of 16
Search for Subsolar-Mass Binaries in the First Half of Advanced LIGO
s and
Advanced Virgo
s Third Observing Run
R. Abbott
etal.
*
(LIGO Scientific Collaboration and Virgo Collaboration)
(Received 1 October 2021; revised 18 March 2022; accepted 7 June 2022; published 5 August 2022)
We report on a search for compact binary coalescences where at least one binary component has a mass
between
0
.
2
M
and
1
.
0
M
in Advanced LIGO and Advanced Virgo data collected between 1 April 2019
1500 UTC and 1 October 2019 1500 UTC. We extend our previous analyses in two main ways: we include
data from the Virgo detector and we allow for more unequal mass systems, with mass ratio
q
0
.
1
.Wedo
not report any gravitational-wave candidates. The most significant trigger has a false alarm rate of
0
.
14
yr
1
. This implies an upper limit on the merger rate of subsolar binaries in the range
½
220
24200

Gpc
3
yr
1
, depending on the chirp mass of the binary. We use this upper limit to derive
astrophysical constraints on two phenomenological models that could produce subsolar-mass compact
objects. One is an isotropic distribution of equal-mass primordial black holes. Using this model, we find
that the fraction of dark matter in primordial black holes in the mass range
0
.
2
M
<m
PBH
<
1
.
0
M
is
f
PBH
Ω
PBH
=
Ω
DM
6%
. This improves existing constraints on primordial black hole abundance by a
factor of
3
. The other is a dissipative dark matter model, in which fermionic dark matter can collapse and
form black holes. The upper limit on the fraction of dark matter black holes depends on the minimum mass
of the black holes that can be formed: the most constraining result is obtained at
M
min
¼
1
M
, where
f
DBH
Ω
DBH
=
Ω
DM
0
.
003%
. These are the first constraints placed on dissipative dark models by
subsolar-mass analyses.
DOI:
10.1103/PhysRevLett.129.061104
Introduction.
The first detection of gravitational waves
from a binary black hole (BBH) merger in 2015
[1]
has
given us a new way to study the Universe. Since then,
dozens of gravitational waves (GWs) have been detected in
Advanced LIGO
[2]
and Advanced Virgo
[3]
data. The
LIGO Scientific, Virgo, and KAGRA Collaboration (LVK)
have reported the discovery of GWs from approximately
fifty BBHs, binary neutron stars (BNSs), or neutron star
black hole mergers
[4
6]
. Further analyses on public data
[7,8]
have resulted in the discovery of other compact
binaries
[9
13]
. The gravitational-wave sources presented
in
[4,5]
are already being used to answer key questions
including cosmological measurements
[14
18]
, analyses of
the mass and spin distribution of compact objects, their
formation channels
[19
28]
, and tests of general relativity
[29
31]
The black holes detected with gravitational waves can
have masses larger than those discovered in x-ray binaries
[32
35]
. Several GW sources have challenged our under-
standing of astrophysics and stellar evolution
[36
44]
.One
such source is GW190521
[37,38]
, a system whose most
massive black hole might have a mass in the pair instability
mass gap
[38,45
47]
(but see, e.g., Refs.
[48
53]
). With a
mass of
142
M
, the merger product of GW190521 was
likely an intermediate mass black hole
[38,54]
. At the other
end of the mass spectrum, the lightest object in GW190814,
a
2
.
6
M
compact object, was either the heaviest neutron
star or the lightest black hole ever discovered
[39,55
58]
.
There are no widely accepted astrophysical channels that
predict the formation of subsolar-mass (SSM) objects
significantly more compact than white dwarfs. Since the
end point of stellar evolution of massive stars is either a
neutron star or a supersolar-mass black hole, the existence
of a compact object below
1
M
would be indicative of a
new formation mechanism, and potentially of new physics.
One possible scenario for the formation of SSM black
holes is the collapse of overdensities in the early Universe,
resulting in primordial black holes (PBHs)
[59
62]
. The
amplitude of primordial fluctuations on very small scales
[63,64]
, together with the equation of state of the early
Universe
[65,66]
, determines the mass and abundance of
these objects
[67,68]
. In particular, their masses might be in
the range probed by ground-based detectors
[64,69,70]
, and
so the mass spectrum is constrained by gravitational-wave
data
[71
78]
. Alternatively, if dark matter has a sufficiently
complex particle composition, which allows for chemistry
and dissipation, small compact objects could form through
the cooling and gravitational collapse of dark matter halos
[79
81]
. If dark matter is sufficiently dissipative, compact
objects would form through pathways similar to known
*
Full author list given at the end of the article.
