Event Horizon Telescope Observations Research Articles

Photon Rings and Shadow Size for General Axisymmetric and Stationary Integrable Spacetimes

There are now multiple direct probes of the region near black hole horizons, including direct imaging with the Event Horizon Telescope (EHT). As a result, it is now of considerable interest to identify what aspects of the underlying spacetime are constrained by these observations. For this purpose, we present a new formulation of an existing broad class of integrable, axisymmetric, stationary spinning black hole spacetimes, specified by four free radial functions, that makes manifest which functions are responsible for setting the location and morphology of the event horizon and ergosphere. We explore the size of the black hole shadow and higher-order photon rings for polar observers, approximately appropriate for the EHT observations of M87*, finding analogous expressions to those for general spherical spacetimes. Of particular interest, we find that these are independent of the properties of the ergosphere, but do directly probe the free function that defines the event horizon. Based on those expressions, we extend the nonperturbative, nonparametric characterization of the gravitational implications of various near-horizon measurements to spinning spacetimes. Finally, we demonstrate this characterization for a handful of explicit alternative spacetimes.

General upper limit on the electric charge of Sgr A* in the Reissner–Nordström metric

ABSTRACT In general relativity, the gravitational field of an electrically charged, non-rotating, spherically symmetric body is described by the Reissner–Nordström (RN) metric. Depending on the charge to mass ratio, the solution describes a black hole or a naked singularity. In the naked-singularity regime, a general property of this metric is the existence of a radius, known as the zero-gravity radius, where a test particle would remain at rest. As a consequence of repulsive gravity there is no circular orbit inside this radius, and at least a part of any quasi-stable structure must necessarily lie outside of it. Assuming the iconic torus in the compact source Sgr A* at the Galactic centre observed by the Event Horizon Telescope (EHT) to be the image of a quasi-stationary fluid structure, we provide rigorous constraints in the RN metric on the electric charge-to-mass ratio Q/M of Sgr A*. A comparison between the EHT observations and the space–time zero-gravity radius provides the most conservative limit on the charge of Sgr A* to be |Q/M| < 2.32 in geometrized units. A charged naked singularity respecting this charge-to-mass constraint is consistent with the current EHT observations, if the image is not interpreted as a photon ring.

Probing the vector charge of Sagittarius A* with pulsar timing

Timing a pulsar orbiting around Sagittarius A* (Sgr A*) can provide uswith a unique opportunity of testing gravity theories. We investigate thedetectability of a vector charge carried by the Sgr A* black hole (BH) in thebumblebee gravity model with simulated future pulsar timing observations. Thespacetime of a bumblebee BH introduces characteristic changes to the orbitaldynamics of the pulsar and the light propagation of radio signals. Assuming atiming precision of 1 ms, our simulation shows that a 5-yr observation of apulsar with an orbital period Pb ∼ 0.5 yr and an orbitaleccentricity e ∼ 0.8 can probe a vector charge-to-mass ratio as small asQ/M ∼ 10-3, which is much more stringent than the current constraint fromthe Event Horizon Telescope (EHT) observations, and comparable to theprospective constraint from extreme mass-ratio inspirals with the LaserInterferometer Space Antenna (LISA).

Balanced Turbulence and the Helicity Barrier in Black Hole Accretion

Horizon-scale observations from the Event Horizon Telescope (EHT) have enabled precision study of supermassive black hole accretion. Contemporary accretion modeling often treats the inflowing plasma as a single, thermal fluid, but microphysical kinetic effects can lead to significant deviations from this idealized picture. We investigate how the helicity barrier influences EHT-accessible electromagnetic observables by employing a simple model for electron heating based on kinetic physics and the cascade of energy and helicity in unbalanced turbulence. Although the helicity barrier plays only a minor role in regions with high plasma β, like in standard and normal evolution (SANE) disks, it may substantially impact regions with more ordered magnetic fields, such as the jet and its surrounding wind in SANE flows as well as throughout the entire domain in magnetically arrested disk (MAD) flows. In SANE flows, emission shifts from the funnel wall toward the lower-magnetization disk region; in MAD flows the emission morphology remains largely unchanged. Including the helicity barrier leads to characteristically lower electron temperatures, and neglecting it can lead to underestimated accretion rates and inferred jet powers. The corresponding higher plasma densities result in increased depolarization and Faraday depths thereby decreasing the amplitude of the β 2 coefficient while leaving its angle unchanged. Both the increased jet power and lower β2 may help alleviate outstanding tensions between modeling and EHT observations. We also find that the estimated ring diameter may be underestimated when the helicity barrier is neglected. Our results underscore the significance of the helicity barrier in shaping black hole observables and inferred accretion system parameters.

