The parametric method of moments for solving the Smolukhovsky coagulation equation in the theory of accumulation of dust bodies in a preplanetary disk

In the paper, as applied to the problem of combining dust particles, which are the main structure-forming element of planetesimals in the preplanetary cloud, a parametric method of moments for solving the Smoluchowski integro-differential equation describing dispersed coagulation of disk matter is proposed. A parametric approach to finding the distributions is considered, based on the Pearson diagram, which is used to satisfactorily find the adequate distributions from the knowledge of their first four moments. This approach is especially effective when it is necessary to know only the general properties of the distribution function of coagulating bodies by volume and their temporal evolution. Since the kinetics of the enlargement of pre-planetary bodies substantially depends on the specific type of coagulation nuclei, a sufficiently general approximation method was proposed in the work, which allows us to obtain simplified expressions for them for both laminar and turbulent motion modes. As a practical application, the parametric method of moments is demonstrated on a number of examples of the growth of pre-planetary bodies. The obtained results provide a new approach to solving the key problem of stellar-planetary cosmogony, associated with the explanation of the process of growth of interstellar dust particles to large planetesimals.