2017ApJ...834..198Z

The S-stars discovered in the Galactic center are expected to provide unique dynamical tests of the Kerr metric of the massive black hole (MBH) that they orbit. In order to obtain unbiased measurements of its spin and the related relativistic effects, a comprehensive understanding of the gravitational perturbations of the stars and stellar remnants around the MBH is quite essential. Here, we study the perturbations on the observables of a typical target star, i.e., the apparent orbital motion and the redshift, due to both the spin-induced relativistic effects and the Newtonian attractions of a single object or a cluster of disturbing objects. We find that, in most cases, the Newtonian perturbations on the observables are mainly attributed to the perturbed orbital period of the target star rather than the Newtonian orbital precessions. Looking at the currently detected star S2/S0-2, we find that its spin-induced effects are very likely obscured by the gravitational perturbations from the star S0-102 alone. We also investigate and discuss the Newtonian perturbations on a hypothetical S-star located inside the orbits of those currently detected. By considering a number of possible stellar distributions near the central MBH, we find that the spin-induced effects on the apparent position and redshift dominate over the stellar perturbations for target stars with orbital semimajor axis smaller than 100-400 au if the MBH is maximally spinning. Our results suggest that, in principle, the stellar perturbations can be removed because they have morphologies distinct from those of the relativistic Kerr-type signatures.