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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. 

Abstract The Event Horizon Telescope (EHT) has produced resolved images of the supermassive black holes (SMBHs) Sgr A* and M87*, which present the largest shadows on the sky. In the next decade, technological improvements and extensions to the array will enable access to a greater number of sources, unlocking studies of a larger population of SMBHs through direct imaging. In this paper, we identify 12 of the most promising sources beyond Sgr A* and M87* based on their angular size and millimeter flux density. For each of these sources, we make theoretical predictions for their observable properties by ray tracing general relativistic magnetohydrodynamic models appropriately scaled to each target’s mass, distance, and flux density. We predict that these sources would have somewhat higher Eddington ratios than M87*, which may result in larger optical and Faraday depths than previous EHT targets. Despite this, we find that visibility amplitude size constraints can plausibly recover masses within a factor of 2, although the unknown jet contribution remains a significant uncertainty. We find that the linearly polarized structure evolves substantially with the Eddington ratio, with greater evolution at larger inclinations, complicating potential spin inferences for inclined sources. We discuss the importance of 345 GHz observations, milli-Jansky baseline sensitivity, and independent inclination constraints for future observations with upgrades to the EHT through ground updates with the next-generation EHT program and extensions to space through the black hole Explorer. 

Abstract Models of highly sub-Eddington accretion onto black holes commonly use a single-fluid model for the collisionless, near-horizon plasma. These models must specify an equation of state. It is common to use an ideal gas withp = (γ − 1)uandγ = 4/3, 13/9, or 5/3, but these produce significantly different outcomes. We discuss the origins of this discrepancy and the assumptions underlying the single-fluid model. The main result of this investigation is that under conditions relevant to low-luminosity black hole accretion the best choice of single-fluid adiabatic index is close to but slightly less than 5/3. Along the way we provide a simple equilibrium model for the relation between the ion-to-electron dissipation ratio and the ion-to-electron temperature ratio, and explore the implications for electron temperature fluctuations in Event Horizon Telescope sources. 

Abstract Very long baseline interferometry observations reveal that relativistic jets like the one in M87 have a limb-brightened, double-edged structure. Analytic and numerical models struggle to reproduce this limb-brightening. We propose a model in which we invoke anisotropy in the distribution function of synchrotron-emitting nonthermal electrons such that electron velocities are preferentially directed parallel to magnetic field lines, as suggested by recent particle-in-cell simulations of electron acceleration and the effects of synchrotron cooling. We assume that the energy injected into nonthermal electrons is proportional to the jet Poynting flux, and we account for synchrotron cooling via a broken power-law energy distribution. We implement our emission model in both general relativistic magnetohydrodynamic (GRMHD) simulations and axisymmetric force-free electrodynamic (GRFFE) jet models and produce simulated jet images at multiple scales and frequencies using polarized general relativistic radiative transfer. We find that the synchrotron emission is concentrated parallel to the local helical magnetic field and that this feature produces limb-brightened jet images on scales ranging from tens of microarcseconds to hundreds of milliarcseconds in M87. We present theoretical predictions for horizon-scale M87 jet images at 230 and 345 GHz that can be tested with next-generation instruments. Due to the scale-invariance of the GRMHD and GRFFE models, our emission prescription can be applied to other targets and serve as a foundation for a unified description of limb-brightened synchrotron images of extragalactic jets. 

Abstract General relativistic magnetohydrodynamics (GRMHD) simulations are an indispensable tool in studying accretion onto compact objects. The Event Horizon Telescope (EHT) frequently uses libraries of ideal GRMHD simulations to interpret polarimetric, event-horizon-scale observations of supermassive black holes at the centers of galaxies. In this work, we present a library of 10 nonradiative, ideal GRMHD simulations that were utilized by the EHT Collaboration in their analysis of Sagittarius A*. The parameter survey explores both low (SANE) and high (MAD) magnetization states across five black hole spinsa_* = −15/16, −1/2, 0, +1/2, +15/16 where each simulation was run out to 30,000GM/c⁻³. We find the angular momentum and energy flux in SANE simulations closely matches the thin-disk value, with minor deviations in prograde models due to fluid forces. This leads to spin equilibrium arounda_* ∼ 0.94, consistent with previous studies. We study the flow of conserved quantities in our simulations and find mass, angular momentum, and energy transport in SANE accretion flows to be primarily inward and fluid dominated. MAD models produce powerful jets with outflow efficiency >1 fora_* = + 0.94, leading to black hole spin-down in prograde cases. We observe outward directed energy and angular momentum fluxes on the horizon, as expected for the Blandford–Znajek mechanism. MAD accretion flows are sub-Keplerian and exhibit greater variability than their SANE counterpart. They are also hotter than SANE disks withinr ≲ 10GM/c⁻². This study is accompanied by a public release of simulation data athttp://thz.astro.illinois.edu/. 

