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This paper describes a model which can explain the observed clumpy structuresof debris disks. Clumps arise because after a planetary system forms itsplanets migrate due to angular momentum exchange with the remainingplanetesimals. Outward migration of the outermost planet traps planetesimalsoutside its orbit into its resonances and resonant forces cause azimuthalstructure in their distribution. The model is based on numerical simulations ofplanets of different masses, Mpl, migrating at different rates, dapl/dt,through a dynamically cold (e<0.01) planetesimal disk initially at a semimajoraxis a. Trapping probabilities and the resulting azimuthal structures arepresented for a planet's 2:1, 5:3, 3:2, and 4:3 resonances. Seven possibledynamical structures are identified from migrations defined by mu=Mpl/Mstar andtheta=dapl/dt*sqrt(a/Mstar). Application of this model to the 850um image ofVega's disk shows its two clumps of unequal brightness can be explained by themigration of a Neptune-mass planet from 40 to 65AU over 56Myr; tightconstraints are set on possible ranges of these parameters. The clumps arecaused by planetesimals in the 3:2 and 2:1 resonances; the asymmetry arisesbecause 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 ownNeptune hints that Vega's planetary system may be much more akin to the solarsystem than previously thought. Predictions are made which would substantiatethis model, such as the orbital motion of the clumpy pattern, the location ofthe planet, and the presence of lower level clumps.Comment: 30 pages, accepted by Ap

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