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Abstract We develop a “dual-cone” model for millimeter wavelength emission near a spinning black hole. The model consists of optically thin, luminous cones of emission, centered on the spin axis, which are meant to represent jet walls. The resulting image is dominated by a thin ring. We first consider the effect of the black hole’s spin on the image and show that the dominant effect is to displace the ring perpendicular to the projection of the spin axis on the sky by $2a_{*}\sin i+\mathit{}\left(a_{*}^3\right)$. This effect is lower order ina_*than changes in the shape and size of the photon ring itself but is undetectable without a positional reference. We then show that the centerline of the jet can provide a suitable reference: its location is exactly independent of spin if the observer is outside the cone and nearly independent of spin if the observer is inside the cone. If astrophysical uncertainties can be controlled, then spin displacement is large enough to be detectable by future space very long baseline interferometry missions. Finally, we consider ring substructure in the dual-cone model and show that features in total intensity are not universal and depend on the cone-opening angle. 

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. 

Abstract We present an in-depth analysis of the newly proposed correlation function in visibility space, between the E and B modes of linear polarization, hereafter the EB correlation, for a set of time-averaged general relativistic magnetohydrodynamical simulations compared with the phase map from different semianalytic models and the Event Horizon Telescope (EHT) 2017 data for M87*. We demonstrate that the phase map of time-averaged EB correlation contains novel information that might be linked to black hole (BH) spin, accretion state, and electron temperature. A detailed comparison with a semianalytic approach with different azimuthal expansion modes shows that to recover the morphology of real/imaginary part of the correlation function and its phase, we require higher orders of azimuthal modes. To extract the phase features, we use Zernike polynomial reconstruction developing an empirical metric to break degeneracies between models with different BH spins that are qualitatively similar. We use a set of geometrical ring models with various magnetic and velocity field morphologies, showing that both the image space and visibility-based EB -correlation morphologies in magnetically arrested disk  simulations can be explained with simple fluid and magnetic field geometries as used in ring models. Standard and normal evolutions by contrast are harder to model, demonstrating that the simple fluid and magnetic field geometries of ring models are not sufficient to describe them owing to higher Faraday rotation depths. A qualitative comparison with the EHT data demonstrates that some of the features in the phase of EB correlation might be well explained by the current models for BH spins and electron temperatures, while others require larger theoretical surveys. 

Abstract 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. 

Abstract We investigate general relativistic magnetohydrodynamic simulations to determine the physical origin of the twisty patterns of linear polarization seen in spatially resolved black hole images and explain their morphological dependence on black hole spin. By characterizing the observed emission with a simple analytic ring model, we find that the twisty morphology is determined by the magnetic field structure in the emitting region. Moreover, the dependence of this twisty pattern on spin can be attributed to changes in the magnetic field geometry that occur due to the frame dragging. By studying an analytic ring model, we find that the roles of Doppler boosting and lensing are subdominant. Faraday rotation may cause a systematic shift in the linear polarization pattern, but we find that its impact is subdominant for models with strong magnetic fields and modest ion-to-electron temperature ratios. Models with weaker magnetic fields are much more strongly affected by Faraday rotation and have more complicated emission geometries than can be captured by a ring model. However, these models are currently disfavoured by the recent EHT observations of M87*. Our results suggest that linear polarization maps can provide a probe of the underlying magnetic field structure around a black hole, which may then be usable to indirectly infer black hole spins. The generality of these results should be tested with alternative codes, initial conditions, and plasma physics prescriptions. 

