First Sagittarius A* Event Horizon Telescope Results. IV. Variability, Morphology, and Black Hole Mass

In this paper we quantify the temporal variability and image morphology of the horizon-scale emission from Sgr A*, as observed by the EHT in 2017 April at a wavelength of 1.3 mm. We find that the Sgr A* data exhibit variability that exceeds what can be explained by the uncertainties in the data or by the effects of interstellar scattering. The magnitude of this variability can be a substantial fraction of the correlated flux density, reaching $\sim$100\% on some baselines. Through an exploration of simple geometric source models, we demonstrate that ring-like morphologies provide better fits to the Sgr A* data than do other morphologies with comparable complexity. We develop two strategies for fitting static geometric ring models to the time-variable Sgr A* data; one strategy fits models to short segments of data over which the source is static and averages these independent fits, while the other fits models to the full dataset using a parametric model for the structural variability power spectrum around the average source structure. Both geometric modeling and image-domain feature extraction techniques determine the ring diameter to be $51.8 \pm 2.3$ $\mu$as (68\% credible intervals), with the ring thickness constrained to have an FWHM between $\sim$30\% and 50\% of the ring diameter. To bring the diameter measurements to a common physical scale, we calibrate them using synthetic data generated from GRMHD simulations. This calibration constrains the angular size of the gravitational radius to be $4.8_{-0.7}^{+1.4}$ \mathrm{\mu as}, which we combine with an independent distance measurement from maser parallaxes to determine the mass of Sgr A* to be $4.0_{-0.6}^{+1.1} \times 10^6$ M$_{\odot}$.Comment: 65 pages, 35 figures, published in The Astrophysical Journal Letters on May 12, 2022. See the published paper for the full authors lis

First M87 Event Horizon Telescope Results. IX. Detection of Near-horizon Circular Polarization

Event Horizon Telescope (EHT) observations have revealed a bright ring of emission around the supermassive black hole at the center of the M87 galaxy. EHT images in linear polarization have further identified a coherent spiral pattern around the black hole, produced from ordered magnetic fields threading the emitting plasma. Here, we present the first analysis of circular polarization using EHT data, acquired in 2017, which can potentially provide additional insights into the magnetic fields and plasma composition near the black hole. Interferometric closure quantities provide convincing evidence for the presence of circularly polarized emission on event-horizon scales. We produce images of the circular polarization using both traditional and newly developed methods. All methods find a moderate level of resolved circular polarization across the image ($\langle|v|\rangle < 3.7\%$), consistent with the low image-integrated circular polarization fraction measured by the ALMA array ($|v_{\rm int}| < 1\%$). Despite this broad agreement, the methods show substantial variation in the morphology of the circularly polarized emission, indicating that our conclusions are strongly dependent upon the imaging assumptions because of the limited baseline coverage, uncertain telescope gain calibration, and weakly polarized signal. We include this upper limit in an updated comparison to general relativistic magnetohydrodynamic (GRMHD) simulation models. This analysis reinforces the previously reported preference for magnetically arrested accretion flow models. We find that most simulations naturally produce a low level of circular polarization consistent with our upper limit, and that Faraday conversion is likely the dominant production mechanism for circular polarization at 230 GHz in M87*.Comment: 47 pages, 31 figures, published in The Astrophysical Journal Letters on Nov. 8, 2023. See the published paper for the full authors lis

Polarimetric Geometric Modeling for mm-VLBI Observations of Black Holes

The Event Horizon Telescope (EHT) is a millimeter very long baseline interferometry (VLBI) array that has imaged the apparent shadows of the supermassive black holes M87* and Sagittarius A*. Polarimetric data from these observations contain a wealth of information on the black hole and accretion flow properties. In this work, we develop polarimetric geometric modeling methods for mm-VLBI data, focusing on approaches that fit data products with differing degrees of invariance to broad classes of calibration errors. We establish a fitting procedure using a polarimetric "m-ring" model to approximate the image structure near a black hole. By fitting this model to synthetic EHT data from general relativistic magnetohydrodynamic models, we show that the linear and circular polarization structure can be successfully approximated with relatively few model parameters. We then fit this model to EHT observations of M87* taken in 2017. In total intensity and linear polarization, the m-ring fits are consistent with previous results from imaging methods. In circular polarization, the m-ring fits indicate the presence of event-horizon-scale circular polarization structure, with a persistent dipolar asymmetry and orientation across several days. The same structure was recovered independently of observing band, used data products, and model assumptions. Despite this broad agreement, imaging methods do not produce similarly consistent results. Our circular polarization results, which imposed additional assumptions on the source structure, should thus be interpreted with some caution. Polarimetric geometric modeling provides a useful and powerful method to constrain the properties of horizon-scale polarized emission, particularly for sparse arrays like the EHT.Comment: 34 pages, 15 figures, published in The Astrophysical Journal Letter

Quantitative symmetry breaking of groundstates for a class of weighted Emden–Fowler equations

We prove that symmetrybreaking occurs in dimensions N ≥ 3 for the groundstate solutions to a class of Emden-Fowler equa-tions on the unit ball, with Dirichlet boundary conditions. We show that this phenomenon occurs forlarge values of a certain exponent for a radial weight function appearing in the equation. The problemreads as a possibly large perturbation of the classical H ́enon equation. In particular we consider aweight function having a spherical shell of zeroes centred at the origin and of radius R. A quantitativecondition on R for this phenomenon to occur is given by means of universal constants, such as thebest constant for the subcritical Sobolev embedding

Observing---and Imaging---Active Galactic Nuclei with the Event Horizon Telescope

Originally developed to image the shadow region of the central black hole in Sagittarius A* and in the nearby galaxy M87, the Event Horizon Telescope (EHT) provides deep, very high angular resolution data on other AGN sources too. The challenges of working with EHT data have spurred the development of new image reconstruction algorithms. This work briefly reviews the status of the EHT and its utility for observing AGN sources, with emphasis on novel imaging techniques that offer the promise of better reconstructions at 1.3 mm and other wavelengths.Comment: 10 pages, proceedings contribution for Blazars through Sharp Multi-Wavelength Eyes, submitted to Galaxie

First M87 Event Horizon Telescope Results and the Role of ALMA

In April 2019, the Event Horizon Telescope (EHT) collaboration revealed the first image of the candidate super-massive black hole (SMBH) at the centre of the giant elliptical galaxy Messier 87 (M87). This event-horizon-scale image shows a ring of glowing plasma with a dark patch at the centre, which is interpreted as the shadow of the black hole. This breakthrough result, which represents a powerful confirmation of Einstein's theory of gravity, or general relativity, was made possible by assembling a global network of radio telescopes operating at millimetre wavelengths that for the first time included the Atacama Large Millimeter/ submillimeter Array (ALMA). The addition of ALMA as an anchor station has enabled a giant leap forward by increasing the sensitivity limits of the EHT by an order of magnitude, effectively turning it into an imaging array. The published image demonstrates that it is now possible to directly study the event horizon shadows of SMBHs via electromagnetic radiation, thereby transforming this elusive frontier from a mathematical concept into an astrophysical reality. The expansion of the array over the next few years will include new stations on different continents - and eventually satellites in space. This will provide progressively sharper and higher-fidelity images of SMBH candidates, and potentially even movies of the hot plasma orbiting around SMBHs. These improvements will shed light on the processes of black hole accretion and jet formation on event-horizon scales, thereby enabling more precise tests of general relativity in the truly strong field regime.Comment: 11 pages + cover page, 6 figure