The Orbital Distribution of Trans-Neptunian Objects Beyond 50 au

The dynamical structure of the Kuiper Belt beyond 50 au is not well understood. Here we report results of a numerical model with long-range, slow, and grainy migration of Neptune. The model implies that bodies scattered outward by Neptune to semimajor axes a\gt 50 {au} often evolve into resonances which subsequently act to raise the perihelion distances of orbits to q\gt 40 {au}. The implication of the model is that the orbits with 50\lt a\lt 100 {au} and q\gt 40 {au} should cluster near (but not in) the resonances with Neptune (3:1 at a = 62.6 au, 4:1 at a=75.9 {au}, 5:1 at a=88.0 {au}, etc.). The recent detection of several distant Kuiper Belt Objects (KBOs) near resonances is consistent with this prediction, but it is not yet clear whether the orbits are really non-resonant as our model predicts. We estimate from the model that there should presently be ∼1600-2400 bodies at the 3:1 resonance and ∼1000-1400 bodies at the 4:1 resonance (for q\gt 40 {au} and diameters D\gt 100 km). These results favorably compare with the population census of distant KBOs inferred from existing observations.