of 14
Directional limits on persistent gravitational waves using data
from Advanced LIGO
s first two observing runs
B. P. Abbott
etal.
*
(The LIGO Scientific Collaboration and the Virgo Collaboration)
(Received 19 April 2019; published 4 September 2019)
We perform an unmodeled search for persistent, directional gravitational wave (GW) sources using data
from the first and second observing runs of Advanced LIGO. We do not find evidence for any GW signals.
We place limits on the broadband GW flux emitted at 25 Hz from point sources with a power law spectrum
at
F
α
;
Θ
<
ð
0
.
05
25
Þ
×
10
8
erg cm
2
s
1
Hz
1
and the (normalized) energy density spectrum in GWs at
25 Hz from extended sources at
Ω
α
ð
Θ
Þ
<
ð
0
.
19
2
.
89
Þ
×
10
8
sr
1
where
α
is the spectral index of the
energy density spectrum. These represent improvements of
2
.
5
3
× over previous limits. We also consider
point sources emitting GWs at a single frequency, targeting the directions of Sco X-1, SN 1987A, and the
Galactic center. The best upper limits on the strain amplitude of a potential source in these three directions
range from
h
0
<
ð
3
.
6
4
.
7
Þ
×
10
25
,
1
.
5
× better than previous limits set with the same analysis method. We
also report on a marginally significant outlier at 36.06 Hz. This outlier is not consistent with a persistent
gravitational-wave source as its significance diminishes when combining all of the available data.
DOI:
10.1103/PhysRevD.100.062001
I. INTRODUCTION
The stochastic gravitational wave (GW) background
(SGWB) is the superposition of many sources of GWs in
the Universe
[1]
. Anisotropies in the SGWB can be
generated by spatially extended sources such as a population
of neutron stars in the Galactic plane or a nearby galaxy
[2,3]
, or from perturbations in statistically isotropic back-
grounds formed at cosmological distances such as the
compact binary background
[4
9]
or the background from
cosmic strings
[10]
. Cross-correlation based methods have
been used to search for the anisotropic background in pre-
vious observing runs
[11
14]
of the initial and Advanced
Laser Interferomter Gravitational-wave Observatory (LIGO)
[15]
, and future searches will incorporate data from the
Advanced Virgo
[16]
detector. Using very similar techniques,
one can also search for point sources with an unknown phase
evolution, which could include rotating neutron stars in the
Galaxy
[17,18]
. Since a SGWB search is by nature unmod-
eled, performing the anisotropic SGWB search allows us to
take an eyes-wide-open approach to exploring the GW sky.
For an analysis that focuses on searching for an isotropic
SGWB using the same data, see
[19]
.
In this paper, we present the results of three comple-
mentary searches, which probe different types of ani-
sotropy. All of the searches are based on cross-correlation
methods; for a review see
[20]
. A spherical harmonic
decomposition (SHD) of the GW power on the sky
[12,21]
is optimized to search for extended sources on the sky with
a smooth frequency spectrum. The broadband radiometer
analysis
[17,18]
(BBR) is optimized for detecting resolv-
able, persistent point-sources emitting GWs across a wide
frequency band. Finally, the directed narrow band radiom-
eter (NBR) looks at the frequency spectrum for three
astrophysically interesting directions: Scorpius X-1 (Sco
X-1)
[22,23]
, Supernova 1987A (SN 1987A)
[24,25]
, and
the Galactic center
[26,27]
. We do not find a significant
detection for any of the searches, and so we place upper
limits on the amplitude of the anisotropic SGWB, and on
point sources with broad and narrow frequency ranges. Our
upper limits improve on the best results from previous runs
[11]
by approximately a factor of 2.5
3 for the broadband
searches and a factor of 1.5 for the narrow band searches.
For the narrow band radiometer search, we find a margin-
ally significant outlier in the direction of SN 1987A, when
analyzing just the data from LIGO
s second observing run
(O2). Its significance diminishes, however, when including
all of the available data.
II. DATA
We analyze strain data from the first (O1) and second
(O2) observing runs of Advanced LIGO
s 4 km detectors in
Hanford, Washington (H1) and Livingston, Louisiana (L1).
The O1 data set used here was collected from 15
00 UTC
on 18 September, 2015 to 16
00 UTC on 12 January, 2016,
while the O2 data set was collected from 16
00:00 UTC on
30 November, 2016 to 22
00:00 UTC on 25 August, 2017.
In O2, linearly coupled noise was removed from the
strain time series at H1 and L1 using Wiener filtering
[28
32]
. The Virgo (V1) detector started to collect data
*
Full author list given at the end of the article.
