Full band all-sky search for periodic gravitational waves
in the O1 LIGO data
B. P. Abbott
etal.
*
(LIGO Scientific Collaboration and Virgo Collaboration)
(Received 15 February 2018; published 11 May 2018)
We report on a new all-sky search for periodic gravitational waves in the frequency band 475
–
2000 Hz
and with a frequency time derivative in the range of
½
−
1
.
0
;
þ
0
.
1
×
10
−
8
Hz
=
s. Potential signals could be
produced by a nearby spinning and slightly nonaxisymmetric isolated neutron star in our Galaxy. This
search uses the data from Advanced LIGO
’
s first observational run O1. No gravitational-wave signals were
observed, and upper limits were placed on their strengths. For completeness, results from the separately
published low-frequency search 20
–
475 Hz are included as well. Our lowest upper limit on worst-case
(linearly polarized) strain amplitude
h
0
is
∼
4
×
10
−
25
near 170 Hz, while at the high end of our frequency
range, we achieve a worst-case upper limit of
1
.
3
×
10
−
24
. For a circularly polarized source (most favorable
orientation), the smallest upper limit obtained is
∼
1
.
5
×
10
−
25
.
DOI:
10.1103/PhysRevD.97.102003
I. INTRODUCTION
In this paper, we report the results of an all-sky, multi-
pipeline search for continuous, nearly monochromatic
gravitational waves in data from Advanced LIGO
’
s first
observational run (O1)
[1]
. The search covered signal
frequencies from 475 through 2000 Hz and frequency
derivatives over the range
½
−
1
.
0
;
þ
0
.
1
×
10
−
8
Hz
=
s.
Rapidly rotating neutron stars in our Galaxy could
generate detectable continuous gravitational waves via
various processes. For example, crustal deformation from
cooling accompanied by cracking or magnetic field energy
buried below the crust could lead to the nonaxisymmetry
necessary for emission. See Refs.
[2,3]
for recent, com-
prehensive reviews of continuous gravitational-wave emis-
sion mechanisms from neutron stars. Detection of such
radiation, combined with a campaign of electromagnetic
observations of the same source, could yield valuable
insight into the structure of neutron stars and into the
equation of state of matter under extreme conditions.
A number of searches for periodic gravitational waves
from isolated neutron stars have been carried out previously
in LIGO and Virgo data
[4
–
32]
. These searches have
included coherent searches for continuous wave (CW)
gravitational radiation from known radio and x-ray pulsars,
directed searches for known stars or locations having
unknown signal frequencies, and spotlight or all-sky
searches for signals from unknown sources. None of those
searches has found any signals, establishing limits on
strength of any putative signals. No previous search for
continuous waves covered the band 1750
–
2000 Hz.
Three search methods were employed to analyze O1 data:
(i) The
PowerFlux
pipeline has been used in previous
searches of LIGO
’
s S4, S5, and S6 and O1 runs
[15,17,19,22,31]
and uses a
loosely coherent
method
for following up outliers
[33]
. A new
universal
statistic
[34]
provides correct upper limits regardless
of the noise distribution of the underlying data,
while still showing close to optimal performance
for Gaussian data.
The follow-up of outliers uses a newly imple-
mented dynamic programming algorithm similar to
the Viterbi method
[35]
implemented in another
recent CW search of Scorpius X-1
[36]
.
(ii) The
SkyHough
pipeline has been used in previous
all-sky searches of the initial LIGO S2, S4 and S5
and Advanced LIGO O1 data
[14,15,26,31]
. The use
of the Hough algorithm makes it more robust than
other methods with respect to noise spectral dis-
turbances and phase modeling of the signal
[15,37]
.
Population-based frequentist upper limits are de-
rived from the estimated average sensitivity depth
obtained by adding simulated signals into the data.
(iii) The Time-Domain
F
-statistic pipeline has been used
inthe all-sky searches of the Virgo VSR1data
[27]
and
of the low-frequency part of the LIGO O1 data
[31]
.
The core of the pipeline is a coherent analysis of
narrow band time-domain sequences with the
F
-
statistic method
[38]
. Because of heavy computing
requirements of the coherent search, the data are
divided into time segments of a few days long, which
areseparately coherentlyanalyzed with the
F
-statistic.
This is followed by a search for coincidences among
candidates found in different short time segments
*
Full author list given at the end of the article.
PHYSICAL REVIEW D
97,
102003 (2018)
2470-0010
=
2018
=
97(10)
=
102003(31)
102003-1
© 2018 American Physical Society
(Ref.
[27]
, Sec.
