# The jet and resolved features of the central supermassive black hole
of M 87 observed with EHT

Makoto Miyoshi National Astronomical Observatory, Japan, 2-21-1, Osawa,
Mitaka, Tokyo, Japan, 181-8588  Yoshiaki Kato Computational Astrophysics
Laboratory RIKEN, 2-1 Hirosawa, Wako, Saitama, 351-0198, Japan, e-mail:
<EMAIL_ADDRESS>Junichiro Makino Department of Planetology, Kobe
University, 1-1 Rokkodaicho, Nada-ku, Kobe, Hyogo 650-0013, Japan, e-mail:
<EMAIL_ADDRESS>
(Accepted 2022/05/05)

###### Abstract

We report our independent image reconstruction of the M 87 from the public
data of the Event Horizon Telescope Collaborators (EHTC). Our result is
different from the image published by the EHTC. Our analysis shows that (a)
the structure at 230 GHz is consistent with those of lower frequency VLBI
observations, (b) the jet structure is evident at 230 GHz extending from the
core to a few mas, though the intensity rapidly decreases along the axis, and
(c) the “unresolved core” is resolved into bright three features presumably
showing an initial jet with a wide opening angle of $\sim 70^{\circ}$.

The ring-like structures of the EHTC can be created not only from the public
data, but also from the simulated data of a point image. Also, the rings are
very sensitive to the FOV size. The u-v coverage of EHT lack $\sim 40~{}\mu\rm
as$ fringe spacings. Combining with a very narrow FOV, it created the $\sim
40~{}\mu\rm as$ ring structure. We conclude that the absence of the jet and
the presence of the ring in the EHTC result are both artifacts owing to the
narrow FOV setting and the u-v data sampling bias effect of the EHT array.
Because the EHTC’s simulations only take into account the reproduction of the
input image models, and not those of the input noise models, their optimal
parameters can enhance the effects of sampling bias and produce artifacts such
as the $\sim 40~{}\mu\rm as$ ring structure, rather than reproducing the
correct image.

jets, accretion disks — black hole physics — galaxies: active — galaxies:
individual (M 87) — interferometer: VLBI — data calibrations — data sampling
bias

††journal: ApJ††facilities: EHT††software: AIPS (Greisen, 2003), DIFMAP
(Shepherd, 1997)

##  1 Introduction

Supermassive black holes (SMBHs) at the centers of galaxies often have
spectacular jets sharply collimated and extended to intergalactic scale.
However, the mechanism of the generation of such jets by the black holes has
been an enigma for over a century (Blandford et al., 2019).

The SMBH of the elliptical galaxy M 87, the first object of the astrophysical
jet discovery (Curtis, 1918), is the best place to study the origin of the jet
because it has the largest apparent angular size for black holes with strong
jets, due to the relatively small distance (16.7 Mpc; Mei et al. (2007)) and
large mass ($6.1\pm~{}0.4\times 10^{9}~{}M_{\odot}$; Gebhardt et al. (2011)),
which implies that $1~{}R_{\rm S}$ = 7$~{}\mu\rm as$. The black hole with the
largest apparent angular size, Sgr A∗ is present in our galaxy, but
unfortunately, it has no jet and its activity is very low in comparison to
that of a typical AGN. In addition, it is difficult to obtain high-resolution
images of Sgr A∗ owing to its rapid time variability during VLBI observations
(Miyoshi et al., 2019; Iwata et al., 2020).

Observations of the core and jet of M 87 have been performed in multiple
wavelengths, from X-ray to radio (Biretta et al., 1995; Sparks, Biretta &
Macchetto, 1996; Biretta, Sparks & Macchetto, 1999; Perlman et al., 1999,
2001; Marshall et al., 2002; Wilson & Yang, 2002; Lister & Homan, 2005;
Perlman & Wilson, 2005; Harris et al., 2006; Madrid et al., 2007; Wang & Zhou,
2009). Also, with high spatial resolution observations using VLBI of the SMBH
of M 87 have been performed in multiple frequencies up to 86 GHz (Reid et al.,
1989; Junor, Biretta & Livio, 1999; Lobanov, Hardee & Eilek, 2003; Ly, Walker
& Wrobel, 2004; Cheung, Harris & Stawartz, 2007; Kovalev et al., 2007; Ly et
al., 2007; Walker et al., 2008; Hada et al., 2011; Hardee & Eilek, 2011; Asada
& Nakamura, 2012; Giroletti et al., 2012; Hada et al., 2013; Nakamura & Asada,
2013; Asada et al., 2014; Hada et al., 2016; Mertens et al., 2016; Walker et
al., 2016; Britzen et al., 2017; Hada et al., 2017; Kim et al., 2018). Using
the ”core shift” technique, the distance between the brightness peak of the
core and the actual location of the SMBH has been estimated to be from 14 to
23 $R_{\rm S}$ (Hada et al., 2011). Observations with higher spatial
resolution at 230 GHz should allow further exploration of the core and jet.
Pioneering observations of EHT 111https://eventhorizontelescope.org/ were
started at 2008 (Doeleman et al., 2008).

In 2017, EHT attained sufficient sensitivity by including phased-ALMA in the
array and equipping all stations with 32 Gbps recording systems. The EHTC
reported their findings of a ring-shaped black hole shadow from the
observational data (the EHTC, 2019). The ring diameter was approximately
$42~{}\mu\rm as$, which is consistent with that expected from the measured
mass of M 87 SMBH ($6\times 10^{9}~{}M_{\odot}$) using stellar dynamics
(Gebhardt et al., 2011) 222The M 87 black hole mass is still controversial. A
mass of $M_{\mathrm{BH}}=(3.5^{+0.9}_{-0.7})\times 10^{9}\ M_{\odot}$ (68 $\%$
confidence) is obtained from gas dynamics (Walsh et al., 2013)..

We found three problems in the EHTC imaging results. First, although the EHT’s
intrinsic FOV (Field Of View) is large enough to cover both the core and the
jet structure together, no jet structure has been reported by the EHTC. The M
87 jet is powerful and has been detected in lower frequency VLBI observations.

There was no detailed description of the investigation of the jet structure in
(the EHTC, 2019); in 2017, the EHT array achieved unprecedented sensitivity,
so it is not surprising that many AGN experts have strong expectations for
detecting new jet structures of M 87.

Second, the ring diameter of the EHTC imaging ($d=42\pm~{}3~{}\mu\rm as$;
Event Horizon Telescope collaboration  (2019a)) coincides with the separation
between the main beam and the first sidelobe in the dirty beam (identical to
point spread function (PSF)) of the EHT u-v coverage for the M 87
observations. In the EHTC paper, there is no description of the concrete
structure of the dirty beam, such as sidelobes. Misidentification of sidelobes
as real images is a common occurrence in radio interferometer observations
with a small number of stations such as the EHT array. The EHTC do not seem to
take such a risk into account (at least it is not clearly mentioned in their
paper). There is a possibility that the EHTC ring is a mixture of the real
image and the residual sidelobes in the diffraction patterns.

The last problem is the brightness temperature of the ring reported by the
EHTC ($T_{\rm b}=6\times 10^{9}~{}K$ at most from Figure 3 in Event Horizon
Telescope collaboration  (2019a)

333 The EHTC show several different ”fiducial” images in their papers. We
believe that the images shown in Figure 3 of Event Horizon Telescope
collaboration  (2019a) are the FINAL ”fiducial” images of the EHTC because
Event Horizon Telescope collaboration  (2019a) is for reporting the scientific
results about ”the shadow of the supermassive black hole”.

), which is significantly lower than that of their previous M 87 observations
($T_{\rm b}$ from 1.23 to 1.42 $\times 10^{10}$ K; Akiyama et al. (2015))
despite having higher spatial resolutions. 444 The possibility of time
variation in brightness temperature cannot be ruled out. The number of
measurements is extremely small, and future observations are desirable.  The
86 GHz Very Long Baseline Array (VLBA; Napier et al. (1993)) observations have
shown that the core brightness temperature is $T_{\rm b}=1.8\times 10^{10}$ K
(Hada et al., 2016). Kim et al. (2018) also reported the brightness
temperature is $T_{\rm b}\sim(1-3)\times 10^{10}$ K at 86 GHz. The spatial
resolutions of both observations are lower than that of EHT
($\theta_{BEAM}>100~{}\mu\rm as$), but they show higher brightness
temperatures. In any case, it is quite rare to observe a brightness
temperature of less than $10^{10}~{}K$ for the M 87 core by VLBI.

In observations of very compact objects, if the spatial resolution is low, the
measured brightness temperature could be underestimated because the solid
angle of the emission region tends to be estimated larger than the actual
size. If the spatial resolution is higher, the measured brightness temperature
can be expected to be higher because the solid angle of the emission region
can be more accurately identified. The measured brightness temperature
increases until the spatial resolution becomes sufficient to determine the
fine structure of the compact object. However, the measured brightness
temperature may surely decrease once sufficient spatial resolution is achieved
and the fine structure is recognized. The EHTC observations show a ring
diameter of about $40~{}\mu\rm as$, almost the same as the estimated source
size in Akiyama et al. (2015). However, since it is a ring structure, the
center of the image is darker, so assuming that the flux density is the same
555 The EHTC papers do not show the flux density of the ring image. , the
highest-brightness part in the ring image should show a higher brightness
temperature than that indicated by Akiyama et al. (2015). The lower brightness
temperatures and/or flux densities in the images obtained by the EHTC could be
the result of the insufficient recovery of the data coherence by improper
calibrations.

Because of these three problems we decided to reanalyze the data released by
the EHTC 666First M 87 EHT Results: Calibrated Data
https://eventhorizontelescope.org/for-astronomers/data
http://datacommons.cyverse.org/browse/iplant/home/shared/commons_repo/curated/theEHTC_FirstM87Results_Apr2019
DOI:10.25739/g85n-f134 . Using the public data released by the EHTC, we
succeeded in reconstructing the core and jet structure in M 87.

We have resolved the region containing the SMBH in M 87 for the first time and
found the structure of the core and knot separated by $\sim 33~{}\mu\rm as$
($550~{}\rm au$ or 4.7 $R_{\rm S}$) on the sky, which shows time variation.
This could be the scene of the initial ejection of the jet from the core. We
also found a feature to the west, $\sim 83~{}\mu\rm as$ away from the core.
These facts are important for identifying the jet formation mechanism from
SMBHs. We need further observations to determine the nature of the features.

We also found emissions along the axis of the jet up to a point a few mas from
the core, showing that the edges of the jet are brighter, similar to what was
observed at low frequencies.

We first describe the observational data released by the EHTC in Section 2,
our data calibration and imaging process in Section 3, and our imaging results
in Section 4. Then, we investigate how the EHTC ring was created in Section 5.
In Appendix A, we show that the EHT array cannot detect any feature whose size
is larger than $30~{}\mu\rm as$. As a supplement to Section 5.2, Appendix B
shows the dirty beam (PSF) shapes of the EHT array for the M 87 observations
in two different types: natural weighting and uniform weighting. Both show the
substructure with a scale of $\sim 40~{}\mu\rm as$. In Appendix C, we show
that the missing spatial Fourier components of $\sim 40~{}\mu\rm as$ also
affect the structure in our CLEAN map.

##  2 Observational data

The observational data were recorded on 5, 6, 10, and 11 April 2017. The EHT
array consists of seven submillimeter radio telescopes located at five places
across the globe, yielding a baseline length over 10000 km (the EHTC, 2019).
For the observational details and the instruments, refer to the series of the
EHTC papers (Event Horizon Telescope collaboration , 2019a, b, c, d, e, f).
The raw data archives have not been released by the EHTC yet, but they
released the calibrated visibility data with their recipe of the data
reduction procedure. We first analyzed the released EHT data sets of M 87
using the standard VLBI data calibration procedure and imaging methods without
referring to their data procedure. The data are time-averaged into 10 sec bins
and are stored into 2 IF channels. According to the header of the public FITS
data the IF bandwidth is 1.856 GHz in each IF. Because of the removal of data
of the strong calibrator source (3C 279), we could not perform the fringe
search to correct the errors of station positions, clock parameters, and the
receiving band-path calibration by ourselves. Therefore, our independent
calibration was limited to the self-calibration method.

We checked the details of the data and noticed that the visibility values of
the RR-channel and LL-channel are exactly the same. The headers of the EHTC
open FITS data files contain two data columns labeled RR and LL, respectively;
the FITS format data does indeed contain data columns labeled RR and LL. We
checked all the original public FITS data sets (there are 8 sets) and
confirmed that the data in the RR and LL columns are the same in all the data
sets; there are a total of 51119 pairs of RR and LL, and all the pairs have
exactly the same real, imaginary, and weight values.

We found in a document of the EHTC the following description: 777 README.md in
https://github.com/eventhorizontelescope/2019-D01-01

> The data are time averaged over 10 seconds and frequency averaged over all
> 32 intermediate frequencies (IFs). All polarization information is
> explicitly removed. To make the resulting ‘uvfits‘ files compatible with
> popular very-long-baseline interferometry (VLBI) software packages, the
> circularly polarized cross-hand visibilities ‘RL‘ and ‘LR‘ are set to zero
> along with their errors, while parallel-hands ‘RR‘ and ‘LL‘ are both set to
> an estimated Stokes *I* value. Measurement errors for ‘RR‘ and ‘LL‘ are each
> set to sqrt(2) times the statistical errors for Stokes *I*.

In other words, the open data in the EHTC FITS format are not the visibility
of either polarization, but the Stokes I, $V_{ij,I}=(V_{ij,RR}+V_{ij,LL})/2$,
(Event Horizon Telescope collaboration , 2019c), and the above-calculated
values are stored in the columns of RR and LL. This information is not
included in the attached tables or files of the FITS data. For this, the EHTC
should have used the FITS format for intensity data instead of using that for
dual polarization data. Also, it means that the corrections made between the
correlator output and the open data cannot be independently verified.
EHTC’s open data integrates the wide frequency band of 1.86 GHz into a single
channel. Such wideband integration is extremely rare and unsuitable for public
data because it results in loss of information over a wide field in the data
due to the bandwidth smearing effect. The effect is similar to the peripheral
light fall-off of optical camera lenses. Visibility data integrated in the
frequency direction reduces the sensitivity in peripheral vision. This
phenomenon occurs because originally independent (u, v) points are integrated
in frequency domain. The further away from the center of the field of view
(phase center), become larger the size of the PSF and lower the peak; the
detection sensitivity in the peripheral vision becomes worse (Thompson et al.,
2001; Bridle & Schwab , 1989, 1999).
Due to the bandwidth smearing effect, the peak of the PFS away from the phase
center is suffered attenuation as shown in Figure 1. In the case of the EHTC
open data, the ratios of peak heights relative to that at the phase center are
$\sim~{}50~{}\%$ at a radius of 5 mas, and $\sim~{}27~{}\%$ at a radius of 10
mas. Even at a radius of 20 mas from the center, the ratio is
$\sim~{}14~{}\%$. If a component of sufficient intensity is present at an even
far position from the center, it will be detected. We did not abandon such a
possibility and set a wide field for imaging as explained in Section 3.

