Black Hole Polarimetry. II. The Connection between Spin and Polarization

The Event Horizon Telescope (EHT) Collaboration has recently published the first horizon-scale images of the supermassive black holes M87* and Sgr A* and provided some first information on the physical conditions in their vicinity. The comparison between the observations and the three-dimensional general relativistic magnetohydrodynamic (GRMHD) simulations has enabled the EHT to set initial constraints on the properties of these black hole spacetimes. However, accurately distinguishing the properties of the accretion flow from those of the spacetime, most notably, the black hole mass and spin, remains challenging because of the degeneracies the emitted radiation suffers when varying the properties of the plasma and those of the spacetime. The next-generation EHT (ngEHT) observations are expected to remove some of these degeneracies by exploring the complex interplay between the disk–jet dynamics, which represents one of the most promising tools for extracting information on the black hole spin. By using GRMHD simulations of magnetically arrested disks and general relativistic radiative transfer (GRRT) calculations of the emitted radiation, we have studied the properties of the jet and the accretion disk dynamics on spatial scales that are comparable with the horizon. In this way, we are able to highlight that the radial and azimuthal dynamics of the jet are well correlated with the black hole spin. Based on the resolution and image reconstruction capabilities of the ngEHT observations of M87*, we can assess the detectability and associated uncertainty of this correlation. Overall, our results serve to assess the prospects for constraining the black hole spin with future EHT observations.

The M87 jet is extensively examined by utilizing general relativistic magnetohydrodynamic (GRMHD) simulations, as well as the steady axisymmetric force-free electrodynamic (FFE) solution. Quasi-steady funnel jets are obtained in GRMHD simulations up to the scale of ∼100 gravitational radii (r g) for various black hole (BH) spins. As is known, the funnel edge is approximately determined by the following equipartitions: (i) the magnetic and rest-mass energy densities and (ii) the gas and magnetic pressures. Our numerical results give an additional factor that they follow the outermost parabolic streamline of the FFE solution, which is anchored to the event horizon on the equatorial plane. We also show that the matter-dominated, nonrelativistic corona/wind plays a dynamical role in shaping the funnel jet into the parabolic geometry. We confirm a quantitative overlap between the outermost parabolic streamline of the FFE jet and the edge of the jet sheath in very long baseline interferometry (VLBI) observations at ∼(101–105)r g, suggesting that the M87 jet is likely powered by the spinning BH. Our GRMHD simulations also indicate a lateral stratification of the bulk acceleration (i.e., the spine-sheath structure), as well as an emergence of knotty superluminal features. The spin characterizes the location of the jet stagnation surface inside the funnel. We suggest that the limb-brightened feature could be associated with the nature of the BH-driven jet, if the Doppler beaming is a dominant factor. Our findings can be examined with (sub)millimeter VLBI observations, giving a clue for the origin of the M87 jet.

The Event Horizon Telescope (EHT) has unveiled the horizon-scale radiation properties of Sagittarius A* (Sgr A*), the supermassive black hole at the center of our galaxy, providing a novel platform for testing gravitational theories by comparing observations with theoretical models. A key next step is to investigate the nature of accretion flows and spacetime structures near black holes by analyzing the time variability observed in EHT data alongside general relativistic magnetohydrodynamic (GRMHD) simulations. We explored the dynamics of accretion flows in spherically symmetric black hole spacetimes with deviations from general relativity utilizing two dimensional GRMHD simulations based on the Rezzolla–Zhidenko parameterized spacetime. This study marks the first systematic investigation into how variability amplitudes in light curves, derived from non-Kerr GRMHD simulations, depend on deviations from the Schwarzschild spacetime. The deviation parameters are consistent with the constraints from weak gravitational fields and the size of Sgr A*’s black hole shadow. We find that the dynamics of accretion flows systematically depend on these parameters. In spacetimes with a deeper gravitational potential, fluid and Alfvén velocities consistently decrease relative to the Schwarzschild metric, indicating weaker dynamical behavior. We also examined the influence of spacetime deviations on radiation properties by computing luminosity fluctuations at 230 GHz using general relativistic radiative transfer simulations, in line with EHT observations. The amplitude of these fluctuations exhibits a systematic dependence on the deviation parameters, decreasing for deeper gravitational potentials compared to the Schwarzschild metric. These features are validated using one of the theoretically predicted metrics, the Hayward metric, a model that describes nonsingular black holes. This characteristic is expected to have similar effects in more comprehensive simulations that include more realistic accretion disk models and electron cooling in the future, potentially aiding in distinguishing black hole solutions that explain the variability of Sgr A*.

