The structure of dust aggregates in hierarchical coagulation

Dust coagulation in interstellar space and protoplanetary disks is usually treated as one of 2 extreme cases: Particle-Cluster Aggregation and Cluster-Cluster Aggregation. In this paper we study the process of hierarchical growth, where aggregates are built from significantly smaller aggregates (but not monomers). We show that this process can be understood as a modified, PCA-like process that produces porous, but non-fractal particles whose filling factor is chiefly determined by the porosity of the building blocks. We also show that in a coagulation environment where relative velocities are driven by turbulence, a logarithmically flat mass distribution (equal mass per mass decade) as it is typically found in environments where fragmentation replenishes small grains, leads to a situation where small particles and aggregates dominate the growth of large ones. Therefore, in such environments, hierarchical growth should be seen as the norm. Consequently, we predict that the aggregates in such environments are not fractals with extremely low densities as they would result from extrapolation fractal laws to large sizes. The compactification of aggregates does not only result from collisions with enough energy to restructure aggregates - it starts already earlier by filling voids in particles with smaller grains that contribute to the growth.