The position of Sagittarius A*. III. Motion of the stellar cusp

In the first two papers of this series, we determined the position of Sgr A* on infrared images by aligning the positions of red giant stars with positions measured at radio wavelengths for their circumstellar SiO masers. In this paper, we report the detections of five new stellar SiO masers within 50 (2 pc) of Sgr A* and new and/or improved positions and proper motions of 15 stellar SiO masers. The current accuracies are approximate to 1 mas in position and approximate to 0.3 mas yr(-1) in proper motion. We find that the propermotion of the central stellar cluster with respect to Sgr A* is less than 45 km s(-1). One star, IRS 9, has a three-dimensional speed of approximate to 370 km s(-1) at a projected distance of 0.33 pc from Sgr A*. If IRS 9 is bound to the inner parsec, this requires an enclosed mass that exceeds current estimates of the sum of the mass of Sgr A* and luminous stars in the stellar cusp by approximate to 0.8 x 10(6) M-circle dot. Possible explanations include: (1) that IRS 9 is not bound to the central parsec and has fallen'' from a radius greater than 9 pc, (2) that a cluster of dark stellar remnants accounts for some of the excess mass, and/or (3) that R-0 is considerably greater than 8 kpc.