First narrow-band search for continuous gravitational waves from known
pulsars in advanced detector data
B. P. Abbott
etal.
*
(LIGO Scientific Collaboration and Virgo Collaboration)
(Received 6 October 2017; published 28 December 2017)
Spinning neutron stars asymmetric with respect to their rotation axis are potential sources of
continuous gravitational waves for ground-based inte
rferometric detectors. In the case of known pulsars a
fully coherent search, based on matched filtering
, which uses the position and rotational parameters
obtained from electromagnetic observations, can be carried out. Matched filtering maximizes the signal-
to-noise (SNR) ratio, but a large sensitivity loss is expected in case of even a very small mismatch
between the assumed and the true signal parameters. For this reason,
narrow-band
analysis methods have
been developed, allowing a fully coherent search for gravitational waves from known pulsars over a
fraction of a hertz and several spin-down values. In this paper we describe a narrow-band search of
11 pulsars using data from Advanced LIGO
’
s first observing run. Although we have found several initial
outliers, further studies show no significant evidence for the presence of a gravitational wave signal.
Finally, we have placed upper limits on the signal strain amplitude lower than the spin-down limit for 5 of
the 11 targets over the bands searched; in the case of J
1813-1749 the spin-down limit has been beaten for
the first time. For an additional 3 targets, the media
n upper limit across the search bands is below the
spin-down limit. This is the most sensitive narrow-band search for continuous gravitational waves carried
out so far.
DOI:
10.1103/PhysRevD.96.122006
I. INTRODUCTION
On September 14, 2015, the gravitational wave (GW)
signal emitted by a binary black hole merger was detected
by the LIGO interferometers (IFOs)
[1]
followed on
December 26, 2015, by the detection of a second event
again associated to a binary black hole merger
[2]
, thus
opening the era of gravitational waves astronomy. More
recently, the detection of a third binary black hole merger
on January 4, 2017, was announced
[3]
. Binary black hole
mergers, however, are not the only detectable sources of
GW. Among the potential sources of GW there are also
spinning neutron stars (NS) asymmetric with respect to
their rotation axis. These sources are expected to emit
nearly monochromatic continuous waves (CW), with a
frequency at a given fixed ratio with respect to the star
’
s
rotational frequency, e.g. two times the rotational frequency
for an asymmetric NS rotating around one of its principal
axes of inertia. Different flavors of CW searches exist,
depending on the degree of knowledge on the source
parameters.
Targeted
searches assume source position
and rotational parameters to be known with high accuracy,
while
all-sky
searches aim at neutron stars with no observed
electromagnetic counterpart. Various intermediate searches
have also been developed. Among these,
narrow-band
searches are an extension of targeted searches for which the
position of the source is accurately known but the rotational
parameters are slightly uncertain. Narrow-band searches
allow for a possible small mismatch between the GW
rotational parameters and those inferred from electromag-
netic observations. This can be crucial if, for instance, the
CW signal is emitted by a freely precessing neutron star
[4]
,
or in the case no updated ephemeris is available for a given
pulsar. In both cases a targeted search could assume wrong
rotational parameters, resulting in a significant sensitivity
loss. In this paper we present the results of a fully coherent,
narrow-band search for 11 known pulsars using data from
the first observation run (O1) of the Advanced LIGO
detectors
[5]
. The paper is organized as follows. In
Sec.
II
we briefly summarize the main concepts of the
analysis. Section
III
is dedicated to an outline of the
analysis method. Section
IV
describes the selected pulsars.
In Sec.
V
we discuss the analysis results, while the reader
can refer to the Appendix for some technical details on the
computation of upper limits. Finally, Sec.
VI
is dedicated to
the conclusions and future prospects.
II. BACKGROUND
The GW signal emitted by an asymmetric spinning NS
can be written, following the formalism first introduced in
[6]
, as the real part of
h
ð
t
Þ¼
H
0
ð
H
þ
A
þ
ð
t
Þþ
H
×
A
×
ð
t
ÞÞ
e
2
π
if
gw
ð
t
Þ
t
þ
i
φ
0
ð
1
Þ
where
f
gw
ð
t
Þ
is the GW frequency,
φ
0
an initial phase. The
polarization amplitudes
H
þ
;H
×
are given by
*
Full author list given at the end of the article.
