of 25
Search of the early O3 LIGO data for continuous gravitational
waves from the Cassiopeia A and Vela Jr. supernova remnants
R. Abbott
etal.
*
(LIGO Scientific Collaboration and Virgo Collaboration)
(Received 30 November 2021; accepted 21 March 2022; published 28 April 2022)
We present directed searches for continuous gravitational waves from the neutron stars in the Cassiopeia
A (Cas A) and Vela Jr. supernova remnants. We carry out the searches in the LIGO detector data from the
first six months of the third Advanced LIGO and Virgo observing run using the
WEAVE
semicoherent
method, which sums matched-filter detection-statistic values over many time segments spanning the
observation period. No gravitational wave signal is detected in the search band of 20
976 Hz for assumed
source ages greater than 300 years for Cas A and greater than 700 years for Vela Jr. Estimates from
simulated continuous wave signals indicate we achieve the most sensitive results to date across the explored
parameter space volume, probing to strain magnitudes as low as
6
.
3
×
10
26
for Cas A and
5
.
6
×
10
26
for Vela Jr. at frequencies near 166 Hz at 95% efficiency.
DOI:
10.1103/PhysRevD.105.082005
I. INTRODUCTION
We report the results of the deepest search to date for
continuous gravitational waves from the neutron stars at the
centers of the Cassiopeia A (Cas A, G
111
.
7
2
.
1
)
[1]
and
Vela Jr. (G
266
.
2
1
.
2
)
[2]
supernova remnants. Cas A is
just over 300 years old
[3,4]
, and Vela Jr. may be as young
as 700 years old
[2]
. These extremely young objects have
been the target of multiple searches for continuous gravi-
tational waves since 2010
[5
11]
because they may retain
high rotation frequencies and may possess appreciable
nonaxisymmetries from their recent births
[12
20]
.
Continuous emission due to unstable
r
-mode s is also
possible in such young stars
[21
25]
.
In this search, we analyze the first six months of data
from the third observing run (O3a period) of the Advanced
Laser Interferometer Gravitational wave Observatory
(Advanced LIGO
[26,27]
). We achieve significantly
improved sensitivity for Vela Jr. with respect to a recent
O3a search using a different method
[11]
and dramatically
improved sensitivity for Cas A with respect to previous
searches of O1, O2 and O3a LIGO and Virgo data
[5
11]
.
The improvement with respect to similar, previous analyses
of O1 data
[8,9]
comes largely from the improved detector
noise due to a variety of instrument upgrades
[28]
,
including a (
3
db) improvement achieved with quantum
squeezing
[29]
.
Given the immense pressure on its nuclear matter, one
expects a neutron star to assume a highly spherical shape in
the limit of no rotation and, with rotation, to form an
axisymmetric oblate spheroid. A number of physical
processes can disrupt the symmetry, however, to produce
quadrupolar gravitational waves from the stellar rotation.
Those processes include crustal distortions from cooling or
accretion, buried magnetic field energy and excitation of
r-modes. Comprehensive reviews of continuous gravita-
tional wave emission mechanisms from neutron stars can
be found in
[30,31]
Central compact objects (CCOs) at the cores of super-
nova remnants present interesting potential sources, espe-
cially those in remnants inferred from their sizes and
expansion rates to be young. Both the Cas A and Vela
Jr. remnants contain such objects, thought to be young
neutron stars. One can derive an estimated age-based upper
limit
1
on a CCO
s continuous-wave strain amplitude by
assuming the star
s current rotation frequency is much
lower than its rotation frequency at birth and that the star
s
spin-down since birth has been dominated by gravitational
wave energy loss (
gravitar
emission)
[32]
:
h
age
¼ð
2
.
3
×
10
24
Þ

