Studying the Twotinos: High Inclination Kuiper Belt Objects

A study of the high-inclination population in the Kuiper belt - II. The Twotinos

Authors:

Li et al

Abstract:

As the second part of our study, in this paper we proceed to explore the dynamics of the high-inclination Twotinos in the 1:2 Neptune mean motion resonance (NMMR). Depending on the inclination i, we show the existence of two critical eccentricities ea(i) and ec(i), which are lower limits for the eccentricity e for the resonant angle σ to exhibit libration and asymmetric libration, respectively. Accordingly, we have determined the libration centres σ0 for inclined orbits, which are strongly dependent on i and could be very different from the zero-i case. With the initial σ=σ0 on a fine grid of (e,i), the long-term stability of orbits in the 1:2 NMMR is probed by numerical integrations for the age of the Solar system. It is shown that symmetric librators are totally unstable for i≥30∘; while stable asymmetric librators do exist for i as high as 90∘, and they generally have resonant amplitudes Aσ less than 50∘.

We further investigate the 1:2 NMMR capture and retention of planetesimals with initial inclinations i0≤90∘ in the planet migration model using a long time-scale of 2×107 yr. We find that: (1) the capture efficiency of the 1:2 NMMR decreases drastically with the increase of i0, and it goes to 0 when i0 exceeds ∼60∘; (2) the probability of discovering Twotinos with i greater than 25∘, beyond their observed values, is roughly estimated to be only ∼0.1 per cent; (3) more particles are captured into the leading rather than the trailing asymmetric resonance for i0≤10∘, but this number difference appears to be the opposite at i0=20∘ and is continuously varying for even larger i0; (4) captured Twotinos residing in the trailing islands or having i greater than 15∘ are practically outside the Kozai mechanism, like currently observed samples.