Figure 1:  The bandwidth smearing effect calculated explicitly for the EHTC
open data by following equations 6-75 and 6-76 in Thompson et al. (2001).
Adapted synthesized beam size is $\theta_{b}=21.06~{}\mu as$, which is the
geometric mean of major and minor axes of the beam shapes of the four
observing days shown in Table 1 of Event Horizon Telescope collaboration
(2019d). We substituted $\Delta\nu~{}=1.856~{}GHz$ for the bandwidth and
$\nu_{0}=~{}229.071~{}GHz$ for the observing frequency.

The coherence time of the obtained data has a significant impact on the data
analysis and imaging results; the EHTC shows the atmospheric coherence time
for all observations in the 2017 campaign (Event Horizon Telescope
collaboration , 2019b), but not for those limited to the M 87 observations
only. Therefore, we used the AIPS task COHER to check the coherence time of
the visibility data. Here, the coherence time is defined as the time when the
amplitude becomes $1/e\sim 0.36$ by vector averaging. The task COHER cannot
identify the reasons for the coherence loss. In any case, the calculated
coherence time implies the total amount of coherence loss that the data has
suffered. The coherence time $T_{cor}=0.45\pm 0.7\rm~{}min$ was obtained from
the entire data set (average of all baselines). However, the coherence time
was not constant; the data from the first two days showed $T_{cor}=0.54\pm
0.91\rm~{}min$ and the data from the last two days showed $T_{cor}=0.35\pm
0.36\rm~{}min$. We took it as significant that $39\%$ of the total data showed
$T_{cor}\sim 0.167\rm~{}min~{}(\sim 10~{}sec)$. Without any kind of
calibrations, we do not expect to improve SNR by long time integration. We
decided that no meaningful solution could be obtained by increasing the
integration time (SOLINT, solution interval) in self-calibration. Therefore,
we always set SOLINT to $0.15~{}min$ when performing self-calibration.

We used both data channels in their original form. We found that our
calibrations of the EHT data sets can be significantly improved and also
obtained an improved solution for calibrations using the hybrid mapping method
(Pearson & Readhead, 1984; Readhead & Wilkinson, 1978; Schwab, 1980). The
observations were performed over four days. We succeeded in increasing the
sensitivity by integrating two days’ data or all of them.

##  3 Our data calibration and Imaging

In this section, we report on the procedures and results of data calibration
and imaging using standard methods of VLBI data analysis for sources with
unknown structures. In Section 3.1 we describe the hybrid mapping procedures
used in this study. Section 3.2 describes how we identified the second feature
from the first map, and Section 3.3 describes the process that followed. In
Section 3.4 , we present our final images. In Section 3.5, we present a
solution for self-calibration of both amplitude and phase, using the final
image as a model to determine the quality of the EHT public data.

###  3.1 Hybrid mapping process

In the analysis of VLBI data, the hybrid mapping method is widely used to
obtain a calibration solution for the data and to reconstruct the brightness
distribution. Hybrid mapping, which consists of repeatedly assuming one image
model, performing self-calibration, obtaining a trial solution for
calibration, and improving the image model for the next self-calibration, is
the only method that is essential for precise calibration of VLBI data
(Pearson & Readhead, 1984; Readhead & Wilkinson, 1978; Schwab, 1980). VLBI
systems are not so stable in phase and amplitude as connected radio
interferometers. In addition, millimeter- and submillimeter-wave observations
are more affected by atmospheric variations. Therefore, the hybrid mapping
method is becoming more and more important in the calibration of high
frequency VLBI data such as the EHT observations. We performed a standard
hybrid mapping process using the tasks CALIB and IMAGR in AIPS (the NRAO
Astronomical Image Processing System 888http://www.aips.nrao.edu/index.shtm,
Greisen (2003)).

###  3.2 The first step in hybrid mapping process

####  3.2.1 Solutions of self-calibration using a point source model

As a first step in this process, a single point source (located at the origin)
was used as the first image model to obtain a solution for the visibility
phase calibration from the self-calibration. The parameters used for the task
CALIB are listed in Table 1.

As mentioned in Section 2, the coherence time of EHT public data is very
short. The solution interval (SOLINT) was set to 0.15 minutes. We set the
$SNR~{}cutoff=3$ for safety. This SNR cutoff value is larger than what many
researchers use in the end. Solutions that did not meet the criteria (SNR
cutoff) were flagged and abandoned.

Figure 2 shows the phase solution for the first step. Because phase is a
relative quantity, the phase of the ALMA station (AA) is used here as a
reference. For all stations, the non-zero and time-varying phase values were
calculated by self-calibration. The four stations, APEX (AP), SMT (AZ), LMT
(LM), and Pico Veleta (PV), always show the same respective trends over the
four days of observations, suggesting that errors in station positions remain
(a sinusoidal curve with a period of one sidereal day is observed at all
stations when there is an error in the position of the observed object).

Another feature is the phase difference that occurs between IF1 and IF2, which
is almost fixed for all stations except JCMT (JC) and AA (phase reference
station), respectively.

If the EHT public data were sufficiently calibrated, the above two phenomena
should not appear. In conclusion, the ”calibrated” data published by the EHTC
is not yet sufficiently calibrated. In order to obtain reliable images, the
EHT’s public data needs to be further calibrated.

Parameters |
---|---
SOLTYPE | ’L1’
SOLMODE | ’P’ (phase only)
SMODEL | 1,0 (1 Jy single point)
REFANT | 1 (ALMA)
SOLINT (solution interval) | 0.15 (min)
APARM(1) | 1
APARM(7) (SNR cut off) | 3
Table 1: Parameters of CALIB for the first self-calibration. Figure 2: Initial
phase (only) solutions obtained by self-calibration using one-point model. The
red dots are the solutions for IF 1 data, and the blue dots are those for IF 2
data. The solution for L (left-handed circular) polarization is not plotted
here; the visibility data for LL is exactly the same as for RR, so the
solution for L is the same as the solution for R in the Figure.

####  3.2.2 The first CLEAN map

Figure 3 shows the CLEAN (Clark, 1980; H$\ddot{o}$gbom, 1974) image obtained
from the data after applying the first phase calibration solution shown in
Figure 2. The parameters of the imaging of IMAGR are shown in Table 2. (In all
figures showing the imaging results, the x-axis indicates relative Right
Ascension and the y-axis relative Declination.) The purpose of this imaging is
to find the second brightest component following the central brightest peak.
As will be explained in Section 5.1, despite the fact that the EHTC has
involved the largest number of stations ever, the u-v coverage of the EHT
array is formed by only 7 stations, or actually 5 stations if we exclude the
very short baselines. The synthesized beam (dirty beam) is not as sharply
shaped as the dirty beams of multi-element interferometers such as ALMA and
VLA. It is not easy to find the complex brightness distribution of the
observed sources from a tentative map composed of such a scattered dirty beam
(PSF). Therefore, we performed CLEAN, specified by the parameters shown in
Table 2. This method is effective when the structure of the observed source is
not point symmetric. We set the loop gain (GAIN) to 1.0 and extracted all of
the brightest peak from the dirty map in the first CLEAN subtraction. Next,
this component was replaced by a sharp Gaussian restoring beam and combined
with the brightness distribution of the remaining dirty map. The image in
Figure 3 was created in this way.

This has the effect of removing the bright but scattered PSF shape of the
brightest point that dominates the dirty map, and clarifying the presence of
the second brightest component in the image. Note that if the data is not
properly calibrated and the actual PSF corresponding to a point source differs
from the theoretically calculated PSF shape, the brightness distribution
caused by the brightest point may remain in the afterimage. However, such
remaining brightness distribution also shows a point-symmetric structure with
respect to the location of the brightest point (practically the same location
as the center of the map), and does not contribute to the asymmetric structure
of the image. Therefore, if there is an asymmetric structure in the image, it
is not related to the brightest component, but is due to another bright point
source. So, by searching for the asymmetric structure, we can find the second
component of the observed source.

This image (Figure 3 shows its central $600~{}\mu as$ square) has a nearly
point-symmetric structure with respect to the center of the map. The overall
feature is a series of multiple ridges in the $PA=55^{\circ}$ direction. This
structure is due to the non-uniformity of the u-v coverage. In addition to the
central P, there are several other bright features. The peak brightness of
these features is shown in Table 3. Features a, b, c, d, e, f, g, h, i, j, and
k have corresponding features located at their symmetry points (denoted as a∗,
b∗, c∗, d∗, e∗, f∗, g∗, h∗, i∗, j∗, and k∗). Curiously, the features located
in the upper right from the center are always brighter than the symmetric
features located in the lower left, i.e., the brightness ratio is greater than
one. This may indicate the existence of a large-scale asymmetric brightness
distribution in the observed object, extending from the center to the upper
right. This is roughly consistent with the M 87 jet propagation direction
$PA=-72~{}^{\circ}$ (Walker et al., 2018). Examining the brightness ratio of
each pair, we find that the pair c & c∗ ($ratio=1.146$) is the largest,
followed by the pair a & a∗ ($ratio=1.122$). Regarding the absolute value of
brightness, the brightness of a ($2.396\times 10^{-2}$ Jy/Beam) is larger than
that of c ($1.982\times 10^{-2}$ Jy/Beam). In addition, there is a ridge
extending from the central bright point (P) toward feature a. The direction of
this ridge ($PA=-45~{}^{\circ}$) is completely different from the direction of
multiple ridges seen in the entire image, and no other ridge shows the same
direction. Based on these characteristics, we decided to continue the hybrid
mapping by adopting two points for the next image model. In other words, we
chose to use a model with a point at each of the two locations, the center and
the location of feature a.

Parameters |
---|---
DOCALIB | 2
CELLSIZE |  $1.22011\times 10^{-6}$, $1.22011\times 10^{-6}$ (asec)
FLDSIZE | 8192, 8192 (pix)
ROBUST | 0
NITER | 1
GAIN | 1.0
Table 2: Parameters of IMAGR for the first trial imaging. Figure 3: First step image of our hybrid mapping process. The restored beam size is about $20~{}\mu\rm as$, and the center $600~{}\mu\rm as$ square of the map is magnified. Contour lines are drawn at every 20$\%$ level of the peak brightness of $3.981~{}\times 10^{-1}$ (arbitrary units are used in the figure, not Jy/beam). One pixel corresponds to $1.22011~{}\mu\rm as$.  Name | Brightness (Jy/beam) | Name | Brightness (Jy/beam) | Ratio | Order
---|---|---|---|---|---
P | $8.736\times 10^{-2}$ |  |  |  |
a | $2.396\times 10^{-2}$ |  a∗ | $2.136\times 10^{-2}$ | 1.122 | 2
b | $2.438\times 10^{-2}$ |  b∗ | $2.187\times 10^{-2}$ | 1.115 | 3
c | $1.982\times 10^{-2}$ |  c∗ | $1.729\times 10^{-2}$ | 1.146 | 1
d | $2.099\times 10^{-2}$ |  d∗ | $1.889\times 10^{-2}$ | 1.111 | 4
e | $2.780\times 10^{-2}$ |  e∗ | $2.534\times 10^{-2}$ | 1.097 | 5
f | $2.420\times 10^{-2}$ |  f∗ | $2.257\times 10^{-2}$ | 1.072 | 7
g | $2.368\times 10^{-2}$ |  g∗ | $2.205\times 10^{-2}$ | 1.074 | 6
h | $2.334\times 10^{-2}$ |  h∗ | $2.282\times 10^{-2}$ | 1.023 | 9
i | $2.364\times 10^{-2}$ |  i∗ | $2.337\times 10^{-2}$ | 1.012 | 10
j | $2.475\times 10^{-2}$ |  j∗ | $2.404\times 10^{-2}$ | 1.030 | 8
k | $2.328\times 10^{-2}$ |  k∗ | $2.319\times 10^{-2}$ | 1.004 | 11
Table 3:  Peak brightness of the features that appeared in the first step
image. The 11 features near the center are shown. P is the peak in the center
that was replaced by the restoring beam. Features other than P are as shown in
the brightness distribution of the residual dirty map.

###  3.3 Our hybrid mapping process

After obtaining the image models for the two points, more than 100 iterations,
including trials and errors, were performed in the hybrid mapping process.
Most of the CLEAN images were run with the parameters listed in Table 4.

As described in Event Horizon Telescope collaboration  (2019d), care must be
taken in the choice of FOV, as incorrect restrictions will result in incorrect
image structures. Considering the well-known structure of M 87, we restricted
the imaging region by eight BOXes where emission could be detected. For the
self-calibration, the selected CLEAN components were used as the next imaging
model and the parameters in Table 1 were used. By repeating the phase-only
self-calibration in this way, we were able to find better images and
calibration solutions. This is because the method of simultaneously solving
the amplitude solution with hybrid mapping has the risk of going in the wrong
direction. Self-calibration of phase-only can be done with a certain degree of
safety. Even if the wrong model is used and a completely wrong solution is
obtained, the closed phase is automatically preserved and convergence to a
completely wrong image can usually be avoided. On the other hand, the
amplitude solution from self-calibration can be infinitely large or small by
using the wrong image model. It is safe to try the self-calibration of the
amplitude solution after a confident correct image model is obtained from the
phase self-calibration.

Parameters |
---|---
ANTENNAS | 0 (all)
DOCALIB | 2
CELLSIZE |  $1.5\times~{}10^{-6}$, $1.5\times~{}10^{-6}$ (asec)
UVRANGE | 0, 0 (no limit)
FLDSIZE | 16384, 16384 (pix)
ROBUST | 0
NITER | 40000
GAIN | 0.05 or 0.005
FLUX | -1.0 (Jy)
BMAJ, BMIN | 0.00002, 0.0002, and 0 (asec)
BPA |  0 (∘)
RASHIFT |  $-9.25\times~{}10^{-3}$ (asec)
DECSHIFT |  $8.15\times~{}10^{-3}$ (asec)
NBOXES | 8
BOX(1) | -1, 912, 1329, 2185 (pix)
BOX(2) | -1, 820, 2049, 2729 (pix)
BOX(3) | -1, 912, 3105, 3129 (pix)
BOX(4) | -1, 1184, 4481, 3689 (pix)
BOX(5) | -1, 1792, 6321, 4473 (pix)
BOX(6) | -1, 2448, 8753, 5673 (pix)
BOX(7) | -1, 2848, 11537, 7001 (pix)
BOX(8) | -1, 2800, 13377, 7833 (pix)
Table 4: Typical parameters of IMAGR for our hybrid mapping process. The
imaging area is $24.576~{}\rm mas$ square, but it is limited by the BOX
setting. ”$Flux=-1.0$” means that the terminating condition of CLEAN
subtraction is the first occurrence of a negative maximum value.

