NUMERICAL MODELING OF THE COAGULATION AND POROSITY EVOLUTION OF DUST AGGREGATES

Porosity evolution of dust aggregates is crucial in understanding dust evolution in protoplanetary disks. In this study, we present useful tools to study the coagulation and porosity evolution of dust aggregates. First, we present a new numerical method for simulating dust coagulation and porosity evolution as an extension of the conventional Smoluchowski equation. This method follows the evolution of the mean porosity for each aggregate mass simultaneously with the evolution of the mass distribution function. This method reproduces the results of previous Monte Carlo simulations with much less computational expense. Second, we propose a new collision model for porous dust aggregates on the basis of our N-body experiments on aggregate collisions. As the first step, we focus on 'hit-and-stick' collisions, which involve neither compression nor fragmentation of aggregates. We first obtain empirical data on porosity changes between the classical limits of ballistic cluster-cluster and particle-cluster aggregation. Using the data, we construct a recipe for the porosity change due to general hit-and-stick collisions as well as formulae for the aerodynamical and collisional cross sections. Our collision model is thus more realistic than a previous model of Ormel et al. based on the classical aggregation limits only. Simple coagulation simulations using the extended Smoluchowski method show that our collision model explains the fractal dimensions of porous aggregates observed in a full N-body simulation and a laboratory experiment. By contrast, similar simulations using the collision model of Ormel et al. result in much less porous aggregates, meaning that this model underestimates the porosity increase upon unequal-sized collisions. Besides, we discover that aggregates at the high-mass end of the distribution can have a considerably small aerodynamical cross section per unit mass compared with aggregates of lower masses. This occurs when aggregates drift under uniform acceleration (e.g., gravity) and their collision is induced by the difference in their terminal velocities. We point out an important implication of this discovery for dust growth in protoplanetary disks.