1
kpc
r

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

1000
yr
τ

I
zz
I
0

s
;
ð
1
Þ
where
r
is the distance to the source,
τ
is its age and
I
zz
is
the star
s moment of inertia about its spin axis, with a
fiducial value of
I
0
¼
10
38
kg · m
2
.
Cas A is perhaps the most promising example of a
potential gravitational wave CCO source in a supernova
*
Deceased.
1
This strain estimate gives a rough benchmark upper limit on
what is possible in an optimistic scenario; its assumption that
current rotation frequency is small relative to the star
s birth
frequency becomes less plausible for the highest frequencies
searched in this analysis.
PHYSICAL REVIEW D
105,
082005 (2022)
2470-0010
=
2022
=
105(8)
=
082005(25)
082005-1
© 2022 American Physical Society
remnant. Its birth aftermath may have been observed by
Flamsteed
[3]
340
years ago in 1680, and the expansion
of the visible shell is consistent with that date
[4]
. Hence
Cas A, which is visible in x-rays
[33,34]
but shows no
pulsations
[35]
, is almost certainly a very young neutron
star at a distance of about 3.3 kpc
[36,37]
. From Eq.
(1)
,
one finds an age-based strain limit of
1
.
2
×
10
24
, which
is readily accessible to LIGO and Virgo detectors in their
most sensitive band.
The Vela Jr. CCO is observed in x-rays
[38]
and is
potentially quite close (
0
.
2
kpc) and young (690 yr)
[2]
,
for which one finds a quite high age-based strain limit of
1
.
4
×
10
23
. Some prior continuous gravitational wave
searches have also conservatively assumed a more pessi-
mistic distance (
1
kpc) and age (5100 yr), based on other
measurements
[39]
, for which the age-based strain limit is
1
.
0
×
10
24
, still comparable to that of Cas A. As in the
case of Cas A, no pulsations have been detected from Vela
Jr.
[40,41]
.
The remainder of this article is organized as follows:
Section
II
describes the data set used. Section
III
briefly
describes the
WEAVE
search program
[42]
which uses
semicoherent summing of a matched-filter detection sta-
tistic known as the
F
-statistic
[43]
. Section
IV
presents the
results of the search. Section
V
discusses the method used
to determine 95% sensitivity as an approximation to
rigorous upper limits for bands in which all initial search
outliers have been followed up with more sensitive but
computationally costly methods and dismissed as not
credible signals. Section
VI
concludes with a discussion
of the results and prospects for future searches.
II. DATASETS USED
Advanced LIGO consists of two detectors, one in
Hanford, Washington (designated H1), and the other in
Livingston, Louisiana (designated L1), separated by a
3000
-km baseline
[26]
. Each site hosts one, 4-km-long
interferometer inside a vacuum envelope with the primary
interferometer optics suspended by a cascaded, quadruple
suspension system, affixed beneath an in-series pair of
suspended optical tables, in order to isolate them from
external disturbances. The interferometer mirrors act as test
masses, and the passage of a gravitational wave induces a
differential-arm length change which is proportional to the
gravitational-wave strain amplitude.
The third Advanced LIGO and Virgo data run (O3)
began April 1, 2019 and ended March 27, 2020. The first
six months (April 1, 2019 to October 1, 2019), prior to a
1-month commissioning break, is designated as the O3a
period. The analysis presented here uses only the O3a
dataset from the LIGO interferometers. The Virgo data has
not been used in this analysis because of an unfavorable
tradeoff in computational cost for sensitivity gain, given the
interferometer
s higher noise level during the O3 run. The
systematic error in the amplitude calibration is estimated to
be lower than 7% (68% confidence interval) for both LIGO
detectors over all frequencies throughout O3a
[44]
.
Prior to searching the O3a data for continuous wave
(CW) signals, the quality of the data was assessed and steps
taken to mitigate the effects of instrumental artifacts. As in
previous Advanced LIGO observing runs
[45]
, instrumen-
tal
lines
(sharp peaks in fine-resolution, run-averaged
H1 and L1 spectra) are marked, and where possible, their
instrumental or environmental sources identified
[46]
. The
resulting database of artifacts proved helpful in eliminating
spurious signal candidates emerging from the search; no
bands were vetoed
a priori
, however. In general, the
number of H1 lines in the O3a data was similar to that
observed in the O2 run, while the number of lines for L1
O3a data was substantially reduced.
As discussed in
[47]
, another type of artifact observed in
the O3a data for both H1 and L1 were relatively frequent
and loud
glitches
(short, high-amplitude instrumental
transients) with most of their spectral power lying below
500
Hz. To mitigate the effects of these glitches on O3a
CW searches for signals below 475 Hz, a simple glitch-
gating algorithm was applied
[48,49]
to excise the tran-
sients from the data.
III. ANALYSIS METHOD
This search relies upon semicoherent averaging of
F
-statistic
[43]
values computed for many short (several-
day) segments spanning nearly all of the O3a run period
(2019 April 1 15
00 UTC
2019 October 1 15
00 UTC).
Section
III A
describes the signal model used in the analysis.
Section
III B
describes the mean
F
-statistic detection sta-
tistic at the core of the analysis. Section
III C
describes the
WEAVE
infrastructure for summing individual
F
-statistic
values over the observation period, including the configu-
ration choices for the searches presented in this article.
Section
III D
describes the procedure used to follow up on
outliers found in the first stage of the hierarchical search.
A. Signal model and parameter space searched
The signal templates assume a classical model of a
spinning neutron star with a time-varying quadrupole
moment that produces circularly polarized gravitational
radiation along the rotation axis, linearly polarized radia-
tion in the directions perpendicular to the rotation axis and
elliptical polarization for the general case. The strain signal
model
h
ð
t
Þ
for the source, as seen by the detector, is
assumed to be the following function of time
t
:
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
2
Þ
R. ABBOTT
et al.
PHYS. REV. D
105,
082005 (2022)
082005-2
In Eq.
(2)
,
h
0
is the intrinsic strain amplitude,
Φ
ð
t
Þ
is the
signal phase,
F
þ
and
F
×
characterize the detector responses
to signals with
þ
and
×
quadrupolar polarizations
[50]
,
and the sky location is described by right ascension
α
0
and
declination
δ
0
. In this equation, the star
s orientation, which
determines the polarization, is parametrized by the incli-
nation angle
ι
of its spin axis relative to the detector line-of-
sight and by the angle
ψ
of the axis projection on the plane
of the sky. The linear polarization case (
ι
¼
π
=
2
) is the most
unfavorable because the gravitational wave flux impinging
on the detectors is smallest for an intrinsic strain amplitude
h
0
, possessing eight times less incident strain power than
for circularly polarized waves (
ι
¼
0
;
π
).
In a rotating triaxial ellipsoid model for a star at distance
r
spinning at frequency
f
rot
about its (approximate)
symmetry axis (
z
), the amplitude
h
0
can be expressed as
h
0
¼
4
π
2
G
ε
I
zz
f
2
c
4
r
ð
3
Þ
¼½
1
.
1
×
10
24


