First M87 Event Horizon Telescope Results. VII.
Polarization of the Ring
The Event Horizon Telescope Collaboration
(
See the end matter for the full list of authors.
)
Abstract
In 2017 April, the Event Horizon Telescope
(
EHT
)
observed the near-horizon region around the supermassive
black hole at the core of the M87 galaxy. These 1.3 mm wavelength observations revealed a compact asymmetric
ring-like source morphology. This structure originates from synchrotron emission produced by relativistic plasma
located in the immediate vicinity of the black hole. Here we present the corresponding linear-polarimetric EHT
images of the center of M87. We
fi
nd that only a part of the ring is signi
fi
cantly polarized. The resolved fractional
linear polarization has a maximum located in the southwest part of the ring, where it rises to the level of
∼
15%.
The polarization position angles are arranged in a nearly azimuthal pattern. We perform quantitative measurements
of relevant polarimetric properties of the compact emission and
fi
nd evidence for the temporal evolution of the
polarized source structure over one week of EHT observations. The details of the polarimetric data reduction and
calibration methodology are provided. We carry out the data analysis using multiple independent imaging and
modeling techniques, each of which is validated against a suite of synthetic data sets. The gross polarimetric
structure and its apparent evolution with time are insensitive to the method used to reconstruct the image. These
polarimetric images carry information about the structure of the magnetic
fi
elds responsible for the synchrotron
emission. Their physical interpretation is discussed in an accompanying publication.
Uni
fi
ed Astronomy Thesaurus concepts:
Polarimetry
(
1278
)
;
Radio interferometry
(
1346
)
;
Very long baseline
interferometry
(
1769
)
;
Supermassive black holes
(
1663
)
;
Active galactic nuclei
(
16
)
;
Low-luminosity active
galactic nuclei
(
2033
)
;
Astronomy data modeling
(
1859
)
;
Galaxy accretion disks
(
562
)
; Galaxies: individual: M87
1. Introduction
The Event Horizon Telescope
(
EHT
)
Collaboration has recently
reported the
fi
rst images of the event-horizon-scale structure
around the supermassive black hole in the core of the massive
elliptical galaxy M87, one of its two main targets.
130
The EHT
images of M87
ʼ
s core at 230 GHz
(
1.3 mm wavelength
)
revealed
a ring-like structure whose diameter of 42
μ
as, brightness
temperature, shape, and asymmetry are interpreted as synchrotron
emission from relativistic electrons gyrating around magnetic
fi
eld lines in close vicinity to the event horizon. We have
described the details of the EHT
’
s instrumentation, data
calibration pipelines, data analyses and imaging procedures,
and the theoretical interpretation of these
fi
rst images in a series
of publications
(
Event Horizon Telescope Collaboration et al.
2019a
,
2019b
,
2019c
,
2019d
,
2019e
,
2019f
, hereafter Papers
I
,
II
,
III
,
IV
,
V
,
VI
, respectively
)
.
In this Letter, we present the
fi
rst
polarimetric
analysis of the
2017 EHT observations of M87 and the
fi
rst images of the linearly
polarized radiation surrounding the M87 black hole shadow. These
polarimetric images provide esse
ntial new information about the
structure of magnetic
fi
eld lines near the event horizon of M87
ʼ
s
central supermassive black hole, and they put tight constraints on
the theoretical interpretations of the nature of the ring and of
relativistic jet-launch
ing theories. The theoretical implications of
these images and the constraints
that they place on the magnetic
fi
eld structure and accretion state
of the black hole are discussed in
an accompanying work
(
Event Horizon Telescope Collaboration
et al.
2021
, hereafter Paper
VIII
)
. Readers interested in the details
of the data reduction, methodology, and validation can
fi
nd a
detailed index of this Letter in Section
1.2
. Readers primarily
interested in the results ma
y skip directly to Section
5
and to
subsequent discussion and conclusions in Section
6
.