Imaging ultracompact objects with radiatively inefficient accretion flows

Context. Recent Event Horizon Telescope observations of M 87* and Sgr A* strongly suggest the presence of a supermassive black hole at their respective cores. We use the semi-analytic radiatively inefficient accretion flows (RIAF) model to investigate the resulting images of the Joshi–Malafarina–Narayan (JMN-1) naked singularity and the Schwarzschild black hole. Aims. We chose the JMN-1 naked singularity model and compared the synchrotron images with the Schwarzschild solution to search for any distinct features that can distinguish the two objects and to find an alternative to the solution with a black hole. Methods. We performed general relativistic ray-tracing and radiative transfer simulations using the Brahma code to generate synchrotron-emission images using the thermal distribution function for emissivity and absorptivity. We investigated effects in the images by varying the inclination angle, the disk width, and the frequency. Results. The shadow images simulated with the JMN-1 model closely resemble those generated by the Schwarzschild black hole. The disparities between the two images are very small. We conducted simulations using various plasma parameters, but the resulting images remained largely consistent for both scenarios. This similarity is evident in the horizontal cross-sectional brightness profiles of the two scenarios. Notably, the JMN-1 model exhibits a slightly higher intensity than the Schwarzschild black hole. Conclusions. We conclude that JMN-1 is a viable substitute for the black hole scenario. This conclusion is not solely grounded in the fact that the two scenarios are indistinguishable from their respective shadow observations, but also in the consideration that JMN-1 emerges as an end state of a continual gravitational collapse. This paradigm not only allows for constraints on spacetime, but also provides a good probe for the nature of the central compact object.

The persistent shadow of the supermassive black hole of M 87

In April 2019, the Event Horizon Telescope (EHT) Collaboration reported the first-ever event-horizon-scale images of a black hole, resolving the central compact radio source in the giant elliptical galaxy M 87. These images reveal a ring with a southerly brightness distribution and a diameter of ∼42 μas, consistent with the predicted size and shape of a shadow produced by the gravitationally lensed emission around a supermassive black hole. These results were obtained as part of the April 2017 EHT observation campaign, using a global very long baseline interferometric radio array operating at a wavelength of 1.3 mm. Here, we present results based on the second EHT observing campaign, taking place in April 2018 with an improved array, wider frequency coverage, and increased bandwidth. In particular, the additional baselines provided by the Greenland telescope improved the coverage of the array. Multiyear EHT observations provide independent snapshots of the horizon-scale emission, allowing us to confirm the persistence, size, and shape of the black hole shadow, and constrain the intrinsic structural variability of the accretion flow. We have confirmed the presence of an asymmetric ring structure, brighter in the southwest, with a median diameter of 43.3−3.1+1.5 μas. The diameter of the 2018 ring is remarkably consistent with the diameter obtained from the previous 2017 observations. On the other hand, the position angle of the brightness asymmetry in 2018 is shifted by about 30° relative to 2017. The perennial persistence of the ring and its diameter robustly support the interpretation that the ring is formed by lensed emission surrounding a Kerr black hole with a mass ∼6.5 × 109 M⊙. The significant change in the ring brightness asymmetry implies a spin axis that is more consistent with the position angle of the large-scale jet.

Future Prospects for Constraining Black Hole Spacetime: Horizon-scale Variability of Astrophysical Jets

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.

