MNRAS
512,
490–504
(2022)
https://doi.org/10.1093/mnras/stac531
Advance
Access
publication
2022
February
26
MeqSilhouette
v2:
spectrally
resolved
polarimetric
synthetic
data
generation
for
the
event
horizon
telescope
Iniyan
Natarajan
,
1
,
2
,
3
‹
Roger
Deane
,
1
,
4
Iv
́
an
Mart
́
ı-Vidal
,
5
,
6
Freek
Roelofs,
7
,
8
,
9
Michael
Janssen,
9
,
10
Maciek
Wielgus
,
7
,
8
,
10
Lindy
Blackburn,
7
,
8
Ta r i q
Blecher,
2
,
3
Simon
Perkins,
2
Oleg
Smirnov,
2
,
3
Jordy
Davelaar,
9
,
11
,
12
Monika
Moscibrodzka
,
9
Andrew
Chael
,
13
Katherine
L.
Bouman,
14
Jae-Young
Kim,
10
,
15
Gianni
Bernardi,
2
,
3
,
16
Ilse
van
Bemmel,
17
Heino
Falcke,
9
Feryal
̈
Ozel
18
and
Dimitrios
Psaltis
18
1
Wits
Centre
for
Astrophysics,
School
of
Physics,
University
of
the
Witwatersrand,
Private
Bag
3,
2050,
Johannesburg,
South
Africa
2
South
African
Radio
Astronomy
Observatory,
Observatory
7925,
Cape
Town,
South
Africa
3
Centre
for
Radio
Astronomy
Techniques
and
Technologies,
Department
of
Physics
and
Electronics,
Rhodes
University,
Makhanda
6140,
South
Africa
4
Department
of
Physics,
University
of
Pretoria,
Hatfield,
Pretoria,
0028,
South
Africa
5
Departament
d’Astronomia
i
Astrof
́
ısica,
Universitat
de
Val
`
encia,
C.
Dr.
Moliner
50,
E-46100
Burjassot,
Val
`
encia,
Spain
6
Observatori
Astron
`
omic,
Universitat
de
Val
`
encia,
C.
Catedr
`
atico
Jos
́
e
Beltr
́
an
2,
E-46980
Paterna,
Val
`
encia,
Spain
7
Center
for
Astrophysics
|
Harvard
&
Smithsonian,
60
Garden
Street,
Cambridg
e
,
MA
02138,
USA
8
Black
Hole
Initiative
at
Harvard
University,
20
Garden
Street,
Cambridg
e
,
MA
02138,
USA
9
Department
of
Astrophysics,
Institute
for
Mathematics,
Astrophysics
and
Particle
Physics
(IMAPP),
Radboud
University,
PO
Box
9010,
6500
GL
Nijmegen,
the
Netherlands
10
Max-Planck-Institut
f
̈
ur
Radioastronomie,
Auf
dem
H
̈
ugel
69,
D-53121
Bonn,
Germany
11
Department
of
Astronomy
and
Columbia
Astrophysics
Laboratory,
Columbia
University,
550
W
120th
Street,
New
York,
NY
10027,
USA
12
Center
for
Computational
Astrophysics,
Flatiron
Institute,
162
Fifth
Avenue,
New
York,
NY
10010,
USA
13
Princeton
Center
for
Theoretical
Science,
Jadwin
Hall,
Princeton
University,
Princeton,
NJ
08544,
USA
14
California
Institute
of
Technology,
1200
East
California
Boulevard,
Pasadena,
CA
91125,
USA
15
Korea
Astronomy
and
Space
Science
Institute,
Daedeok-daero
776,
Yuseong-gu,
Daejeon
34055,
Republic
of
Korea
16
INAF-Istituto
di
Radioastronomia,
via
Gobetti
101,
40129
Bologna,
Italy
17
Joint
Institute
for
VLBI
ERIC,
Oude
Hoo
g
eveensedijk
4,
7991
PD
Dwingeloo,
Netherlands
18
Department
of
Astronomy
and
Steward
Observatory,
University
of
Arizona,
933
North
Cherry
Avenue,
Tucson,
AZ
85721,
USA
Accepted
2022
February
23.
Received
2022
February
23;
in
original
form
2021
November
25
A
B
S
T
R
A
C
T
We
present
MeqSilhouette
v2.0
(MeqSv2),
a
fully
polarimetric,
time-and
frequenc
y-resolv
ed
synthetic
data
generation
software
for
simulating
millimetre
(mm)
wav
elength
v
ery
long
baseline
interferometry
(VLBI)
observations
with
heterogeneous
arrays.