1.1. Previous Polarimetric Observations of the M87 Jet
The giant elliptical galaxy Messier 87
(
M87, NGC 4486
)
is the
central member of the Virgo cluster of galaxies and hosts a low-
luminosity radio source
(
Virgo A, 3C 274, B1228
+
126
)
.M87is
nearby and bright, and at its center is one of the best-studied active
galactic nuclei
(
AGNs
)
. M87 was the
fi
rst galaxy in which an
extragalactic jet
(
fi
rst described as a
“
narrow ray
”
)
extending from
the nucleus was discovered
(
Curtis
1918
)
. This kiloparsec-scale jet
is visible, with remarkably similar morphology, at all wavelengths
from radio to X-ray. The optical radiation from the jet on kpc
scales was found to be linearly polarized by Baade
(
1956
)
,which
was con
fi
rmed by Hiltner
(
1959
)
, suggesting that the emission
mechanism is synchrotron radiation.
The central engine that powers the jet contains one of the most
massive black holes known, measured from the central stellar
velocity dispersion
(
Gebhardt et al.
2011
;
M
=
(
6.6
±
0.4
)
×
10
9
M
e
)
and directly from the size of the observed emitting
The Astrophysical Journal Letters,
910:L12
(
48pp
)
, 2021 March 20
https:
//
doi.org
/
10.3847
/
2041-8213
/
abe71d
© 2021. The Author
(
s
)
. Published by the American Astronomical Society.
Received 2020 November 23; revised 2021 February 15; accepted 2021 February 16; published 2021 March 24
127
NASA Hubble Fellowship Program, Einstein Fellow.
128
EACOA Fellow.
129
UKRI Stephen Hawking Fellow.
Original content from this work may be used under the terms
of the
Creative Commons Attribution 4.0 licence
. Any further
distribution of this work must maintain attribution to the author
(
s
)
and the title
of the work, journal citation and DOI.
130
The other primary target being the black hole in Sgr A
*
in the center of the
Milky Way.
1
region surrounding the black hole shadow
(
Paper
VI
;
M
=
(
6.5
±
0.7
)
×
10
9
M
e
)
. For this mass, the Schwarzschild radius is
R
s
=
2
GM
/
c
2
=
1.8
×
10
15
cm. At the distance of M87,
-
+
16.8
0.7
0.8
Mpc
(
Blakeslee et al.
2009
; Bird et al.
2010
; Cantiello et al.
2018
,
Paper
VI
)
, the EHT resolution of about 20 micro-arcseconds
(
μ
as
)
translates into a linear scale of 0.0016 pc
=
2.5
R
s
.
The M87 jet has been imaged at subarcsecond resolution in
both total intensity and linear polarization at optical wave-
lengths with the Hubble Space Telescope
(
Thomson et al.
1995
; Capetti et al.
1997
)
, and at radio wavelengths with the
Very Large Array
(
e.g., Owen et al.
1989
)
. Observing the
launching region of the jet closer to the black hole and the
region surrounding the black hole requires milliarcsecond
(
mas
)
resolution or better, and hence very-long-baseline
interferometry
(
VLBI
)
techniques used at the highest frequen-
cies
(
e.g., Boccardi et al.
2017
and references therein
)
.
Milliarcsecond-scale VLBI observations show that the core itself
is unpolarized even at millimeter wavelengths. Zavala & Taylor
(
2002
)
, observing at 8, 12, and 15 GHz, set upper limits on the
fractional polarization of the compact core of
m
<
0.1%. About
20 mas downstream from the core, patchy linear polarization starts
to become visible in the jet at the level of 5%
–
10%, although no
large-scale coherent pattern to the electric-vector position angles
(
EVPAs
)
χ
is apparent. However, at each patch in the downstream
jet, the EVPAs exhibit a linear change with
λ
2
, allowing the
rotation measures
(
RMs
)
to be estimated. These RMs range from
−
4000 rad m
−
2
to 9000 rad m
−
2
(
Zavala & Taylor
2002
)
.The
linear dependence of EVPA on
λ
2
over several radians is
important, as it shows that the Faraday-rotating plasma in the jet
cannot be mixed in with the relativistic emitting particles
(
Burn
1966
)
but must be in a cooler
(
sub-relativistic
)
foreground screen.
On kiloparsec scales, Owen et al.
