of 37
All-sky search for continuous gravitational waves from isolated neutron
stars using Advanced LIGO and Advanced Virgo O3 data
R. Abbott
etal.
*
(LIGO Scientific Collaboration, Virgo Collaboration, and KAGRA Collaboration)
(Received 3 January 2022; accepted 17 October 2022; published 28 November 2022)
We present results of an all-sky search for continuous gravitational waves which can be produced by
spinning neutron stars with an asymmetry around their rotation axis, using data from the third observing
run of the Advanced LIGO and Advanced Virgo detectors. Four different analysis methods are used to
search in a gravitational-wave frequency band from 10 to 2048 Hz and a first frequency derivative from
10
8
to
10
9
Hz
=
s. No statistically significant periodic gravitational-wave signal is observed by any of
the four searches. As a result, upper limits on the gravitational-wave strain amplitude
h
0
are calculated. The
best upper limits are obtained in the frequency range of 100 to 200 Hz and they are
1
.
1
×
10
25
at
95% confidence level. The minimum upper limit of
1
.
10
×
10
25
is achieved at a frequency 111.5 Hz. We
also place constraints on the rates and abundances of nearby planetary- and asteroid-mass primordial black
holes that could give rise to continuous gravitational-wave signals.
DOI:
10.1103/PhysRevD.106.102008
I. INTRODUCTION
The Advanced LIGO
[1]
and Advanced Virgo
[2]
detectors have made numerous detections of gravitational
waves (GWs), to date consisting of short-duration (tran-
sient) GWs emitted during the inspirals and mergers of
compact binary systems of black holes (BHs), neutron stars
(NSs),
[3,4]
, as well as mixed NS-BH binaries
[5]
. Among
still undiscovered types of GW radiation are long-lasting,
almost-monochromatic continuous waves (CWs), whose
amplitudes and frequencies change much more slowly
compared to those of transient sources (on the timescale
of years rather than seconds). Astrophysically, promising
sources of CWs are rotating, nonaxisymmetric NSs, emit-
ting GWs at a frequency close to, or related to, their spin
frequency. Deviations from the symmetry (a NS
defor-
mation
) may be caused by fluid instabilities, such as in the
case of r-modes, or by elastic, thermal, or magnetic stresses
in the crust and/or core of NS, and may be acquired at
various stages of stars
isolated evolution, or during an
interaction with a companion in a binary system (for recent
reviews on sources of CW, see, e.g.,
[6
8]
). Discovery
of CWs emitted by NS would allow to probe their still
mysterious interiors, study properties of dense matter in
conditions distinct from those occurring in inspirals and
mergers of binary NS systems, as well as carry out
additional tests of the theory of gravity
[9]
. Due to
intrinsically smaller GW amplitude of CWs in comparison
to the already-detected transient sources, searches for CWs
from rotating nonaxisymmetric NSs are essentially limited
to the Galaxy.
The search presented here is not limited to gravitational-
wave signals from deformed rotating neutron stars. Another
source of quasimonochromatic, persistent GWs are very
light, planetary- and asteroid-mass, inspiraling primordial
black holes (PBHs), which could comprise a fraction
or the totality of dark matter
[10]
. Such signals would
arise from inspiraling PBHs whose chirp masses are less
than
O
ð
10
5
Þ
M
and whose GW frequencies are less than
250
Hz, and would be indistinguishable from those
arising from nonaxisymmetric rotating NSs spinning up.
Recent detections of black holes made by the LIGO-
Virgo-KAGRA Collaboration have revived interest in
PBHs: low spin measurements and the rate inferences
are consistent with those expected for BHs that formed in
the early Universe
[11]
. Existence of light PBHs is well
motivated theoretically and experimentally: recent detec-
tions of star and quasar microlensing events
[12
14]
suggest compact objects or PBHs with masses between
10
6
and
10
5
M
could constitute a fraction of dark
matter of order
f
PBH
0
.
01
, which is consistent within the
unified scenario for PBH formation presented in
[15]
,but
greater than expected for free-floating (i.e., not bound to an
orbit) planets
[16]
(e.g., the hypothetical Planet 9 could be a
PBH with a mass of
10
6
M
that was captured by the
solar system
[17]
). PBHs may also collide with NSs and be
responsible for the origin of NS-mass BHs, potentially
detectable in the LIGO-Virgo-KAGRA searches
[18]
.
However, constraints arising from such observations
[10]
, even those that come from the LIGO-Virgo merging
*
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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© 2022 American Physical Society
rate inferences
[19,20]
and stochastic background
searches
[21,22]
, rely on modeling assumptions, and
can be evaded if, for example, PBHs formed in clusters
[23
28]
. It is therefore important to develop complemen-
tary probes of these mass regimes to test different PBH
