ar X iv : 0 80 1 . 45 05 v 2 [ as tr o - ph ] 2 7 M ar 2 00 8 Limits on the Position

We present measurements with the VLBA of the variability in the centroid position of Sgr A* relative to a background quasar at 7mm wavelength. We find an average centroid wander of 71 ± 45μas for time scales between 50 and 100 min and 113± 50μas for timescales between 100 and 200 min, with no secular trend. These are sufficient to begin constraining the viability of the accretion hot-spot model for the radio variability of Sgr A*. It is possible to rule out hot spots with orbital radii above 15GMSgrA∗/c 2 that contribute more than 30% of the total 7mm flux. However, closer or less luminous hot spots remain unconstrained. Since the fractional variability of Sgr A* during our observations was ∼ 20% on time scales of hours, the hot-spot model for Sgr A*’s radio variability remains consistent with these limits. Improved monitoring of Sgr A*’s centroid position has the potential to place significant constraints upon the existence and morphology of inhomogeneities in a supermassive black hole accretion flow. Subject headings: accretion disks – astrometry – black hole physics – Galaxy: center – gravitational lensing – instrumentation: high angular resolution