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

## TL;DR

This paper explores the potential of space-VLBI, especially with Low Earth Orbit satellites, to achieve high-resolution imaging of Sgr A*'s near-horizon structure on timescales comparable to the black hole's innermost stable circular orbit, overcoming limitations of Earth-based arrays.

## Contribution

It develops a new metric for assessing imaging capabilities of space-VLBI arrays and demonstrates the feasibility of adding small orbiters to the Event Horizon Telescope for rapid, high-resolution imaging.

## Key findings

- Space-VLBI with LEO satellites can sample Sgr A*'s Fourier plane in less than 30 minutes.
- Adding small orbiters to EHT enhances imaging speed and resolution for near-horizon structures.
- High-sensitivity sites like ALMA enable effective integration of space-based stations.

## Abstract

Very-long-baseline interferometry (VLBI) at frequencies above 230 GHz with Earth-diameter baselines gives spatial resolution finer than the ${\sim}50 \mu$as "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 intra-day variability. Expansions of ground-based arrays to include space-VLBI stations may enable imaging capability on time scales 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 (EHT) 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 normalized root-mean-square error $\lesssim0.3$ on sub-ISCO timescales.