(
1990
)
found a complex
distribution of RM. Over most of the source the RM is typically
of order 1000 rad m
−
2
, but there are patches where values as
high as 8000 rad m
−
2
are found.
More recently, Park et al.
(
2019
)
studied Faraday RMs in the
jet using multifrequency Very Long Baseline Array
(
VLBA
)
data at
8 GHz. They found that the RM magnitude system-
atically decreases with increasing distance from 5,000 to
200,000
R
s
. The observed large
(
45
°
)
EVPA rotations at
various locations of the jet suggest that the dominant Faraday
screen in this distance range would be external to the jet,
similar to the conclusion of Zavala & Taylor
(
2002
)
. Homan &
Lister
(
2006
)
, also observing at 15 GHz with the VLBA
(
as part
of the MOJAVE project
)
found a tight upper limit on the
fractional linear polarization of the core of
<
0.07%. They also
detect circular polarization of
(
−
0.49
±
0.10
)
%.
At 43 GHz, Walker et al.
(
2018
)
presented results from 17
years of VLBA observations of M87, with polarimetric images
presented at two epochs. These show signi
fi
cant polarization
(
up to 4%
)
in the jet near the 43 GHz core, but at the position of
the total intensity peaks the fractional polarizations are only
1.5% and 1.1%. They interpret these fractions as coming from a
mix of emission from the unresolved, unpolarized core and a
more polarized inner jet.
Hada et al.
(
2016
)
showed images at four epochs at 86 GHz
made with the VLBA and the Gre
en Bank Telescope. At this
frequency, the resolution is about
(
0.4
×
0.1
)
mas, corresponding
to
(
56
×
14
)
R
s
. Again, the core is unpolarized with no linear
polarization detected at the positio
n of the total intensity emission
’
s
peak, while there is a small patch of signi
fi
cant
(
3.5%
)
polarization
located 0.1 mas downstream. At 0.4 mas downstream from the
peak, there is another patch of signi
fi
cant polarization
(
20%
)
.
These results indicate that
there are regions of signi
fi
cantly ordered
magnetic
fi
eld very close to the central engine.
Very recently, new observations by Kravchenko et al.
(
2020
)
using the VLBA at 22 and 43 GHz show two components of
linear polarization and a smooth rotation of EVPA around the
43 GHz core. Comparison with earlier observations show that
the global polarization pattern in the jet is largely stable over an
11 year timescale. They suggest that the polarization pattern is
associated with the magnetic structure in a con
fi
ning magneto-
hydrodynamic wind, which is also the source of the observed
Faraday rotation.
The EHT presently observes at
∼
230 GHz and has previously
reported polarimetric measurements only for Sagittarius A
*
(
Sgr
A
*
;Johnsonetal.
2015
)
. The only previous polarimetric
measurements of M87 at this frequency were done by Kuo
et al.
(
2014
)
using the Submillimeter Array
(
SMA
)
on Maunakea,
Hawai
’
i, USA. The SMA is a compact array with a
(
1.2
×
0.8
)
arcsec beam, 10000 times larger than the EHT beam.
Li et al.
(
2016
)
used the value from this work to calculate a limit
on the accretion rate onto the M87 black hole. Most recently,
Goddi et al.
(
2021
)
reported results on M87 around 230 GHz as
part of the Atacama Large Millimeter
/
submillimeter Array
(
ALMA
)
interferometric connected-element array portion of the
EHT observations in 2017. The ALMA-only 230 GHz observa-
tions
(
with a FWHM synthesized beam in the range 1
′′
–
2
′′
,
depending on the day
)
resolve the M87 inner region into a
compact central core and a kpc-scale jet across approximately 25
′′
.
It has been found that the 230 GHz core at these scales has a
total
fl
ux density of
∼
1.3 Jy, a low linear polarization fraction
|
m
|
∼
2.7%, and even less circular polarization,
|
v
|
<
0.3%.
Notably, ALMA-only observa
tions show strong variability in
the RM estimated based on four frequencies within ALMA Band
6
(
four spectral windows centered at 213, 215, 227, and 229 GHz;
Matthews et al.
