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  1. Abstract We introduceMahakala, aPython-based, modular, radiative ray-tracing code for curved spacetimes. We employ Google’sJAXframework for accelerated automatic differentiation, which can efficiently compute Christoffel symbols directly from the metric, allowing the user to easily and quickly simulate photon trajectories through non-Kerr spacetimes.JAXalso enablesMahakalato run in parallel on both CPUs and GPUs.Mahakalanatively uses the Cartesian Kerr–Schild coordinate system, which avoids numerical issues caused by the pole in spherical coordinate systems. We demonstrateMahakala’s capabilities by simulating 1.3 mm wavelength images (the wavelength of Event Horizon Telescope observations) of general relativistic magnetohydrodynamic simulations of low-accretion rate supermassive black holes. The modular nature ofMahakalaallows us to quantitatively explore how different regions of the flow influence different image features. We show that most of the emission seen in 1.3 mm images originates close to the black hole and peaks near the photon orbit. We also quantify the relative contribution of the disk, forward jet, and counterjet to 1.3 mm images. 
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    Free, publicly-accessible full text available May 13, 2026
  2. Abstract A new image-reconstruction algorithm, Principal-component Interferometric Modeling (PRIMO), applied to the interferometric data of the M87 black hole collected with the Event Horizon Telescope (EHT), resulted in an image that reached the native resolution of the telescope array.PRIMOis based on learning a compact set of image building blocks obtained from a large library of high-fidelity, physics-based simulations of black hole images. It uses these building blocks to fill the sparse Fourier coverage of the data that results from the small number of telescopes in the array. In this paper, we show that this approach is readily justified. Since the angular extent of the image of the black hole and of its inner accretion flow is finite, the Fourier space domain is heavily smoothed, with a correlation scale that is at most comparable to the sizes of the data gaps in the coverage of Fourier space with the EHT. Consequently,PRIMOor other machine learning algorithms can faithfully reconstruct the images without the need to generate information that is unconstrained by the data within the resolution of the array. We also address the completeness of the eigenimages and the compactness of the resulting representation. We show thatPRIMOprovides a compact set of eigenimages that have sufficient complexity to recreate a broad set of images well beyond those in the training set. 
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    Free, publicly-accessible full text available April 29, 2026
  3. Abstract Light passing near a black hole can follow multiple paths from an emission source to an observer due to strong gravitational lensing. Photons following different paths take different amounts of time to reach the observer, which produces an echo signature in the image. The characteristic echo delay is determined primarily by the mass of the black hole, but it is also influenced by the black hole spin and inclination to the observer. In the Kerr geometry, echo images are demagnified, rotated, and sheared copies of the direct image and lie within a restricted region of the image. Echo images have exponentially suppressed flux, and temporal correlations within the flow make it challenging to directly detect light echoes from the total light curve. In this Letter, we propose a novel method to search for light echoes by correlating the total light curve with the interferometric signal at high spatial frequencies, which is a proxy for indirect emission. We explore the viability of our method using numerical general relativistic magnetohydrodynamic simulations of a near-face-on accretion system scaled to M87-like parameters. We demonstrate that our method can be used to directly infer the echo delay period in simulated data. An echo detection would be clear evidence that we have captured photons that have circled the black hole, and a high-fidelity echo measurement would provide an independent measure of fundamental black hole parameters. Our results suggest that detecting echoes may be achievable through interferometric observations with a modest space-based very long baseline interferometry mission. 
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  4. Abstract The first very long baseline interferometry (VLBI) detections at 870μm wavelength (345 GHz frequency) are reported, achieving the highest diffraction-limited angular resolution yet obtained from the surface of the Earth and the highest-frequency example of the VLBI technique to date. These include strong detections for multiple sources observed on intercontinental baselines between telescopes in Chile, Hawaii, and Spain, obtained during observations in 2018 October. The longest-baseline detections approach 11 Gλ, corresponding to an angular resolution, or fringe spacing, of 19μas. The Allan deviation of the visibility phase at 870μm is comparable to that at 1.3 mm on the relevant integration timescales between 2 and 100 s. The detections confirm that the sensitivity and signal chain stability of stations in the Event Horizon Telescope (EHT) array are suitable for VLBI observations at 870μm. Operation at this short wavelength, combined with anticipated enhancements of the EHT, will lead to a unique high angular resolution instrument for black hole studies, capable of resolving the event horizons of supermassive black holes in both space and time. 
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  5. 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. 
