Numerical simulation of density evolution of dust aggregates in protoplanetary disks. I. Head-on collisions

The bulk density of dust aggregates is an important factor in collisional growth of dust in protoplanetary disks. The density of aggregates changes the coupling with the disk gas, which governs the motion of aggregates in disks. Collisional outcomes also depend on the aggregate density. We perform three-dimensional N-body simulations of sequential collisions of aggregates composed of a number of submicron-sized icy particles in order to investigate the density evolution of dust aggregates growing in protoplanetary disks. In the present simulation of sequential collisions, as the initial aggregates at each collision, we use the resultant aggregate obtained at the previous collision. By repeating N-body calculations of aggregate collisions, we examined the density evolution of aggregate collisions. At an early stage of dust growth, aggregates stick to each other without restructuring, and the density of these aggregates decreases. At a later stage, in which the impact energy exceeds a critical energy, aggregates are gradually compressed. The compressed aggregates have a fractal dimension of 2.5. Because of this small fractal dimension, their density remains very low even at this compression stage. We also derive an equation describing the density evolution of growing aggregates. Applying this equation to dust growth in protoplanetary disks, we find that dust aggregates have an extremely low density (<0.1 kg m^-3). In the simulation of the present study, we consider only head-on collisions. The effect of oblique collisions would further reduce the aggregate density.