Stellar discs and intermediate-mass black holes in galactic nuclei II. Fragmenting the disc and forming the S-stars in a live nuclear star cluster

We present direct N-body simulations of a stellar disc around the supermassive black hole Sgr A*, perturbed by an intermediate-mass black hole (IMBH) and embedded in a live nuclear star cluster. A retrograde IMBH with m=2000,M, relative inclination θ=150, and initial semi-major axis a=0.15 pc breaks the disc into three disc-like components and an angular momentum filament. The stochastic torques of the cluster, together with the IMBH's inward migration, increase the angular separation between these substructures. By about 5 Myr, their separations become comparable to those among the observed Galactic-centre young star structures. The innermost (a 0.04 pc) disc stars evolve into an S-star-like population. Relaxation driven by the cluster disperses their orbital planes, excites their eccentricities and depletes the `zone of avoidance' within about 10 Myr even without an IMBH. The IMBH further accelerates their orbital-plane reorientation. However, the most eccentric S-stars may require an additional formation channel, such as the Hills mechanism. The distinctive signatures of the IMBH are the well-separated disc components and the eccentricity excitation confined to the radial range swept by its orbit. Dynamical friction from the cluster reduces the orbital size of a 2000,M IMBH initially at 0.15 pc by more than a factor of two within 10 Myr. Prograde IMBHs tend to align with the stellar disc, whereas a 2000,M retrograde IMBH can anti-align with the radially overlapping disc stars. We also quantify how the IMBH affects the supply of stars to the loss cone and the rates of stellar tidal disruptions and binary separations.