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As the second part of our study, in this paper, we proceed to explore the dynamics of the highinclination Twotinos in the 1:2 Neptune mean motion resonance (NMMR). Depending on the inclination i, we show the existence of two critical eccentricities e a (i) and e c (i), which are lower limits of the eccentricity e for the resonant angle to exhibit libration and asymmetric libration, respectively. Accordingly, we have determined the libration centres 0 for inclined orbits, which are strongly dependent on i. With initial = 0 on a fine grid of (e, i), the stability of orbits in the 1:2 NMMR is probed by 4-Gyr integrations. It is shown that symmetric librators are totally unstable for i 30 ; while stable asymmetric librators exist for i up to 90 . We further investigate the 1:2 NMMR capture and retention of planetesimals with initial inclinations i 0 90 in the planet migration model using a time-scale of 2 10 7 yr. We find that: (1) the capture efficiency of the 1:2 NMMR decreases drastically with the increase of i 0 , and it goes to 0 when i 0 60 ; (2) the probability of discovering Twotinos with i > 25 , beyond observed values, is roughly estimated to be 0.1 per cent; (3) more particles are captured into the leading rather than the trailing asymmetric resonance for i 0 10 , but this number difference appears to be the opposite at i 0 = 20 and is continuously varying for even larger i 0 ; (4) captured Twotinos residing in the trailing resonance or having i > 15 are practically outside the Kozai mechanism, like currently observed samples.
Li et al. (Mon,) studied this question.