Asymmetric capture into Neptunian 1:2 resonance

The asymmetric resonance configuration characterised by the critical angle librating around centres other than 0 degrees or 180 degrees is found in the 1:N mean motion resonance. The asymmetric 1:2 resonance with Neptune is of particular interest because the two asymmetric islands seem to host different populations, and this might be a direct clue to understanding the early evolution of the Solar System. The asymmetry has been investigated from both observational and theoretical perspectives, but conclusions among studies vary widely. In this paper, using toy models, we carefully designed a series of tests to systematically study the capture of planetesimals into the leading and trailing resonance islands. Although these tests may not exactly reproduce the real processes the Solar System experienced, they reveal some typical dynamics in the resonance capture. Since the real Twotinos have small to moderate inclinations, as a first attempt, we adopted planar models in this paper in order to investigate the mechanisms that may lead to asymmetric capture by the leading and trailing islands, including their size variation during the outward migration of Neptune, the stickiness of the leading island, and the migration slowdown effect. We find that the ratio between the populations of the leading and trailing islands can be easily tuned by introducing the slowdown effect into the migration model, and thus it may not be a good tracer of the migration history. However, the eccentricity of objects trapped in two asymmetric islands may conserve some valuable information of the early evolution of the Solar System.