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Sagittarius A*, the super-massive black hole at the center of the Milky Way,is surrounded by a small cluster of high velocity stars, known as the S-stars.We aim to constrain the amount and nature of stellar and dark mass associatedwith the cluster in the immediate vicinity of Sagittarius A*. We usenear-infrared imaging to determine the $K_\mathrm{s}$-band luminosity functionof the S-star cluster members, and the distribution of the diffuse backgroundemission and the stellar number density counts around the central black hole.This allows us to determine the stellar light and mass contribution expectedfrom the faint members of the cluster. We then use post-Newtonian N-bodytechniques to investigate the effect of stellar perturbations on the motion ofS2, as a means of detecting the number and masses of the perturbers. We findthat the stellar mass derived from the $K_\mathrm{s}$-band luminosityextrapolation is much smaller than the amount of mass that might be presentconsidering the uncertainties in the orbital motion of the star S2. Also theamount of light from the fainter S-cluster members is below the amount ofresidual light at the position of the S-star cluster after removing the brightcluster members. If the distribution of stars and stellar remnants is stronglyenough peaked near Sagittarius A*, observed changes in the orbital elements ofS2 can be used to constrain both their masses and numbers. Based on simulationsof the cluster of high velocity stars we find that at a wavelength of 2.2$\mu$m close to the confusion level for 8 m class telescopes blend stars willoccur (preferentially near the position of Sagittarius A*) that last fortypically 3 years before they dissolve due to proper motions.

The S-Star Cluster at the Center of the Milky Way: On the nature of diffuse NIR emission in the inner tenth of a parsec