Bayesian Accretion Modeling: Axisymmetric Equatorial Emission in the Kerr Spacetime

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.

Recent observations by the Event Horizon Telescope (EHT) of supermassive black holes M87* and Sgr A* offer valuable insights into their space–time properties and astrophysical conditions. Utilizing a library of model images ($\sim 2$ million for Sgr A*) generated from general-relativistic magnetohydrodynamic (GRMHD) simulations, limited and coarse insights on key parameters such as black hole spin, magnetic flux, inclination angle, and electron temperature were gained. The image orientation and black hole mass estimates were obtained via a scoring and an approximate rescaling procedure. Lifting such approximations, probing the space of parameters continuously, and extending the parameter space of theoretical models is both desirable and computationally prohibitive with existing methods. To address this, we introduce a new Bayesian scheme that adaptively explores the parameter space of ray-traced, GRMHD models. The general relativistic radiative transfer code IPOLE is integrated with the EHT parameter estimation tool THEMIS. The pipeline produces a ray-traced model image from GRMHD data, computes predictions for very long baseline interferometric (VLBI) observables from the image for a specific VLBI array configuration and compares to data, thereby sampling the likelihood surface via a Markov chain Monte Carlo scheme. At this stage we focus on four parameters: accretion rate, electron thermodynamics, inclination, and source position angle. Our scheme faithfully recovers parameters from simulated VLBI data and accommodates time-variability via an inflated error budget. We highlight the impact of intrinsic variability on model fitting approaches. This work facilitates more informed inferences from GRMHD simulations and enables expansion of the model parameter space in a statistically robust and computationally efficient manner.

Accretion physics has become more important recently due to the detection of the first horizon-scale images of the supermassive black holes of M 87* and Sgr A* by the Event Horizon Telescope. General relativistic magnetohydrodynamic (GRMHD) simulations of magnetized accretion flows onto a Kerr black hole have been used to interpret them. However, further testing the theory of gravity by using horizon-scale images requires performing consistent GRMHD simulations in non-Kerr spacetime. In this paper, we revisited the hydrodynamical equilibrium solution of the Fishbone and Moncrief (FM) torus that can be used to study any stationary, axisymmetric, vacuum, or nonvacuum spacetime. Further, we check the stability of the FM torus in non-Kerr spacetime by general relativistic hydrodynamic simulations. We find that FM torus in non-Kerr spacetime is indeed stable under long-term evolution. We conclude that the generalized FM torus solution would be very useful for creating new GRMHD libraries in extended Kerr black holes.

Context. In the first two papers of this publication series, we present a comprehensive library of synthetic Event Horizon Telescope (EHT) observations and used this library to train and validate Bayesian neural networks for the parameter inference of accreting supermassive black hole systems. The considered models are ray-traced general relativistic magnetohydrodynamic (GRMHD) simulations of Sgr A* and M87*. Aims. In this work, we infer the best-fitting accretion and black hole parameters from 2017 EHT data and predict improvements that will come with future upgrades of the array. Methods. Compared to previous EHT analyses, we considered a substantially larger synthetic data library and the most complete set of information from the observational data. We made use of the Bayesian nature of the trained neural networks and apply bootstrapping of known systematics in the observational data to obtain parameter posteriors. Results. Within a wide GRMHD parameter space, we find M87* to be best described by a spin between 0.5 and 0.94 with a retrograde MAD accretion flow and strong synchrotron emission from the jet. Sgr A* has a high spin of ∼0.8–0.9 and a prograde accretion flow beyond the standard MAD/SANE models with a comparatively weak jet emission, seen at a ∼ 20°–40° inclination and ∼106°–137° position angle. While previous EHT analyses could rule out specific regions in the model parameter space considered here, we are able to obtain narrow parameter posteriors with our ZINGULARITY framework without being impacted by the unknown foreground Faraday screens and data calibration biases. We further demonstrate that the Africa Millimeter Telescope extension to the EHT will reduce parameter inference errors by a factor of three for non-Kerr models, enabling more robust tests of general relativity. Conclusions. Our results agree with multiwavelength constraints from the literature. It will be instructive to produce new GRMHD models with the inferred interpolated parameters for in depth model-data comparisons and to study their accretion rate plus jet power.

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.

Testing gravitational lensing effects by supermassive massive black holes with superstring theory metric: Astrophysical implications and EHT constraints

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.

The Event Horizon Telescope Collaboration (EHTC) observed the Galactic centre source Sagittarius A$^\ast$ (Sgr A$^{\ast }$) and used emission models primarily based on single ion temperature (1T) general relativistic magnetohydrodynamic (GRMHD) simulations. This predicted emission is strongly dependent on a modelled prescription of the ion-to-electron temperature ratio. The most promising models are magnetically arrested disc (MAD) states. However, nearly all MAD models exhibit larger temporal fluctuations in radiative 230 GHz emission compared to observations. This limitation possibly stems from the fact that the actual temperature ratio depends on microphysical dissipation, radiative processes, and other effects not captured in ideal fluid simulations. Therefore, we investigate the effects of two-temperature (2T) thermodynamics in MAD GRMHD simulations of Sgr A$^{\ast }$, where the temperatures of both species are evolved. We find that the 230 GHz synchrotron flux variability more closely matches historical observations when we include the 2T treatment compared to 1T simulations. For the low accretion rates of Sgr A$^{\ast }$, a common assumption is to neglect radiative cooling. However, we find that the radiative cooling of electrons – via synchrotron, inverse Compton, and bremsstrahlung processes – reduces the electron temperature in the inner disc, where the EHT observes, by about 10 per cent, which, in turn, decreases both the (sub)millimetre synchrotron flux and its temporal fluctuations compared to uncooled simulations.

