of 25
First targeted search for gravitational-wave bursts from core-collapse
supernovae in data of first-generation laser interferometer detectors
B. P. Abbott
etal.
*
(LIGO Scientific Collaboration and Virgo Collaboration)
(Received 25 May 2016; published 15 November 2016)
We present results from a search for gravitational-wave bursts coincident with two core-collapse
supernovae observed optically in 2007 and 2011. We employ data from the Laser Interferometer
Gravitational-wave Observatory (LIGO), the Virgo gravitational-wave observatory, and the GEO 600
gravitational-wave observatory. The targeted core-collapse supernovae were selected on the basis of
(1) proximity (within approximately 15 Mpc), (2) tightness of observational constraints on the time of core
collapse that defines the gravitational-wave search window, and (3) coincident operation of at least two
interferometers at the time of core collapse. We find no plausible gravitational-wave candidates. We present
the probability of detecting signals from both astrophysically well-motivated and more speculative
gravitational-wave emission mechanisms as a function of distance from Earth, and discuss the implications
for the detection of gravitational waves from core-collapse supernovae by the upgraded Advanced LIGO
and Virgo detectors.
DOI:
10.1103/PhysRevD.94.102001
I. INTRODUCTION
Core-collapse supernovae (CCSNe) mark the violent
death of massive stars. It is believed that the initial collapse
of a star
s iron core results in the formation of a proto-
neutron star and the launch of a hydrodynamic shock wave.
The latter, however, fails to immediately explode the star,
but stalls and must be
revived
by a yet-uncertain supernova
mechanism
on a
0
.
5
1
s timescale to explode the star
(e.g., Refs.
[1
3]
). If the shock is not revived, a black hole
is formed, and no explosion, or only a very weak explosion,
results (e.g., Refs.
[4
6]
). If the shock is revived, it reaches
the stellar surface and produces the spectacular electro-
magnetic display of a type-II or type-Ib/c supernova. The
type classification is based on the explosion light curve and
spectrum, which depend largely on the nature of the
progenitor star (e.g., Ref.
[7]
). The time from core collapse
to breakout of the shock through the stellar surface and first
supernova light is minutes to days, depending on the radius
of the progenitor and energy of the explosion (e.g.,
Refs.
[8
10]
).
Any core-collapse event generates a burst of neutrinos
that releases most of the protoneutron star
s gravitational
binding energy (
3
×
10
53
erg
0
.
15
M
c
2
) on a time
scale of order 10 seconds. This neutrino burst was detected
from SN 1987A and confirmed the basic theory of CCSNe
[1,11
13]
.
Gravitational waves (GWs) are emitted by aspherical
mass-energy dynamics that include quadrupole or higher-
order contributions. Such asymmetric dynamics are
expected to be present in the pre-explosion stalled-shock
phase of CCSNe and may be crucial to the CCSN explosion
mechanism (see, e.g., Refs.
[14
17]
). GWs can serve as
probes of the magnitude and character of these asymmetries
and thus may help in constraining the CCSN mechanism
[18
20]
.
Stellar collapse and CCSNe were considered as potential
sources of detectable GWs already for resonant bar
detectors in the 1960s
[21]
. Early analytic and semianalytic
estimates of the GW signature of stellar collapse and
CCSNe (e.g., Refs.
[22
26]
) gave optimistic signal
strengths, suggesting that first-generation laser interferom-
eter detectors could detect GWs from CCSNe in the Virgo
cluster (at distances
D
10
Mpc). Modern detailed multi-
dimensional CCSN simulations (see, e.g., Refs.
[20,27
35]
and the reviews in Refs.