PHYSICAL REVIEW D
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=
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=
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=
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© 2019 American Physical Society
from August 2017 but does not contribute significantly to
the sensitivity of SGWB searches in O2, both because its
noise level is much higher than the LIGO detectors and
because it ran for a much shorter period of time. Therefore,
we do not include Virgo in this analysis. We plan, however,
to include Virgo in the analysis of data from future
observation runs.
Our data processing methods follow the procedure used
in O1
[11,33]
. First, we down-sample the strain time series
from 16,384 Hz to 4,096 Hz. We then divide the data into
192 s, 50% overlapping, Hann-windowed segments and
apply a cascading 16th order Butterworth digital high-pass
filter with a knee frequency of 11 Hz. We compute the
cross-correlation of coincident 192 s segments at both
detectors in the frequency domain and then coarse-grain to
a frequency resolution of
1
=
32
Hz. Finally, we optimally
combine results from those overlapping time segments to
produce the final cross-correlation estimate
[34]
.
In order to account for non-Gaussian features in the data,
we remove segments associated with instrumental artifacts
and hardware injections used for signal validation
[35,36]
.
Segments containing known GW signals
[37]
are also
excluded. Finally, we apply a nonstationarity cut (see, e.g.,
[38]
) to eliminate segments where the power spectral
density of the noise changes on time scales that are of
the same order as the chosen segment length. In total these
cuts removed 16% of the data, leading to a total search live
time of 99 days from the O2 run. For our results where we
combine data between the O1 and O2 observing runs we
have a total search live time of 129 days. In addition,
frequency bins associated with known instrumental arti-
facts are removed
[39]
. These frequency domain cuts
discarded 4% of the most sensitive frequency band for
the BBR and SHD searches and 15% of the observing band
for the NBR search. The subtraction of linearly coupled
noise did not introduce any new frequency domain cuts.
The broadband searches integrate over frequencies
between 20 and 500 Hz. This range accounts for more
than 99% of the sensitivity for the power law spectral
models that we use (see Table 1 of
[40]
). The narrow band
analysis searches over the frequency band from 20 to
1726 Hz using frequency bins of various sizes depending
upon frequency and sky direction. The lower edge of this
range is chosen because of increased noise and nonstatio-
narity at lower frequencies, while the upper edge of the
range is a product of the filter used to resample the data
from 16,384 Hz to 4,096 Hz.
III. METHODS
The anisotropic SGWB background can be defined in
terms of the dimensionless energy density
Ω
gw
ð
f;
Θ
Þ
per
unit frequency
f
and solid angle
Θ
,
Ω
gw
ð
f;
Θ
Þ¼
f
ρ
c
d
3
ρ
GW
d
f
d
2
Θ
;
ð
1
Þ
where
ρ
c
¼
3
H
2
0
c
2
=
ð
8
π
G
Þ
is the critical energy density
needed to have a spatially flat universe. We take the Hubble
constant to be
H
0
¼
67
.
9
km s
1
Mpc
1
[41]
. Following
past analyses, we assume that we can factorize
Ω
gw
into
frequency and sky-direction dependent terms,
Ω
gw
ð
f;
Θ
Þ¼
2
π
2
3
H
2
0
f
3
H
ð
f
Þ
P
ð
Θ
Þ
:
ð
2
Þ
This quantity has units of the dimensionless energy
density parameter per steradian. For the radiometer
searches it is useful to define a different representation in
terms of energy flux,
F
ð
f;
Θ
Þ¼
c
3
π
4
G
f
2
H
ð
f
Þ
P
ð
Θ
Þ
;
ð
3
Þ
which has units of erg cm
2
s
1
Hz
1
sr
1
, where
c
is the
speed of light and
G
is Newton
s gravitational constant.
We divide the searches into the
broadband
searches
(SHD and BBR), which produce sky maps where the flux
has been integrated over a broad range of frequencies, and
the
narrow band
search (NBR), which looks at the strain
amplitude spectrum in a fixed sky direction. For the
broadband searches, we typically assume that the energy
spectrum has a power law form,
H
ð
f
Þ¼ð
f=f
ref
Þ
α
3
,
where
α
¼f
0
;
2
=
3
;
3
g
describes a range of astrophysical
and cosmological models
[11]
, and
f
ref
is a reference
frequency which we take to be 25 Hz, as in
[11]
. The SHD
search looks for sources with a large angular extent. We
express the results in terms of the spherical harmonic
decomposition of
Ω
gw
ð
f;
Θ
Þ
assuming a power-law in
frequency of spectral index
α
. We then report the energy
density in each direction at a reference frequency of 25 Hz,
denoted by
Ω
α
ð
Θ
Þ
.