Synthetic
data
are
a
critical
component
in
understanding
real
observations,
testing
calibration
and
imaging
algorithms,
and
predicting
performance
metrics
of
existing
or
proposed
sites.
MeqSv2
applies
physics-based
instrumental
and
atmospheric
signal
corruptions
constrained
by
empirically
derived
site
and
station
parameters
to
the
data.
The
new
version
is
capable
of
applying
instrumental
polarization
effects
and
various
other
spectrally
resolved
effects
using
the
Radio
Interferometry
Measurement
Equation
(RIME)
formalism
and
produces
synthetic
data
compatible
with
calibration
pipelines
designed
to
process
real
data.
We
demonstrate
the
various
corruption
capabilities
of
MeqSv2
using
different
arrays,
with
a
focus
on
the
effect
of
complex
bandpass
gains
on
closure
quantities
for
the
EHT
at
230
GHz.
We
validate
the
frequency-dependent
polarization
leakage
implementation
by
performing
polarization
self-calibration
of
synthetic
EHT
data
using
PolSolve.
We
also
note
the
potential
applications
for
cm-wavelength
VLBI
array
analysis
and
design
and
future
directions.
Key
words:
techniques:
high
angular
resolution
– techniques:
interferometric
– software:
simulations.
1
INTRODUCTION
Ve r y
long
baseline
interferometry
(VLBI)
enables
the
highest
angular
resolution
in
astronomy,
on
the
order
of
milli-arcseconds
(mas)
to
micro-arcseconds
(
μ
as),
by
operating
radio
antennas
separated
E-mail:
iniyan.natarajan@wits.ac.za
by
thousands
of
kilometres
synchronously
using
atomic
clocks.
The
Event
Horizon
Telescope
(EHT,
Event
Horizon
Telescope
Collaboration
2019b
)
is
a
global
mm-VLBI
array
whose
principal
goal
is
to
spatially
resolve
the
supermassive
black
holes
at
the
cores
of
the
Milky
Wa y
Galaxy
(Sgr
A
∗
)
and
M87,
and
image
their
shadows
,
the
depression
in
observed
intensity
inside
the
apparent
boundary
of
the
black
hole
(e.g.
Falcke,
Melia
&
Agol
2000
;
Dexter,
McKinney
&
Agol
2012
;
Psaltis
et
al.
2015
;
Mo
́
scibrodzka,
Falcke
&
© 2022
The
Author(s)
Published
by
Oxford
University
Press
on
behalf
of
Royal
Astronomical
Society
Downloaded from https://academic.oup.com/mnras/article/512/1/490/6537429 by California Institute of Technology user on 04 April 2022
MeqSilhouette
v2:
Synthetic
data
generation
for
the
EHT
491
MNRAS
512,
490–504
(2022)
Shiokawa
2016
),
together
with
a
bright
crescent-shaped
emission
ring
(e.g.
Bromley,
Melia
&
Liu
2001
;
Broderick
&
Loeb
2009
;
Kamruddin
&
Dexter
2013
;
Lu
et
al.
2014
).
The
EHT
2017
campaign
has
yielded
total
intensity
images
of
the
shadow
of
the
black
hole
at
the
centre
of
M87
at
230
GHz
(Event
Horizon
Telescope
Collabora-
tion
2019a
,
d
,
f
).
Assuming
statistically
preferred
geometric
crescent
models
and
general-relativistic
magnetohydrodynamic
(GRMHD)
models,
measurements
of
physical
properties
such
as
the
diameter
of
the
shadow
(42
±
3
μ
as)
and
angular
size
of
one
gravitational
radius
(3
.
8
±
0
.
4
μ
as)
hav
e
been
obtained
(Ev
ent
Horizon
Telescope
Collaboration
2019d
,
e
,
f
).
These
measurements
correspond
to
a
mass
of
6.5
±
0.7
×
10
9
M
at
the
estimated
distance
16
.
8
+
0
.
8
−
0
.
7
Mpc
(Event
Horizon
Telescope
Collaboration
2019f
),
consistent
with
prior
mass
measurements
based
on
stellar
dynamics
(Gebhardt
et
al.
2011
).
