Event Horizon Telescope Observations Research Articles

Black hole shadows, photon rings, and lensing rings

The presence of a bright "photon ring" surrounding a dark "black hole shadow" has been discussed as an important feature of the observational appearance of emission originating near a black hole. We clarify the meaning and relevance of these heuristics with analytic calculations and numerical toy models. The standard usage of the term "shadow" describes the appearance of a black hole illuminated from all directions, including from behind the observer. A backlit black hole casts a somewhat larger shadow. Neither shadow heuristic is particularly relevant to understanding the appearance of emission originating near the black hole, where the emission profile and gravitational redshift play the dominant roles in determining the observed size of the central dark area. A photon ring results from light rays that orbit near the black hole before escaping to infinity, where they arrive near a ring-shaped "critical curve" on the image plane. Although the brightness can become arbitrarily large near this critical curve in the case of optically thin emitting matter, we show that the enhancement is only logarithmic, and hence is of no relevance to present observations. For optically thin emission from a geometrically thin or thick disk, photons that make only a fraction of an orbit will generically give rise to a much wider "lensing ring," which is a demagnified image of the back of the disk, superimposed on top of the direct emission. The lensing ring is centered at a radius ~5% larger than the photon ring and its width is ~0.5-1M. It can be relatively brighter by a factor of 2-3 and thus could provide a significant feature in high resolution images. Nevertheless, the characteristic features of the observed image are dominated by the location and properties of the emitting matter near the black hole. We comment on the recent M87* Event Horizon Telescope observations and mass measurement.

Constraints on Black Hole Jet Models Used As Diagnostic Tools of Event Horizon Telescope Observations of M87

Abstract Jet models of Event Horizon Telescope (EHT) data should also conform to the observed jet profiles just downstream. This study evaluates conformance of models of black hole (BH) jets to images of the innermost jet of M87. This is a basic test that should be passed before using them to perform a physical interpretation of EHT data. Recent 86 GHz very long baseline interferometry observations of M87 have revealed the morphology and size of the jet near its source (<65 M, or 0.06 lt-yr after correcting for the line of sight to the jet, where M is the BH mass in geometrized units) for the first time. Current transverse resolution indicates that this region is dominated by flux emanating from the edge of the jet. The observed inner jet profiles are compared to all existing published synthetic radio images constructed from “state of the art” 3D numerical simulations of the BH accretion system in M87. Despite efforts to produce the characteristic wide, edge-dominated jet, these models are too narrow (by a factor of ∼2) in the region 0.06–0.32 lt-yr from the source, even though the jets (spine and/or sheath) in the image plane might appear conformant farther downstream. Furthermore, the synthetic radio images are not edge dominated 0.06–0.32 lt-yr from the source, but spine dominated. Analyses that implement these models as physical diagnostics of EHT visibility amplitudes are therefore suspect. Thus, these inner-jet characteristics are important considerations before applying simulations to the EHT data.

First M87 Event Horizon Telescope Results. II. Array and Instrumentation

Abstract The Event Horizon Telescope (EHT) is a very long baseline interferometry (VLBI) array that comprises millimeter- and submillimeter-wavelength telescopes separated by distances comparable to the diameter of the Earth. At a nominal operating wavelength of ∼1.3 mm, EHT angular resolution (λ/D) is ∼25 μas, which is sufficient to resolve nearby supermassive black hole candidates on spatial and temporal scales that correspond to their event horizons. With this capability, the EHT scientific goals are to probe general relativistic effects in the strong-field regime and to study accretion and relativistic jet formation near the black hole boundary. In this Letter we describe the system design of the EHT, detail the technology and instrumentation that enable observations, and provide measures of its performance. Meeting the EHT science objectives has required several key developments that have facilitated the robust extension of the VLBI technique to EHT observing wavelengths and the production of instrumentation that can be deployed on a heterogeneous array of existing telescopes and facilities. To meet sensitivity requirements, high-bandwidth digital systems were developed that process data at rates of 64 gigabit s−1, exceeding those of currently operating cm-wavelength VLBI arrays by more than an order of magnitude. Associated improvements include the development of phasing systems at array facilities, new receiver installation at several sites, and the deployment of hydrogen maser frequency standards to ensure coherent data capture across the array. These efforts led to the coordination and execution of the first Global EHT observations in 2017 April, and to event-horizon-scale imaging of the supermassive black hole candidate in M87.

