Weighing the cusp at the Galactic Centre

This paper has been withdrawn temporarily by the authors. As stars close to the galactic centre have short orbital periods it has been possible to trace large fractions of their orbits in the recent years. Previously the data of the orbit of the star S2 have been fitted with Keplerian orbits corresponding to a massive black hole (MBH) with a mass of M$_{BH}$=3-4$\times10^6$M_sun implying an insignificant cusp mass.However, it has also been shown that the central black hole resides in a ~1'' diameter stellar cluster of a priori unknown mass. In a spherical potential which is neither Keplerian nor harmonic, orbits will precess resulting in inclined rosetta shaped trajectories on the sky. In this case, the assumption of non-Keplerian orbits is a more physical approach. It is also the only approach through which cusp mass information can be obtained via stellar dynamics of the cusp members. This paper presents the first exemplary modelling efforts in this direction. Using positional and radial data of star S2, we find that there could exist an unobserved extended mass component of several 10$^5$M$_{\odot}$ forming a so-called 'cusp' centred on the black hole position. Considering only the fraction of the cusp mass M$_{S2_{apo}}$ within the apocenter of the S2 orbit we find as an upper limit that M$_{S2_{apo}}$/(M$_{BH}$ + M$_{S2_{apo}}$) $\le$ 0.05. A large extended cusp mass, if present, is unlikely to be composed of sub-solar mass constituents, but could be explained rather well by a cluster of high M/L stellar remnants, which we find to form a stable configuration