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Abstract The Event Horizon Telescope (EHT) has produced resolved images of the supermassive black holes (SMBHs) Sgr A* and M87*, which present the largest shadows on the sky. In the next decade, technological improvements and extensions to the array will enable access to a greater number of sources, unlocking studies of a larger population of SMBHs through direct imaging. In this paper, we identify 12 of the most promising sources beyond Sgr A* and M87* based on their angular size and millimeter flux density. For each of these sources, we make theoretical predictions for their observable properties by ray tracing general relativistic magnetohydrodynamic models appropriately scaled to each target’s mass, distance, and flux density. We predict that these sources would have somewhat higher Eddington ratios than M87*, which may result in larger optical and Faraday depths than previous EHT targets. Despite this, we find that visibility amplitude size constraints can plausibly recover masses within a factor of 2, although the unknown jet contribution remains a significant uncertainty. We find that the linearly polarized structure evolves substantially with the Eddington ratio, with greater evolution at larger inclinations, complicating potential spin inferences for inclined sources. We discuss the importance of 345 GHz observations, milli-Jansky baseline sensitivity, and independent inclination constraints for future observations with upgrades to the EHT through ground updates with the next-generation EHT program and extensions to space through the black hole Explorer. 

Abstract Reconstructing images from the Event Horizon Telescope (EHT) observations of M87*, the supermassive black hole at the center of the galaxy M87, depends on a prior to impose desired image statistics. However, given the impossibility of directly observing black holes, there is no clear choice for a prior. We present a framework for flexibly designing a range of priors, each bringing different biases to the image reconstruction. These priors can be weak (e.g., impose only basic natural-image statistics) or strong (e.g., impose assumptions of black hole structure). Our framework uses Bayesian inference with score-based priors, which are data-driven priors arising from a deep generative model that can learn complicated image distributions. Using our Bayesian imaging approach with sophisticated data-driven priors, we can assess how visual features and uncertainty of reconstructed images change depending on the prior. In addition to simulated data, we image the real EHT M87* data and discuss how recovered features are influenced by the choice of prior. 

Abstract The near-horizon region of a black hole impacts linear (LP) and circular polarization (CP) through strong lensing of photons, adding large-scale symmetries and anti-symmetries to the polarized image. To probe the signature of lensing in polarimetry, we utilize a geometric model of concentric Gaussian rings of equal radius to investigate the transition in the Fourier plane at which the photon ring signal begins to dominate over the direct image. We find analytic, closed-form expressions for the transition radii in total intensity, LP, and CP, wherein the resultant formulae are composed of ratios of tunable image parameters, with the overall “scale” set primarily by the thickness of the direct image. Using these formulae, we compute the transition radii for time-averaged images of M87* simulations at 230 GHz, studying both magnetically arrested disk (MAD) and standard and normal evolution configurations for various spin and electron heating models. We compare geometric values to radii obtained directly from the simulations through a coherent averaging scheme. We find that nearly all MAD models have a photon ring-dominated CP signal on long baselines shorter than Earth's diameter at 230 GHz. Across favored models for the M87* accretion flow identified by the Event Horizon Telescope (EHT) polarimetric constraints, we quantify the sensitivity and antenna size requirements for the next-generation EHT and the Black Hole Explorer orbiter to detect these features. We find that the stringent requirements for CP favor explorations using long baselines on the ground, while LP remains promising on Earth-space baselines. 

Abstract The Event Horizon Telescope has released polarized images of the supermassive black holes Messier 87* (M87*) and Sagittarius A* accretion disks. As more images are produced, our understanding of the average polarized emission from near the event horizon improves. In this Letter, we use a semianalytic model for optically thin, equatorial emission near a Kerr black hole to study how spin constraints follow from measurements of the average polarization spiral pitch angle. We focus on the case of M87* and explore how the direct, weakly lensed image spiral is coupled to the strongly lensed indirect image spiral, and how a precise measurement of both provides a powerful spin tracer. We find a generic result that the spin twists the direct and indirect image polarization in opposite directions. Using a grid search over model parameters, we find a strong dependence of the resulting spin constraint on plasma properties near the horizon. Grid constraints suggest that, under reasonable assumptions for the accretion disk, a measurement of the direct and indirect image spiral pitch angles to ±5° yields a dimensionless spin amplitude measurement with uncertainty ${\sigma }_{\mid a_{*}\mid }\sim 0.25$for radially infalling models but otherwise provides only weak constraints; an error of 1^∘can reach ${\sigma }_{\mid a_{*}\mid }\sim 0.15$. We also find that a well-constrained rotation measure greatly improves spin measurements. Assuming that equatorial velocity and magnetic field are oppositely oriented, we find that the observed M87* polarization pattern favors models with strong radial velocity components, which are close to optimal for future spin measurements. 

