Planetary bodies form by accretion of smaller bodies. It has been suggested
that a very efficient way to grow protoplanets is by accreting particles of
size <<km (e.g., chondrules, boulders, or fragments of larger bodies) as they
can be kept dynamically cold. We investigate the effects of gas drag on the
impact radii and the accretion rates of these particles. As simplifying
assumptions we restrict our analysis to 2D settings, a gas drag law linear in
velocity, and a laminar disk characterized by a smooth (global) pressure
gradient that causes particles to drift in radially. These approximations,
however, enable us to cover an arbitrary large parameter space. The framework
of the circularly restricted three body problem is used to numerically
integrate particle trajectories and to derive their impact parameters. Three
accretion modes can be distinguished: hyperbolic encounters, where the 2-body
gravitational focusing enhances the impact parameter; three-body encounters,
where gas drag enhances the capture probability; and settling encounters, where
particles settle towards the protoplanet. An analysis of the observed behavior
is presented; and we provide a recipe to analytically calculate the impact
radius, which confirms the numerical findings. We apply our results to the
sweepup of fragments by a protoplanet at a distance of 5 AU. Accretion of
debris on small protoplanets (<50 km) is found to be slow, because the
fragments are distributed over a rather thick layer. However, the newly found
settling mechanism, which is characterized by much larger impact radii, becomes
relevant for protoplanets of ~10^3 km in size and provides a much faster
channel for growth.Comment: accepted for publication in Astronomy & Astrophysic