PHYSICAL REVIEW LETTERS
129,
061104 (2022)
0031-9007
=
22
=
129(6)
=
061104(16)
061104-1
© 2022 American Physical Society
astrophysical channels, with details dependent on the
interactions specific to the dark sector. Dissipative dark
matter models that produce black holes in the subsolar to
supersolar range were recently constrained in
[82]
by
analyzing LVK data. Another possibility is that ultralight
bosonic fields clump together to form self-gravitating,
horizonless compact objects, known as boson stars
[83
85]
. Their maximum mass depends on the mass of the
bosonic particle, hence they might be subsolar if the latter is
larger than
10
10
eV
=c
2
[86,87]
. Finally, some dark matter
models predict the formation of
1
M
black holes
through the accumulation of dark matter particles in
neutron star cores
[88
94]
. Black holes formed via this
class of mechanisms would have masses comparable to or
smaller than the mass of the neutron star.
Searches for compact binaries with at least one SSM
component have been carried out in both Initial LIGO
[95
97]
and Advanced LIGO and Advanced Virgo data
[98,99]
. Advanced LIGO and Advanced Virgo data have
more recently been analyzed in
[100
102]
for systems with
lower mass ratios and higher eccentricities than those
considered by the LVK. No detections were reported. In
this Letter, we report the results of searches for SSM
compact binaries in the first half of Advanced LIGO and
Advanced Virgo
s third observing run (this is the first half
of the third science run, henceforth O3a). While no sources
are detected, we obtain limits on the abundance of mono-
chromatic PBHs and black holes formed by dissipative
fermionic dark matter.
Search.
The data used for this Letter were collected
during O3a by the Advanced LIGO and Advanced Virgo
interferometers between 1 April 2019 1500 UTC
and 1 October 2019 1500 UTC. The data characterization
and calibration were performed as described in
Refs.
[5,103
105]
with the addition of a nonlinear removal
of spectral lines
[106,107]
.
We present results from three matched-filter based
pipelines:
G
st
LAL
[108
110]
,
MBTA
[111]
, and
P
y
CBC
[112
117]
. These analyses correlate the data with a
bank of templates that model the gravitational-wave
signals expected from binaries in quasicircular orbit. The
bank is designed to recover binaries with (redshifted)
primary mass
m
1
½
0
.
2
;
10

M
and secondary mass
m
2
½
0
.
2
;
1
.
0

M
. The lower mass bound is set for
consistency with previous searches
[98,99]
and to limit
the computational cost of the search. We additionally limit
the binary mass ratio,
q
m
2
=m
1
, to range from
0
.
1
<q<
1
.
0
. We include the effect of spins aligned with
the orbital angular momentum in the gravitational wave-
form used in the template bank
[118]
. When a binary
component
m
i
has a mass
m
i
0
.
5
M
, we allow for a
dimensionless component spin up to 0.9. For compact
objects with
m
i
<
0
.
5
M
, we limit the maximum dimen-
sionless spin to 0.1. We chose to restrict the possible spin
magnitude in the low-mass part of the template bank, and
not to allow for spin precession in order to reduce the
computational cost. All three searches use the same
template bank, constructed using a geometric placement
algorithm
[119]
with a minimum match
[120]
of 0.97. This
ensures that no more than 10% of astrophysical signals can
be missed due to the discrete template placement. We use
the
TaylorF2
waveform
[121
131]
, including phase
terms up to 3.5 post-Newtonian order, but no amplitude
corrections.
This search covers a larger mass and spin range than the
last LVK analysis for SSM objects
[99]
. As a result, we
require approximately twice as many template waveforms
to effectively cover the search parameter space. To reduce
the computational cost of the search, we analyze the data
from 45 Hz instead of 15 Hz (as in the searches described in
[5]
). We estimate that this restricted bandwidth results in a
maximum loss of signal-to-noise ratio of 9%, relative to
what would be obtained filtering from 15 Hz. In turn, this
results in a maximum reduction of the surveyed volume
of 24%.