Shadows of loop quantum black holes: semi-analytical simulations of loop quantum gravity effects on Sagittarius A* and M87*

In this study, we delve into the observational implications of rotating Loop Quantum Black Holes (LQBHs) within an astrophysical framework. We employ semi-analytical General Relativistic Radiative Transfer (GRRT) computations to study the emission from the accretion flow around LQBHs. Our findings indicate that the increase of Loop Quantum Gravity (LQG) effects results in an enlargement of the rings from LQBHs, thereby causing a more circular polarization pattern in the shadow images. We make comparisons with the Event Horizon Telescope (EHT) observations of Sgr A* and M87*, which enable us to determine an upper limit for the polymetric function P in LQG. The upper limit for Sgr A* is 0.2, while for M87* it is 0.07. Both black holes exhibit a preference for a relatively high spin (a ≳ 0.5 for Sgr A* and 0.5 ≲ a ≲ 0.7 for M87*). The constraints for Sgr A* are based on black hole spin and ring diameter, whereas for M87*, the constraints are further tightened by the polarimetric pattern. In essence, our simulations provide observational constraints on the effect of LQG in supermassive black holes (SMBH), providing the most consistent comparison with observation.

Exploring tidal force effects and shadow constraints for Schwarzschild-like black hole in Starobinsky–Bel-Robinson gravity

The current manuscript deals with the tidal force effects, geodesic deviation, and shadow constraints of the Schwarzschild-like black hole theorised in Starobinsky–Bel-Robinson gravity exhibiting M-theory compactification. In the current analysis, we explore the radial and angular tidal force effects on a radially in-falling particle by the central black hole, which is located in this spacetime. We also numerically solve the geodesic deviation equation and study the variation of the geodesic separation vector with the radial coordinate for two nearby geodesics using suitable initial conditions. All the obtained results are tested for Sag A* and M87* by constraining the value of the stringy gravity parameter β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta $$\\end{document} using the shadow data from the event horizon telescope observations. All the results are compared with Schwarzschild black hole spacetime. In our study, we found that both the radial and angular tidal forces experienced by a particle switch their initial behaviour and turn compressive and stretching, respectively, before reaching the event horizon. The geodesic deviation shows an oscillating trend as well for the chosen initial condition. For the constrained value of β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta $$\\end{document}, we see that the spacetime geometry generated by Sag A* and M87* is effectively same for both Schwarzschild and Starobinsky–Bel-Robinson black hole. Furthermore, we also calculated the angular diameter of the shadow in Starobinsky–Bel-Robinson black hole and compared with the Schwarzschild black hole. It is observed that the angular diameter of shadow for M87* and Sgr A* in Starobinsky–Bel-Robinson black hole is smaller than the Schwarzschild black hole. The calculated results satisfy the event horizon telescope observational constraints.

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 (〈∣v∣〉 < 3.7%), consistent with the low image-integrated circular polarization fraction measured by the Atacama Large Millimeter/submillimeter Array (∣v 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 on 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 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*.

Black Hole Polarimetry I. A Signature of Electromagnetic Energy Extraction

In 1977, Blandford and Znajek showed that the electromagnetic field surrounding a rotating black hole can harvest its spin energy and use it to power a collimated astrophysical jet, such as the one launched from the center of the elliptical galaxy M87. Today, interferometric observations with the Event Horizon Telescope (EHT) are delivering high-resolution, event-horizon-scale, polarimetric images of the supermassive black hole M87* at the jet launching point. These polarimetric images offer an unprecedented window into the electromagnetic field structure around a black hole. In this paper, we show that a simple polarimetric observable—the phase ∠β 2 of the second azimuthal Fourier mode of the linear polarization in a near-horizon image—depends on the sign of the electromagnetic energy flux and therefore provides a direct probe of black hole energy extraction. In Boyer–Lindquist coordinates, the Poynting flux for axisymmetric electromagnetic fields is proportional to the product B ϕ B r . The phase ∠β 2 likewise depends on the ratio B ϕ /B r , thereby enabling an observer to determine the direction of electromagnetic energy flow in the near-horizon environment experimentally. Data from the 2017 EHT observations of M87* are consistent with electromagnetic energy outflow. Currently envisioned multifrequency observations of M87* will achieve higher dynamic range and angular resolution, and hence deliver measurements of ∠β 2 closer to the event horizon as well as better constraints on Faraday rotation. Such observations will enable a definitive test for energy extraction from the black hole M87*.