For the BBR search, we assume that the angular
distribution of the power is localized in a
1
deg
2
pixel,
P
ð
Θ
Þ¼
P
Θ
0
δ
2
ð
Θ
;
Θ
0
Þ
. The results of the BBR are then
given in terms of the quantity
F
α
;
Θ
0
, which is the flux
evaluated at the reference frequency of 25 Hz, assuming a
power law, after integrating over solid angle. The explicit
definitions of
F
α
;
Θ
0
and
Ω
α
ð
Θ
Þ
are given in the
Supplemental Material
[42]
.
Finally, the NBR search does not integrate over fre-
quency and attempts to measure the strain amplitude,
h
0
,of
a putative monochromatic source in each frequency bin
independently. This includes combining adjacent 0.031 Hz
frequency bins together to account for the Doppler modu-
lation due to the motion of the Earth around the Solar
System barycenter and any binary motion of the source
itself
[11]
.
The full description of the methods used to search for an
anisotropic SGWB is presented in the Supplemental
Material
[42]
and in the paper describing the analysis of
B. P. ABBOTT
et al.
PHYS. REV. D
100,
062001 (2019)
062001-2
the Advanced LIGO O1 data. We follow the notation
presented in that letter
[11]
.
The searches all generally start by estimating the dirty
map
X
ν
, and its corresponding covariance matrix
Γ
μν
,
referred to here as the Fisher matrix
[11,21,43]
. The dirty
map represents an estimate of the GW power as seen
through the detector
s beam matrix.
Given the Fisher matrix
Γ
I
μν
and dirty map
X
I
ν
, where
I
labels the observing run, we can form a combined Fisher
matrix and dirty map by summing the results from the two
runs, O1 and O2
[20]
,
Γ
μν
¼
Γ
ð
O
1
Þ
μν
þ
Γ
ð
O
2
Þ
μν
;
X
μ
¼
X
ð
O
1
Þ
μ
þ
X
ð
O
2
Þ
μ
:
ð
4
Þ
From the combined Fisher matrix and dirty map, we can
construct estimators of the power on the sky via
ˆ
P
μ
¼
X
ν
ð
Γ
1
R
Þ
μν
X
ν
:
ð
5
Þ
Intheaboveequations,
μ
,
ν
labeleither pixels(i.e.,directions
on the sky) or spherical harmonic components
i.e.,
μ
ð
lm
Þ
, depending on which basis is used to represent
the sky maps. The subscript
R
on the Fisher matrix
means that regularization has been applied (e.g., singular
value decomposition) in order to perform the matrix
inversion
[11]
.
We can also construct an estimate of the angular power
spectrum,
C
l
, for the SGWB from the estimate of the
spherical harmonics coefficients,
ˆ
P
lm
. The
C
l
s describe the
angular scale of the structure found in the clean maps
[21]
,
ˆ
C
l
¼

2
π
2
f
3
ref
3
H
2
0

2
1
1
þ
2
l
X
l
m
¼
l
½j
ˆ
P
lm
j
2
ð
Γ
1
R
Þ
lm;lm

:
ð
6
Þ
We have also used theoretical models for the SGWB
from compact binaries
[4]
and from Nambu-Goto cosmic
strings
[10]
to check our assumption that the SGWB energy
density
Ω
gw
ð
f;
Θ
Þ
can be factorized into a spectral shape
term and an angular power term. We find that both models
predict
C
l
s that follow the appropriate frequency power
laws (
α
¼
2
=
3
for compact binaries and
α
¼
0
for cosmic
strings) across the frequency range in which the LIGO
stochastic searches are most sensitive, thereby supporting
this assumption (see also
[44]
).
IV. RESULTS
A. Broadband radiometer and spherical
harmonic decomposition results
The sky maps for the BBR search are shown in Fig.
1
, and
for the SHD search in Fig.
2
. Converting maps from the
spherical harmonics basis [i.e.,
μ
¼ð
lm
Þ
] to the pixel basis is
discussed in detail in
[21]
. Each column indicates a different
value of the spectral index,
α
. The top row shows a map of
the signal-to-noise ratio (SNR) for each sky direction.
The SNR sky maps are consistent with Gaussian noise
(see the
p
-values given in Table
I
). Consequently, we
place upper limits on the amount of GW power in each
pixel using the methods outlined in
[45]
. The bottom rows of
Figs.