Two-temperature, Magnetically Arrested Disc simulations of the jet from the supermassive black hole in M87

We present two-temperature, radiative general relativistic magnetohydrodynamic simulations of Magnetically Arrested Discs (MAD) that launch powerful relativistic jets. The mass accretion rates of our simulations are scaled to match the luminosity of the accretion flow around the supermassive black hole in M87. We consider two sub-grid prescriptions for electron heating: one based on a Landau-damped turbulent cascade, and the other based on heating from trans-relativistic magnetic reconnection. The simulations produce jets with power on the order of the observed value for M87. Both simulations produce spectra that are consistent with observations of M87 in the radio, millimetre, and submillimetre. Furthermore, the predicted image core-shifts in both models at frequencies between 15 GHz and 86 GHz are consistent with observations. At 43 and 86 GHz, both simulations produce wide opening angle jets consistent with VLBI images. Both models produce 230~GHz images with distinct black hole shadows that are resolvable by the Event Horizon Telescope (EHT), although at a viewing angle of 17 degrees, the 230 GHz images are too large to match EHT observations from 2009 and 2012. The 230 GHz images from the simulations are dynamic on time-scales of months to years, suggesting that repeated EHT observations may be able to detect the motion of rotating magnetic fields at the event horizon.

Multi-wavelength torus–jet model for Sagittarius A*

Context. The properties of the accretion/ejection flow surrounding the supermassive central black hole of the Galaxy Sgr A* will be scrutinized by the new-generation instrument GRAVITY and the Event Horizon Telescope (EHT). Developing fast, robust, and simple models of such flows is therefore important and very timely. Aims. We want to model the quiescent emission of Sgr A* from radio to mid-infrared wavelengths, using thermal and nonthermal synchrotron. The radiation is emitted by the overlay of a magnetized compact torus close to the black hole, and a large-scale magnetized jet. We compare model spectra and images to the multi-wavelength observable constraints available to date. We simulate EHT observations at 1.3 mm of the best-fit model for different inclinations. methods. We use a simple analytic description for the geometry of the torus and jet. We model their emission by thermal synchrotron and κ-distribution synchrotron, respectively. We use relativistic ray tracing to compute simulated spectra and images, restricting our analysis to the Schwarzschild (zero spin) case. A best-fit is found by adjusting the simulated spectra to the latest observed data, and we check the consistency of our spectral best fits with the radio-image sizes and infrared spectral index constraints. We use the open-source eht-imaging library to generate EHT-reconstructed images. Results. We find perfect spectral fit ( χred2 ≈ 1) both for nearly face-on and nearly edge-on views. These best fits give parameter values very close to those found by the most recent numerical simulations, which are much more complex than our model. The intrinsic radio size of Sgr A* is found to be in reasonable agreement with the centimetric observed constraints. Our best-fit infrared spectral index is in perfect agreement with the latest constraints. Our emission region at 1.3 mm, although larger than the early-EHT Gaussian best fit, does contain bright features at the ≲40 μas scale. EHT-reconstructed images show that torus/jet-specific features persist after the reconstruction procedure, and that these features are sensitive to inclination. Conclusions. The main interest of our model is to provide a simple and fast model of the quiescent state of Sgr A*, which gives extremely similar results to those of state-of-the-art numerical simulations. Our model is easy to use and we publish all the material necessary to reproduce our spectra and images, meaning that anyone interested can use our results relatively straightforwardly. We hope that such a public tool will be useful in the context of the recent and near-future GRAVITY and EHT results.

Predictions of the pseudo-complex theory of gravity for EHT observations – I. Observational tests

Abstract A modified theory of gravity, avoiding singularities in the standard theory of gravitation, has been developed by Hess & Greiner, known as the pseudo-complex theory of gravitation. The pseudo-complex General Relativity (pc-GR) theory shows remarkable observational differences with respect to standard GR. The intensity profiles are significantly different between both theories, which is a rare phenomenon in astrophysics. This will allow robust tests of both theories using Event Horizon Telescope observations of the Galactic Centre. We also predict the time evolution of orbiting matter. In this paper we summarize the observational tests we have developed to date. The theory is described in the second paper of this series (referred to as paper II hereafter).

