We performed, for the first time, the simulation of spiral-in of a star cluster formed close to the Galactic center (GC) using a fully self-consistent $N$-body model. In our model, the central super-massive black hole (SMBH) is surrounded by stars and the star cluster. Not only are the orbits of stars and the cluster stars integrated self-consistently, but the stellar evolution, collisions and merging of the cluster stars are also included. We found that an intermediate-mass black hole (IMBH) is formed in the star cluster and stars escaped from the cluster are captured into a 1:1 mean motion resonance with the IMBH. These Trojan stars are brought close to the SMBH by the IMBH, which spirals into the GC due to the dynamical friction. Our results show that, once the IMBH is formed, it brings the massive stars to the vicinity of the central SMBH even after the star cluster itself is disrupted. Stars carried by the IMBH form a disk similar to the observed disks and the core of the cluster including the IMBH has properties similar to those of IRS13E, which is a compact assembly of several young stars.
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