VIII
), for a given band. In order to
estimate the sensitivity, frequentist upper limits are
obtained by injecting simulated signals into the data.
The pipelines present diverse approaches to data analy-
sis, with coherence lengths from 1800 s to a few days, and
different responses to line artifacts present in the data.
After following up numerous early stage outliers, no
evidence was found for continuous gravitational waves in
the O1 data over the band and range of frequency derivatives
searched. We therefore present bounds on detectable gravi-
tational radiation in the form of 95% confidence level upper
limits (Fig.
1
) for worst-case (linear) polarization. The
worst-case upper limits apply to any combination of
parameters covered by the search. Best-case (circular) upper
limits are presented as well, allowing one to compute the
maximum distance to detected objects, under certain
assumptions. Population average upper limits are produced
by SkyHough and Time-Domain
F
-statistic pipelines.
II. LIGO INTERFEROMETERS AND O1
OBSERVING RUN
The LIGO gravitational-wave network consists of two
observatories, one in Hanford, Washington, and the other in
Livingston, Louisiana, separated by a 3000 km baseline.
During the O1 run, each site housed one suspended inter-
ferometer with 4-km-long arms. The interferometer mirrors
act as test masses, and the passage of a gravitational wave
induces a differential armlengthchange that isproportional to
thegravitational-wave strain amplitude. The Advanced LIGO
[40]
detectors came online in September 2015 after a major
upgrade. While not yet operating at design sensitivity, both
detectors reached an instrument noise three to four times
lower than ever measured before in their most sensitive
frequency band between 100 and 300 Hz
[41]
.
The suspension systems of the optical elements were
greatly improved, extending the usable frequency range
down to 20 Hz. The use of monolithic suspensions
provided for sharper resonances of so-called violin modes,
resulting in narrower (in frequency) detector artifacts. An
increase in mirror mass has shifted the resonances to the
vicinity of 500 Hz, opening up previously contaminated
frequency bands.
With these positive effects came some new difficulties:
the increase in the number of optical elements resulted in
more violin modes as well as new less-well-understood
resonances
[31]
.
Frequency (Hz)
h0
20
200
400
600
800
1000
1200
1400
1600
1800
2000
1e−25
1e−24
1e−23
−
−
−
−
PowerFlux worst case (linear)
PowerFlux best case (circular)
TimeDomain F−stat pop. average
SkyHough population average
FIG. 1. O1upperlimits.Thedimensionlessstrain(verticalaxis)isplotted againstsignalfrequency.Lookingattherightsideoftheplot,the
upper (red) curve shows Time Domain F-statistic 95% C.L. population averaged upper limits, the next lower curve (blue) shows maximum
population average upper limits from SkyHough, followed by yellow curve showing PowerFlux worst-case (linearly polarized) 95% C.L.
upper limits in analyzed bands. PowerFlux upper limits are maximized over sky and all intrinsic signal parameters for each frequency band
displayed. The lower (black) curve shows upper limits assuming a circularly polarized source. We include the data from the low-frequency
paper
[31]
to present the entire range 20
–
2000 Hz. As the computational demands grow with frequencies, each pipeline tunes parameters to
reduce computation load. This accounts for jumps in curves at 475, 1200, and 1475 Hz. The SkyHough upper limit curve shows the
maximum of the range of different upper limits shown in Fig.
7
with different upper limit values corresponding to different search depths.
Becauseof highly non-Gaussian data, the SkyHough search depths are not expected to bewell estimated for each individual search band but
are representative of the noise behavior in the entire frequency range. The data for this plot can be found in Ref.
[39]
.
B. P. ABBOTT
et al.
PHYS. REV. D
97,
102003 (2018)
102003-2
Advanced LIGO
’
s first observing run occurred between
September 12, 2015, and January 19, 2016, from which
approximately 77 and 66 days of analyzable data were
produced by the Hanford (H1) and Livingston (L1)
interferometers, respectively. Notable instrumental contam-
inants affecting the searches described here included
spectral combs of narrow lines in both interferometers,
many of which were identified after the run ended and
mitigated for future runs. These artifacts included an 8 Hz
comb in H1 with the even harmonics (16 Hz comb) being
especially strong. This comb was later tracked down to
digitization roundoff error in a high-frequency excitation
applied to servocontrol the cavity length of the output mode
cleaner (OMC). Similarly, a set of lines found to be linear
combinations of 22.7 and 25.6 Hz in the L1 data was
tracked down to OMC excitation at a still higher frequency,
for which digitization error occurred.
