A&A, 699, A279 (2025)
https://doi.org/10.1051/0004-6361/202555235
c© The Authors 2025
Astronomy
&Astrophysics
Origin of the ring ellipticity in the black hole images of M87∗
Rohan Dahale1,?,?? , Ilje Cho2,3,1,?? , Kotaro Moriyama1,4 , Kaj Wiik5,6,7 , Paul Tiede8,9 , José L. Gómez1 ,
Chi-kwan Chan10,11,12 , Roman Gold13,14,15 , Vadim Y. Bernshteyn10,12 , Marianna Foschi1 , Britton Jeter16 ,
Hung-Yi Pu17,18,16 , Boris Georgiev10 , Abhishek V. Joshi19 , Alejandro Cruz-Osorio20,21 , Iniyan Natarajan8,9 ,
Avery E. Broderick22,23,24 , León D. S. Salas25 , Koushik Chatterjee26 , Kazunori Akiyama27,28,9 , Ezequiel Albentosa-Ruíz29 ,
Antxon Alberdi1 , Walter Alef30, Juan Carlos Algaba31 , Richard Anantua32,33,9,8 , Keiichi Asada16 , Rebecca Azulay29,34,30 ,
Uwe Bach30 , Anne-Kathrin Baczko35,30 , David Ball10, Mislav Balokovic´36 , Bidisha Bandyopadhyay37 , John Barrett27 ,
Michi Bauböck19 , Bradford A. Benson38,39 , Dan Bintley40,41, Lindy Blackburn9,8 , Raymond Blundell8 ,
Katherine L. Bouman42 , Geoffrey C. Bower43,44 , Michael Bremer45, Roger Brissenden9,8 , Silke Britzen30 ,
Dominique Broguiere45 , Thomas Bronzwaer46 , Sandra Bustamante47 , Douglas Ferreira Carlos48 ,
John E. Carlstrom49,39,50,51 , Andrew Chael52 , Dominic O. Chang9,8 , Shami Chatterjee53 , Ming-Tang Chen54 ,
Yongjun Chen55,56 , Xiaopeng Cheng2 , Pierre Christian57 , Nicholas S. Conroy58,8 , John E. Conway35 ,
Thomas M. Crawford39,49 , Geoffrey B. Crew27 , Yuzhu Cui59,60 , Brandon Curd32,9,8 , Jordy Davelaar61,??? ,
Mariafelicia De Laurentis62,63 , Roger Deane64,65,66 , Jessica Dempsey40,41,67 , Gregory Desvignes30,68 , Jason Dexter69 ,
Vedant Dhruv19 , Indu K. Dihingia60 , Sheperd S. Doeleman9,8 , Sergio A. Dzib30 , Ralph P. Eatough70,30 , Razieh Emami8 ,
Heino Falcke46 , Joseph Farah71,72 , Vincent L. Fish27 , Edward Fomalont73 , H. Alyson Ford10 , Raquel Fraga-Encinas46 ,
William T. Freeman74,75, Per Friberg40,41 , Christian M. Fromm76,21,30 , Antonio Fuentes1 , Peter Galison9,77,78 ,
Charles F. Gammie19,58,79 , Roberto García45 , Olivier Gentaz45 , Gertie Geertsema80 , Ciriaco Goddi81,82,83,84 ,
Arturo I. Gómez-Ruiz85,86 , Minfeng Gu55,87 , Mark Gurwell8 , Kazuhiro Hada88,4 , Daryl Haggard89,90 , Ronald Hesper91 ,
Dirk Heumann10 , Luis C. Ho92,93 , Paul Ho16,41,40 , Mareki Honma4,94,95 , Chih-Wei L. Huang16 , Lei Huang55,87 ,
David H. Hughes85, Shiro Ikeda28,96,97,98 , C. M. Violette Impellizzeri99,73 , Makoto Inoue16 , Sara Issaoun8,??? ,
David J. James100,101 , Buell T. Jannuzi10 , Michael Janssen46,30 , Wu Jiang55 , Alejandra Jiménez-Rosales46 ,
Michael D. Johnson9,8 , Svetlana Jorstad102 , Adam C. Jones39, Taehyun Jung2,103 , Ramesh Karuppusamy30 ,
Tomohisa Kawashima104 , Garrett K. Keating8 , Mark Kettenis105 , Dong-Jin Kim106 , Jae-Young Kim107,30 , Jongsoo Kim2 ,
Junhan Kim108 , Motoki Kino28,109 , Jun Yi Koay16 , Prashant Kocherlakota9 , Yutaro Kofuji4,95, Patrick M. Koch16 ,
Shoko Koyama110,16 , Carsten Kramer45 , Joana A. Kramer30 , Michael Kramer30 , Thomas P. Krichbaum30 ,
Cheng-Yu Kuo111,16 , Noemi La Bella46 , Sang-Sung Lee2 , Aviad Levis42 , Zhiyuan Li112,113 , Rocco Lico114,1 ,
Greg Lindahl115 , Michael Lindqvist35 , Mikhail Lisakov116 , Jun Liu30 , Kuo Liu55,56 , Elisabetta Liuzzo117 ,
Wen-Ping Lo16,118 , Andrei P. Lobanov30 , Laurent Loinard119,9,120 , Colin J. Lonsdale27 , Amy E. Lowitz10 ,
Ru-Sen Lu55,56,30 , Nicholas R. MacDonald30 , Jirong Mao121,122,123 , Nicola Marchili117,30 , Sera Markoff25,124 ,
Daniel P. Marrone10 , Alan P. Marscher102 , Iván Martí-Vidal29,34 , Satoki Matsushita16 , Lynn D. Matthews27 ,
Lia Medeiros61,??? , Karl M. Menten30,† , Izumi Mizuno40,41 , Yosuke Mizuno60,125,21 , Joshua Montgomery90,39 ,
James M. Moran9,8 , Monika Moscibrodzka46 , Wanga Mulaudzi25 , Cornelia Müller30,46 , Hendrik Müller30 ,
Alejandro Mus82,114 , Gibwa Musoke25,46 , Ioannis Myserlis126 , Hiroshi Nagai28,94 , Neil M. Nagar37 , Dhanya G. Nair37,30 ,
Masanori Nakamura127,16 , Gopal Narayanan47 , Antonios Nathanail128,21 , Santiago Navarro Fuentes126, Joey Neilsen129 ,
Chunchong Ni23,24,22 , Michael A. Nowak130 , Junghwan Oh105 , Hiroki Okino4,95 , Héctor Raúl Olivares Sánchez131 ,
Tomoaki Oyama4 , Feryal Özel132 , Daniel C. M. Palumbo9,8 , Georgios Filippos Paraschos30 , Jongho Park133,16 ,
Harriet Parsons40,41 , Nimesh Patel8 , Ue-Li Pen16,22,134,135,136 , Dominic W. Pesce8,9 , Vincent Piétu45,
Aleksandar PopStefanija47, Oliver Porth25,21 , Ben Prather19 , Giacomo Principe137,138,114 , Dimitrios Psaltis132 ,
Venkatessh Ramakrishnan37,6,7 , Ramprasad Rao8 , Mark G. Rawlings139,40,41 , Luciano Rezzolla21,140,141 , Angelo Ricarte9,8 ,
Bart Ripperda134,142,135,22 , Jan Röder1 , Freek Roelofs46 , Cristina Romero-Cañizales16 , Eduardo Ros30 ,
Arash Roshanineshat10 , Helge Rottmann30, Alan L. Roy30 , Ignacio Ruiz126 , Chet Ruszczyk27 , Kazi L. J. Rygl117 ,
Salvador Sánchez126 , David Sánchez-Argüelles85,86 , Miguel Sánchez-Portal126 , Mahito Sasada143,4,144 , Kaushik Satapathy10 ,
Saurabh30 , Tuomas Savolainen145,7,30 , F. Peter Schloerb47, Jonathan Schonfeld8 , Karl-Friedrich Schuster146 ,
Lijing Shao93,30 , Zhiqiang Shen55,56 , Sasikumar Silpa37 , Des Small105 , Bong Won Sohn2,103,3 , Jason SooHoo27 ,
Kamal Souccar47 , Joshua S. Stanway147 , He Sun148,149 , Fumie Tazaki150 , Alexandra J. Tetarenko151 ,
Remo P. J. Tilanus10,46,99,152 , Michael Titus27 , Kenji Toma153,154 , Pablo Torne126,30 , Teresa Toscano1 , Efthalia Traianou1,30 ,
Tyler Trent10, Sascha Trippe155 , Matthew Turk58 , Ilse van Bemmel67 , Huib Jan van Langevelde105,99,156 ,
Daniel R. van Rossum46 , Jesse Vos46 , Jan Wagner30 , Derek Ward-Thompson147 , John Wardle157 , Jasmin E. Washington10 ,
Jonathan Weintroub9,8 , Robert Wharton30 , Maciek Wielgus1 , Gunther Witzel30 , Michael F. Wondrak46,158 ,
George N. Wong159,52 , Qingwen Wu160 , Nitika Yadlapalli42 , Paul Yamaguchi8 , Aristomenis Yfantis46 , Doosoo Yoon25 ,
André Young46 , Ziri Younsi161,21 , Wei Yu8 , Feng Yuan162 , Ye-Fei Yuan163 , Ai-Ling Zeng1 , J. Anton Zensus30 ,
Shuo Zhang164 , Guang-Yao Zhao1,30 , and Shan-Shan Zhao55
(Affiliations can be found after the references)
Received 21 April 2025 / Accepted 14 May 2025
? Corresponding author: astrorohandahale@gmail.com
?? These authors have contributed equally to this work.
??? NASA Hubble Fellowship Program, Einstein Fellow.
† Deceased.
Open Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0),
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A279, page 1 of 18
Dahale, R., et al.: A&A, 699, A279 (2025)
ABSTRACT
We investigate the origin of the elliptical ring structure observed in the images of the supermassive black hole M87∗, aiming to disentangle
contributions from gravitational, astrophysical, and imaging effects. Leveraging the enhanced capabilities of the Event Horizon Telescope (EHT)’s
2018 array, including improved (u, v)-coverage from the Greenland Telescope, we measured the ring’s ellipticity using five independent imaging
methods, obtaining a consistent average value of τ = 0.08+0.03−0.02 with a position angle of ξ = 50.1
+6.2
−7.6 degrees. To interpret this measurement, we
compared it to general relativistic magnetohydrodynamic (GRMHD) simulations spanning a wide range of physical parameters including the
thermal or nonthermal electron distribution function, spins, and ion-to-electron temperature ratios in both low- and high-density regions. We find
no statistically significant correlation between spin and ellipticity in GRMHD images. Instead, we identify a correlation between ellipticity and
the fraction of non-ring emission, particularly in nonthermal models and models with higher jet emission. These results indicate that the ellipticity
measured from the M87∗ emission structure is consistent with that expected from simulations of turbulent accretion flows around black holes,
where it is dominated by astrophysical effects rather than gravitational ones. Future high-resolution imaging, including space very long baseline
interferometry and long-term monitoring, will be essential to isolate gravitational signatures from astrophysical effects.