The three pipelines used in this Letter are described in
more detail in Refs.
[5,107]
. Here, we only highlight
differences in the way each pipeline has been run for this
analysis, as compared to Refs.
[5,107]
.
G
st
LAL
s
[108
110]
detection statistic is unchanged
relative to Ref.
[5]
.
G
st
LAL
reweighs waveforms in the
template bank according to the characteristics of the
expected population
[132]
. However, because SSM pop-
ulations are yet to be observed we use a population model
uniform in template density for this search.
G
st
LAL
uses a
similar procedure to the one it employed in Ref.
[39]
and
includes all events from the analyzed period in the noise
background to provide a conservative false-alarm-rate
estimate. As in previous SSM searches
[98,99]
we do
not use a gating scheme to account for loud noise artifacts
[108]
; instead we rely on statistical data quality information
from the iDQ algorithm
[133,134]
.
The
MBTA
pipeline splits the matched filtering in two
different frequency bands in order to reduce the computa-
tional cost
[135,136]
. The setup of the search is unchanged
with respect to Ref.
[111]
with two exceptions in order to
adapt to the extended duration of low mass binaries: we use
longer stretches of data to perform fast Fourier transforms
(FFTs) and to calculate the noise power spectral density
(PSD). For the FFT, we use from seconds to hundreds of
seconds of data, while the PSD update time is up to 2 times
longer than for standard BNS searches, depending on the
frequency region under consideration.
The
P
y
CBC
pipeline
[112,114
117,137]
is unchanged
relative to the configuration described in Ref.
[107]
.
However, the sine-Gaussian veto described in Ref.
[138]
is not used, due to the low total mass of the template bank.
Results.
No gravitational-wave candidates were iden-
tified by any of the search pipelines. The most significant
candidate has a false-alarm rate of
0
.
14
yr
1
. The lack of
PHYSICAL REVIEW LETTERS
129,
061104 (2022)
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detections can be recast as an upper limit on the merger rate
of compact binaries. First, we estimate the sensitivity of
each search pipeline for binaries in a given population. This
can be done by computing the surveyed time volume:
h
VT
T
Z
dz
dV
ð
1
þ
z
Þ
dz
ε
ð
z
Þ
;
ð
1
Þ
where
T
is the analyzed time and
ε
ð
z
Þ
is the efficiency. The
efficiency represents the fraction of astrophysical sources in
the population which are detectable at a redshift
z
. The
efficiency can be written as the probability that a binary
with parameters
θ
is detectable (a quantity often referred to
as
p
det
ð
θ
Þ
in the literature, e.g., Ref.
[19]
) integrated over
the distribution of all parameters but the redshift. Therefore,
in order to calculate Eq.
(1)
we need to assume a model for
the mass distribution, spin distribution, sky positions, and
orbital orientations
[139
141]
. Since we are only sensitive
to nearby (
z
0
.
12
) sources we treat the merger rate as
constant.
Each pipeline estimates its sensitivity by simulating
gravitational-wave signals from a population of SSM
compact binaries and adding them into the collected data.
We simulate a population with a uniform distribution of
source masses in the range
0
.
2
M
<m
1
<
10
.
0
M
and
0
.
2
M
<m
2
<
1
.
0
M
. We make an additional detector
frame mass cut
m
1
<
10
M
(
m
2
<
1
M
) due to the
template bank coverage. We reject binaries with mass ratios
exceeding the
0
.
1
<q<
1
.
0
bounds of our search. The
dimensionless spins are again assumed to be oriented in the
direction of the angular momentum for computational
reasons. The spin magnitude is uniform in the range
0
.
1
<
χ
k
<
0
.
1
(
0
.
9
<
χ
k
<
0
.
9
) when
m
k
<
0
.
5
M
(
m
k
>
0
.
5
M
). The sources are uniform in comoving
volume, isotropically distributed on the sphere, and
randomly oriented. We use the Planck
TT
;
TE
;
EE
þ
lowP
þ
lensing
þ
ext
cosmology
[142]
.
Since the search sensitivity is primarily a function of
chirp mass,
M
ð
m
1
m
2
Þ
3
=
5
=
ð
m
1
þ
m
2
Þ
1
=
5
[143]
,we
break this population into nine equally spaced chirp mass
bins in the range
0
.