ε
10
6

I
zz
I
0

f
1
kHz

2

1
kpc
r

;
ð
4
Þ
for which the gravitational radiation is emitted at frequency
f
¼
2
f
rot
. The equatorial ellipticity
ε
is a useful, dimen-
sionless measure of stellar nonaxisymmetry:
ε
j
I
xx
I
yy
j
I
zz
:
ð
5
Þ
Unstable
r
-mode emission
[21
25]
at gravitational wave
frequency
f
(which for this model is
ð
4
=
3
Þ
f
rot
) can be
parametrized by a dimensionless amplitude
α
governing the
strain amplitude
[51]
:
h
0
¼½
3
.
6
×
10
23


α
0
.
001

f
1
kHz

3

1
kpc
r

:
ð
6
Þ
The phase evolution of the signal is given in the
reference frame of the Solar System barycenter (SSB) by
the third-order approximation:
Φ
ð
t
Þ¼
2
π
ð
f
·
ð
t
t
0
Þþ
1
2
_
f
·
ð
t
t
0
Þ
2
þ
1
6
̈
f
·
ð
t
t
0
Þ
3
ÞÞþ
φ
0
;
ð
7
Þ
where
f
is the SSB source frequency,
_
f
is the first
frequency derivative (which, when negative, is termed
the spin-down),
̈
f
is the second frequency derivative,
t
is
the SSB time, and the initial phase
φ
0
is computed relative
to reference time
t
0
(taken here to be the approximate
midpoint of the O3a period: 2019 June 30 15
07
45 UTC-
GPS 1245942483). When expressed as a function of the
local time of ground-based detectors, Eq.
(7)
acquires sky-
position-dependent Doppler shift terms
[43]
.
In this analysis, we search a band of gravitational wave
signal
f
from 20 to 976 Hz and a frequency derivative
_
f
range governed by assumed minimum ages
τ
of each
source. Detector noise deteriorates badly below 20 Hz
because of ground motion, and in the band around 1000 Hz
because of resonant mechanical disturbances. Similar
previous searches
[5
7]
have assumed a power law spin-
down:
_
f
∝−
f
n
with braking index
n
, with
n
taking on
values of 3 for magnetic dipole emission, 5 for GW
quadrupole emission (gravitar) and 7 for
r
-mode emission.
For a source that begins at a high frequency and spins down
to a much lower present-day frequency with a constant
braking index, one expects
_
f
1
n
1
ð
f=
τ
Þ
. Allowing for
n
to
range between 2 and 7 because of multiple potential spin-
down contributions leads to the search range:
f
τ
_
f
≤−
1
6
f
τ
;
ð
8
Þ
which has been assumed in several previous searches
[5
7]
.
Here we take a slightly more conservative approach,
allowing the upper limit on
_
f
to reach zero, at modest
additional computational cost, while allowing for some
time-dependent braking indices and uncertainties in the
source
s effective age. The range in second frequency
derivative
̈
f
is determined for any frequency
f
and first
derivative
_
f
by the same relation used in previous searches
(governed by the braking index range considered):
2
_
f
2
f
̈
f
7
_
f
2
f
:
ð
9
Þ
Table
I
lists the maximum absolute values of
_
f
and
̈
f
at
the lowest and highest search frequencies, along with the
right ascensions and declinations used in the Cas A and
Vela Jr. searches.
In searching this parameter space, we do not enforce a
relation among (
f
,
_
f
,
̈
f
), which means that for an arbitrary
combination, the implied
current
braking index
n
c
, defined
by
n
c
f
̈
f=
ð
_
f
Þ
2
, may take on arbitrarily large (unphysical)
values. For a true power-law behavior over the observation
TABLE I. Sky locations and maximum
j
_
f
j
,
̈
f
values used in the
Cas A and Vela Jr. searches at the lowest and highest frequencies.
Source
Cassiopeia A
[52]
Vela Jr.
[53]
Right ascension
23h 23m 27.85s 8h 52m 1.4s
Declination
þ
58
°48
42.8
46
°17
53
Maximum
j
_
f
j
(Hz
=
s) @20 Hz
2
.
1
×
10
9
9
.
1
×
10
10
Maximum
j
_
f
j
(Hz
=
s) @976 Hz
1
.
0
×
10
7
4
.
4
×
10
8
Maximum
̈
f
(Hz
=
s
2
) @20 Hz
1
.
6
×
10
18
2
.
9
×
10
19
Maximum
̈
f
(Hz
=
s
2
) @976 Hz
7
.
6
×
10
17
1
.
4
×
10
17
SEARCH OF THE EARLY O3 LIGO DATA FOR CONTINUOUS
...
PHYS. REV. D
105,
082005 (2022)
