Measuring Photon Rings with the ngEHT

Event Horizon Telescope (EHT) observations of M87* provide a means of constraining the parameters of both the black hole and its surrounding plasma. However, the intrinsic variability of the emitting material introduces major sources of uncertainty, which complicates parameter inference. The precise nature of this variability remains uncertain, and previous studies have largely relied on general relativistic magnetohydrodynamic simulations to estimate its effects. Here, we fit a semianalytic, dual-cone model of the emitting plasma to multiple years of EHT observations to empirically assess the impact of intrinsic variability and improved array coverage on key measurements, including the black hole mass-to-distance ratio, spin, and viewing inclination. Despite substantial differences in the images of the two epochs, we find that the inferred mass-to-distance ratio remains stable and mutually consistent. The black hole spin is unconstrained for both observations, despite the improved baseline coverage in 2018. We show that intrinsic variability can contribute significantly to the inference error and that the inferred position angle and inclination of the black hole spin axis are discrepant between the two years. Our findings highlight both the promise and challenges of multiepoch EHT observations: while they can refine parameter constraints, they also reveal the limitations of simple parametric models in capturing the full source complexity. Our analysis—the first to fit semianalytic emission models to 2018 EHT observations—underscores the importance of quantifying data contributions from intrinsic variability in future high-resolution imaging studies of black hole environments and the role of repeated observations in quantifying these uncertainties.

Context. Active galactic nuclei (AGNs) exhibit a wide range of black hole masses and inflow/outflow properties. It is now possible to probe regions close to the event horizons of nearby supermassive black holes (SMBHs) using very long baseline interferometry (VLBI) with earth-sized baselines, as performed by the Event Horizon Telescope (EHT). Aims. This study explores the emission properties of accretion and outflows near the event horizon of both low-mass and high-mass SMBHs. Using resistive general relativistic magnetohydrodynamic (GR-MHD) simulations, we model AGNs with thin Keplerian disks. This contrasts with widely studied models featuring thick disks, such as magnetically arrested disks (MADs) or the standard and normal evolution (SANE) scenario. Methods. Our GR-MHD models serve as simplified representations to study disk-jet-wind structures. These simulations are postprocessed and ray-traced, using constraints of black hole mass and observed spectral energy distributions (SEDs). Thermal synchrotron emission generated near the event horizon is used to create emission maps, which are analysed by separating accretion and outflow components to determine their contributions to the total intensity. Results. Whether the emission appears optically thick or thin at a given frequency depends on its position relative to the synchrotron SED peak. At 230 GHz, low-mass SMBHs appear optically thicker than high-mass ones, even at lower accretion rates. Doppler beaming affects the brightness of emission from outflows with changing viewing angles in low-mass systems. Conclusions. Eddington ratios from our models align with those inferred by the EHTC for M87 and SgrA* using thicker MAD/SANE models. Although thin disks are optically thicker, their spectral properties make high-mass systems appear optically thinner at 230 GHz-ideal for probing GR effects like photon rings. In contrast, low-mass systems remain optically thicker at these frequencies because of synchrotron self-absorption, making outflow emissions near the horizon more pronounced. However, distinguishing these features remains challenging with current EHT resolution.

Context. The Event Horizon Telescope (EHT) will soon provide the first high-resolution images of the Galactic Centre supermassive black hole candidate Sagittarius A* (Sgr A*), enabling us to probe gravity in the strong-field regime. In addition to studying the accretion process in extreme environments, the obtained data and reconstructed images could be used to investigate the underlying spacetime structure. In its current configuration, EHT is able to distinguish between a rotating Kerr black hole and a horizon-less object such as a boson star. Future developments can increase the ability of EHT to tell different spacetimes apart. Aims. We investigate the capability of an advanced EHT concept, including an orbiting space antenna, to image and distinguish different spacetimes around Sgr A*. Methods. We used general-relativistic magneto-hydrodynamical simulations of accreting compact objects (Kerr and dilaton black holes as well as boson stars) and computed their radiative signatures via general-relativistic radiative transfer. To facilitate a comparison with upcoming and future EHT observations, we produced realistic synthetic data including the source variability, diffractive, and refractive scattering while incorporating the observing array, including a space antenna. From the generated synthetic observations, we dynamically reconstructed black hole shadow images using regularised maximum entropy methods. We employed a genetic algorithm to optimise the orbit of the space antenna with respect to improved imaging capabilities and u − v-plane coverage of the combined array (ground array and space antenna) and developed a new method to probe the source variability in Fourier space. Results. The inclusion of an orbiting space antenna improves the capability of EHT to distinguish the spin of Kerr black holes and dilaton black holes based on reconstructed radio images and complex visibilities.

