For experiments in the very near future the LBT (Large Binocular Telescope on Mount Graham in Arizona) is ideally suited to search for and monitor the flux of a Sgr A^∗ NIR counterpart. High sensitivity combined with adaptive optics and interferometry using the two LBT mirrors will provide the required accuracy to separate the Sgr A^∗ NIR counterpart from neighboring stars. The unprecedented combination of high sensitivity and high angular resolution over a large field of view will allow significant motions in most of the 600 stars brighter than m_K < 14 covering the inner parsec of the central stellar cluster to be detected. Combined with imaging spectroscopy this may result in a large number of sources with measurements of all three velocity components. Full space velocities are essential to improve the analysis of the dynamical properties of the late type stars and the inner bright higher velocity He I stars. This will undoubtedly help to determine the origin of the He I stars which may represent the remains of a dissolved young cluster (see Gerhard 2000). The spectra from fast moving stars will be of special importance. Knowing their full space velocity will result in complete information on their orbits.

It is even more desirable to find and track the motion of stars that are as close to the center as possible. Orbital timescales at the resolution limit of the LBT interferometer could be in the range of a few months. A detection of a relativistic or Newtonian periastron shift would ultimately result in a determination of the compactness of the enclosed central mass. The prograde relativistic periastron rotation is of the order of 17 arcminutes per revolution for a 60 mas (2.4 mpc; orbital timescale 6.8 yr) orbit with an eccentricity of ϵ = 0.9. For a 15 mas (0.6 mpc; orbital timescale 0.9 yr) orbit with the same eccentricity the shift is already of the order of 1.1 degrees per revolution. Periastron shifts of 2 degrees could be observed with the LBTI with ∼1σ yr⁻¹.

When a small amount of the compact mass is extended the retrograde Newtonian periastron shift would be much larger. For orbits with a half axis as before and a modest eccentricity of ϵ = 0.5 the shift may amount to several tens of degrees per revolution. This assumes that the extended mass is contained in a compact cluster of less than 6 mpc core radius. Comparing the relative magnitudes of the relativistic and Newtonian periastron shift one finds that if for S2-like orbits only about 0.1% of the currently measured 3 × 10⁶ M_ּ is extended the periastron shifts of the two mechanisms compensate each other. The percentage will be higher for stars on closer orbits of similar or even higher eccentricity.

Figure 1.1. Left: measured data points and elements of the high velocity star S2. Right: NACO AO (adaptive optics) image from the central few arcseconds with some of the sources labeled.

Note added in proof

Recently the combination of the 10 years of SHARP measurements at the ESO NTT combined with new VLT UT4 adaptive optics measurements using NACO at the ESO VLT UT4 allowed us (Schodel et al 2002) to trace two thirds of the complete orbit of the star S2, currently closest to the compact radio source and massive black hole candidate Sgr A^∗. The observations confirm the result by Eckart et al (2002) that the star is on a bound, highly elliptical Keplerian orbit around Sgr A^∗. The orbital period is 15.4 years and the distance during the pericenter passage has been only 17 light hours. The orbital elements require an enclosed point mass of 3.7 ± 1.5 × 10⁶ solar masses, which agrees well with the mass at much larger distances. See figure 1.1.