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At least 19 records

Ordered magnetic fields around the 3C 84 central black hole

Context. 3C 84 is a nearby radio source with a complex total intensity structure, showing linear polarisation and spectral patterns. A detailed investigation of the central engine region necessitates the use of very-long-baseline interferometry (VLBI) above the hitherto available maximum frequency of 86 GHz.Aims. Using ultrahigh resolution VLBI observations at the currently highest available frequency of 228 GHz, we aim to perform a direct detection of compact structures and understand the physical conditions in the compact region of 3C 84.Methods. We used Event Horizon Telescope (EHT) 228 GHz observations and, given the limited (u, v)-coverage, applied geometric model fitting to the data. Furthermore, we employed quasi-simultaneously observed, ancillary multi-frequency VLBI data for the source in order to carry out a comprehensive analysis of the core structure.Results. We report the detection of a highly ordered, strong magnetic field around the central, supermassive black hole of 3C 84. The brightness temperature analysis suggests that the system is in equipartition. We also determined a turnover frequency of νm = (113 ± 4) GHz, a corresponding synchrotron self-absorbed magnetic field of BSSA = (2.9 ± 1.6) G, and an equipartition magnetic field of Beq = (5.2 ± 0.6) G. Three components are resolved with the highest fractional polarisation detected for this object (mnet = (17.0 ± 3.9)%). The positions of the components are compatible with those seen in low-frequency VLBI observations since 2017–2018. We report a steeply negative slope of the spectrum at 228 GHz. We used these findings to test existing models of jet formation, propagation, and Faraday rotation in 3C 84.Conclusions. The findings of our investigation into different flow geometries and black hole spins support an advection-dominated accretion flow in a magnetically arrested state around a rapidly rotating supermassive black hole as a model of the jet-launching system in the core of 3C 84. However, systematic uncertainties due to the limited (u, v)-coverage, however, cannot be ignored. Our upcoming work using new EHT data, which offer full imaging capabilities, will shed more light on the compact region of 3C 84.Key words: techniques: high angular resolution / techniques: interferometric / galaxies: active / galaxies: individual: NGC 1275 / galaxies: jets

79 ASTRONOMY AND ASTROPHYSICS↗

Event Horizon Telescope imaging of the archetypal blazar 3C 279 at an extreme 20 microarcsecond resolution

3C 279 is an archetypal blazar with a prominent radio jet that show broadband flux density variability across the entire electromagnetic spectrum. We use an ultra-high angular resolution technique – global Very Long Baseline Interferometry (VLBI) at 1.3 mm (230 GHz) – to resolve the innermost jet of 3C 279 in order to study its fine-scale morphology close to the jet base where highly variable γ-ray emission is thought to originate, according to various models. The source was observed during four days in April 2017 with the Event Horizon Telescope at 230 GHz, including the phased Atacama Large Millimeter/submillimeter Array (ALMA), at an angular resolution of ∼20 μas (at a redshift of z = 0.536 this corresponds to ∼0.13 pc ∼ 1700 Schwarzschild radii with a black hole mass MBH = 8 × 108 M⊙). Imaging and model-fitting techniques were applied to the data to parameterize the fine-scale source structure and its variation. We find a multicomponent inner jet morphology with the northernmost component elongated perpendicular to the direction of the jet, as imaged at longer wavelengths. The elongated nuclear structure is consistent on all four observing days and across different imaging methods and model-fitting techniques, and therefore appears robust. Owing to its compactness and brightness, we associate the northern nuclear structure as the VLBI “core”. This morphology can be interpreted as either a broad resolved jet base or a spatially bent jet. We also find significant day-to-day variations in the closure phases, which appear most pronounced on the triangles with the longest baselines. Our analysis shows that this variation is related to a systematic change of the source structure. Two inner jet components move non-radially at apparent speeds of ∼15 c and ∼20 c (∼1.3 and ∼1.7 μas day−1, respectively), which more strongly supports the scenario of traveling shocks or instabilities in a bent, possibly rotating jet. The observed apparent speeds are also coincident with the 3C 279 large-scale jet kinematics observed at longer (cm) wavelengths, suggesting no significant jet acceleration between the 1.3 mm core and the outer jet. The intrinsic brightness temperature of the jet components are ≲1010 K, a magnitude or more lower than typical values seen at ≥7 mm wavelengths. The low brightness temperature and morphological complexity suggest that the core region of 3C 279 becomes optically thin at short (mm) wavelengths.Key words: galaxies: active / galaxies: jets / galaxies: individual: 3C 279 / techniques: interferometric⋆ The data are only available at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/cat/J/A+A/640/A69 and at https://eventhorizontelescope.org/for-astronomers/data⋆⋆ Deceased.

