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 ($e\gtrsim 0.1$), 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 $e\ge e_c^0$, where the critical eccentricity $e_c^0$ increases as a function of increasing inclination $i$. Correspondingly, we introduce a limiting curve $e_c^0(i)$, 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 $i\gtrsim 20^{\circ }$. 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.

arXiv comment15 pages, 19 figures, Accepted for publication in MNRAS

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• A study of the high-inclination population in the Kuiper belt -- IV. High-order mean motion resonances in the classical region
• A new multiple-arc model of the resonant Kuiper belt objects -- Plutinos