Estimating the Parameters of Collisions between Fractal Dust Clusters in a Gas–Dust Protoplanetary Disk

Abstract

Studying the origin and evolution of the Solar system is among the fundamental problems of modern natural science. This problem is interdisciplinary and requires the development of mathematical models for the physical structure and evolution of a gas–dust accretion disk from the initial stages of its formation to the formation of a planetary system. One of the key problems is the formation and growth of bodies in a protoplanetary disk, the basis for which is a study of the collisional processes of the solidbody component. We have performed a parametric analysis of the cluster–cluster collision processes occurring in a protoplanetary disk within the model of permeable particles being developed by us. The outcome of such collisions is shown to be affected significantly by the topological properties of colliding dust clusters with a fractal internal structure. The results of our parametric analysis show that for sufficiently “dense” fractal dust clusters, at low relative collision velocities, there exists a range in which the colliding clusters bounce. At the same time, for “porous” fractal clusters the bounce is impossible for any sets of collision parameters. As the relative collision velocities increase, the cluster coalescence processes begin to dominate due to a rearrangement of the fractal structure in the contact zone. However, as the kinetic energy of collisions increases further, a critical threshold is reached beyond which the collision energy exceeds the particle binding energy in clusters and the fractal dust cluster destruction processes are switched on during collisions. Thus, our parametric analysis imposes quite definite constraints on the dynamics and chronology of the evolution processes during the formation of primordial solid bodies and planetesimals. The proposed approach and the results obtained are fairly realistic and open prospects for more comprehensive model studies of the initial evolutionary phase of a protoplanetary disk.