1
and
2
show maps of these upper limits for the BBR
and SHD analyses, respectively. The minimum and maxi-
mum 95% confidence upper limits across all pixels for both
the BBRandSHD searchesareshowninTable
I
.Theselimits
representamedianimprovementacrossthe skyof2.6
2.7for
the BBR search and 2.8
3 for the SHD search, depending on
the power-law spectral index,
α
.
B. Limits on angular power spectra
We also use the maps from the SHD analysis to set upper
limits on the angular power spectrum components,
C
l
.
FIG. 1. Broadband radiometer maps illustrating a search for pointlike sources. The top row shows maps of SNR, while the bottom row
shows maps of the upper limits at 95% confidence on energy flux
F
α
;
Θ
0
[erg cm
2
s
1
Hz
1
]. Three different power-law indices,
α
¼
0
,
2
=
3
and 3, are represented from left to right. The
p
-values associated with the maximum SNR are (from left to right)
p
¼
9%
,
p
¼
20%
,
p
¼
66%
(see Table
I
).
DIRECTIONAL LIMITS ON PERSISTENT GRAVITATIONAL
...
PHYS. REV. D
100,
062001 (2019)
062001-3
The upper limits are shown for three spectral indices in
Fig.
3
. The upper limit for
α
¼
2
=
3
can be compared with
theoretical predictions in the literature for the SGWB from
compact binaries
[4,6,46]
. In particular, the calculation in
Refs.
[4,46]
gives
C
1
=
2
l
3
×
10
11
sr
1
for
1
l
4
(the
calculation in Ref.
[6]
gives values that are
10
× smaller).
Similarly, the upper limit for
α
¼
0
can be compared with
predictions for the SGWB from Nambu-Goto cosmic
strings in Ref.
[10]
, using the same models for the string
network as in Ref.
[47]
. Assuming the isotropic component
of the cosmic string SGWB is consistent with the upper
limits set by LIGO
s second observing run
[40]
, the dipole
(
l
¼
1
) can be as large as
C
1
=
2
1
10
10
sr
1
, though the
values for higher multipoles
l>
1
are many orders of
magnitude smaller. These predictions are therefore con-
sistent with the upper limits obtained here and present an
important target for future observing runs.
Looking forward towards the prospect of detection, it is
important to note that the finite sampling of the Galaxy
distribution and the compact binary coalescence event rate
induces a shot noise in the anisotropies of the astrophysical
GW background. As it has been recently shown
[48]
this
shot noise leads to a scale-invariant bias term in the angular
power spectrum
C
l
and it scales with observing time.
Such a bias will dominate over the true cosmological power
spectrum, which to be recovered will need either
sufficiently long observing times or subtraction of the
foreground.
C. Narrow band radiometer results
The narrow band radiometer search estimates the strain
amplitude,
h
0
, of a potential source of GWs in three
different directions. The maximum SNR across the fre-
quency band and an estimate of the significance of that
FIG. 2. All-sky maps reconstructed from a spherical harmonic decomposition. This search is optimized for extended sources, and the
plots above show SNR (top) and upper limits at 95% confidence on the energy density of the SGWB
Ω
α
[sr
1
] (bottom). Results for
three different power-law spectral indices,
α
¼
0
,
2
=
3
and 3 are shown from left to right. These three different sets of maps have an
l
max
of 3, 4, and 16 respectively. The
p
-values associated with the maximum SNR are (from left to right)
p
¼
9%
,
p
¼
31%
,
p
¼
27%
(see
Table
I
).
TABLE I. Search information for BBR and SHD. On the left side of the table we show the value of the power-law spectral index,
α
,
and the scaling of
Ω
gw
and
H
ð
f
Þ
with frequency. To the right we show results for the broadband radiometer (BBR) and spherical
harmonic decomposition (SHD) searches for the combined O1 and O2 analysis, as well as the results from O1 for comparison. We show
the maximum SNR across all sky positions for each spectral index, as well as an estimated
p
-value. We also show the range of 95%
upper limits on energy flux set by the BBR search across the whole sky [erg cm
2
s
1
Hz
1
] and the SHD range of upper limits on
normalized energy density across the whole sky [sr
1
]. These limits use data from both O1 and O2. The median improvement across the
sky compared to limits set in O1 is 2.6
2.7 for the BBR search and 2.8
3 for the SHD search, depending on power-law spectral index.