The Event Horizon Telescope (EHT) has mapped the central compact radio source of the elliptical galaxy M87 at 1.3 mm with unprecedented angular resolution. Here we consider the physical implications of the asymmetric ring seen in the 2017 EHT data. To this end, we construct a large library of models based on general relativistic magnetohydrodynamic (GRMHD) simulations and synthetic images produced by general relativistic ray tracing. We compare the observed visibilities with this library and confirm that the asymmetric ring is consistent with earlier predictions of strong gravitational lensing of synchrotron emission from a hot plasma orbiting near the black hole event horizon. The ring radius and ring asymmetry depend on black hole mass and spin, respectively, and both are therefore expected to be stable when observed in future EHT campaigns. Overall, the observed image is consistent with expectations for the shadow of a spinning Kerr black hole as predicted by general relativity. If the black hole spin and M87’s large scale jet are aligned, then the black hole spin vector is pointed away from Earth. Models in our library of non-spinning black holes are inconsistent with the observations as they do not produce sufficiently powerful jets. At the same time, in those models that produce a sufficiently powerful jet, the latter is powered by extraction of black hole spin energy through mechanisms akin to the Blandford-Znajek process. We briefly consider alternatives to a black hole for the central compact object. Analysis of existing EHT polarization data and data taken simultaneously at other wavelengths will soon enable new tests of the GRMHD models, as will future EHT campaigns at 230 and 345 GHz.

Context. In the 2017 observation campaign, the Event Horizon Telescope (EHT) for the first time gathered enough data to image the shadow of the supermassive black hole (SMBH) in M 87. Most recently in 2022, the EHT has published the results for the SMBH at the Galactic Center, Sgr A*. In the vicinity of black holes, the influence of strong gravity, plasma physics, and emission processes govern the behavior of the system. Since observations such as those carried out by the EHT are not yet able to unambiguously constrain models for astrophysical and gravitational properties, it is imperative to explore the accretion models, particle distribution function, and description of the spacetime geometry. Our current understanding of these properties is often based on the assumption that the spacetime is well described by the Kerr solution to general relativity, combined with basic emission and accretion models. We explore alternative models for each property performing general relativistic magnetohydrodynamic (GRMHD) and general relativistic radiative transfer (GRRT) simulations. Aims. By choosing a Kerr solution to general relativity and a dilaton solution to Einstein-Maxwell-dilaton-axion gravity as exemplary black hole background spacetimes, we aim to investigate the influence of accretion and emission models on the ability to distinguish black holes in two theories of gravity. Methods. We carried out 3D GRMHD simulations of both black holes, matched at their innermost stable circular orbit, in two distinct accretion scenarios: standard and normal evolution (SANE) and a magnetically arrested disk (MAD). Using GRRT calculations, we modeled the thermal synchrotron emission and subsequently applied a nonthermal electron distribution function, exploring representative parameters to compare with multiwavelength observations. We further considered Kerr and dilaton black holes matched at their unstable circular photon orbits, as well as their event horizons. Results. From the comparison of GRMHD simulations, we find a wider jet opening angle and higher magnetization in the Kerr spacetime. Generally, MAD models show larger magnetic flux than SANE, as is expected. The GRRT image morphology shows differences between spacetimes due to the Doppler boosting in the Kerr spacetime. However, from pixel-by-pixel comparison, we find that in a real-world observation an imaging approach may not be sufficient to distinguish the spacetimes using the current finite resolution of the EHT. From multiwavelength emission and spectral index analysis, we find that the accretion model and spacetime have only a small impact on the spectra compared to the choice of the emission model. Matching the black holes at the unstable photon orbit or the event horizon further decreases the observed differences.

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.

Blazars are among the most powerful astrophysical objects in the universe. Their multiwavelength emission displays traces of non-thermal radiation whose origin is not yet fully understood, and it is dominated by the presence of a relativistic jet. Blazar emission is characterized by high-variability across different wavelenghts, which is associated with a spinning black hole and relativistic effects in the jet. Using blazars as a laboratory, in this thesis we set out to answer a few fundamental questions, such as where and how does the non-thermal emission in blazars originate?, how robust are theoretical models in explaining the efficiency of jet formation?, and can these models accurately predict the spins of the black holes associated with these jets? To answer these questions, we employ two different methods: -ray observations and general relativistic magnetohydrodynamic (GRMHD) simulations. In the first study, we used the luminosities of a class of blazars to calculate the jet efficiency, and we estimated the black holes spins. We found a mean spin of a * 0.84 +0.11 -0.25 , with a lower limit estimated at a lower * 0.59. These results show compatibility with cosmological merger-driven evolution of SMBHs which support rapidly rotating black holes. Moreover, we found a correlation between the black hole mass and the -ray luminosity L . In the second study, we used GRMHD simulations and applied an algorithm to identify the regions in which non-thermal emission must occur. We ran simulations with different initial conditions, varying the magnetic field topology and black hole spin, and we found these regions in all simulations. In particular, we found that this also occurs in the jet for some simulations, thus suggesting i I'm not sure if having taken an Introduction to Astronomy course during my first year as an undergrad counts as having some experience in Astronomy, but this is all Astronomy I had when I decided to switch after a Masters in Theoretical Physics. As it turns out, I ended up doing Theoretical Astrophysics, and the whole transition was smoother than I had anticipated.