A subset of these lines with common origins at the two
observatories contaminated the O1 search for a stochastic
background of gravitational waves, which relies upon
cross-correlation of H1 and L1 data, requiring excision
of affected bands
[29,42,43]
.
Although most of these strong and narrow lines are
stationary in frequency and hence do not exhibit the
Doppler modulations due to the Earth
’
s motion expected
for a CW signal from most sky locations, the lines pollute
the spectrum for such sources. In sky locations near the
ecliptic poles, where a putative CW signal would have little
Doppler modulation, the lines contribute extreme contami-
nation for certain signal frequencies. This effect was
particularly severe for the low-frequency results in the
20
–
475 Hz range
[31]
.
III. SIGNAL WAVEFORM
In this paper, we assume a standard model of a spinning
nonaxisymmetric neutron star. Such a neutron star radiates
circularly polarized gravitational radiation along the rota-
tion axis and linearly polarized radiation in the directions
perpendicular to the rotation axis. For the purposes of
detection and establishing upper limits, the linear polari-
zation is the worst case, as such signals contribute the
smallest amount of power to the detector.
The strain signal template measured by a detector is
assumed to be
h
ð
t
Þ¼
h
0
F
þ
ð
t;
α
0
;
δ
0
;
ψ
Þ
1
þ
cos
2
ð
ι
Þ
2
cos
ð
Φ
ð
t
ÞÞ
þ
F
×
ð
t;
α
0
;
δ
0
;
ψ
Þ
cos
ð
ι
Þ
sin
ð
Φ
ð
t
ÞÞ
;
ð
1
Þ
where
F
þ
and
F
×
characterize the detector responses to
signals with
þ
and × quadrupolar polarizations
[15,17,19]
,
the sky location is described by right ascension
α
0
and
declination
δ
0
, the inclination of the source rotation axis to
the line of sight is denoted
ι
, and we use
ψ
to denote the
polarization angle (i.e. the projected source rotation axis in
the sky plane).
The phase evolution of the signal is given by
Φ
ð
t
Þ¼
2
π
ð
f
source
·
ð
t
−
t
0
Þþ
f
ð
1
Þ
·
ð
t
−
t
0
Þ
2
=
2
Þþ
φ
;
ð
2
Þ
with
f
source
being the source frequency and
f
ð
1
Þ
denoting
the first frequency derivative (which, when negative, is
termed the
“
spin-down
”
). We use
t
to denote the time in the
Solar System barycenter frame. The initial phase
φ
is
computed relative to reference time
t
0
. When expressed as a
function of local time of ground-based detectors, Eq.
(2)
acquires sky-position-dependent Doppler shift terms.
Most natural
“
isolated
”
sources are expected to have a
negative first frequency derivative, as the energy lost in
gravitational or electromagnetic waves would make the
source spin more slowly. The frequency derivative can be
positive when the source is affected by a strong slowly
variable Doppler shift, such as due to a long-period orbit.
IV. POWERFLUX SEARCH FOR CONTINUOUS
GRAVITATIONAL RADIATION
A. Overview
This search has two main components. First, the main
PowerFlux algorithm
[15,17,19,44
–
46]
is run to establish
upper limits and produce lists of outliers with signal-to-
noise ratio (SNR) greater than 5. Next, the Loosely
Coherent detection pipeline
[19,33,47]
is used to reject
or confirm collected outliers.
Both algorithms calculate power for a bank of signal
model templates and compute upper limits and signal-to-
noise ratios for each template based on comparison to
templates with nearby frequencies and the same sky
location and spin-down. The input time series is broken
into 50%-overlapping long segments with durations shown
in Table
I
, which are then Hann windowed and Fourier
transformed. The resulting
short Fourier transforms
(SFTs) are arranged into an input matrix with time and
frequency dimensions. The power calculation can be
expressed as a bilinear form of the input matrix
f
a
t;f
g
:
P
½
f
¼
X
t
1
;t
2
a
t
1
;f
þ
δ
f
ð
t
1
Þ
a
t
2
;f
þ
δ
f
ð
t
2
Þ
K
t
1
;t
2
;f
:
ð
3
Þ
Here,
δ
f
ð
t
Þ
denotes the detector frame frequency drift
due to the effects from both Doppler shifts and the
first frequency derivative. The sum is taken over all
times
t
corresponding to the midpoint of the short
Fourier transform time interval. The kernel
K
t
1
;t
2
;f
includes
the contribution of time-dependent SFT weights, antenna
response, signal polarization parameters, and relative phase
terms
[33,47]
.
FULL BAND ALL-SKY SEARCH FOR PERIODIC
...
PHYS. REV. D
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102003 (2018)
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