Key words. accretion, accretion disks – black hole physics – gravitation – galaxies: active
1. Introduction
The Event Horizon Telescope (EHT) collaboration published
the first image of a black hole shadow of the supermas-
sive black hole (SMBH) at the center of the giant ellip-
tical galaxy M87, featuring a distinctive ring-like structure
(Event Horizon Telescope Collaboration 2019a,b,c,d,e,f). In the
context of general relativity (GR), the standard usage of the term
“black hole shadow” is defined as the appearance of a black
hole illuminated from all directions, including from behind the
observer (e.g., Falcke et al. 2000), corresponding to the interior of
the so-called critical curve formed by photon trajectories asymp-
totically approaching bound photon orbits (Gralla et al. 2019).
The ring-like structure in EHT images is primarily a “direct
image” (n = 0 emission, where n is the number of half-orbits)
that consists of photons from the accretion flow that are strongly
lensed by the black hole’s gravity but complete zero half-orbits
around it before reaching the observer (e.g., Gralla et al. 2019;
Johnson et al. 2020). The “photon ring” is an infinite series of
self-similar subrings of light from photons that complete one or
more half-orbits (n ≥ 1) around the black hole before reaching
the observer (Johnson et al. 2020). GR predicts that the critical
curve is nearly circular for low inclination angles, such as the∼17◦
inclination estimated for the M87 black hole, M87∗ (Mertens et al.
2016). Because the black hole spin introduces asymmetry in the
shape of the critical curve, if the EHT can provide observational
access to the critical curve then the measurement of its shape is a
pathway to spin measurement. In this paper, we use “gravitational
ellipticity” to refer to the shape distortion of the critical curve.
For M87∗, spin-induced shadow ellipticity is expected to reach
up to ∼0.02 for a spin parameter a ∼ 0.94 and inclination i = 17◦
(e.g., Fig. 7, Johnson et al. 2020). Moreover, gravitational effects
such as the displacement of the inner shadow relative to the pho-
ton ring, which are dependent on black hole spin and inclination,
can also contribute to observed asymmetries (e.g., Gralla et al.
2019; Chael et al. 2021). Some exotic spacetimes could produce
even larger distortions (e.g., Johannsen-Psaltis Metric in Fig. 5 of
Younsi et al. 2023).
However, very long baseline interferometry (VLBI) obser-
vations do not directly resolve the shadow itself, but rather
an observed emission structure that appears ring-like due
to synchrotron radiation from plasma near the photon orbit
(e.g., Event Horizon Telescope Collaboration 2019e, hereafter
M87∗ 2017 V). This observed shape, which we refer to as the
“emission ellipticity”, can deviate from circularity due to asym-
metric plasma distributions. For instance, emission from turbu-
lent flows can introduce ring ellipticity (e.g., Tiede et al. 2022a;
Tiede & Broderick 2024). Finally, we note that limited (u, v)-
coverage, noise, and algorithmic choices can introduce asym-
metries or artifacts in the reconstructed image, even if the
underlying source is circular. In this study, we aim to disentangle
the contributions to ellipticity by systematically comparing these
two sources: gravitational ellipticity and emission ellipticity. Our
goal is to assess the degree to which the observed ellipticity in
M87∗ EHT images is a result of fundamental spacetime prop-
erties, astrophysical factors, or artifacts introduced by imaging
algorithms.
In the EHT 2017 results of M87∗, the observed ring-
like structure appeared with approximately zero ellipticity,
with a diameter of 42 ± 3 µas. While ellipticity was mea-
sured in the reconstructed images (∼0.05−0.06), no inter-
pretation or calibration was performed (see Figure 18 in
Event Horizon Telescope Collaboration 2019f). A subsequent
analysis by Tiede et al. (2022a) demonstrated that images recon-
structed using the best set of imaging parameter combina-
tions, the so-called Top Set of eht-imaging, could not reli-
ably recover ellipticity, often favoring circular rings and yielding
an upper limit of ellipticity of ∼0.3. This limitation was pri-
marily due to sparse (u, v)-coverage, particularly in the north-
south direction, as well as the Top Set imaging parameter com-
binations that were not fully optimized for elliptical models.
Later, Tiede & Broderick (2024) reported an M87∗ ring elliptic-
ity of 0.09+0.07−0.06 using THEMIS, a Bayesian imaging approach
that was consistent with general relativistic magnetohydrody-
namic (GRMHD) simulations. These results raised important
questions about the origins of the ellipticity in the M87∗ images
and the effectiveness of different imaging methods in accurately
recovering it.
The 2018 observations confirmed the persistent struc-
ture of the M87∗ black hole shadow with a consistent ring
diameter of 43.3+1.5−3.1 µas, consistent with the 2017 results
Event Horizon Telescope Collaboration (2024, hereafter
M87∗ 2018 I). However, annual changes in brightness asymmetry
were observed with the position angle shifting from about 180◦
in 2017 to 210◦ in 2018 which may be attributed to turbulence
in the accretion flow. Changes in the brightness asymmetry
were previously reported by Wielgus et al. (2020). The addition
of the Greenland Telescope (GLT; Inoue et al. 2014) in 2018
substantially improved (u, v)-coverage (Fig. 1), particularly in
the north-south direction, leading to improved image fidelity. We
note that the EHT 2018 observations included four frequency
bands: two at lower frequencies (band 1 and 2 at 213.1 GHz
and 215.1 GHz) and two at higher frequencies (band 3 and 4 at
227.1 GHz and 229.1 GHz). The GLT participated only in bands
3 and 4, so we focused on data from the higher frequency bands in
this study. Among the four observing days, we used data from
April 21, which had the highest number of participating stations.
In this study, we followed the formalism based on
Tiede & Broderick (2024) to measure the ellipticity of the
ring-like emission structure in M87∗ using the 2018 EHT
A279, page 2 of 18
Dahale, R., et al.: A&A, 699, A279 (2025)
1050510
u (G )
10
5
0
5
10
v (
G
)
50
as
25
as
Fig. 1. EHT 2017 and 2018 (u, v)-coverage. The plot shows observa-
tions from April 10, 2017 (gray) and April 21, 2018 (blue and orange).
Both are at 229.1 GHz, which corresponds to the hi-band and band 4
in EHT 2017 and 2018, respectively. Orange points highlight the GLT
baselines. Red circles show the coverage gaps in 2017, and dashed cir-
cles mark the 25 and 50 µas resolution.
observations. We begin by evaluating the precision of elliptic-
ity measurements using a Fisher information analysis in Sect. 2.
Next, in Sect. 3, we refine the Top Set imaging parameter com-
binations for the regularized maximum likelihood (RML) and
deconvolution imaging methods from M87∗ 2018 I using ellip-
tical crescent models. Additionally, we tested a broader range
of elliptical crescent models with various ellipticities and ellip-
ticity position angles to assess any biases in the imaging meth-
ods using the data with the new 2018 (u, v)-coverage. In Sect. 4,
we apply the same imaging pipelines (and parameter combina-
tions) to the EHT 2018 M87∗ data to measure the ellipticity of
the M87∗ emission ring. We then compare these results with
those obtained from GRMHD model reconstructions. Finally,
in Sect. 5, we investigate the origin of the observed ellipticity
by comparing our results with theoretical models; we provide a
summary and conclusions in Sect. 6.
2. Fisher information analysis
The Fisher information matrix quantifies the amount of informa-
tion that observed data carry about certain model parameters θ.
The Fisher information matrix is given by
Fi j = E
[
∂ lnL(θ)
∂θi
∂ lnL(θ)
∂θ j
]
, (1)
where L(θ) is the likelihood function of the data conditioned
on the parameters θ. The terms θi and θ j are elements of the
parameter vector θ. The expectation E is taken with respect to the
probability distribution of the data. For independent Gaussian-
distributed data with variance σ2, the Fisher matrix simplifies to
Fi j =
∑
k
1
σ2k
(
∂Vk
∂θi
∂V∗k
∂θ j
+
∂V∗k
∂θi
∂Vk
∂θ j
)
, (2)
where Vk represents the observed complex visibilities. The
inverse of the Fisher information matrix gives the covariance
matrix of the parameter estimates. Hence, Σ = F−1, where Σi j
represents the covariance between parameters θi and θ j. We
assumed a Gaussian posterior distribution for the parameters,
where the standard deviations are given by the square root of
the diagonal elements of the covariance matrix,
σi =
√
Σii, (3)
which represents the uncertainty in the estimation of each param-
eter θi.
Given the improved EHT array in 2018, as shown in Fig. 1,
we estimated the precision with which the EHT can measure
ellipticity using Fisher information analysis.
For this analysis, we used an extension of the m-ring model
from Johnson et al. (2020). This model has a simple analytic
form in both the image and visibility domains, with analytic
gradients. This model was also used for the feature extraction
done in Event Horizon Telescope Collaboration (2019d, here-
after M87∗ 2017 IV) and M87∗ 2018 I, making it useful for phys-
ical interpretation. The m-ring model consists of a thin ring with
nonuniform brightness in azimuthal directions given by a Fourier
series. In polar coordinates (ρ, ϕ), it is defined as
I(ρ, ϕ) = S
pid
δ
(
ρ − d
2
) m∑
k=−m
βkeikϕ, (4)
where S is the total flux density of the ring, d is the diameter
of the ring, δ is the Dirac delta function. The coefficients satisfy
β−k = β∗k for a real image, and we set β0 = 1 to ensure that
S > 0. The parameter m represents the azimuthal order of the
m-ring. A finite-width m-ring is obtained by convolving Eq. (4)
with a Gaussian of FWHM α. This blurred m-ring is given by
I(ρ, ϕ;α) = 4 ln 2
piα2
S exp
(
−4 ln 2
α2
(ρ2 + d2/4)
)
×
m∑
k=−m
βkIk
(
4 ln 2
ρd
2α2
)
eikϕ, (5)
where Ik denotes the k-th modified Bessel function of the first
kind (Roelofs et al. 2023). A stretched m-ring with ellipticity τ,
rotated by an ellipticity position angle ξ and width α is given by
I(1 − τ cos(2(ϕ − ξ))ρ, ϕ;α).
