Parametric Method of Moments for Solving the Smoluchowski Coagulation Equation in the Theory of Accumulation of Dust Bodies in a Protoplanetary Disk

In relation to the problem of accumulation of dust particles, which are the main structure-forming element of planetesimals in a protoplanetary cloud, we propose a parametric method of moments for solving the Smoluchowski integro-differential equation that describes dispersed coagulation of disk matter. We consider a parametric approach to finding the size distribution function of protoplanetary bodies based on the Pearson diagram, with the aid of which the corresponding distributions are quite satisfactorily found by their first four moments. This approach is especially effective when it is necessary to know only the general properties of the volume distribution functions of coagulating bodies and their temporal evolution. Since the kinetics of the processes of aggregation of protoplanetary bodies substantially depends on the specific type of coagulation kernels, a fairly general method for their approximation is proposed in the study, which allows one to obtain simplified expressions. As a practical application, the parametric method of moments is demonstrated by a number of examples of the growth of protoplanetary bodies. The results provide a new productive approach to solving the key problem of stellar-planetary cosmogony associated with an explanation of the process of growth of interstellar dust particles to large planetesimals.