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We developed a new direct-tree hybrid N-body algorithm for fullyself-consistent N-body simulations of star clusters in their parent galaxies.In such simulations, star clusters need high accuracy, while galaxies need afast 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 calculatedaccurately using the direct Hermite scheme with individual timesteps and allother motions are calculated using the tree code with second-order leapfrogintegrator. The direct and tree schemes are combined using an extension of themixed variable symplectic (MVS) scheme. Thus, the Hamiltonian corresponding toeverything other than the internal motion of the star cluster is integratedwith the leapfrog, which is symplectic. Using this algorithm, we performedfully self-consistent N-body simulations of star clusters in their parentgalaxy. The internal and orbital evolutions of the star cluster agreed wellwith those obtained using the direct scheme. We also performed fullyself-consistent N-body simulation for large-N models ($N=2\times 10^6$). Inthis case, the calculation speed was seven times faster than what would be ifthe direct scheme was used.

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