[36
38]
) find GW signals of short
duration (
1
s) and emission frequencies in the most
sensitive
10
2000
Hz band of ground-based laser inter-
ferometer detectors. Predicted total emitted GW energies
are in the range
10
12
10
8
M
c
2
for emission mechanisms
and progenitor parameters that are presently deemed
realistic. These numbers suggest that the early predictions
were optimistic and that even second-generation laser
interferometers (operating from 2015+) such as
Advanced LIGO
[39]
, Advanced Virgo
[40]
, and
KAGRA
[41]
will only be able to detect GWs from very
nearby CCSNe at
D
1
100
kpc. Only our own
Milky Way and the Magellanic Clouds are within that
range. The expected event rate is very low and estimated to
be
2
3
CCSNe
=
100
yr
[42
47]
.
However, there are also a number of analytic and
semianalytic GW emission models of more extreme sce-
narios, involving nonaxisymmetric rotational instabilities,
centrifugal fragmentation, and accretion disk instabilities.
The emitted GW signals may be sufficiently strong to be
detectable to much greater distances of
D
10
15
Mpc,
*
Full author given at the end of the article.
PHYSICAL REVIEW D
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=
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=
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=
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© 2016 American Physical Society
perhaps even with first-generation laser interferometers (e.
g., Refs.
[48
51]
). These emission scenarios require special
and rare progenitor characteristics, but they cannot pres-
ently be strictly ruled out on theoretical grounds. In a
sphere of radius
15
Mpc centered on Earth, the CCSN
rate is
1
=
yr
[8,52]
. This makes Virgo cluster CCSNe
interesting targets for constraining extreme GW emission
scenarios.
Previous observational constraints on GW burst sources
applicable to CCSNe come from all-sky searches for short-
duration GW burst signals
[53
59]
. These searches did not
target individual astrophysical events. In addition, a
matched-filter search looking for monotonic GW chirps
has been performed for the type-Ib/c SN 2010br using
publicly released LIGO data
[60]
; no candidate GW
detections were identified. Targeted searches have the
advantage over all-sky searches that potential signal can-
didates in the data streams have to arrive in a well-defined
temporal
on-source window
and have to be consistent with
coming from the sky location of the source. Both con-
straints can significantly reduce the noise background and
improve the sensitivity of the search (e.g., Ref.
[61]
).
Previous targeted GW searches have been carried out for
gamma-ray bursts
[62
69]
, soft gamma repeater flares
[70,71]
, and pulsar glitches
[72]
. A recent study
[73]
confirmed that targeted searches with Advanced LIGO
and Virgo at design sensitivity should be able to detect
neutrino-driven CCSNe out to several kiloparsecs and
rapidly rotating CCSNe out to tens of kiloparsecs, while
more extreme GW emission scenarios will be detectable to
several megaparsecs. An extended analysis
[74]
of GW
spectrograms shows that several characteristic CCSN
signal features can be extracted with KAGRA, Advanced
LIGO and the Virgo network.
In this paper, we present a targeted search for GWs from
CCSNe using the first-generation Initial LIGO (iLIGO)
[75]
, GEO 600
[76]
, and Virgo
[77]
laser interferometer
detectors. The data searched were collected over 2005
2011 in the S5, A5, and S6 runs of the iLIGO and GEO 600
detectors, and in the VSR1
VSR4 runs of the Virgo
detector. From the set of CCSNe observed in this period
[78]
, we make a preliminary selection of four targets for our
search: SNe 2007gr, 2008ax, 2008bk, and 2011dh. These
CCSNe exploded in nearby galaxies (
D
10
Mpc), have
well constrained explosion dates, and have at least partial
coverage by coincident observation of more than one
interferometer. SNe 2008ax and 2008bk occurred in the
astrowatch (A5) period between the S5 and S6 iLIGO
science runs. In A5, the principal goal was detector
commissioning, not data collection. Data quality and
sensitivity were not of primary concern. Preliminary
analyses of the gravitational-wave data associated with
SNe 2008ax and 2008bk showed that the sensitivity was
much poorer than the data for SNe 2007gr and 2011dh.
Because of this, we exclude SNe 2008ax and 2008bk and
focus our search and analysis on SNe 2007gr and 2011dh.
