  In this paper we consider the evolution of small planetesimals in marginally
stable, self-gravitating protoplanetary discs. The drag force between the disc
gas and the embedded planetesimals generally causes the planetesimals to drift
inwards through the disc at a rate that depends on the particle size. In a
marginally stable, self-gravitating disc, however, the planetesimals are
significantly influenced by the non-axisymmetric spiral structures resulting
from the growth of the gravitational instability. For small particles, that are
strongly coupled to the disc gas, and for large particles, that have
essentially decoupled from the disc gas, the effect is not particularly
significant. Intermediate sized particles, which would generally have the
largest radial drift rates, do, however, become significantly concentrated at
the peaks of the spiral arms. These high density regions may persist for, of
order, an orbital period and may attain densities comparable to that of the
disc gas. Although at the end of the simulation only ~ 25 % of the planetesimal
particles lie in regions of enhanced density, during the course of the
simulation at least 75 % of the planetesimal particles have at some stage been
in a such a region. We find that the concentration of particles in the spiral
arms results in an increased collision rate, an effect that could significantly
accelerate planetesimal growth. The density enhancements may also be sufficient
for the growth of planetesimals through direct gravitational collapse. The
interaction between small planetesimals and self-gravitating spiral structures
may therefore play an important role in the formation of large planetesimals
that will ultimately coagulate to form terrestrial planets or the cores of
gas/ice giant planets.