We used a first-order (i.e., m = 1) stretched m-ring model
as shown in Fig. 2, as it is the simplest case (e.g., Tiede et al.
2022a; Tiede & Broderick 2024). The ellipticity parameter τ is
defined as τ = 1 − b/a, where a and b are the major and minor
axes of the ellipse, respectively. The ellipticity position angle
ξ represents the angle of the major axis a, measured counter-
clockwise from the north (east of north), as shown in Fig. 2.
For this analysis, we kept the brightness position angle (PA), η,
aligned with the ellipticity PA, ξ. Hence, we define ξ over the
full range of 0 to 360◦. We estimate the precision with which the
parameters of this model, fit to data on April 21, 2018 at band 4,
can be recovered. We employed the above Fisher information
approach implemented within the ngEHTforecast package1.
This method does not explicitly fit the m-ring model to the
data. Instead, it performs a second-order expansion of the log-
arithmic probability density around the best-fit location, provid-
ing an estimate of the uncertainty of each of fitted parameter.
1 https://github.com/aeb/ngEHTforecast, accessed with the
git commit 115bf73.
A279, page 3 of 18
Dahale, R., et al.: A&A, 699, A279 (2025)
0.30
0.25
0.20
0.15
0.10
0.05
All Stations Without GLT Without JCMT
1.8
2.4
3.1
3.7
4.3x10
3
0 90 180 270 360
0.30
0.25
0.20
0.15
0.10
0.05
0 90 180 270 360
 (E of N) degrees
0 90 180 270 360 5.7
9.7
13.8
17.8
21.9x10
3
a b
 = 1 - b/a
North
Fig. 2. Definition of parameters τ, ξ for m-ring model, along with respective marginalized uncertainties using Fisher information analysis. Left: A
visualization of a stretched m-ring model with parameters τ = 0.1, ξ = 45◦, a brightness asymmetry of 0.23, and a diameter of d = 46 µas, blurred
with a Gaussian kernel with a full width at half maximum of 10 µas. The brightness position angle, η = 45◦, is aligned with ξ. Right: Maps of
marginalized uncertainties in the parameters τ (top row) and ξ (bottom row) for m-ring models with various values of τ and ξ, derived using Fisher
information analysis on M87∗ band 4 data.
The parameter precision estimates assume that the fitting pro-
cess utilizes complex visibilities as input data, with broad priors
imposed on the station gain amplitudes and phases for each scan
(Pesce et al. 2022).
For this analysis, we tested m-ring models with τ ranging
from 0 to 0.3 and ξ ranging from 0 to 360◦. The diameter of
the thin elliptical m-rings is d =
√
ab = 46 µas, which is then
blurred by a 10 µas circular Gaussian (Tiede et al. 2022a). We
assume a brightness asymmetry β1 = 0.23 for the m-ring (see
Table 7 in M87∗ 2018 I). Figure 2 shows the marginalized uncer-
tainties στ and σξ, calculated using Eq. (3), for the parameters
τ and ξ, respectively. We computed στ and σξ for data with and
without GLT to assess its relevance in (u, v)-coverage. As seen
in Fig. 2, στ and σξ are approximately three to five times larger
for the data without GLT. This demonstrates that the additional
(u, v)-coverage provided by GLT baselines enhances the preci-
sion in constraining τ and ξ. Furthermore, στ and σξ are nearly
three times larger for the models with north-south alignment
(i.e., ξ = 0◦ or 180◦). For models with the same ξ but different
τ, στ and σξ remain approximately constant. During the 2017
and 2018 EHT campaigns, the James Clerk Maxwell Telescope
(JCMT) only recorded a single polarization feed, which could
have contributed to systematic polarization leakage in 2018. To
evaluate this issue, we performed a similar analysis for data with-
out JCMT. As shown in Fig. 2, removing JCMT has a mini-
mal effect (<10%) on the marginalized uncertainties of τ and
ξ. Therefore, JCMT data are retained for the remainder of the
analysis.
3. Geometric tests
Before analyzing the M87∗ data, two sets of tests with geo-
metric models were conducted to evaluate the accuracy of the
imaging and feature extraction methods in recovering the true
values and assessing potential biases in the imaging meth-
ods. We used geometric models with various ellipticity, τ,
and the position angle of the ellipse’s major axis, ξ (north to
east), to check potential biases depending on (u, v)-coverage.
The first test selects the Top Set imaging parameter combi-
nations of the RML and CLEAN methods using four ellip-
tical crescent models (m = 1) of τ = 0.187 and ξ =
[0◦, 45◦, 90◦, 315◦]. The values of τ and ξ are chosen to be con-
sistent with Tiede et al. (2022a). The second test evaluates the
ellipticity feature extraction using 42 elliptical crescent mod-
els (m = 1) with τ = [0.0, 0.05, 0.1, 0.15, 0.2, 0.25, 0.3] and
ξ = [0◦, 60◦, 120◦, 180◦, 240◦, 300◦]. We used eht-imaging
to generate synthetic data using the geometric models listed
above. Before generating the synthetic data, we also added
a milliarcsec-scale Gaussian to these geometric models. This
Gaussian mimics jet emission on scales of milliarcseconds to
arcseconds, to which short intra-site baselines of the EHT are
sensitive (M87∗ 2017 IV). We added station gain corruptions
derived from M87∗ and thermal noise to mimic the real obser-
vational data (M87∗ 2018 I). Synthetic data with random gain
corruptions are also tested using Bayesian imaging, where the
posterior distribution of the gain parameters is estimated.
Imaging was performed using both forward and inverse
modeling techniques. The forward modeling consists of RML
and Bayesian methods, while the inverse modeling employs
a CLEAN-based deconvolution method. For RML imaging,
we used eht-imaging (Chael et al. 2016, 2018, 2019) and
SMILI (Akiyama et al. 2017a,b, 2019). For Bayesian imaging,
we used Comrade (Tiede 2022) and THEMIS (Broderick et al.
2020a,b). For CLEAN-based deconvolution, we used DIFMAP
(Shepherd 1997, 2011). A more detailed explanation of each
imaging method is provided in M87∗ 2017 IV and M87∗ 2018 I
A279, page 4 of 18
Dahale, R., et al.: A&A, 699, A279 (2025)
30 as
Tr
ut
h
ecres000 ecres045 ecres090 ecres315
eh
tim
sm
ili
Di
fm
ap
Fig. 3. Elliptical crescent models with different ellipse position angles.
From left to right, ecres000, ecres045, ecres090, and ecres315.
From top to bottom, groundtruth images and fiducial images from
eht-imaging, SMILI, and DIFMAP for band 4. DIFMAP images are
presented with a beam convolution of a 20 µas circular Gaussian
(M87∗ 2018 I).
(see Appendix A for updates to the Bayesian imaging meth-
ods). We note that while M87∗ 2018 I has employed both imag-
ing methods and visibility domain model fitting, we focused on
the imaging methods in this study.
3.1. Imaging parameter selection with the elliptical crescent
models
The dataset for the first test is used to sub-select the Top Set
imaging parameter combinations for the RML and CLEAN
methods. Bayesian methods do not require a parameter survey,
and thus the geometric models used in this step were not tested.
Imaging results from the RML and CLEAN methods depend on
a set of parameters determined by various imaging assumptions,
including hyperparameters and optimization choices. Each com-
bination of parameters can yield slightly different image mor-
phology and fit quality for the data. Therefore, it is necessary
to survey different parameter combinations and select those that
provide the best fit to the data and most closely reproduce the
groundtruth image (if from synthetic data), referred to as the
Top Set. For eht-imaging, SMILI, and DIFMAP, the Top Set
was previously selected in M87∗ 2018 I based on four geometric
models (cres180, dblsrc, disk, ring), using data from M87∗.
The number of Top Set parameter combinations varies across
methods due to differences in their parameter space. Addition-
ally, variations between bands arise from different (systematic)
uncertainties inherent to each dataset (see M87∗ 2018 I). How-
ever, we did not test whether the Top Set parameters are valid
for different elliptical structures. To investigate this, we selected
a new Top Set by imaging four additional geometric models
of elliptical crescents: ecres000, ecres045, ecres090, and
ecres315 (Fig. 3, top). The imaging survey is performed over
the original Top Set from M87∗ 2018 I, meaning the new Top Set
corresponds to a subset of the original.
The Top Set selection is based on two metrics: (i) the nor-
malized cross-correlation (ρNX) between the reconstructed and
Table 1. Number of new Top Set parameter combinations.
Band eht-imaging SMILI DIFMAP
Band 3 860/874 (98%) 4429/5333 (83%) 189/303 (62%)
Band 4 1332/1469 (91%) 3457/5108 (68%) 215/465 (46%)
Notes. This table shows the number of new Top Set parameter combi-
nations compared to the original Top Set. The number ratio relative to
the original Top Set is given in parentheses.
groundtruth images for synthetic data and (ii) the reduced χ2 on
the real M87∗ data. Since the latter was already satisfied in the
original Top Set (i.e., χ2 < 2), the new Top Set is selected based
solely on the ρNX of the elliptical crescent geometric models. The
ρNX cutoff was determined in the same manner as described in
M87∗ 2017 IV and M87∗ 2018 I, by convolving the groundtruth
image with the effective resolution from the longest baseline
(∼24 µas; see Fig. 1). Then, the cutoff value was determined as
0.75 for both band 3 and band 4, with no variations across the
models.
As a result, several parameter combinations passed the
thresholds, demonstrating their ability to reconstruct the ellipti-
cal crescent structure while distinguishing the structural position
angle. Table 1 summarizes the number of new Top Set parameter
combinations for each pipeline and band compared to the origi-
nal Top Set. The images reconstructed using the fiducial param-
eters are shown in Fig. 3.
3.2. Evaluation with the elliptical crescent models
After selecting the new Top Set parameters for the RML
(eht-imaging and SMILI) and CLEAN (DIFMAP) methods, we
performed additional imaging of the geometric models using
all methods for performance evaluation. The Bayesian methods,
THEMIS and Comrade, do not require a Top Set selection since
their only hyperparameters are the field of view and the number
of pixels. Therefore, we directly performed the geometric tests
with these two methods. For these models, ξ coincides with the
position angle of the brightest spot (see Appendix B for tests
with different alignments). This approach aims to identify spe-
cific cases where ellipticity or position angle models are not well
recovered due to (u, v)-coverage limitations. To measure elliptic-
ity and the ellipticity position angle, we used a stretched m-ring
template from VIDA (Tiede et al. 2022b). For all feature extrac-
tion in this work, we used a m-ring of order four in azimuth and
order one in width, following Tiede et al. (2022a).
