Masses of Nearby Supermassive Black Holes with Very-Long Baseline
  Interferometry
  Dynamical mass measurements to date have allowed determinations of the mass M
and the distance D of a number of nearby supermassive black holes. In the case
of Sgr A*, these measurements are limited by a strong correlation between the
mass and distance scaling roughly as M ~ D^2. Future very-long baseline
interferometric (VLBI) observations will image a bright and narrow ring
surrounding the shadow of a supermassive black hole, if its accretion flow is
optically thin. In this paper, we explore the prospects of reducing the
correlation between mass and distance with the combination of dynamical
measurements and VLBI imaging of the ring of Sgr A*. We estimate the signal to
noise ratio of near-future VLBI arrays that consist of five to six stations,
and we simulate measurements of the mass and distance of Sgr A* using the
expected size of the ring image and existing stellar ephemerides. We
demonstrate that, in this best-case scenario, VLBI observations at 1 mm can
improve the error on the mass by a factor of about two compared to the results
from the monitoring of stellar orbits alone. We identify the additional sources
of uncertainty that such imaging observations have to take into account. In
addition, we calculate the angular diameters of the bright rings of other
nearby supermassive black holes and identify the optimal targets besides Sgr A*
that could be imaged by a ground-based VLBI array or future space-VLBI missions
allowing for refined mass measurements.