All-sky (broadband) results
Max SNR (%
p
-value)
Upper limit ranges
O1 Upper limit ranges
α
Ω
gw
H
ð
f
Þ
BBR
SHD
BBR (×
10
8
)SHD(×
10
8
) BBR (×
10
8
) SHD (×
10
8
)
0
constant
f
3
3.09 (9)
2.98 (9)
4.4
25
0.78
2.90
15
65
3.2
8.7
2
=
3
f
2
=
3
f
7
=
3
3.09 (20)
2.61 (31)
2.3
14
0.64
2.47
7.9
39
2.5
6.7
3
f
3
constant
3.27 (66)
3.57 (27)
0.05
0.33
0.19
1.1
0.14
1.1
0.5
3.1
B. P. ABBOTT
et al.
PHYS. REV. D
100,
062001 (2019)
062001-4
SNR for each direction are shown in Table
II
. The
uncertainty on the frequency for the SNR reported in
Table
II
is a reflection of the original (uncombined)
frequency bin width. The ephemeris for Scorpius X-1
has been updated since the publication of
[11]
, and so
the search presented below assumes a projected semimajor
axis,
a
0
, in the center of the range presented by
[49]
.
In the direction of Sco X-1 and the Galactic center, the
maximum SNR is consistent with what one expects from
Gaussian noise. In the direction of SN 1987A, there is a
frequency bin with a 1-sided, single-direction
p
-value 1.7%
at 181.8 Hz. This
p
-value includes a trials factor for the
number of frequency bins in the analysis. Under the
assumption that we search over three independent direc-
tions, an extra trials factor would be applied and this
p
-value
rises to 5%. Therefore, we find no compelling evidence for
GWs from the analysis that combines frequency bins
together. We set 95% upper limits on the strain amplitude
of a putative sinusoidal gravitational wave signal,
h
0
, in each
individual frequency bin, taking into account any Doppler
modulation in the signal as well as marginalizing over
inclination angle and polarization angle of the source
[11]
.
These limits, along with the
1
σ
sensitivity of the search, are
shown in Fig.
4
. To avoid reporting our best limits from
downward fluctuations of noise, we take a running median
over each1 Hz frequency band and report the best limit on
h
0
and the frequency band of that limit in Table
II
.
The best limits on Sco-X1 set in this paper are higher
than the best limit set in O1 using a model-based
cross-correlation method
[22]
and are now lower than
those set using hidden Markov model tracking
[23]
. The
torque-balance limit, set by assuming that torque due to
accretion is equal to the braking torque due to GW
emission, is still around a factor of 5 lower than the limits
set in this paper. The best limits on
h
0
in the direction
of the Galactic center and SN 1987A are generally higher
than previous modeled searches for isolated neutron stars
[24,26,27,50,51]
in the frequency bands where those
analyses overlap with the one presented here. This search
spans a wider frequency band (20
1726 Hz) than any one
of those individual analyses. It is important to note that the
search presented in this paper is inherently unmodeled,
meaning it makes no assumption about the phase evolution
of a potential signal past time scales of 192 s.
V. OUTLIER AT 36.06 Hz IN THE O2 DATA
In the process of performing the narrow band radiometer
search, a natural intermediate step of the analysis is to look
directly at the 0.03125 Hz bins for the O2 data, before
combining with O1 and before combining over adjacent
bins to account for Doppler modulation. We call these
sub-
bins
. For this intermediate data product, the maximum
SNRs for the Galactic center, Sco X-1, and SN 1987A are
4.6, 4.3, and 5.3, respectively. These first two values
correspond to
p
-values greater than 5%, consistent with
Gaussian noise. But for SN 1987A, the maximum SNR of
5.3 at 36.0625 Hz has a corresponding
p
-value of 0.27%, or
3
σ
, which is marginally significant.
Assuming that the maximum SNR is due to a pulsar
which is spinning down due to GW emission, we can relate
the observed strain
h
0
¼
7
.
3
×
10
25
(assuming circular
polarization) at
f
¼
36
.
06
Hz to other parameters describ-
ing the pulsar,
h
0
¼
4
π
G
c
4
ε
I
z
f
2
r
;
_
f
¼
G
5
π
c
5
ε
2
I
z
ð
2
π
f
Þ
5
:
ð
7
Þ
We use a fiducial value for the moment of inertia
I
z
¼
10
39
kg m
2
. If the source is associated with SN
1987A, then the distance to Earth is approximately
r
¼
51
kpc
[52,53]
, leading to an ellipticity
ε
¼
3
×
10
2
and
spin down
_
f
¼
7
.