082005-3
period, the implied third frequency derivative can be
written
f
¼
n
c
ð
2
n
c
1
Þð
_
f
Þ
2
=f
3
. In the initial search and
first two stages of outlier follow-up, the third derivative is
taken to be zero, which is a good approximation for braking
indices below 7 for both sources.
B. The mean
F
-statistic
This search is based on a semicoherent average of
F
-statistic values over many individual intervals of the 6-
month observing period. Within each segment of coher-
ence time duration
T
coh
,the
F
-statistic
[43]
is computed
as in previous searches, as a
detection statistic propor-
tional to the signal amplitude
h
2
0
, maximized over
h
0
,the
unknown orientation angles
ι
and
ψ
,andthephase
constant
φ
0
. In Gaussian noise with no signal present,
the value of
2
F
follows a
χ
2
distributionwithfourdegrees
of freedom and has an expectation value of four. The
presence of a signal leads to a non central
χ
2
distribution
with a noncentrality parameter proportional to
h
2
0
·
T
coh
and inversely proportional to the average power spectral
density of the detector noise. The noncentrality parameter
also depends on the source
s orientation and sky location,
and on the orientations and locations of the LIGO
interferometers
[43]
.
We compute a semicoherent mean
F
-statistic we call
2
̄
F
from the average value of
2
F
over the
N
seg
segments into
which the observing period is divided:
2
̄
F
¼
1
N
seg
X
N
seg
i
¼
1
2
F
i
:
ð
10
Þ
In the absence of signal, this detection statistic too has an
expectation value of four, but has the underlying shape of a
χ
2
distribution with
4
N
seg
degrees of freedom with a
(rescaled) standard deviation of
ffiffiffiffiffiffiffiffiffiffiffiffiffiffi
8
=N
seg
p
. The presence
of a signal leads to an offset in the mean that is approx-
imately the same as the noncentrality parameter above, for a
fixed
T
coh
.
C. The
WEAVE
infrastructure
The
WEAVE
software infrastructure provides a systematic
approach to covering the parameter space volume in a
templated search to ensure acceptable loss of signal-to-
noise ratio (SNR) for true signals lying between template
points
[42]
. The
WEAVE
program combines together recent
developments in template placement to use an optimal
parameter-space metric
[54,55]
and optimal template lat-
tices
[56]
. The package is versatile enough to be used in all-
sky searches for unknown sources. Here we use a simpler
configuration applicable to well localized sources, such as
Cas A and Vela Jr.
In brief, a template grid in the parameter space is created
for each time segment, a grid that is appropriate to
computing the
F
-statistic
2
for a coherence time
T
coh
equal
to the total observation period
T
obs
divided by
N
seg
. The
spacing of the grid points in (
f
,
_
f
,
̈
f
) is set according to a
metric
[54,55]
that ensures a worst-case maximum mis-
match
m
coh
defined by the fractional loss in
2
F
value due to
a true signal not coinciding with a search template.
Separately, a much finer grid is defined for the full
observation period with respect to the midpoint of the
observation period, one with its own mismatch parameter
m
semi
coh
, analogous to
m
coh
, but defined to be the average
of the coherent mismatch values over all segments
[55]
. Its
choice is set empirically in a tradeoff between sensitivity
and computational cost. The
WEAVE
package creates at
initialization a mapping between each point in the semi-
coherent template grid and a nearest corresponding point in
each of the separate, coarser segment grids, accounting for
frequency evolution. The semicoherent detection statistic
2
̄
F
is constructed for each semicoherent template from this
mapping
[42]
.
For the Cas A and Vela Jr. searches presented here, a