Hypothetical ultralight bosonic fields will spontaneously form macroscopic bosonic halos around Kerr black holes, via superradiance, transferring part of the mass and angular momentum of the black hole into the halo. Such a process, however, is only efficient if resonant—when the Compton wavelength of the field approximately matches the gravitational scale of the black hole. For a complex-valued field, the process can form a stationary, bosonic field black hole equilibrium state—a black hole with synchronised hair. For sufficiently massive black holes, such as the one at the centre of the M87 supergiant elliptic galaxy, the hairy black hole can be robust against its own superradiant instabilities, within a Hubble time. Studying the shadows of such scalar hairy black holes, we constrain the amount of hair which is compatible with the Event Horizon Telescope (EHT) observations of the M87 supermassive black hole, assuming the hair is a condensate of ultralight scalar particles of mass μ ∼ 10 − 20 eV, as to be dynamically viable. We show the EHT observations set a weak constraint, in the sense that typical hairy black holes that could develop their hair dynamically, are compatible with the observations, when taking into account the EHT error bars and the black hole mass/distance uncertainty.

Supermassive black holes (SMBHs) like M87* and Sgr A* have been observed with the Event Horizon Telescope (EHT), facilitating the investigation of null geodesics near a black hole. The null geodesic around black holes and relevant features such as photon ring, lensing ring and black hole shadow, have been modeled analytically. The emission and absorption of plasmas surrounding a black hole is highly related to the physical quantities such as mass density, momentum, internal energy, magnetic field, black hole spin and angular momentum. The images of accretion disks around black holes are affected by Doppler shift, gravitational redshift, and frequency-dependent emissivity and absorption coefficient, which can be assessed by numerical simulations. In this work, a numerical ray-tracing scheme and a covariant radiative transfer scheme are proposed to simulate the photon trajectories emitting from the accretion disks around Kerr black holes, hence to reconstruct their images. A set of magnetized, geometrically thick accretion disks are adopted to compute the emissivity and absorption coefficient, which are then used to reconstruct the images of the subject accretion disks. The effects of magnetization, black hole spin, angular momentum and geometry of the disks are studied. The effects of Doppler shift, gravitational lensing, and frequency-dependent emissivity and absorption coefficient are investigated by simulations.

Shadow of Kerr black hole surrounded by a cloud of strings in Rastall gravity and constraints from M87*

Black hole (BH) shadow observations and gravitational wave astronomy have become crucial approaches for exploring BH physics and testing gravitational theories in extreme environments. This paper investigates the charged black hole with scalar hair (CBH-SH) derived from the Einstein–Maxwell-conformal coupled scalar (EMCS) theory. We first constrain the parameter space $$(Q/M, s/M^2)$$ ( Q / M , s / M 2 ) of the BH using the Event Horizon Telescope (EHT) observations of M87* and Sgr A*. The results show that M87* provides stronger constraints on positive scalar hair, constraining the scalar hair s within $$0\le s/M^2\le 0.4632$$ 0 ≤ s / M 2 ≤ 0.4632 and the charge Q within the range $$0\le Q/M\le 0.6806.$$ 0 ≤ Q / M ≤ 0.6806 . In contrast, Sgr A* imposes tighter constraints on negative scalar hair. When Q approaches zero, s is constrained within the range $$0\ge s/M^2\ge -0.0277.$$ 0 ≥ s / M 2 ≥ - 0.0277 . Overall, EHT observations can provide constraints at most on the order of $${\mathcal {O}}\left( {10}^{-1}\right) .$$ O 10 - 1 . Subsequently, we construct extreme mass ratio inspiral (EMRI) systems and calculate their gravitational waves to assess the detection capability of the LISA detector for these BHs. The results indicate that for central BHs of $$M={10}^6M_\odot ,$$ M = 10 6 M ⊙ , LISA is expected to detect scalar hair $$s/M^2$$ s / M 2 at the $${\mathcal {O}}\left( {10}^{-4}\right) $$ O 10 - 4 level and charge Q/M at the $${\mathcal {O}}\left( {10}^{-2}\right) $$ O 10 - 2 level, with detection sensitivity far exceeding the current EHT capabilities. This demonstrates the immense potential of EMRI gravitational wave observations in testing EMCS theory.

