Metrics and Motivations for Earth-Space VLBI: Time-resolving Sgr A* with the Event Horizon Telescope

Very-long-baseline interferometry (VLBI) at frequencies above 230 GHz with Earth-diameter baselines gives spatial resolution finer than the ~50 μas "shadow" of the supermassive black hole at the Galactic Center, Sagittarius A* (Sgr A*). Imaging static and dynamical structure near the "shadow" provides a test of general relativity and may allow measurement of black hole parameters. However, traditional Earth-rotation synthesis is inapplicable for sources (such as Sgr A*) with intraday variability. Expansions of ground-based arrays to include space-VLBI stations may enable imaging capability on timescales comparable to the prograde innermost stable circular orbit (ISCO) of Sgr A*, which is predicted to be 4–30 minutes, depending on black hole spin. We examine the basic requirements for space VLBI, and we develop tools for simulating observations with orbiting stations. We also develop a metric to quantify the imaging capabilities of an array irrespective of detailed image morphology or reconstruction method. We validate this metric on example reconstructions of simulations of Sgr A* at 230 and 345 GHz, and use these results to motivate expanding the Event Horizon Telescope to include small dishes in Low Earth Orbit (LEO). We demonstrate that high-sensitivity sites such as the Atacama Large Millimeter/Submillimeter Array (ALMA) make it viable to add small orbiters to existing ground arrays, as space-ALMA baselines would have sensitivity comparable to ground-based non-ALMA baselines. We show that LEO-enhanced arrays sample half of the diffraction-limited Fourier plane of Sgr A* in less than 30 minutes, enabling reconstructions of near-horizon structure with a normalized root-mean-square error ≾0.3 on sub-ISCO timescales