formation models
[29,30]
, which is possible by searching
for continuous GWs.
Searches for continuous waves are usually split in three
different domains:
targeted searches
look for signals from
known pulsars;
directed searches
look for signals from
known sky locations;
all-sky searches
look for signals
from unknown sources. All-sky searches for
apriori
unknown CW sources have been carried out in the
Advanced LIGO and Advanced Virgo data previously
[31
43]
. A recent review on pipelines for wide parameter-
space searches can be found in
[44]
.
Here we report on results from an all-sky, broad
frequency range search using the most-sensitive data to
date, the LIGO-Virgo O3 observing run, employing four
different search pipelines: the
FrequencyHough
[45]
,
SkyHough
[46]
,
Time-Domain
F
-
statistic
[47,48]
, and
SOAP
[49]
. Each pipeline uses different data analysis
methods and covers different regions of the frequency
and frequency time derivative parameter space, although
there exist overlaps between them (see Table
I
and Fig.
1
for details). The search is performed for frequencies
between 10 and 2048 Hz and for a range of frequency
time derivative between
10
8
and
10
9
Hz
=
s, covering
the whole sky. We note here that the search is generally
agnostic to the type of the GW source, so the results are
not actually limited to signals from nonaxisymmetric
rotating NSs in our Galaxy. A comprehensive multistage
analysis of the signal outliers obtained by the four pipe-
lines has not revealed any viable candidate for a continu-
ous GW signal. However we improve the broad-range
frequency upper limits with respect to previous O1 and O2
observing runs and also with respect to the recent analysis
of the first half of the O3 run
[39]
.Thisisalsothefirstall-
sky search for CW sources that uses the Advanced Virgo
detector
sdata.
The article is organized as follows: in Sec.
II
we describe
the O3 observing run and provide details about the data
used. In Sec.
III
we present an overview of the pipelines
used in the search. In Sec.
IV
details of the data-analysis
pipelines are described. In Sec.
V
, we describe the results
obtained by each pipeline, namely the signal candidates and
the sensitivity of the search; whereas Sec.
VI
contains a
discussion of the astrophysical implications of our results.
II. DATASETS USED
The dataset used in this analysis was the third observing
run (O3) of the Advanced LIGO and Advanced Virgo GW
detectors
[1,2]
. LIGO is made up of two laser interfero
meters, both with 4 km long arms. One is at the LIGO
Livingston Observatory (L1) in Louisiana, USA and the
other is at the LIGO Hanford Observatory (H1) in
Washington, USA. Virgo (V1) consists of one interferom-
eter with 3 km arms located at European Gravitational
Observatory in Cascina, Italy. The O3 run took place
between April 1, 2019, and March 27, 2020. The run
was divided into two parts, O3a and O3b, separated by
one month commissioning break that took place in October
2019. The duty factors for this run were
76%
,
71%
,
76%
for L1, H1, V1, respectively. The maximum
uncertainties (68% confidence interval) on the calibration
of the LIGO data were of 7%/11% in magnitude and
4
deg
=
9
deg in phase for O3a/O3b data (
[50,51]
). For
Virgo, it amounted to 5% in amplitude and 2 deg in phase,
with the exception of the band 46
51 Hz, for which the
maximum uncertainty was estimated as 40% in amplitude
and 34 deg in phase during O3b. For the smaller range
49.5
50.5 Hz, the calibration was unreliable during the
whole run
[52]
.
III. OVERVIEW OF SEARCH PIPELINES
In this section we provide a broad overview of the
four pipelines used in the search. The three pipelines:
FIG. 1. Frequency and frequency derivative search ranges of
the four pipelines: the
FrequencyHough
pipeline ranges marked
in grey,
SkyHough
in red,
Time-Domain
F
-
statistic
in blue, and
SOAP
in magenta. See Table
I
for details.
TABLE I. Frequency and frequency derivative search ranges of
the four pipelines.
Pipeline
Frequency (Hz)
Frequency
derivative (Hz
=
s)
FrequencyHough
10
2048
10
8
10
9
SkyHough
65
350
10
9
5
×
10
12
SOAP
40
1000
10
9
10
9
1000
2000
10
8
10
8
TD Fstat
20
200
3
.
2
×
10
9
f=
100
0
200
750
2
×
10
10
2
×
10
11
R. ABBOTT
et al.
PHYS. REV. D
106,
102008 (2022)
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FrequencyHough
,
SkyHough
,and
Time-Domain
F
-
statistic
have been used before in several all-sky searches of the LIGO
data. The
SOAP
pipeline is a new pipeline applied for the first
time to an all-sky search. It uses novel algorithms.
SOAP
aims
at a fast, preliminary search of the data before more sensitive
but much more time consuming methods are applied (see
[44]
for a review on pipelines for wide parameter-space searches).
The individual pipelines are described in more detail in the
following section.
A. Signal model
The GW signal in the detector frame from an isolated,
asymmetric NS spinning around one of its principal axis of
inertia is given by
[47]
h
ð
t
Þ¼
h
0