Event Horizon Telescope (EHT) observations at 230 GHz have now imaged polarized emission around the supermassive black hole in M87 on event-horizon scales. This polarized synchrotron radiation probes the structure of magnetic fields and the plasma properties near the black hole. Here we compare the resolved polarization structure observed by the EHT, along with simultaneous unresolved observations with the Atacama Large Millimeter/submillimeter Array, to expectations from theoretical models. The low fractional linear polarization in the resolved image suggests that the polarization is scrambled on scales smaller than the EHT beam, which we attribute to Faraday rotation internal to the emission region. We estimate the average density n e ∼ 104–7 cm−3, magnetic field strength B ∼ 1–30 G, and electron temperature T e ∼ (1–12) × 1010 K of the radiating plasma in a simple one-zone emission model. We show that the net azimuthal linear polarization pattern may result from organized, poloidal magnetic fields in the emission region. In a quantitative comparison with a large library of simulated polarimetric images from general relativistic magnetohydrodynamic (GRMHD) simulations, we identify a subset of physical models that can explain critical features of the polarimetric EHT observations while producing a relativistic jet of sufficient power. The consistent GRMHD models are all of magnetically arrested accretion disks, where near-horizon magnetic fields are dynamically important. We use the models to infer a mass accretion rate onto the black hole in M87 of (3–20) × 10−4 M ⊙ yr−1.

Context. In this second paper in our publication series, we present the open-source ZINGULARITY framework for parameter inference with deep Bayesian artificial neural networks. We carried out supervised learning with synthetic millimeter very long baseline interferometry observations of the Event Horizon Telescope (EHT). Our ground-truth models are based on general relativistic magnetohydrodynamic simulations of Sgr A* and M87* on horizon scales. The models predict the synchrotron emission produced by these accreting supermassive black hole systems. Aims. We investigated how well ZINGULARITY neural networks are able to infer key model parameters from EHT observations, such as the black hole spin and the magnetic state of the accretion disk, when uncertainties in the data are accurately taken into account. Methods. ZINGULARITY makes use of the TENSORFLOW PROBABILITY library and is able to handle large amounts of data with a combination of the efficient TFRecord data format plus the HOROVOD framework for distributed deep learning. Our approach is the first analysis of EHT data with Bayesian neural networks, where an unprecedented training data size, under consideration of a closely modeled EHT signal path, and the full information content of the observational data are used. ZINGULARITY infers parameters based on salient features in the data and is containerized for scientific reproducibility. Results. Through parameter surveys and dedicated validation tests, we identified neural network architectures, that are robust against internal stochastic processes and unaffected by noise in the observational and model data. We give examples of how different data properties affect the network training. We show how the Bayesian nature of our networks gives trustworthy uncertainties and uncovers failure modes for uncharacterizable data. Conclusions. It is easy to achieve low validation errors during training on synthetic data with neural networks, particularly when the forward modeling is too simplified. Through careful studies, we demonstrate that our trained networks can generalize well so that reliable results can be obtained from observational data.

The Event Horizon Telescope (EHT) is a millimeter very long baseline interferometry (VLBI) array that has imaged the apparent shadows of the supermassive black holes M87* and Sagittarius A*. Polarimetric data from these observations contain a wealth of information on the black hole and accretion flow properties. In this work, we develop polarimetric geometric modeling methods for mm-VLBI data, focusing on approaches that fit data products with differing degrees of invariance to broad classes of calibration errors. We establish a fitting procedure using a polarimetric “m-ring” model to approximate the image structure near a black hole. By fitting this model to synthetic EHT data from general relativistic magnetohydrodynamic models, we show that the linear and circular polarization structure can be successfully approximated with relatively few model parameters. We then fit this model to EHT observations of M87* taken in 2017. In total intensity and linear polarization, the m-ring fits are consistent with previous results from imaging methods. In circular polarization, the m-ring fits indicate the presence of event-horizon-scale circular polarization structure, with a persistent dipolar asymmetry and orientation across several days. The same structure was recovered independently of observing band, used data products, and model assumptions. Despite this broad agreement, imaging methods do not produce similarly consistent results. Our circular polarization results, which imposed additional assumptions on the source structure, should thus be interpreted with some caution. Polarimetric geometric modeling provides a useful and powerful method to constrain the properties of horizon-scale polarized emission, particularly for sparse arrays like the EHT.

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 ${\sim}10\%$ of the true mass and within ${\sim}10^\circ$ 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.