simulation study was carried out to evaluate tradeoffs in
achievable sensitivity for a small but diverse set of segment
length choices (
T
coh
) and mismatch parameters
m
coh
and
m
semi
coh
, with a goal of staying within a maximum
computational cost of
3
×
10
6
CPU core hours for the
two searches combined, including for outlier follow-up
(
10%
). Searching over only
f
and
_
f
was also explored,
but yielded poorer sensitivity. In the end, we chose the
WEAVE
configuration parameters shown in Table
II
.
Search jobs are carried out in 0.1-Hz bands of
f
, with
further divisions in
_
f
, as needed, to keep each job
s computa-
tional duration between approximately 6 and 12 hours, for
practical reasons. Tables
III
and
IV
show the number of
_
f
divisions
vs.
frequency band for the two searches.
D. Outlier follow-up
Each individual job returns the (
f
,
_
f
,
̈
f
) values of the
1000 templates (
top-list
) with the largest (
loudest
)
2
̄
F
values. For 0.1-Hz bands with
N
_
f
divisions in the
_
f
range,
there are
N
_
f
×
1000
values returned. Outlier templates to
be followed up are those in these top-lists exceeding a
frequency-dependent threshold
2
̄
F
thresh
ð
f
Þ
which rises
slowly with
f
as the number of distinct templates searched
grows, thereby increasing the statistical trials factor. A
nominal threshold is set based on the signal-free
χ
2
distribution with four degrees of freedom per segment
such that the expectation value of outliers is one per 1-Hz
2
To understand better the effects of instrumental line artifacts,
in this initial exploration of the O3 data with the
WEAVE
method, a
pure
F
-statistic was used rather than the Bayesian-motivated
F
þ
veto
-statistic
[57,58]
, in which the
F
-statistic value is sup-
pressed by the presence of line artifacts in one detector, but not in
the other.
R. ABBOTT
et al.
PHYS. REV. D
105,
082005 (2022)
082005-4
band in Gaussian noise, given the empirically obtained
trials factor. Using the template counts from the
WEAVE
configuration yields an empirical fitted function
2
̄
F
thresh
ð
f
Þ¼
2
̄
F
0
f
a
, where the parameters
2
̄
F
0
and
a
are listed in Table
V
.
In practice, non-Gaussian artifacts lead to much higher
outlier counts in particular bands contaminated by instru-
mental line sources (Sec.
II
). In some cases strong
instrumental lines can lead to more than 1000 templates
from a single job that exceed the threshold for a particular
0.1-Hz band and range of
_
f
searched. We refer to those
cases as
saturated
since potentially interesting templates
may be suppressed by the top-list cap. Each of those cases
is examined manually to assess instrumental contamina-
tion. Where such contamination is confirmed, those bands
are marked and excluded from those in which we quote
strain sensitivities. The Appendix lists these 0.1-Hz bands.
For nonsaturated subranges of individual 0.1-Hz bands,
outliers exceeding the threshold
2
̄
F
thresh
ð
f
Þ
are followed up
in a sequential procedure where at each step, the coherence
time
T
coh
is doubled (and hence the number of segments
N
seg
is halved). Because the noncentrality parameter for the
mean
2
̄
F
detection statistic scales approximately linearly
with
T
coh
, one expects a nominal doubling of the
excess
mean
2
̄
F
defined by
2
̄
F
4
.
To be conservative and guided by simulations, we
require outliers passing a follow-up stage to display an
increase of 60%
70% in excess mean
2
̄
F
with respect to
the previous stage, depending on source and follow-up
stage. Table
VI
lists the required increases, which are lower
for Cas A than for Vela Jr. in the first follow-up stages
because its younger age leads to higher possible 3rd
frequency derivatives which are not searched over in those