Probing the Innermost Accretion Flow Geometry of Sgr A* with Event Horizon Telescope

Abstract Upcoming Event Horizon Telescope (EHT) observations will provide a unique opportunity to reveal the innermost region of the radiative inefficient accretion flow (RIAF) around the Galactic black hole, Sgr A*. Depending on the flow dynamics and accumulated magnetic flux, the innermost region of an RIAF could have a quasi-spherical or disk-like geometry. Here we present a phenomenological model to investigate the characteristics of the black hole shadow images with different flow geometries, together with the effect of black hole spin and flow dynamics. The resulting image consists in general of two major components: a crescent, which may surround the funnel region of the black hole or the black hole itself, and a photon ring, which may be partially luminous and overlapped with the crescent component. Compared to a quasi-spherical flow case, a disk-like flow in the vicinity of a black hole exhibits the following image features: (i) due to less material near the funnel region, the crescent structure has a smaller size, and (ii) due to the combination of emission from the flow beside and behind the black hole, the crescent structure has a more irregular shape, and a less smooth brightness distribution. How these features can result in different observables for EHT observations is discussed.

Event Horizon Telescope observations as probes for quantum structure of astrophysical black holes

The need for a consistent quantum evolution for black holes has led to proposals that their semiclassical description is modified not just near the singularity, but at horizon or larger scales. If such modifications extend beyond the horizon, they influence regions accessible to distant observeration. Natural candidates for these modifications behave like metric fluctuations, with characteristic length and time scales set by the horizon radius. We investigate the possibility of using the Event Horizon Telescope to observe these effects, if they have a strength sufficient to make quantum evolution consistent with unitarity. We find that such quantum fluctuations can introduce a strong time dependence for the shape and size of the shadow that a black hole casts on its surrounding emission. For the black hole in the center of the Milky Way, detecting the rapid time variability of its shadow will require non-imaging timing techniques. However, for the much larger black hole in the center of the M87 galaxy, a variable black-hole shadow, if present with these parameters, would be readily observable in the individual snapshots that will be obtained by the Event Horizon Telescope.

GRMHD Simulations of Visibility Amplitude Variability for Event Horizon Telescope Images of Sgr A*

Abstract The Event Horizon Telescope will generate horizon scale images of the black hole in the center of the Milky Way, Sgr A*. Image reconstruction using interferometric visibilities rests on the assumption of a stationary image. We explore the limitations of this assumption using high-cadence disk- and jet-dominated GRMHD simulations of Sgr A*. We also employ analytic models that capture the basic characteristics of the images to understand the origin of the variability in the simulated visibility amplitudes. We find that, in all simulations, the visibility amplitudes for baselines oriented parallel and perpendicular to the spin axis of the black hole follow general trends that do not depend strongly on accretion-flow properties. This suggests that fitting Event Horizon Telescope observations with simple geometric models may lead to a reasonably accurate determination of the orientation of the black hole on the plane of the sky. However, in the disk-dominated models, the locations and depths of the minima in the visibility amplitudes are highly variable and are not related simply to the size of the black hole shadow. This suggests that using time-independent models to infer additional black hole parameters, such as the shadow size or the spin magnitude, will be severely affected by the variability of the accretion flow.

Multiwavelength Observations of Relativistic Jets from General Relativistic Magnetohydrodynamic Simulations

This work summarizes a program intended to unify three burgeoning branches of the high-energy astrophysics of relativistic jets: general relativistic magnetohydrodynamic (GRMHD) simulations of ever-increasing dynamical range, the microphysical theory of particle acceleration under relativistic conditions, and multiwavelength observations resolving ever-decreasing spatiotemporal scales. The process, which involves converting simulation output into time series of images and polarization maps that can be directly compared to observations, is performed by (1) self-consistently prescribing models for emission, absorption, and particle acceleration and (2) performing time-dependent polarized radiative transfer. M87 serves as an exemplary prototype for this investigation due to its prominent and well-studied jet and the imminent prospect of learning much more from Event Horizon Telescope (EHT) observations this year. Synthetic observations can be directly compared with real observations for observational signatures such as jet instabilities, collimation, relativistic beaming, and polarization. The simplest models described adopt the standard equipartition hypothesis; other models calculate emission by relating it to current density or shear. These models are intended for application to the radio jet instead of the higher frequency emission, the disk and the wind, which will be subjects of future investigations.