###  3.4 Our final image

In the latter half of the imaging process, we selected several candidates for
the final image by comparing the difference in closure phase between the image
and the real data. Furthermore, we created several image models using the
CLEAN components of the candidate images to find the best image with the
minimum closure residuals. Since we found that the source structure has time
variation, we divided the data into the data of the first two days and the
data of the last two days. As a result, we obtained the best images as shown
in Figure 4. The data from the first two days was a composite of seven raw
CLEAN maps, and the data from the last two days was a composite of nine raw
CLEAN maps. Both consist of CLEAN components only. In the images of the first
two days, adjacent CLEAN components within $2~{}\mu\rm as$ are merged into one
component. In the images of the last two days, adjacent CLEAN components
within $5~{}\mu\rm as$ are merged into one component.

Since the eight BOXes cover a large area, the resulting CLEAN component
contains three types of emission: real emission, associated diffraction
(sidelobes), and false acquisitions. For example, the bright emission on the
right edge is not real. Such unreal bright spots often appear when the VLBI
data is analyzed and imaged. When such unreal brightness appears, there may
actually be strong emissions outside the BOXes. We produced a large image (30
arcsec field of view) using very short baseline (SM-JC and AA-AP) visibility
data, but could not detect any new strong features.

To get a more complete image, we need to select only the real ones from these
CLEAN components and perform CLEAN imaging again with each narrow BOX to cover
the selected ones. However, since our data did not have enough u-v coverage
and quality to select the correct ones among the CLEAN components, we gave up
the task of extracting the CLEAN components this time. Nevertheless, the
quality of the final image does not seem to be too bad. The closure residuals
of the resulting image show a small variance comparable to the EHTC ring
image. The residual of our map for the first two days of data is
$-4.90~{}\pm~{}37.93^{\circ}$ (the residual of the EHTC ring is
$-0.73~{}\pm~{}45.33^{\circ}$) and the residual of our map for the last two
days of data is $1.79~{}\pm~{}42.11^{\circ}$ (the residual of the EHTC ring is
$4.22~{}\pm~{}45.74^{\circ}$). Here, we integrated the 5-minute data points
and calculated the closure phase of all triangles. For more information on
closure phase residuals, see Section 4.3.3. The EHTC ring images for
comparison were generated using the EHTC-DIFMAP pipeline. It should be
emphasized that the final image clearly contains an unrealistic CLEAN
component, but still shows the same level of closure phase residuals as the
image of the EHTC ring.

We also used this final image model to attempt self-calibration of the
amplitude and phase for the solution, performed CLEAN, and obtained new
images. However, the residuals of the closure phase in the new image were not
improved. Therefore, we terminated the hybrid mapping without amplitude
calibration. The images shown in Figure 4 are our best final images. The two
upper panels in Figures 7 and the panels in Figure 10 are partial extracts
from the final images. Figure 8 shows the full image of the last two days of
data.

Figure 4:  The best images obtained from the analysis. The left panel shows
the best image for the data of the first two days. The right panel shows the
best image for the data of the last two days. In both images, the grouped-
CLEAN components are convolved with a circular Gaussian restoring beam of HPBW
$=200~{}\mu\rm as$. A logarithmic pseudo-color is used to express the large
differences in brightness distribution (arbitrary unit). The eight red circles
indicate the BOX area used. The bright spot seen on the right (west) edge is
not real brightness distributions (see the content in this Section 3.4).

###  3.5 Solutions of self-calibration both amplitude and phase using a final
image model

Here we show solutions of the self-calibration for both amplitude and phase
using one of the final images, although we did not apply it to the data
calibration. The reason we dare to show the unused solutions here is that we
believe this study provides insight into the quality of EHT public data and
the reliability of our images. We performed our self-calibration using CALIB
in the AIPS task in ”A&P” mode with the image (CLEAN components). Other
parameters of CALIB are the same as in the first self-calibration (Table 1).
Figures 5 and 6 show the self-calibration solutions (the total amount of
solutions to be applied for data calibration).

Figure 5 shows the phase solution. Compared to the initial phase solution
shown in Figure 2, there is no significant change in the overall perspective.
This can be attributed to the fact that the brightness distribution of the
observed source is concentrated in the center and does not deviate
significantly from the self-calibration solution assuming a single point
source. However, there are offsets in the phase changes of JC, LM, PV, and SM
stations. In addition, the phases of the two stations in Hawaii, JC and SM,
show a larger phase dispersion than the solution of self-calibration assuming
a point source on the 100 and 101 days’ data. Although small in comparison,
the phases of JC and SM on 95 and 96 days’ data also show phase scatters on
the same hours.

The amplitude solution is shown in Figure 6. In general, errors in amplitude
are due to noise in the atmosphere and in the receiving system. In addition,
changes in aperture efficiency depending on the elevation angle of antenna
often cause systematic errors in amplitude. These effects can be measured by
an auxiliary method.

For large aperture antennas, gain loss due to offset tracking of the target
source from the narrow main beam angle may occur, which is difficult to
calibrate.

Furthermore, coherency (phase stability) loss is observed due to the
variations in each station clock and atmospheric variations, which is more
difficult to measure correctly than other error factors.

Amplitude solutions for AA, AP, PV and SM stations are within $50\%$
fluctuation ($\sim 1.0\pm 0.5$). Such values are often found in amplitude
solutions of most of the self-calibrations of VLBI data. On the other hand, JC
and LM stations occasionally show large amplitude solutions reaching 10 and
30, respectively. The JCMT station shows a large amplitude value at $T~{}\sim
4.25~{}$hour on the last observation day (101 day). On the other hand, for the
LMT station, the amplitude is large for several times as follows.
(a) $T\sim 1~{}hour$ and $T\sim 2.6~{}hour$ on the first observing day (095
day)
(b) $T\sim 1~{}hour$ on the second observing day (096 day)
(c) $T\sim 2.25~{}hour$ and $T\sim 6.25~{}hour$ on the 3rd observing day (100
day).
The EHTC did not show the overall calibrations to be applied, but noticed the
sudden large-amplitude errors at the LMT station (Figure 21 in Event Horizon
Telescope collaboration  (2019d)).

These large amplitude solutions may have implied that the resultant image is
significantly wrong. For comparisons, we examined the solutions of self-
calibration in the case of the EHTC ring image. Consequently, we found that
the self-calibration solutions by the EHTC ring image also demonstrate large
amplitudes occasionally, similar to those of our image (Section 5.6).
Therefore, if such large amplitudes found in self-calibration solutions are
negative signs against the resultant image quality, the results obtained by
both the EHTC and our work should be rejected. The EHTC is concerned and
considering the fact that some stations require large-amplitude corrections
during data analysis. EHTC then analyzed the data from 3C 279, which was
observed with M 87, and obtained consistent imaging results from all imaging
methods. At the same time, the EHTC found that the amplitude correction was
consistent with that obtained with M 87 (Event Horizon Telescope collaboration
(2019d)). The amplitude corrections they found are also consistent with those
we showed above. In other words, it is natural to consider that such a large
amount of amplitude variation actually occurred. To add, the fact that the
EHTC obtained a non-ring structure from the 3C 279 data and that the amount of
error corrections the EHTC obtained at that time were consistent with those
obtained from the M 87 data does not mean that the ring image of the EHTC is
the correct image of M 87. The large amplitude solutions from the self-
calibrations indicate that the ”calibrated” data released by the EHTC are not
of high quality with respect to the amplitude.

Figure 5: Phase solutions obtained from self-calibration with A&P mode using
CALIB in AIPS. As the image model, all of the grouped CLEAN components of the
last two days’ image were used. The red points show the solutions for IF 1
data, the blue ones show those for IF 2 data.  Figure 6: Amplitude solutions
obtained from self-calibration with A&P mode using CALIB in AIPS. As the image
model, all of the grouped CLEAN components of the last two days’ image were
used. The red points show the solutions for IF 1 data, the blue ones show
those for IF 2 data.

##  4 Imaging results

In this section, we describe the brightness distribution obtained in our final
image models. Unlike the EHTC result, we could not detect any ring structure
but found that the emissions at 230 GHz come not only from the narrow central
region less than $128~{}\mu\rm as$ in diameter (the EHTC’s FOV), but also from
the jet region. We found a core-knot structure at the center and weak spot-
like features along the M 87 jet stream though the reliability must be
discussed.

In Section 4.1, we show the structure of the central region. In Section 4.2,
features seeming to belong to jet are presented. In Section 4.3, we
investigate the reliability of our final image from three points of views: the
attainable sensitivity (Section 4.3.1), the robustness of the main features
(Section 4.3.2), and the self-consistency of our imaging (Section 4.3.3),
where we compare with those of the EHTC.

###  4.1 The core

Figure 7:  Images of the central core region: The top left panel is the image obtained from the data of the first two days. The upper right panel is that obtained from the data of the last two days. In both images, the CLEAN components are grouped and convolved with the restoring beam of a circular Gaussian with HPBW of $20~{}\mu\rm as$. The brightness distribution is shown in pseudo-color (arbitrary unit). As shown in the upper left panel, three features, C(core), K(knot), and W(west component), were detected. The lower left panel shows the difference between the last image and the first image, i.e., the time variation of the brightness distribution during 5 days. The lower right panel shows the positions of the C, K, and W peaks. The red crosses are for the first two days, and the blue crosses are for the last two days. The size of the crosses is ten times the size of the error bars in position. The small squares also indicate the location of the large increase in intensity.  | the first two days’ | the last two days’
---|---|---
Peak position |  R. A. ($\mu\rm as$) |  $\delta$ ($\mu\rm as$) |  R. A. ($\mu\rm as$) |  $\delta$ ($\mu\rm as$)
Core | $~{}-1.8\pm 0.6$ | $~{}-1.5\pm 0.6$ | $~{}-2.3\pm 0.5$ | $~{}-1.5\pm 0.5$
Knot | $-22.2\pm 0.5$ | $~{}27.0\pm 0.5$ | $-23.1\pm 0.3$ | $~{}22.5\pm 0.3$
West | $-78.1\pm 0.3$ | $-33.0\pm 0.3$ | $-77.2\pm 0.3$ | $-37.5\pm 0.3$
|  $\Delta$ R. A. ($\mu\rm as$) |  $\Delta\delta$ ($\mu\rm as$)
Core |  |  | $-0.5$ | $~{}~{}0.0$
Knot | $-0.9$ | $~{}-4.5$
West | $0.9$ | $~{}-4.5$
Position of intensity increase |  |  R. A. ($\mu\rm as$) |  $\delta$ ($\mu\rm as$)
Core area a |  | $-22.4\pm 0.4$ | $~{}15.0\pm 0.4$
Knot area a |  | $-29.8\pm 0.7$ | $~{}40.5\pm 0.7$
b |  | $-40.8\pm 0.3$ | $~{}33.0\pm 0.3$
c |  | $-48.0\pm 0.4$ | $~{}43.5\pm 0.4$
West area a |  | $-74.7\pm 0.7$ | $-43.5\pm 0.7$
b |  | $-79.9\pm 0.5$ | $-15.0\pm 0.5$
c |  | $-99.8\pm 0.7$ | $-25.5\pm 0.7$
Integrated Intensity | (mJy) | (mJy)
Core | $55.6\pm 5.2$ | $66.1\pm 4.7$
Knot | $33.5\pm 2.7$ | $44.9\pm 2.3$
West | $22.5\pm 1.2$ | $30.2\pm 1.4$
Brightness temperature | (K) | (K)
Core | $>1.0\times 10^{10}$ | $>1.2\times 10^{10}$
Knot | $>6.0\times 10^{~{}9}$ | $>8.1\times 10^{~{}9}$
West | $>4.0\times 10^{~{}9}$ | $>5.4\times 10^{~{}9}$
Grouped CLEAN components | (mJy) | (mJy)
$F_{GCC}>0.1mJy$ | $707.4~{}(n=1151)$ | $1032.6~{}(n=1657)$
All | $767.8~{}(n=2824)$ | $1154.6~{}(n=7844)$
Table 5:  Properties of main features: positional offsets from the map phase
center in $\mu\rm as$, flux densities in mJy, and minimum brightness
temperatures in Kelvin calculated with the assumption that the emission area
is $15~{}\mu\rm as$ in diameter. Positions of intensity increase in features
are also shown. At the bottom, the sum-up intensities and the numbers of the
grouped CLEAN components in the whole images are shown.

In the central core region, we could not find the ring structure reported by
the EHTC, but found a core-knot structure. Figure 7 shows the images of the
central region ($300~{}\mu\rm as$ square). As noted in Section 3.4, since the
data calibration is not yet complete, our final images show the sidelobe
structure around actual features. This is a common phenomenon in synthesis
imaging with radio interferometers with only a few stations. The images in
Figure 7 show that “the unresolved VLBI core” in M 87 has finally resolved
into substructures.

The high spatial resolution of the EHT array clearly shows the presence of two
bright peaks, i.e., the core and knot structure. The core is indicated by ”C”
and the knot by ”K” in the upper left panel of Figure 7. In addition, we found
a feature, ”W”, located west about $83~{}\mu\rm as$ apart from the core C. The
flux densities from the obtained CLEAN components are $F_{C}\sim 60~{}mJy$ for
the core (C), $F_{K}\sim 40~{}mJy$ for the knot (K), and $F_{W}\sim 25~{}mJy$
for the west feature (W). In this observation, the solid angle of features was
not so clear. Here, we assume that the solid angle of the emission is
$15~{}\mu\rm as$ in diameter, and calculate the brightness temperatures (lower
limit). The average brightness of feature C is $T_{\rm b}=1.1~{}\times
10^{10}$ K. Feature K has a brightness of $T_{\rm b}=7.1~{}\times 10^{9}$ K.
Feature W is $T_{\rm b}=4.7~{}\times 10^{9}$ K. Thus, we have detected central
features with brightness temperatures higher than the EHTC ring (up to $T_{\rm
b}\sim 6\times 10^{9}$ K). The solid angle assumed here is the maximum size of
a single, smoothed object that the EHT array can detect in the 230 GHz
(Appendix A). Therefore, the actual brightness temperature is likely to be
much higher. If the solid angle of the emission is $5~{}\mu\rm as$ in
diameter, the brightness temperature of core C reaches $10^{11}~{}K$. If this
is the case, the brightness temperature is an order of magnitude higher than
the previous measurement cases (Kim et al., 2018; Hada et al., 2016; Akiyama
et al., 2015). This is mainly because the size of the emitting region has been
identified as smaller due to the higher spatial resolution.