Figure 4 presents a subset of the measured τ − ξ distribu-
tions from the respective geometric model reconstructions for
different imaging pipelines. The results indicate that ξ is less
constrained at 0◦ and 180◦ due to relatively poorer (u, v) cov-
erage in these directions, as expected from the Fisher informa-
tion analysis (Sect. 2). The measured ellipticity is still influenced
by the underlying angular resolution. For instance, convolving
the images and models with a 5 µas circular Gaussian reduces
the ellipticity measurement of 0.1 by ∼3% (see Appendix C for
more discussions about the resolution effect on measured ring
features). In our results, the resolution limit of DIFMAP is given
as ∼20 µas (M87∗ 2018 I), while the forward modeling results
from RML methods including Bayesian approaches can achieve
super-resolution. Therefore, measured ellipticities from recon-
structed images that are up to ∼30% lower than the true value
are considered acceptable (gray shaded, vertical area in Fig. 4;
see also Fig. C.1). As a result, all imaging methods successfully
recovered the true τ and ξ values within their own resolution
limit. However, it is worth noting that, ignoring the resolution
A279, page 5 of 18
Dahale, R., et al.: A&A, 699, A279 (2025)
=0
.1
, 
=
0
Comrade
30 as
=0
.0
5,
 
=
60
=0
.1
, 
=
12
0
=0
.1
5,
 
=
18
0
=0
.2
, 
=
24
0
0.1 0.2 0.3
=0
.2
5,
 
=
30
0
THEMIS
0.1 0.2 0.3
ehtim
0.1 0.2 0.3
Ellipticity ( )
smili
0.1 0.2 0.3
25
0
25
Difmap
25
0
25
25
0
25
25
0
25
Tr
ut
h (
de
g)
25
0
25
0.1 0.2 0.3
25
0
25
Fig. 4. Subset ellipticity measurements for geometric models (6 out of 42) for all imaging methods. From left to right: groundtruth image of a given
geometric model, τ−ξ distribution using Comrade, THEMIS, eht-imaging, SMILI, and DIFMAP for band 4 synthetic data. Each row corresponds
to a different geometric model, with the true model shown in the leftmost column. The vertical and horizontal dashed lines in each panel of τ − ξ
distribution indicate the true values. The contours denote 68% and 95% confidence intervals. The vertical dashed line shows τ measured with
VIDA for the groundtruth model. The gray shaded region spans the range of τ values for the groundtruth model, from the unconvolved case to the
convolution of a circular Gaussian of 20 µas FWHM.
effects, the RML and deconvolution imaging methods tend to
underestimate the ellipticity for models with extreme elliptici-
ties in all 42 tests.
4. Ring ellipticity of M87∗ and its comparison with
GRMHD simulation snapshots
4.1. Ring ellipticity of M87 ∗
Following the geometric tests that validated the imaging
pipelines and their parameter combinations for ellipticity mea-
surement, they were applied to the M87∗ data2 (see Fig. 5). The
imaging results correspond to a subset of images in M87∗ 2018 I
for RML and CLEAN methods (Table 1), while remaining con-
sistent for Bayesian methods. Ring features were extracted from
the images using VIDA3, as summarized in Table 2. The mea-
sured ellipticities are consistent across all imaging approaches
2 Data accessed from https://datacommons.cyverse.org/
browse/iplant/home/shared/commons_repo/curated/EHTC_
M87-2018_Mar2024/
3 A m-ring model of first-order in width and fourth-order in azimuth
template was used, consistent with the template used in the geometric
tests (see also, Tiede et al. 2022a).
A279, page 6 of 18
Dahale, R., et al.: A&A, 699, A279 (2025)
Table 2. Measured ellipticity and position angle for EHT 2018 M87∗ images.
Band Comrade THEMIS eht-imaging SMILI DIFMAP Average Band average
τ
Band 3 0.07+0.04−0.03 0.05
+0.02
−0.03 0.07
+0.03
−0.03 0.09
+0.04
−0.03 0.10
+0.04
−0.04 0.07
+0.03
−0.03 0.08+0.03−0.02Band 4 0.09+0.04−0.03 0.09
+0.01
−0.01 0.06
+0.02
−0.02 0.07
+0.02
−0.02 0.05
+0.03
−0.02 0.08
+0.03
−0.02
ξ
Band 3 44.1+10.5−12.8 48.3
+4.0
−4.3 56.0
+9.8
−7.2 66.6
+2.3
−8.9 54.2
+6.2
−4.0 53.5
+6.0
−6.2 50.1+6.2−7.6Band 4 40.0+11.2−18.3 38.9
+6.0
−4.1 48.4
+10.6
−19.7 50.4
+4.9
−11.3 52.4
+6.5
−10.7 44.0
+6.7
−9.7
Notes. Ellipticity, τ (in rows labeled τ), and its position angle, ξ in degrees (in rows labeled ξ), measured from the EHT 2018 M87∗ images. The
position angle ξ is measured east of north. For each method and band, the main value reported is the median, and the error range represents the
1σ uncertainty around the median. The “Average” column provides the weighted median and 1σ error across methods for each band. The “Band
Average” column gives the overall weighted median and 1σ error across all methods and both bands for τ and ξ, respectively.
Ba
nd
 3
30 as
Comrade THEMIS ehtim smili Difmap
 
- Comrade
- THEMIS
- ehtim
- smili
- Difmap
Ellipticity
De
ns
ity
PA (E of N)
Ba
nd
 4
0.1 0.2
 
50 0 50
 (deg)
De
ns
ity
Fig. 5. EHT 2018 M87∗ images and ellipticity (τ) and ellipticity position angle (ξ) distributions. (left to right) Images from each imaging method
(Comrade, THEMIS, eht-imaging, SMILI, and DIFMAP). For Comrade and THEMIS, mean posterior images are shown. Fiducial images from
the respective Top Sets are shown for the other methods. The two right panels show the distributions of τ and ξ for each method. Top and bottom
rows show results for band 3 and band 4, respectively. Colors correspond to each method (see legend).
and at both frequency bands, 3 and 4, yielding an average ellip-
ticity of τ = 0.08+0.03−0.02. The average position angle of the ellipse
is ξ = 50.1+6.2−7.6 degrees, consistent across different imaging meth-
ods within 2σ. The average across all methods and bands is
computed by taking weighted median and 1σ error. Given the
relatively better performance of Bayesian imaging methods, as
described in Sect. 3 and shown in Fig. 4, we computed the aver-
age τ = 0.08+0.02−0.02 and ξ = 44.4
+5.8
−6.4 only from these methods.
These averages are in good agreement with the values obtained
by averaging over all methods. Notably, the direction of ξ is
approximately aligned with the angle of brightest spot on the
ring, ∼200−230◦ (M87∗ 2018 I).
The measured τ is also consistent with results of Tiede et al.
(2022a), which reported τ = 0−0.3 and inferred accretion turbu-
lence as the dominant source of the measured ellipticity, and with
those of Tiede & Broderick (2024) which reported τ = 0.09+0.07−0.06.
We note that while this work used 2018 EHT observations, the
above comparisons are made with the works that used 2017
EHT observations. The uncertainties in our results are lesser than
those of previous studies from the 2017 EHT data, owing to the
improved (u, v)-coverage in the 2018 EHT.
4.2. Comparison with GRMHD simulations
With the results, we applied the same imaging and feature
extraction methods to GRMHD models with different physi-
cal parameters to investigate the underlying physical depen-
dencies. For this purpose, we used two GRMHD libraries
of KHARMA (Prather et al. 2021) and BHAC (Porth et al. 2017).
Thermal electron distribution (Maxwell-Jüttner distribution)
models were drawn from KHARMA, while nonthermal electron
distribution (kappa distribution) models were sourced from BHAC
(Fromm et al. 2022; Cruz-Osorio et al. 2022). Out of the 299
GRMHD models that were considered in M87∗ 2018 II, we
selected 218 models with an outflow power exceeding 1042 erg/s
(M87∗ 2017 I, M87∗ 2017 V, M87∗ 2018 II). After the outflow
threshold was applied, we selected 100 models for imaging and
feature extraction, of which roughly 75% were thermal models
and the remainder nonthermal. There were 18 models for each
spin value of −0.94, −0.5, +0.5, and +0.94 from the KHARMA
thermal models, resulting in 72 thermal models in total. The
remaining 28 models were chosen from the BHAC nonthermal
models that met the threshold; we selected seven models for each
spin. Since black hole spin and inclination determine a displace-
ment of the inner shadow that can manifest as non-circularity
(e.g., Tiede et al. 2022a), this sample can investigate the poten-
tial correlation between spin and ellipticity. Among the 100
selected GRMHD models, 83 are strongly magnetized, magnet-
ically arrested disk (MAD) models, and 17 are weakly magne-
tized standard and normal evolution (SANE) models. Random
snapshots were taken from each model and scaled to the best-fit
mass based on snapshot scoring implemented in M87∗ 2018 II.
A279, page 7 of 18
Dahale, R., et al.: A&A, 699, A279 (2025)
Tr
ut
h
40 as
Co
m
ra
de
eh
tim
Fig. 6. Subset of GRMHD images (10 out of 100 models) from KHARMA and BHAC libraries: (from top to bottom) ground truth, reconstructed
images by Comrade (mean image) and eht-imaging (one random from Top Set) for band 4. Thermal models from KHARMA are marked in orange
and nonthermal models are marked in blue. The ground truths are shown after blurring with a 12 µas circular Gaussian.
The scaling factor is a ratio of observed-to-simulated mass-to-
distance ratios.
