Dust coagulation in protoplanetary disks: porosity matters

Context. Sticking of colliding dust particles through van der Waals forces is the first stage in the grain growth process in protoplanetary disks, eventually leading to the formation of comets, asteroids and planets. A key aspect of the collisional evolution is the coupling between dust and gas motions, which depends on the internal structure (porosity) of aggregates. Aims. To quantify the importance of the internal structure on the collisional evolution of particles, and to create a new coagulation model to investigate the difference between porous and compact coagulation in the context of a turbulent protoplanetary disk. Methods. We have developed simple prescriptions for the collisional evolution of porosity of grain-aggregates in grain-grain collisions. Three regimes can then be distinguished: "hit-and-stick" at low velocities, with an increase in porosity; compaction at intermediate velocities, with a decrease of porosity; and fragmentation at high velocities. This study has been restricted to physical regimes where fragmentation is unimportant. The temporal evolution has been followed using a Monte Carlo coagulation code. Results. This collision model is applied to the conditions of the (gas dominated) protoplanetary disk, with an alpha(T) parameter characterising the turbulent viscosity. We can discern three different stages in the particle growth process. Initially, growth is driven by Brownian motion and the relatively low velocities involved lead to a rapid increase in porosity of the growing aggregate. The subsequent second stage is characterised by much higher, turbulent driven velocities and the particles compact. As they compact, their mass-to-surface area increases and eventually they enter the third stage, the settling out to the mid-plane. We find that when compared to standard, compact models of coagulation, porous growth delays the onset of settling, because the surface area-to-mass ratio is higher, a consequence of the build-up of porosity during the initial stages. As a result, particles grow orders of magnitudes larger in mass before they rain-out to the mid-plane. Depending on the precise value of alpha(T) and on the position in the nebula, aggregates can grow to (porous) sizes of similar to 10 cm in a few thousand years. We also find that collisional energies are higher than in the limited PCA/CCA fractal models, thereby allowing aggregates to restructure. It is concluded that the microphysics of collisions plays a key role in the growth process.