2018
)
. The RM difference is clear between
the start of the EHT observing campaign on 2017 April 5
(
RM
≈
0.6
×
10
5
rad m
−
2
)
and the end on 2017 April 11
(
RM
≈−
0.4
×
10
5
rad m
−
2
)
. Because these measurements were
taken simultaneously with the E
HT VLBI observations presented
here, the ALMA-only linear polar
ization fraction measurements
can be used as a point of reference, and we discuss possible
implications of the strong RM evolution on the EHT polarimetric
images of M87.
1.2. This Work
This Letter presents the details of the polarimetric data
calibration, the procedures for polarimetric imaging, and the
resulting images of the M87 core. In Section
2
, we brie
fl
y
overview the basics of polarimetric VLBI. In Section
3
,we
summarize the EHT 2017 observations, describe the initial data
calibration procedure and validation tests, and describe the
basic properties of the polarimetric data. In Section
4
,we
describe our methods, strategy, and test suite for our
polarimetric calibration and imaging. In Section
5
, we present
and analyze the polarimetric images of the M87 ring and
examine the calibration
’
s impact on the polarimetric image. We
discuss the results and summarize the work in Sections
6
and
7
.
This Letter is supplemented with a number of appendices
supporting our analysis and results. The appendices summar-
ize: polarimetric data issues
(
Appendix
A
)
; novel VLBI closure
data products
(
Appendix
B
)
; details of calibration and imaging
methods
(
Appendix
C
)
; validation of polarimetric calibration
2
The Astrophysical Journal Letters,
910:L12
(
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)
, 2021 March 20
EHT Collaboration et al.
for telescopes with an intra-site partner
(
Appendix
D
)
;
fi
ducial
leakage D-terms from M87 imaging
(
Appendix
E
)
; preliminary
results of polarimetric imaging of M87
(
Appendix
F
)
;
polarimetric imaging scoring procedures
(
Appendix
G
)
; details
of Monte Carlo D-term simulations
(
Appendix
H
)
; consistency
of low- and high-band results for M87
(
Appendix
I
)
;
comparison to polarimetric properties of calibrator sources
(
Appendix
J
)
; and validations of assumptions made in
polarimetric imaging of the main target and the calibrators
(
Appendix
K
)
.
2. Basic De
fi
nitions
A detailed introduction to polarimetric VLBI can be found in
Thompson et al.
(
2017
, their Chapter 4
)
. Here we brie
fl
y
introduce the basic concepts and notation necessary to
understand the analysis presented throughout this Letter. The
polarized state of the electromagnetic radiation at a given
spatial coordinate
x
=
(
x
,
y
)
is described in terms of four Stokes
parameters,
x
(
)
(
total intensity
)
,
x
()
(
difference in horizontal
and vertical linear polarization
)
,
x
()
(
difference in linear
polarization at 45
°
and
−
45
°
position angle
)
, and
x
()
(
circular
polarization
)
.Wede
fi
ne the complex linear polarization
as
º+=
c
ime
,1
i
2
∣∣
()
where
=+
mi
()
represents the
(
complex
)
fractional
polarization, and
c
=
0.5 arg
()
is the EVPA, measured from
north to east. Total-intensity VLBI observations directly
sample the Fourier transform
̃
as a function of the spatial
frequency
u
=
(
u
,
v
)
of the total-intensity image; similarly,
polarimetric VLBI observations also sample the Fourier
transform of the other Stokes parameters
,,
̃
̃
̃
.
EHT data are represented in a circular basis, related to the
Stokes visibility components by the following coordinate
system transformation:
r
º=
++
--
RR RL
LR LL
i
i
2
jk
j
k
j
k
j
k
j
k
jk
jk
jk
jk
jk
jk jk
jk
**
**
⎛
⎝
⎜
⎜
⎞
⎠
⎟
⎟
⎛
⎝
⎜
⎜
⎞
⎠
⎟
⎟
̃ ̃ ̃
̃
̃
̃
̃ ̃
()
for a baseline between two stations
j
and
k
. The notation
R
L
j
k
*
indicates the complex correlation
(
where the asterisk denotes
conjugation
)
of the electric
fi
eld components measured by the
telescopes; in this example, the right-hand circularly polarized
component
R
j
measured by the telescope
j
and the left-hand
circularly polarized component
L
k
measured by the telescope
k
.