High brightness temperatures were often detected from some active galactic
nuclei (Horiuchi et al., 2004; Homan et al., 2011), and can be explained by
the Doppler boosting effect of relativistic motion of jet approaching toward
us. Previous observations found no high velocity movement in the M 87 central
core. Therefore, the brightness temperatures are not due to such Doppler
boosting effects. If they actually reflect the physical temperatures, they can
be explained easily by the simple RIAF (Radiatively Inefficient Accretion
Flow) disks (Kato, Fukue, & Mineshige , 2008; Nakamura et al., 1997). Our
observational results are consistent with those of previous studies,
supporting the existence of the RIAF disk in the M 87 core (Di Matteo et al.,
2003).

There is a clear difference between the two images observed over the five
days. According to Event Horizon Telescope collaboration  (2019c), they found
a change in the closure phase between data sets from the first two days and
the last two days. In other words, there was a clear time variation. However,
the EHTC could not clearly identify from the structure of that ring where that
change occurred (Event Horizon Telescope collaboration , 2019d). We identified
the change in the closure phase as due to a change in the core knot structure
(features C and K). In particular, the change in the position of feature K was
also seen in the trial images during the hybrid mapping process.

Assuming that features are single components, we fitted a Gaussian brightness
distribution to each feature and measured the central position and
displacement over five days. Relative to the position of feature C, the change
in position of feature K is $\Delta\alpha=-0.4~{}\mu\rm as$,
$\Delta\delta=-4.5~{}\mu\rm as$ in 5 days, and the proper motion is
$0.33~{}\rm mas/yr~{}(v\sim 0.1~{}c)$. Feature K appears to be approaching
feature C as if showing an inflow motion. However, if we look at the
differences in the brightness distributions shown in the lower left of the
Figure 7, we can see that the changes in the brightness distribution of
feature K occur in three places, all at the north end of feature K. In the
latter measurement of the position of feature K, feature K appears to be
moving south because the brightness distribution of feature C affects the
measurement; K is moving north on the line of $PA=-38^{\circ}$ as a whole. The
position of feature C has hardly changed, but the location of ”a” where the
intensity increased is at the northwest side of feature C. In other words, the
structure of features C and K and their time variation can be interpreted as
an outflow emanating in the direction of $PA=-38^{\circ}$ from the origin.
There has never been a measurement of the motion of a knot so close to the
central core.

In comparison, it is difficult to interpret what feature W is. Three
hypotheses are presented below.

  1. 1.

Gravitational lensing image. Feature W is morphologically similar to feature
K, and the pattern of brightness variation is also similar. This can be
attributed to the formation of the gravitational lens image of feature K due
to the strong gravitational field of the SMBH in M 87. Assuming that the
position of SMBH is approximately equal to the position of feature C (the
distance between the core of M 87 and SMBH is $41~{}\mu\rm as$ or 6 $R_{\rm
S}$; Hada et al. (2011)), feature W would be located (or at least projected)
at 12 $R_{\rm S}$ from the SMBH. There is a possibility that the radio waves
emitting from feature K to the far side, orbiting in the strong gravity field
of the SMBH, and being changed the propagation direction, come towards us
(Black Hole Echo; Saida (2017)). If feature W is such a lensing image caused
by the strong gravity field of the SMBH, it should be the image of the
backside of feature K, so it is most likely a mirror image of feature K.
However, the shape of feature W does not look like such an image. Needless to
say, there are many possibilities for a gravitational lensing due to a strong
gravity field, so detailed calculations are required to deny it completely;
however, the possibility that feature W is a gravitational lensing image is
not very high.

  2. 2.

Another central black hole. Feature C is the primary SMBH of M 87, and feature
W is a secondary SMBH orbiting the primary SMBH. If there is a binary SMBH in
M 87, it can be permanently observed with the EHT array. Based on these
observations, we calculated two possible orbits.

    1. (a)

The proper motion of feature W ($\mu=0.34~{}\rm mas/yr,~{}\rm v\sim 0.09~{}c$)
is assumed to be due to a circular orbit motion, and its orbital radius is
assumed to be the separation $R=83~{}\mu\rm as$ from feature C. In this case,
the orbital period T is $\sim 1.5$ years. If the real radius is
$R=1.4\times~{}10^{3}~{}au$, the mass of central object $M_{c}$ is only
$1.2\times~{}10^{6}~{}M_{\odot}$. Since the estimated mass is too small as
compared to those of the previous M 87 studies, this assumption must be
rejected.

    2. (b)

We assume that the observed proper motions and structure change of feature W
are only due to changes in surrounding matters, and that the measured proper
motions of feature W have nothing to do with its orbital motion. In other
words, we assume here that no change in the position of the center of gravity
of feature W is observed. Also, it is assumed that feature C has an SMBH with
a mass of $6\times 10^{9}~{}M_{\odot}$ and that the orbital radius of feature
W is the distance between features C and W. The distance between them is
$83~{}\mu\rm as$ ($1.4\times 10^{3}$ au or $11.9~{}R_{\rm S}$). It is
consistent with the 86 GHz core size of $\sim 80~{}\mu\rm as$ at 86 GHz
observed in 2014 (Hada et al., 2016), suggesting that the two features C and W
are not transient. Also sinusoidal oscillations of the position angle of the
jet were observed with a period of roughly 8 to 10 years (Walker et al.,
2018). If the two features C, and W compose a binary of black holes, its
orbital motion can cause such jet oscillations. Certainly, the apparent
separation of approximately $1.4\times 10^{3}$ au is too short to explain the
observed period of the jet oscillation. However, if the real distance is
longer by a factor of about 3.42, which is the correction factor of the
viewing angle of the jet axis from us ($\sim 17~{}^{\circ}$), the orbital
period of the binary can be $\sim 10$ years.

  3. 3.

Unstable initial knot. Feature W is another knot moving toward a different
direction. The jet of M 87 is known to have a wide opening angle at scales
well below $1\rm~{}mas$ (Junor, Biretta & Livio, 1999). Furthermore, Walker et
al. (2018) found evidence from 43 GHz observations that the initial opening
angle $\theta_{app}$ is $\sim 70~{}^{\circ}$. We found the angle $\angle KCW$
is $70~{}^{\circ}$, and further that the line of the average jet axis
($PA=-72^{\circ}$) divides its angle almost evenly into
$34^{\circ},~{}36^{\circ}$. Furthermore, the lines CK and CW extend in the
directions of $PA=-38^{\circ}$ and $PA=252^{\circ}$, respectively. These
directions are very similar to the ridges observed at 43 GHz from where Walker
et al. (2018) measured the initial opening angle. We guess that not only
feature K, feature W is also an initial knot that has just emerged from the
core, and still, the shape is very unstable and shows changes significantly.

Adopting the most conservative hypothesis, feature W, like feature K, can be
understood to be a knot that represents the initial jet structure.

As we will discuss in Section 4.3.2, the core-knot structure (features C and
K) is robust in the sense that it can be obtained with different imaging
parameters. On the other hand, the $40~{}\mu\rm as$ ring of the EHTC is
sensitive to BOX parameters and can be easily destroyed, even if it can be
created as shown in Section 5.7. Due to the robustness of the core-knot
structure, we consider it to be a real structure. On the other hand, the
feature W is sensitive to the BOX size, so its detection is not as reliable as
it could be. However, the structure corresponding to feature W had already
appeared in the first imaging results (Section 3.2.2). That is, feature c in
Table 3 is in a similar position to feature W and also shows the largest
asymmetry. Also, if we run the EHTC-DIFMAP pipeline without its BOX setting,
an emission feature appears at the position close to feature W (lower right
panel of Figure 24). These suggest that the feature W is also a real
structure.

###  4.2 The jet

Here, we show the overall brightness distribution (Section 4.2.1) and that of
so-called the jet launching region, which is a few mas away from the core
(Section 4.2.2).

####  4.2.1 The overall structure

Figure 8: The overall structure of M 87 we obtained (image from the data of
the last two days). The grey line shows the average direction of the jet axis
($PA=-72^{\circ}$ from Walker et al. (2018)). The restoring beam is
$200~{}\mu\rm as$ circular Gaussian, which is much larger than the default
beam in order to make the emission obvious. The logarithmic pseudo-color
(arbitrary unit) is used to enhance the darker parts of the image. The image
consists only of the grouped CLEAN components obtained. For comparison, the
average image at 43 GHz from VLBA observations taken from Figure 1 in Walker
et al. (2018) is shown in the inset. The bright spot seen on the right (west)
edge is not real brightness distribution (see Section 3.4).  Figure 9:  Flux
density distribution corrected for the band width smearing effects. Here we
show the sum of the flux densities of the CLEAN components obtained in each
small region. The horizontal axis shows the distance along the average
direction of the jet axis ($PA=-72^{\circ}$ from Walker et al. (2018)) from
the map center (near the peak of the core). The binning intervals are 0.25
mas. The vertical axis shows the sum of the flux densities in Jy (logarithmic
scale). The green line shows the flux density distribution for the image from
data of the first two days, and the red line shows the flux density
distribution for the image from data of the last two days. The peaks seen on
the right edge are not real flux densities (see Section 3.4).

Figure 8 shows the overall structure of the M 87 we obtained. In order to make
the emission obvious, we used a restoring beam of $200~{}\mu\rm as$ circular
Gaussian, 10 times larger than the default beam size. As already mentioned, it
is found that the emission at 230 GHz comes not only from the central point
source, but also from other regions.

The EHTC either assumed or concluded that there is no bright source outside
the narrow region ($128~{}\mu\rm as$ in diameter) where the ring was found.
However, we found that the emission was not from such a narrow range, but from
a wide range of more than a few milli-arcseconds (mas). This is consistent
with the results of VLBI observations at 43 GHz and 86 GHz.

Our final image shows a similar structure to the average image in the 43 GHz
band (the inset of Figure 8). There are two main similarities.

First, as in the 43 GHz image, our image shows that the ”jet” has an extended
structure leading to the core. Then, up to a few mas away from the core along
the jet axis, both edges are bright, as in the previous observations.

Second, the brightness distribution of the jet in the 230-GHz is consistent
with the trend of those obtained from lower-frequency observations. The core
is vastly brighter than the jet structure. Within the radius of 0.25 mas
($250~{}\mu\rm as$) from the center, 63 % (the first two days’ image) and 75 %
(the last two days’ image) of all obtained flux densities are concentrated.
However, features C, K, and W (several tens mJy at most, see Table 5) do not
occupy them, rather the flux densities are distributed over a wider area. In
contrast, the EHTC rings have a total of about 500 mJy that is contained
entirely within a diameter of only a few tens of $\mu\rm as$.
The results of this observation at 230 GHz show that the brightness in the jet
region is orders of magnitude lower than that in the core region. In addition,
the decay of the flux density along the jet is more rapid at 230 GHz than in
the lower frequency observations. Compared to the peak luminosity of the core,
the relative intensities are $6.6\times~{}10^{-2}$ at 0.25 mas from the core,
$9.9\times~{}10^{-3}$ at 0.5 mas, and $2.3\times 10^{-3}$ at 1 mas (Figure 9).
While, in the observation at 43 GHz, the decreases of intensity are
$2.8\times~{}10^{-1}$ at 0.25 mas from the core peak, $8.5\times~{}10^{-2}$ at
0.5 mas, and $2.5\times~{}10^{-2}$ at 1 mas (from the upper panel of Figure 6
in Walker et al. (2018)). At 1 mas position, the intensity of the jet
structure is 2.5 $\%$ of the core peak at 43 GHz, however the intensity at 230
GHz is only 0.2 $\%$ of the core peak, namely the intensity of the jet
structure is greatly attenuated at 230 GHz. However, with respect to the
structure of the brightness and intensity distribution of both edges, the
trend is in great agreement with the previous results of the M 87 jet.

The total flux density measured by the EHTC (Event Horizon Telescope
collaboration , 2019c) was 1.12 and 1.18 Jy, for the first two days and the
last two days, respectively. In contrast, the total flux density of the CLEAN
component in our analysis is 767.8 and 1154.6 mJy, respectively. That is,
there are missing flux densities of 353 and 25.4 mJy, respectively 999The sum
of the flux densities we obtained as CLEAN components is larger than that of
the EHTC ring. We made the ring according to their open procedure and measured
its flux density ($\sim 500~{}\rm mJy$)..

The difference between the total flux density of our image and the single-dish
flux density is most likely due to the presence of extended emission
somewhere, which the present EHT array cannot detect. As shown in Appendix A,
the EHT array cannot detect an smoothed emission feature (like Gaussian
brightness distributions) with size larger than $30~{}\mu\rm as$.

####  4.2.2 The Jet launching region

In this section, we present the structure within a few mas from the core. We
have found emission belonging to the jet component that was not detected by
the EHTC.

In Figure 10, the brightness distribution in this region is represented in
three ways. The logarithmic pseudo-color (arbitrary unit) is used to represent
the large differences in brightness distribution. The upper panels (a) and (b)
are composed by restoring beams of a circular Gaussian with HPBW of
$20~{}\mu\rm as$, which corresponds to the size of the spatial resolution of
the EHT array for M 87 observations. The middle panels (c) and (d) are
composed by restoring beams of circular Gaussian with HPBW of $200~{}\mu\rm
as$. In order to facilitate comparison with previous results, the beam size is
close to the spatial resolution of previous lower frequency observations (43,
86 GHz). Panels (e) and (f) in the bottom row show the image by the large
restoring beam overlaid with the 43 GHz averaged image by the VLBA (Walker et
al., 2018). Note that the 43 GHz image is time-averaged over 17 years, so
knot-like features have been averaged out. It can be seen that the brightness
distribution at 230 GHz is consistent with that at 43 GHz. The left panels
(a), (c), and (e) show images of the data from the first two days. Panels (b),
(d), and (f) on the right show images of the data from the last two days.
Obviously, they are different from each other. However, the differences seen
in the regions of a few mas cannot be attributed to the intrinsic variability
of the source that occurred during the five days. Rather, it seems to be
mainly dependent on the observational conditions.

