Computational Imaging Sheds Light on the Black Hole in Our Galactic Center

Black holes, which were once considered a mathematical peculiarity of Einstein’s theory of general relativity, are nowadays one of the most exciting research topics in astronomy and astrophysics. Though these bodies are not directly visible, they may leave a fingerprint in the form of a dark central region (or shadow) amid the surrounding bright gas. In May 2022, the Event Horizon Telescope (EHT) collaboration debuted the first image of the supermassive black hole at the center of our galaxy: Sagittarius A* (Sgr A*, pronounced “sadge-ay-star”) [3]. This result provided direct visual evidence of a black hole, depicting the tell-tale sign of a ring-like structure (see Figure 1).

The image of Sgr A* was not captured like a regular photograph; it is a computational image that was reconstructed from measurements by synchronized telescopes around the globe (see Figure 2). When joined together with an imaging technique called very large baseline interferometry, these separate telescopes form a virtual instrument that is sensitive enough to resolve an image of a donut on the moon. During this powerful approach, each telescope pair probes a single frequency in the image’s Fourier transform. The probed frequency is proportional to the projected baseline between the two telescopes. Simply put, nearby telescopes are sensitive to low spatial frequencies (broad, diffuse features in the image) and distant telescopes are sensitive to high spatial frequencies (sharp edges and details).

Analyzing the EHT observations of Sgr A* was not an easy feat. In fact, it took more than 300 scientists from over 80 institutions almost five years to interpret and reveal the first images. One of the key computational challenges stems from the rapid evolution of Sgr A* during the EHT acquisition; scientists believe that this apparent evolution occurs because of the hot gas that swirls around Sgr A*. Taking an image of the rapidly changing gas is somewhat analogous to trying to photograph a fast-moving sprinter.

Our first imaging attempts sought to capture the average structure of the black hole by treating the evolution as a form of noise (see Figure 1). While this “static” image certainly offers interesting insights, we also wanted to uncover the dynamic evolution of Sgr A*. To that end, we developed algorithms that can recover a video sequence from the same telescope measurements [1]. We spent years analyzing the data with these video reconstruction methods, but the results were ultimately inconclusive (see Figure 3).

Recovering the dynamic evolution is difficult because we only have access to a sparse set of measurements at any given time; this is similar to only seeing a few pixels of the sprinter over time. Adding additional telescopes could provide more information for the recovery of a movie. The Next Generation EHT collaboration is focused on expanding the EHT network with further telescope sites to image the dynamic evolution of supermassive black holes [2]. With the help of computational algorithms, we recently discovered that this supercharged EHT array might allow us to go beyond a two-dimensional (2D) image or movie and recover the three-dimensional (3D) structure of gas swirling around Sgr A*.

We therefore seek to answer the following questions: Can we use EHT observations to recover more than a 2D image or movie? For example, can we recover the 3D distribution of light around a black hole over time? To achieve this goal, we are currently developing new computational algorithms that fuse physics models with machine learning tools to extract as much data as possible from future observations. Recovery of the 3D volume of Sgr A* will require a form of tomography. Computed tomography (CT) is a computational inverse problem that aims to recover densities of a medium from lower-dimensional projections. For example, X-ray CT is a well-established medical imaging technology for non-intrusive diagnosis.

Unlike medical CT, black hole tomography faces some unique computational challenges in the form of gravitational lensing and the limits that are imposed by having a single viewpoint. The former occurs because the strong gravitational field of a black hole bends the trajectory of light as it travels nearby (see Figure 4). This phenomenon is called gravitational lensing because the mass acts as a sort of lens. It necessitates a change from typical CT or 3D reconstruction, wherein light is assumed to move along straight paths. Utilizing the physics of gravitational lensing to model this unique image projection is a crucial component of the solution to the black hole tomography problem.

Additionally, while tomography typically relies on multiple viewpoints, Sgr A*’s distance from Earth means that we only have access to a single view. To overcome this limitation, we incorporated a model for orbital dynamics that effectively replaces multiple views with multiple frames over time. Doing so is akin to having access to a single X-ray view but asking the patient to rotate in order to obtain a full CT volume recovery. While gas does not rigidly rotate like a person might, its orbit around a supermassive black hole is predictable (to some degree).

We have taken the first steps towards 3D recovery by revealing a new imaging possibility for the future of EHT observations. While we are still far from determining the 3D structure of gas around Sgr A*, our initial simulations have shown promising results on simplified test cases [4]. We are now in the process of expanding these ideas to more realistic simulated data. 

Recently, astronomers have found exciting evidence—via measurements from the Atacama Large Millimeter/submillimeter Array (ALMA) Observatory—of a hot gas bubble orbiting Sgr A* [5] (see Figure 1). However, the evidence is thus far inconclusive; being able to resolve a 3D image of an orbiting gas bubble would therefore have immense scientific implications. Through simulations, we have shown that only 40 minutes of (future) EHT observations might sufficiently reveal such a bubble as it orbits close to the event horizon of Sgr A* (see Figure 5). Nevertheless, we still have a ways to go before we can use this technique on real data with sufficient measurement coverage. In the meantime, we are working on extending the applicability of our approach to realistic data and its associated complexities. We hope that by utilizing the entire EHT array, including ALMA, we might be able to reveal the 3D structure and evolution of these gas bubbles.

All of the aforementioned imaging approaches—including recovery of a static image, a movie, and the 3D evolution around Sgr A*—are complimentary. We need every one of them (and more) to reveal different aspects of Sgr A*. One could say that these methods lie on a spectrum of model assumptions. Static images and videos of Sgr A*—for which we avoid biasing our algorithms towards the existence of a ring, in order to encourage flexibility and allow for scientific discovery—fall on one end of the spectrum. Because of our modest model assumptions, these procedures are limited in the types of information that they can extract from the data. On the other end of the spectrum, 3D imaging relies on a black hole model to characterize light propagation and orbital dynamics. With some reasonable model assumptions, we might be able to recover the 3D structure around Sgr A*. However, these assumptions mean that such an approach would be blind to any model inaccuracies and the possibility that Sgr A* is not a black hole.

Ultimately, the goal of this type of imaging is slightly different. Instead of establishing the existence of a black hole, we ask the following question: If Sgr A* is a black hole, can we study the 3D structure of gas around it? We hope that these new imaging methods will shed light on the complex plasma processes in our galactic center in the not-so-distant future. Through EHT tomography, we may even catch a glimpse of the very nature of space-time itself around the most extreme environment in our galaxy.

Acknowledgments: The author would like to acknowledge Katherine Bouman (California Institute of Technology) for her help with and review of this article. 

References

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[2] Doeleman, S., Blackburn, L., Dexter, J., Gomez, J.L., Johnson, M.D., Palumbo, D.C., … Zhao, G. (2019). Studying black holes on horizon scales with VLBI ground arrays. In Astro2020: Decadal survey on astronomy and astrophysics (APC white papers). Bull. Amer. Astronom. Soc., 51(7), 256.
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[5] Wielgus, M., Moscibrodzka, M., Vos, J., Gelles, Z., Marti-Vidal, I., Farah, J., … Messias, H. (2022). Orbital motion near Sagittarius A*: Constraints from polarimetric ALMA observations. Astron. Astrophys., 665, L6.