A quantification of hydrodynamical effects on protoplanetary dust growth

Context. The growth process of dust particles in protoplanetary disks can be modeled via numerical dust coagulation codes. In this approach, physical effects that dominate the dust growth process often must be implemented in a parameterized form. Due to a lack of these parameterizations, existing studies of dust coagulation have ignored the effects a hydrodynamical gas flow can have on grain growth, even though it is often argued that the flow could significantly contribute either positively or negatively to the growth process. Aims. We intend to qualitatively describe the factors affecting small particle sweep-up under hydrodynamical effects, followed by a quantification of these effects on the growth of dust particles, such that they can be parameterized and implemented in a dust coagulation code. Methods. Using a simple model for the flow, we numerically integrate the trajectories of small dust particles in disk gas around a proto-planetesimal, sampling a large parameter space in proto-planetesimal radii, headwind velocities, and dust stopping times. Results. The gas flow deflects most particles away from the proto-planetesimal, such that its effective collisional cross section, and therefore the mass accretion rate, is reduced. The gas flow however also reduces the impact velocity of small dust particles onto a proto-planetesimal. This can be beneficial for its growth, since large impact velocities are known to lead to erosion. We also demonstrate why such a gas flow does not return collisional debris to the surface of a proto-planetesimal. Conclusions. We predict that a laminar hydrodynamical flow around a proto-planetesimal will have a significant effect on its growth. However, we cannot easily predict which result, the reduction of the impact velocity or the sweep-up cross section, will be more important. Therefore, we provide parameterizations ready for implementation into a dust coagulation code.