7
×
10
8
Hz
=
s. But this value of the
spin down parameter is inconsistent with the fact that the
FIG. 3. Upper limits on
C
l
s at 95% confidence for the SHD
analyses for
α
¼
0
(top, black triangles),
α
¼
2
=
3
(middle, red
circles) and
α
¼
3
(bottom, blue squares). These represent an
improvement in upper limits over O1 of 2.5
3 depending on
spectral index,
α
, and
l
.
TABLE II. Results for the narrow band radiometer search. We give the maximum SNR, corresponding
p
-value, and the frequency bin
of the maximum SNR for each direction in which we searched. We also give the best 95% GW strain upper limits achieved, and the
corresponding frequency band, for all three sky locations. The best upper limits are taken as the median of the most sensitive 1 Hz band.
Narrow band radiometer results
Direction
Max SNR
p
-value (%)
Frequency (Hz) (

0
.
016
Hz)
Best UL (×
10
25
)
Frequency band (Hz)
Sco X-1
4.80
4.5
1602.09
4.2
183.6
184.6
SN 1987A
4.95
1.7
181.81
3.6
247.75
248.75
Galactic center
3.80
98
20.28
4.7
156.8
157.8
DIRECTIONAL LIMITS ON PERSISTENT GRAVITATIONAL
...
PHYS. REV. D
100,
062001 (2019)
062001-5
signal is seen in only one frequency bin. For the signal to
remain in a single frequency bin, it either needs to have
some balancing torque, perhaps from accretion
[54]
, or the
signal would need to be at
r
1
kpc (corresponding to
_
f
¼
2
.
9
×
10
11
Hz
=
s). In the latter case, the ellipticity
ε
¼
5
×
10
4
is still much larger than that predicted for
typical pulsars. An ellipticity this large is unlikely to be
caused by elastic deformations
[55]
, but could in principle
be caused by large internal magnetic fields
[56
58]
,
especially if the protons form a type II superconductor
[59]
. It is important to note that an all-sky search for
continuous GWs from isolated systems has set limits more
stringent than our estimate of
h
0
for this outlier
[51]
.
Using the techniques described in
[39]
, we have not been
able to identify a coherent instrumental witness channel
that would explain this large SNR. But the fact that the sky
direction of the maximum SNR is close to the equatorial
pole is consistent with the behavior of instrumental noise
lines, since the equatorial poles have no sidereal-time
modulation. The signal appears to turn on during O2, with
the SNR exceeding 1 on March 13th, 2017, as shown in
Fig.
5
. In addition, the signal does not exhibit any
significant short-term nonstationarity, indicating that this
outlier is not generated from a small number of misbehaved
time chunks with large SNRs. The turn-on feature of the
cumulative SNR is not evidence of a real signal, however,
as we have performed simulations of Gaussian noise
conditioned on getting a maximum SNR
5
and have
found examples where a turn-on like this can be produced.
In addition, upon combining O2 and O1 data together, the
SNR of this frequency bin is reduced to 4.7, which
corresponds to a
p
-value of 10%, which is consistent
with noise.
VI. CONCLUSIONS
We have placed upper limits on the anisotropic SGWB
using three complementary methods. In each case we do
not find conclusive evidence for a GW signal, and so we
place upper limits by combining data from Advanced
LIGO
s first and second observing runs. A marginal outlier
at a frequency of 36.06 Hz was seen by the narrow band
radiometer search in O2 in the direction of SN 1987A;
however it does not appear in the combined O1+O2 data
and is not consistent with a persistent signal. We will
continue to monitor this particular frequency bin during the
next observing run, taking advantage of the greater con-
fidence that comes with increased observation periods and
more sensitive detectors.
In the future, the anisotropic searches will include data
from Advanced Virgo as well and can be used to study
specific astrophysical models. Additionally, new algo-
rithms can take advantage of folded data to produce a
wider search of every frequency and sky position
[60
63]
.
ACKNOWLEDGMENTS
The authors gratefully acknowledge the support of the
United States National Science Foundation (NSF) for the
construction and operation of the LIGO Laboratory and
FIG. 4. Upper limit spectra using data from O1 and O2 on the dimensionless strain amplitude,
h
0
, at the 95% level for the narrow band
radiometer search are indicated by the gray bands for Sco X-1 (left), SN 1987A (middle) and the Galactic center (right). The dark black
line indicates the
1
σ
sensitivity of the search in all three directions. The large spikes are the result of the calibration lines injected into the
detector and suspension-wire resonances for various optical elements throughout the instruments.