PHYSICAL REVIEW D
96,
122006 (2017)
2470-0010
=
2017
=
96(12)
=
122006(20)
122006-1
© 2017 American Physical Society
H
þ
¼
cos
ð
2
ψ
Þ
−
i
η
sin
ð
2
ψ
Þ
ffiffiffiffiffiffiffiffiffiffiffiffiffi
1
þ
η
2
p
;
H
×
¼
sin
ð
2
ψ
Þ
−
i
η
cos
ð
2
ψ
Þ
ffiffiffiffiffiffiffiffiffiffiffiffiffi
1
þ
η
2
p
;
η
being the ratio of the polarization ellipse semiminor to
semimajor axis and
ψ
the polarization angle, defined as the
direction of the major axis with respect to the celestial
parallel of the source (measured counterclockwise). The
detector
sidereal response
to the GW polarizations is
encoded in the functions
A
þ
ð
t
Þ
;A
×
ð
t
Þ
. It can be shown
that the waveform defined by Eq.
(1)
is equivalent to the
GW signal expressed in the more standard formalism of
[7]
,
given by the following relations:
η
¼
−
2
cos
ι
1
þ
cos
2
ι
;
ð
2
Þ
where
ι
is the angle between the line of sight and the star
rotation axis, and
H
0
¼
h
0
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1
þ
6
cos
2
ι
þ
cos
4
ι
4
r
ð
3
Þ
with
h
0
¼
1
d
4
π
2
G
c
4
I
zz
f
2
gw
ε
;
ð
4
Þ
where
d; I
zz
and
ε
are respectively the star
’
s distance, its
moment of inertia with respect to the rotation axis and the
ellipticity
, which measures the star
’
s degree of asymmetry.
The signal at the detector is not monochromatic; i.e. the
frequency
f
gw
ð
t
Þ
in Eq.
(1)
is a function of time. In fact the
signal is modulated by several effects, such as the
Römer
delay
due to the detector motion and the source
’
s intrinsic
spin-down due to the rotational energy loss from the source.
In order to recover all the signal-to-noise ratio all these
effects must be properly taken into account. If we have a
measure of the pulsar rotational frequency
f
rot
, frequency
derivative
_
f
rot
and distance
d
, the GW signal amplitude can
be constrained, assuming that all the rotational energy is
lost via gravitational radiation. This strict upper limit,
called the
“
spin-down limit,
”
is given by
[8]
h
sd
¼
8
.
06
×
10
−
19
I
1
=
2
38
1
kpc
d
_
f
rot
Hz
=
s
1
=
2
Hz
f
rot
1
=
2
ð
5
Þ
where
I
38
is the star
’
s moment of inertia in units of
10
38
kgm
2
. The corresponding spin-down limit on the
star
’
s equatorial fiducial ellipticity can be easily obtained
from Eq.
(4)
:
ε
sd
¼
0
.
237
I
−
1
38
h
sd
10
−
24
Hz
f
rot
2
d
1
kpc
:
ð
6
Þ
Even in the absence of a detection, establishing an
amplitude upper limit below the spin-down limit for a
given source is an important milestone, as it allows us to put
a nontrivial constraint on the fraction of rotational energy
lost through GWs.
III. THE ANALYSIS
The results discussed in this paper have been obtained by
searching for CW signals from 11 known pulsars using data
from the O1 run from the Advanced LIGO detectors
[Hanford (LIGO H) and Livingston (LIGO L) jointly].
The run started on September 12, 2015, at 01
∶
25:03 UTC
and 18
∶
29:03 UTC, respectively, and finished on January 19,
2016, at 17
∶
07:59. LIGO H had a duty cycle of
∼
60%
and
LIGO L had a duty cycle of
∼
51%
, which correspond
respectively to 72 and 62 days of science data available for
the analysis. In this paper we have used an initial calibration
of the data
[9]
. In order to perform a joint search between the
two detectors a common period from September 13, 2015, to
January 12, 2016,
1
with a total observation time of about
T
obs
≈
121
days is selected. The natural frequency and spin-
down grid spacings of the search are
δ
f
¼
1
=T
obs
≈
9
.