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.

Distributed Control Software for the Active Surface System of Tian-ma Radio Telescope

The Tian-ma Radio Telescope (TMRT) applies an Active Surface System (ASFS), which corrects for large-scale deformations due to gravity and thermal on the primary reflector. The centralized and automated management of the ASFS using software has become a challenge, for which we have developed the TMRT Active Surface System Control Software (TASCS). This paper describes the design and implementation of TASCS for device control, status monitoring, human-computer interaction, and data management functionalities. TASCS adopts the open-source Tango Controls framework and distributes middleware technology to realize real-time automated adjustment of the primary reflector through remote centralized control of a large number of actuators. At present, it has been successfully deployed on the TMRT and has played an important role in Event Horizon Telescope observations.

Photon region and shadow of a rotating 5D black string

To explore the possible clues for the extra dimension from the Event Horizon Telescope (EHT) observations, we study the shadow of the rotating 5D black string in General Relativity (GR). Instead of investigating the shadow in the effective 4D theory, we concern the motion of photons along the extra dimension z with a conserved momentum P_z, which appears as an effective mass in the geodesic equations of photons. The existence of P_z enlarges the photon regions and the shadow of the rotating 5D black string while it has slight impact on the distortion. The EHT observations of M87* and SgrA* can rule out the black string model with an infinite length along the extra dimension, and support the hypothesis that the extra dimension is compact to avoid the Gregory-Laflamme (GL) instability, where the length of the black string/the compact extra dimension can be constrained as 2.03125~textrm{mm} lesssim ell lesssim 2.6~textrm{mm} and 2.28070~textrm{mm} lesssim ell lesssim 2.6~textrm{mm} respectively.

Shadows of Kerr–Vaidya-like black holes

In this work, we study the shadow boundary curves of rotating time-dependent black hole solutions which have well-defined Kerr and Vaidya limits. These solutions are constructed by applying the Newman–Janis algorithm to a spherically symmetric seed metric conformal to the Vaidya solution with a mass function that is linear in Eddington–Finkelstein coordinates. Equipped with a conformal Killing vector field, this class of solution exhibits separability of null geodesics, thus allowing one to develop an analytic formula for the boundary curve of its shadow. We find a simple power law describing the dependence of the mean radius and asymmetry factor of the shadow on the accretion rate. Applicability of our model to recent Event Horizon Telescope observations of M87 and Sgr A is also discussed.

Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Telescope image of Sagittarius A

Horizon-scale images of black holes (BHs) and their shadows have opened an unprecedented window onto tests of gravity and fundamental physics in the strong-field regime. We consider a wide range of well-motivated deviations from classical general relativity (GR) BH solutions, and constrain them using the Event Horizon Telescope (EHT) observations of Sagittarius A (Sgr A), connecting the size of the bright ring of emission to that of the underlying BH shadow and exploiting high-precision measurements of Sgr A’s mass-to-distance ratio. The scenarios we consider, and whose fundamental parameters we constrain, include various regular BHs, string-inspired space-times, violations of the no-hair theorem driven by additional fields, alternative theories of gravity, novel fundamental physics frameworks, and BH mimickers including well-motivated wormhole and naked singularity space-times. We demonstrate that the EHT image of Sgr A places particularly stringent constraints on models predicting a shadow size larger than that of a Schwarzschild BH of a given mass, with the resulting limits in some cases surpassing cosmological ones. Our results are among the first tests of fundamental physics from the shadow of Sgr A and, while the latter appears to be in excellent agreement with the predictions of GR, we have shown that a number of well-motivated alternative scenarios, including BH mimickers, are far from being ruled out at present.