17
M
<
M
<
2
.
39
M
to determine
h
VT
M
Þ
.
Treating each chirp mass bin as a different population,
labeled by an index
i
, we can use the surveyed time-volume
[144]
h
VT
i
i
for each chirp mass bin to estimate a
frequentist upper limit (90% confidence interval) on the
merger rate of that population by using the loudest event
statistic
[98,99,145]
:
R
90
;i
¼
2
.
3
h
VT
i
i
:
ð
2
Þ
This is shown in Fig.
1
for the three pipelines. Although
the pipelines generally agree, differences in background
estimation and ranking statistics can lead to
h
VT
i
measurements that agree to within
O
ð
30%
Þ
. In what
follows, we use the
MBTA
results as our fiducial rate
constraint. Instrumental calibration errors were at most
3%
in amplitude in the bandwidth relevant for our
analysis, and usually much smaller
[103]
. At most, they
could contribute a
10%
uncertainty in our
h
VT
i
i
meas-
urement. We follow
[19,107]
and neglect their impact in the
remainder of this work.
Modeling dark matter constraints.
For any astrophysi-
cal model that could generate SSM binaries, the merger rate
upper limits can be used to set constraints on the model
parameters. Here, we focus on two such models: formation
of PBHs catalyzed by three-body interactions
[146]
, and
dark-matter black holes formed by late-time gravitational
collapse of dark matter substructure
[80]
.
We use a phenomenological model for PBHs, rather than
a first-principles model derived from an inflationary poten-
tial (see, for example,
[147,148]
for work connecting PBH
distributions to inflationary models). Following
[146]
we
assume PBHs produced at a single mass, and randomly
distributed in space (see Supplemental Material
[149]
for details). This model predicts a merger rate given the
mass of the PBHs in the binary and the abundance of PBHs,
parametrized as a fraction of the dark matter density,
f
PBH
Ω
PBH
=
Ω
DM
. By using the merger rate upper limits
derived above, we can thus obtain an upper limit on
f
PBH
as
a function of the component mass of the black holes in the
binary
[146]
. This is shown in Fig.
2
.
In this analysis, it is assumed that the two objects in the
binary have the same mass. Because the detectors
sensi-
tivity depends more strongly on the chirp mass than on the
mass ratio, for this analysis we assume that the rate upper
limits we presented above (which included unequal mass
binaries) can be used to assess the rate of equal mass
FIG. 1. Upper limit on the merger rate of binaries with at least
one SSM component as a function of source frame chirp mass.
The dotted, dashed, and solid lines represent the 90% confidence
limits obtained by
G
st
LAL
,
MBTA
, and
P
y
CBC
, respectively.
PHYSICAL REVIEW LETTERS
129,
061104 (2022)
061104-3
binaries:
R
90
ð
M
;q
¼
1
Þ
R
90
ð
M
Þ
. Under these assump-
tions, we find
f
PBH
6%
for PBHs in equal-mass binaries
with component objects in the range
½
0
.
2
1
.
0

M
. The
method of Ref.
[161]
may be used to interpret these
constraints on generic PBH mass functions. Recent work
[162
164]
has shown that there are a number of mecha-
nisms that can alter and suppress the PBH merger rate from
that derived in Ref.
[146]
and used here; these include
binary disruption from other close PBHs, clusters of black
holes, and matter inhomogeneities
[165]
. Suppression of
the theoretical merger rate leads to looser constraints on the
allowable fraction of the dark matter contained in PBHs.
Next, we consider a dissipative dark-matter model which
consists of two fermions, oppositely charged under a dark
version of electromagnetism, together with a massless dark
photon. The dark matter can form bound states analogous
to atomic and molecular hydrogen, and dissipate energy by
radiative processes including Bremsstrahlung, recombina-
tion, and collisional excitation
[166]
. In dense regions,
some dark matter gas can cool efficiently enough for
gravitational collapse to proceed, eventually forming black
holes
[80]
. In contrast to the PBH case, here we assume a
power-law distribution for the black hole masses, with an
unknown low-mass cutoff. We calculate an upper limit on
the fraction of the dissipative dark matter that ends up in
black holes (
f
DBH
Ω
DBH
=
Ω
DM
) as a function of the low-
mass cutoff for the dark matter black holes, marginalized
over all other parameters of the model (e.g., the slope of the
dark matter black hole mass function). More details on
the model are given in Supplemental Material
[149]
, and
the marginalization procedures are discussed in depth in
[82]
. In Fig.