5
×
10
−
8
Hz and
δ
_
f
¼
1
=T
2
obs
≈
4
.
57
×
10
−
15
Hz
=
s. A
follow-up analysis based on the LIGO
’
s second observation
run (O2) has been carried out. For this data set we have
analyzed data from December 16, 2016, to May 8, 2017;
more details will be given in Appendix
C
. The analysis
pipeline consists of several steps, schematically depicted in
Fig.
1
, which we summarize here. The starting point is a
FIG. 1. Simplified flowchart of the narrow-band search pipeline for CW. The method relies on the use of FFTs to simultaneously compute
the detection statistic, for each given spin-down value, over the full explored frequency range. See
[13]
for more details on the method.
1
An exception is pulsar J
0205
þ
6449
; see later.
B. P. ABBOTT
et al.
PHYSICAL REVIEW D
96,
122006 (2017)
122006-2
collection of FFTs obtained from several interlaced data
chunks [the short FFT Database (SFDB)] built from cali-
brated detector data chunks of duration 1024 seconds
[10]
.
At this stage, a first cleaning procedure is applied to the data
in order to remove large, short-duration disturbances, that
could reduce the search sensitivity. A frequency band is then
extracted from the SFDBs covering typically a range larger
(of the order of a factor of 2) than the frequency region
analyzed in the narrow-band search. The actual search
frequency and spin-down bands,
Δ
f
and
Δ
_
f
, around the
reference values,
f
0
and
_
f
0
, have been chosen according to
the following relations
[11]
:
Δ
f
¼
2
f
0
δ
ð
7
Þ
Δ
_
f
¼
2
_
f
0
δ
;
ð
8
Þ
δ
being a factor parametrizing a possible discrepancy
between the GW rotation parameters and those derived
from electromagnetic observations. Previous narrow-band
searches used values of
δ
of the order
∼
O
ð
10
−
4
Þ
, motivated
partly by astrophysical considerations
[4]
, and partly by
computational limitations
[12]
. Here we exploit the high
computation efficiency of our pipeline to enlarge the search
somewhat, depending on the pulsar, to a range between
δ
∼
10
−
4
and
10
−
3
. The frequency and spin-down ranges
explored in this analysis are listed in Table
I
.
The narrow-band search is performed using a pipeline
based on the
five-vector method
[12]
and, in particular, its
latest implementation, fully described in
[13]
, to which the
reader is referred for more details. The basic idea is that of
exploring a range of frequency and spin-down values by
properly applying barycentric and spin-down corrections to
the data in such a way that a signal would become
monochromatic apart from the sidereal modulation.
While a single barycentric correction applied in the time
domain holds for all the explored frequency bands, several
spin-down corrections, one for each point in the spin-down
grid, are needed. A detection statistic (DS) is then com-
puted for each point of the explored parameter space. By
using the FFT algorithm for each given spin-down value it
is possible to compute the statistic simultaneously over the
whole range of frequencies; this process is done for each
detector, and then data are combined. The frequency/
spin-down plane is then divided into frequency subbands
(
10
−
4
Hz) and, for each of them, the local maximum, over
TABLE II. Distance and spin-down limit on the GW amplitude
and ellipticity for the 11 selected pulsars. Distance and spin-down
limit uncertainties refer to the
1
σ
confidence level.
Name
Distance (kpc)
h
sd
×
10
−
25
ε
sd
×
10
−
4
J
0205
þ
6449
a
2
.
0
0
.
3
b
6
.
9
1
.
1
14
J
0534
þ
2200
(Crab)
2
.
0
0
.
5
c
14
3
.
5
7.6
J0835-4510 (Vela)
0
.
28
0
.
02
c
34
2
.
4
18
J1400-6326
10
3
d
0
.
90
0
.
27
2.1
J1813-1246
>
2
.
5
e
<
1
.
8
<
2
.
4
J1813-1749
4
.
8
0
.
3
f
3
.
0
0
.
2
7.0
J1833-1034
4
.
8
0
.
4
g
3
.
1
0
.
3
13
J
1952
þ
3252
3
.
0
0
.
5
h
1
.
0
0
.
2
1.1
J
2022
þ
3842
10
2
i
1
.
0
0
.
3
6.0
J
2043
þ
2740
1
.
5
0
.