Asymptotically locally flat and AdS higher-dimensional black holes of Einstein–Horndeski–Maxwell gravity in the light of EHT observations: shadow behavior and deflection angle

Unification of gravity with other interactions, achieving the ultimate framework of quantum gravity, and fundamental problems in particle physics and cosmology motivate to consider extra spatial dimensions. The impact of these extra dimensions on the modified theories of gravity has attracted a lot of attention. One way to examine how extra dimensions affect the modified gravitational theories is to analytically investigate astrophysical phenomena, such as black hole shadows. In this study, we aim to investigate the behavior of the shadow shapes of higher-dimensional charged black hole solutions including asymptotically locally flat (ALF) and asymptotically locally AdS (ALAdS) in Einstein–Horndeski–Maxwell (EHM) gravitational theory. We utilize the Hamilton–Jacobi method to find photon orbits around these black holes as well as the Carter approach to formulate the geodesic equations. We examine how extra dimensions, negative cosmological constant, electric charge, and coupling constants of the EHM gravity affect the shadow size of the black hole. Then, we constrain these parameters by comparing the shadow radius of these black holes with the shadow size of M87* supermassive black hole captured by the Event Horizon Telescope (EHT) collaborations. We discover that generally the presence of extra dimensions within the EHM gravity results in reducing the shadow size of higher-dimensional ALF and ALAdS charged black holes, whereas the impact of electric charge on the shadow of these black holes is suppressible. Interestingly, we observe that decreasing the negative cosmological constant, i.e., increasing its absolute value, leads to increase the shadow size of the ALAdS charged higher-dimensional black hole in the EHM gravity. Surprisingly, based on the constraints from EHT observations, we discover that only the shadow size of the four dimensional ALF charged black hole lies in the confidence levels of EHT data, whereas owing to the presence of the negative cosmological constant, the shadow radius of the four, five, and seven dimensional ALAdS charged black holes lie within the EHT data confidence levels.

Rotation in Event Horizon Telescope Movies

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° per GMc −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 p depends 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.

Investigating effects of dark matter on photon orbits and black hole shadows

We consider Kerr black holes (BHs) surrounded by perfect dark fluid matter (PFDM), with an additional parameter (k) because of PFDM, apart from mass (M) and rotation parameter (a) — the rotating PFDM BHs. We analyse the photon orbits around PFDM BHs and naked singularities (NSs) and emphasize the effect of PFDM on photon boomerangs. Interestingly, the azimuthal oscillations first increase and then decrease for retrograde orbits, whereas they first decrease and then increase for prograde orbits, with increasing k. Unlike in the Kerr NSs, photon boomerangs can form around rotating PFDM NSs. We use the Event Horizon Telescope (EHT) observational results for Schwarzschild shadow deviations of M87* and Sgr A*, δM87∗=−0.01±0.17 and δSgrA∗=−0.08−0.09+0.09(VLTI),−0.04−0.10+0.09(Keck), to report the upper bounds on the PFDM parameter: 0≤k≤0.0792M and kmax∈[0.0507M,0.0611M] respectively. Together with the EHT bounds on the shadows of Sgr A∗ and M87∗, our analysis concludes that a substantial part of the rotating PFDM BH parameter space agrees with the EHT observations. Thus, one must consider the possibility of the rotating PFDM BHs being strong candidates for the astrophysical BHs.

Shadow revisiting and weak gravitational lensing with Chern-Simons modification

Dynamical Chern-Simons (dCS) gravity has been attracting plenty of attentions due to the fact that it is a parity-violating modified theory of gravity that corresponds to a well-posed effective field theory in weak coupling approximation. In particular, a rotating black hole in dCS gravity is in contrast to the general relativistic counterparts. In this paper, we revisit the shadow of analytical rotating black hole spacetime in dCS modified gravity, based on which we study the shadow observables, discuss the constraint on the model parameters from the Event Horizon Telescope (EHT) observations, and analyze the real part of quasi-normal modes (QNMs) in the eikonal limit. In addition, we explore the deflection angle in weak gravitational field limit with the use of Gauss-Bonnet theorem. We find that the shadow related physics and the weak gravitational lensing effect are significantly influenced by the CS coupling, which could provide theoretical predictions for a future test of the dCS theory with EHT observations.