  We show that condensation is an efficient particle growth mechanism, leading
to growth beyond decimeter-sized pebbles close to an ice line in protoplanetary
discs. As coagulation of dust particles is frustrated by bouncing and
fragmentation, condensation could be a complementary, or even dominant, growth
mode in the early stages of planet formation. Ice particles diffuse across the
ice line and sublimate, and vapour diffusing back across the ice line
recondenses onto already existing particles, causing them to grow. We develop a
numerical model of the dynamical behaviour of ice particles close to the water
ice line, approximately 3 AU from the host star. Particles move with the
turbulent gas, modelled as a random walk. They also sediment towards the
midplane and drift radially towards the central star. Condensation and
sublimation are calculated using a Monte Carlo approach. Our results indicate
that, with a turbulent alpha-value of 0.01, growth from millimeter to at least
decimeter-sized pebbles is possible on a time scale of 1000 years. We find that
particle growth is dominated by ice and vapour transport across the radial ice
line, with growth due to transport across the atmospheric ice line being
negligible. Ice particles mix outwards by turbulent diffusion, leading to net
growth across the entire cold region. The resulting particles are large enough
to be sensitive to concentration by streaming instabilities, and in pressure
bumps and vortices, which can cause further growth into planetesimals. In our
model, particles are considered to be homogeneous ice particles. Taking into
account the more realistic composition of ice condensed onto rocky ice nuclei
might affect the growth time scales, by release of refractory ice nuclei after
sublimation. We also ignore sticking and fragmentation in particle collisions.
These effects will be the subject of future investigations.
