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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.'
author:
- 'Michiko <span style="font-variant:small-caps;">Fujii</span>'
- 'Masaki <span style="font-variant:small-caps;">Iwasawa</span>, Yoko <span style="font-variant:small-caps;">Funato</span>'
- 'Junichiro <span style="font-variant:small-caps;">Makino</span>'
title: 'BRIDGE: A Direct-tree Hybrid $N$-body Algorithm for Fully Self-consistent Simulations of Star Clusters and their Parent Galaxies'
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Introduction
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Accuracy and Performance
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Summary and Discussion
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The authors thanks Piet Hut for useful comments and the name of the hybrid scheme, Keigo Nitadori and Ataru Tanikawa for fruitful discussions, and the referee, Simon F. Portegies Zwart, for useful comments on the manuscript. M. F. is financially supported by Research Fellowships of the Japan Society for the Promotion of Science (JSPS) for Young Scientists. This research is partially supported by the Special Coordination Fund for Promoting Science and Technology (GRAPE-DR project), Ministry of Education, Culture, Sports, Science and Technology, Japan. Part of calculations were done using the GRAPE system at the Center for Computational Astrophysics (CfCA) of the National Astronomical Observatory of Japan.
