An improved Representative Particle Monte Carlo method for the simulation of particle growth

Institute of Theoretical Astrophysics (ITA), Center for Astronomy (ZAH), Ruprecht-Karls-Universität Heidelberg, Albert-Ueberle-Str. 2, 69120 Heidelberg, Germany
e-mail: moritz.beutel@ziti.uni-heidelberg.de

Received: 12 September 2022
Accepted: 21 November 2022

Abstract

Context. A rocky planet is formed out of the agglomeration of around 10⁴⁰ cosmic dust particles. As dust aggregates grow by coagulation, their number decreases. But until they have grown to hundreds of kilometres, their number still remains well above the number of particles a computer model can handle directly. The growth from micrometres to planetesimal-sized objects therefore has to be modelled using statistical methods, often using size distribution functions or Monte Carlo methods. However, when the particles reach planetary masses, they must be treated individually. This can be done by defining two classes of objects: a class of many small bodies or dust particles treated in a statistical way, and a class of individual bodies such as one or more planets. This introduces a separation between small and big objects, but it leaves open how to transition from small to big objects, and how to treat objects of intermediate sizes.

Aims. We aim to improve the Representative Particle Monte Carlo (RPMC) method, which is often used for the study of dust coagulation, to be able to smoothly transition from the many-particle limit into the single-particle limit.

Results. Our new version of the RPMC method allows for variable swarm masses, making it possible to refine the mass resolution where needed. It allows swarms to consist of few numbers of particles, and it includes a treatment of the transition from swarm to individual particles. The correctness of the method for a simplified two-component test case is validated with an analytical argument. The method is found to retain statistical balance and to accurately describe runaway growth, as is confirmed with the standard constant kernel, linear kernel, and product kernel tests as well as by comparison with a fiducial non-representative Monte Carlo simulation.