Localizing Sagittarius A* and M87 on Microarcsecond Scales with Millimeter VLBI

With the advent of the Event Horizon Telescope (EHT), a millimeter/sub-millimeter very-long baseline interferometer (VLBI), it has become possible to image a handful of black holes with sub-horizon resolutions. However, these images do not translate into microarcsecond absolute positions due to the lack of absolute phase information when an external phase reference is not used. Due to the short atmospheric coherence time at these wavelengths, nodding between the source and phase reference is impractical. However, here we suggest an alternative scheme which makes use of the fact that many of the VLBI stations within the EHT are arrays in their own right. With this we show that it should be possible to absolutely position the supermassive black holes at the centers of the Milky Way (Sgr A*) and M87 relative to nearby objects with precisions of roughly 1 microarcsecond. This is sufficient to detect the perturbations to Sgr A*'s position resulting from interactions with the stars and stellar-mass black holes in the Galactic cusp on year timescales, and severely constrain the astrophysically relevant parameter space for an orbiting intermediate mass black hole, implicated in some mechanisms for producing the young massive stars in the Galactic center. For M87, it allows the registering of millimeter images, in which the black hole may be identified by its silhouette against nearby emission, and existing larger scale radio images, eliminating present ambiguities in the nature of the radio core and inclination, opening angle, and source of the radio jet.