On the delivery of planetesimals to a protoplanet in the solar nebula

A planetesimal moving in the solar nebula experiences an aerodynamic drag which causes its orbit to circularize and shrink. However resonant perturbations from a protoplanet interior to the planetesimal's orbit can counteract both the orbital decay and the damping of the eccentricity: the planetesimal can be captured into an orbital resonance and its eccentricity pumped up to an equilibrium value. The resonance trapping phenomenon is sensitive to several factors and we elaborate on these below. Orbital resonances form (partial) barriers to the transport of planetesimals into the feeding zone of the protoplanet. Here we report on a systematic study of the idealized system of a single protoplanet of mass much larger than the masses of the planetesimals, comparing relevant analytic estimates with numerical simulations. Our principal conclusion is that in a gas-rich environment, the bulk of the solid material delivered to the feeding zone of the protoplanet is in the form of bodies of small radius.