Eccentricity growth of planetesimals in a self-gravitating protoplanetary disc

We investigate the orbital evolution of planetesimals in a self-gravitating circumstellar disc in the size regime ($\sim 1-5000$ km) where the planetesimals behave approximately as test particles in the disc's non-axisymmetric potential. We find that the particles respond to the stochastic, regenerative spiral features in the disc by executing large random excursions (up to a factor of two in radius in $\sim 1000$ years), although typical random orbital velocities are of order one tenth of the Keplerian speed. The limited time frame and small number of planetesimals modeled does not permit us to discern any {\it net} direction of planetesimal migration. Our chief conclusion is that the high eccentricities ($\sim 0.1$) induced by interaction with spiral features in the disc is likely to be highly unfavourable to the collisional growth of planetesimals in this size range while the disc is in the self-gravitating regi me. Thus {\it if}, as recently argued by Rice et al 2004, 2006, the production of planetesimals gets under way when the disc is in the self-gravitating regime (either at smaller planetesimal size scales, where gas drag is important, or via gravitational fragmentation of the solid component), then the planetesimals thus produced would not be able to grow collisionally until the disc ceased to be self-gravitating. It is unclear, however,given the large amplitude excursions undergone by planetesimals in the self-gravitating disc, whether they would be retained in the disc throughout this period, or whether they would instead be lost to the central star.