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Images of supermassive black hole accretion flows contain features of both curved spacetime and plasma structure. Inferring properties of the spacetime from images requires modeling the plasma properties, and vice versa. The Event Horizon Telescope Collaboration has imaged near-horizon millimeter emission from both Messier 87* (M87*) and Sagittarius A* (Sgr A*) with very long baseline interferometry (VLBI) and has found a preference for magnetically arrested disk (MAD) accretion in each case. MAD accretion enables spacetime measurements through future observations of the photon ring, the image feature composed of near-orbiting photons. The ordered fields and relatively weak Faraday rotation of MADs yield rotationally symmetric polarization when viewed at modest inclination. In this letter, we utilize this symmetry along with parallel transport symmetries to construct a gain-robust interferometric quantity that detects the transition between the weakly lensed accretion flow image and the strongly lensed photon ring. We predict a shift in polarimetric phases on long baselines and demonstrate that the photon rings in M87* and Sgr A* can be unambiguously detected with sensitive, long-baseline measurements. For M87*, we find that photon ring detection in snapshot observations requires ∼1 mJy sensitivity on >15 Gλbaselines at 230 GHz and above, which could be achieved with space-VLBI or higher-frequency ground-based VLBI. For Sgr A*, we find that interstellar scattering inhibits photon ring detectability at 230 GHz, but ∼10 mJy sensitivity on >12 Gλbaselines at 345 GHz is sufficient and is accessible from the ground. For both sources, these sensitivity requirements may be relaxed by repeated observations and averaging.

 

The Event Horizon Telescope (EHT) Collaboration has successfully produced images of two supermassive black holes, enabling novel tests of black holes and their accretion flows on horizon scales. The EHT has so far published total intensity and linear polarization images, while upcoming images may include circular polarization, rotation measure, and spectral index, each of which reveals different aspects of the plasma and space-time. The next-generation EHT (ngEHT) will greatly enhance these studies through wider recorded bandwidths and additional stations, leading to greater signal-to-noise, orders of magnitude improvement in dynamic range, multi-frequency observations, and horizon-scale movies. In this paper, we review how each of these different observables informs us about the underlying properties of the plasma and the spacetime, and we discuss why polarimetric studies are well-suited to measurements with sparse, long-baseline coverage. 

General relativity predicts that images of optically thin accretion flows around black holes should generically have a “photon ring”, composed of a series of increasingly sharp subrings that correspond to increasingly strongly lensed emission near the black hole. Because the effects of lensing are determined by the spacetime curvature, the photon ring provides a pathway to precise measurements of the black hole properties and tests of the Kerr metric. We explore the prospects for detecting and measuring the photon ring using very long baseline interferometry (VLBI) with the Event Horizon Telescope (EHT) and the next-generation EHT (ngEHT). We present a series of tests using idealized self-fits to simple geometrical models and show that the EHT observations in 2017 and 2022 lack the angular resolution and sensitivity to detect the photon ring, while the improved coverage and angular resolution of ngEHT at 230 GHz and 345 GHz is sufficient for these models. We then analyze detection prospects using more realistic images from general relativistic magnetohydrodynamic simulations by applying “hybrid imaging”, which simultaneously models two components: a flexible raster image (to capture the direct emission) and a ring component. Using the Bayesian VLBI modeling package Comrade.jl, we show that the results of hybrid imaging must be interpreted with extreme caution for both photon ring detection and measurement—hybrid imaging readily produces false positives for a photon ring, and its ring measurements do not directly correspond to the properties of the photon ring. 

The Event Horizon Telescope (EHT) images of the supermassive black hole at the center of the galaxy M87 provided the first image of the accretion environment on horizon scales. General relativity (GR) predicts that the image of the shadow should be nearly circular given the inclination angle of the black hole M87*. A robust detection of ellipticity in image reconstructions of M87* could signal new gravitational physics on horizon scales. Here we analyze whether the imaging parameters used in EHT analyses are sensitive to ring ellipticity, and measure the constraints on the ellipticity of M87*. We find that the top set is unable to recover ellipticity. Even for simple geometric models, the true ellipticity is biased low, preferring circular rings. Therefore, to place a constraint on the ellipticity of M87*, we measure the ellipticity of 550 synthetic data sets produced from GRMHD simulations. We find that images with intrinsic axis ratios of 2:1 are consistent with the ellipticity seen from EHT image reconstructions.

 

Objects orbiting in the presence of a rotating massive body experience a gravitomagnetic frame-dragging effect, known as the Lense-Thirring effect, that has been experimentally confirmed in the weak-field limit. In the strong-field limit, near the horizon of a rotating black hole, frame dragging becomes so extreme that all objects must co-rotate with the black hole’s angular momentum. In this work, we perform general relativistic numerical simulations to identify observable signatures of frame dragging in the strong-field limit that appear when infalling gas is forced to flip its direction of rotation as it is being accreted. In total intensity images, infalling streams exhibit “S”-shaped features due to the switch in the tangential velocity. In linear polarization, a flip in the handedness of spatially resolved polarization ticks as a function of radius encodes a transition in the magnetic field geometry that occurs due to magnetic flux freezing in the dragged plasma. Using a network of telescopes around the world, the Event Horizon Telescope collaboration has demonstrated that it is now possible to directly image black holes on event horizon scales. We show that the phenomena described in this work would be accessible to the next-generation Event Horizon Telescope and extensions of the array into space, which would produce spatially resolved images on event horizon scales with higher spatial resolution and dynamic range.

