Resonant Trapping of Planetesimals by Planet Migration: Debris Disk Clumps and Vega's Similarity to the Solar System

This paper describes a model that can explain the observed clumpy structures of debris disks. Clumps arise because after a planetary system forms, its planets migrate because of angular momentum exchange with the remaining planetesimals. Outward migration of the outermost planet traps planetesimals outside its orbit into its resonances, and resonant forces cause azimuthal structure in their distribution. The model is based on numerical simulations of planets of different masses, M_pl, migrating at different rates, a_pl, through a dynamically cold (e<0.01) planetesimal disk initially at a semimajor axis a. Trapping probabilities and the resulting azimuthal structures are presented for a planet's 2:1, 5:3, 3:2, and 4:3 resonances. Seven possible dynamical structures are identified from migrations defined by μ=M_pl/M_* and θ=a_pl(a/M_*)^1/2. Application of this model to the 850 μm image of Vega's disk shows that its two clumps of unequal brightness can be explained by the migration of a Neptune-mass planet from 40 to 65 AU over 56 Myr; tight constraints are set on possible ranges of these parameters. The clumps are caused by planetesimals in the 3:2 and 2:1 resonances; the asymmetry arises because of the overabundance of planetesimals in the 2:1(u) over the 2:1(l) resonance. The similarity of this migration to that proposed for our own Neptune hints that Vega's planetary system may be much more akin to the solar system than previously thought. Predictions are made that would substantiate this model, such as the orbital motion of the clumpy pattern, the location of the planet, and the presence of lower level clumps.