FIG. 5. The accumulation of SNR as a function of time for SN
1987a, including both O1 and O2 data. The curve shows the
observed cumulative SNR in the 36.06 Hz frequency bin. The
green arrows indicate the point where the SNR moves above 1 for
the remainder of the available observation time.
B. P. ABBOTT
et al.
PHYS. REV. D
100,
062001 (2019)
062001-6
Advanced LIGO as well as 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 Foundation
for Fundamental Research on Matter supported by the
Netherlands Organisation for Scientific Research, 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 and Engineering Research
Board (SERB), India, the Ministry of Human Resource
Development, India, the Spanish Agencia Estatal de Inves-
tigación, 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
Educació, Investigació, Cultura i Esport de
la Generalitat Valenciana, the National Science Centre of
Poland, the Swiss National Science Foundation (SNSF), the
RussianFoundationfor Basic Research,the RussianScience
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 Lyon Institute of Origins (LIO), the Paris Île-
de-France Region, the National Research, Development and
Innovation Office Hungary (NKFIH), the National Research
Foundation of Korea, Industry Canada and the Province of
OntariothroughtheMinistry ofEconomicDevelopmentand
Innovation, the Natural Science and Engineering Research
Council Canada, the Canadian Institute for Advanced
Research, the Brazilian Ministry of Science, Technology,
Innovations, and Communications, 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 and the Kavli Foundation.
The authors gratefully acknowledge the support of the NSF,
STFC, MPS, INFN, CNRS and the State of Niedersachsen/
Germany for provision of computational resources.
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M. Davier,
25
D. Davis,
41
E. J. Daw,
107
D. DeBra,
48
M. Deenadayalan,
3
J. Degallaix,
22
M. De Laurentis,
78,5
S. Del ́
eglise,
70
W. Del Pozzo,
18,19
L. M. DeMarchi,
58
N. Demos,
12
T. Dent,
8,9,108
R. De Pietri,
109,56
J. Derby,
26
R. De Rosa,
78,5
C. De Rossi,
22,28
R. DeSalvo,
110
O. de Varona,
8,9
S. Dhurandhar,
3
M. C. Díaz,
103
T. Dietrich,
36
L. Di Fiore,
5
M. Di Giovanni,
111,95
T. Di Girolamo,
78,5
A. Di Lieto,
18,19
B. Ding,
99
S. Di Pace,
112,31
I. Di Palma,
112,31
F. Di Renzo,
18,19
A. Dmitriev,
11
Z. Doctor,
89
F. Donovan,
12
K. L. Dooley,
67,84
S. Doravari,
8,9
I. Dorrington,
67
T. P. Downes,
23
M. Drago,
14,15
J. C. Driggers,
44
Z. Du,
82
J.-G. Ducoin,
25
P. Dupej,
43
I. Dvorkin,
35
S. E. Dwyer,
44
P. J. Easter,
6
T. B. Edo,
107
M. C. Edwards,
93
A. Effler,
7
P. Ehrens,
1
J. Eichholz,
1
S. S. Eikenberry,
47
M. Eisenmann,
32
R. A. Eisenstein,
12
R. C. Essick,
89
H. Estelles,
98
D. Estevez,
32
Z. B. Etienne,
38
T. Etzel,
1
M. Evans,
12
T. M. Evans,
7
V. Fafone,
29,30,14
H. Fair,
41
S. Fairhurst,
67
X. Fan,
82
S. Farinon,
59
B. Farr,
69
W. M. Farr,
11
E. J. Fauchon-Jones,
67
M. Favata,
34
M. Fays,
107
M. Fazio,
113
C. Fee,
114
J. Feicht,
1
M. M. Fejer,
48
F. Feng,
27
