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The Event Horizon Telescope (EHT) has produced images of M87* and Sagittarius A*, and will soon produce time sequences of images, or movies. In anticipation of this, we describe a technique to measure the rotation rate, or pattern speed Ω_p, from movies using an autocorrelation technique. We validate the technique on Gaussian random field models with a known rotation rate and apply it to a library of synthetic images of Sgr A* based on general relativistic magnetohydrodynamics simulations. We predict that EHT movies will have Ω_p≈ 1° perGMc⁻³, which is of order 15% of the Keplerian orbital frequency in the emitting region. We can plausibly attribute the slow rotation seen in our models to the pattern speed of inward-propagating spiral shocks. We also find that Ω_pdepends strongly on inclination. Application of this technique will enable us to compare future EHT movies with the clockwise rotation of Sgr A* seen in near-infrared flares by GRAVITY. Pattern speed analysis of future EHT observations of M87* and Sgr A* may also provide novel constraints on black hole inclination and spin, as well as an independent measurement of black hole mass.

 

The variance and fractional variance on a fixed time window (variously known as “rms percent” or “modulation index”) are commonly used to characterize the variability of astronomical sources. We summarize properties of this statistic for a Gaussian process.

 

We develop a “dual-cone” model for millimeter wavelength emission near a spinning black hole. The model consists of optically thin, luminous cones of emission, centered on the spin axis, which are meant to represent jet walls. The resulting image is dominated by a thin ring. We first consider the effect of the black hole’s spin on the image and show that the dominant effect is to displace the ring perpendicular to the projection of the spin axis on the sky by$2a_{*}\sin i+\mathit{}(a_{*}^3)$. This effect is lower order ina_*than changes in the shape and size of the photon ring itself but is undetectable without a positional reference. We then show that the centerline of the jet can provide a suitable reference: its location is exactly independent of spin if the observer is outside the cone and nearly independent of spin if the observer is inside the cone. If astrophysical uncertainties can be controlled, then spin displacement is large enough to be detectable by future space very long baseline interferometry missions. Finally, we consider ring substructure in the dual-cone model and show that features in total intensity are not universal and depend on the cone-opening angle.

 

The centers of our Galaxy and the nearby Messier 87 are known to contain supermassive black holes, which support accretion flows that radiate across the electromagnetic spectrum. Although the composition of the accreting gas is unknown, it is likely a mix of ionized hydrogen and helium. We use a simple analytic model and a suite of numerical general relativistic magnetohydrodynamic accretion simulations to study how polarimetric images and spectral energy distributions of the source are influenced by the hydrogen/helium content of the accreting matter. We aim to identify general trends rather than make quantitatively precise predictions, since it is not possible to fully explore the parameter space of accretion models. If the ion-to-electron temperature ratio is fixed, then increasing the helium fraction increases the gas temperature; to match the observational flux density constraints, the number density of electrons and magnetic field strengths must therefore decrease. In our numerical simulations, emission shifts from regions of low to high plasmaβ—both altering the morphology of the image and decreasing the variability of the light curve—especially in strongly magnetized models with emission close to the midplane. In polarized images, we find that the model gas composition influences the degree to which linear polarization is (de)scrambled and therefore affects estimates for the resolved linear polarization fraction. We also find that the spectra of helium-composition flows peak at higher frequencies and exhibit higher luminosities. We conclude that gas composition may play an important role in predictive models for black hole accretion.

 

The Event Horizon Telescope (EHT) has released analyses of reconstructed images of horizon-scale millimeter emission near the supermassive black hole at the center of the M87 galaxy. Parts of the analyses made use of a large library of synthetic black hole images and spectra, which were produced using numerical general relativistic magnetohydrodynamics fluid simulations and polarized ray tracing. In this article, we describe thePATOKApipeline, which was used to generate the Illinois contribution to the EHT simulation library. We begin by describing the relevant accretion systems and radiative processes. We then describe the details of the three numerical codes we use,iharm,ipole, andigrmonty, paying particular attention to differences between the current generation of the codes and the originally published versions. Finally, we provide a brief overview of simulated data as produced byPATOKAand conclude with a discussion of limitations and future directions.

 

Gravitational lensing near a black hole is strong enough that light rays can circle the event horizon multiple times. Photons emitted in multiple directions at a single event, perhaps because of localized, impulsive heating of accreting plasma, take multiple paths to a distant observer. In the Kerr geometry, each path is associated with a distinct light travel time and a distinct arrival location in the image plane, producing black hole glimmer. This sequence of arrival times and locations uniquely encodes the mass and spin of the black hole and can be understood in terms of properties of bound photon orbits. We provide a geometrically motivated treatment of Kerr glimmer and evaluate it numerically for simple hot-spot models to show that glimmer can be measured in a finite-resolution observation. We discuss potential measurement methods and implications for tests of the Kerr hypothesis.