The scaled snapshots were then used to generate synthetic
data following the same procedure described in Sect. 3. The
synthetic data were imaged using eht-imaging and Comrade,
as representatives of RML and Bayesian methods, respec-
tively. As presented in Fig. 6, the images were consistent with
the groundtruth. We then extracted the ellipticities from these
images using VIDA and compared them with the true elliptic-
ity. The groundtruth GRMHD snapshot images were convolved
with a 12 µas circular Gaussian to take resolution effect into
account. The 12 µas size corresponds to the obtained super-
resolution from Comrade and eht-imaging, which is esti-
mated by comparing ρNX of the original and blurred groundtruth
images with different sizes of circular Gaussian kernel. This is
an average from results for all 100 GRMHD models and is con-
sistent between Comrade and eht-imaging. Figure 7 shows
the differences of τ and ξ between reconstructed images (from
eht-imaging and Comrade) and the true values that are cen-
tered at zero in both parameters. This suggests that the observed
ellipticity and its angle are real and not an artifact of the imaging
process or instrumental limitations. The broader spread in ξ is
due to models with low ellipticity, where the orientation angle is
naturally more difficult to constrain.
5. Origin of the M87∗ ring ellipticity
As introduced in Sect. 1, observed ellipticity in EHT images
can arise from two main sources: (i) gravitational ellipticity due
to spacetime curvature and (ii) emission ellipticity from astro-
physical structure. In this section, we focus on disentangling the
contributions using GRMHD simulations with varying physical
parameters. We utilized all 299 GRMHD models described in
Sect. 4.2, which span a wide range of parameters, including
black hole spin, electron distribution function (eDF) (thermal
and nonthermal), magnetic field states (SANE and MAD), and
ion-to-electron temperature ratios in both low- and high-density
regions (Rlow and Rhigh, respectively; see Mos´cibrodzka et al.
2016 for definitions). For each model, we measured the image
ellipticity from the corresponding groundtruth GRMHD snap-
shot, scaled to the best-fit mass and blurred with a 12 µas
Gaussian, as described in Sect. 4.2. Figure 8 shows that the
observed M87∗ ellipticity is consistent with the distribution of
all 299 GRMHD models, falling within their median and 68%
confidence intervals.
General relativistic magnetohydrodynamic simulations are
uniquely suited to probing both gravitational ellipticity and
emission ellipticity. The gravitational ellipticity arises from the
curvature of spacetime near the event horizon and is directly
influenced by black hole spin. For instance, a Kerr black hole
with spin of a = 0.94−0.999 and viewed at an inclination of
17◦ can produce a gravitational ellipticity of ∼0.02 (see Fig. 8,
top right). This level of distortion cannot explain the mea-
sured ellipticity of M87∗. Even if we consider a 3◦ uncertainty
(Mertens et al. 2016) on the inclination of M87∗, with 20◦ incli-
nation and spin a = 0.999, the maximum ellipticity reaches only
∼0.03 (Johnson et al. 2020). Moreover, as shown in Table 3 and
Fig. 8, there is no statistically significant correlation between the
spin and the measured ellipticity in full GRMHD images. This
indicates that while spin contributes to the gravitational ellip-
ticity, it does not dominate the total observed ellipticity in the
images. Table 3 also shows no significant correlation between
ellipticity and magnetic field state (SANE and MAD), implying
that the global magnetic field structure does not have a strong
influence on ellipticity. In contrast, Fig. 8 and Table 3 suggest
that nonthermal models and simulations with higher values of
Rhigh are correlated with larger emission ellipticity. Nonther-
mal models tend to generate more extended or diffuse emis-
sion, and increasing Rhigh shifts emission from the disk to the
jet region; both effects increase the ellipticity of the ring in the
image.
To quantify the role of asymmetric non-ring emission, we
defined a “non-ring flux fraction” by subtracting the best-fit cir-
cular Gaussian ring (using VIDA) from each GRMHD image
and setting negative residuals to zero. The ratio of the remain-
ing positive flux to the total flux defines the non-ring flux frac-
tion. We computed Spearman correlation coefficients between
this quantity and the measured image ellipticity, using a boot-
strapping method to account for sample variance (e.g., Curran
2014; Cheng et al. 2023). Figure 9 reveals a positive correlation
between the non-ring flux fraction and ellipticity. We note that
upon visual inspection, it does not seem that the outliers appear
from transient flux eruption events. This supports the conclu-
sion that emission ellipticity, driven by turbulent accretion struc-
tures outside the ring, is the dominant contributor to elliptic-
ity in GRMHD images. These results suggest that the observed
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0.2 0.0 0.2
Reconstructions Truth
0
5
10
15
20
25
30
Co
un
t
Comrade
ehtim
200 100 0 100 200
Reconstructions Truth (deg)
0
5
10
15
20
25
Co
un
t
Fig. 7. Histograms of differences in τ (top) and ξ (bottom) between
reconstructed and true GRMHD values. Results from Comrade (blue)
and eht-imaging (orange) are shown, both centered around zero for
each parameter.
ellipticity in the M87∗ image is naturally explained by emission
ellipticity arising from astrophysical effects such as turbulent
accretion flow.
6. Summary and conclusions
In this study, we measured the ellipticity of the emission
ring in the black hole images of M87∗ using the EHT 2018
observations. Fisher information analysis was employed to first
assess the feasibility of ellipticity measurements, after the addi-
tion of the GLT, which filled gaps in the north-south (u, v)-
coverage. This analysis shows that the inclusion of the GLT
improves the precision in constraining ellipticity parameters by
∼3−5 times. With the improved (u, v)-coverage compared to the
EHT 2017, we then managed to extract the ellipticity success-
fully from five different methods that cross-compare the results.
This is the first method-wide confirmation of the ellipticity
measurement.
For imaging with the RML and deconvolution meth-
ods, the imaging parameter combinations were sub-selected
from the original ones in M87∗ 2018 I, based on imag-
ing results for four elliptical geometric models. This step
is not required for Bayesian imaging methods such as
Comrade and THEMIS. All imaging methods (and parame-
ters) were then evaluated using various geometric elliptical
ring models with differing position angles and ellipticities, and
they successfully recovered the groundtruth values in most
cases.
Applying these approaches to the M87 data, we measured
the ellipticity to be τ = 0.08+0.03−0.02 on average, with consis-
tency across all imaging methods and previous findings from
EHT 2017 (Tiede & Broderick 2024). In addition, the position
angle of the ellipse is measured as ξ = 50.1+6.2−7.6 degrees,
indicating that the ring structure is slightly elongated along
an axis that is roughly aligned with the brightest spot on
the ring, ∼200−230◦ (M87∗ 2018 I). We also note that while
Kim et al. (2025) reported τ = 0.06 ± 0.04 for the image of
M87 at 86 GHz, which is consistent with our measurements at
230 GHz, this is an astrophysical effect at 86 GHz. Compari-
son with GRMHD simulations first confirms that the measured
ellipticity is real, but no strong constraints on the parameters
including the spin are yet found. However, the parameters pro-
viding more non-ring flux (that is, nonthermal emission and
higher Rhigh) tend to reproduce larger ellipticity. This is con-
firmed by comparison with the non-ring flux fraction to the
measured ellipticity. In line with this, to explain the measured
ellipticity of M87, the astrophysical effects such as turbulent
accretion flow are required. It is worth noting that the addi-
tional non-circularity by the inclined black hole (e.g., tilted
accretion disk) or exotic spacetime are not completely ruled
out.
With the current ground-based array, our ability to pre-
cisely measure the ellipticity of the emission ring is constrained
by the dominance of turbulent astrophysical effects associated
with the direct image (Gralla & Lupsasca 2020; Johnson et al.
2020). In the case of M87∗, detecting the gravitational influ-
ence on ellipticity, and hence measuring the spin, requires us
to overcome these limitations through one of two approaches.
The first approach involves continued long-term monitoring
of M87∗, allowing for temporal averaging of the turbulent
effects, thereby enabling the underlying gravitational signa-
ture to emerge more clearly. For instance, in Fig. 10, we
present the measured ellipticities of 1000 snapshots spanning
∼370 days for one of the GRMHD models, along with the ellip-
ticity of the time-averaged image in the right panel. The aver-
age image clearly reveals the photon ring, while the turbu-
lent accretion flow is averaged out. This example illustrates
that future observations could detect ellipticity arising from
gravitational effects, as highlighted by the red line in the left
panel.
The second approach entails space VLBI observations,
which would provide the necessary angular resolution to detect
the photon ring (Gralla et al. 2019; Johnson et al. 2020). Unlike
the direct image, the photon ring is expected to be less affected
by astrophysical turbulence, making it a more direct probe of
the underlying spacetime structure and gravitational effects near
the black hole. We also note that the direct image is more ellip-
tical than the photon ring (see Figure 6 in Gralla & Lupsasca
2020). To better distinguish the relative effects on the
A279, page 9 of 18
Dahale, R., et al.: A&A, 699, A279 (2025)
Non-Thermal Thermal
eDF
0.0
0.1
0.2
0.3
0.4
0.5
El
lip
tic
ity
 (
)
MAD SANE
Magnetic Field State
-0.94 -0.5 0.0 0.5 0.94
Spin
1.0 10.0 40.0 80.0 160.0
Rhigh
0.0
0.1
0.2
0.3
0.4
0.5
El
lip
tic
ity
 (
)
0.0 1.0 10.0
Rlow
All Models
Pjet > 1042 erg/s
Median and 68% CI
M87
Spin = 0.999
Spin = 0.94
Spin = 0.50
Fig. 8. Ellipticity of truth GRMHD models (blurred with 12 µas Gaussian) for different GRMHD parameters. All 299 models are shown in blue,
and the models that pass the jet power criteria are shown in orange (note that while plotting we combined the nonthermal models with the same
parameters but different nonthermal emission fraction ()). The over-plotting on the histograms shows the median value and the 68% confidence
interval. The ellipticity of M87 is shown as a dashed green line, with its error range shown in the shaded green region. In the top rightmost panel,
the ellipticity of the critical curve for a Kerr black hole (see Figure 7, Johnson et al. 2020) for different spins (inclination = 17◦) is plotted to
compare it with the histograms of the respective spins. The spin = 0.5 case is shown by dashed black line; the spin = +0.94 is represented by a solid
black line and the spin = +0.999 case is given by a dotted black line.
Table 3. Spearman correlation for ellipticity of GRMHD truth models and their physical parameters.
Models eDF Magnetic field state Spin Rhigh Rlow
All C = −0.31, p = 0.05 C = −0.09, p = 0.44 C = −0.12, p = 0.22 C = 0.20, p = 0.04 C = −0.02, p = 0.50
Pjet > P0 C = −0.35, p = 0.03 C = −0.17, p = 0.26 C = −0.13, p = 0.18 C = 0.22, p = 0.03 C = −0.02, p = 0.48
Notes. Spearman correlation coefficient C and its associated p-value for the ellipticity of GRMHD truth models and their physical parameters.