6
j
6
.
9
2
.
8
23
J
2229
þ
6114
3
.
0
2
c
3
.
4
2
.
2
6.2
a
This pulsar had a glitch on November 11, 2015.
b
Distance from neutral hydrogen absorption of pulsar wind
nebula 3C 58
[14]
.
c
Distance taken from independent measures reported in the
ATNF catalog; see text for references.
d
Distance from dispersion measures
[15]
.
e
Lower limit of
[16]
.
f
Distance from Chandra and XMM-Newton from
[17]
.
g
Distance from the Parkes telescope
[18]
.
h
Distance from the kinematic distance of the associated
supernova remnant
[19]
.
i
Distance of the hosting supernova remnant
[20]
. In some
papers a distance value of
∼
10
kpc is considered
[21]
.
j
Distances taken from v1.56 of the ATNF Pulsar Catalog
[22]
.
TABLE I. This table reports the explored range for the rotational parameters of each pulsar. The columns are the central frequency of
the search (
f
0
), explored frequency band (
Δ
f
), central spin-down value of the search (
_
f
0
), explored spin-down band (
Δ
_
f
0
), the number
of frequency bins explored (
n
f
), and the number of spin-down values explored (
n
_
f
). All the rotational parameters are scaled at the
common reference time on September 12, 2015.
Name
f
0
(Hz)
Δ
f
(Hz)
_
f
0
(Hz
=
s)
Δ
_
f
(Hz
=
s)
n
f
n
_
f
J
0205
þ
6449
30.4095820
0.03
−
8
.
9586
×
10
−
11
1
.
75
×
10
−
13
2
.
5
×
10
6
19
J
0534
þ
2200
(Crab)
59.32365204
0.10
−
7
.
3883
×
10
−
10
1
.
48
×
10
−
12
18
.
5
×
10
6
161
J0835-4510 (Vela)
22.3740981
0.03
−
3
.
1191
×
10
−
11
6
.
43
×
10
−
14
2
.
5
×
10
6
7
J1400-6326
64.1253722
0.07
−
8
.
0017
×
10
−
11
1
.
75
×
10
−
13
6
.
5
×
10
6
19
J1813-1246
41.6010333
0.04
−
1
.
2866
×
10
−
11
6
.
43
×
10
−
14
3
.
4
×
10
6
7
J1813-1749
44.7128464
0.05
−
1
.
5000
×
10
−
10
3
.
03
×
10
−
13
2
.
5
×
10
6
33
J1833-1034
32.2940958
0.04
−
1
.
0543
×
10
−
10
2
.
11
×
10
−
13
3
.
4
×
10
6
23
J
1952
þ
3252
50.5882336
0.05
−
7
.
4797
×
10
−
12
6
.
43
×
10
−
14
4
.
3
×
10
6
7
J
2022
þ
3842
41.1600845
0.04
−
7
.
2969
×
10
−
11
1
.
60
×
10
−
13
3
.
4
×
10
6
17
J
2043
þ
2740
20.8048628
0.05
−
3
.
4390
×
10
−
11
6
.
43
×
10
−
14
4
.
3
×
10
6
7
J
2229
þ
6114
38.7153156
0.06
−
5
.
8681
×
10
−
11
1
.
19
×
10
−
13
5
.
1
×
10
6
13
FIRST NARROW-BAND SEARCH FOR CONTINUOUS
...
PHYSICAL REVIEW D
96,
122006 (2017)
122006-3
the spin-down grid, of the DS is selected as a
candidate
.
The initial
outliers
are identified among the candidates
using a threshold nominally corresponding to 1% (taking
into account the number of trials
[12]
) on the p-value of the
DS
’
s noise-only distribution
2
and are subject to a follow-up
stage in order to understand their nature. The follow-up
procedure consists of the following steps: check if the
outlier is close to known instrumental noise lines; compute
the signal amplitude and check if it is constant throughout
the run; compute the time evolution of the SNR (which we
expect to increase as the square root of the observation time
for stationary noise); and compute the
five-vector coher-
ence
, which is an indicator measuring the degree of
consistency between the data and the estimated waveform
[6]
. For each target, if no outlier is confirmed by the follow-
up we set an upper limit on the GW amplitude and NS
ellipticity; see Appendix
A
for more details.