Equation
(
2
)
de
fi
nes the coherency matrix
ρ
jk
. Following
Johnson et al.
(
2015
)
, we also de
fi
ne the fractional polarization
in the visibility domain,
º
+
==
+
*
**
m
iRL
RR LL
2
.3
̃
̃
̃ ̃
()
Note that Equation
(
3
)
implies that
u
m
()
and
-
u
m
()
constitute
independent measurements for
u
≠
0. Moreover,
u
m
()
and
m
(
x
)
are
not
a Fourier pair. While the image-domain fractional
polarization magnitude is restricted to values between 0
(
unpolarized radiation
)
and 1
(
full linear polarization
)
, there
is no such restriction on the absolute value of
m
. Useful
relationships between
m
and
m
are discussed in Johnson et al.
(
2015
)
.
Imperfections in the instrumental response distort the
relationship between the measured polarimetric visibilities
and the source
’
s intrinsic polarization. These imperfections can
be conveniently described by a Jones matrix formalism
(
Jones
1941
)
, and estimates of the Jones matrix coef
fi
cients
can then be used to correct the distortions. The Jones matrix
characterizing a particular station can be decomposed into
a series of complex matrices
G
,
D
, and
Φ
(
Thompson et al.
2017
)
,
=F=
f
f
-
JGD
G
G
D
D
e
e
0
0
1
1
0
0
.4
R
L
R
L
i
i
⎛
⎝
⎜
⎞
⎠
⎟
⎛
⎝
⎜
⎞
⎠
⎟
⎛
⎝
⎜
⎞
⎠
⎟
()
Time-dependent
fi
eld rotation matrices
Φ
≡
Φ
(
t
)
are known
a priori, with the
fi
eld rotation angle
f
(
t
)
dependent on the
source
’
s elevation
θ
el
(
t
)
and parallactic angle
ψ
par
(
t
)
. The angle
f
takes the form
fq yf
=+ +
ff
,5
el
el
par
par
off
()
where
f
off
is a constant offset, and the coef
fi
cients
f
el
and
f
par
are speci
fi
c to the receiver position type. The gain matrices
G
,
containing complex station gains
G
R
and
G
L
, are estimated
within the EHT
’
s upstream calibration and total-intensity
imaging pipeline; see Section
3.2
. Estimation of the D-terms,
the complex coef
fi
cients
D
R
and
D
L
of the leakage matrix
D
,
generally requires simultaneous modeling of the resolved
calibration source, and hence cannot be easily applied at the
upstream data calibration stage. The details of the leakage
calibration procedures adopted for the EHT polarimetric data
sets analysis are described in Section
4
.
For a pair of VLBI stations
j
and
k
the measured coherency
matrix
r
¢
jk
is related to the true-source coherency matrix
ρ
jk
via
the Radio Interferometer Measurement Equation
(
RIME;
Hamaker et al.
1996
; Smirnov
2011
)
,
rr
¢
=
JJ
,6
jk
j
jk
k
()
†
where the dagger
†
symbol denotes conjugate transposition.
Once the Jones matrices for the stations
j
and
k
are well
characterized, Equation
(
6
)
can be inverted to give the source
coherency matrix
ρ
jk
. From
ρ
jk
, Stokes visibilities can be
obtained by inverting Equation
(
2
)
:
=
+
+
--
-
RR LL
RL LR
iRL LR
RR LL
1
2
.7
jk
jk
jk
jk
j
k
j
k
j
k
j
k
j
k
j
k
j
k
j
k
**
**
**
**
⎛
⎝
⎜
⎜
⎜
⎜
⎜
⎞
⎠
⎟
⎟
⎟
⎟
⎟
⎛
⎝
⎜
⎜
⎜
⎜
⎜
⎞
⎠
⎟
⎟
⎟
⎟
⎟
̃
̃
̃
̃
()
()
The collection of Stokes visibilities sampled in
(
u
,
v
)
space by
the VLBI array can
fi
nally be used to reconstruct the
polarimetric images
xxx
,,
() () ()
, and
x
()
.