These were computed using a bootstrapping method (e.g., Curran 2014; Cheng et al. 2023). A p-value≤ 0.05 indicates a rejection of the null
hypothesis that the parameters are not correlated. Cases considered correlated (p≤ 0.05) are highlighted in green. P0 = 1042 erg/s is the jet-power
threshold applied to the models.
ellipticity from different potential origins, higher precision
measurements of ellipticities from better angular resolution
are necessary. Looking ahead, future observations with higher
angular resolution, such as those from the next-generation
EHT (ngEHT; Johnson et al. 2023; Doeleman et al. 2023), the
Event Horizon Imager (EHI; Roelofs et al. 2019), the Tera-
hertz Exploration and Zooming-in for Astrophysics (THEZA;
Gurvits et al. 2022), and the Black Hole Explorer (BHEX;
Johnson et al. 2024; Akiyama et al. 2024), will offer further con-
straints by resolving finer photon ring structures. As demon-
strated by the addition of the GLT to the EHT array, the
inclusion of future sites in the EHT and ngEHT arrays will
improve the precision of measurements of the ring ellipticity
of M87∗.
A279, page 10 of 18
Dahale, R., et al.: A&A, 699, A279 (2025)
0.0 0.2 0.4 0.6 0.8 1.0
Non-ring flux fraction
0.0
0.1
0.2
0.3
0.4
0.5
0.6
El
lip
tic
ity
 (
)
Non-Thermal ( = 0.117)
Thermal ( = 0.072)
 (C=0.43, p=0.00)
0.0 0.2 0.4 0.6 0.8 1.0
Non-ring flux fraction
Rhigh = 1 ( = 0.067)
Rhigh = 10 ( = 0.078)
Rhigh = 40 ( = 0.089)
Rhigh = 80 ( = 0.108)
Rhigh = 160 ( = 0.112)
Fig. 9. Ellipticity of all 299 GRMHD truths (convolved with 12 µas Gaussian) compared with the non-ring flux fraction. The left and right panels
are the same, but the colors are different for (non)thermal models (left) and Rhigh values (right). The ellipticity of M87 is shown by a dashed black
line, with its error range shown in the shaded gray region. The median τ for each case is shown in the legend.
0 50 100 150 200 250 300 350
Days
0.0
0.1
0.2
0.3
El
lip
tic
ity
 (
)
Snapshot Median & 68% CI Average Image
40 as
Fig. 10. Ellipticities of 1000 snapshots spanning ∼370 days for a GRMHD model with the following parameters: magnetic field configura-
tion = MAD; thermal eDF; black hole spin =−0.5; Rhigh = 160, Rlow = 1; and inclination angle = 17◦. The ellipticity of each snapshot is measured
after blurring with a 12 µas Gaussian (blue). The median and 68% confidence interval of the time series are shown with a solid green line and
shaded region, respectively. The ellipticity of the time-averaged image (right) is shown with a red line.
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1 Instituto de Astrofísica de Andalucía-CSIC, Glorieta de la
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Yuseong-gu, Daejeon 34055, Republic of Korea
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Appendix A: Bayesian imaging methods
In M87∗ 2018 I, THEMIS used a 5 × 5 pixel grid (raster) as it
was used in M87∗ 2017 IV. Since this size, may not be suit-
able for the 2018 EHT coverage or elliptical rings, similar to
Tiede & Broderick (2024), we performed a small survey of dif-
ferent imaging models, changing the number of pixels and com-
puting the Bayesian evidence to find the optimal raster size. The
Bayesian evidence (Z) of a model M with parameters θ is given
by,
Z(M) =
∫
L(V|θ,M)p(θ,M)dθ. (A.1)
where L is the log-likelihood, and V is the observed data.
In a Bayesian setting, the optimal model corresponds to the one
with the highest evidence. The Bayesian evidence was computed
using thermodynamic integration (Lartillot & Philippe 2006),
utilizing the parallel tempering scheme from Syed et al. (2021).
Given the computational complexity of running a survey for each
set of data, we instead focused on one of the geometric ellipti-
cal ring synthetic datasets in Sect. 3. Specifically, we considered
the elliptical ring with τ = 0.1 and ξ = 120◦. The evidence for
this survey is given in Tab A.1. According to these values, 6 × 6
raster has the highest evidence. Furthermore, Fig. A.1, which
shows how the true value of τ = 0.1 and ξ = 120◦ is recovered
correctly by the 6 × 6 raster. Hence, throughout the analysis in
this paper, we used the 6 × 6 raster for THEMIS.
Table A.1. Evidence of different raster sizes.
Raster size 5 × 5 6 × 6 7 × 7
Evidence −2890 −2885 −2889
Truth
30 as
5x5
0.1 0.2
25
0
25
Tr
ut
h (
de
g)
6x6
0.1 0.2
Ellipticity ( )
7x7
0.1 0.2
Fig. A.1. Evaluation of different rasters of THEMIS through synthetic
data tests. The true m-ring model with τ=0.1 and ξ = 120◦ is shown
on the top. The posterior mean images from THEMIS for 5 × 5, 6 × 6,
and 7 × 7 rasters are shown in the middle. τ and ξ - ξTruth posteriors
are shown at the bottom. The contours are shown for 68% and 95%
confidence intervals. The dashed line marks the truth values.
In M87∗ 2018 I, Comrade imaging used closure phases and
visibility amplitudes as the data products, and fit only for gain
amplitudes. The prior used for the raster assumed that the pixels
are independently distributed (Dirichlet prior). There have been
several developments in Comrade since then. In this paper, we
used complex visibilities as the data products and fit for both
amplitude and phase gains (with reference to one station). The
image model is a 64 × 64 raster with a field of view of 200 µas.
An extended Gaussian component was used to model the emis-
sion on milliarcsecond scales. The location, position angle, and
fractional flux are the model parameters, while the size is fixed
as 1000 µas. The total flux of the image plus the Gaussian com-
ponent was fixed to 1.1 Jy as assumed in network calibration
for the M87* data. For the raster, we use a first-order Gaus-
sian Markov random field (GMRF) prior on the log-ratio trans-
formed pixel intensities. Hence, the pixels are spatially corre-
lated. The GMRF is added to a mean image which is a 40 µas
Gaussian (size of the Gaussian does not drastically change the
reconstructed images). The variance and correlation length of
the random field are the hyperparameters. The variance and the
correlation length are included as parameters in the model. The
amplitude gain priors are the same as used in M87∗ 2018 I. We
allow gains to vary every scan. For the gain phases, the gain
phase for ALMA is set to be zero. In the case when ALMA is
not present in the scan, we select the next reference station alpha-
betically. For rest of the gain phase priors, we use von Mises
prior with zero mean and a concentration parameter pi−2 (which
is essentially a uniform prior on the interval [−pi, pi]). Sampling
is performed using Hoffman & Gelman (2014), in the Julia sam-
pling package AdvancedHMC.jl4, in the same way as done in
M87∗ 2018 I.
Appendix B: Additional geometric tests
In Sect. 3, we performed the tests with geometric models where
the ellipticity position angle ξ was aligned with the brightness
position angle η. In order to be certain that an offset between
position angles, will not introduce any additional biases in mea-
suring ellipticity, we performed this additional test shown in
Fig. B.1. We chose the η to be perpendicular to ξ to test the
extreme case. This test was performed with Comrade for all τ
and ξ but Fig. B.1 shows only the two cases when ξ = 0◦ and
ξ = 120◦. In all cases, Comrade recovers the true τ correctly. For
ξ, we see the same pattern as seen in Fig. 4 and as mentioned in
Sec. 3. Even in these tests, we found that true ξ can be recovered
with narrow posteriors for all cases, except when ξ is aligned
North-South, for which we get broad posteriors.
Appendix C: The effect of resolution on the
measured ellipticity
VIDA stretched m-ring template models the ellipticity of a m-ring
by stretching a symmetric m-ring template in x-direction and
compressing it in y-direction. Assuming this definition of mea-
sured ellipticity, we want to solve for an analytical equation that
relates τ with a Gaussian blurring kernel. To do so, consider a
zero-order symmetric m-ring with flux F0 and radius r0,
F0
2pir0
δ(r−
r0), which has a Fourier transform given by, F0J0(2pir0|u|). J0 is
a zeroth-order Bessel function of the first kind and u, v are the
spatial coordinates in the Fourier domain. Stretching the m-ring
in the u-direction by β and compressing in the v-direction by β,
4 https://github.com/TuringLang/AdvancedHMC.jl
A279, page 15 of 18
Dahale, R., et al.: A&A, 699, A279 (2025)
Truth
=0.1, = 0 , =90
30 as
=0.1, = 120 , =210
Comrade
25
0
25
0.1 0.2
Ellipticity ( )
25
0
25
Tr
ut
h (
de
g)
Fig. B.1. Geometric tests for the cases when brightness PA η is perpen-
dicular to ξ. The leftmost column shows the ground truth for the cases
τ = 0.1, ξ = 0◦, η = 90◦ (top) and ξ = 120◦ (bottom). Mean images
from Comrade posteriors are shown in the middle. The rightmost col-
umn shows measured τ and ξ posteriors (68% and 95% confidence
contours) compared with true values in dashed lines. The gray shaded
region marks the region between τ of the groundtruth model without
any convolution and with convolution of a Gaussian up to 20 µas size.
we get:
I˜(u, v; r0, τ) = F0J0
2pir0
√
u2
1 − τ + (1 − τ)v
2
 (C.1)
where I˜(u, v) is the intensity profile in the Fourier domain
(or the amplitude visibilities at u, v), τ = 1 − b/a = 1 −
(2r0β)/(2r0/β) = 1 − β2. If we blur this stretched m-ring with
a circular Gaussian of full-width at half maximum (FWHM) α,
we get,
I˜(u, v; r0, τ, α) = I˜(u, v; r0, τ) × exp
(−pi2|u|2α2
4 log 2
)
(C.2)
From Eq. C.2, it is not possible to get a τ − α rela-
tion without the u and v dependence. Instead, we used geo-
metric elliptical m-ring models with ξ = 120◦ and τ0 =
[0.05, 0.1, 0.15, 0.2, 0.25, 0.3] and measured the ellipticity with
VIDA by blurring the models with different circular Gaussian
FWHM (α). We then fitted a Gaussian to each measured τ − α
data (see Eq. C.3) for all different τ0 − ξ models.