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    Free, publicly-accessible full text available March 1, 2026
  6. The Event Horizon Telescope (EHT) observation of M87in 2018 has revealed a ring with a diameter that is consistent with the 2017 observation. The brightest part of the ring is shifted to the southwest from the southeast. In this paper, we provide theoretical interpretations for the multi-epoch EHT observations for M87by comparing a new general relativistic magnetohydrodynamics model image library with the EHT observations for M87in both 2017 and 2018. The model images include aligned and tilted accretion with parameterized thermal and nonthermal synchrotron emission properties. The 2018 observation again shows that the spin vector of the M87supermassive black hole is pointed away from Earth. A shift of the brightest part of the ring during the multi-epoch observations can naturally be explained by the turbulent nature of black hole accretion, which is supported by the fact that the more turbulent retrograde models can explain the multi-epoch observations better than the prograde models. The EHT data are inconsistent with the tilted models in our model image library. Assuming that the black hole spin axis and its large-scale jet direction are roughly aligned, we expect the brightest part of the ring to be most commonly observed 90 deg clockwise from the forward jet. This prediction can be statistically tested through future observations. 
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    Free, publicly-accessible full text available January 1, 2026
  7. Context.Many active galaxies harbor powerful relativistic jets, however, the detailed mechanisms of their formation and acceleration remain poorly understood. Aims.To investigate the area of jet acceleration and collimation with the highest available angular resolution, we study the innermost region of the bipolar jet in the nearby low-ionization nuclear emission-line region (LINER) galaxy NGC 1052. Methods.We combined observations of NGC 1052 taken with VLBA, GMVA, and EHT over one week in the spring of 2017. Our study is focused on the size and continuum spectrum of the innermost region containing the central engine and the footpoints of both jets. We employed a synchrotron-self absorption model to fit the continuum radio spectrum and we combined the size measurements from close to the central engine out to ∼1 pc to study the jet collimation. Results.For the first time, NGC 1052 was detected with the EHT, providing a size of the central region in-between both jet bases of 43 μas perpendicular to the jet axes, corresponding to just around 250 RS(Schwarzschild radii). This size estimate supports previous studies of the jets expansion profile which suggest two breaks of the profile at around 3 × 103 RSand 1 × 104 RSdistances to the core. Furthermore, we estimated the magnetic field to be 1.25 Gauss at a distance of 22 μas from the central engine by fitting a synchrotron-self absorption spectrum to the innermost emission feature, which shows a spectral turn-over at ∼130 GHz. Assuming a purely poloidal magnetic field, this implies an upper limit on the magnetic field strength at the event horizon of 2.6 × 104 Gauss, which is consistent with previous measurements. Conclusions.The complex, low-brightness, double-sided jet structure in NGC 1052 makes it a challenge to detect the source at millimeter (mm) wavelengths. However, our first EHT observations have demonstrated that detection is possible up to at least 230 GHz. This study offers a glimpse through the dense surrounding torus and into the innermost central region, where the jets are formed. This has enabled us to finally resolve this region and provide improved constraints on its expansion and magnetic field strength. 
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    Free, publicly-accessible full text available December 1, 2025
  8. Context.The nearby elliptical galaxy M87 contains one of only two supermassive black holes whose emission surrounding the event horizon has been imaged by the Event Horizon Telescope (EHT). In 2018, more than two dozen multi-wavelength (MWL) facilities (from radio toγ-ray energies) took part in the second M87 EHT campaign. Aims.The goal of this extensive MWL campaign was to better understand the physics of the accreting black hole M87*, the relationship between the inflow and inner jets, and the high-energy particle acceleration. Understanding the complex astrophysics is also a necessary first step towards performing further tests of general relativity. Methods.The MWL campaign took place in April 2018, overlapping with the EHT M87* observations. We present a new, contemporaneous spectral energy distribution (SED) ranging from radio to very high-energy (VHE)γ-rays as well as details of the individual observations and light curves. We also conducted phenomenological modelling to investigate the basic source properties. Results.We present the first VHEγ-ray flare from M87 detected since 2010. The flux above 350 GeV more than doubled within a period of ≈36 hours. We find that the X-ray flux is enhanced by about a factor of two compared to 2017, while the radio and millimetre core fluxes are consistent between 2017 and 2018. We detect evidence for a monotonically increasing jet position angle that corresponds to variations in the bright spot of the EHT image. Conclusions.Our results show the value of continued MWL monitoring together with precision imaging for addressing the origins of high-energy particle acceleration. While we cannot currently pinpoint the precise location where such acceleration takes place, the new VHEγ-ray flare already presents a challenge to simple one-zone leptonic emission model approaches, and it emphasises the need for combined image and spectral modelling. 
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    Free, publicly-accessible full text available December 1, 2025