Abstract We propose an analytic dual-cone accretion model for horizon-scale images of the cores of low-luminosity active galactic nuclei, including those observed by the Event Horizon Telescope (EHT). Our model is of synchrotron emission from an axisymmetric, magnetized plasma, constrained to flow within two oppositely oriented cones that are aligned with the black hole’s spin axis. We show this model can accurately reproduce images of a variety of time-averaged general relativistic magnetohydrodynamic simulations and that it accurately recovers the black hole spin, orientation, emission scale height, peak emission radius, and fluid flow direction from these simulations within a Bayesian inference framework using radio interferometric data. We show that nontrivial topologies in the images of relativistic accretion flows around black holes can result in nontrivial multimodal solutions when applied to observations with a sparse array, such as the EHT 2017 observations of M87*. The presence of these degeneracies underscores the importance of employing Bayesian techniques to adequately sample the posterior space for the interpretation of EHT measurements. We fit our model to the EHT observations of M87* and find a 95% highest posterior density interval for the mass-to-distance ratio ofθ_g∈ (2.84, 3.75)μas, and give an inclination ofθ_o∈ (11°, 24°). These new measurements are consistent with mass measurements from the EHT and stellar dynamical estimates and with the spin axis inclination inferred from properties of the M87* jet. 

Abstract Event Horizon Telescope (EHT) images of the horizon-scale emission around the Galactic center supermassive black hole Sagittarius A* (Sgr A*) favor accretion flow models with a jet component. However, this jet has not been conclusively detected. Using the “best-bet” models of Sgr A* from the EHT Collaboration, we assess whether this nondetection is expected for current facilities and explore the prospects of detecting a jet with very-long-baseline interferometry (VLBI) at four frequencies: 86, 115, 230, and 345 GHz. We produce synthetic image reconstructions for current and next-generation VLBI arrays at these frequencies that include the effects of interstellar scattering, optical depth, and time variability. We find that no existing VLBI arrays are expected to detect the jet in these best-bet models, consistent with observations to date. We show that next-generation VLBI arrays at 86 and 115 GHz—in particular, the EHT after upgrades through the ngEHT program and the ngVLA—successfully capture the jet in our tests due to improvements in instrument sensitivity and (u,v) coverage at spatial scales critical to jet detection. These results highlight the potential of enhanced VLBI capabilities in the coming decade to reveal the crucial properties of Sgr A* and its interaction with the Galactic center environment. 

Abstract Very long baseline interferometry (VLBI) provides the highest-resolution images in astronomy. The sharpest resolution is nominally achieved at the highest frequencies, but as the observing frequency increases, so too does the atmospheric contribution to the system noise, degrading the sensitivity of the array and hampering detection. In this paper, we explore the limits of high-frequency VLBI observations usingngehtsim, a new tool for generating realistic synthetic data.ngehtsimuses detailed historical atmospheric models to simulate observing conditions, and it employs heuristic visibility detection criteria that emulate single- and multifrequency VLBI calibration strategies. We demonstrate the fidelity ofngehtsim’spredictions using a comparison with existing 230 GHz data taken by the Event Horizon Telescope (EHT), and we simulate the expected performance of EHT observations at 345 GHz. Though the EHT achieves a nearly 100% detection rate at 230 GHz, our simulations indicate that it should expect substantially poorer performance at 345 GHz; in particular, observations of M87* at 345 GHz are predicted to achieve detection rates of ≲20% that may preclude imaging. Increasing the array sensitivity through wider bandwidths and/or longer integration times—as enabled through, e.g., the simultaneous multifrequency upgrades envisioned for the next-generation EHT—can improve the 345 GHz prospects and yield detection levels that are comparable to those at 230 GHz. M87* and Sgr A* observations carried out in the atmospheric window around 460 GHz could expect to regularly achieve multiple detections on long baselines, but analogous observations at 690 and 875 GHz consistently obtain almost no detections at all. 