Synthetic
data
play
a
significant
role
in
understanding
the
char-
acteristics
of
an
instrument,
de
veloping
ne
w
algorithms
for
data
analysis,
and
realistically
representing
the
underlying
physics
that
give
rise
to
the
observed
data.
Feasibility
studies
and
identification
of
new
sites
for
upgrading
existing
arrays
such
as
the
EHT,
the
Karl
G
Jansky
Ve r y
Large
Array
(VLA)
(Perley
et
al.
2011
),
European
VLBI
Network
(EVN)
(Porcas
2010
),
East
Asian
VLBI
Network
(EAVN)
(An,
Sohn
&
Imai
2018
),
the
Atacama
Large
Millimeter
Array
(ALMA)
(Matthews
et
al.
2018
;
Goddi
et
al.
2019
),
and
MeerKAT
(Jonas
2009
),
and
for
building
new
arrays
such
as
the
next-generation
EHT
(ngEHT)
(Blackburn
et
al.
2019
),
the
next-generation
VLA
(ngVLA)
(Selina
et
al.
2018
),
and
the
Square
Kilometre
Array
(SKA)
(e.g.
Schilizzi
et
al.
2007
)
can
benefit
greatly
from
realistic
simulations
of
interferometric
observations.
These
benefits
include
predictive
analyses
of
new
hardware
enhancements,
as
well
as
testing
and
optimization
of
calibration
and
imaging
algorithms
and
pipelines.
Powerful
analyses
can
be
performed
by
the
average
user
when
the
synthetic
data
tools
are
user-friendly
and
can
be
seamlessly
integrated
with
the
calibration
and
analysis
tools.
MEQSV
2
has
been
designed
with
this
as
a
guiding
principle.
Roelofs
et
al.
(
2020
)
provide
a
brief
re
vie
w
of
the
various
synthetic
data
generation
approaches
used
for
simulating
EHT
observations
o
v
er
the
past
decade.
Most
of
these
incorporate
thermal
noise
arising
from
the
characteristics
of
the
instrument
and
the
atmosphere
as
the
only
data
corruption
effect.
More
complex
signal
corruptions
are
introduced
by
EHT
-
IMAGING
(Chael
et
al.
2016
,
2018
)
and
MEQSILHOUETTE
(Blecher
et
al.
2017
,
and
this
paper),
the
two
synthetic
data
generation
packages
used
for
generating
synthetic
M87
observations
in
Event
Horizon
Telescope
Collaboration
(
2019a
),
Event
Horizon
Telescope
Collaboration
(
2019d
).
EHT
-
IMAGING
can
introduce
randomly
varying
complex
gains
and
ele
v
ation-dependent
atmospheric
opacity
corruptions,
and
also
simulates
scattering
due
to
the
interstellar
medium
(ISM),
which
af
fects
observ
ations
of
Sgr
A
∗
(Johnson
2016
;
Johnson
et
al.
2018
).
Instrumental
polarization
is
introduced
using
previous
measurements
of
leakage
characteristics
of
the
EHT
antennas
(Johnson
et
al.
2015
)
and
the
antenna
gains
are
generated
as
random
offsets
sampled
from
a
normal
distribution
with
a
standard
deviation
that
is
within
a
fixed
percentage
of
the
visibility
amplitudes
of
actual
EHT
data.
EHT
-
IMAGING
also
adds
randomized
station-dependent
inter-scan
phases,
that
are
kept
coherent
within
a
single
scan
to
mimic
the
phases
of
fringe-fitted
visibilities.
MEQSILHOUETTE
takes
a
complementary
approach
to
synthetic
data
generation
by
introducing
corruptions
based
on
physical
models
and
tuned
to
match
empirical
station
measurements.
It
was
designed
to
adapt
the
simulation
and
calibration
techniques
developed
for
metre
and
cm-wavelength
observations
to
mm-VLBI
observations.
The
version
presented
in
Blecher
et
al.
(
2017
)
could
simulate
simple
Gaussian
sources
and
narrow-field
comple
x
sk
y
models
and
introduce
physically-moti
v
ated
tropospheric
phase
and
amplitude
corruptions,
interstellar
scattering
using
SCATTERBRANE
1
(Johnson
&
Gwinn
2015
),
and
time-variable
antenna
pointing
errors.
