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Search of the Early O3 LIGO Data for Continuous Gravitational Waves from the
Cassiopeia A and Vela Jr. Supernova Remnants
LIGO Scientific Collaboration and Virgo Collaboration
(compiled March 23, 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
semi-coherent 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.
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, G111.7
2.1) [1]
and Vela Jr. (G266.2
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 ob-
jects have been the target of multiple searches for contin-
uous gravitational waves since 2010 [5–11] because they
may retain high rotation frequencies and may possess ap-
preciable non-axisymmetries from their recent births [12–
20]. Continuous emission due to unstable
r
-modes 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 Ad-
vanced Laser Interferometer Gravitational wave Obser-
vatory (Advanced LIGO [26, 27]). We achieve signifi-
cantly 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 instru-
ment 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 pro-
cesses can disrupt the symmetry, however, to produce
quadrupolar gravitational waves from the stellar rota-
tion. Those processes include crustal distortions from
cooling or accretion, buried magnetic field energy and
excitation of r-modes. Comprehensive reviews of contin-
uous gravitational wave emission mechanisms from neu-
tron stars can be found in [30, 31]
Central compact objects (CCOs) at the cores of su-
pernova remnants present interesting potential sources,
especially 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 ampli-
tude 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
= (2
.
3
×
10
24
)
(
1 kpc
r
)
(
1000 yr
τ
)(
I
zz
I
0
)
,
(1)
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
= 10
38
kg
·
m
2
.
Cas A is perhaps the most promising example of a
potential gravitational wave CCO source in a supernova
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 equa-
tion 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
pessimistic 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.
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.
arXiv:2111.15116v2 [gr-qc] 22 Mar 2022
2
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 semi-
coherent summing of a matched-filter detection statistic
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. DATA SETS USED
Advanced LIGO consists of two detectors, one in Han-
ford, 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 data set 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 dur-
ing the O3 run. The systematic error in the amplitude
calibration is estimated to be lower than 7% (68% confi-
dence interval) for both LIGO detectors over all frequen-
cies 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 instrumen-
tal artifacts. As in previous Advanced LIGO observ-
ing runs [45], instrumental “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 fre-
quent and loud “glitches” (short, high-amplitude instru-
mental 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
transients from the data.
III. ANALYSIS METHOD
This search relies upon semi-coherent 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 anal-
ysis. Section III B describes the mean
F
-statistic detec-
tion statistic at the core of the analysis. Section III C de-
scribes the
Weave
infrastructure for summing individual
F
-statistic values over the observation period, including
the configuration 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 radi-
ation in the directions perpendicular to the rotation axis
and elliptical polarization for the general case. The strain
signal model
h
(
t
) for the source, as seen by the detector,
is assumed to be the following function of time
t
:
h
(
t
) =
h
0
(
F
+
(
t,α
0
0
)
1 + cos
2
(
ι
)
2
cos(Φ(
t
))
+
F
×
(
t,α
0
0
) cos(
ι
) sin(Φ(
t
))
)
,
(2)
In Eq. 2,
h
0
is the intrinsic strain amplitude, Φ(
t
) is the
signal phase,
F
+
and
F
×
characterize the detector re-
sponses to signals with “+” and “
×
” quadrupolar polar-
izations [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 inclination 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 lin-
ear polarization case (
ι
=
π/
2) is the most unfavorable
because the gravitational wave flux impinging on the de-
tectors is smallest for an intrinsic strain amplitude
h
0
,
possessing eight times less incident strain power than for
circularly polarized waves (
ι
= 0
, π
).
In a rotating triaxial ellipsoid model for a star at dis-
tance
r
spinning at frequency
f
rot
about its (approxi-
mate) symmetry axis (
z
), the amplitude
h
0
can be ex-