The coherency matrices on a quadrangle of baselines can be
combined to form
“
closure traces,
”
data products that are
insensitive to any calibration effects that can be described using
Jones matrices. Appendix
B
de
fi
nes these closure traces and
outlines their utility for describing the EHT data.
3. EHT 2017 Polarimetric Data
3.1. Observations and Initial Processing
Eight observatories at six geographical locations participated
in the 2017 EHT observing campaign: ALMA and the Atacama
Path
fi
nder Experiment
(
APEX
)
in the Atacama Desert in Chile;
3
The Astrophysical Journal Letters,
910:L12
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48pp
)
, 2021 March 20
EHT Collaboration et al.
the Large Millimeter Telescope Alfonso Serrano
(
LMT
)
on the
Volcán Sierra Negra in Mexico; the South Pole Telescope
(
SPT
)
at the geographic south pole; the IRAM 30 m telescope
(
PV
)
on Pico Veleta in Spain; the Submillimeter Telescope
(
SMT
)
on Mt. Graham in Arizona, USA; SMA and the James
Clerk Maxwell Telescope
(
JCMT
)
on Maunakea in Hawai
’
i,
USA.
131
The EHT observations were carried out on
fi
ve nights
between 2017 April 5 and 11. M87 was observed on April 5, 6,
10, and 11. Along with the main EHT targets M87 and Sgr A
*
,
several other AGN sources were observed as science targets
and calibrators.
Observations were conducted using two contiguous fre-
quency bands of 2 GHz bandwidth each, centered at frequen-
cies of 227.1 and 229.1 GHz, hereby referred to as low and
high band, respectively. The observations were arranged in
scans alternating different sources, with durations lasting
between 3 and 7 minutes. Apart from the JCMT, which
observed only a single polarization
(
right-circular polarization
on 2017 April 5
–
7 and left-circular polarization on 2017 April
10
–
11
)
, all stations observed in full polarization mode. ALMA
is the only station to natively record data in a linear polarization
basis. Visibilities measured on baselines to ALMA were
converted from a mixed linear-circular basis to circular
polarization after correlation using the
PolConvert
software
(
Martí-Vidal et al.
2016
; Matthews et al.
2018
; Goddi et al.
2019
)
. A technical description of the EHT array is presented in
Paper
II
and a summary of the 2017 observations and data
reduction is presented in Paper
III
.
3.2. Correlation and Data Calibration
After the sky signal received at each telescope was mixed to
baseband, digitized, and recorded directly to hard disk, the data
from each station were sent to MIT Haystack Observatory and
the Max-Planck-Institut für Radioastronomie
(
MPIfR
)
for
correlation using the DiFX software correlators
(
Deller et al.
2011
)
. The accumulation period adopted at correlation is 0.4 s,
with a frequency resolution of 0.5 MHz. The clock model used
during correlation to align the wavefronts arriving at different
telescopes is imperfect, owing to an approximate a priori model
for Earth
’
s geometry as well as rapid stochastic variations in
path length due to local atmospheric turbulence
(
Paper
III
)
.
Before the data can be averaged coherently to build up signal-
to-noise ratio
(
S
/
N
)
, these effects must be accurately measured
and corrected. This process, referred to as fringe
fi
tting, was
conducted using three independent software packages: the
Haystack Observatory Processing System
(
HOPS; Whitney
et al.
2004
; Blackburn et al.
2019
)
; the Common Astronomy
Software Applications package
(
CASA; McMullin et al.
2007
;
Janssen et al.
2019a
)
; and the NRAO Astronomical Image
Processing System
(
AIPS; Greisen
2003
, Paper
III
)
. Automated
reduction pipelines were designed speci
fi
cally to address the
unique challenges related to the heterogeneity, wide bandwidth,
and high observing frequency of EHT data. The
fi
eld rotation
angle is corrected with Equations
(
4
)
–
(
5
)
, using coef
fi
cients
given in Table
1
. Flux density
(
amplitude
)
calibration is applied
via a common post-processing framework for all pipelines
(
Blackburn et al.