It
has
been
significantly
enhanced
since
then,
first
in
step
with
the
publication
of
the
first
results
from
2017
EHT
observations,
and
then
with
the
development
of
SYMBA
(Roelofs
et
al.
2020
)
and
the
first
polarimetric
results
of
the
2017
M87
observations
(Event
Horizon
Telescope
Collaboration
2021a
,
b
).
MEQSILHOUETTE
V
2
(hereafter
MEQSV
2
2
)
introduces
full
polari-
metric,
time-variable,
spectrally
resolved
synthetic
data
generation
and
corruption
capabilities
and
is
capable
of
handling
wide-field
source
models
with
complex
substructures.
MEQSV
2
has
been
rewrit-
ten
and
expanded
from
Blecher
et
al.
(
2017
).
The
code
has
been
refactored
to
be
fully
compatible
with
the
same
pipelines
used
for
the
analysis
of
real
EHT
data.
The
pointing
and
atmospheric
models
have
been
rewritten
to
include
more
sophisticated
effects.
Source
and
instrumental
polarization
simulation
capabilities
have
been
introduced.
MEQSV
2
also
accounts
for
the
effects
of
bandwidth
on
various
propagation
path
effects
at
mm-wavelengths.
These
features
facilitate
a
variety
of
studies
for
both
the
EHT
and
upcoming
VLBI
arrays,
such
as
performing
rotation
measure
(RM)
synthesis
studies
(Brentjens
&
de
Bruyn
2005
)
and
multi-frequency
synthesis
imaging
with
the
increasing
fractional
bandwith
of
the
EHT,
as
well
as
the
envisioned
multi-band
imaging
at
230
GHz
and
345
GHz
for
the
ngEHT.
The
ability
to
vary
instrumental
polarization
across
the
receiver
bandwidth
is
crucial
to
take
full
advantage
of
ultra-
wideband
receivers
and
high
dynamic-range
polarimetric
imaging.
With
the
polarimetric
primary
beam
module,
full
Stokes
primary
beam
modelling
for
upcoming
arrays
such
as
the
ngEHT
can
be
undertaken.
Roelofs
et
al.
(
2020
)
seamlessly
combines
the
function-
ality
of
MEQSV
2
and
RPICARD
(Janssen
et
al.
2019
),
the
CASA
-based
VLBI
pipeline
for
calibrating
data
from
the
EHT
and
other
VLBI
facilities.
Synthetic
data
generated
by
both
EHT
-
IMAGING
and
SYMBA
,
representing
complementary
approaches,
have
been
found
to
be
consistent
with
each
other
(Event
Horizon
Telescope
Collaboration
2019d
).
In
this
paper,
we
present
the
components
of
MEQSV
2
and
illus-
trate
its
simulation
capabilities.
In
particular,
we
illustrate
the
new
polarimetric
and
spectral
resolution
capabilities
using
synthetic
data
and
validate
them.
We
study
the
effects
of
bandpass
gains
on
closure
quantities,
which
can
limit
or
bias
constraints
on
intrinsic
source
structure
asymmetry,
by
generating
synthetic
data
with
realistic
bandpasses.
The
polarimetric
capabilities
of
MEQSV
2
are
validated
using
POLSOLVE
,
a
CASA
task
developed
for
polarization
calibration
of
VLBI
observations
(Mart
́
ı-Vidal
et
al.
2021
).
Unlike
conventional
VLBI
polarimetric
calibration
software
packages
such
as
LPCAL
(Leppanen,
Zensus
&
Diamond
1995
)
that
use
a
linear
approximation
to
model
polarization
leakage,
POLSOLVE
uses
a
non-linear
model
derived
from
the
full
RIME
to
handle
high
leakage
values
for
specialized
cases
such
as
the
EHT.
In
addition,
POLSOLVE
uses
a
combined
multi-source
model
when
the
parallactic
angle
co
v
erage
for
individual
calibrators
is
limited
and
can
model
the
frequency-
dependence
of
the
leakage
terms
for
calibrating
large
fractional
bandwidths.
This
paper
is
organized
as
follows:
Section
2
provides
a
brief
o
v
erview
of
the
RIME
formalism
that
forms
the
basis
of
how
1
https://
github.com/krosenfeld/
scatterbrane
.
2
‘Measurement
EQuation’
(see
Section
2
)
+
‘Silhouette’
(referring
to
the
black
hole
‘shadow’).
