Planet Migration through a Self-Gravitating Planetesimal Disk
  We simulate planet migration caused by interactions between planets and a planetesimal disk. We use an N-body integrator optimized for near-Keplerian motion that runs in parallel on a video graphics card, and that computes all pair-wise gravitational interactions. We find that the fraction of planetesimals found in mean motion resonances is reduced and planetary migration rates are on average about 50% slower when gravitational interactions between the planetesimals are computed than when planetesimal self-gravity is neglected. This is likely due to gravitational stirring of the planetesimal disk that is not present when self-gravity is neglected that reduces their capture efficiency because of the increased particle eccentricity dispersion. We find that migration is more stochastic when the disk is self-gravitating or comprised of more massive bodies. Previous studies have found that if the planetesimal disk density is below a critical level, migration is "damped" and the migration rate decays exponentially, otherwise it is "forced" and the planet's migration rate could accelerate exponentially. Migration rates measured from our undamped simulations suggest that the migration rate saturates at a level proportional to disk density and subsequently is approximately power law in form with time. 
Alexander J. Moore, Alice C. Quillen, Richard G. Edgar