The emission areas of our 230 GHz results are consistent with that of the 43
GHz average image. They also show that both edges of the jet are brightened,
which phenomena have been observed so far. Based on our data analysis, it
seems that the detection of emissions in the range of several mas from the
core of the M 87 has been successful to some extent.

Figure 10: Images of the core and the jet launching region: Panels (a), (c),
and (e) on the left show images of data from the first two days. The right
panels (b), (d), and (f) show the images of data from the last two days. The
logarithmic pseudo-color (arbitrary unit) is used to represent the large
differences in brightness distribution. The upper panels (a) and (b) are
composed by a circular Gaussian restoring beam with HPBW of $20~{}\mu\rm as$.
The middle panels (c) and (d) are composed by a circular Gaussian restoring
beam with HPBW of $200~{}\mu\rm as$. The levels of contour lines in the panels
(c) and (d) are $10^{-5}$, $10^{-4}$, $10^{-3}$, $10^{-2}$, and $10^{-1}$ of
the peak brightness. The lower two panels, (e) and (f), show overlaid ones
with the VLBA averaged image at 43 GHz. The contour lines show the VLBA
averaged image at 43 GHz taken from Figure 3 in Walker et al. (2018), and the
levels of contour lines are -0.3, 0.3, 0.6, 0.85, 1.2, 1.7 mJy beam-1. Their
restoring beam shape is $0.43\times$ 0.21 mas with $PA=-16^{\circ}$. Peak
positions of the two images are used for the alignment of the two images.

###  4.3 Reliability of our final images

As mentioned in Section 3, our calibration method was limited to self-
calibration because the public the EHTC data do not contain raw data.

We also had to give up on the amplitude self-calibration because the closure
phase residuals were not reduced as compared to the case when only phase
calibration was performed. Therefore, the calibration is not yet fully
complete. As clues to the reliability, we describe the properties of the final
images from three aspects: detection limit (Section 4.3.1), robustness
(Section 4.3.2), and the self-consistency of our imaging (Section 4.3.3),
where our images show better self-consistency than those of the EHTC.

####  4.3.1 From sensitivity

Figure 11:  Distributions of the grouped CLEAN components with flux densities
larger than 0.1 mJy. Red dots are from the image of the first two days, blue
dots are from the image of the last two days. The sloped line indicates the
average direction of the jet axis ($PA=-72^{\circ}$ from Walker et al.
(2018)).

Event Horizon Telescope collaboration  (2019c) shows that the typical
sensitivity of a baseline connected to ALMA is $\sim 1~{}mJy$. We estimate
that this sensitivity is for an integration of about 5 minutes. For an on-
source time of 2 days, the attainable sensitivity reaches close to $0.1~{}mJy$
(ALMA-LMT baseline, $S/N~{}=~{}4$, assuming a point source). It is difficult
to estimate the practical sensitivity of the synthesized image of an
interferometer composed of antennas with different performances, such as the
EHT array. However, it is unlikely that the image sensitivity will not be
worse than the baseline sensitivity noted above.

Here, we consider $0.1~{}mJy$ to be a reliable detection limit for our final
images. Figure 11 shows the distribution of the grouped CLEAN components with
flux densities larger than $0.1~{}mJy$. Almost all of the components are
concentrated within a few mas of the core. (The remaining components are
located in a false bright spot created outside the range of this figure, about
$20~{}mas$ west of the center.) The image from the core to a few mas along the
average jet axis seems to be reliable in terms of detection limits.

A large number of grouped CLEAN components with flux densities larger than
$0.1~{}mJy$ are found in our final images. The number of grouped CLEAN
components with flux densities larger than $0.1~{}mJy$ is 1151 from the images
of the first two days (with a sum of flux density of $707.4~{}mJy$), and 1657
from the images of the last two days (with a sum of flux density of
$1032.6~{}mJy$) (Table 5).

####  4.3.2 The robustness of our final image

In this section, we discuss another property of our final images: the
robustness of the image structure.

If the data is not yet completely calibrated, BOX technique is effective. As
well as the EHTC, we also used the BOX technique to limit the imaging area
(FOV). This technique has the potential to produce good images even if the
calibration is incomplete. On the other hand, it may be creating structures
that do not actually exist. In fact, the bright spot on the right side of our
final image (Figure 8) is such an example. Therefore, care must be taken when
using the BOX technique, because a false structure will be created in the BOX
area, and the real structure outside of the BOX area will be removed from the
image.

We examine how the image is affected when we change the BOX parameters. In
other words, we investigate the stability of the image. We compare the images
obtained by changing the size of the BOX. The panels in Figure 12 show the
four cases. The upper left panel (a) is the image without BOX (the FOV is
$24.576~{}\rm mas$ square). The top right panel (b) shows the image with the
same 8 BOXes that we used to obtain our final images. The lower right panel
(c) is the image with a small BOX (circle with diameter $D=5~{}\rm mas$ is
used). The lower right panel (d) is the image with a very narrow BOX (circle
with diameter $D=128~{}\mu\rm as$ that corresponds to the FOV the EHTC used).
These four CLEAN images were produced using data of the entire four days.

In all panels, the emission can be seen at the positions of features C (core)
and K (knots). On the other hand, feature W disappears in the case where the
BOX setting is omitted (no BOX case). In the case of the EHTC FOV, no emission
is seen at the position of feature W because the position of feature W is
outside the BOX setting.

Without the BOX setting, the S/N of the image is degraded. From the comparison
between panel (a) and the other panels, we can see that the BOX setting
compensates for the lack of calibration and improves the image quality. Thus,
presence or absence of the BOX setting seems to have an effect on the image
quality. Another noteworthy point is that in the case of the very narrow BOX
setting (panel d), several different bright spots newly appear in the BOX.
Moreover, some of them are located at the boundaries of the BOX. In such a
case, other actual brightness distributions could exist outside the BOX
setting.

Since feature W disappears in the CLEAN image without the BOX setting. Feature
W is considered to be less reliable than features C and K. As mentioned at the
end of the Section 4.1, there are other reasons to consider that feature W is
a real existence.

Figure 12: Comparison of images obtained by changing the size of Box. Panel
(a) is the image without BOX (the FOV is $24.576~{}\rm mas$ square). Panel (b)
shows the image with the same 8 BOXes that we used to obtain our final images.
Panel (c) is the image with a small BOX (circle with diameter $D=5~{}\rm mas$
is used). Panel (d) is the image with a very narrow BOX (circle with diameter
$D=128~{}\mu\rm as$ that corresponds to the FOV the EHTC used). These four
CLEAN images were produced using data of the entire four days.

####  4.3.3  Self-consistency of our imaging as compared to those of the EHTC
images

At the end of this section on image reliability, we present the degree of
matching between the visibility and the image model. Here, we compare the
results with those of the EHTC ring.

  1. 1.

Relations between the visibility amplitude and u-v distance (projected
baseline length): The amplitude of visibility obtained by inverse Fourier
transforming the image model is compared with those of the observed visibility
data. Figures 13, and 14 correspond to Figure 12 in Event Horizon Telescope
collaboration  (2019d). This kind of comparison of visibilities is often
performed to check the reliability of an image. However, here, the observed
visibility data are calibrated by self-calibration solutions using the image
model. Therefore, it is important to note that the amplitudes of the observed
visibility data and those from the image model are no longer independent of
each other. What can be safely determined from this comparison is the internal
consistency of the imaging and calibration process. Figure 13 shows the data
from the first two days, and Figure 14 shows the data from the last two days.
The top row of each shows the variation of the visibility amplitude with
respect to the projected baseline length. The red dots are those of the image
model. The middle and bottom panels show the normalized residual amplitudes
between the image model and the calibrated observation data. The plotted
points are the calibrated raw data that have not been time-integrated, and we
can see that the scatter is much larger than seen in their Figure 12 (Event
Horizon Telescope collaboration  (2019d)), where the time-integrated points
have been plotted. We can see that the average and standard deviation of the
normalized residuals of our final image are much smaller than any of the EHTC
ring images in Figure 15. As an example, we show the normalized residual
values for $t=180~{}sec$ integration.
For the data of the first two days, our image shows $\rm NR_{ours}=0.030\pm
0.539$, while the EHTC images show $\rm NR_{EHTC}=0.148\pm 0.933$.
For the data of the last two days, our image shows $\rm NR_{ours}=0.127\pm
1.259$, while the EHTC images show $\rm NR_{EHTC}=0.589\pm 2.370$. Here, in
the case of EHTC, we used the simple averages of those values for the four
EHTC images. One thing that interests us is the large discrepancy in amplitude
of the EHTC ring image cases at the longest baseline lengths over $8\times
10^{9}\lambda$. It is three times larger than those of our final image cases.
Since the EHTC ring images are very compact, if the images are really correct,
the amplitude residuals at the longer baseline should become small at least.
Another is the amplitudes at the very shorter baselines nearly $\rm
zero~{}\lambda$. They contain the components of the extended structure which
are resolved by high spatial resolution by EHT, so it is not surprising even
if they do not match. Our images reproduce the amplitudes of the very short
baselines well, but the differences are more significant in the cases of the
EHTC rings. In our cases, the normalized residuals are 4 at most, but in the
cases of the EHTC rings, they are distributed widely in the range of 0 to 15,
which is not surprising since the EHTC rings are compact and have no extended
components. However, in the Figure 12 in Event Horizon Telescope collaboration
(2019d), the maximum is 4, as if the result shows good self-consistency. The
EHTC Figure also shows the same results for the normalized residuals at the
longest baselines. This is not consistent with our own analysis. Perhaps a
different integration time of the data may cause this apparent discrepancy.
(There is no explanation for the integration time of the data points in Figure
12 in Event Horizon Telescope collaboration  (2019d)). Since the scatter of
data points is affected by thermal noise, its value changes depending on the
integration time of the data. Therefore, we examined the amounts of normalized
residuals by changing the integration time. Figure 15 shows the average and
standard deviation of the obtained normalized residuals. It can be seen that
at any integration time, our final image always shows smaller values than that
of the EHTC ring image. The averages of the 10-second integrations and
integrations over 180 seconds differ by a factor of 3, which explains the
discrepancy above.
The diagram of the visibility amplitude and u-v distance shows that our final
images, both the first and the last days, show a better consistency of imaging
and calibration processing compared to the cases of the EHTC ring images. The
diagrams indicate that our images, not those of EHTC, are supported by the
data.

  2. 2.

Closure phase variations: Following Figure 13 of Event Horizon Telescope
collaboration  (2019d), we show the closure phases of the observed data and
those derived from image models for some triangles in Figure 16. We added the
closure phases of ALMA-LMT-SMA and LMT-PV-SMA to the three triangles (ALMA-
LMT-PV, ALMA-SMT-LMT, SMT-LMT-SMA) shown by the EHTC. Closure phase is a
quantity that is free from systematic phase errors and reflects the observed
source structure. All panels in Figure 16 show large phase variations, which
correspond not to time variation in the structure of the observed source, but
to time variation of the shape of the triangle composed by the three stations
as seen from the observed source. The green dots are the closure phase
corresponding to the EHTC ring image, and the red dots correspond to our
image. The dots of our image (green dots) appear to be more aligned with the
observed data than those of the EHTC ring image. Our image is more complex
than the EHTC ring, resulting in short-term small closure phase variations.
The three panels from the top right toward the bottom correspond to the panels
shown in Figure 13 of Event Horizon Telescope collaboration  (2019d). In the
case of the two triangles ALMA-LMT-PV and SMT-LMT-SMA, our results are
consistent with those of EHTC. However, our results for the closure phase in
ALMA-SMT-LMT triangle differ from those of EHTC. In our case, the closure
phase shows an increase from $+25^{\circ}$ to $+85^{\circ}$, while that of the
EHTC shows a decrease from $-25^{\circ}$ to $-80^{\circ}$. Both the first and
last values and the amount of change are opposite in positive and negative.
All triangles were examined, but none were identical to the closure phase
variation shown by the EHTC for the ALMA-SMT-LMT triangle. Our closure phase
values are from the AIPS task, CLPLT. All triangles were examined, and none
showed the similar variation that the EHTC showed for the triangle. Also,
there are no significant closure phase discrepancies between the real and
model data. There seems nothing wrong with the CLPLT calculations.

In our analysis, there is no clear difference in closure phase matching
between our images and the EHTC rings. A notable difference is in the case of
the LMT-PV-SMA triangle, where the closure phase in the EHTC rings is beyond
$\pm 3~{}\sigma$ error bars, whereas in our final images, it manages to fall
within it.

The values of the closure phases also change depending on the integration time
of the data; however, even when the integration time is changed, the residuals
of either of them do not become overwhelmingly small. Figure 17 shows the
statistics of the closure phase residuals for all triangles. As far as the
closure phase residuals are concerned, between our images and the EHTC rings,
there is no significant difference. Our image of the core-knot structure also
shows the same magnitude of closure phase residuals as those of the EHTC ring
image. As an example, we show the standard deviations of the closure phase
residuals at $t=180~{}sec$ integration. For the data of the first two days,
our image shows $\sigma_{ours}=40.5^{\circ}$, while the EHTC image shows
$\sigma_{EHTC}=38.5^{\circ}$. For the data of the last two days, our image
shows $\sigma_{ours}=43.2^{\circ}$, while the EHTC image shows
$\sigma_{EHTC}=43.7^{\circ}$.

As for closure phase residual, there is no significant difference between ours
and the EHTC rings. If we claim that the EHTC ring image is correct due to the
closure phase residual, then our images are also correct at the same
time.101010 The correct image satisfies the closure phase of the observed
data. However, the opposite is not always true. Moreover, there are numerous
image models that show small closure phase residuals.
If these residuals are due to thermal noise, they should decrease inversely
proportional to the root square of the integration time T, but as Figure 16
shows, they do not decrease in that way. It means that both images of ours and
the EHTC’s still have differences from the true image.

