The effect of gas drag on the growth of protoplanets. Analytical expressions for the accretion of small bodies in laminar disks

How do planetesimals and protoplanets grow? One likely possibility is that they grow by accumulation of a population of smaller bodies and that most of this growth occurs early, within gaseous protoplanetary disks. So far, analytical work on the problem has considered three-body interactions (among the central protostar, the protoplanet, and the small particle) without including the effect of the gas. Ormel & Klahr provide analytical expressions for protoplanetary growth in the framework of the restricted three-body problem with a linear gas drag law and a smooth pressure gradient. They highlight three modes of growth: hyperbolic encounters, for which growth depends on gravitational focusing; three-body encounters where gas drag enhances the capture probability; and settling encounters, where particles settle towards the protoplanet. This new mechanism may provide a much faster channel for growth in the case of ~1000km-sized protoplanets embedded in a swarm of small particles and gas.