τ = A ∗ e−(α−µ)2/(2σ2) (C.3)
When Eq. C.3 is fit to different τ − α data for the τ0 cases,
we get µ = 0 and A = τ0 for all the cases as shown in Eq. C.4.
τ = τ0e−α
2/(2σ2) (C.4)
where σ was measured as 21.5±0.5 µas for all the cases. We
note that we have data only up to one σ of the fitted Gaussians.
The drop in τ is high when τ0 is high, as shown in Fig. C.1 (top).
The maximum change is seen in the τ0 = 0.3 case, when it is
blurred by α = 20 µas, τ goes from 0.3 to ∼ 0.225. When 0.05 <
τ0 < 1.0, given the nominal resolution of ∼ 20 µas, the change in
true ellipticity ∆τ is 0.017 . ∆τ . 0.034. While the diameter of
the m-ring drops by a maximum of ∼ 4 µas, the width increases
by a maximum of ∼ 13 µas, after blurring with α = 20 µas as
shown in Fig. C.1 (bottom).
0.00
0.05
0.10
0.15
0.20
0.25
0.30
El
lip
tic
ity
 (
)
0e
2/(2 2)
0 5 10 15 20
Convolving Gaussian FWHM ( ) ( as)
10
15
20
25
30
35
40
45
W
idt
h/
Di
am
et
er
 (
as
)
3.
38
as
12
.8
3
as
Diameter
Width
0.00
0.05
0.10
0.15
0.20
0.25
0.30
El
lip
tic
ity
 (
0)
Fig. C.1. The effect of blurring with different Gaussian FWHM (α) on
the ring parameters measured by VIDA. (Top) Ellipticity of a stretched
m-ring with true ξ = 120◦ and τ0 = [0.05, 0.1, 0.15, 0.2, 0.25, 0.3]. The
black dashed line marks the fitted curves. (Bottom) Diameter (circle)
and width (diamond) of a stretched m-ring with the same true ξ and τ0
as on the top.
Acknowledgements. R.D. acknowledges that the project that gave rise to these
results received the support of a fellowship from “la Caixa” Foundation (ID
100010434), with the fellowship code LCF/BQ/DI22/11940030. I.C. is sup-
ported by the KASI-Yonsei Postdoctoral Fellowship. The Event Horizon Tele-
scope Collaboration thanks the following organizations and programs: the
Academia Sinica; the Academy of Finland (projects 274477, 284495, 312496,
315721); the Agencia Nacional de Investigación y Desarrollo (ANID), Chile
via NCN19_058 (TITANs), Fondecyt 1221421 and BASAL FB210003; the
Alexander von Humboldt Stiftung; an Alfred P. Sloan Research Fellowship;
Allegro, the European ALMA Regional Centre node in the Netherlands, the
NL astronomy research network NOVA and the astronomy institutes of the
University of Amsterdam, Leiden University, and Radboud University; the
ALMA North America Development Fund; the Astrophysics and High Energy
Physics programme by MCIN (with funding from European Union NextGener-
ationEU, PRTR-C17I1); the Black Hole Initiative, which is funded by grants
from the John Templeton Foundation (60477, 61497, 62286) and the Gor-
don and Betty Moore Foundation (Grant GBMF-8273) – although the opin-
ions expressed in this work are those of the author and do not necessarily
reflect the views of these Foundations; the Brinson Foundation; the Canada
Research Chairs (CRC) program; Chandra DD7-18089X and TM6-17006X; the
China Scholarship Council; the China Postdoctoral Science Foundation fellow-
ships (2020M671266, 2022M712084); ANID through Fondecyt Postdoctorado
(project 3250762); Conicyt through Fondecyt Postdoctorado (project 3220195);
Consejo Nacional de Humanidades, Ciencia y Tecnología (CONAHCYT, Mex-
ico, projects U0004-246083, U0004-259839, F0003-272050, M0037-279006,
F0003-281692, 104497, 275201, 263356, CBF2023-2024-1102, 257435); the
A279, page 16 of 18
Dahale, R., et al.: A&A, 699, A279 (2025)
Colfuturo Scholarship; the Consejo Superior de Investigaciones Científicas
(grant 2019AEP112); the Delaney Family via the Delaney Family John A.
Wheeler Chair at Perimeter Institute; Dirección General de Asuntos del Personal
Académico-Universidad Nacional Autónoma de México (DGAPA-UNAM,
projects IN112820 and IN108324); the Dutch Research Council (NWO) for
the VICI award (grant 639.043.513), the grant OCENW.KLEIN.113, and the
Dutch Black Hole Consortium (with project No. NWA 1292.19.202) of the
research programme the National Science Agenda; the Dutch National Super-
computers, Cartesius and Snellius (NWO grant 2021.013); the EACOA Fel-
lowship awarded by the East Asia Core Observatories Association, which con-
sists of the Academia Sinica Institute of Astronomy and Astrophysics, the
National Astronomical Observatory of Japan, Center for Astronomical Mega-
Science, Chinese Academy of Sciences, and the Korea Astronomy and Space
Science Institute; the European Research Council (ERC) Synergy Grant “Black-
HoleCam: Imaging the Event Horizon of Black Holes” (grant 610058) and
Synergy Grant “BlackHolistic: Colour Movies of Black Holes: Understand-
ing Black Hole Astrophysics from the Event Horizon to Galactic Scales”
(grant 10107164); the European Union Horizon 2020 research and innova-
tion programme under grant agreements RadioNet (No. 730562), M2FINDERS
(No. 101018682) and FunFiCO (No. 777740); the European Research Council
for advanced grant “JETSET: Launching, propagation and emission of relativis-
tic jets from binary mergers and across mass scales” (grant No. 884631); the
European Horizon Europe staff exchange (SE) programme HORIZON-MSCA-
2021-SE-01 grant NewFunFiCO (No. 10108625); the Horizon ERC Grants 2021
programme under grant agreement No. 101040021; the FAPESP (Fundação
de Amparo á Pesquisa do Estado de São Paulo) under grant 2021/01183-8;
the Fondes de Recherche Nature et Technologies (FRQNT); the Fondo CAS-
ANID folio CAS220010; the Generalitat Valenciana (grants APOSTD/2018/177
and ASFAE/2022/018) and GenT Program (project CIDEGENT/2018/021);
the Gordon and Betty Moore Foundation (GBMF-3561, GBMF-5278, GBMF-
10423); the Institute for Advanced Study; the ICSC – Centro Nazionale di
Ricerca in High Performance Computing, Big Data and Quantum Comput-
ing, funded by European Union – NextGenerationEU; the Istituto Nazionale
di Fisica Nucleare (INFN) sezione di Napoli, iniziative specifiche TEON-
GRAV; the International Max Planck Research School for Astronomy and Astro-
physics at the Universities of Bonn and Cologne; the Italian Ministry of Uni-
versity and Research (MUR) – Project CUP F53D23001260001, funded by
the European Union – NextGenerationEU; DFG research grant “Jet physics on
horizon scales and beyond” (grant No. 443220636); Joint Columbia/Flatiron
Postdoctoral Fellowship (research at the Flatiron Institute is supported by the
Simons Foundation); the Japan Ministry of Education, Culture, Sports, Sci-
ence and Technology (MEXT; grant JPMXP1020200109); the Japan Soci-
ety for the Promotion of Science (JSPS) Grant-in-Aid for JSPS Research
Fellowship (JP17J08829); the Joint Institute for Computational Fundamen-
tal Science, Japan; the Key Research Program of Frontier Sciences, Chi-
nese Academy of Sciences (CAS, grants QYZDJ-SSW-SLH057, QYZDJSSW-
SYS008, ZDBS-LY-SLH011); the Leverhulme Trust Early Career Research Fel-
lowship; the Max-Planck-Gesellschaft (MPG); the Max Planck Partner Group
of the MPG and the CAS; the MEXT/JSPS KAKENHI (grants 18KK0090,
JP21H01137, JP18H03721, JP18K13594, 18K03709, JP19K14761, 18H01245,
25120007, 19H01943, 21H01137, 21H04488, 22H00157, 23K03453); the
MICINN Research Projects PID2019-108995GB-C22, PID2022-140888NB-
C22; the MIT International Science and Technology Initiatives (MISTI) Funds;
the Ministry of Science and Technology (MOST) of Taiwan (103-2119-M-
001-010-MY2, 105-2112-M-001-025-MY3, 105-2119-M-001-042, 106-2112-
M-001-011, 106-2119-M-001-013, 106-2119-M-001-027, 106-2923-M-001-
005, 107-2119-M-001-017, 107-2119-M-001-020, 107-2119-M-001-041, 107-
2119-M-110-005, 107-2923-M-001-009, 108-2112-M-001-048, 108-2112-M-
001-051, 108-2923-M-001-002, 109-2112-M-001-025, 109-2124-M-001-005,
109-2923-M-001-001, 110-2112-M-001-033, 110-2124-M-001-007 and 110-
2923-M-001-001); the National Science and Technology Council (NSTC) of Tai-
wan (111-2124-M-001-005, 112-2124-M-001-014 and 112-2112-M-003-010-
MY3); the Ministry of Education (MoE) of Taiwan Yushan Young Scholar Pro-
gram; the Physics Division, National Center for Theoretical Sciences of Tai-
wan; the National Aeronautics and Space Administration (NASA, Fermi Guest
Investigator grant 80NSSC23K1508, NASA Astrophysics Theory Program
grant 80NSSC20K0527, NASA NuSTAR award 80NSSC20K0645); NASA
Hubble Fellowship Program Einstein Fellowship; NASA Hubble Fellowship
grants HST-HF2-51431.001-A, HST-HF2-51482.001-A, HST-HF2-51539.001-
A, HST-HF2-51552.001A awarded by the Space Telescope Science Institute,
which is operated by the Association of Universities for Research in Astronomy,
Inc., for NASA, under contract NAS5-26555; the National Institute of Natural
Sciences (NINS) of Japan; the National Key Research and Development Program
of China (grant 2016YFA0400704, 2017YFA0402703, 2016YFA0400702); the
National Science and Technology Council (NSTC, grants NSTC 111-2112-M-
001 -041, NSTC 111-2124-M-001-005, NSTC 112-2124-M-001-014); the US
National Science Foundation (NSF, grants AST-0096454, AST-0352953, AST-
0521233, AST-0705062, AST-0905844, AST-0922984, AST-1126433, OIA-
1126433, AST-1140030, DGE-1144085, AST-1207704, AST-1207730, AST-
1207752, MRI-1228509, OPP-1248097, AST-1310896, AST-1440254, AST-
1555365, AST-1614868, AST-1615796, AST-1715061, AST-1716327, AST-
1726637, OISE-1743747, AST-1743747, AST-1816420, AST-1935980, AST-
1952099, AST-2034306, AST-2205908, AST-2307887); NSF Astronomy and
Astrophysics Postdoctoral Fellowship (AST-1903847); the Natural Science
Foundation of China (grants 11650110427, 10625314, 11721303, 11725312,
11873028, 11933007, 11991052, 11991053, 12192220, 12192223, 12273022,
12325302, 12303021); the Natural Sciences and Engineering Research Coun-
cil of Canada (NSERC); the National Research Foundation of Korea (the
Global PhD Fellowship Grant: grants NRF-2015H1A2A1033752; the Korea