Abstract In a companion paper, we present the first spatially resolved polarized image of Sagittarius A* on event horizon scales, captured using the Event Horizon Telescope, a global very long baseline interferometric array operating at a wavelength of 1.3 mm. Here we interpret this image using both simple analytic models and numerical general relativistic magnetohydrodynamic (GRMHD) simulations. The large spatially resolved linear polarization fraction (24%–28%, peaking at ∼40%) is the most stringent constraint on parameter space, disfavoring models that are too Faraday depolarized. Similar to our studies of M87*, polarimetric constraints reinforce a preference for GRMHD models with dynamically important magnetic fields. Although the spiral morphology of the polarization pattern is known to constrain the spin and inclination angle, the time-variable rotation measure (RM) of Sgr A* (equivalent to ≈46° ± 12° rotation at 228 GHz) limits its present utility as a constraint. If we attribute the RM to internal Faraday rotation, then the motion of accreting material is inferred to be counterclockwise, contrary to inferences based on historical polarized flares, and no model satisfies all polarimetric and total intensity constraints. On the other hand, if we attribute the mean RM to an external Faraday screen, then the motion of accreting material is inferred to be clockwise, and one model passes all applied total intensity and polarimetric constraints: a model with strong magnetic fields, a spin parameter of 0.94, and an inclination of 150°. We discuss how future 345 GHz and dynamical imaging will mitigate our present uncertainties and provide additional constraints on the black hole and its accretion flow. 

Abstract The Event Horizon Telescope observed the horizon-scale synchrotron emission region around the Galactic center supermassive black hole, Sagittarius A* (Sgr A*), in 2017. These observations revealed a bright, thick ring morphology with a diameter of 51.8 ± 2.3μas and modest azimuthal brightness asymmetry, consistent with the expected appearance of a black hole with massM≈ 4 × 10⁶M_⊙. From these observations, we present the first resolved linear and circular polarimetric images of Sgr A*. The linear polarization images demonstrate that the emission ring is highly polarized, exhibiting a prominent spiral electric vector polarization angle pattern with a peak fractional polarization of ∼40% in the western portion of the ring. The circular polarization images feature a modestly (∼5%–10%) polarized dipole structure along the emission ring, with negative circular polarization in the western region and positive circular polarization in the eastern region, although our methods exhibit stronger disagreement than for linear polarization. We analyze the data using multiple independent imaging and modeling methods, each of which is validated using a standardized suite of synthetic data sets. While the detailed spatial distribution of the linear polarization along the ring remains uncertain owing to the intrinsic variability of the source, the spiraling polarization structure is robust to methodological choices. The degree and orientation of the linear polarization provide stringent constraints for the black hole and its surrounding magnetic fields, which we discuss in an accompanying publication. 

Abstract Event Horizon Telescope (EHT) observations have revealed a bright ring of emission around the supermassive black hole at the center of the M87 galaxy. EHT images in linear polarization have further identified a coherent spiral pattern around the black hole, produced from ordered magnetic fields threading the emitting plasma. Here we present the first analysis of circular polarization using EHT data, acquired in 2017, which can potentially provide additional insights into the magnetic fields and plasma composition near the black hole. Interferometric closure quantities provide convincing evidence for the presence of circularly polarized emission on event-horizon scales. We produce images of the circular polarization using both traditional and newly developed methods. All methods find a moderate level of resolved circular polarization across the image (〈∣v∣〉 < 3.7%), consistent with the low image-integrated circular polarization fraction measured by the Atacama Large Millimeter/submillimeter Array (∣v_int∣ < 1%). Despite this broad agreement, the methods show substantial variation in the morphology of the circularly polarized emission, indicating that our conclusions are strongly dependent on the imaging assumptions because of the limited baseline coverage, uncertain telescope gain calibration, and weakly polarized signal. We include this upper limit in an updated comparison to general relativistic magnetohydrodynamic simulation models. This analysis reinforces the previously reported preference for magnetically arrested accretion flow models. We find that most simulations naturally produce a low level of circular polarization consistent with our upper limit and that Faraday conversion is likely the dominant production mechanism for circular polarization at 230 GHz in M87*.