PENTACLE: Parallelized particle–particle particle-tree code for planet formation

Abstract

Abstract We have newly developed a parallelized particle–particle particle-tree code for planet formation, PENTACLE, which is a parallelized hybrid N-body integrator executed on a CPU-based (super)computer. PENTACLE uses a fourth-order Hermite algorithm to calculate gravitational interactions between particles within a cut-off radius and a Barnes–Hut tree method for gravity from particles beyond. It also implements an open-source library designed for full automatic parallelization of particle simulations, FDPS (Framework for Developing Particle Simulator), to parallelize a Barnes–Hut tree algorithm for a memory-distributed supercomputer. These allow us to handle 1–10 million particles in a high-resolution N-body simulation on CPU clusters for collisional dynamics, including physical collisions in a planetesimal disc. In this paper, we show the performance and the accuracy of PENTACLE in terms of $\tilde{R}_{\rm cut}$ and a time-step Δt. It turns out that the accuracy of a hybrid N-body simulation is controlled through $\Delta t / \tilde{R}_{\rm cut}$ and $\Delta t / \tilde{R}_{\rm cut} \sim 0.1$ is necessary to simulate accurately the accretion process of a planet for ≥106 yr. For all those interested in large-scale particle simulations, PENTACLE, customized for planet formation, will be freely available from https://github.com/PENTACLE-Team/PENTACLE under the MIT licence.