stages. The simulated signals used to guide these choices
are nominally detectable but not loud, having strain
TABLE II.
WEAVE
configuration parameters used for the Cas A and Vela Jr. searches.
Parameter
Cas A
Vela Jr.
Coherent mismatch
m
coh
0.1
0.1
Semicoherent mismatch
m
semi
coh
0.2
0.2
Coherence time (number of segments) for initial search
5.0 days (36)
7.5 days (24)
Coherence time (number of segments) for 1st follow-up
10.0 days (18)
15.0 days (12)
Coherence time (number of segments) for 2nd follow-up
20.0 days (9)
30.0 days (6)
Coherence time (number of segments) for 3rd follow-up
45.0 days (4)
60.0 days (3)
TABLE III. Numbers of
_
f
sub-ranges into which the initial Cas
A search jobs (0.1-Hz sub-bands) are divided for different
frequency search bands, in order to maintain job durations
between about 6 and 12 computational hours. Each subband is
subject to a 1000-candidate top-list.
Frequency band
Number of
_
f
subranges
20
151 Hz
1
151
251 Hz
5
251
301 Hz
10
301
401 Hz
20
401
501 Hz
30
501
555 Hz
35
551
651 Hz
45
651
701 Hz
55
701
801 Hz
85
801
926 Hz
105
926
976 Hz
130
TABLE IV. Numbers of
_
f
subranges into which the initial Vela
Jr. search jobs (0.1-Hz subbands) are divided for different
frequency search bands, in order to maintain job durations
between about 6 and 12 computational hours. Each subband is
subject to a 1000-candidate top-list.
Frequency band
Number of
_
f
subranges
20
201 Hz
1
201
401 Hz
5
401
501 Hz
10
501
701 Hz
20
701
901 Hz
40
901
976 Hz
60
TABLE V. Parameters defining the analytic threshold function
2
̄
F
thresh
ð
f
Þ¼
2
̄
F
0
f
a
applied to the
2
̄
F
detection statistic to
define initial outliers for follow-up. Threshold values evaluated
for
f
¼
20
and 976 Hz are also shown.
Source
2
̄
F
0
a
2
̄
F
thresh
ð
20
Hz
Þ
2
̄
F
thresh
ð
976
Hz
Þ
Cassiopeia A 7.64 0.0227
8.18
8.93
Vela Jr.
8.48 0.027
9.19
10.21
TABLE VI. Required increases in excess mean
2
̄
F
in each
stage of outlier follow-up. The third frequency derivative
f
is
taken to be zero in the first two stages, but explicitly searched
over in the third follow-up stage.
Source
Round 1
Round 2
Round 3
Increase
Increase
Increase
Cassiopeia A
65%
60%
70%
Vela Jr.
70%
70%
70%
SEARCH OF THE EARLY O3 LIGO DATA FOR CONTINUOUS
...
PHYS. REV. D
105,
082005 (2022)
082005-5
TABLE VII. Frequency parameters for the loudest Cas A outlier in each cluster that survived round 2 follow-up. Outliers marked with
asterisks were followed up with a third round.
f
_
f
̈
f
f
_
f
̈
f
f
_
f
̈
f
f
_
f
̈
f
(Hz)
(nHz
=
s) (aHz
=
s
2
)
(Hz)
(nHz
=
s) (aHz
=
s
2
)
(Hz)
(nHz
=
s) (aHz
=
s
2
)
(Hz)
(nHz
=
s) (aHz
=
s
2
)
22.2597
0
.
18
85.6
64.8765
0
.
54
24.5
515.1569
1
.
86
20.2
630.3393
65
.
77
9
.
6
22.6684
0
.
41
50.4
64.9955
0
.
71
3.7
520.4822
3
.
13
4.3
630.3606
66
.
06
30.6
24.9982
0
.
27
1.5
67.9953
0
.
74
4.0 *520.6814
2
.
86
28
.
5
630.3788
64
.
06
4
.
5
28.0001
0
.
13
1.7
73.9948
0
.
82
2.4 *520.7275
10
.
13
47.5
630.6003
33
.
38
20.4
29.7984
0
.
33
0.9
74.1949
0
.
81
3.2 *520.7408
12
.
02
7.6
630.7146
56
.
47
13.4
30.1978
0
.
38
5
.
5
74.9948
0
.
81
4.9 *521.4661
0
.
62
6
.
4
638.3140
4
.
82
0.8
30.8993
0
.
11
65.0
79.9947
0
.
78
19.6 *521.4895
4
.
25
17.9
640.4433
7
.
18
63
.
6
30.9979
0
.
32
4.1
84.3942
0
.
91
4.0
521.5134
7
.
75
27
.
4
799.9366
8
.
06
51.6
*31.3903
0
.
33
2.4
90.8932
1
.
11
12
.
7
521.5494
5
.
77
21.0
898.7328
18
.
60
135.3
32.4983
0
.
10
57.7
92.4500
0
.
21
50.1 *522.1882
4
.
01
1.0
898.9294
46
.
32
36.2
33.8982
0
.
10
64.0
107.2843
0
.
33
79.8
527.3181
5
.
26
10
.
7
898.9575
41
.
81
58.2
35.8831
0
.
13
72.6
107.4488
1
.
15
2.3
528.5258
3
.
66
5
.
6
898.9840
34
.
74
56.2
37.9276
0
.
43
28
.
1
119.9910
1
.
30
6.1 *533.4444
5
.
94
0
.
1
