A study of the high-inclination population in the Kuiper belt – III. The 4:7 mean-motion resonance

ABSTRACT The high-inclination population in the 4: 7 mean-motion resonance (MMR) with Neptune has also substantial eccentricities (e ≳ 0. 1), with more inclined objects tending to occupy more eccentric orbits. For this high-order resonance, there are two different resonant modes. The principal one is the eccentricity-type mode, and we find that libration is permissible for orbits with e e_ c⁰, where the critical eccentricity e_ c⁰ increases as a function of increasing inclination i. Correspondingly, we introduce a limiting curve e_ c⁰ (i), which puts constraints on the (e, i) distribution of possible 4: 7 resonators. We then perform numerical simulations on the sweep-up capture and long-term stability of the 4: 7 MMR, and the results show that the simulated resonators are well constrained by this theoretical limiting curve. The other 4: 7 resonant mode is the mixed- (e, i) -type, and we show that stable resonators should exist at i ≳ 20○. We predict that the intrinsic number of these mixed- (e, i) -type resonators may provide a new clue into the Solar system’s evolution, but, so far, only one real object has been observed resonating in this mode.