It is also worth mentioning that a matched filter search for a
type-Ib/c supernovae GW database was performed on
publicly released LIGO data
[79]
with no detection
claimed. The search was not targeted in the sense used here.
We find no evidence for GW signals from SNe 2007gr or
2011dh in the data. Using gravitational waveforms from
CCSN simulations, waveforms generated with phenom-
enological astrophysical models, and
ad hoc
waveforms,
we measure the sensitivity of our search. We show that
none of the considered astrophysical waveforms would
likely be detectable at the distances of SNe 2007gr and
2011dh for the first-generation detector networks.
Furthermore, even a very strong gravitational wave could
potentially be missed due to incomplete coverage of the
CCSN on-source window by the detector network.
Motivated by this, we provide a statistical approach for
model exclusion by combining observational results for
multiple CCSNe. Using this approach, we quantitatively
estimate how increased detector sensitivity and a larger
sample of targeted CCSNe will improve our ability to
rule out the most extreme emission models. This suggests
that observations with second-generation
advanced
interferometers
[39
41]
will be able to put interesting
constraints on the GW emission of extragalactic CCSN
at
D
10
Mpc.
The remainder of this paper is structured as follows: In
Sec.
II
, we discuss the targeted CCSNe and the determi-
nation of their on-source windows. In Sec.
III
, we describe
the detector networks, the coverage of the on-source
windows with coincident observation, and the data
searched. In Sec.
IV
, we present our search methodology
and the waveform models studied. We present the search
results in Sec.
V
and conclusions in Sec.
VI
.
II. TARGETED CORE-COLLAPSE SUPERNOVAE
For the present search, it is important to have an estimate
of the time of core collapse for each supernova. This time
coincides (within one to a few seconds; e.g., Ref.
[36]
) with
the time of strongest GW emission. The better the estimate
of the core-collapse time, the smaller the
on-source window
of detector data that must be searched and the smaller the
confusion background due to non-Gaussian nonstationary
detector noise.
For a Galactic or Magellanic Cloud CCSN, the time of
core collapse would be extremely well determined by the
time of arrival of the neutrino burst that is emitted
coincident with the GW signal
[80]
. A very small on-
source window of seconds to minutes could be used for
such a special event.
For CCSNe at distances
D
1
Mpc, an observed
coincident neutrino signal is highly unlikely
[81
83]
.In
this case, the time of core collapse must be inferred based
on estimates of the explosion time, explosion energy, and
the radius of the progenitor. The explosion time is defined
B. P. ABBOTT
et al.
PHYSICAL REVIEW D
94,
102001 (2016)
102001-2
as the time at which the supernova shock breaks out of the
stellar surface and the electromagnetic emission of the
supernova begins. Basic information about the progenitor
can be obtained from the light curve and spectrum of the
supernova (e.g., Ref.
[7]
). Much more information can be
obtained if pre-explosion imaging of the progenitor is
available (e.g., Ref.
[84]
). A red supergiant progenitor
with a typical radius of
500
1500
R
produces a type-IIP
supernova and has an explosion time of
1
2
days after
core collapse and a typical explosion energy of
10
51
erg;
subenergetic explosions lead to longer explosion times
(e.g., Refs.
[8
10]
). A yellow supergiant that has been
partially stripped ofits hydrogen-rich envelope, giving rise to
a IIb supernova (e.g., Ref.
[85]
), is expected to have a radius
of
200
500
R
and an explosion time of
0
.
5
days after
core collapse
[10,85]
. A blue supergiant, giving rise to a
peculiar type-IIPsupernova (such asSN 1987A),hasa radius
of
100
R
and an explosion time of
2
3
hours after core
collapse. AWolf-Rayet star progenitor, giving rise to a type-
Ib/c supernova, has been stripped of its hydrogen (and
helium) envelope by stellar winds or binary interactions
and has a radius of only a few to
10
R
and shock breakout
occurs within
10
100
s of core collapse
[8,9]
.