Context. In a series of publications, we describe a comprehensive comparison of Event Horizon Telescope (EHT) data with theoretical models of the observed Sagittarius A* (Sgr A*) and Messier 87* (M87*) horizon-scale sources. Aims. In this article, we report on improvements made to our observational data reduction pipeline and present the generation of observables derived from the EHT models. We make use of ray-traced general relativistic magnetohydrodynamic simulations that are based on different black hole spacetime metrics and accretion physics parameters. These broad classes of models provide a good representation of the primary targets observed by the EHT. Methods. We describe how we combined multiple frequency bands and polarization channels of the observational data to improve our fringe-finding sensitivity and stabilization of atmospheric phase fluctuations. To generate realistic synthetic data from our models, we took the signal path as well as the calibration process, and thereby the aforementioned improvements, into account. We could thus produce synthetic visibilities akin to calibrated EHT data and identify salient features for the discrimination of model parameters. Results. We have produced a library consisting of an unparalleled 962 000 synthetic Sgr A* and M87* datasets. In terms of baseline coverage and noise properties, the library encompasses 2017 EHT measurements as well as future observations with an extended telescope array. Conclusions. We differentiate between robust visibility data products related to model features and data products that are strongly affected by data corruption effects. Parameter inference is mostly limited by intrinsic model variability, which highlights the importance of long-term monitoring observations with the EHT. In later papers in this series, we will show how a Bayesian neural network trained on our synthetic data is capable of dealing with the model variability and extracting physical parameters from EHT observations. With our calibration improvements, our newly reduced EHT datasets have a considerably better quality compared to previously analyzed data.

We investigate whether photon ring observations in black hole imaging are able to distinguish between the Kerr black hole in general relativity and alternative black holes that deviate from Kerr. Certain aspects of photon rings have been argued to be robust observables in very-long-baseline interferometry black hole observations which carry imprints of the underlying spacetime. The photon ring shape, as well as its Lyapunov exponent (which encodes the narrowing of successive photon subrings), are detailed probes of the underlying geometry; measurements thereof have been argued to provide a strong null test of general relativity and the Kerr metric. However, a more complicated question is whether such observations of the photon ring properties can distinguish between Kerr and alternative black holes. We provide a first answer to this question by calculating photon rings of the Johannsen, Rasheed-Larsen, and Manko-Novikov black holes. We find that large deviations from Kerr and large observer inclinations are needed to obtain measurable differences in the photon ring shape. In other words, the Kerr photon ring shape appears to be the universal shape even for deviating black holes at low inclinations. On the other hand, the Lyapunov exponent shows more marked variations for deviations from the Kerr metric. Our analysis lays out the groundwork to determine deviations from the Kerr spacetime in photon rings that are potentially detectable by future observing missions.

Very long baseline interferometry (VLBI) makes it possible to recover the images of astronomical sources with extremely high angular resolution. Most recently, the Event Horizon Telescope (EHT) has extended VLBI to short millimeter wavelengths with a goal of achieving angular resolution sufficient for imaging the event horizons of nearby supermassive black holes. Interferometry provides measurements related to the underlying source image through a sparse set spatial frequencies. An image can then be recovered from these measurements by making assumptions about the underlying image. One of the most important assumptions made by conventional imaging methods is that over the course of a night's observation the image is static. However, for quickly evolving sources, such as the galactic center's supermassive black hole (SgrA*) targeted by the EHT, this assumption is violated and these conventional imaging approaches fail. This paper presents a new way to model VLBI measurements that allows for the recovery of both the appearance and dynamics of an evolving source by reconstructing a video rather than a static image. By modeling VLBI measurements using a Gaussian Markov Model, information can be propagated across observations in time to reconstruct a video, while simultaneously learning about the dynamics of the source's emission region. This paper demonstrates our proposed expectation-maximization algorithm, StarWarps, on realistic synthetic observations of black holes, and shows how it substantially improves the results compared to conventional imaging methods. In addition to synthetic data, the technique is demonstrated on real VLBA data of the M87 jet.

The Event Horizon Telescope (EHT) 2017 campaign successfully imaged the black hole shadow for the first time. To achieve this image, we used the very long baseline interferometry (VLBI) technique at the wavelength of 1.3 mm (frequency of 230 GHz) with utilizing eight millimeter- and submillimeter-wavelength telscopes all over the world. For the interferometry, the distance between two telescopes (i.e., baseline length) decides the angular resolution. The EHT telescopes extends near the diameter of the Earth, so together with the short wavelength, it is possible to reach the angular resolution of about 25 micro-arcsec. This resolution is sufficient to image the shadows of nearby supermassive black holes (SMBHs), and indeed, we have succeessfully imaged the shadow of the SMBH at the center of the nearby giant elliptical galaxy M87. In this talk, I will give an overview of the technologies we have used in the EHT 2017 campaign, and also present the plans of the future development.