79 ASTRONOMY AND ASTROPHYSICS↗

A multifrequency study of sub-parsec jets with the Event Horizon Telescope

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 factor δ ∝ 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 radius B ∝ r−3, hinting at jet acceleration or efficient magnetic energy dissipation.Key words: techniques: interferometric / galaxies: active / galaxies: jets / galaxies: nuclei / quasars: general / quasars: supermassive black holes⋆⋆ Deceased.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Exploring Interferometry Diagnostics for Optical Stochastic Cooling at FAST/IOTA

Optical Stochastic Cooling (OSC) is an advanced beam-cooling technique that will precede the traditional stochastic cooling. This method leverages optical radiation and high-precision feedback to cool the particles more efficiently than traditional stochastic methods by more than three orders of magnitude. As such, it is an enabler for the development of next generation discovery science machines at the frontiers of energy and intensity. This paper focuses on the development of the second phase of OSC and improving extreme beam cooling technique in accelerators. Along with the assembly and use of an interferometer to provide diagnostics and optimization to OSC systems. The interferometer can allow for the observation and analysis of fringe patterns from a recreated simpler version in the laser room. By leveraging interferometric techniques, OSC can achieve higher efficiency, verification, stability and performance.

Teriba, Folashade↗

Revisiting the Kinematics of the Cylinder Test

The cylinder expansion experiment is a well-established performance test for condensed explosives that is utilized routinely to determine pressure-energy-volume relationships for detonation products. The modern cylinder test employs optical interferometric techniques to measure velocity, as opposed to older realizations where streak cameras were commonplace. Despite their widespread use, questions sometimes remain as to what kind of data the velocity diagnostics in a cylinder test provide along with how to interpret such measurements and relate them to physical quantities of interest. Here in this study, equations are derived that fully describe the kinematics of the cylinder wall during expansion. These equations are then applied to experimental as well as synthetic data generated via a hydrodynamic simulation in order to verify the mathematical framework developed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Sound Velocity of Hematite up to 13 GPa

We performed acoustic measurements on polycrystalline hematite using ultrasonic interferometric techniques in a Kawai-type multi-anvil apparatus. The elastic moduli and their pressure derivatives were determined by fitting the experimental data to third-order finite strain equations, yielding: 𝐾 𝑆,0 = 214.8 (20) GPa, 𝐺 0 = 92.0 (2) GPa, 𝐾$^{′}_{S,0}$ = 5.70 (1), and 𝐺$^{′}_{0}$ = 0.88 (4). Modeling of the velocity profiles of hematite along hot and cold slab geotherms shows that compressional (V P ) and shear (V S ) wave velocities are 22%–24% and 53%–55% lower, respectively, compared to the Preliminary Reference Earth Model at the top of the lower mantle. Furthermore, these findings likely offer a potential explanation for the low-velocity anomalies associated with slab graveyards at the base of the lower mantle.

36 MATERIALS SCIENCE↗

The putative center in NGC 1052

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 RS and 1 × 104 RS distances 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.Key words: methods: observational / techniques: high angular resolution / techniques: interferometric / galaxies: active / galaxies: jets / galaxies: Seyfert⋆⋆ NASA Hubble Fellowship Program, Einstein Fellow.

79 ASTRONOMY AND ASTROPHYSICS↗

Full-polarization millimeter wavelength variability of Sagittarius A * during the 2018 EHT campaign