Figure 13:  Relation between the visibility amplitude and u-v distance for the
first two days of data. The left panels are for our image, and the right
panels are for the EHTC ring image model with the EHTC DIFMAP pipeline using
096H data (April 6). Every dot is a raw visibility point for a 10-second
integration. The top panels show the plots of visibility amplitude versus u-v
distance. The black dots in them show those calibrated by self-calibration
solutions using the image model. The red dots are those from the Fourier-
transformation of the image model. The middle and bottom panels show
normalized amplitude residuals. The middle panel shows all data points. The
vertical axis scale is very large due to data points with very large values,
as indicated by black lines. The bottom panels show a magnified view of the
range of normalized residuals from -5 to +15. In all cases, the minimum value
of the normalized residuals is greater than -1.  Figure 14:  Relation between
the visibility amplitude and u-v distance for the last two days of data. The
left panels are for our image, and the right panels are for the EHTC ring
image model with the EHTC DIFMAP pipeline using 101H data (April 11). Every
dot is a raw visibility point for a 10-second integration. The top panels show
the plots of visibility amplitude versus u-v distance. The black dots in them
show those calibrated by self-calibration solutions using the image model. The
red dots are those from the Fourier-transformation of the image model. The
middle and bottom panels show normalized amplitude residuals. The middle panel
shows all data points. The vertical axis scale is very large due to data
points with very large values, as indicated by black lines. The bottom panels
show a magnified view of the range of normalized residuals from -5 to +15. In
all cases, the minimum value of the normalized residuals is greater than -1.
Figure 15:  Statistics of normalized residuals. The upper panels show the
average values of the normalized residuals. The lower panels show the standard
deviations. The left panels are the data of the first two days, and the right
ones are the data of the last two days. The black line shows the case of our
final image, and other color lines show the cases of the EHTC images.  Figure
16:  Closure phase variations of five triangles (ALMA-LMT-PV, ALMA-SMT-LMT,
SMT-LMT-SMA, ALMA-LMT-SMA, and LMT-PV-SMA). Closure phases of the observed
data are shown by black dots with $\pm 3~{}\sigma$ error bars, which are
obtained from 5 minutes integration. Red dots show those from our image
models. Green dots show those from EHTC ring image models (the EHTC 096H image
for the first two day’s data, the EHTC 101H image for the last two day’s).
Figure 17:  Standard deviations of the closure phase residuals from all
triangles. The case of the EHTC image (for the first two days) is shown by
black line, that for the last two days by cyan line. The cases of our final
images are shown by red line for the first days and blue line for the last
days. The green line shows in the case that the residuals are due from thermal
noise.

##  5 Why the EHTC found their $\sim 40~{}\mu\rm as$ ring?

In Sections 3 and 4, we tried to reconstruct the image from the EHT public
data using the hybrid mapping process. Our final images contain a core-knot
structure at the center and features along the jet axis towards the outside.
It is consistent with those obtained by 43 GHz or 86 GHz observations. On the
other hand, three of the EHTC imaging teams all obtained $\sim 40~{}\mu\rm as$
rings similar to each other, but no jet structure. In this section, we show
the evidences that the EHTC ring is an artifact.

The essential reason why the ring image was obtained by all the EHTC imaging
teams is the limited u-v coverage of the EHT array for M 87, namely the data
sampling bias, though the EHTC realized 230 GHz VLBI observations on a scale
that has never been accomplished before. In addition, the very narrow FOV
settings of the EHTC strongly help to create $\sim 40~{}\mu\rm as$ ring shape
from the EHT u-v data sampling bias.

First, in Section 5.1, we discuss the nature of the u-v coverage of EHT for
the M 87 observations. The spatial Fourier components for the fringe spacing
of $\sim 40~{}\mu\rm as$ are lacking. Second, in Section 5.2, we discuss how
the dirty beam (PSF) of the M 87 EHT observations is affected by this lack of
the spatial Fourier components for the fringe spacing of $\sim 40~{}\mu\rm
as$. Third, in Section 5.3, we show the dirty map is greatly affected by the
PSF shape in the case of the EHTC data. Fourth, in Section 5.4, we show that
even from the simulated visibility data of a point source we can create $\sim
40~{}\mu\rm as$ rings. This means that the u-v coverage of the EHT array for M
87 can create the $\sim 40~{}\mu\rm as$ ring regardless of the real structure
of the observed object. In other words, the EHTC result is indistinguishable
from an artifact. Fifth, in Section 5.5, we investigate one of their open
procedures for imaging demonstration. The EHTC used three methods for their
imaging. We investigated their DIFMAP(Shepherd, 1997) pipeline, which is the
closest to traditional procedures for VLBI, and found an improper point. In
the EHTC-DIFMAP pipeline, they set a very narrow FOV setting by using BOX
technique. When we ran the EHTC-DIFMAP pipeline without the BOX, the
$40~{}\mu\rm as$ ring disappeared. Instead, a core-knot structure appeared. We
also checked the output of the simulated data for other shape model images and
found that the EHTC-DIFMAP pipeline did not reproduce the input model images
correctly. In other words, the EHTC-DIFMAP pipeline does not prove the
correctness of the EHTC ring image from the data. In addition, we estimate the
amount of calibrations that the EHTC performed during their imaging process
(by the DIFMAP method), and compare them with those we did in our analysis. We
found that a large amount of additional ”calibrations” are required to make
the $40~{}\mu\rm as$ ring (Section 5.6). Also, we discuss the robustness of
the EHTC $\sim 40~{}\mu\rm as$ ring structure in Section 5.7. The structure is
very sensitive to the imaging parameters. If we change the BOX size larger,
the ring image changes significantly.

Despite their ”isolated image analysis” and surveys involving large-scale
simulations, the EHTC have obtained artificial ring images. Finally, we
explain in Section 5.8 why their objective survey has produced artifacts. They
determined their optimal imaging parameters through large-scale simulations.
However, they did not take into account the sampling bias that tends to
produce the $\sim 40~{}\mu\rm as$ structure. The EHTC focused only on the
reproducibility of the input image models and not on the simultaneous
reproducibility of the input error models. It cannot be ruled out that their
optimal parameters may have had the property of creating the EHTC’s $\sim
40~{}\mu\rm as$ ring by not performing proper calibration and imaging, but
rather by enhancing the sampling bias effect. The facts shown in this section
are strong evidence that the EHTC $\sim 40~{}\mu\rm as$ ring image is a
forcibly created artifact. In Section 5.9, we summarize the reasons why the
EHTC obtained the artifact image unintentionally.

###  5.1 u-v coverage of the EHT array for M 87

We here investigate the u-v sampling of the EHT array for M 87 observations.
The u-v coverage itself is shown in the EHTC paper I (Event Horizon Telescope
collaboration , 2019a). It shows a good u-v coverage as an interferometer of
practically 5 stations and 10 baselines. We looked at the number of data
samples from another point of view. Figure 18 shows the distribution of
spatial Fourier components (fringe spacings) sampled by EHT for M 87 during
the four observational days. The number of sampled data is plotted against the
fringe spacings in $\mu\rm as$ unit. We can see that there are no sample for
ranges $d=26-28~{}\mu\rm as$, $d=44-46~{}\mu\rm as$, and $d=95-100~{}\mu\rm
as$ 111111 Fringe spacings larger than $100~{}\mu\rm as$ are omitted in the
histogram. We are interested in the samplings contributing to very high
spatial resolutions less than $100~{}\mu\rm as$. . The number of sampled data
for the size of the EHT ring ($d=42\pm~{}3~{}\mu\rm as$) is quite small, and
for spacing between $d=44-46~{}\mu\rm as$, there are no sampled data.

The few numbers of sampling around $42~{}\mu\rm as$ fringe spacings should
affect the imaging performance. In the following subsections, we investigate
how this lack of spatial Fourier components can affect the imaging result.

Figure 18: Distribution of the sampling data (all data of the four days from
all baselines). The x-axis shows the fringe spacings of sampled visibility
data in $\mu\rm as$ unit. The y-axis shows the number of sampled data. Here,
samples larger than the fringe spacing of $100~{}\mu\rm as$ are omitted. The
red line segment indicates the range of the diameter of the ring measured by
the EHTC ($d=42\pm 3~{}\mu\rm as$).

###  5.2 Substructures in the dirty beam

The EHTC show no description of the dirty beam structure. We, then, examine
the dirty beam calculated from the u-v coverage. Dirty beam is the term used
in the field of radio interferometer and its meaning is the same as that of
PSF (Point Spread Function) in optics. In other words, it is the diffraction
image of a single point when the data calibration is perfect. If we can obtain
all spatial Fourier components, the dirty beam becomes a two-dimensional
$\delta$-function.

In practice, we can obtain only a limited sample of spatial Fourier
components, and thus the dirty beam has a complex shape. Figure 19 shows the
dirty beam of the EHT array on the first day observation of M 87. The FWHM of
the main beam is approximately 20$~{}\mu\rm as$. We can see a point-symmetric
pattern around the main beam. This pattern includes peaks lower than the main
beam. Such peaks are often called “sidelobes” in radio astronomy. We can see
that the distances between the main peak and the first peaks of sidelobes are
about 45$~{}\mu\rm as$. 121212 Further, the first sidelobe levels reach more
than 70 % of the height of the main beam. The sidelobe level is still
extremely high even when changing u-v weights. Natural and uniform weighting
cases, both show that the first sidelobe levels reach more than 60 % of the
height of the main beam (see Appendix B).  The separation between them
corresponds to the radial range for which the spatial Fourier components are
missing, and is very close to the diameter of the EHTC ring
($42~{}\pm~{}3~{}\mu\rm as$). Thus, it is important to clarify whether or not
this PSF structure has affected the ring image or not. In addition, Appendix B
shows other PSF shapes by different weightings of u-v points. Even in these
PSF shapes, the separations between the main beam and adjacent sidelobes do
not change much. They also show substructures with $\sim 40~{}\mu\rm as$
spacings.

Figure 19: Point spread function (dirty beam) of EHT on the first day
observation of M 87. The contour levels are at every $10~{}\%$ points of the
peak from $-100$ to $100~{}\%$. Positive levels are shown by white lines, and
negative levels by black dotted lines. The white dotted lines are for zero
levels. The grayscale ranges from the minimum to the maximum brightness of the
dirty beam image. The first sidelobe levels reach more than 70 % of the height
of the main beam. We put two red arrows with a length of $45~{}\mu\rm as$
between the main beam and the first sidelobes. For the dirty beam image, we
set the parameter $ROBUST=0$ in IMAGR (its default setting).

###  5.3 The relation between the dirty map convolved by the PSF shape and the
ring structure

Here, we show what happens if we are not very careful in using the dirty map
when applying the hybrid mapping process. A dirty map is an image created by
simply performing an inverse Fourier transform on the obtained spatial Fourier
components. Therefore, it is influenced by the data sampling bias, that is,
the structure of PSF is convoluted into the dirty map. Furthermore, if the
data calibration is insufficient, it will be reflected in the dirty map, and
the obtained structure in such a dirty map can be far from the actual image.
Therefore, it is dangerous to perform self-calibration using the dirty map as
the image model.

It is certain that in the case of multi-element radio interferometers like
ALMA, or VLA, the dirty beams have sharp main beams and very low sidelobes.
Only in such cases, it is not so dangerous to estimate the true image by the
dirty map. While, in the case of VLBI observations, the dirty beam is
comparatively dirty, usually, we do not estimate the true image from them and
do not use them as the model image for self-calibration.

We, however, try that here and show what happens. The left-side panels of
Figure 20 show the dirty maps from the data of the first day observations by
EHT. To obtain these maps, we applied the phase-only calibration by the self-
calibration technique using a point source as the image model. We can see a
ring-like structure at the center, and many images which look like the ghosts
of this central ring-like structure.

This is not a blurred intrinsic image of M 87, but a strong reflection of the
substructure in the dirty beam (PSF) of the EHT array. Figure 21 shows the
dirty map and the dirty beam. Not surprisingly, they agree rather well, and
that means the central ring-like structure we showed in Figure 21 is just the
reflection of the shape of the dirty beam and not a physical reality. If we
were to believe there should be a ring, it would be very natural to select the
partial image from what looks like a ring in the dirty map. If we do so, what
will happen? To answer this question, we tried the calibration of phase and
amplitude using this ring-like structure at the center as the image model. We
calculated the amount of calibration of the amplitude and phase by the self-
calibration method. After the calibration is applied, we made an image using
the CLEAN algorithm assuming that the source is single and compact. Here, the
CLEAN subtraction area is limited by a circle with $30~{}\mu\rm as$ radii
centered at ($+2~{}\mu\rm as$, $+22~{}\mu\rm as$) from the map center, which
is the BOX setting as used in the EHTC-DIFMAP pipeline (Section 5.5).

The obtained ring image is shown in the right panel of Figure 20. The size of
the ring is close to that of the EHTC ring. What we also would like to
emphasize here is that in order to create a ring structure, we need a narrow
BOX setup. Without a narrow BOX, a ring structure cannot be created. If we
change the position or size of the BOX, the ring deforms. When we use BOX
offset setting of $22~{}\mu\rm as$ from the center, we get a ring very similar
to the EHTC ring. In other words, the shape strongly depends on the location
of the imaging region. As we will show in Section 5.4, the EHTC BOX setting
limits the FOV so narrowly that it can produce the EHTC $\sim 40~{}\mu\rm as$
ring shape even from simulated data that does not contain the ring shape.

Close inspection reveals that the ring-like structure of the dirty map is at
an offset position from the center. Since the structure of the PSF always
shows center symmetry, we can suppose that the offset ring-like structure is
not due to the PSF, but really exists at the offset position. However, the
shape of Figure 3 shows that this is not the case. Figure 3 shows the
structure of the dirty beam shape after deconvolution from only the brightest
point at the center of the dirty map. There is no ring-like structure here. We
can see that the ring-like structure of the dirty map (Figure 20) is created
by convolution of the dirty beam to the brightest point in the center. The
ring-like structure is offset because the true source image inherent in the
data does indeed exhibit non-center symmetry, but it is not an offset ring,
but a core-knot structure as shown in Figure 7.

Figure 20:  Ring image obtained using the dirty map. The left panels show the
dirty map of the first day data from the EHT observation. The right panels
show the image resulting from self-calibration of the central part of the
dirty map as an image model. The upper panels show a larger area of
$500~{}\mu\rm as$ width, and the lower panels show the enlargements of the
central part of the images.

Figure 21: Comparison of the dirty beam (PSF) and the dirty map. The left
panel shows the dirty beam (PSF) and the center panel shows the dirty map. The
right panel shows a case where the two images were adjusted to fit well
together and overlap. The yellow contours show the dirty beam, and the
grayscale show the dirty map. The dirty beam (PSF) here is the same as shown
in Figure 19, but the number of contours has been reduced. The dirty map here
is the same as in the left panels of Figure 20, but the grayscale shows the
intensity inversion image.

