Within the central parsec of the Galaxy, several tens of young stars orbiting a central supermassive black hole are observed. A subset of these stars forms a coherently rotating disc. Other observations reveal a massive molecular torus which lies at
a radius ~1.5pc from the centre. In this paper we consider the gravitational influence of the molecular torus upon the stars of the stellar disc. We derive an analytical formula for the rate of precession of individual stellar orbits and we show that it is highly sensitive upon the orbital semi-major axis and inclination with respect to the plane of the torus as well as on the mass of the torus. Assuming that both the stellar disc and the molecular torus are stable on the time-scale >6Myr, we constrain the mass of the torus and its inclination with respect to the young stellar disc. We further suggest that all young stars observed in the Galactic Centre may have a common origin in a single coherently rotating structure with an opening angle <5deg, which was partially destroyed (warped) during its lifetime by the gravitational influence of the molecular torus.
Mass segregation stands as one of the most robust features of the dynamical evolution of self-gravitating star clusters. In this paper we formulate parametrised models of mass segregated star clusters in virial equilibrium. To this purpose we introdu
ce mean inter-particle potentials for statistically described unsegregated systems and suggest a single-parameter generalisation of its form which gives a mass-segregated state. We describe an algorithm for construction of appropriate star cluster models. Their stability over several crossing-times is verified by following the evolution by means of direct N-body integration.