The breakout of the supernova shock through the surface
of the progenitor star leads to a short-duration high-
luminosity burst of electromagnetic radiation with a spec-
tral peak dependent on the radius of the progenitor. The
burst from shock breakout precedes the rise of the optical
light curve, which occurs on a time scale of days after shock
breakout (depending, in detail, on the nature of the
progenitor star; Refs.
[7,10,85,86]
).
With the exception of very few serendipitous discoveries
of shock breakout bursts (e.g., Refs.
[87,88]
), core-collapse
supernovae in the 2007
2011 time frame of the present GW
search were usually discovered days after explosion, and
their explosion time is constrained by one or multiple of
(i) the most recent nondetection, i.e., by the last date of
observation of the host galaxy without the supernova
present; (ii) the comparison of the observed light curve
and spectra with those of other supernovae for which the
explosion time is well known; (iii) the light-curve extrapo-
lation
[89]
; or, (iv), for type IIP supernovae, light-curve
modeling using the expanding photosphere method (EPM;
e.g., Refs.
[90,91]
).
More than 100 core-collapse supernovae were discov-
ered in the optical by amateur astronomers and professional
astronomers (e.g., Ref.
[78]
) during the S5/S6 iLIGO and
the VSR2, VSR3, VSR4 Virgo data-taking periods. In
order to select optically discovered core-collapse super-
novae as triggers for this search, we impose the following
criteria: (i) A distance from Earth not greater than
10
15
Mpc. Since GWs from core-collapse supernovae
are most likely very weak and because the observable GW
amplitude scales with 1 over the distance, nearer events are
greatly favored. (ii) A well-constrained time of explosion
leading to an uncertainty in the time of core collapse of less
than
2
weeks. (iii) At least partial availability of science-
quality data of coincident observations of more than one
interferometer in the on-source window.
The core-collapse supernovae making these cuts are SN
2007gr, SN 2008ax, SN 2008bk, and SN 2011dh. Table
I
summarizes key properties of these supernovae, and we
discuss each in more detail in the following.
SN 2007gr
, a type-Ic supernova, was discovered on 2007
August 15.51 UTC
[92]
. A prediscovery empty image
taken by KAIT
[93]
on August 10.44 UTC provides a
baseline constraint on the explosion time. The progenitor of
this supernova was a compact stripped-envelope star
[94
97]
through which the supernova shock propagated
within tens to hundreds of seconds. In order to be
conservative, we add an additional hour to the interval
between discovery and last nondetection and arrive at a GW
on-source window of 2007 August 10.39 UTC to 2007
August 15.51 UTC. The sky location of SN 2007gr is
R
:
A
:
¼
02
h
43
m
27
s
.
98
, Decl
¼þ
37
°
20
0
44
′′
.
7
[92]
. The
host galaxy is NGC 1058. Schmidt
et al.
[98]
used EPM
to determine the distance to SN 1969L, which exploded in
the same galaxy. They found
D
¼ð
10
.
6
þ
1
.
9
1
.
1
Þ
Mpc.
This is broadly consistent with the more recent Cepheid-
based distance estimate of
D
¼ð
9
.
29

0
.
69
Þ
Mpc to
TABLE I. Core-collapse supernovae selected as triggers for the gravitational-wave search described in this paper. Distance gives the
best current estimate for the distance to the host galaxy.
t
1
and
t
2
are the UTC dates delimiting the on-source window.
Δ
t
is the temporal
extent of the on-source window. iLIGO/Virgo run indicates the data-taking campaign during which the supernova explosion was
observed. Detectors lists the interferometers taking data during at least part of the on-source window. The last column provides the
relative coverage of the on-source window with science-quality or Astrowatch-quality data of at least two detectors. For SN 2007gr, the
relative coverage of the on-source window with the most sensitive network of four active interferometers is 67%. See the text in Sec.
II
for details and references on the supernovae, and see Sec.
III
for details on the detector networks, coverage, and data quality.