###  5.4 Ring from the simulated data of different structures

In this section, we demonstrate that, with the u-v coverage of EHT for M 87,
one could “observe” a ring even if the physical sources have different
structures. As the physical source structure, we consider a single point with
flux density of 1 Jy at the center. We made the simulation visibility data by
applying the Fourier transformation to the single point image (We used UVMOD,
a task in AIPS.). The u-v coverage is exactly the same as that of EHT for M 87
observations. As for noise, we consider two cases, one with relatively large
noise (case 1) and the other with no noise (case 2). For case 1, we added
thermal noise. The noise level is proportional to the weight of each data
noted in original FITS public data. The signal-to-noise ratio (S/N) is 0.01 on
average. We then perform experiments of calibration and imaging. For
calibration, we obtain solutions from self-calibration with incorrect image
models that are different from the true structures of the source, then apply
the solutions to the data. We inspect what kinds of images appear from CLEAN
imaging. For the self-calibration, we assume models of two incorrect images.
One is the EHTC ring image (model A) and the other is a pair of two points
separated by $45~{}\mu\rm as$ (model B). Model B is a pair of points of 0.5 Jy
located at ($0~{}\mu\rm as$, $0~{}\mu\rm as$) and ($0~{}\mu\rm as$,
$+45~{}\mu\rm as$) respectively. The locations of these two points roughly
correspond to the positions of the main peak and the first sidelobe peak in
dirty beam. We get calibration solutions of amplitude and phase from the self-
calibrations (We used CALIB, a task in AIPS.).

By using IMAGR, a task in AIPS, we performed the CLEAN imagings. We limit the
CLEAN subtraction area by a narrow BOX setting; a circle with $30~{}\mu\rm as$
radii centered at ($+2~{}\mu\rm as$, $+22~{}\mu\rm as$) from the map center,
which is a mimic BOX setting as used in the EHTC-DIFMAP pipeline (Section
5.5). The left panel in Figure 22 shows the ring image obtained from the large
noise data (case 1). The obtained image from CLEAN is identical to the model
image A used in self-calibration. When the S/N is very low, the CLEAN image
after self-calibration can be identical to the model image used. Therefore,
the result of case 1 does not tell much.

The results of case 2 are surprising. The middle panel in Figure 22 shows the
ring image obtained from no noise data. The obtained image from CLEAN is very
close to the model image A used in self-calibration. Even when there is no
noise, if we start with the assumption that there is a ring in the self-
calibration image model, with the u-v coverage of EHT, we obtain a ring
similar to that obtained by the EHTC.

The right panel in Figure 22 shows the result of using model image B for self-
calibration. Though we used the data of a single point with no noise, we
obtained a two-point image, which is very close to model B used in self-
calibration. In addition, the appeared two points show small shifts from the
positions in model B. The center point shifted towards the east, while the
upper point shifted towards the west. These shifts seem to be the influence of
the structure of the dirty beam. The shift of the center point is along the
ridge elongated from the main beam in the dirty beam, while the shift of the
upper point is towards the peak position of the first sidelobe.

The results of these experiments show that the reproduced images are very
close to the image model used in the self-calibration. Such a result does not
occur when there is sufficient u-v coverage, as in the case of VLA and ALMA.
Unfortunately, the u-v coverage of EHT is not sufficient, and it has a special
bias that makes it prone to producing shapes (including rings) with a size of
$\sim 40~{}\mu\rm as$. We have shown that the shape of the PSF (essentially
the effect of the sampling bias that makes it easy to create $\sim 40~{}\mu\rm
as$ structures) has the power to create $\sim 40~{}\mu\rm as$ ring structures
even from data with only one central point structure (centrosymmetry).
However, the most powerful factor is not data correction by self-calibration
with wrong model images. Here and in Section 5.3, we showed that the very
narrow FOV setting of the BOX has great power to create a $\sim 40~{}\mu\rm
as$ ring structure. In Section 5.5, we will discuss the setting of BOX in the
EHT-DIFMAP pipeline.

Figure 22:  Resultant images from the simulated data sets. Case 1-A (left
panel) shows the ring shape created from nearly noise data set, after applying
the solution by self-calibration using the EHTC ring as the image model. Case
2-A (middle panel) shows the ring shape created from a single point data set
with infinite S/R (no noise), after applying the solution by self-calibration
using the EHTC ring as the image model. Case 2-B (right panel) is a two-point
image created by applying the solution by self-calibration with two points as
image models to a single point data (no noise data) with infinite S/N. The two
red crosses indicate the positions of the points in the model image used in
self-calibration.

###  5.5 What the EHTC really did in their DIFMAP imaging process

In this section, we investigate the data processing pipeline that the EHTC
used for imaging the EHTC ring with DIFMAP
131313https://github.com/eventhorizontelescope/2019-D01-02. Among the three
methods the EHTC used for the imaging, DIFMAP is the closest to the usual
procedure 141414difmap/EHT_Difmap in the above web page. Other two are rather
new, and difficult to study here. Since all three methods gave essentially the
same image, we believe it is sufficient to analyze one of the three methods to
find out why the ring structure was formed. The EHTC-DIFMAP imaging team used
the hybrid mapping technique to calibrate the data and obtained the image. The
hybrid mapping method is the standard method of VLBI calibration and imaging.

Let us first summarize the standard procedure of VLBI data calibration and
imaging. The radio interferometer samples the spatial Fourier components of
the brightness distribution of the observed source (often called visibility).
Theoretically, the brightness distribution of the observed source can be
obtained by collecting the samples and performing the inverse Fourier
transform. However, there are actually two problems as follows. (a) The
sampled visibility data contain errors, so they are not the correct spatial
Fourier components. Therefore, it is necessary to calibrate them. Self-
calibration is a method of obtaining calibration solutions by using an assumed
image. If the assumed image is not correct, the correct calibration solution
cannot be obtained. (b) The number of observed samples is limited. The inverse
Fourier transform alone does not produce the correct image. The PSF does not
become a point. Therefore, the PSF shape must be deconvolved. For this
purpose, image processing is performed. As a method to obtain correct
calibration solutions and to attain clear imaging results, hybrid mapping,
which alternates between the above two tasks, is usually used in VLBI imaging.
We use self-calibration for calculating the calibration solution using a
tentative image model, and CLEAN for performing deconvolution of the scattered
PSF shape.

Hybrid mapping is the following algorithm. (a) Assume an image model for self-
calibration. For the first one, a 1-point model is usually used. (b) Calculate
tentative calibration solutions from self-calibration using the image model.
(c) Calibrate visibility data using the tentative calibration solutions. (d)
Obtain the next tentative image using CLEAN from the calibrated visibility
data. CLEAN image is composed of point sources (CLEAN components). (e) Make
the next image model for self-calibration by picking up reliable CLEAN
components from the image. (f) Go back to (b) and repeat the iteration from
(b) to (e) until a satisfactory image is obtained.

The visibility (spatial Fourier component) is a complex quantity and so it has
amplitude and phase. It is safe first to repeat self-calibrations only for
phase solutions until a nearly satisfactory image is obtained and to perform
self-calibration for amplitude and phase by using that image. This is because
self-calibration for amplitude tends to give a solution which is too close to
the model image used in self-calibration (Cornwell & Fomalont, 1999).

However, the repetition of amplitude self-calibration is often performed under
the careful check of the practical quality of the data, and then, in many
cases, good calibration solutions can be obtained.

In addition, the BOX technique is an auxiliary means used for imaging with
CLEAN. (It is essentially unrelated to the hybrid mapping method.) We can
limit the area of CLEAN subtraction intentionally by the BOX setting. The
technique may give us a good image, despite an incomplete calibration. As
already mentioned, we used the BOX technique in our analysis. Also the EHTC-
DIFMAP team did.

Now we investigate the EHTC-DIFMAP procedure. The EHTC-DIFMAP imaging team
performed the self-calibration only for phase solutions with a single point
source model, following the general procedure of the hybrid mapping method.
However, after the first phase self-calibration, they used the BOX technique
with a very narrow BOX151515BOXCircMask_r30_x-0.002_y0.022.win in the web in
the first imaging trial. The CLEAN subtraction area was restricted to within
the circle of $60~{}\mu\rm as$ diameter specified by the BOX. This means that
from the beginning of their data analysis, the EHTC-DIFMAP team assumed that
the image is a very compact single one, and excluded other possibilities.

The BOX is roughly a circle of diameter $60~{}\mu\rm as$ composed of 30 small
rectangles. By comparing the BOX shape and the dirty beam we found that the
BOX covers the main beam and the first sidelobe, but leaves out the second and
other sidelobes. The BOX is not located at the phase center but offset by
$+22~{}\mu\rm as$ in the y-direction ($\delta$ direction). This offset of
$22~{}\mu\rm as$ coincides with the radius of the EHTC ring. Figure 23 shows
the EHTC BOX position on the dirty beam (PSF) aligned by their phase centers.
The area of the EHTC BOX covers (1) the main beam peak, (2) the ridge
extending to the left (east) from the main beam peak, (3) a part of the first
sidelobe located north of the main beam, and (4) an area of negative strength
near the center of the box area. The structure of the dirty beam within the
EHTC BOX is close to the shape of the EHTC $\sim 40~{}\mu\rm as$ ring.

The PSF structure within the BOX explains not only the diameter of the EHTC
ring, which is $\sim 40~{}\mu\rm as$, but also the asymmetric structure of the
EHTC ring. The EHTC ring has an asymmetric structure with a bright south side.
The brighter south side corresponds to the main beam (the brightest in the
box), while the darker north side of the ring corresponds to the first
sidelobe in the north (the less bright peak in the box).

If such a narrow BOX with the offset is used from the beginning to the end of
the hybrid mapping process, the effect of the dirty beam can be enhanced as we
showed in Section 5.3. It is quite clear that the EHTC $\sim 40~{}\mu\rm as$
ring is the result of such enhancement of $\sim 40~{}\mu\rm as$ substructures
in PSF.

Figure 23: The size and position of the BOX used in their DIFMAP pipeline
(blue shaded area). We overlaid the BOX on the dirty beam (PSF) which is
already shown in Figure 19. We align the two figures at their phase centers.

We actually ran the EHTC-DIFMAP pipeline to investigate its behavior and
performance. The left panel of Figure 24 shows the resultant ring image from
running the EHTC-DIFMAP pipeline with the default parameter settings. On the
other hand, the right panel of Figure 24 shows the image obtained by removing
the BOX setting (Figure 23) from the EHTC-DIFMAP pipeline. The ring in the BOX
setting region has been destroyed and the brightness distribution has been
moved to outside the BOX setting region. The new brightness distribution shows
a core-knot structure in the center, similar to the results of our analysis.
In addition, several emission peaks appear in the $PA=45^{\circ}$ and
$PA=225^{\circ}$ directions from the center. These are probably sidelobes, but
it is very interesting that one emission peak in the $PA=225^{\circ}$
direction corresponds to the feature W we found in our analysis. This result
implies that the very narrow BOX setting of the EHTC-DIFMAP pipeline is the
main factor that creates the EHTC ring image.

We also created simulated data and applied the EHTC-DIFMAP pipeline to it to
investigate what kind of images are obtained. The purpose of this is to check
if the EHTC-DIFMAP pipeline always calibrates the data correctly and
reproduces the true picture of the data. We created simulated data with the
task UVMOD in AIPS and acquired images with both the task IMAGR in AIPS and
the EHTC-DIFMAP pipeline for comparison. Figure 25 shows examples of the
simulation results. Three cases are shown. (1) a core-knot model aligned in
about $PA=-38.7^{\circ}$ direction (left panels), (2) a two-point model
aligned North-South direction (center panels), and (3) a $40~{}\mu\rm as$
diameter ring, but the ring width is $2~{}\mu\rm as$, different from that of
the EHTC ring (right panels).

The top panels show images obtained from data simulated using the AIPS IMAGR
task with the same box settings as the EHTC-DIFMAP pipeline. The IMAGR
produced the expected image.

The bottom panels of Figure 25 show the results of the EHTC-DIFMAP pipeline.
The original images of the simulated data could not be reproduced. In the case
of the core-knot model (lower left panel), the knot component is lost. Also,
in the case of the two-point model (bottom center), the weak north point has
disappeared. Even more surprisingly, in the case of the $40~{}\mu\rm as$
diameter ring model (bottom right panel), the image quality is degraded and
the ring structure is obscured.

Since these images are compact and fit within the BOX setting of the EHTC-
DIFMAP pipeline, this phenomenon is not due to a narrow field of view caused
by the BOX setting. This is probably because the performance of the hybrid
mapping process of the EHTC-DIFMAP pipeline strongly depends on the image
structure and noise structure of the input data.

Note that our simulation this time is not only that shown in Figure 25. The
summary of the simulation is as follows.

  1. 1.

A single point source model of 1 Jy with no noise. The image was reproduced
from both IMAGR in AIPS and the EHTC-DIFMAP pipeline.

  2. 2.

Complete noise model. No specific image was detected from the IMAGR in AIPS,
but a single point was obtained from the EHTC-DIFMAP pipeline. This is
probably due to the fact that the first self-calibration was performed using
the image model of a single point source. This is a common phenomenon that
occurs when self-calibration is applied to data sets with very low S/N.

  3. 3.

Core knot model. Two points model consisting of a point of 1 Jy at the center
($0~{}\mu\rm as$, $0~{}\mu\rm as$) and a point of 0.25 Jy at ($-25~{}\mu\rm
as$, $+20~{}\mu\rm as$). The distance between them is about $32~{}\mu\rm as$ s
and they are located along a line in the direction $PA=-38.7^{\circ}$. 12
simulation data with noise ranging from zero to 640 Jy/weight were generated.
IMAGR in AIPS detected the core-knot structure as expected. In the EHTC-DIFMAP
pipeline, the knot component disappeared in 11 of the 12 cases.

  4. 4.

Ring images with diameters around $40~{}\mu\rm as$. The ring width is
$2~{}\mu\rm as$, and the ring diameters are 30, 35, 40, and 45 $\mu\rm as$.
The flux density of the image is 1 Jy. No noise was added. Using IMAGR in
AIPS, the hole in the center of the ring is obscured when the ring diameter is
smaller than $30~{}\mu\rm as$. When the ring diameter is larger, the ring can
be recognized. On the other hand, using the EHTC-DIFMAP pipeline, the
structure of the ring became ambiguous in all images, like the example shown
in Figure 25.

  5. 5.