 

Abstract Interpretation of resolved polarized images of black holes by the Event Horizon Telescope (EHT) requires predictions of the polarized emission observable by an Earth-based instrument for a particular model of the black hole accretion system. Such predictions are generated by general relativistic radiative transfer (GRRT) codes, which integrate the equations of polarized radiative transfer in curved spacetime. A selection of ray-tracing GRRT codes used within the EHT Collaboration is evaluated for accuracy and consistency in producing a selection of test images, demonstrating that the various methods and implementations of radiative transfer calculations are highly consistent. When imaging an analytic accretion model, we find that all codes produce images similar within a pixel-wise normalized mean squared error (NMSE) of 0.012 in the worst case. When imaging a snapshot from a cell-based magnetohydrodynamic simulation, we find all test images to be similar within NMSEs of 0.02, 0.04, 0.04, and 0.12 in Stokes I , Q , U , and V , respectively. We additionally find the values of several image metrics relevant to published EHT results to be in agreement to much better precision than measurement uncertainties. 

Abstract We report on the observations of the quasar NRAO 530 with the Event Horizon Telescope (EHT) on 2017 April 5−7, when NRAO 530 was used as a calibrator for the EHT observations of Sagittarius A*. At z = 0.902, this is the most distant object imaged by the EHT so far. We reconstruct the first images of the source at 230 GHz, at an unprecedented angular resolution of ∼20 μ as, both in total intensity and in linear polarization (LP). We do not detect source variability, allowing us to represent the whole data set with static images. The images reveal a bright feature located on the southern end of the jet, which we associate with the core. The feature is linearly polarized, with a fractional polarization of ∼5%–8%, and it has a substructure consisting of two components. Their observed brightness temperature suggests that the energy density of the jet is dominated by the magnetic field. The jet extends over 60 μ as along a position angle ∼ −28°. It includes two features with orthogonal directions of polarization (electric vector position angle), parallel and perpendicular to the jet axis, consistent with a helical structure of the magnetic field in the jet. The outermost feature has a particularly high degree of LP, suggestive of a nearly uniform magnetic field. Future EHT observations will probe the variability of the jet structure on microarcsecond scales, while simultaneous multiwavelength monitoring will provide insight into the high-energy emission origin. 

Abstract The blazar J1924–2914 is a primary Event Horizon Telescope (EHT) calibrator for the Galactic center’s black hole Sagittarius A*. Here we present the first total and linearly polarized intensity images of this source obtained with the unprecedented 20 μ as resolution of the EHT. J1924–2914 is a very compact flat-spectrum radio source with strong optical variability and polarization. In April 2017 the source was observed quasi-simultaneously with the EHT (April 5–11), the Global Millimeter VLBI Array (April 3), and the Very Long Baseline Array (April 28), giving a novel view of the source at four observing frequencies, 230, 86, 8.7, and 2.3 GHz. These observations probe jet properties from the subparsec to 100 pc scales. We combine the multifrequency images of J1924–2914 to study the source morphology. We find that the jet exhibits a characteristic bending, with a gradual clockwise rotation of the jet projected position angle of about 90° between 2.3 and 230 GHz. Linearly polarized intensity images of J1924–2914 with the extremely fine resolution of the EHT provide evidence for ordered toroidal magnetic fields in the blazar compact core. 

Abstract The Event Horizon Telescope (EHT) observed the compact radio source, Sagittarius A* (Sgr A*), in the Galactic Center on 2017 April 5–11 in the 1.3 mm wavelength band. At the same time, interferometric array data from the Atacama Large Millimeter/submillimeter Array and the Submillimeter Array were collected, providing Sgr A* light curves simultaneous with the EHT observations. These data sets, complementing the EHT very long baseline interferometry, are characterized by a cadence and signal-to-noise ratio previously unattainable for Sgr A* at millimeter wavelengths, and they allow for the investigation of source variability on timescales as short as a minute. While most of the light curves correspond to a low variability state of Sgr A*, the April 11 observations follow an X-ray flare and exhibit strongly enhanced variability. All of the light curves are consistent with a red-noise process, with a power spectral density (PSD) slope measured to be between −2 and −3 on timescales between 1 minute and several hours. Our results indicate a steepening of the PSD slope for timescales shorter than 0.3 hr. The spectral energy distribution is flat at 220 GHz, and there are no time lags between the 213 and 229 GHz frequency bands, suggesting low optical depth for the event horizon scale source. We characterize Sgr A*’s variability, highlighting the different behavior observed just after the X-ray flare, and use Gaussian process modeling to extract a decorrelation timescale and a PSD slope. We also investigate the systematic calibration uncertainties by analyzing data from independent data reduction pipelines.