Host
Distance
t
1
t
2
Δ
t
iLIGO/Virgo
Active
Coincident
Identifier Type Galaxy
[Mpc]
[UTC]
[UTC]
[days]
Run
Detectors Coverage
SN 2007gr Ic NGC 1058
10
.
55

1
.
95
2007 Aug 10.39 2007 Aug 15.51 5.12 S5/VSR1 H1, H2, L1, V1 93%
SN 2008ax IIb NGC 4490
9
.
64
þ
1
.
38
1
.
21
2008 Mar 2.19 2008 Mar 3.45 1.26
A5
G1, H2
8%
SN 2008bk IIP NGC 7793
3
.
53
þ
0
.
21
0
.
29
2008 Mar 13.50 2008 Mar 25.14 11.64
A5
G1, H2
38%
SN 2011dh IIb
M51
8
.
40

0
.
70
2011 May 30.37 2011 May 31.89 1.52 S6E/VSR4
G1, V1
37%
TARGETED SEARCH FOR GRAVITATIONAL-WAVE BURSTS
...
PHYSICAL REVIEW D
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NGC 925 by Ref.
[99]
. This galaxy is in the same
galaxy group as NGC 1058 and thus presumed to be
in close proximity. For the purpose of the present study,
we use the conservative combined distance estimate
of
D
¼ð
10
.
55

1
.
95
Mpc
Þ
.
SN 2008ax
, a type-IIb supernova
[100]
, was discovered
by KAIT on 2008 March 3.45 UTC
[101]
. The fortuitous
nondetection observation made by Arbour on 2008 March
3.19 UTC
[102]
, a mere 6.24 h before the SN discovery,
provides an excellent baseline estimate of the explosion
time. Spectral observations indicate that the progentior of
SN 2008ax was almost completely stripped of its hydrogen
envelope, suggesting that is exploded either as a yellow
supergiant or as a Wolf-Rayet star
[103,104]
. Most
recent observations and phenomenological modeling by
Ref.
[105]
suggest that the progenitor was in a binary
system and may have had a blue-supergiant appearance and
an extended (
30
40
R
) low-density (thus, low-mass)
hydrogen-rich envelope at the time of explosion. To be
conservative, we add an additional day to account for the
uncertainty in shock propagation time and define the GW
on-source window as 2008 March 2.19 UTC to 2008
March 3.45 UTC. The coordinates of SN 2008ax are
R
:
A
:
¼
12
h
30
m
40
s
.
80
,Decl
¼þ
41
°
38
0
14
′′
.
5
[101]
.Its
host galaxy is NGC 4490, which together with NGC
4485 forms a pair of interacting galaxies with a high star
formation rate. We adopt the distance
D
¼ð
9
.
64
þ
1
.
38
1
.
21
Þ
Mpc given by Pastorello
et al.
[106]
.
SN 2008bk
, a type-IIP supernova, was discovered on
2008 March 25.14 UTC
[107]
. Its explosion time is poorly
constrained by a pre-explosion image taken on 2008
January 2.74 UTC
[107]
. Morrell and Stritzinger
[108]
compared a spectrum taken of SN 2008bk on 2008 April
12.4 UTC to a library of SN spectra
[109]
and found a best
fit to the spectrum of SN 1999em taken at 36 days after
explosion
[108]
. However, the next other spectra available
for SN 1999em are from 20 and 75 days after explosion, so
the uncertainty of this result is rather large. EPM modeling
by Dessart
[110]
suggests an explosion time of March
19
.
5

5
UTC, which is broadly consistent with the light-
curve data and hydrodynamical modeling presented in
Ref.
[111]
. The progenitor of SN 2008bk was most likely
a red supergiant with a radius of
500
R
[112
114]
, which
suggests an explosion time of
1
day after core collapse
[8
10]
. Hence, we assume a conservative on-source win-
dow of 2008 March 13.5 UTC to 2008 March 25.14 UTC.