Abstract Frequency phase transfer (FPT) is a technique designed to increase coherence and sensitivity in radio interferometry by making use of the nondispersive nature of the troposphere to calibrate high-frequency data using solutions derived at a lower frequency. While the Korean very long baseline interferometry (VLBI) network has pioneered the use of simultaneous multiband systems for routine FPT up to an observing frequency of 130 GHz, this technique remains largely untested in the (sub)millimeter regime. A recent effort has been made to outfit dual-band systems at (sub)millimeter observatories participating in the Event Horizon Telescope (EHT) and to test the feasibility and performance of FPT up to the observing frequencies of the EHT. We present the results of simultaneous dual-frequency observations conducted in 2024 January on an Earth-sized baseline between the IRAM 30-m in Spain and the James Clerk Maxwell Telescope (JCMT) and Submillimeter Array (SMA) in Hawai‘i. We performed simultaneous observations at 86 and 215 GHz on the bright sources J0958+6533 and OJ 287, with strong detections obtained at both frequencies. We observe a strong correlation between the interferometric phases at the two frequencies, matching the trend expected for atmospheric fluctuations and demonstrating for the first time the viability of FPT for VLBI at a wavelength of  ∼1 millimeter. We show that the application of FPT systematically increases the 215 GHz coherence on all averaging timescales. In addition, the use of the colocated JCMT and SMA as a single dual-frequency station demonstrates the feasibility of paired-antenna FPT for VLBI for the first time, with implications for future array capabilities (e.g., Atacama Large Millimeter/submillimeter Array subarraying and ngVLA calibration strategies). 

Abstract Reconstructing images from the Event Horizon Telescope (EHT) observations of M87*, the supermassive black hole at the center of the galaxy M87, depends on a prior to impose desired image statistics. However, given the impossibility of directly observing black holes, there is no clear choice for a prior. We present a framework for flexibly designing a range of priors, each bringing different biases to the image reconstruction. These priors can be weak (e.g., impose only basic natural-image statistics) or strong (e.g., impose assumptions of black hole structure). Our framework uses Bayesian inference with score-based priors, which are data-driven priors arising from a deep generative model that can learn complicated image distributions. Using our Bayesian imaging approach with sophisticated data-driven priors, we can assess how visual features and uncertainty of reconstructed images change depending on the prior. In addition to simulated data, we image the real EHT M87* data and discuss how recovered features are influenced by the choice of prior. 

Abstract We carry out idealized three-dimensional general-relativistic magnetohydrodynamic simulations of prograde, weakly magnetized, and geometrically thick accretion flows where the gas distribution is misaligned from the black hole (BH) spin axis. We evolve the disk for three BH spins:a= 0.5, 0.75, and 0.9375, and we contrast them with a standard aligned disk simulation witha= 0.9375. The tilted disks achieve a warped and twisted steady-state structure, with the outer disk misaligning further away from the BH and surpassing the initial 24° misalignment. However, closer to the BH, there is evidence of partial alignment, as the inclination angle decreases with radius in this regime. Standing shocks also emerged in proximity to the BH, roughly at ∼6 gravitational radii. We show that these shocks act to partially align the inner disk with the BH spin. The rate of alignment increases with increasing BH spin magnitude, but in all cases is insufficient to fully align the gas before it accretes. Additionally, we present a toy model of orbit crowding that can predict the location of the shocks in moderate-to-fast rotating BHs, illustrating a potential physical origin for the behavior seen in simulations—with possible applications in determining the positions of shocks in real misaligned astrophysical systems. 

Abstract Measuring the properties of black hole images has the potential to constrain deviations from general relativity on horizon scales. Of particular interest is the ellipticity of the ring that is sensitive to the underlying spacetime. In 2019, the Event Horizon Telescope (EHT) produced the first-ever image of a black hole on horizon scales. Here, we reanalyze the M87* EHT 2017 data using Bayesian imaging (BI) techniques, constructing a posterior of the ring shape. We find that BI recovers the true on-sky ring shape more reliably than the original imaging methods used in 2019. As a result, we find that M87*'s ring ellipticity is ${0.09}_{-0.06}^{+0.07}$and is consistent with the measured ellipticity from general relativistic magnetohydrodynamic simulations. 

Abstract We propose an analytic dual-cone accretion model for horizon-scale images of the cores of low-luminosity active galactic nuclei, including those observed by the Event Horizon Telescope (EHT). Our model is of synchrotron emission from an axisymmetric, magnetized plasma, constrained to flow within two oppositely oriented cones that are aligned with the black hole’s spin axis. We show this model can accurately reproduce images of a variety of time-averaged general relativistic magnetohydrodynamic simulations and that it accurately recovers the black hole spin, orientation, emission scale height, peak emission radius, and fluid flow direction from these simulations within a Bayesian inference framework using radio interferometric data. We show that nontrivial topologies in the images of relativistic accretion flows around black holes can result in nontrivial multimodal solutions when applied to observations with a sparse array, such as the EHT 2017 observations of M87*. The presence of these degeneracies underscores the importance of employing Bayesian techniques to adequately sample the posterior space for the interpretation of EHT measurements. We fit our model to the EHT observations of M87* and find a 95% highest posterior density interval for the mass-to-distance ratio ofθ_g∈ (2.84, 3.75)μas, and give an inclination ofθ_o∈ (11°, 24°). These new measurements are consistent with mass measurements from the EHT and stellar dynamical estimates and with the spin axis inclination inferred from properties of the M87* jet.