Magnetic reconnection is a process that plays a critical role inplasma astrophysics by converting magnetic energy into plasmaparticle energy. Recently, Comisso and Asenjo demonstrated thatrapid magnetic reconnection within a black hole's ergosphere canefficiently extract energy from a rotating black hole. In thispaper, by considering a Kerr black hole in the MOdified gravity(MOG) framework, we investigate the impact of the MOG parameter α on the rotational energy extraction via theComisso-Asenjo process (CAP). To model energy extraction from supermassive black holes located in the center of galaxies, we set the value of α within the range inferred from the recent observation of Sgr A* by the Event Horizon Telescope (EHT). Ourresults indicate that the Kerr-MOG black hole is a more efficienthost for CAP-based rotational energy extraction compared to theKerr black hole, since it amplifies the power of energy extractionand efficiency of the plasma energization process. We show that,from the energy extraction viewpoint, the CAP is more efficientthan the Blandford-Znajek process (BZP). The latter is anothermagnetic field-based energy extraction model which is widelybelieved to be an engine for powering the high-energyastrophysics jets emerging from the supermassive black holes atactive galactic nuclei. In particular, we show that the ratio ofthe energy extraction power of CAP to BZP in the presence of theMOG parameter is greater than that of the Kerr black hole. Ourresults promise this phenomenological message that theMOG-induced correction on the Kerr black hole background plays animportant role in favor of energy extraction via the CAP.

The Event Horizon Telescope (EHT) collaboration has produced the first resolved images of the supermassive black holes at the centre of our galaxy and at the centre of the elliptical galaxy M87. As both technology and analysis pipelines improve, it will soon become possible to produce spectral index maps of black hole accretion flows on event horizon scales. In this work, we predict spectral index maps of both M87* and Sgr A* by applying the general relativistic radiative transfer (GRRT) code ipole to a suite of general relativistic magnetohydrodynamic (GRMHD) simulations. We analytically show that the spectral index increases with increasing magnetic field strength, electron temperature, and optical depth. Consequently, spectral index maps grow more negative with increasing radius in almost all models, since all of these quantities tend to be maximized near the event horizon. Additionally, photon ring geodesics exhibit more positive spectral indices, since they sample the innermost regions of the accretion flow with the most extreme plasma conditions. Spectral index maps are sensitive to highly uncertain plasma heating prescriptions (the electron temperature and distribution function). However, if our understanding of these aspects of plasma physics can be tightened, even the spatially unresolved spectral index around 230 GHz can be used to discriminate between models. In particular, Standard and Normal Evolution (SANE) flows tend to exhibit more negative spectral indices than Magnetically Arrested Disc (MAD) flows due to differences in the characteristic magnetic field strength and temperature of emitting plasma.

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.

The Event Horizon Telescope (EHT) collaboration recently unveiled the first image of the supermassive black hole M87*, which exhibited a ring of angular diameter θ d = 42 ± 3 μas, a circularity deviation of ΔC ≤ 0.1, and also inferred a black hole mass of M = (6.5 ± 0.7) × 109 M ⊙. This provides a new window onto tests of theories of gravity in the strong-field regime, including probes of violations of the no-hair theorem. It is widely believed that the Kerr metric describes astrophysical black holes, as encapsulated in the critical but untested no-hair theorem. Modeling Horndeski gravity black holes—with an additional hair parameter h besides the mass M and spin a of the Kerr black hole—as the supermassive black hole M87*, we observe that to be a viable astrophysical black hole candidate, the EHT result constrains the (a, h) parameter space. However, a systematic bias analysis indicates that rotating Horndeski black hole shadows may or may not capture Kerr black hole shadows, depending on the parameter values; the latter is the case over a substantial part of the constrained parameter space, allowing Horndeski gravity and general relativity to be distinguishable in the said space, and opening up the possibility of potential modifications to the Kerr metric.

Some apparently quiescent supermassive black holes (BHs) at centers of galaxies show quasi-periodic eruptions (QPEs) in the X-ray band, the nature of which is still unknown. A possible origin for the eruptions is an accretion disk. However, the properties of such disks are restricted by the timescales of recurrence and the duration of the flares. In this work, we test the possibility that the temporal properties of known QPEs can be explained by accretion from a compact accretion disk with an outer radius out g and we focus on a particular object, GSN 069. We ran several 3D general relativistic magnetohydrodynamic (GRMHD) simulations with the H-AMR code of thin and thick disks and studied how the initial disk parameters such as thickness, magnetic field configuration, magnetization, and Kerr parameter affect the observational properties of QPEs. We show that accretion onto a slowly rotating BH through a small, moderately thin accretion disk with an initially low plasma beta can explain the observed time between outbursts and the lack of evidence for a variable jet emission. In order to form such a disk, the accreting matter should have a low net angular momentum. A potential source for such low angular momentum matter with a quasi-periodic feeding mechanism might be a tight binary of wind-launching stars. Apart from their primary application, our results can also be useful for general studies of systems with small accretion disks, in which evolution occurs very rapidly so that the disks cannot be considered stationary. For such systems, it is important to understand how the initial conditions affect the results.