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

Abstract

Very-long-baseline interferometry (VLBI) at frequencies above 230 GHz with Earth-diameter baselines gives spatial resolution finer than the ∼50µas "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 0.3 on sub-ISCO timescales.

Learning a Probabilistic Strategy for Computational Imaging Sensor Selection

“…For instance, in imaging applications with Fourier component measurements, such as VLBI and MRI, since the images are approximately band-limited, the signal sampling rate in the Fourier domain (e.g., κ-space) can be reduced to twice the maximum frequency [22]. This observation can be used to define metrics that characterize sampling quality independent of image reconstruction techniques [23]. Modern advances in the theory of compressed sensing demonstrate that, when the underlying image is sparse, certain sampling schemes can achieve the same quality reconstruction with an even smaller number of samples [10], [24].…”

An Event Horizon Imager (EHI) Mission Concept Utilizing Medium Earth Orbit Sub-mm Interferometry<sup>*</sup>

“…Considering radio regulations [52] , a wide-enough frequency allocation band to downlink a radio-telescope's electrical field data (IF), which is of the order of tens/ hundreds Gbit•s −1 , does not exist, and hence an optical link would be required. Using a hybrid system like this could provide the possibility of creating moving images of a black hole [53] , and one might be able to observe even more and also weaker sources.…”

“…One could also consider alternative concepts. For instance, Palumbo et al [53] consider launching satellites into Low Earth Orbits (LEOs) to observe in conjunction with the EHT at 230 and 345 GHz. This setup allows for a fast (u, v)-plane filling rate so that the dynamics of Sgr A* may be captured, allowing for the reconstruction of movies of the surrounding plasma.…”

Visible Shapes of Black Holes M87* and SgrA*

“…The construction of an advanced EHT version opens the new stage of the investigation of dark black hole silhouettes, as well as the testing of general relativity and modified gravitation theories in the strong field limit [68,. The promising breakthrough for similar future investigations would be a construction of cosmic interferometer with a nanosecond angular resolution [155][156][157].…”