N-body calculations of cluster growth in proto-planetary disks

We investigated numerically the dust growth driven by Brownian motion in a proto-planetary disc around a solar-type young stellar object. This process is considered as the first stage in the transformation of the initially micron-sized solid particles to a planetary system. In contrast to earlier studies the growth was investigated at the small particle number densities typical for the conditions in a proto-planetary disc. Under such circumstances, the mean particle distance exceeds the typical aggregate diameter by orders of magnitude, and a collision will be a very rare event. We derived a criterion which allows an efficient detection of candidates for imminent collisions. The N-particle-method we used is based upon an adaptive time step scheme respecting the individual dynamical states of the aggregates. Its basic concept is to perform on average constant ``length steps'', instead of using constant time steps. The numerical cost of the algorithm scales with the particle number better than N log N. In order to minimise the influence of the decreasing number of particles within the simulation box, a new rescaling method is used throughout the aggregation process. Our numerical results indicate that at very low number densities, the growth process is influenced by spatial number density fluctuations.