Observational Signatures of Mass-loading in Jets Launched by Rotating Black Holes

Abstract It is widely believed that relativistic jets in X-ray binaries (XRBs) and active-galactic nuclei are powered by the rotational energy of black holes. This idea is supported by general-relativistic magnetohydrodynamic (GRMHD) simulations of accreting black holes, which demonstrate efficient energy extraction via the Blandford–Znajek mechanism. However, due to uncertainties in the physics of mass loading, and the failure of GRMHD numerical schemes in the highly magnetized funnel region, the matter content of the jet remains poorly constrained. We investigate the observational signatures of mass loading in the funnel by performing general-relativistic radiative transfer calculations on a range of 3D GRMHD simulations of accreting black holes. We find significant observational differences between cases in which the funnel is empty and cases where the funnel is filled with plasma, particularly in the optical and X-ray bands. In the context of Sgr A*, current spectral data constrains the jet filling only if the black hole is rapidly rotating with a ≳ 0.9. In this case, the limits on the infrared flux disfavor a strong contribution from material in the funnel. We comment on the implications of our models for interpreting future Event Horizon Telescope observations. We also scale our models to stellar-mass black holes, and discuss their applicability to the low-luminosity state in XRBs.

Dynamical Imaging with Interferometry

Abstract By linking widely separated radio dishes, the technique of very long baseline interferometry (VLBI) can greatly enhance angular resolution in radio astronomy. However, at any given moment, a VLBI array only sparsely samples the information necessary to form an image. Conventional imaging techniques partially overcome this limitation by making the assumption that the observed cosmic source structure does not evolve over the duration of an observation, which enables VLBI networks to accumulate information as Earth rotates and changes the projected array geometry. Although this assumption is appropriate for nearly all VLBI, it is almost certainly violated for submillimeter observations of the Galactic center supermassive black hole, Sagittarius A* (Sgr A*), which has a gravitational timescale of only s and exhibits intrahour variability. To address this challenge, we develop several techniques to reconstruct dynamical images (“movies”) from interferometric data. Our techniques are applicable to both single-epoch and multiepoch variability studies, and they are suitable for exploring many different physical processes including flaring regions, stable images with small time-dependent perturbations, steady accretion dynamics, or kinematics of relativistic jets. Moreover, dynamical imaging can be used to estimate time-averaged images from time-variable data, eliminating many spurious image artifacts that arise when using standard imaging methods. We demonstrate the effectiveness of our techniques using synthetic observations of simulated black hole systems and 7 mm Very Long Baseline Array observations of M87, and we show that dynamical imaging is feasible for Event Horizon Telescope observations of Sgr A*.

The immediate environment of an astrophysical black hole

Abstract In view of the upcoming observations with the Event Horizon Telescope (EHT), we present our thoughts on the immediate environment of an astrophysical black hole. We are concerned that two approximations used in general relativistic magnetohydrodynamic numerical simulations, namely numerical density floors implemented near the base of the black hole jet, and a magnetic field that comes from large distances, may mislead our interpretation of the observations. We predict that three physical processes will manifest themselves in EHT observations, namely dynamic pair formation just above the horizon, electromagnetic energy dissipation along the boundary of the black hole jet, and a region of weak magnetic field separating the black hole jet from the disc wind.

Unique probe of dark matter in the core of M87 with the Event Horizon Telescope

We demonstrate the unprecedented capabilities of the Event Horizon Telescope (EHT) to image the innermost dark matter profile in the vicinity of the supermassive black hole at the center of the M87 radio galaxy. We present the first model of the synchrotron emission induced by dark matter annihilations from a spiky profile in the close vicinity of a supermassive black hole, accounting for strong gravitational lensing effects. Our results show that the EHT should readily resolve dark matter spikes if present. Moreover, the photon ring surrounding the silhouette of the black hole is clearly visible in the spike emission, which introduces observable small-scale structure into the signal. We find that the dark matter-induced emission provides an adequate fit to the existing EHT data, implying that in addition to the jet, a dark matter spike may account for a sizable portion of the millimeter emission from the innermost (subparsec) region of M87. Regardless, our results show that the EHT can probe very weakly annihilating dark matter. Current EHT observations already constrain very small cross sections, typically down to a few 10^{-31} cm^{3} s^{-1} for a 10 GeV candidate, close to characteristic values for p-wave-suppressed annihilation. Future EHT observations will further improve constraints on the DM scenario.

