  We study particle dynamics in local two-dimensional simulations of
self-gravitating accretion discs with a simple cooling law. It is well known
that the structure which arises 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 using global simulations indicate that spiral
density waves are highly efficient at collecting dust particles, creating
significant local over-densities which may be able to undergo gravitational
collapse. We expand on these findings, using a range of cooling times to mimic
the conditions at a large range of radii within the disc. Here we use the
Pencil Code to solve the 2D local shearing sheet equations for gas on a fixed
grid together with the equations of motion for solids coupled to the gas solely
through aerodynamic drag force. We find that spiral density waves can create
significant enhancements in the surface density of solids, equivalent to 1-10cm
sized particles in a disc following the profiles of Clarke (2009) around a
solar mass star, causing it to reach concentrations several orders of magnitude
larger than the particles mean surface density. We also study the velocity
dispersion of the particles, finding that the spiral structure can result in
the particle velocities becoming highly ordered, having a narrow velocity
dispersion. This implies low relative velocities between particles, which in
turn suggests that collisions are typically low energy, lessening the
likelihood of grain destruction. Both these findings suggest that the density
waves that arise due to gravitational instabilities in the early stages of star
formation provide excellent sites for the formation of large,
planetesimal-sized objects.
