Masses of nearby Supermassive Black Holes with Very Long Baseline Interferometry

Dynamical mass measurements to date have allowed determinations of themass M and the distance D of a number of nearby supermassive blackholes. In the case of Sgr A*, these measurements are limited by a strongcorrelation between the mass and distance scaling roughly as M ~ D². Future very long baseline interferometric (VLBI)observations will image a bright and narrow ring surrounding the shadowof a supermassive black hole, if its accretion flow is optically thin.In this paper, we explore the prospects of reducing the correlationbetween mass and distance with the combination of dynamical measurementsand VLBI imaging of the ring of Sgr A*. We estimate the signal-to-noiseratio of near-future VLBI arrays that consist of five to six stations,and we simulate measurements of the mass and distance of Sgr A* usingthe expected size of the ring image and existing stellar ephemerides. Wedemonstrate that, in this best-case scenario, VLBI observations at 1 mmcan improve the error on the mass by a factor of about two compared tothe results from the monitoring of stellar orbits alone. We identify theadditional sources of uncertainty that such imaging observations have totake into account. In addition, we calculate the angular diameters ofthe bright rings of other nearby supermassive black holes and identifythe optimal targets besides Sgr A* that could be imaged by aground-based VLBI array or future space-VLBI missions allowing forrefined mass measurements.