A Signature of Planetary Migration: The Origin of Asymmetric Capture in the 2:1 Resonance

The spatial distribution of Kuiper belt objects (KBOs) in 2:1 exterior resonance with Neptune constrains that planet's migration history. Numerical simulations demonstrate that fast planetary migration generates a larger population of KBOs trailing rather than leading Neptune in orbital longitude. This asymmetry corresponds to a greater proportion of objects caught into asymmetric resonance such that their resonance angles librate about values > pi (trailing) as opposed to < pi (leading). We provide, for the first time, an explanation of this phenomenon, using physical, analytic, and semi-analytic arguments. Central to our understanding is how planetary migration shifts the equilibrium points of the superposed direct and indirect potentials. Large capture asymmetries appear for exponential timescales of migration shorter than 10 Myr. The observed distribution of 2:1 KBOs (2 trailing and 7 leading) excludes migration timescales < 1 Myr with 99.65% confidence.