898.9993
32
.
69
58.5
37.9974
0
.
41
2.4
301.9999
28
.
76
113.5
599.6389
53
.
61
32.4
899.1333
41
.
93
110.5
38.8732
0
.
09
70.0
316.7777
3
.
49
12.2
599.9509
6
.
48
0.7
899.1675
30
.
36
107.9
40.7971
0
.
45
1.5
333.3861
27
.
40
0.2
604.7859
56
.
67
11.9
899.1826
24
.
69
31
.
6
42.3823
1
.
10
73.6
348.5643
5
.
62
49
.
1
606.4225
62
.
43
30.0
899.2032
12
.
52
17.5
43.3672
1
.
14
30
.
9
368.5754
3
.
85
32.5
606.7767
49
.
63
9.0
906.6986
17
.
85
120.9
44.3524
1
.
18
1.8
485.2598
9
.
74
13.7
606.8898
52
.
72
33.0
909.7752
49
.
35
67.2
45.3311
0
.
17
66.3
485.2772
4
.
83
2.7
612.2997
50
.
45
34.4
910.1130
6
.
43
10
.
9
46.5430
0
.
06
30.6 *487.9915
4
.
36
11.2
612.4531
54
.
58
38.2
918.6993
15
.
63
7.8
46.7866
4
.
35
9.6 *489.5465
12
.
82
33.2
615.0071
57
.
32
42.1
918.7291
27
.
25
15.9
51.6816
0
.
15
97.0
493.7602
0
.
14
104.8
615.0244
59
.
39
19.3
918.8026
1
.
51
1.9
52.8052
0
.
85
9.3
494.7315
2
.
90
5.3
615.0373
61
.
00
79.0
918.8164
24
.
96
18.9
54.7779
0
.
28
74
.
9
495.0989
0
.
03
4
.
9
615.0512
60
.
78
74.8
922.5653
18
.
33
7.3
54.8952
0
.
55
11.6
501.1989
47
.
07
31.7
629.8061
10
.
30
9
.
6
922.5866
13
.
49
34
.
6
57.0006
3
.
78
20
.
8
504.7002
3
.
39
1
.
6
629.8195
9
.
25
2.2 *945.1703
19
.
85
20.8
60.7084
0
.
09
8.9
506.4994
28
.
63
20.5
629.8375
15
.
47
16.1
945.1870
14
.
94
0
.
3
60.8843
0
.
36
59.6
511.9005
35
.
97
92
.
9
630.3149
64
.
10
1
.
9
945.5873
13
.
65
76
.
8
TABLE VIII. Frequency parameters for the loudest Vela Jr. outlier in each cluster that survived round 2 follow-up. Outliers marked
with asterisks were followed up with a third round.
f
_
f
̈
f
f
_
f
̈
f
f
_
f
̈
f
f
_
f
̈
f
(Hz)
(nHz
=
s) (aHz
=
s
2
) (Hz) (nHz
=
s) (aHz
=
s
2
)
(Hz)
(nHz
=
s) (aHz
=
s
2
)
(Hz)
(nHz
=
s) (aHz
=
s
2
)
20.0010
0
.
19
1
.
4
40.5022
0
.
40
1.9
90.0002
0
.
35
3
.
0
612.1648
3
.
19
2.9
21.2899
0
.
10
26
.
8
40.7002
0
.
71
3
.
2
96.0010
1
.
12
0.7
614.7653
3
.
77
3.7
22.2618
0
.
19
16
.
8
43.8618
0
.
43
1.0
107.2955
1
.
01
8
.
8
629.8914
18
.
55
6.2
22.6708
0
.
53
1.2
45.0022
0
.
35
16
.
4
130.9282
0
.
94
18
.
8
651.2010
7
.
28
7.6
23.6569
0
.
57
24
.
6
50.5949
0
.
44
5
.
9
299.3549
11
.
33
3.0
652.8396
1
.
20
8
.
6
24.6429
0
.
59
0.3
51.1027
0
.
53
6.9
487.2795
14
.
83
26.2 *861.6319
9
.
66
7.7
25.9183
0
.
26
2.4
52.8106
0
.
83
1
.
3
*488.2895
14
.
54
7.3
898.8810
15
.
84
0.4
27.9117
0
.
25
3
.
4
53.8008
0
.
95
8
.
9
493.2190
7
.
06
2.9
899.4151
27
.
55
7.2
28.9086
0
.
29
1.9
54.7814
0
.
25
0.8
*494.6662
22
.
17
5.4
906.9044
14
.
44
5.2
29.8928
0
.
20
3.3
57.0029
0
.
50
8
.
1
499.9158
4
.
49
21
.
5
910.0385
17
.
82
12.3
35.8866
0
.
24
21
.
4
60.7141
0
.
51
6
.
0
504.0999
12
.
64
7.1
918.7510
16
.
75
4.1
37.5019
0
.
35
1
.
5
67.0034
0
.
63
0
.
9
510.9000
2
.
30
13.1
918.8933
27
.
56
3.5
38.5020
0
.
37
0.2
68.0035
0
.
66
2.6
519.2834
14
.
17
6.2
945.2994
7
.
15
20.0
38.8775
0
.
38
0.9
73.4020
0
.
03
1
.
7
519.2962
10
.
62
5.5
945.3565
17
.
64
1.7
38.9301
0
.
07
28
.
6
74.6306
0
.
70
0.5
520.5149
5
.
31
14.3
39.8743
0
.
39
1.5
85.6896
1
.
06
3
.
7
521.6642
18
.
22
3.0
R. ABBOTT
et al.
PHYS. REV. D
105,
082005 (2022)
082005-6
amplitudes ranging from
1
.
1
1
.
5
times the estimated
strain amplitude
h
95%
sens
for which the
2
̄
F
thresh
ð
f
Þ
threshold
yields 95% efficiency (see Sec.
V
). The required increases
in
2
̄
F
leads to an losses in overall signal efficiency below
2%
for braking indices below 7. For each follow-up stage,
the search space around each outlier
s values of
f
,
_
f
and
̈
f
FIG. 1. Upper panel: example of
strain histogram
graph for Cas A used in vetoing outliers for which instrumental contamination is
apparent. The curves show the O3a-run-averaged H1 (red dashed) and L1 (blue solid) amplitude spectral densities in a narrow band