2019
; Paper
III
)
, taking into account estimated
station sensitivities
(
Issaoun et al.
2017
; Janssen et al.
2019b
)
.
Under the assumption of zero circular polarization of the
primary
(
solar system
)
calibrator sources, elevation-indepen-
dent station gains possess independent statistical uncertainties
for the right-hand-circular polarization
(
RCP
)
and left-hand-
circular polarization
(
LCP
)
signal paths, estimated to be
∼
20%
for the LMT and
∼
10% for all other stations
(
Janssen et al.
2019b
)
.
To remove the instrumental amplitude mismatch between the
LL
*
and
RR
*
visibility components
(
the
R
–
L
phases are correctly
calibrated in all scans by using ALMA as the reference station
)
,
calibration of the complex polarimetric gain ratios
(
the ratios of
the
G
R
and
G
L
terms in the
G
matrices
)
is performed. This is
done by
fi
tting global
(
multi-source, multi-days
)
piecewise
polynomial gain ratios as functions of time. The aim of this
approach is to preserve differences in
LL
*
and
RR
*
visibilities
intrinsic to the source
(
Steel et al.
2019
)
. After this step,
preliminary polarimetric Stokes visibilities
,,,
̃
̃
̃
̃
can be
constructed. However, the gain calibration requires signi
fi
cant
additional improvements. The
fi
nal calibration of the station
phase and amplitude gains takes place in a self-calibration step
as part of imaging or modeling the Stokes
brightness
distribution, preserving the complex polarimetric gain ratios
(
e.g., Papers
IV
,
VI
)
. Fully calibrating the D-terms requires
modeling the polarized emission.
The Stokes
(
total intensity
)
analysis of a subset of the
2017 observations
(
Science Release 1
(
SR1
))
, including M87,
was the subject of Papers
I
–
VI
. The quality of these Stokes
data was assured by a series of tests covering self-consistency
over bands and parallel hand polarizations, and consistency of
trivial closure quantities
(
Wielgus et al.
2019
)
. Constraints on
the residual non-closing errors were found to be at a 2% level.
For additional information on the calibration, data reduc-
tion, and validation procedures for EHT, see Paper
III
.
Information about accessing SR1 data and the software used
for analysis can be found on the EHT website
ʼ
s data portal.
132
In this Letter, we utilize the HOPS pipeline full-polarization
band-averaged
(
i.e., averaged over frequency within each band
)
and 10-second averaged data set from the same reduction path
as SR1, but containing a larger sample of calibrator sources for
polarimetric leakage studies. In addition, the ALMA linear-
polarization observing mode allows us to measure and recover
the absolute EVPA in the calibrated VLBI visibilities
(
Martí-Vidal et al.
2016
; Goddi et al.
2019
)
. Other minor
subtleties in the handling of polarimetric data are presented in
Appendix
A
.
Table 1
Field Rotation Parameters for the EHT Stations
Station
Receiver Location
f
par
f
el
f
off
°
ALMA
Cassegrain
1
0
0
APEX
Nasmyth-Right
1
1
0
JCMT
Cassegrain
1
0
0
SMA
Nasmyth-Left
1
−
145
LMT
Nasmyth-Left
1
−
10
SMT
Nasmyth-Right
1
1
0
PV
Nasmyth-Left
1
−
10
SPT
Cassegrain
1
0
0
131
In the EHT array, there are stations with a co-located element of the array:
ALMA and APEX
(
with
∼
2 km baseline
)
and JCMT and SMA
(
with
∼
0.2 km
baseline
)
. We further refer to these two baselines as
zero
baselines or
intra-site
baselines.
132
https:
//
eventhorizontelescope.org
/
for-astronomers
/
data
4
The Astrophysical Journal Letters,
910:L12
(
48pp
)
, 2021 March 20
EHT Collaboration et al.