IV. SELECTED TARGETS
We have selected pulsars whose spin-down limit could
possibly be beaten, or at least approached, based on the
average sensitivity of O1 data; see Fig.
2
. Pulsar distances
and spin-down limits are listed in Table
II
. As distance
estimations for the pulsars we have used the best fit value
and relative uncertainties given by each independent
measure; see pulsars list below and Table
II
for more
details. The uncertainty on the spin-down limit in Table
II
can be computed using the relation for the variance
propagation.
3
For two of these pulsars (Crab and Vela)
the spin-down limit has been already beaten in a past
narrow-band search using Virgo VSR4 data
[11]
. The other
targets are analyzed in a narrow-band search for the first
time. The timing measures for the 11 pulsars were provided
by the 76-meter Lovell telescope and the 42-foot radio
telescopes at Jodrell Bank (UK), the 26-meter telescope at
Hartebeesthoek (South Africa), the 64-meter Parkes radio
telescope (Australia) and the Fermi Large Area Telescope
(LAT) which is a space satellite. For seven of these pulsars
(Crab, Vela, J
0205
þ
6449
, J1813-1246, J
1952
þ
3252
,
J
2043
þ
2740
and J
2229
þ
6114
) updated ephemerides
covering the O1 period were available and a targeted
search was done in a recent work
[7]
beating the
FIG. 2. Blue points:Valueof the theoretical spin-down limit computed for the 11 known pulsars in ouranalysis, correspondingto Table
II
;
error bars correspond to the
1
σ
confidence level. Black triangles: Median over the analyzed frequency band of the upper limits on the GW
amplitude, corresponding to Table
VI
. Red dashed line: Estimated sensitivity at 95% confidence level of a narrow-band search using data
from LIGO H. Green dashed line: Estimated sensitivity at 95% confidence level of a narrow-band search using data from LIGO L.
2
The noise-only distribution is computed from the values of the
DS excluded in each frequency subband when selecting the local
maxima and then an extrapolation of the long tail of the done.
3
If variable
Y
is defined from
x
i
random variables with
variance
σ
2
x
i
, then the variance
σ
2
Y
can be estimated as
σ
2
Y
¼
X
i
∂
Y
∂
x
i
2
σ
2
x
i
:
B. P. ABBOTT
et al.
PHYSICAL REVIEW D
96,
122006 (2017)
122006-4
spin-down limit for all of them, while for the remaining
four pulsars we have used older measures extrapolating the
rotational parameters to the O1 epoch. A list of the
analyzed pulsars follows.
J
0205
þ
6449
: Ephemerides obtained from Jodrell
Bank. This pulsar had a glitch on November 11, 2015,
which can affect the CW search
[23]
. For this reason we
have performed the narrow-band search only on data before
the glitch as done in
[7]
. The distances are set according
to
[14]
.
J
0534
þ
2200
(Crab): One of the high value targets for
CW searches
[7]
due to its large spin-down value. For this
pulsar it was possible to beat the spin-down limit in a
narrow-band search using Virgo VSR4 data
[11]
.
Ephemerides have been obtained from the Jodrell Bank
telescope.
4
The nominal distance for the Crab pulsar and its
nebula is quoted in the literature as
2
.
0
0
.
5
kpc
[24]
;we
therefore assume uncertainty corresponding to the
1
σ
confidence level.
J0835-4510 (Vela): Like the Crab pulsar, Vela is one of
the traditional targets for CW searches. Although it spins at
a relatively low frequency (compared to the others), it is
very close to the Earth (
d
≃
0
.
28
kpc), thus making it a
potentially interesting source. Ephemerides were obtained
from the Hartebeesthoek Radio Astronomy Observatory in
South Africa.
5
The distance and its uncertainty are taken
according to
[25]
.
J1400-6326: First discovered as an INTEGRAL source
and then identified as a pulsar by the Rossi X-ray Timing
Explorer (RXTE). This NS is located in the galactic
supernova remnant G310.6-1.6 and it is supposed to be
quite young; the distance and its uncertainty correspond to
the
1
σ
confidence level
[15]
.
J1813-1246: Ephemerides covering the O1 time span
have been provided by the Fermi-LAT Collaboration
[7]
.
