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

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 $e_a(i)$ and $e_c(i)$, which are lower limits of the eccentricity $e$ for the resonant angle $\sigma$ to exhibit libration and asymmetric libration, respectively. Accordingly, we have determined the libration centres $\sigma_0$ for inclined orbits, which are strongly dependent on $i$. With initial $\sigma=\sigma_0$ 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 $i\ge30^{\circ}$; while stable asymmetric librators exist for $i$ up to $90^{\circ}$. We further investigate the 1:2 NMMR capture and retention of planetesimals with initial inclinations $i_0\le90^{\circ}$ in the planet migration model using a time-scale of $2\times10^7$ 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 $i_0\ge60^{\circ}$; (2) the probability of discovering Twotinos with $i>25^{\circ}$, beyond observed values, is roughly estimated to be $\le0.1$ per cent; (3) more particles are captured into the leading rather than the trailing asymmetric resonance for $i_0\le10^{\circ}$, but this number difference appears to be the opposite at $i_0=20^{\circ}$ and is continuously varying for even larger $i_0$; (4) captured Twotinos residing in the trailing resonance or having $i>15^{\circ}$ are practically outside the Kozai mechanism, like currently observed samples.Comment: 13 pages, 10 figures, Accepted by MNRAS. Comments welcome

Transit of asteroids across the 7/3 Kirkwood gap under the Yarkovsky effect

Many asteroids in the main belt are continuously pushed by Yarkovsky effect into regions of different mean motion resonances (MMRs) and then ejected out. They are considered as the principal source of near-Earth objects. We investigate in this paper the effects of the 7/3 MMR with Jupiter (J7/3 MMR) on the transportation of asteroids from Koronis and Eos families that reside respectively on the inner and outer side of the resonance. The fraction of asteroids that make successful crossing through the resonance and the escaping rate from the resonance are found to depend on the Yarkovsky drifting rate, the initial inclination and the migrating direction. The excitation of eccentricity and inclination due to the combined influence from both the resonance and Yarkovsky effect is discussed. Only the eccentricity can be pumped up considerably, and it is attributed mainly to the resonance. In the observational data, family members are also found in the resonance and on the opposite side of the resonance with respect to the corresponding family centre. The existence of these family members is explained using our results of numerical simulations. Finally, the replenishment of asteroids in the J7/3 MMR and the transportation of asteroids by it are discussed.Comment: 10 pages, 10 figures. Accepted by A&