3
, we show our constraints. The lowest upper
limit is found at
M
min
¼
1
M
, where
f
DBH
0
.
003%
.No
meaningful constraints can be set for
M
min
2
×
10
2
M
since below that mass none of the black holes in the
population would be detectable with the current sensitivity,
hence a nondetection does not yield any constraint.
Conclusions and outlook.
Gravitational waves from
compact object mergers provide a unique probe of dark
matter structures on the smallest scales. Here, we have
considered two possible dark matter candidates: PBHs and
fermionic dark matter particles that can dissipate and form
dark matter black holes. Both of these formation mecha-
nisms can potentially produce both subsolar and supersolar
mass black holes. We have focused on the SSM regime,
which cannot be populated with black holes by any known
astrophysical channel.
We have used three different algorithms to search the
data from O3a for compact binaries in which at least one of
the component objects had a mass between
½
0
.
2
1
.
0

M
.
We have found no candidates, and obtained upper limits
on the merger rate of SSM black holes in the range
½
220
24200

Gpc
3
yr
1
. The upper limit is dependent
on the chirp mass of the source and shown in Fig.
1
. These
upper limits can be recast into limits on the physical
parameters of SSM black holes populations.
FIG. 2. Constraints on the fraction of dark matter in PBHs. The
horizontal axis shows the source frame mass of the black hole in
each model; for LVK results this is the component mass for each
object in the binary. Each constraint shown carries a model
dependency. Shown (pink) are the LVK results from O1
[98]
,O2
[99]
, and O3a (this work); (orange) microlensing constraints from
MACHO
[155]
,EROS
[156]
, and OGLE
[157]
; (green) dynami-
cal constraints from observations of Segue I
[158]
and Eridanus II
[159]
dwarf galaxies; (blue) supernova lensing constraints from
the Joint Light-curve Analysis and Union 2.1 datasets
[160]
.LVK
results use the Planck
TT
;
TE
;
EE
þ
lowP
þ
lensing
þ
ext
cosmology
[142]
.
FIG. 3. Constraints on the fraction of dark matter
f
DBH
in black
holes formed from cooling of dissipative dark matter and their
minimum possible source frame mass
M
min
.
PHYSICAL REVIEW LETTERS
129,
061104 (2022)
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By considering a phenomenological model for SSM
PBHs in which the compact objects are all formed with the
same mass, we have obtained a limit on the abundance of
these black holes as a function of their mass at formation:
f
PBH
6%
in the mass range, as seen in Fig.
2
.This
significantly improves microlensing and supernova lens-
ing constraints in the same mass region as well as our
previous constraints from Ref.
[99]
, though we note that
there are uncertain mechanisms that can reduce the
expected PBH merger rate and raise the allowed value
of
f
PBH
[162,163,165]
. Our work focuses on a small slice
of the mass spectrum; we refer the reader to
[167]
for
constraints on this model across the full parameter space.
We have also considered a model for fermionic dissipative
dark matter, parametrized by the abundance of the
black holes it produces, and by their minimum mass.
The most stringent limit is obtained at
M
min
¼
1
M
for
which
f
DBH
0
.
003%
,asshowninFig.
3
. The constraint
on the minimum mass can be interpreted in two ways.
The most straightforward is as a constraint on the
Chandrasekhar limit of the fermionic particle progenitors
of dark matter black holes
[80]
, which constrains the
mass of a dark fermion analogous to the proton to be
in the range
0
.
66
8
.
8
GeV
=c
2
. Additionally, the minimum
mass of black holes formed when the dark matter gas
cools and fragments depends on the coldest temperature
the gas can reach, that is, on the dark matter chemistry.
For the model we considered, this temperature is set
by the energy difference of the lowest energy mole-
cular radiative transition. Therefore, a constraint on the
minimum mass of any dark black holes also implies
a constraint on the dark molecular energy spacing,
although the precise relationship depends on astrophysical
modeling.