Only a lower upper limit is present on the distance.
J1813-1749: Located in one of the brightest and most
compact TeV sources discovered in the HESS Galactic
Plane Survey, HESS J1813-178. It is a young energetic
pulsar that is responsible for the extended x rays, and
probably the TeV radiation as well. Timing was obtained
from Chandra and XMM Newton data
[17]
; the pulsar
’
s
distance and uncertainty are taken from
[26]
and corre-
spond to the
1
σ
confidence level.
J1833-1034: Located in the supernova remnant G21.5-
0.9. This source has been known for a long time as one of
the Crab-like remnants. The evidence for a pulsar was
found by analyzing Chandra data; the distance and its
uncertainty are set according to
[18]
and correspond to the
1
σ
confidence level.
J
1952
þ
3252
: Ephemerides have been obtained from
Jodrell Bank
[7]
. Distance and uncertainty are taken from
kinematic measures of
[19]
.
J
2022
þ
3842
: It is a young energetic pulsar that was
discovered in Chandra observations of the radio supernova
remnant SNR G
76
.
9
þ
1
.
0
. Distance and uncertainty are
set according to
[21]
.
J
2043
þ
2740
: Ephemerides obtained from the Fermi-
LAT Collaboration
[7]
. The distance is estimated using the
dispersion measure by
[22]
and using the model from
[27]
.
The uncertainty on distance is set according to the model
and correspond to the
1
σ
confidence level.
J
2229
þ
6114
: Ephemerides obtained from Jodrell Bank
[7]
. Distance and uncertainty are estimated by
[28]
using
the model
[29]
.
V. RESULTS
In this section we discuss the results of the analysis. First,
in Sec.
VA
we briefly describe the initial outliers, for most
of which the follow-up described in Sec.
III
has been
enough to exclude a GW origin. Two outliers, belonging
respectively to the Vela and J1833-1034 pulsars, needed a
deeper study. The studies discussed in detail in the next
section disfavor the signal hypothesis and seem to suggest
these outliers as marginal noise events. Nevertheless the
outliers showed some promising features and for this
reason a follow-up using O2 data has been carried out
and described in Appendix
C
. The outliers were no longer
present in O2 data and therefore they were inconsistent
with the persistent nature of CW signals. Finally, in
Sec.
VB
upper limits on the strain amplitude for the 11
targets are discussed.
Fraction of data
2
4
6
8
10
Signal-to-noise ratio
0
0.2
0.4
0.6
0.8
1
Fraction of data
2
4
6
8
10
12
Signal-to-noise ratio
FIG. 3. Top panel: SNR computed with respect to the fraction
of data for the J1833-1034 outlier in the Hanford (red line),
Livingston (green) and joint (blue) analysis respectively. Bottom
panel: SNR computed with respect to the fraction of data for the
Vela outlier in the Hanford (red line), Livingston (green) and joint
(blue) analysis respectively.
4
http://www.jb.man.ac.uk/pulsar/crab.html.
5
http://www.hartrao.ac.za/
FIRST NARROW-BAND SEARCH FOR CONTINUOUS
...
PHYSICAL REVIEW D
96,
122006 (2017)
122006-5
A. Outliers outlook
We have found initial outliers for 9 of the 11 analyzed
pulsars. More precisely, for most pulsars we have found
one or two outliers, with the exception of J1813-1749 (36
outliers) and J
1952
þ
3252
(6 outliers). For J
2043
þ
2740
and J
2229
þ
6114
no outlier has been found. A summary
of the outliers found in the analysis is given in Table
III
.
The follow-up has clearly shown that in the case of J
1952
þ
3252
and J1813-1749 the outliers arise from noise dis-
turbances in LIGO H (for J1813-1749) and in LIGO L (for
J
1952
þ
3252
); see Appendix
B
for more details. Most of
the remaining outliers show an inconsistent time evolution
of the SNR together with a low coherence between LIGO H
and LIGO L and hence have been ruled out. As mentioned
before, two outliers, one for J1833-1034 and one for Vela,
have shown promising features during the basic follow-up
steps: no known noise line is present in their neighborhood,
the amplitude estimation is compatible and nearly constant
among the LIGO L and LIGO H runs and their SNR
appears to increase with respect to the integration time (see
Fig.
