Masses of Nearby Supermassive Black Holes with Very-Long Baseline Interferometry
by Johannsen, Tim and Psaltis, Dimitrios and Gillessen, Stefan and Marrone, Daniel P. and Ozel, Feryal and Doeleman, Sheperd S. and Fish, Vincent L.
7 pages, 4 figures, 2 tables, submitted to ApJ
Dynamical mass measurements to date have allowed determinations of the mass M and the distance D of the galactic center black hole Sgr A* as well as those of other nearby supermassive black holes. In the case of Sgr A*, these measurements are limited by a degeneracy between the mass and distance scaling roughly as M ~ D^2. Future very-long baseline interferometric observations will image a bright and narrow ring surrounding the shadow of the supermassive black hole, if its accretion flow is optically thin. In this paper, we show that the combination of dynamical measurements and VLBI imaging of the ring of Sgr A* breaks the degeneracy between mass and distance. We estimate the signal to noise ratio of near-future VLBI arrays consisting of five to six stations and simulate measurements of the mass and distance of Sgr A* using the expected size of the ring image and existing data of stellar ephemerides. We demonstrate that VLBI observations at 1 mm can already improve the error on the mass by a factor of three compared to the results from the monitoring of stellar orbits alone; observations at 0.5 mm can reduce the error by as much as a factor of 7.5. In addition, we calculate the angular sizes of the bright rings of a number 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 a future space-VLBI mission allowing for refined mass measurements.