BRIDGE: A Direct-tree Hybrid N-body Algorithm for Fully Self-consistent Simulations of Star Clusters and their Parent Galaxies

TL;DR

This paper introduces a hybrid N-body algorithm combining direct and tree methods, enabling accurate and efficient simulations of star clusters within galaxies, significantly improving speed for large particle numbers.

Contribution

The paper presents a novel hybrid algorithm that integrates direct and tree N-body schemes using an extended MVS approach for self-consistent star cluster and galaxy simulations.

Findings

The algorithm accurately reproduces cluster evolution compared to direct methods.

Simulation speed increased by a factor of seven for large N=2 million models.

The method effectively balances accuracy and computational efficiency.

Abstract

We developed a new direct-tree hybrid N-body algorithm for fully self-consistent N-body simulations of star clusters in their parent galaxies. In such simulations, star clusters need high accuracy, while galaxies need a fast scheme because of the large number of the particles required to model it. In our new algorithm, the internal motion of the star cluster is calculated accurately using the direct Hermite scheme with individual timesteps and all other motions are calculated using the tree code with second-order leapfrog integrator. The direct and tree schemes are combined using an extension of the mixed variable symplectic (MVS) scheme. Thus, the Hamiltonian corresponding to everything other than the internal motion of the star cluster is integrated with the leapfrog, which is symplectic. Using this algorithm, we performed fully self-consistent N-body simulations of star clusters in their parent galaxy. The internal and orbital evolutions of the star cluster agreed well with those obtained using the direct scheme. We also performed fully self-consistent N-body simulation for large-N models ($N=2\times 10^6$). In this case, the calculation speed was seven times faster than what would be if the direct scheme was used.