3.3. Polarimetric Data Properties
In Figure
1
(
top row
)
, we show the
(
u
,
v
)
coverage and low-
band interferometric polarization of our main target M87 as a
function of the baseline
(
u
,
v
)
after the initial calibration stage
but before D-term calibration. The colors code the scan-
averaged amplitude of the complex fractional polarization
m
(
i.e., the fractional polarization in visibility space; for analysis
of
m
in another source, Sgr A
*
, see Johnson et al.
2015
)
. M87 is
weakly polarized on most baselines,
m
0.5
∣
∣
. Several data
points on SMA
–
SMT baselines have very high fractional
polarization
~
muv
,
2
∣
()∣
that occur at
(
u
,
v
)
spacings where
the Stokes
visibility amplitude enters a deep minimum. The
fractional polarization
m
of the M87 core is broadly consistent
across the four days of observations and between low- and
high-frequency bands, therefore high-band results are omitted
in the display.
In Figure
1
(
bottom row
)
we show the
fi
eld rotation angles
f
for each station observing M87 on the four observing days. The
data are corrected for this angle during the initial calibration
stage, but the precision of the leakage calibration depends on
how well this angle is covered and on the difference in the
fi
eld
angles at the two stations forming a baseline. In the M87 data
the
fi
eld rotation for stations forming long baselines
(
LMT,
SMT, and PV
)
is frequently larger than 100
°
except for April
10, for which the
(
u
,
v
)
tracks are shorter.
In addition to the M87 data, a number of calibrators are
utilized in this Letter for leakage calibration studies. To
estimate D-terms for each of the EHT stations we use several
EHT targets observed near in time to M87. In VLBI, weakly
polarized sources are more sensitive to polarimetric calibration
errors so they are preferred calibrators. For full-array leakage
calibration, we focus on two additional sources: J1924
–
2914
and NRAO 530
(
calibrators for the second EHT primary target,
Sgr A
*
)
, which are compact and relatively weakly polarized.
The main calibrator for M87 in total intensity, 3C 279
(
Kim et al.
2020
; Paper
IV
)
, is bright and strongly polarized
on longer baselines and is not used in this work. The properties
and analysis of the calibrators are discussed in more detail in
Appendices
J
and
K
.
The closure traces for M87 and the calibrators can be used
both to probe the data for uncalibrated systematic effects
(
see
Appendix
B.2
)
and to ascertain the presence of polarized
fl
ux
density in a calibration-insensitive manner
(
see Appendix
B.3
)
.
Unless otherwise stated, the following analysis is focused on
the low-band half of the data sets.
4. Methods for Polarimetric Imaging and Leakage
Calibration
4.1. Methods
Producing an image of the linearly polarized emission
requires both solving for the sky distribution of Stokes
parameters
and
and for the instrumental polarization of
the antennas in the EHT array. In this work, we use several
distinct methods to accomplish these tasks. Our approaches can
be classi
fi
ed into three main categories: imaging via sub-
component
fi
tting; imaging via regularized maximum like-
lihood; and imaging as posterior exploration. In this section we
only brie
fl
y describe each method; fuller descriptions are
presented in Appendix
C
.
The calibration of the instrumental polarization by sub-
component
fi
tting was performed using three different codes
(
LPCAL
,
GPCAL
,and
polsolve
)
that depend on two standard
software packages for interfe
rometric data analysis: AIPS
133
and
CASA.
134
In all of these methods, the Stokes
imaging step is
performed using the CLEAN algorithm
(
Högbom
1974
)
, and
sub-components with constant complex fractional polarization
Figure 1.
Top row:
(
u
,
v
)
coverage of the four M87 observing days in the 2017 campaign. The color of the data points codes the fractional polarization amplitude
muv
,
∣
()∣
in the range from 0 to 2. The data shown are derived from low-band visibilities after the initial calibration pipeline described in Section
3.2
but before any
D-term calibration. The data points are coherently scan-averaged. Bottom row: M87
fi
eld rotation angle
f
for each station as a function of time
(
Equation
(
5
))
.
133
http:
//
www.aips.nrao.edu
134
https:
//
casa.nrao.edu
5
The Astrophysical Journal Letters,
910:L12
(
48pp
)
, 2021 March 20
EHT Collaboration et al.