Using very long baseline interferometry, the Event Horizon Telescope (EHT) collaboration has resolved the shadows of two supermassive black holes. Model comparison is traditionally performed in image space, where imaging algorithms introduce uncertainties in the recovered structure. Here, we develop a deep learning framework to infer the physical parameters of General Relativistic Magnetohydrodynamic (GRMHD) simulations directly from visibility space data. By working in the native domain of the interferometer, our method avoids introducing potential errors and biases from image reconstruction. First, we train and validate our framework on synthetic data derived from GRMHD simulations that vary in magnetic field state, spin, and Rhigh. Applying these models to the real data obtained during the 2017 EHT campaign, and only considering total intensity, we do not derive meaningful constraints on either spin or Rhigh. At present, our method is limited both by theoretical uncertainties in the GRMHD simulations and variations between snapshots of the same underlying physical model. However, we demonstrate that spin and Rhigh could be recovered using this framework through continuous monitoring of our sources, which mitigates variations due to turbulence. In future work, we anticipate that including spectral or polarimetric information will greatly improve the performance of this framework.

The X-ray spectra of accretion discs of eight stellar-mass black holes have been analyzed to date using the thermal continuum fitting method, and the spectral fits have been used to estimate the spin parameters of the black holes. However, the underlying model used in this method of estimating spin is the general relativistic thin-disc model of Novikov & Thorne, which is only valid for razor-thin discs. We therefore expect errors in the measured values of spin due to inadequacies in the theoretical model. We investigate this issue by computing spectra of numerically calculated models of thin accretion discs around black holes, obtained via three-dimensional general relativistic magnetohydrodynamic (GRMHD) simulations. We apply the continuum fitting method to these computed spectra to estimate the black hole spins and check how closely the values match the actual spin used in the GRMHD simulations. We find that the error in the dimensionless spin parameter is up to about 0.2 for a non-spinning black hole, depending on the inclination. For black holes with spins of 0.7, 0.9 and 0.98, the errors are up to about 0.1, 0.03 and 0.01 respectively. These errors are comparable to or smaller than those arising from current levels of observational uncertainty. Furthermore, we estimate that the GRMHD simulated discs from which these error estimates are obtained correspond to effective disc luminosities of about 0.4-0.7 Eddington, and that the errors will be smaller for discs with luminosities of 0.3 Eddington or less, which are used in the continuum-fitting method. We thus conclude that use of the Novikov-Thorne thin-disc model does not presently limit the accuracy of the continuum-fitting method of measuring black hole spin.

We provide a semi-analytic comparison between the Blandford-Znajek (BZ) and the magnetic reconnection power for accreting black holes in the curved spacetime of a rotating black hole. Our main result is that for a realistic range of astrophysical parameters, the reconnection power may compete with the BZ power. The field lines anchored close to or on the black hole usually evolve to open field lines in general relativistic magnetohydrodynamic (GRMHD) simulations. The BZ power is dependent on the black hole spin while magnetic reconnection power is independent of it for the force-free magnetic configuration with open field lines adopted in our theoretical study. This has obvious consequences for the time evolution of such systems particularly in the context of black hole X-ray binary state transitions. Our results provide analytical justification of the results obtained in GRMHD simulations.

We present a set of 11 two-temperature, radiative, general relativistic magnetohydrodynamic simulations of the black hole M87* in the magnetically arrested state, surveying different values of the black hole spin $a_*$. Our 3-D simulations self-consistently evolve the temperatures of separate electron and ion populations under the effects of adiabatic compression/expansion, viscous heating, Coulomb coupling, and synchrotron, bremsstrahlung, and inverse Compton radiation. We adopt a subgrid heating prescription from gyrokinetic simulations of plasma turbulence. Our simulations have accretion rates $\dot{M}=(0.5-1.5)\times 10^{-6}\dot{M}_{\rm Edd}$ and radiative efficiencies $\epsilon _{\rm rad}=$ 3–35 per cent. We compare our simulations to a fiducial set of otherwise identical single-fluid general relativistic magnetohydrodynamic (GRMHD) simulations and find no significant changes in the outflow efficiency or black hole spin-down parameter. Our simulations produce an effective adiabatic index for the two-temperature plasma of $\Gamma _{\rm gas}\approx 1.55$, larger than the $\Gamma _{\rm gas}=13/9$ value often adopted in single-fluid GRMHD simulations. We find moderate ion-to-electron temperature ratios in the 230 GHz emitting region of $R=T_{\rm i}/T_{\rm e}\,{\approx }\,5$. While total intensity 230 GHz images from our simulations are consistent with Event Horizon Telescope (EHT) results, our images have significantly more beam-scale linear polarization ($\langle |m|\rangle \approx 30~{{\rm per\ cent}}$) than is observed in EHT images of M87* ($\langle |m|\rangle \lt 10~{{\rm per\ cent}}$). We find a trend of the average linear polarization pitch angle $\angle \beta _2$ with black hole spin consistent with what is seen in single-fluid GRMHD simulations, and we provide a simple fitting function for $\angle \beta _2(a_*)$ motivated by the wind-up of magnetic field lines by black hole spin in the Blandford–Znajek mechanism.

