to be sensitive to the maximum eccentricity reached by Neptune during the planetary instability phase. Additional work will be needed to resolve this dependency in detail.
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