  During their formation, nascent planetary systems are subject to FU Orionis
outbursts that heat a substantial part of the disc. This causes water ice in
the affected part of the disc to sublimate as the ice line moves outwards to
several to tens of astronomical units. In this paper, we investigate how the
subsequent cooling of the disc impacts the particle sizes. We calculate the
resulting particle sizes in a disc model with cooling times between 100 and
1,000 years, corresponding to typical FU Orionis outbursts. As the disc cools
and the ice line retreats inwards, water vapour forms icy mantles on existing
silicate particles. This process is called heterogeneous nucleation. The
nucleation rate per surface area of silicate substrate strongly depends on the
degree of super-saturation of the water vapour in the gas. Fast cooling results
in high super-saturation levels, high nucleation rates, and limited
condensation growth because the main ice budget is spent in the nucleation.
Slow cooling, on the other hand, leads to rare ice nucleation and efficient
growth of ice-nucleated particles by subsequent condensation. We demonstrate
that close to the quiescent ice line, pebbles with a size of about centimetres
to decimetres form by this process. The largest of these are expected to
undergo cracking collisions. However, their Stokes numbers still reach values
that are high enough to potentially trigger planetesimal formation by the
streaming instability if the background turbulence is weak. Stellar outbursts
may thus promote planetesimal formation around the water ice line in
protoplanetary discs.
