  The emission region and black hole shadow of Sagittarius A*, the supermassive
black hole at the Galactic Center, can be probed with millimeter Very Long
Baseline Interferometry. Our goal is to probe the geometry of the emitting
plasma around Sgr A* by using modeled mm-VLBI closure phase calculations at 1.3
mm and to constrain the observer's inclination angle and position angle of the
black hole spin axis. We have simulated images for three different models of
the emission of Sgr A*: an orbiting spot, a disk model, and a jet model. The
orbiting spot model was used as a test case scenario, while the disk and jet
models are physically driven scenarios based on standard three-dimensional
general relativistic magnetohydrodynamic simulations of hot accretion flows.
Our results are compared to currently available closure phase observational
limits. Our results indicate that more models with closer to edge-on viewing
angles are consistent with observational limits. In general, jet and disk
geometries can reproduce similar closure phases for different sets of viewing
and position angles. Consequently, the favored black hole spin orientation and
its magnitude are strongly model dependent. We find that both the jet and the
disk models can explain current VLBI limits. We conclude that new observations
at 1.3 mm and possibly at longer wavelengths including other triangles of VLBI
baselines are necessary to interpret Sgr A* emission and the putative black
hole spin parameters.
