| Summary: | Millimeter wave very long baseline interferometry (mm-VLBI) provides access to the emission region surrounding Sagittarius A* (Sgr A*), the supermassive black hole at the center of the Milky Way, on sub-horizon scales. Recently, a closure phase of 0° ± 40° was reported on a triangle of Earth-sized baselines (SMT-CARMA-JCMT) representing a new constraint upon the structure and orientation of the emission region, independent from those provided by the previously measured 1.3 mm-VLBI visibility amplitudes alone. Here, we compare this to the closure phases associated with a class of physically motivated, radiatively inefficient accretion flow models and present predictions for future mm-VLBI experiments with the developing Event Horizon Telescope (EHT). We find that the accretion flow models are capable of producing a wide variety of closure phases on the SMT-CARMA-JCMT triangle and thus not all models are consistent with the recent observations. However, those models that reproduce the 1.3 mm-VLBI visibility amplitudes overwhelmingly have SMT-CARMA-JCMT closure phases between ±30°, and are therefore broadly consistent with all current mm-VLBI observations. Improving station sensitivity by factors of a few, achievable by increases in bandwidth and phasing together multiple antennas at individual sites, should result in physically relevant additional constraints upon the model parameters and eliminate the current 180° ambiguity on the source orientation. When additional stations are included, closure phases of order 45°-90° are typical. In all cases, the EHT will be able to measure these with sufficient precision to produce dramatic improvements in the constraints upon the spin of Sgr A*.
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