The coordinates of SN 2008bk are R
:
A
:
¼
23
h
57
m
50
s
.
42
,
Decl
¼
32
°
33
0
21
′′
.
5
[115]
. Its host galaxy is
NGC 7793, which is located at a Cepheid distance
D
¼ð
3
.
44
þ
0
.
21
0
.
2
Þ
Mpc
[116]
. This distance esti-
mate is consistent with
D
¼ð
3
.
61
þ
0
.
13
0
.
14
Þ
Mpc
obtained by Ref.
[117]
based on the tip of the red-giant
branch method (e.g., Ref.
[118]
). For the purpose of
this study, we use a conservative averaged estimate of
D
¼ð
3
.
53
þ
0
.
21
0
.
29
Þ
Mpc.
SN 2011dh
, a type-IIb supernova, has an earliest dis-
covery date in the literature of 2011 May 31.893, which
was by amateur astronomers
[119
122]
. An earlier dis-
covery date of 2011 May 31.840 is given by Alekseev
[123]
and a most recent nondetection by Dwyer on 2011 May
31.365
[123]
. The progenitor of SN 2011dh was with high
probability a yellow supergiant star
[124]
with a radius of a
few
100
R
[85,125,126]
. We conservatively estimate an
earliest time of core collapse of a day before the most recent
nondetection by Dwyer and use an on-source window of
2011 May 30.365 to 2011 May 31.893. SN 2011dh
s
location is R
:
A
:
¼
13
h
30
m
05
s
.
12
, Decl
¼þ
47
°
10
0
11
′′
.
30
[127]
in the nearby spiral galaxy M51. The best estimates
for the distance to M51 come from Vinkó
et al.
[125]
,who
give
D
¼
8
.
4

0
.
7
Mpc on the basis of EPM modeling of
SN 2005cs and SN 2011dh. This is in agreement with
Feldmeier
et al.
[128]
, who give
D
¼
8
.
4

0
.
6
Mpc on the
basis of planetary nebula luminosity functions. Estimates
using surface brightness variations
[129]
or the Tully-
Fisher relation
[130]
are less reliable, but give somewhat
lower distance estimates of
D
¼
7
.
7

0
.
9
and
D
¼
7
.
7

1
.
3
, respectively. We adopt the conservative
distance
D
¼
8
.
4

0
.
7
Mpc for the purpose of this
study.
III. DETECTOR NETWORKS AND COVERAGE
This search employs data from the 4 km LIGO Hanford,
Washington, and LIGO Livingston, Louisiana, interferom-
eters (denoted
H1
and
L1
, respectively), from the 2 km
LIGO Hanford, Washington, interferometer (denoted as
H2
), from the 0.6 km GEO 600 detector near Hannover,
Germany (denoted as
G1
), and from the 3 km Virgo
interferometer near Cascina, Italy (denoted as
V1
).
Table
II
lists the various GW interferometer data-taking
periods (
runs
) in the 2005
2011 time frame from which
we draw data for our search. The table also provides the
duty factor and
coincident
duty factor of the GW interfer-
ometers. The duty factor is the fraction of the run time a
given detector was taking science-quality data. The coinci-
dent duty factor is the fraction of the run time at least two
detectors were taking science quality data. The coincident
duty factor is most relevant for GW searches like ours that
require data from at least two detectors to reject candidate
events that are due to non-Gaussian instrumental or
environmental noise artifacts (
glitches
) but can mimic
real signals in shape and time-frequency content (see, e.g.,
Refs.
[57,75]
).
One notes from Table
II
that the duty factor for the first-
generation interferometers was typically
50%
80%
. The
relatively low duty factors are due to a combination of
environmental causes (such as distant earthquakes causing
loss of interferometer lock) and interruptions for detector
commissioning or maintenance.
The CCSNe targeted by this search and described in
Sec.
II
are the only 2007
2011 CCSNe located within
B. P. ABBOTT
et al.