Downloaded from https://academic.oup.com/mnras/article/512/1/490/6537429 by California Institute of Technology user on 04 April 2022
492
I.
Natarajan
et
al.
MNRAS
512,
490–504
(2022)
MEQSV
2
models
visibilities
to
make
this
a
self-contained
publica-
tion.
Section
3
provides
a
detailed
account
of
the
control
flow
of
MEQSV
2
,
its
signal
corruption
capabilities,
and
their
Jones
matrix
implementations.
Section
4
describes
the
CASA
POLSOLVE
tool
for
es-
timating
polarization
leakage
in
heterogenous
VLBI
arrays.
Section
5
demonstrates
the
synthetic
data
generation
capabilities
of
MEQSV
2
for
three
different
mm-wave
telescopes.
Section
6
quantifies
the
effect
of
complex
bandpass
gains
on
EHT
observations
at
230
GHz
and
Section
7
demonstrates
and
validates
the
polarimetric
simulation
capabilities
of
MEQSV
2
using
multiple
polarized
source
models.
Section
8
provides
a
general
discussion
on
the
potential
uses
of
MEQSV
2
and
Section
9
summarizes
the
results
and
future
outlook.
2
THE
RADIO
INTERFEROMETER
MEASUREMENT
EQUATION
Hamaker,
Bregman
&
Sault
(
1996
)
originally
developed
the
mathe-
matical
formalism
for
describing
radio
polarimetry
using
the
Jones
(Jones
1941
)
and
Mueller
(Mueller
1948
)
calculi
from
optics.
Smirnov
(
2011a
)
extended
this
formulation
to
incorporate
direction-
dependent
effects
(DDEs)
in
calibration.
Here
we
provide
only
a
brief
summary
of
the
rele
v
ant
aspects
of
this
formalism
and,
given
the
range
of
notations
in
use,
establish
the
notation
used
in
this
paper.
An
interferometer
produces
four
pairwise
correlations
between
the
voltage
vectors
from
two
stations
p
and
q
(each
with
two
feeds
x
and
y
),
that
can
be
arranged
into
the
2
×
2
visibility
matrix
3
:
V
pq
=
2
(
v
px
v
∗
qx
v
px
v
∗
qy
v
py
v
∗
qx
v
py
v
∗
qy
)
,
(1)
where
the
angled
brackets
denote
averaging
over
some
small
time
and
frequency
bin,
based
on
considerations
of
smearing
and
decoherence
,
field
of
interest,
and
processing
requirements.
In
terms
of
the
voltage
two-vectors
v
p
,
equation
(
1
)
can
be
represented
as
V
pq
=
2
〈(
v
px
v
py
)
(
v
∗
qx
,
v
∗
qy
)
〉
=
2
v
p
v
H
q
,
=
2
J
p
e
(
J
q
e
)
H
=
2
J
p
(
e
e
H
)
J
H
q
,
(2)
where
e
is
the
incoming
electromagnetic
wave,
J
p
are
the
2
×
2
Jones
matrices
that
describe
any
linear
transformation
acting
on
the
incoming
wave,
and
H
is
the
Hermitian
conjugate.
The
matrix
product
e
e
H
in
equation
(
2
)
is
related
to
the
four
Stokes
parameters
I
,
Q
,
U
,
and
V
that
describe
the
polarization
state
of
electromagnetic
radiation
(Hamaker
et
al.
1996
;
Thompson,
Moran
&
George
W.
Swenson
2017
)
by
the
following
relation
4
:
2
(
e
x
e
∗
x
e
x
e
∗
y
e
y
e
∗
x
e
y
e
∗
y
)
=
(
I
+
Q
U
+
iV
U
−
iV
I
−
Q
)
≡
B
.
(3)
B
is
the
brightness
matrix
which
describes
the
intrinsic
source
brightness.
e
x
and
e
y
are
the
orthogonal
polarizations
as
measured
by
the
two
feeds
x
and
y
.
In
the
ideal
case
of
corruption-free
reception,
the
phase
delay
associated
with
signal
propagation,
denoted
by
the
scalar
K-Jones
3
The
factor
of
2
is
introduced
in
this
equation
to
ensure
that
the
brightness
matrix
(introduced
shortly)
becomes
1
for
a
1
Jy
unpolarized
source
(Smirnov
2011a
).
4
This
equation
is
valid
for
linear
(XY)
feeds.