Aims.We investigated the polarization and Faraday properties of Messier 87 (M87) and seven other radio-loud active galactic nuclei (AGNs) atλ0.87 mm (345 GHz) using the Atacama Large Millimeter/submillimeter Array (ALMA). Our goal was to characterize the linear polarization (LP) fractions, measure Faraday rotation measures (RMs), and examine the magnetic field structures in the emission regions of these AGNs. Methods.We conducted full-polarization observations as part of the ALMA Band 7 very long baseline interferometry (VLBI) commissioning during the April 2021 Event Horizon Telescope (EHT) campaign. We analyzed the LP fractions and RMs to assess the nature of Faraday screens and magnetic fields in the submillimeter emission regions. Results.We find LP fractions between 1% and 17% and RMs exceeding 10⁵ rad m⁻², which are 1–2 orders of magnitude higher than typically observed at longer wavelengths (λ>3 mm). This suggests denser Faraday screens or stronger magnetic fields. Additionally, we present the first submillimeter polarized images of the M87 jet and the observed AGNs, revealing RM gradients and sign reversals in the M87 jet indicative of a kiloparsec-scale helical magnetic field structure. Conclusions.Our results provide essential constraints for calibrating, analyzing, and interpreting VLBI data from the EHT at 345 GHz, representing a critical step toward submillimeter VLBI imaging. 

We investigate the origin of the elliptical ring structure observed in the images of the supermassive black hole M87^*, aiming to disentangle contributions from gravitational, astrophysical, and imaging effects. Leveraging the enhanced capabilities of the Event Horizon Telescope (EHT)'s 2018 array, including improved (u,v)-coverage from the Greenland Telescope, we measured the ring's ellipticity using five independent imaging methods, obtaining a consistent average value ofτ = 0.08_−0.02^+0.03with a position angle ofξ = 50.1_−7.6^+6.2 degrees. To interpret this measurement, we compared it to general relativistic magnetohydrodynamic (GRMHD) simulations spanning a wide range of physical parameters including the thermal or nonthermal electron distribution function, spins, and ion-to-electron temperature ratios in both low- and high-density regions. We find no statistically significant correlation between spin and ellipticity in GRMHD images. Instead, we identify a correlation between ellipticity and the fraction of non-ring emission, particularly in nonthermal models and models with higher jet emission. These results indicate that the ellipticity measured from the M87^*emission structure is consistent with that expected from simulations of turbulent accretion flows around black holes, where it is dominated by astrophysical effects rather than gravitational ones. Future high-resolution imaging, including space very long baseline interferometry and long-term monitoring, will be essential to isolate gravitational signatures from astrophysical effects. 

Context.The 2017 observing campaign of the Event Horizon Telescope (EHT) delivered the first very long baseline interferometry (VLBI) images at the observing frequency of 230 GHz, leading to a number of unique studies on black holes and relativistic jets from active galactic nuclei (AGN). In total, eighteen sources were observed, including the main science targets, Sgr A* and M 87, and various calibrators. Sixteen sources were AGN. Aims.We investigated the morphology of the sixteen AGN in the EHT 2017 data set, focusing on the properties of the VLBI cores: size, flux density, and brightness temperature. We studied their dependence on the observing frequency in order to compare it with the Blandford-Königl (BK) jet model. In particular, we aimed to study the signatures of jet acceleration and magnetic energy conversion. Methods.We modeled the source structure of seven AGN in the EHT 2017 data set using linearly polarized circular Gaussian components (1749+096, 1055+018, BL Lac, J0132–1654, J0006–0623, CTA 102, and 3C 454.3) and collected results for the other nine AGN from dedicated EHT publications, complemented by lower frequency data in the 2–86 GHz range. Combining these data into a multifrequency EHT+ data set, we studied the dependences of the VLBI core component flux density, size, and brightness temperature on the frequency measured in the AGN host frame (and hence on the distance from the central black hole), characterizing them with power law fits. We compared the observations with the BK jet model and estimated the magnetic field strength dependence on the distance from the central black hole. Results.Our observations spanning event horizon to parsec scales indicate a deviation from the standard BK model, particularly in the decrease of the brightness temperature with the observing frequency. Only some of the discrepancies may be alleviated by tweaking the model parameters or the jet collimation profile. Either bulk acceleration of the jet material, energy transfer from the magnetic field to the particles, or both are required to explain the observations. For our sample, we estimate a general radial dependence of the Doppler factorδ ∝ r^≤0.5. This interpretation is consistent with a magnetically accelerated sub-parsec jet. We also estimate a steep decrease of the magnetic field strength with radiusB ∝ r⁻³, hinting at jet acceleration or efficient magnetic energy dissipation.