 

We present estimates for the number of supermassive black holes (SMBHs) for which the next-generation Event Horizon Telescope (ngEHT) can identify the black hole “shadow”, along with estimates for how many black hole masses and spins the ngEHT can expect to constrain using measurements of horizon-resolved emission structure. Building on prior theoretical studies of SMBH accretion flows and analyses carried out by the Event Horizon Telescope (EHT) collaboration, we construct a simple geometric model for the polarized emission structure around a black hole, and we associate parameters of this model with the three physical quantities of interest. We generate a large number of realistic synthetic ngEHT datasets across different assumed source sizes and flux densities, and we estimate the precision with which our defined proxies for physical parameters could be measured from these datasets. Under April weather conditions and using an observing frequency of 230 GHz, we predict that a “Phase 1” ngEHT can potentially measure ∼50 black hole masses, ∼30 black hole spins, and ∼7 black hole shadows across the entire sky. 

The Event Horizon Telescope (EHT) recently released the first linearly polarized images of the accretion flow around the supermassive black hole Messier 87*, hereafter M87*. The spiraling polarization pattern found in the EHT images favored magnetically arrested disks as the explanation for the EHT image. With next-generation improvements to very long baseline interferometry on the horizon, understanding similar polarized features in the highly lensed structure known as the “photon ring,” where photons make multiple half orbits about the black hole before reaching the observer, will be critical to the analysis of future images. Recent work has indicated that this image region may be depolarized relative to more direct emission. We expand this observation by decomposing photon half orbits in the EHT library of simulated images of the M 87* accretion system and find that images of magnetically arrested disk simulations show a relative depolarization of the photon ring attributable to destructive interference of oppositely spiraling electric field vectors; this antisymmetry, which arises purely from strong gravitational lensing, can produce up to ∼50% depolarization in the photon ring region with respect to the direct image. In systems that are not magnetically arrested and with the exception of systems with high spin and ions and electrons of equal temperature, we find that highly lensed indirect subimages are almost completely depolarized, causing a modest depolarization of the photon ring region in the complete image. We predict that next-generation EHT observations of M 87* polarization should jointly constrain the black hole spin and the underlying emission and magnetic field geometry.

 

The Event Horizon Telescope (EHT) has produced images of two supermassive black holes, Messier 87* (M 87*) and Sagittarius A* (Sgr A*). The EHT collaboration used these images to indirectly constrain black hole parameters by calibrating measurements of the sky-plane emission morphology to images of general relativistic magnetohydrodynamic (GRMHD) simulations. Here, we develop a model for directly constraining the black hole mass, spin, and inclination through signatures of lensing, redshift, and frame dragging, while simultaneously marginalizing over the unknown accretion and emission properties. By assuming optically thin, axisymmetric, equatorial emission near the black hole, our model gains orders of magnitude in speed over similar approaches that require radiative transfer. Using 2017 EHT M 87* baseline coverage, we use fits of the model to itself to show that the data are insufficient to demonstrate existence of the photon ring. We then survey time-averaged GRMHD simulations fitting EHT-like data, and find that our model is best-suited to fitting magnetically arrested disks, which are the favored class of simulations for both M 87* and Sgr A*. For these simulations, the best-fit model parameters are within ∼10% of the true mass and within ∼10° for inclination. With 2017 EHT coverage and 1% fractional uncertainty on amplitudes, spin is unconstrained. Accurate inference of spin axis position angle depends strongly on spin and electron temperature. Our results show the promise of directly constraining black hole spacetimes with interferometric data, but they also show that nearly identical images permit large differences in black hole properties, highlighting degeneracies between the plasma properties, spacetime, and, most crucially, the unknown emission geometry when studying lensed accretion flow images at a single frequency.

 

Imaging algorithms form powerful analysis tools for very long baseline interferometry (VLBI) data analysis. However, these tools cannot measure certain image features (e.g., ring diameter) by their nonparametric nature. This is unfortunate since these image features are often related to astrophysically relevant quantities such as black hole mass. This paper details a new general image feature-extraction technique that applies to a wide variety of VLBI image reconstructions calledvariational image domain analysis. Unlike previous tools, variational image domain analysis can be applied to any image reconstruction regardless of its structure. To demonstrate its flexibility, we analyze thousands of reconstructions from previous Event Horizon Telescope synthetic data sets and recover image features such as diameter, orientation, and ellipticity. By measuring these features, our technique can help extract astrophysically relevant quantities such as the mass and orientation of the central black hole in M87.