We present a new approach for stably evolving general relativistic magnetohydrodynamic (GRMHD) simulations in regions where the magnetization $\sigma =b^2/\rho c^2$ becomes large. GRMHD codes typically struggle to evolve plasma above $\sigma \approx 100$ in simulations of black hole accretion. To ensure stability, GRMHD codes will inject mass density artificially to the simulation as necessary to keep the magnetization below a ceiling value $\sigma _{\rm max}$. We propose an alternative approach where the simulation transitions to solving the equations of general relativistic force-free electrodynamics (GRFFE) above a magnetization $\sigma _{\rm trans}$. We augment the GRFFE equations in the highly magnetized region with approximate equations to evolve the decoupled field-parallel velocity and plasma energy density. Our hybrid scheme is explicit and easily added to the framework of standard-volume GRMHD codes. We present a variety of tests of our method, implemented in the GRMHD code koral, and we show results from a 3D hybrid GRMHD + GRFFE simulation of a magnetically arrested disc (MAD) around a spinning black hole. Our hybrid MAD simulation closely matches the average properties of a standard GRMHD MAD simulation with the same initial conditions in low magnetization regions, but it achieves a magnetization $\sigma \approx 10^6$ in the evacuated jet funnel. We present simulated horizon-scale images of both simulations at 230 GHz with the black hole mass and accretion rate matched to M87*. Images from the hybrid simulation are less affected by the choice of magnetization cut-off $\sigma _{\rm cut}$ imposed in radiative transfer than images from the standard GRMHD simulation.

Images of black holes encode both astrophysical and gravitational properties. Detecting highly lensed features in images can differentiate between these two effects. We present an accretion disk emission model coupled to the Adaptive Analytical Ray Tracing (AART) code that allows a fast parameter space exploration of black hole photon ring images produced from synchrotron emission from 10 to 670 GHz. As an application, we systematically study several disk models and compute their total flux density, average radii, and optical depth. The model parameters are chosen around fiducial values calibrated to general relativistic magnetohydrodynamic (GRMHD) simulations and observations of M87*. For the parameter space studied, we characterize the transition between optically thin and thick regimes and the frequency at which the first photon ring is observable. Our results highlight the need for careful definitions of photon ring radius in the image domain, as in certain models the highly lensed photon ring is dimmer than the direct emission at certain angles. We find that at low frequencies the ring radii are set by the electron temperature, while at higher frequencies the magnetic field strength plays a more significant role, demonstrating how multifrequency analysis can also be used to infer plasma parameters. Lastly, we show how our implementation can qualitatively reproduce multifrequency black hole images from GRMHD simulations when adding time variability to our disk model through Gaussian random fields. This approach provides a new method for simulating observations from the Event Horizon Telescope and the proposed Black Hole Explorer space mission.

Accretion of magnetized gas on compact astrophysical objects such as black holes (BHs) has been successfully modeled using general relativistic magnetohydrodynamic (GRMHD) simulations. These simulations have largely been performed in the Kerr metric, which describes the spacetime of a vacuum and stationary spinning BH in general relativity (GR). The simulations have revealed important clues to the physics of accretion flows and jets near the BH event horizon and have been used to interpret recent Event Horizon Telescope images of the supermassive BHs M87* and Sgr A*. The GRMHD simulations require the spacetime metric to be given in horizon-penetrating coordinates such that all metric coefficients are regular at the event horizon. Only a few metrics, notably the Kerr metric and its electrically charged spinning analog, the Kerr–Newman metric, are currently available in such coordinates. We report here horizon-penetrating forms of a large class of stationary, axisymmetric, spinning metrics. These can be used to carry out GRMHD simulations of accretion on spinning, nonvacuum BHs and non-BHs within GR, as well as accretion on spinning objects described by non-GR metric theories of gravity.

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 ∼10% of the true mass and within ∼10° 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.