  We study particle dynamics in self-gravitating gaseous discs with a simple
cooling law prescription via two-dimensional simulations in the shearing sheet
approximation. It is well known that structures arising in the gaseous
component of the disc due to a gravitational instability can have a significant
effect on the evolution of dust particles. Previous results have shown that
spiral density waves can be highly efficient at collecting dust particles,
creating significant local over-densities of particles. The degree of such
concentrations has been shown to be dependent on two parameters: the size of
the dust particles and the rate of gas cooling. We expand on these findings,
including the self-gravity of dust particles, to see how these particle
over-densities evolve. We use the PENCIL CODE to solve the local shearing sheet
equations for gas on a fixed grid together with the equations of motion for
solids coupled to the gas through an aerodynamic drag force. We find that the
enhancements in the surface density of particles in spiral density wave crests
can reach levels high enough to allow the solid component of the disc to
collapse under its own self-gravity. This produces many gravitationally bound
collections of particles within the spiral structure. The total mass contained
in bound structures appears nearly independent of the cooling time, suggesting
that the formation of planetesimals through dust particle trapping by
self-gravitating density waves may be possible at a larger range of radii
within a disc than previously thought. So, density waves due to gravitational
instabilities in the early stages of star formation may provide excellent sites
for the rapid formation of many large, planetesimal-sized objects.
