A study of the high-inclination population in the Kuiper belt -- 1. The Plutinos
The dynamics of the high-inclination Plutinos is systematically studied. We first present the peculiar features of the 2:3 Neptune mean motion resonance (NMMR) for inclined orbits, especially for the correlation of resonant amplitude A_{\sigma} with inclination i. Using the numerical integrations for the age of the Solar system, the dynamical structure of the 2:3 NMMR is mapped out on the plane of semi-major axis versus i for different eccentricities. We have shown that i of stable resonant orbits could be as high as 90 deg; and the stable region is roughly surrounded by the contours of A_{\sigma} = 120 deg. These new findings allow us to further explore the 2:3 NMMR capture and retention of planetesimals with initial inclinations i0 =< 90 deg in the frame of the planet migration model. We find that the outward transportation of Plutinos is possible for any inclined or even perpendicular orbits. The role of i0 in the formation of Plutinos during Neptune's migration is highlighted and interesting results are obtained: (1) The capture efficiency of the 2:3 NMMR decreases drastically first with the increase of i0, but it then raises instead when i0 exceeds ~ 50 deg; (2) The magnitude of i-variation is limited to less than 5 deg for any i0, and moreover, for Plutinos with i > 48 deg, their i are forced to decrease throughout the outward migration; (3) Plutinos with i > 48 deg are certainly outside the Kozai mechanism, since an inclination increase is prohibited by the migrating 2:3 NMMR; (4) The 7:11 inclination-type NMMR could be responsible for nearly-circular Plutinos, and a minimum i0 ~ 15 deg is required to intrigue this mechanism.