Measuring Distance and Properties of the Milky Way's Central Supermassive Black Hole with Stellar Orbits

We report new precision measurements of the properties of our Galaxy's supermassive black hole. Based on astrometric (1995-2007) and radial velocity (RV; 2000-2007) measurements from the W. M. Keck 10 m telescopes, a fully unconstrained Keplerian orbit for the short-period star S0-2 provides values for the distance (R₀) of 8.0 ± 0.6 kpc, the enclosed mass (M_bh) of 4.1 ± 0.6 × 10⁶ M_☉, and the black hole's RV, which is consistent with zero with 30 km s⁻¹ uncertainty. If the black hole is assumed to be at rest with respect to the Galaxy (e.g., has no massive companion to induce motion), we can further constrain the fit, obtaining R₀ = 8.4 ± 0.4 kpc and M_bh = 4.5 ± 0.4 × 10⁶ M_☉. More complex models constrain the extended dark mass distribution to be less than 3-4 × 10⁵ M_☉ within 0.01 pc, ~100 times higher than predictions from stellar and stellar remnant models. For all models, we identify transient astrometric shifts from source confusion (up to 5 times the astrometric error) and the assumptions regarding the black hole's radial motion as previously unrecognized limitations on orbital accuracy and the usefulness of fainter stars. Future astrometric and RV observations will remedy these effects. Our estimates of R₀ and the Galaxy's local rotation speed, which it is derived from combining R₀ with the apparent proper motion of Sgr A*, (θ₀ = 229 ± 18 km s⁻¹), are compatible with measurements made using other methods. The increased black hole mass found in this study, compared to that determined using projected mass estimators, implies a longer period for the innermost stable orbit, longer resonant relaxation timescales for stars in the vicinity of the black hole and a better agreement with the M_bh-σ relation.