PHYSICAL REVIEW D
94,
102001 (2016)
102001-4
D
10
15
Mpc for which well-defined on-source win-
dows exist and which are also covered by extended
stretches of coincident observations of at least two inter-
ferometers. In Fig.
1
, we depict the on-source windows for
SNe 2007gr, 2008ax, 2008bk, and 2011dh. We indicate
with regions of different color times during which the
various interferometers were collecting data.
SN 2007gr exploded during the S5/VSR1 joint run
between the iLIGO, GEO 600, and Virgo detectors. It
has the best coverage of all considered CCSNe: 93% of its
on-source window is covered by science-quality data from
at least two of H1, H2, L1, and V1. We search for GWs
from SN 2007gr at times when data from the following
detector networks are available: H1H2L1V1, H1H2L1,
H1H2V1, H1H2, L1V1. The G1 detector was also taking
data during SN 2007gr
s on-source window, but since its
sensitivity was much lower than that of the other detectors,
we do not analyze G1 data for SN 2007gr.
SNe 2008ax and 2008bk exploded in the A5 astrowatch
run between the S5 and S6 iLIGO science runs
(cf. Table
II
). Only the G1 and H2 detectors were operating
at sensitivities much lower than those of the 4 km L1 and
H1 and the 3 km V1 detectors. The coincident duty factor
for SN 2008ax is only 8%, while that for SN 2008bk is
TABLE II. Overview of GW interferometer science runs from which we draw data for our search. H1 and H2 stand for the LIGO
Hanford 4 km and 2 km detectors, respectively. L1 stands for the LIGO Livingston detector. V1 stands for the Virgo detector, and G1
stands for the GEO 600 detector. The duty factor column indicates the approximate fraction of science-quality data during the
observation runs. The coincident duty factor column indicates the fraction of time during which at least two detectors were taking
science-quality data simultaneously. The A5 run was classified as astrowatch and was not a formal science run. The H2 and V1 detectors
operated for only part of A5. The Virgo VSR1 run was joint with the iLIGO S5 run, the Virgo VSR2 and VSR3 runs were joint with the
iLIGO S6 run, and the GEO 600 detector (G1) operated in iLIGO run S6E during Virgo run VSR4. When iLIGO and Virgo science runs
overlap, the coincident duty factor takes into account iLIGO, GEO 600, and Virgo detectors.
Run
Detectors
Run Period
Duty Factors
Coin. Duty Factor
S5
H1, H2, L1, G1 2005/11/04
2007/10/01
75%
(H1),
76%
(H2),
65%
(L1),
77%
(G1)
87%
A5
G1, H2, V1
2007/10/01
2009/05/31
81%
(G1),
18%
(H2),
5%
(V1)
18%
S6
L1, H1, G1
2009/07/07
2010/10/21
51%
(H1),
47%
(L1),
56%
(G1)
67%
S6E
G1
2011/06/03
2011/09/05
77%
66%
VSR1/S5
V1
2007/05/18
2007/10/01
80%
97%
VSR2/S6
V1
2009/07/07
2010/01/08
81%
74%
VSR3/S6
V1
2010/08/11
2010/10/19
73%
94%
VSR4/S6E
V1
2011/05/20
2011/09/05
78%
62%
FIG. 1. On-source windows as defined for the four core-collapse supernovae considered in Sec.
II
. The date given for each core-
collapse supernova is the published date of discovery. Overplotted in color are the stretches of time covered with science-quality and
Astrowatch-quality data of the various GW interferometers. The percentages given for each core-collapse supernova and interferometer
are the fractional coverage of the on-source window with science or astrowatch data by that interferometer. See Table
I
and Secs.
II
and
III
for details.
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...
PHYSICAL REVIEW D
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102001 (2016)
102001-5
38%. Preliminary analysis of the available coincident GW
data showed that due to a combination of low duty factors
and low detector sensitivity, the overall sensitivity to GWs
from these CCSNe was much lower than for SNe 2007gr
and 2011dh. