Fast accretion of small planetesimals by protoplanetary cores

We explore the dynamics of small planetesimals coexisting with massive protoplanetary cores in a gaseous nebula. Gas drag strongly affects the motion of small bodies, leading to the decay of their eccentricities and inclinations, which are excited by the gravity of protoplanetary cores. Drag acting on larger (greater than or similar to1 km), high-velocity planetesimals causes a mere reduction of their average random velocity. By contrast, drag qualitatively changes the dynamics of smaller (less than or similar to0.1-1 km), low-velocity objects: (1) small planetesimals sediment toward the midplane of the nebula, forming a vertically thin subdisk; (2) their random velocities rapidly decay between successive passages of the cores, and as a result, encounters with cores typically occur at the minimum relative velocity allowed by the shear in the disk. This leads to a drastic increase in the accretion rate of small planetesimals by the protoplanetary cores, allowing cores to grow faster than expected in the simple oligarchic picture, provided that the population of small planetesimals contains more than roughly 1% of the solid mass in the nebula. Fragmentation of larger planetesimals (greater than or similar to1 km) in energetic collisions triggered by the gravitational scattering by cores can easily channel this amount of material into small bodies on reasonable timescales (<1 Myr in the outer solar system), providing a means for the rapid growth (within several million years at 30 AU) of rather massive protoplanetary cores. Effects of inelastic collisions between planetesimals and presence of multiple protoplanetary cores are discussed.