A new view on the M 87 jet origin: Turbulent loading leading to large-scale episodic wiggling

Context. The nearby, giant radio galaxy M 87 hosts a supermassive black hole (BH) and is well-known for a bright jet dominating the spectrum over ten orders of magnitude in frequency. Due to its proximity, jet prominence, and the large BH mass, M 87 is the best laboratory for investigating the formation, acceleration, and collimation of relativistic jets. Many kinematic studies have been performed to determine the proper motions in the jet. Despite M 87 providing all proofs of being an active BH, the apparent jet speed remained puzzling, because proper motion measurements between 15 and 43 GHz for the same region of 1–10 mas core distance provided largely discrepant results. This source is a prime object to be studied in exquisite detail with the upcoming Event Horizon Telescope (EHT) observations because it promises to allow a direct view on the jet launching process itself. Aims. We aim to decipher some of the kinematic puzzles in the pc-scale jet with the analysis we present here.Methods. We re-modeled and re-analyzed 31 VLBA observations at 15 GHz obtained within the MOJAVE program. The data span a time range between Jul. 1995 and May 2011. We performed a detailed investigation of the pc-scale jet kinematics on different timescales, the shortest periods between the observations beeing 10 and 80 days, and in different jet modes, making use of VLBA observations. In addition, we studied the jet ridge line behavior as a function of time. Special care was taken to analyze the region close to the 15 GHz core, and the dynamics and distribution of newly emerging jet features in the jet.Results. We find an indication for apparent superluminal motion in the jet. Moreover, we present evidence for acceleration between 0.5 and 10 mas of core separation. The data suggest that the central part of M 87 at 15 GHz seems to be rotating. Jet components and counter-jet components are ejected in different directions under varying angles, explaining the impression of a broad opening angle. In this paper we present evidence for two different operating modes of the jet of M 87. The jet switches between two phases: i) the jet ridge line is at least double or the jet axis is displaced vertically, and ii) an unperturbed phase where the jet ridge line remains almost straight but is smoothly curved and the jet components are aligned along a classical jet axis. The mode change occurs every couple of years. Between the two operating modes, a transition phase is visible.Conclusions. The M 87 jet visible at 15 GHz probes a different physical zone compared to the standard blazar-zone we tend to see in AGN jets. The most likely scenario explaining the observed phenomena is a turbulent mass loading into the jet, most probably due to local, fast reconnection processes driven by turbulence of a tangled magnetic field, which is either generated in the accretion disk or the disk corona. In addition, on large scales, a global magnetic structure is required to channel the turbulent flow into what evolves into a large-scale jet. Large-scale jet instabilities may explain the curved pattern of the observed jet flow.

THE EFFECTS OF ACCRETION FLOW DYNAMICS ON THE BLACK HOLE SHADOW OF SAGITTARIUS A*

ABSTRACT A radiatively inefficient accretion flow (RIAF), which is commonly characterized by its sub-Keplerian nature, is a favored accretion model for the supermassive black hole at the Galactic center, Sagittarius A*. To investigate the observable features of an RIAF, we compare the modeled shadow images, visibilities, and spectra of three flow models with dynamics characterized by (i) a Keplerian shell that is rigidly rotating outside the innermost stable circular orbit (ISCO) and infalling with a constant angular momentum inside ISCO, (ii) a sub-Keplerian motion, and (iii) a free-falling motion with zero angular momentum at infinity. At near-millimeter wavelengths, the emission is dominated by the flow within several Schwarzschild radii. The energy shift due to these flow dynamics becomes important and distinguishable, suggesting that the flow dynamics are an important model parameter for interpreting the millimeter/sub-millimeter very long baseline interferometric observations with the forthcoming, fully assembled Event Horizon Telescope (EHT). As an example, we demonstrate that structural variations of Sagittarius A* on event horizon-scales detected in previous EHT observations can be explained by the non-stationary dynamics of an RIAF.

HIGH-RESOLUTION LINEAR POLARIMETRIC IMAGING FOR THE EVENT HORIZON TELESCOPE

ABSTRACT Images of the linear polarizations of synchrotron radiation around active galactic nuclei (AGNs) highlight their projected magnetic field lines and provide key data for understanding the physics of accretion and outflow from supermassive black holes. The highest-resolution polarimetric images of AGNs are produced with Very Long Baseline Interferometry (VLBI). Because VLBI incompletely samples the Fourier transform of the source image, any image reconstruction that fills in unmeasured spatial frequencies will not be unique and reconstruction algorithms are required. In this paper, we explore some extensions of the Maximum Entropy Method (MEM) to linear polarimetric VLBI imaging. In contrast to previous work, our polarimetric MEM algorithm combines a Stokes I imager that only uses bispectrum measurements that are immune to atmospheric phase corruption, with a joint Stokes Q and U imager that operates on robust polarimetric ratios. We demonstrate the effectiveness of our technique on 7 and 3 mm wavelength quasar observations from the VLBA and simulated 1.3 mm Event Horizon Telescope observations of Sgr A* and M87. Consistent with past studies, we find that polarimetric MEM can produce superior resolution compared to the standard CLEAN algorithm, when imaging smooth and compact source distributions. As an imaging framework, MEM is highly adaptable, allowing a range of constraints on polarization structure. Polarimetric MEM is thus an attractive choice for image reconstruction with the EHT.

