First Sagittarius A* Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole in the Center of the Milky Way

Each interferometric visibility samples a single complex Fourier component of the image on the sky [116, e.g.,]. Interferometric imaging algorithms seek to produce images from this sparse Fourier-domain information that are consistent with the data and physically plausible. Techniques such as the classical CLEAN algorithm and regularized maximum likelihood (RML) methods successfully produced EHT images of M87∗, with remarkable agreement among methods. The EHT baseline coverage for Sgr A∗ is substantially better than for M87∗, primarily because of the additional telescope (SPT) with mutual visibility of the source. Moreover, at λ=1.3mm, Sgr A∗ has a compact flux density that is approximately four times larger than that of M87∗, with no appreciable contribution to the short-baseline visibilities from an extended jet. However, producing an image of Sgr A∗ requires additional assumptions because of the rapid source variability and interstellar scattering.

Specifically, VLBI imaging typically relies on Earth-rotation aperture synthesis, in which the projection of each baseline sweeps out an arc in the (u,v)-plane as the Earth rotates, allowing a sparse array of telescopes to obtain the (u,v)-coverage necessary for the imaging of a static source. To account for the source structural variability, we used a parametric model discussed in section IV. By incorporating this variability error budget, imaging and modeling methods designed for a static source can be applied to analyze data from a variable source.

To account for the interstellar scattering, we used two approaches. The first, “on-sky imaging,” applies no modifications to the data or images. In this approach, the algorithms simply reconstruct the scattered image of the source. The second, “descattered imaging,” adds an error budget to interferometric visibilities to account for stochastic scattering substructure before deconvolving the ensemble-average scattering kernel. Both the ensemble-average kernel and the power spectrum of scattering are used, each of which is precisely known from an analysis combining of decades of observations of Sgr A∗ at centimeter wavelengths.

To test these imaging techniques and to select appropriate imaging parameters, we developed a suite of synthetic observations of seven geometric models that share the scattering and variability properties of Sgr A∗. This suite included models with widely varying morphologies: rings, disks, a crescent, a double source, and a point-like source with an extended halo. Each model was selected to produce visibility amplitudes that were similar to those of Sgr A∗, with two deep visibility minima, a physical scattering model applied, and stochastic temporal evolution generated by a statistical model.

We then selected the sets of imaging parameters that accurately reconstruct images across the entire test suite, including both ring and non-ring data sets. These “top set” parameter choices yield a corresponding collection of reconstructed images of Sgr A∗ that provide both a representative average image and a measure of its uncertainty. In addition, we used a new Bayesian imaging method, which simultaneously estimates both the reconstructed image and its associated variability noise model. This method does not require training on synthetic data, although we used the same test suite for comparison and validation of this method.

When applied to the Sgr A∗ data, over 95% of the top set images have a prominent ring morphology. For an analysis using the combination of April 6 and 7 data, all samples from the Bayesian imaging posterior show a ring morphology. In addition, geometric modeling of the EHT data shows a consistent statistical preference for ring morphologies over alternatives with comparable complexity. The ring has a diameter, width, and central brightness depression that are consistent across the different choices of imaging methods and parameters [39, see]. However, the reconstructed images show diversity in their specific attributes, particularly the azimuthal intensity distribution around the ring. This uncertainty is a consequence of the limited EHT baseline coverage, compounded by the challenges of imaging a variable source. We categorized the reconstructed images into four clusters spanning the primary reconstructed structures: three clusters are ring modes with varying position angle, while the fourth is a comparatively small set of reconstructed images with diverse non-ring morphologies. Figure 3 shows a representative average image of Sgr A∗ on April 7, as well as the average image for each of these clusters along with their relative occurrence frequency.

To quantify the ring parameters in a complementary way, we used several geometrical modeling methods, the parametrization of which were guided by the reconstructed images of Sgr A∗. These models are defined by a thick ring with azimuthal variations determined by low-order Fourier coefficients and an additional Gaussian brightness floor. Because these simple geometric models have a small number of parameters, they can be constrained using instantaneous snapshots of data. Hence, we used two modeling approaches. With “snapshot” modeling, we aggregate a series of independent fits to two-minute data segments. This approach does not require a variability model. With “full-track” modeling, we fit both a static geometric source model and a variability noise model simultaneously to the entire 12-hour observation. Table 1 summarizes the consensus ring parameters measured using these methods [40, for detailed results from individual methods, see].

In, we also used dynamic imaging and snapshot ring modeling to analyze the intraday image variability in Sgr A∗. We applied these analysis methods to the 100-minute intervals on April 6 and 7 with the best sampling, adopting a strong ring prior to counteract the limited baseline coverage. On April 6, most dynamic imaging and modeling methods recover a nearly static image, while many reconstructions on April 7 find an evolving image. However, the results on April 7 are strongly affected by the underlying prior assumptions; different parameters in the dynamic imaging method result in different modes of position angle evolution in the reconstructed images, including some reconstructions that are nearly static. Thus, while the EHT data show detectable signs of image variability, we cannot reliably constrain the underlying image evolution.