F
þ
ð
t;
α
;
δ
;
ψ
Þ
1
þ
cos
2
ι
2
cos
φ
ð
t
Þ
þ
F
×
ð
t;
α
;
δ
;
ψ
Þ
cos
ι
sin
φ
ð
t
Þ

;
ð
1
Þ
where
F
þ
and
F
×
are the antenna patterns of the detectors
dependent on right ascension
α
, declination
δ
of the source
and polarization angle
ψ
,
h
0
is the amplitude of the signal,
ι
is the angle between the total angular momentum vector of
the star and the direction from the star to the Earth, and
φ
ð
t
Þ
is the phase of the signal. The amplitude of the signal is
given by
h
0
¼
4
π
2
G
c
4
ε
I
zz
f
2
d
1
.
06
×
10
26

ε
10
6

×

I
zz
10
38
kg m
2

f
100
Hz

2

1
kpc
d

;
ð
2
Þ
where
d
is the distance from the detector to the source,
f
is
the GW frequency (assumed to be twice the rotation
frequency of the NS),
ε
is the ellipticity or asymmetry
of the star, given by
ð
I
xx
I
yy
Þ
=I
zz
, and
I
zz
is the moment
of inertia of the star with respect to the principal axis
aligned with the rotation axis.
We assume that the phase evolution of the GW signal can
be approximated with a second order Taylor expansion
around a fiducial reference time
τ
r
:
φ
ð
τ
Þ¼
φ
o
þ
2
π

f
ð
τ
τ
r
Þþ
_
f
2!
ð
τ
τ
r
Þ
2

;
ð
3
Þ
where
φ
o
is an initial phase and
f
and
_
f
are the frequency
and first frequency derivative at the reference time. The
relation between the time at the source
τ
and the time at the
detector
t
is given by
τ
ð
t
Þ¼
t
þ
r
ð
t
Þ
·
n
c
þ
Δ
E
Δ
S
;
ð
4
Þ
where
r
ð
t
Þ
is the position vector of the detector in the
Solar System Barycenter frame, and
n
is the unit vector
pointing to the NS;
Δ
E
and
Δ
S
are, respectively, the
relativistic Einstein and Shapiro time delays. In standard
equatorial coordinates with right ascension
α
and declina-
tion
δ
, the components of the unit vector
n
are given
by
ð
cos
α
cos
δ
;
sin
α
cos
δ
;
sin
δ
Þ
.
B. Parameter space analyzed
All the four pipelines perform an all-sky search; however
the frequency and frequency derivative ranges analyzed
are different for each pipeline. The detailed ranges analyzed
by the four pipelines are summarized in Table
I
and
presented in Fig.
1
. The
FrequencyHough
pipeline analyzes
a broad frequency range between 10 and 2048 Hz and a
broad frequency time derivative range between
10
8
and
10
9
Hz
=
s. A very similar range of
f
and
_
f
is analyzed by
the
SOAP
pipeline. The
SkyHough
pipeline analyzes a
narrower frequency range where the detectors are most
sensitive whereas the
Time-Domain
F
-
statistic
pipeline
analyzes
f
and
_
f
ranges of the bulk of the observed pulsar
population (see Fig.
2
in Sec.
IV C
).
C. Detection statistics
As all-sky searches cover a large parameter space they
are computationally very expensive and it is computation-
ally prohibitive to analyze coherently the data from the full
observing run using optimal matched filtering. As a result
each of the pipelines developed for the analysis uses a
semicoherent method. Moreover to reduce the computer
memory and to parallelize the searches the data are divided
into narrow bands. Each analysis begins with sets of
short
Fourier transforms
(SFTs) that span the observation
period, with coherence times ranging from 1024s to
8192s. The
FrequencyHough
,
SkyHough
, and
SOAP
pipe-
lines compute measures of strain power directly from the
SFTs and create detection statistics by stacking those
powers with corrections for frequency evolution applied.
The
FrequencyHough
and
SkyHough
pipelines use
Hough
transform to do the stacking whereas the
SOAP
pipeline
uses the
Viterbi
algorithm. The
Time-Domain
F
-
statistic
pipeline extracts band-limited 6-day long time-domain data
segments from the SFT sets and applies frequency evolu-
tion corrections coherently to obtain the
F
-
statistic
[47]
.
Coincidences are then required among multiple data seg-
ments with no stacking.
D. Outlier follow-up
All four pipelines perform a follow-up analysis of the
statistically significant candidates (outliers) obtained dur-
ing the search. All pipelines perform vetoing of the outliers
ALL-SKY SEARCH FOR CONTINUOUS GRAVITATIONAL WAVES
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