3
). Even if the trend of the SNR does not increase
monotonically with time, as expected for real signals, we
have decided to follow up on these outliers due to the fact
that they show a completely different SNR trend with
respect to all the other outliers found in this work.
Moreover each outlier
’
s significance increases in the
multi-IFOs search, suggesting a possible coherent source.
J1833-1034 and Vela outliers: In order to establish if the
outliers were not artifacts created by the narrow-band
search, we also looked for the two outliers using two other
analysis pipelines for targeted searches, which used a
Bayesian approach: one designed for searching for non-
tensorial modes in CW signals
[30]
, and the other devel-
oped for canonical CW target searches
6
and parameter
estimation
[32]
. Both pipelines produced odds, listed in
Table
IV
, which show a small preference for the presence of
a candidate compatible with general relativity. The odds
values are not surprising due to the fact that we are using
values for the frequency and the spin-down which are fixed
to the ones found in the narrow-band search. Hence, a trial
factor should be taken into account in order to make a
robust estimation on the signal hypothesis preference.
Besides the previous considerations, the values in
Table
IV
clearly show that the outliers are not artifacts
created by the narrow-band pipeline. We have also com-
pared the estimation of the outlier parameters obtained
from the
five-vector
,
F
-statistic and Bayesian
[6,8,32]
pipelines. The inferred parameters are listed in Table
V
and seem to be compatible among the three independently
developed targeted pipelines, thus suggesting the true
presence of these outliers inside the data.
In order to establish each outlier
’
s nature, a complete
understanding of the noise background is needed. For this
reason the first check was to look at the DS distribution in
the narrow-band search. In the presence of a true signal we
expect to see a single significant peak in the DS. Figure
4
shows the distribution of the DS (maximized over the spin-
down corrections) for J1833-1034 and for Vela over the
TABLE III. The table reports the outliers found in our analysis for each analyzed pulsar. The first column is the
name of the pulsar; the second indicates the number of outliers found in the analysis. The third and fourth columns
show respectively the outlier frequency and spin-down. The last column reports the corresponding p-value. For the
two targets J1813-1749 and J
1952
þ
3252
the outliers did not undergo the follow-up procedure due to the fact that
they can easily be associated with known noise lines; see Appendix
B
.
Name
Number of
candidates
Frequency (Hz)
Spin-down (Hz
=
s)
p-value
J
0205
þ
6449
1
30.4046480
−
8
.
937
×
10
−
11
0.003
J
0534
þ
2200
(Crab)
1
59.3702101
−
7
.
3920
×
10
−
10
0.005
J0835-4510 (Vela)
1
22.3884563
−
3
.
12
×
10
−
12
0.009
J1813-1246
2
41.5779102, 41.5852264
−
1
.
285
×
10
−
11
,
−
1
.
284
×
10
−
11
0.007, 0.005
J1813-1749
36
Close to 44.705 Hz
<
10
−
6
J1833-1034
1
32.2807633
−
1
.
0535
×
10
−
10
0.0004
J
1952
þ
3252
6
Close to 50.601
<
10
−
5
J1400-6326
2
64.1089253, 64.1406011
−
8
.
008
×
10
−
11
,
−
8
.
937
×
10
−
11
0.002, 0.003
J
2022
þ
3842
1
41.1603319
−
7
.
297
×
10
−
11
0.007
TABLE IV. Odds obtained for the two outliers by the Bayesian
pipelines
[30,31]
. The second column shows the odds of any
nontensorial signal hypothesis versus the canonical CW signal
hypothesis, the third column is the odds ratio of the canonical
signal hypothesis vs the Gaussian noise hypothesis, and the last
column is the odds ratio between the coherent signal among the
two detectors vs the hypothesis that the outliers arise from an
incoherent noise between LIGO H and L.
Name
log
10
O
nGR
GR
log
10
O
S
N
log
10
O
C
I
J0835-4510 (Vela)
−
0
.
55
2.30
1.07
J1833-1034
−
0
.
73
2.73
1.34
6
Frequency and spin-down value are fixed to the outlier
’
s value
found in the narrow-band search.
B. P. ABBOTT
et al.
PHYSICAL REVIEW D
96,
122006 (2017)
122006-6