Research Fellowship Program: NRF-2015H1D3A1066561; Brain Pool Pro-
gram: RS-2024-00407499; Basic Research Support Grant 2019R1F1A1059721,
2021R1A6A3A01086420, 2022R1C1C1005255, 2022R1F1A1075115); Nether-
lands Research School for Astronomy (NOVA) Virtual Institute of Accretion
(VIA) postdoctoral fellowships; NOIRLab, which is managed by the Associ-
ation of Universities for Research in Astronomy (AURA) under a cooperative
agreement with the National Science Foundation; Onsala Space Observatory
(OSO) national infrastructure, for the provisioning of its facilities/observational
support (OSO receives funding through the Swedish Research Council under
grant 2017-00648); the Perimeter Institute for Theoretical Physics (research
at Perimeter Institute is supported by the Government of Canada through the
Department of Innovation, Science and Economic Development and by the
Province of Ontario through the Ministry of Research, Innovation and Science);
the Portuguese Foundation for Science and Technology (FCT) grants (Indi-
vidual CEEC program – 5th edition, https://doi.org/10.54499/UIDB/
04106/2020, https://doi.org/10.54499/UIDP/04106/2020, PTDC/FIS-
AST/3041/2020, CERN/FIS-PAR/0024/2021, 2022.04560.PTDC); the Prince-
ton Gravity Initiative; the Spanish Ministerio de Ciencia, Innovación y Univer-
sidades (grants PID2022-140888NB-C21, PID2022-140888NB-C22, PID2023-
147883NB-C21, RYC2023-042988-I); the Severo Ochoa grant CEX2021-
001131-S funded by MICIU/AEI/10.13039/501100011033; The European
Union’s Horizon Europe research and innovation program under grant agree-
ment No. 101093934 (RADIOBLOCKS); The European Union “NextGen-
erationEU”, the Recovery, Transformation and Resilience Plan, the CUII of
the Andalusian Regional Government and the Spanish CSIC through grant
AST22_00001_Subproject_10; “la Caixa” Foundation (ID 100010434) through
fellowship codes LCF/BQ/DI22/11940027 and LCF/BQ/DI22/11940030; the
University of Pretoria for financial aid in the provision of the new Clus-
ter Server nodes and SuperMicro (USA) for a SEEDING GRANT approved
toward these nodes in 2020; the Shanghai Municipality orientation program of
basic research for international scientists (grant no. 22JC1410600); the Shang-
hai Pilot Program for Basic Research, Chinese Academy of Science, Shang-
hai Branch (JCYJ-SHFY-2021-013); the Simons Foundation (grant 00001470);
the Spanish Ministry for Science and Innovation grant CEX2021-001131-S
funded by MCIN/AEI/10.13039/501100011033; the Spinoza Prize SPI 78-409;
the South African Research Chairs Initiative, through the South African Radio
Astronomy Observatory (SARAO, grant ID 77948), which is a facility of the
National Research Foundation (NRF), an agency of the Department of Sci-
ence and Innovation (DSI) of South Africa; the Swedish Research Coun-
cil (VR); the Taplin Fellowship; the Toray Science Foundation; the UK Sci-
ence and Technology Facilities Council (grant no. ST/X508329/1); the US
Department of Energy (USDOE) through the Los Alamos National Labora-
tory (operated by Triad National Security, LLC, for the National Nuclear Secu-
rity Administration of the USDOE, contract 89233218CNA000001); and the
YCAA Prize Postdoctoral Fellowship. This work was also supported by the
National Research Foundation of Korea (NRF) grant funded by the Korea
government (MSIT) (RS-2024-00449206). We acknowledge support from the
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) of
Brazil through PROEX grant number 88887.845378/2023-00. We acknowl-
edge financial support from Millenium Nucleus NCN23_002 (TITANs) and
Comité Mixto ESO-Chile. We thank the staff at the participating observatories,
correlation centers, and institutions for their enthusiastic support. This paper
makes use of the following ALMA data: ADS/JAO.ALMA#2017.1.00841.V
and ADS/JAO.ALMA#2016.1.01154.V. ALMA is a partnership of the Euro-
pean Southern Observatory (ESO; Europe, representing its member states), NSF,
and National Institutes of Natural Sciences of Japan, together with National
Research Council (Canada), Ministry of Science and Technology (MOST; Tai-
wan), Academia Sinica Institute of Astronomy and Astrophysics (ASIAA; Tai-
wan), and Korea Astronomy and Space Science Institute (KASI; Republic of
Korea), in cooperation with the Republic of Chile. The Joint ALMA Observa-
tory is operated by ESO, Associated Universities, Inc. (AUI)/NRAO, and the
National Astronomical Observatory of Japan (NAOJ). The NRAO is a facility
of the NSF operated under cooperative agreement by AUI. This research used
resources of the Oak Ridge Leadership Computing Facility at the Oak Ridge
National Laboratory, which is supported by the Office of Science of the U.S.
Department of Energy under contract No. DE-AC05-00OR22725; the ASTRO-
VIVES FEDER infrastructure, with project code IDIFEDER-2021-086; the com-
A279, page 17 of 18
Dahale, R., et al.: A&A, 699, A279 (2025)
puting cluster of Shanghai VLBI correlator supported by the Special Fund for
Astronomy from the Ministry of Finance in China; We also thank the Center for
Computational Astrophysics, National Astronomical Observatory of Japan. This
work was supported by FAPESP (Fundacao de Amparo a Pesquisa do Estado
de Sao Paulo) under grant 2021/01183-8. APEX is a collaboration between
the Max-Planck-Institut für Radioastronomie (Germany), ESO, and the Onsala
Space Observatory (Sweden). The SMA is a joint project between the SAO
and ASIAA and is funded by the Smithsonian Institution and the Academia
Sinica. The JCMT is operated by the East Asian Observatory on behalf of the
NAOJ, ASIAA, and KASI, as well as the Ministry of Finance of China, Chi-
nese Academy of Sciences, and the National Key Research and Development
Program (No. 2017YFA0402700) of China and Natural Science Foundation of
China grant 11873028. Additional funding support for the JCMT is provided
by the Science and Technologies Facility Council (UK) and participating uni-
versities in the UK and Canada. The LMT is a project operated by the Insti-
tuto Nacional de Astrófisica, Óptica, y Electrónica (Mexico) and the Univer-
sity of Massachusetts at Amherst (USA). The IRAM 30-m telescope on Pico
Veleta, Spain is operated by IRAM and supported by CNRS (Centre National
de la Recherche Scientifique, France), MPG (Max-Planck-Gesellschaft, Ger-
many), and IGN (Instituto Geográfico Nacional, Spain). The SMT is operated
by the Arizona Radio Observatory, a part of the Steward Observatory of the
University of Arizona, with financial support of operations from the State of
Arizona and financial support for instrumentation development from the NSF.
Support for SPT participation in the EHT is provided by the National Science
Foundation through award OPP-1852617 to the University of Chicago. Par-
tial support is also provided by the Kavli Institute of Cosmological Physics
at the University of Chicago. The SPT hydrogen maser was provided on loan
from the GLT, courtesy of ASIAA. This work used the Extreme Science and
Engineering Discovery Environment (XSEDE), supported by NSF grant ACI-
1548562, and CyVerse, supported by NSF grants DBI-0735191, DBI-1265383,
and DBI-1743442. XSEDE Stampede2 resource at TACC was allocated through
TG-AST170024 and TG-AST080026N. XSEDE JetStream resource at PTI and
TACC was allocated through AST170028. This research is part of the Fron-
tera computing project at the Texas Advanced Computing Center through the
Frontera Large-Scale Community Partnerships allocation AST20023. Frontera
is made possible by National Science Foundation award OAC-1818253. This
research was done using services provided by the OSG Consortium (Pordes et al.
2007; Sfiligoi et al. 2009), which is supported by the National Science Foun-
dation award Nos. 2030508 and 1836650. Additional work used ABACUS2.0,
which is part of the eScience center at Southern Denmark University, and the
Kultrun Astronomy Hybrid Cluster (projects Conicyt Programa de Astronomia
Fondo Quimal QUIMAL170001, Conicyt PIA ACT172033, Fondecyt Iniciacion
11170268, Quimal 220002). Simulations were also performed on the SuperMUC
cluster at the LRZ in Garching, on the LOEWE cluster in CSC in Frankfurt, on
the HazelHen cluster at the HLRS in Stuttgart, and on the Pi2.0 and Siyuan
Mark-I at Shanghai Jiao Tong University. The computer resources of the Finnish
IT Center for Science (CSC) and the Finnish Computing Competence Infras-
tructure (FCCI) project are acknowledged. This research was enabled in part by
support provided by Compute Ontario (http://computeontario.ca), Calcul
Quebec (http://www.calculquebec.ca), and the Digital Research Alliance
of Canada (https://alliancecan.ca/en). The EHTC has received generous
donations of FPGA chips from Xilinx Inc., under the Xilinx University Program.
The EHTC has benefited from technology shared under open-source license by
the Collaboration for Astronomy Signal Processing and Electronics Research
(CASPER). The EHT project is grateful to T4Science and Microsemi for their
assistance with hydrogen masers. This research has made use of NASA’s Astro-
physics Data System. We gratefully acknowledge the support provided by the
extended staff of the ALMA, from the inception of the ALMA Phasing Project
through the observational campaigns of 2017 and 2018. We would like to thank
A. Deller and W. Brisken for EHT-specific support with the use of DiFX. We
thank Martin Shepherd for the addition of extra features in the Difmap soft-
ware that were used for the CLEAN imaging results presented in this paper. We
acknowledge the significance that Maunakea, where the SMA and JCMT EHT
stations are located, has for the indigenous Hawaiian people.
A279, page 18 of 18