A. Fernandez-Galiana,
12
I. Ferrante,
18,19
E. C. Ferreira,
13
T. A. Ferreira,
13
F. Ferrini,
28
F. Fidecaro,
18,19
I. Fiori,
28
D. Fiorucci,
27
M. Fishbach,
89
R. P. Fisher,
41,115
J. M. Fishner,
12
M. Fitz-Axen,
42
R. Flaminio,
32,116
M. Fletcher,
43
E. Flynn,
26
H. Fong,
117
J. A. Font,
20,118
P. W. F. Forsyth,
21
J.-D. Fournier,
64
S. Frasca,
112,31
F. Frasconi,
19
Z. Frei,
105
A. Freise,
11
R. Frey,
69
V. Frey,
25
P. Fritschel,
12
V. V. Frolov,
7
P. Fulda,
47
M. Fyffe,
7
H. A. Gabbard,
43
B. U. Gadre,
3
S. M. Gaebel,
11
J. R. Gair,
119
L. Gammaitoni,
39
M. R. Ganija,
54
S. G. Gaonkar,
3
A. Garcia,
26
C. García-Quirós,
98
F. Garufi,
78,5
B. Gateley,
44
S. Gaudio,
33
G. Gaur,
120
V. Gayathri,
121
G. Gemme,
59
E. Genin,
28
A. Gennai,
19
D. George,
17
J. George,
60
L. Gergely,
122
V. Germain,
32
S. Ghonge,
76
Abhirup Ghosh,
16
Archisman Ghosh,
36
S. Ghosh,
23
B. Giacomazzo,
111,95
J. A. Giaime,
2,7
K. D. Giardina,
7
A. Giazotto,
19
,
K. Gill,
33
G. Giordano,
4,5
L. Glover,
110
P. Godwin,
86
E. Goetz,
44
R. Goetz,
47
B. Goncharov,
6
G. González,
2
J. M. Gonzalez Castro,
18,19
A. Gopakumar,
123
M. L. Gorodetsky,
61
S. E. Gossan,
1
M. Gosselin,
28
R. Gouaty,
32
A. Grado,
124,5
C. Graef,
43
M. Granata,
22
A. Grant,
43
S. Gras,
12
P. Grassia,
1
C. Gray,
44
R. Gray,
43
G. Greco,
71,72
A. C. Green,
11,47
R. Green,
67
E. M. Gretarsson,
33
P. Groot,
63
H. Grote,
67
S. Grunewald,
35
P. Gruning,
25
G. M. Guidi,
71,72
H. K. Gulati,
106
Y. Guo,
36
A. Gupta,
86
M. K. Gupta,
106
E. K. Gustafson,
1
R. Gustafson,
125
L. Haegel,
98
O. Halim,
15,14
B. R. Hall,
68
E. D. Hall,
12
E. Z. Hamilton,
67
G. Hammond,
43
M. Haney,
65
M. M. Hanke,
8,9
J. Hanks,
44
C. Hanna,
86
O. A. Hannuksela,
90
J. Hanson,
7
T. Hardwick,
2
K. Haris,
16
J. Harms,
14,15
G. M. Harry,
126
I. W. Harry,
35
C.-J. Haster,
117
K. Haughian,
43
F. J. Hayes,
43
J. Healy,
57
A. Heidmann,
70
M. C. Heintze,
7
H. Heitmann,
64
P. Hello,
25
G. Hemming,
28
M. Hendry,
43
I. S. Heng,
43
J. Hennig,
8,9
A. W. Heptonstall,
1
Francisco Hernandez Vivanco,
6
M. Heurs,
8,9
S. Hild,
43
T. Hinderer,
127,36,128
D. Hoak,
28
S. Hochheim,
8,9
D. Hofman,
22
A. M. Holgado,
17
N. A. Holland,
21
K. Holt,
7
D. E. Holz,
89
P. Hopkins,
67
C. Horst,
23
J. Hough,
43
E. J. Howell,
62
C. G. Hoy,
67
A. Hreibi,
64
E. A. Huerta,
17
D. Huet,
25
B. Hughey,
33
M. Hulko,
1
S. Husa,
98
S. H. Huttner,
43
T. Huynh-Dinh,
7
B. Idzkowski,
73
A. Iess,
29,30
C. Ingram,
54
R. Inta,
83
G. Intini,
112,31
B. Irwin,
114
H. N. Isa,
43
J.-M. Isac,
70
M. Isi,
1
B. R. Iyer,
16
K. Izumi,
44
T. Jacqmin,
70
S. J. Jadhav,
129
K. Jani,
76
N. N. Janthalur,
129
P. Jaranowski,
130
A. C. Jenkins,
131
J. Jiang,
47
D. S. Johnson,
17
A. W. Jones,
11
D. I. Jones,
132
R. Jones,
43
R. J. G. Jonker,
36
L. Ju,
62
J. Junker,
8,9
C. V. Kalaghatgi,
67
V. Kalogera,
58
B. Kamai,
1
S. Kandhasamy,
84
G. Kang,
37
J. B. Kanner,
1
S. J. Kapadia,
23
S. Karki,
69
K. S. Karvinen,
8,9
R. Kashyap,
16
M. Kasprzack,
1
S. Katsanevas,
28
DIRECTIONAL LIMITS ON PERSISTENT GRAVITATIONAL
...
PHYS. REV. D
100,
062001 (2019)
062001-9