Context. Sagittarius A* (Sgr A*), the supermassive black hole at the center of the Milky Way, provides a unique laboratory to study accretion dynamics and plasma processes near the event horizon. Aims. We investigated the variability and polarization properties of Sgr A* using ALMA observations during the 2018 Event Horizon Telescope campaign. Methods. We analyzed high-cadence full-polarization light curves from ALMA at millimeter wavelengths, performed time-series analysis, and investigated the temporal behavior during an X-ray flare observed by Chandra on 2018 April 24. The variability characteristics are compared with expectations from standard accretion flow models. Results. We find low variability in total intensity (σ/μ < 10%), but significantly higher variability in linear and circular polarization (∼30% and ∼50%, respectively). A time-series analysis reveals red-noise variability, with power spectral densities between −2 and −3 across all Stokes parameters. Polarized intensity shows stable intra-day timescales, while total intensity exhibits more variable timescales, suggesting distinct emission regions, with polarization likely arising from a coherent structure. On April 24, a statistically significant inter-band delay in polarized intensity coincides with a near-simultaneous X-ray and millimeter peak that deviates from the typical delayed flare scenario. This event also features enhanced millimeter variability and coherent polarization loop evolution. The observed simultaneity challenges standard models of transient synchrotron emission with cooling delays, favoring instead a scenario of continuous energy injection in an optically thin region. Conclusions. Our results offer new constraints on the physical mechanisms driving variability in Sgr A*, and provide key observational input for refining theoretical models of accretion and plasma behavior in the vicinity of supermassive black holes.

Galaxy: center↗

First demonstration of a fiber optic bolometer on a tokamak plasma (invited)

A fiber optic bolometer (FOB) was demonstrated observing a fusion plasma for the first time at the DIII-D tokamak. A FOB uses a fiber optics-based interferometric technique that is designed to have a high sensitivity to temperature changes [75 mK/(W/m2) responsivity in high vacuum with 0.38 mK noise level] with a negligible susceptibility to electromagnetic interference (EMI) that can be problematic for resistive bolometers in a tokamak environment. A single-channel test apparatus was installed on DIII-D consisting of a measurement FOB and shielded reference FOB. The single-channel FOB showed a negligible increase in the noise level during typical plasma operations (0.39 mK) compared to the benchtop results (0.38 mK), confirming an insignificant EMI impact to the FOB. Comparisons to DIII-D resistive bolometers showed good agreement with the single-channel FOB, indicating that the FOB is comparable to a resistive bolometer when the impulse calibration is applied. The noise-equivalent power density of the calibrated FOB during a plasma operation was 0.55 W/m2 with an average sampling time of 20 ms. The major potential effect of ionizing radiation on the FOB would be the radiation-induced attenuation, which can be efficiently compensated for by adjusting the probing light power.

Lee, S. (ORCID:0000000170289004)↗

Three-dimensional full-field velocity measurements in shock compression experiments using stereo digital image correlation

Shock compression plate impact experiments conventionally rely on point-wise velocimetry measurements based on laser-based interferometric techniques. This study presents an experimental methodology to measure the free surface full-field particle velocity in shock compression experiments using high-speed imaging and three-dimensional (3D) digital image correlation (DIC). The experimental setup has a temporal resolution of 100 ns with a spatial resolution varying from 90 to 200 μm/pixel. Experiments were conducted under three different plate impact configurations to measure spatially resolved free surface velocity and validate the experimental technique. First, a normal impact experiment was conducted on polycarbonate to measure the macroscopic full-field normal free surface velocity. Second, an isentropic compression experiment on Y-cut quartz–tungsten carbide assembly is performed to measure the particle velocity for experiments involving ramp compression waves. To explore the capability of the technique in multiaxial loading conditions, a pressure shear plate impact experiment was conducted to measure both the normal and transverse free surface velocities under combined normal and shear loading. The velocities measured in the experiments using digital image correlation are validated against previous data obtained from laser interferometry. Numerical simulations were also performed using established material models to compare and validate the experimental velocity profiles for these different impact configurations. The novel ability of the employed experimental setup to measure full-field free surface velocities with high spatial resolutions in shock compression experiments is demonstrated for the first time in this work.

47 OTHER INSTRUMENTATION↗

Robust Measurements of n -Point Correlation Functions of Driven-Dissipative Quantum Systems on a Digital Quantum Computer

We propose and demonstrate a unified hierarchical method to measure n -point correlation functions that can be applied to driven, dissipative, or otherwise open or nonequilibrium quantum systems. In this method, the time evolution of the system is repeatedly interrupted by interacting an ancilla qubit with the system through a controlled operation, and measuring the ancilla immediately afterward. We discuss the robustness of this method as compared to other ancilla-based interferometric techniques (such as the Hadamard test), and highlight its advantages for near-term quantum simulations of open quantum systems. We implement the method on a quantum computer in order to measure single-particle Green’s functions of a driven-dissipative fermionic system. This Letter shows that dynamical correlation functions for driven-dissipative systems can be robustly measured with near-term quantum computers. Published by the American Physical Society 2024