See
Section
3.1
for
circular
(RL)
feeds.
matrix,
is
al
w
ays
present,
giving
rise
to
the
source
coherency
,
X
pq
:
X
pq
=
K
p
B
K
H
q
,
where
K
p
=
e
−
2
πiφ
p
(
1
0
0
1
)
(4)
in
which
φ
p
denotes
the
phase
delay
between
the
antenna
p
and
the
reference
antenna.
In
the
presence
of
multiple
discrete
sources
in
the
sky,
taking
into
account
the
direction-dependence
of
the
source
coherency
and
some
Jones
matrices,
the
RIME
generalizes
to
V
pq
=
G
p
(
∑
s
E
sp
X
spq
E
H
sq
)
G
H
q
,
(5)
where
the
summation
is
carried
out
o
v
er
all
the
sources
and
E
sp
and
G
p
denote
generic
direction-dependent
effects
(DDEs)
and
direction-
independent
effects
(DIEs)
respectively.
MEQSV
2
does
not
simulate
any
DDEs
for
EHT
observations,
since,
aside
from
scattering,
there
are
no
major
DDEs
that
occur
along
the
signal
path.
3
THE
MEQSILHOUETTE
FRAMEWORK
MEQSV
2
was
designed
to
use
the
Measurement
Set
5
(MS),
a
database
format
designed
to
store
radio
astronomical
data
in
next-generation
facilities
such
as
JVLA,
ALMA,
MeerKAT,
and
SKA.
Fig.
1
shows
the
basic
layout
and
the
components
of
a
typical
MEQSV
2
run.
Scatter-
ing
by
the
ISM
is
not
applied
to
the
input
sky
models
and
is
assumed
to
have
been
applied
externally,
simplifying
the
user
interface
compared
to
v1.
MEQSV
2
uses
a
driver
script
to
set
up
the
sequence
of
steps
to
be
e
x
ecuted
to
generate
the
synthetic
data.
The
fr
ame
work
module
contains
the
various
functions
necessary
to
create
synthetic
data,
corrupt
them,
and
optionally
generate
additional
data
products.
The
inputs
to
the
driver
script
are
presented
as
attribute-value
pairs
in
a
file
in
the
JSON
format
(Crockford
2006
)
containing
information
on
the
source,
weather,
and
antenna
parameters
necessary
for
computing
various
components
of
the
RIME.
The
Jones
matrices
are
applied
to
the
uncorrupted
visibilities
in
the
order
in
which
they
occur
along
the
signal
path
(Noordam
&
Smirnov
2010
),
unless
they
are
scalar,
in
which
case
they
can
be
applied
anywhere
along
the
signal
chain.
Advanced
users
may
write
their
own
driver
scripts
to
tailor
the
basic
strate
gy
pro
vided
by
MEQSV
2
for
their
own
needs.
For
instance,
in
SYMBA
(Roelofs
et
al.
2020
),
we
use
this
framework
to
create
synthetic
data
that
follow
real
EHT
observing
schedules
using
input
VEX
6
files
(the
scheduling
protocol
for
VLBI
experiments)
and
extend
the
pointing
offset
module
to
compute
short
and
long-term
pointing
offsets
mimicking
the
behaviour
of
EHT
stations.
SYMBA
also
performs
additional
a
priori
calibration
so
that
the
output
more
closely
resembles
the
uncalibrated
EHT
data.
MEQSV
2
can
just
as
easily
be
used
for
simulating
observations
with
other
VLBI
arrays
(see
Section
5
),
although
other
propagation
path
effects
that
become
significant
at
longer
wavelengths
may
need
to
be
implemented.
The
following
subsections
explain
the
various
modules
of
MEQSV
2
.
The
plots
shown
are
obtained
using
a
hypothetical
12-h
observing
run
using
the
EHT2017
array
listed
in
Ta b l e
1
at
an
observing
fre-
quency
of
230
GHz
towards
M87
(
α
J2000
=
12
h
30
m
49
s
.
42
,
δ
J2000
=
12
◦
23
28
.
04).
The
SPT
station
from
EHT2017
has
been
excluded
since
M87
is
al
w
ays
below
the
horizon
from
the
south
pole.
5
https://
casa.nrao.edu/
Memos/
229.html
.
6
ht
tps://vlbi.org/vlbi-st
andards/vex
.