In the coming years, the sensitivity of Advanced LIGO
and Advanced Virgo will continue to improve
[168]
, and
the global network of detectors is expected to grow with the
addition of KAGRA
[169]
and LIGO-Aundha
[170]
. These
advances will allow for more stringent limits in the near
future
[171]
, or even the detection of a SSM compact
object.
This material is based upon work supported by
NSF
s LIGO Laboratory which is a major facility fully
funded by the National Science Foundation. The authors
also gratefully acknowledge the support of the Science and
Technology Facilities Council (STFC) of the United
Kingdom, the Max-Planck-Society (MPS), and the State
of Niedersachsen/Germany for support of the construction
of Advanced LIGO and construction and operation of the
GEO600 detector. Additional support for Advanced LIGO
was provided by the Australian Research Council.
The authors gratefully acknowledge the Italian Istituto
Nazionale di Fisica Nucleare (INFN), the French Centre
National de la Recherche Scientifique (CNRS), and the
Netherlands Organization for Scientific Research (NWO),
for the construction and operation of the Virgo detector
and the creation and support of the EGO consortium.
The authors also gratefully acknowledge research
support from these agencies as well as by the Council of
Scientific and Industrial Research of India, the Department
of Science and Technology, India, the Science &
Engineering Research Board (SERB), India, the Ministry
of Human Resource Development, India, the Spanish
Agencia Estatal de Investigación, the Vicepresid`
encia i
Conselleria d
Innovació, Recerca i Turisme and the
Conselleria d
Educació i Universitat del Govern de les
Illes Balears, the Conselleria d
Innovació, Universitats,
Ci`
encia i Societat Digital de la Generalitat Valenciana
and the CERCA Programme Generalitat de Catalunya,
Spain, the National Science Centre of Poland and the
European Union
European Regional Development
Fund; Foundation for Polish Science (FNP), the Swiss
National Science Foundation (SNSF), the Russian
Foundation for Basic Research, the Russian Science
Foundation, the European Commission, the European
Regional Development Funds (ERDF), the Royal Society,
the Scottish Funding Council, the Scottish Universities
Physics Alliance, the Hungarian Scientific Research
Fund (OTKA), the French Lyon Institute of Origins
(LIO), the Belgian Fonds de la Recherche Scientifique
(FRS-FNRS), Actions de Recherche Concert ́
ees (ARC)
and Fonds Wetenschappelijk Onderzoek
Vlaanderen
(FWO), Belgium, the Paris Íle-de-France Region, the
National Research, Development and Innovation Office
Hungary (NKFIH), the National Research Foundation of
Korea, the Natural Science and Engineering Research
Council Canada, Canadian Foundation for Innovation
(CFI), the Brazilian Ministry of Science, Technology,
and Innovations, the International Center for Theoretical
Physics South American Institute for Fundamental
Research (ICTP-SAIFR), the Research Grants Council of
Hong Kong, the National Natural Science Foundation of
China (NSFC), the Leverhulme Trust, the Research
Corporation, the Ministry of Science and Technology
(MOST), Taiwan, the United States Department of
Energy, and the Kavli Foundation. The authors gratefully
acknowledge the support of the NSF, STFC, INFN, and
CNRS for provision of computational resources. Funding
for this project was provided by the Charles E. Kaufman
Foundation of The Pittsburgh Foundation and the Institute
for Computational and Data Sciences at Penn State. This
article has been assigned the document number LIGO-
P2100163-v8.
Note added.
Recently, Ref.
[172]
reported results on a
search for binaries with no spin and component masses
m
1
ð
0
.
1
M
;
7
.
0
M
Þ
,
m
2
ð
0
.
1
M
;
1
.
0
M
Þ
in O3a
data. That search also reported no detections.
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A. D. Huddart,
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B. Hughey,
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V. Hui,
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S. Husa,
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R. Huxford,
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T. Huynh-Dinh,
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B. Idzkowski,
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A. Iess,
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V. JaberianHamedan,
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A. Z. Jan,
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K. Jani,
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J. Janquart,
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N. N. Janthalur,
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A. C. Jenkins,
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M. Llorens-Monteagudo,
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PHYSICAL REVIEW LETTERS
129,
061104 (2022)
061104-10