containing an artifact at 48.000 Hz. The dotted curves show histograms of expected strain excess from H1 (black) and L1 (magenta)
signal templates added to smooth backgrounds interpolated from neighboring frequency bands. In this depiction, the strain amplitude of
the signal template has been magnified by an arbitrary factor large enough to make the signal
s structure clear. The large excess power in
the H1 data, not seen in the L1 data, despite comparable strain sensitivities and comparable sidereal-averaged antenna pattern
sensitivities, excludes an astrophysical source for the H1 artifact. The fact that the artifact aligns in frequency with the putative signal
s
template peak in power confirms contamination of the outlier from an instrumental source. In addition, the line at precisely an integer
frequency is part of a known instrumental spectral comb in the O3a H1 data. Lower panel: graph of the corresponding template signal
frequencies
vs.
time during O3a in the H1 and L1 interferometer reference frames, in which frequency points are plotted for only those
30-minute segments used in the analysis. One sees a relatively stationary period early in the run for Cas A. The inset box shows a
magnification of the frequency
vs.
time graph for a 15-day period starting at the midpoint of the O3a interval, one that includes a multi-
day period during which no data was collected from the L1 interferometer because Hurricane Barry disrupted observatory operations.
The magnification makes more clear the diurnal modulation of the reference-frame frequency by the Earth
s rotation about its axis, with
slightly larger modulations seen for the lower-latitude L1 interferometer than for H1.
SEARCH OF THE EARLY O3 LIGO DATA FOR CONTINUOUS
...
PHYS. REV. D
105,
082005 (2022)
082005-7
was chosen to be three times (in all dimensions) the
template step sizes used in the previous stage. In the third
stage, the range of
f
searches is from zero to twice the
implied value of the 2nd-round survivor, assuming a power
law spindown during the observation period. All of these
follow-up requirements and resulting efficiencies were
evaluated by end-to-end software injections.
In the first stage of follow-up, all outliers above threshold
are evaluated. In that initial stage, which more finely
samples the parameter space, multiple outliers may survive
the next threshold requirement. In successive stages, only
the loudest survivor corresponding to the outlier being
evaluated is passed to the next stage of follow-up. Pursuing
only the loudest survivor per initial outlier preserves high
detectionefficiencyfora true signalwhilereducingcomputa-
tional cost from following up multiple candidate templates
contaminated by the same instrumental disturbance.
IV. SEARCH RESULTS
The search described above was carried out on the O3a
data for the Cas A and Vela Jr. sources. For Cas A (Vela Jr.),
there were
2
×
10
5
(
1
×
10
5
) outliers above threshold
from the initial search in bands that were not excluded from
consideration by severe instrumental artifacts. These out-
liers were all followed up individually with a narrowed
search and a doubling of the coherence time. An outlier was
considered to survive follow-up if the loudest candidate
FIG. 2. Example of strain histogram and template frequency
vs.
time graphs for a Vela Jr. outlier with the same definitions (and colors)
used for Cas A in Fig.
1
. One key difference with respect to Cas A is that the interval of relatively stationary interferometer-frame
frequency corresponding to the 48-Hz instrumental line occurs after the midpoint for Vela Jr. because of its different sky location from
Cas A.
R. ABBOTT
et al.
PHYS. REV. D
105,
082005 (2022)
082005-8