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Characterization and Simulation of Optical Delay System for the Proof-of-Principle Experiment of Optical Stochastic Cooling at IOTA

The Optical Stochastic Cooling (OSC) experiment at Fermilab’s IOTA storage ring uses two undulators to cool the beam over many turns. The radiation emitted by electrons in the first undulator is delayed and imaged in the second undulator where it applies a corrective energy kick on the electrons. Imperfections in the manufacturing of the delay plates can lead to a source of error. This paper presents the experimental characterization of the absolute thickness of these delay plates using an interferometric technique. The measured "thickness maps" are implemented in the Synchrotron Radiation Workshop (SRW) program to assess their impact on the delayed radiation pulse.

43 PARTICLE ACCELERATORS↗

Graphical Optimization of Spectral Shift Reconstructions for Optical Backscatter Reflectometry

Optical backscatter reflectometry (OBR) is an interferometric technique that can be used to measure local changes in temperature and mechanical strain based on spectral analyses of backscattered light from a singlemode optical fiber. The technique uses Fourier analyses to resolve spectra resulting from reflections occurring over a discrete region along the fiber. These spectra are cross-correlated with reference spectra to calculate the relative spectral shifts between measurements. The maximum of the cross-correlated spectra—termed quality—is a metric that quantifies the degree of correlation between the two measurements. Recently, this quality metric was incorporated into an adaptive algorithm to (1) selectively vary the reference measurement until the quality exceeds a predefined threshold and (2) calculate incremental spectral shifts that can be summed to determine the spectral shift relative to the initial reference. Using a graphical (network) framework, this effort demonstrated the optimal reconstruction of distributed OBR measurements for all sensing locations using a maximum spanning tree (MST). By allowing the reference to vary as a function of both time and sensing location, the MST and other adaptive algorithms could resolve spectral shifts at some locations, even if others can no longer be resolved.

47 OTHER INSTRUMENTATION↗

Hybrid interferometric diagnostic for the refractive index measurement across nearly discrete shock waves

The measurement of high temperature gas properties is key for characterizing high speed flows. Nearly discrete changes in density across shock waves, in particular, are difficult to resolve through traditional fringe-counting interferometric methods. Existing techniques for estimating large fringe jumps are either resolution limited or require specialized window configurations. In this Letter, we describe a unique hybrid interferometric technique that combines narrowband fringes for high resolution and broadband fringes as an absolute reference to measure changes in refractive index with a resolution of up to 7 × 10 −8 across nearly discrete index changes of up to 1.5 × 10 −4 . By capturing fringes with an ultrahigh-speed camera, the refractive index changes across discrete shock fronts can be estimated inside a shock tube with high accuracy and time resolution. First, a novel hybrid calibration method for tracking finite fringes is discussed. Next, this technique is used to measure the post-initial-shock refractive indices for Mach 2.7 to 4.2 flows (pressures from 90.4 to 228.4 kPa). Results are then compared with theoretical values showing agreement within 2%.

Wang, Gwendolyn T. (ORCID:000000016271893X)↗

Optimising the processing and storage of visibilities using lossy compression

The next-generation radio astronomy instruments are providing a massive increase in sensitivity and coverage, largely through increasing the number of stations in the array and the frequency span sampled. The two primary problems encountered when processing the resultant avalanche of data are the need for abundant storage and the constraints imposed by I/O, as I/O bandwidths drop significantly on cold storage. An example of this is the data deluge expected from the SKA Telescopes of more than 60 PB per day, all to be stored on the buffer filesystem. While compressing the data is an obvious solution, the impacts on the final data products are hard to predict. In this paper, we chose an error-controlled compressor – MGARD – and applied it to simulated SKA-Mid and real pathfinder visibility data, in noise-free and noise-dominated regimes. As the data have an implicit error level in the system temperature, using an error bound in compression provides a natural metric for compression. MGARD ensures the compression incurred errors adhere to the user-prescribed tolerance. To measure the degradation of images reconstructed using the lossy compressed data, we proposed a list of diagnostic measures, exploring the trade-off between these error bounds and the corresponding compression ratios, as well as the impact on science quality derived from the lossy compressed data products through a series of experiments. We studied the global and local impacts on the output images for continuum and spectral line examples. We found relative error bounds of as much as 10%, which provide compression ratios of about 20, have a limited impact on the continuum imaging as the increased noise is less than the image RMS, whereas a 1% error bound (compression ratio of 8) introduces an increase in noise of about an order of magnitude less than the image RMS. For extremely sensitive observations and for very precious data, we would recommend a 0.1% error bound with compression ratios of about 4. These have noise impacts two orders of magnitude less than the image RMS levels. At these levels, the limits are due to instabilities in the deconvolution methods. We compared the results to the alternative compression tool DYSCO, in both the impacts on the images and in the relative flexibility. MGARD provides better compression for similar error bounds and has a host of potentially powerful additional features.