Meqsilhouette: a mm-VLBI observation and signal corruption simulator

The Event Horizon Telescope (EHT) aims to spatially resolve the silhouette (or shadow) of the supermassive black holes in the Galactic Centre (Sgr A$^\star$) and M87. The primary scientific objectives are to test general relativity in the strong-field regime and to probe accretion and jet-launch physics at event-horizon scales. This is made possible by the technique of Very Long Baseline Interferometry (VLBI) at (sub)millimetre wavelengths, which can achieve angular resolutions of order $\sim10~\mu$-arcsec. However, this approach suffers from unique observational challenges, including scattering in the troposphere and interstellar medium; rapidly time-variable source structure in both polarized and total intensity; as well as non-negligible antenna pointing errors. In this, the first paper in a series, we present the MeqSilhouette software package which is specifically designed to accurately simulate EHT observations. It includes realistic descriptions of a number of signal corruptions that can limit the ability to measure the key science parameters. This can be used to quantify calibration requirements, test parameter estimation and imaging strategies, and investigate systematic uncertainties that may be present. In doing so, a stronger link can be made between observational capabilities and theoretical predictions, with the goal of maximising scientific output from the upcoming order of magnitude increase in EHT sensitivity.

Electromagnetic versus Lense–Thirring alignment of black hole accretion discs

Accretion discs and black holes (BHs) have angular momenta that are generally misaligned with respect to each other, which can lead to warps in the discs and bends in any jets produced. We consider a disc that is misaligned at large radii and torqued by Lense-Thirring (LT) precession and a Blandford-Znajek (BZ) jet torque. We consider a variety of disc states that include radiatively inefficient thick discs, radiatively efficient thin discs, and super-Eddington accretion discs. The magnetic field strength of the BZ jet is chosen as either from standard equipartition arguments or from magnetically arrested disc (MAD) simulations. We show that standard thin accretion discs can reach spin-disc alignment out to large radii long before LT would play a role, as caused by the slow infall time that gives even a weak BZ jet time to align the disc. We show that geometrically thick radiatively inefficient discs and super-Eddington discs in the MAD state reach disc-spin alignment near the black hole when density profiles are shallow as in magnetohydrodynamical simulations, while the BZ jet aligns discs with steep density profiles (as in advection-dominated accretion flows) with the BH spin out to larger radii. Our results imply that the BZ jet torque should affect the cosmological evolution of BH spin magnitude and direction, BH spin measurements in active galactic nuclei and X-ray binaries, and the interpretations for Event Horizon Telescope observations of discs or jets in strong-field gravity regimes.

PERSISTENT ASYMMETRIC STRUCTURE OF SAGITTARIUS A* ON EVENT HORIZON SCALES

ABSTRACT The Galactic Center black hole Sagittarius A* (Sgr A*) is a prime observing target for the Event Horizon Telescope (EHT), which can resolve the 1.3 mm emission from this source on angular scales comparable to that of the general relativistic shadow. Previous EHT observations have used visibility amplitudes to infer the morphology of the millimeter-wavelength emission. Potentially much richer source information is contained in the phases. We report on 1.3 mm phase information on Sgr A* obtained with the EHT on a total of 13 observing nights over four years. Closure phases, which are the sum of visibility phases along a closed triangle of interferometer baselines, are used because they are robust against phase corruptions introduced by instrumentation and the rapidly variable atmosphere. The median closure phase on a triangle including telescopes in California, Hawaii, and Arizona is nonzero. This result conclusively demonstrates that the millimeter emission is asymmetric on scales of a few Schwarzschild radii and can be used to break 180° rotational ambiguities inherent from amplitude data alone. The stability of the sign of the closure phase over most observing nights indicates persistent asymmetry in the image of Sgr A* that is not obscured by refraction due to interstellar electrons along the line of sight.