Downloaded from https://academic.oup.com/mnras/article/512/1/490/6537429 by California Institute of Technology user on 04 April 2022
MeqSilhouette
v2:
Synthetic
data
generation
for
the
EHT
493
MNRAS
512,
490–504
(2022)
Figure
1.
Flo
wchart
sho
wing
the
basic
components
of
synthetic
data
generation
with
MEQSV
2
.
The
inputs
and
outputs
are
shaded
orange,
the
processes
are
shaded
blue,
and
the
decision
boxes
(diamonds)
are
shaded
green.
Multiple
input
configuration
files
are
used
and
various
output
data
products
are
produced.
The
input
values
are
determined
from
empirical
values
obtained
from
the
individual
observations
themselves,
as
well
as
VLBIMONITOR
.
Each
component
in
the
diagram
is
explained
in
Section
3
.
Table
1.
Physical
sizes
and
mount
specifications
of
EHT2017
sta-
tions
participating
in
the
simulations.
Station
Ef
fecti
ve
diameter
(m)
Mount
type
ALMA
†
70
Alt-az
APEX
12
Alt-az
+
Nasmyth-Right
LMT
32
Alt-az
+
Nasmyth-Left
PV
30
Alt-az
+
Nasmyth-Left
SMT
10
Alt-az
+
Nasmyth-Right
JCMT
15
Alt-az
SMA
†
16
Alt-az
+
Nasmyth-Left
Note.
†
Single-antenna
equi
v
alent
of
phased
arrays.
3.1
Input
sky
models
MEQSV
2
introduces
the
capability
to
generate
synthetic
visibilities
from
wide-field
non-parametric
images
and
retains
the
ability
to
input
simple
parametric
source
models
in
the
form
of
ASCII
text
files
describing
point
or
Gaussian
source
models.
Since
im-
ages
are
gridded
representations
of
the
sky,
we
use
WSCLEAN
,
a
fast
generic
widefield
imager
(Offringa
et
al.
2014
),
to
Fourier-
invert
the
model
image
to
the
uv
-plane.
Each
polarized,
time
and
frequency
variable
image
frame
is
F
ourier-inv
erted
into
the
appropriate
subset
of
the
generated
MS.
7
Parametric
sky
models
are
handled
by
MEQTREES
(Noordam
&
Smirnov
2010
),
which
performs
a
direct
Fourier
transform
of
the
sky
model
into
the
MS.
For
the
EHT,
the
visibilities
are
al
w
ays
computed
in
the
circular
polarization
basis
(RR,
RL,
LR,
and
LL),
except
in
the
case
of
ALMA
which
records
signals
in
linear
basis.
In
MEQSV
2
,
we
assume
that
the
ALMA
visibilities
have
been
perfectly
converted
to
circular
polarization
(Marti-Vidal
et
al.
2015
)
so
that
the
basis
is
uniform
7
The
naming
conventions
for
the
image
frames
are
explained
in
the
official
documentation.
Figure
2.
Stokes
I
visibility
amplitudes
for
a
point
source
with
intrinsic
time
variability,
as
a
function
of
time
for
one
frequency
channel.
across
all
stations.
Then,
equation
(
3
)
takes
the
form
B
=
2
(
e
r
e
∗
r
e
r
e
∗
l
e
l
e
∗
r
e
l
e
∗
l
)
=
(
I
+
V
Q
+
iU
Q
−
iU
I
−
V
)
.
(6)
where
‘
’
indicates
circular
polarization
(Smirnov
2011a
).
Fig.
2
shows
the
Stokes
I
visibility
amplitudes
for
all
baselines
for
a
single
channel
of
the
data
set
generated
using
a
point
source
sky
model
with
intrinsic
time
variability.
The
scatter
of
the
visibilities
is
due
to
thermal
noise.
The
capability
to
simulate
time-varying
sources
is
particularly
useful
for
simulating
sources
exhibiting
variability
on
timescales
of
minutes
to
hours,
such
as
the
radio
source
associated
with
the
supermassive
black
hole
Sagittarius
A
∗
(or
Sgr
A
∗
)
located
at
the
Galactic
centre
(e.g.
Lu
et
al.
2016
).
In
addition,
studies
on
decoupling
time-varying
instrumental
effects
from
source
evolution
could
be
undertaken.
Fig.
3
shows
the
stokes
I
visibilities
of
a
point
source
with
a
steep
spectral
index,
across
a
2
GHz
bandwidth
divided
into
64
channels,
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