Techniques: interferometric↗

Spatially resolved polarization swings in the supermassive binary black hole candidate OJ 287 with first Event Horizon Telescope observations

We present the first Event Horizon Telescope 1.3 mm observations of the supermassive binary black hole candidate OJ 287. The observations achieved an unprecedented angular resolution of 18 μas and reveal significant structural and polarization variability over just five days, marking the shortest timescale on which such changes have been directly imaged in this source. The inner jet exhibits a twisted ridgeline structure, with features displaying apparent superluminal motions up to about 22 c. The linear polarization maps reveal three main polarized features whose electric-vector position angles (EVPAs) change substantially over the time span of our observations, including a component with a radial polarization consistent with being produced by a recollimation shock. Most notably, we directly resolved two innermost jet components whose EVPAs rotate in opposite directions. The faster component, moving at 2.4 ± 0.9 μas/day (17.4 ± 6.5 c), exhibits counterclockwise EVPA swings of roughly 3.7° per day, while the slower component, with a proper motion of 1.4 ± 0.3 μas/day (10.2 ± 2.2 c), rotates clockwise at approximately 2.5° per day. Previous studies inferred helical magnetic fields in AGN jets from time-resolved or integrated polarization variability but lacked the angular resolution to directly image this effect. Our results provide spatially resolved evidence that a helical magnetic field threads the jet’s collimation and acceleration zone, ruling out models based on the superposition of unresolved components. Our analysis suggests that propagating shocks interact with a Kelvin–Helmholtz plasma instability, illuminating different phases of the helical magnetic field and producing the observed polarization spatial and temporal variability. Moreover, our model naturally accounts for the more rapid polarization rotation observed in the faster moving component. Our model predicts even more rapid swings in polarization, which could be tested with future observations featuring a more densely sampled time coverage.

OJ 287↗

SYMBA: An end-to-end VLBI synthetic data generation pipeline

Realistic synthetic observations of theoretical source models are essential for our understanding of real observational data. In using synthetic data, one can verify the extent to which source parameters can be recovered and evaluate how various data corruption effects can be calibrated. These studies are the most important when proposing observations of new sources, in the characterization of the capabilities of new or upgraded instruments, and when verifying model-based theoretical predictions in a direct comparison with observational data. We present the SYnthetic Measurement creator for long Baseline Arrays (SYMBA), a novel synthetic data generation pipeline for Very Long Baseline Interferometry (VLBI) observations. SYMBA takes into account several realistic atmospheric, instrumental, and calibration effects. Here, we used SYMBA to create synthetic observations for the Event Horizon Telescope (EHT), a millimetre VLBI array, which has recently captured the first image of a black hole shadow. After testing SYMBA with simple source and corruption models, we study the importance of including all corruption and calibration effects, compared to the addition of thermal noise only. Using synthetic data based on two example general relativistic magnetohydrodynamics (GRMHD) model images of M 87, we performed case studies to assess the image quality that can be obtained with the current and future EHT array for different weather conditions. Our synthetic observations show that the effects of atmospheric and instrumental corruptions on the measured visibilities are significant. Despite these effects, we demonstrate how the overall structure of our GRMHD source models can be recovered robustly with the EHT2017 array after performing calibration steps, which include fringe fitting, a priori amplitude and network calibration, and self-calibration. With the planned addition of new stations to the EHT array in the coming years, images could be reconstructed with higher angular resolution and dynamic range. In our case study, these improvements allowed for a distinction between a thermal and a non-thermal GRMHD model based on salient features in reconstructed images.

79 ASTRONOMY AND ASTROPHYSICS↗