Two-point model (shift in the north-south direction). Place a point of 1Jy at
the center ($0~{}\mu\rm as$, $0~{}\mu\rm as$) and a point of 0.5 Jy north of
it. There are 11 intervals: 0, 5, 10, 15, 20, 25, 30, 35, 40, 45, and 50
$~{}\mu\rm as$. Using IMAGR in AIPS, two points cannot be separated and
resolved when the spacing is very narrow. At a separation of 10$~{}\mu\rm as$,
the image is elongated in the north-south direction. If the separation is
larger than 25$~{}\mu\rm as$, the two points are reproduced separately. Using
the EHTC-DIFMAP pipeline, when the separation is larger than 45$~{}\mu\rm as$,
the two points are reproduced correctly, but otherwise the north point is not
reproduced in the correct position.

  6. 6.

Two-point model (east-west shift). A point of 1Jy is placed at the center
($0~{}\mu\rm as$, $0~{}\mu\rm as$) and a point 0.5-Jy is placed at
$\delta=42~{}\mu\rm as$. The R. A. position of the second point is shifted
every $5~{}\mu\rm as$ from -20$~{}\mu\rm as$ to 20$~{}\mu\rm as$ to create 9
simulation data. The positions of these two points are reproduced from IMAGR
in AIPS. the EHTC-DIFMAP pipeline reproduces these two points in four cases.
In the other four cases, the position of the north point deviated from the
correct position by more than 10 $\mu\rm as$.

Thus, in most cases, the EHTC-DIFMAP pipeline did not reproduce the intrinsic
image of the simulation data. Figure 10 of Event Horizon Telescope
collaboration  (2019d) shows that their procedure successfully reproduces
images from simulated data (ring, crescent, disk, and double source), but
their results are inconsistent with ours (at least for the EHT DIFMAP case).
In our simulations, noise is either not added at all, or if added, it is
thermal noise. IMAGR in AIPS almost reproduces the input model images, while
the EHTC-DIFMAP pipeline does not. The difference between the two methods is
the hybrid mapping process. The EHTC-DIFMAP pipeline lacks the performance of
the general calibration of the data described in Section 5.8.3.

Figure 24:  Resultant images from the EHTC-DIFMAP pipeline. The upper panels
show the entire field of view with the default setting of the EHTC-DIFMAP
pipeline (1 mas square). The lower panels show the enlargement of the central
part of the upper images. The left panels show the result of running the EHTC-
DIFMAP pipeline with the default parameter settings. The light blue circle
shows the location and size of the BOX. The ring-shaped image appears in the
BOX area. The right panels show the resulting image when the EHTC-DIFMAP
pipeline is run without the BOX setting. In the enlarged image (bottom right),
we can see the emission peaks corresponding to the three components we found:
core (C), knots (K), and west component (W). Here, we used the data named
SR1_M87_2017_095_hi_hops_netcal_StokesI.uvfits.  Figure 25:  Resulting images
of simulation data. The upper panels show the imaging results when using IMAGR
in AIPS. The lower panels show the imaging results when using the EHTC-DIFMAP
pipeline with default parameter settings. The same BOX setting is used for
IMAGR as well as the EHTC-DIFMAP pipeline. The light blue circles show the
position and size of the BOX setting. The three results are presented. A core
knot model (left panel), a two-point model (center panel), and a $\sim
40~{}\mu\rm as$ ring model (right panel). The red crosses on the left and in
the center indicate the positions of the emission points placed during the
simulation data preparation.

###  5.6 The amounts of calibrations performed in the EHTC imaging process

The EHTC papers give the detailed description of the data calibrations at the
pre-stage process, but not much about the calibrations performed during the
imaging process (through the self-calibration in the hybrid mapping process of
the EHTC-DIFMAP imaging team case). This is an insufficient description of
data calibrations because it is rare that only the pre-calibrations are
sufficient for obtaining VLBI fine images. We, therefore, estimate and show
the amounts of calibrations performed by the EHTC during their imaging
process. We attempted to reconstruct them in the following procedure. First,
following the EHTC open procedure, we reproduced the EHTC ring image of the
first observing day (the left panel in Figure 26). Then, using the CLEAN
components of the ring image as the model image, we performed self-calibration
by the task CALIB in AIPS and got solutions for both phase and amplitude. The
parameters of CALIB are shown in Table 6. In Figures 27 and 28, we show the
total amount of calibrations both of phase and amplitude in the case of the
EHTC ring image model. Note that we performed CLEAN imaging to verify if the
solutions from the self-calibrations are consistent with the original the EHTC
ring image. First, we flagged out data points where the amplitude solutions
were more than 4 by using the task SNCOR in AIPS. Here we followed the
standard VLBI teaching, which states that ”discarding bad data will make a
better image than keeping them”. Then, we applied the solutions to the
selected data and obtained an image using the task IMAGR in AIPS for CLEAN.
The right panel of Figure 26 shows the resultant image whose quality is
similar to that of the original EHTC ring. Thus, “our” solutions of self-
calibrations successfully reproduced the EHTC ring image.

The phase and amplitude solutions for the EHTC ring image are very similar to,
or worse than our results in Figures 5 and 6. Therefore, if such large
amplitudes and their rapid variations found in the self-calibration solutions
are negative signs against the resultant image quality, both the results of
our final images and the EHTC ring images should be rejected. This implies
that the ”calibrated” data released by the EHTC are not of high quality (as is
often the case with VLBI archival data).

SOLTYPE | ’L1’
---|---
SOLMODE | ’A&P’ (both phase and amplitude)
REFANT | 1 (ALMA)
SOLINT (solution interval) | 0.15 (min)
APARM(1) | 1
APARM(7) (S/N cut off) | 3
Table 6: Parameters of CALIB for the amplitude and phase self-calibration.

Figure 26: Left panel shows the EHTC ring image of the first day observations.
We obtained this image by using their open procedure. The right panel shows
our reconstruction image by applying the self-calibration solutions shown in
Figures 27 and 28. The same BOX setting as that used in the EHTC-DIFMAP
pipeline was used. Also the same restoring beam was applied ($23.1\times
17.0~{}\mu\rm as$ with $PA=44.4^{\circ}$).  Figure 27: Phase solutions
obtained from self-calibration using the EHTC ring image. The red points show
the solutions for IF 1 data, the blue ones show those for IF 2 data.  Figure
28: Amplitude solutions obtained from self-calibration using the EHTC ring
image. The red points show the solutions for IF 1 data, the blue ones show
those for IF 2 data.

###  5.7 Sensitivity of the $\sim 40~{}\mu\rm as$ ring to BOX size

In Section 5.6, we reproduced the ring structure obtained by the EHTC, by
using the very narrow box used by the EHTC. If the ring image is the
definitely correct image, it should only weakly depend on the BOX size. In
fact, we studied the effect of changing the BOX in Section 4.3.2, and found
that the main structure of our final image (features C & K) does not
disappear. In this section, we investigate how sensitive the ring structure
obtained by the EHTC to the BOX method they used.

We calibrated the data by applying the calibration solutions obtained from the
self-calibration using the EHTC ring as the image model, which are shown in
Figures 27 and 28. We performed CLEANs using BOXes of circles with diameters
of (a) $60~{}\mu\rm as$, (b) $80~{}\mu\rm as$, (c) $100~{}\mu\rm as$, (d)
$120~{}\mu\rm as$, (e) $240~{}\mu\rm as$, and (f) $450~{}\mu\rm as$. Their
centers are located at the same position as that of the EHTC-DIFMAP case.
Other parameters of the CLEANs are the same as those used for the right image
in Figure 26.

The results are shown in Figures 29 and 30. Figure 29 shows views of the
entire imaging area of $\rm 2~{}mas$ square, and Figure 30 shows enlarged
views of the central $256~{}\mu\rm as$ square. The BOXes used are indicated by
blue circles. The ring structure in panel (a) ($D=60~{}\mu\rm as$) is the same
as that in the right panel of Figure 26. Here, we can see the ring structure
similar to that obtained by the EHTC. The ring extends beyond the BOX area.
This is because the obtained CLEAN components are near the boundary of the
BOX, and a $20~{}\mu\rm as$ restoring beam is convolved to form the CLEAN map.
In the cases of (b) $D=80~{}\mu\rm as$ and (c) $D=100~{}\mu\rm as$, the ring
is still recognizable. However, we can see CLEAN components not on the ring
but near the boundary of the BOX when the BOX becomes larger. In the case of
(d) $D=120~{}\mu\rm as$, there are several CLEAN components almost on the
boundary of the BOX, though the ring structure is still recognizable. In the
cases of (e) $D=240~{}\mu\rm as$ and (f) $D=450~{}\mu\rm as$, there is no
ring. Instead, one elongated bright spot appears. We also tried larger BOX
cases, $D=900~{}\mu\rm as$, and $D=1300~{}\mu\rm as$, and the resulted image
is similar to the case of $D=450~{}\mu\rm as$. They show a bright spot at the
map center.

If the field of view (FOV) is smaller than the case (d), a ring image will
appear, and if FOV is larger than that, the ring image will be destroyed. In
other words, the boundary FOV is around $120~{}\mu\rm as$. It is a queer
coincidence that the EHTC imaging teams set the FOV to be $128~{}\mu\rm as$
(Event Horizon Telescope collaboration , 2019d), just around the boundary FOV.
(It is $60~{}\mu\rm as$ in the case of the EHTC-DIFMAP pipeline as already
mentioned) 161616Figure 6 in Event Horizon Telescope collaboration  (2019d)
shows similar test results to ours, but they only show the results with BOX
sizes narrower than $100~{}\mu\rm as$ in diameter..

Thus, we can conclude that the EHTC ring appears only when a very narrow BOX
is applied.

Figure 29: Stability of the EHTC ring structure against the BOX sizes: The
whole $2~{}mas$ square images of the CLEAN results by IMAGR (AIPS). Panels (a)
– (f) show the resultant images in cases of expanding the diameter of the BOX
area with $D=60,80,100,120,240$, and $450~{}\mu\rm as$ respectively. The blue
circle shows the respective BOX area. The center positions of the circles are
($-2~{}\mu\rm as$, $+22~{}\mu\rm as$) as followed the BOX the EHTC-DIFMAP team
used.  Figure 30: Stability of the EHTC ring structure against the BOX sizes:
The enlarged views of the central $256~{}\mu\rm as$ square from the resultant
CLEAN images by IMAGR (AIPS). Panels (a) – (f) show the resultant images in
cases of expanding the diameter of the BOX area with $D=60,80,100,120,240$,
and $450~{}\mu\rm as$ respectively. The blue circle shows the respective BOX
area. The center positions of the circles are ($-2~{}\mu\rm as$, $+22~{}\mu\rm
as$) as followed the BOX the EHTC-DIFMAP team used.

###  5.8 Problems in the EHTC analysis

Here we explain why the EHTC created the image of the ring. The EHTC described
the details of their imaging process in Event Horizon Telescope collaboration
(2019d), in which we found some of the reasons why they created the artifact.
The EHTC conducted various surveys, but their methods were not objective and
biased towards their desires from the very beginning of their analysis. They
also failed to perform the basic data checking that VLBI experts always do.
These points are noted below.

####  5.8.1 Blind test by the EHTC

According to Event Horizon Telescope collaboration  (2019d), ”in first stage,
four teams, each blind to the others’ work, produced images of M 87. This
stage allowed us to avoid shared human bias and to assess common features
among independent reconstructions.” They added, ”All four images show an
asymmetric ring structure. For both RML teams and both CLEAN teams, the ring
has a diameter of approximately $40~{}\mu\rm as$, with brighter emission in
the south.” The EHTC first conducted a blind test and obtained consistent
images of each other.

But their isolated imaging processes were not really blind tests. The angular
size of a black hole shadow can be easily calculated from the distance and
mass of the black hole. As every black hole shadow researcher knows, if the
mass of the SMBH in M 87 is $\sim 6\times 10^{9}M_{\odot}$, the expected
shadow size is about $40~{}\mu\rm as$ in diameter. Based on that calculation,
everyone tries to find a ring or arc-shaped image with a diameter of
$40~{}\mu\rm as$. The members of the EHTC imaging team are not exception.

As shown in the previous Section 5.1, the EHT public data has a sampling bias
in that it lacks $\sim 40~{}\mu\rm as$ spatial Fourier component. This bias
tends to create $\sim 40~{}\mu\rm as$ scale structures that are not present in
the original image. It is due to this sampling bias effect that the PFS has a
$\sim 40~{}\mu\rm as$ scale structure (Section 5.2).

Not surprisingly, all the EHTC imaging teams, trying to find the black hole
shadow with a size of $\sim 40~{}\mu\rm as$, were able to find the desired
illusion in the sampling bias. The blind imaging test should be conducted by
researchers with no prior knowledge of the expected image of the SMBH in M 87.

####  5.8.2 Attention to sampling bias

It is well known that sampling bias in data can seriously affect data
analysis. For sampling bias, two things should have been done.

First, PSF (dirty beam) structure should have been checked. In radio
interferometer data analyses, checking the structure of the dirty beam usually
provides insight into the effects of insufficient u-v coverage; in a sparse
array configuration such as the EHT array, it is more important to check the
shape of the dirty beam and utilize it as consideration for false imaging.
Event Horizon Telescope collaboration  (2019d) describes the size and shape of
the main beam of the dirty beam and the corresponding CLEAN beam, but we do
not find any discussion of the overall dirty beam structure in the EHTC
papers. As already shown, the separations between the main beam and the first
sidelobes of the dirty beam structure are $\sim 40~{}\mu\rm as$, which
coincidentally is the same as the expected size of the black hole shadow in M
87. An old-time VLBI expert would have noticed the spacing.

Second, performance of the new imaging method with respect to sampling bias
needs to be verified. The CLEAN algorithm, the well-known imaging method in
radio interferometry, was originally designed to obtain correct images by
deconvolving false structures appearing in dirty beams (the origin of which is
the sampling bias). However, in actual use, it is not easy to completely
eliminate this effect; most of the relevant researchers know the CLEAN
method’s performance against sampling bias from its long history of use, and
pay attention to its residual structure. The EHTC used two new imaging methods
that are unfamiliar to most radio astronomers, and judging from the case of
the CLEAN algorithm, we infer that the performance of the new methods against
sampling data bias is not perfect. Its performance needs to be demonstrated.

####  5.8.3 The EHTC simulations

The EHTC conducted simulations to find the optimal parameters for imaging.
According to Event Horizon Telescope collaboration  (2019d), ”In the second
stage,” the EHTC ”reconstructed synthetic data from a large survey of imaging
parameters and then compared the results with the corresponding ground truth
images. This stage allowed us to select parameters objectively to use when
reconstructing images of M 87.” However, there are two major problems with
this simulation.

First, it seems that the idea of what to be obtained from the simulation was
not well considered: the EHTC created synthetic data from the model images and
searched for optimal parameters to reproduce the input model images. But what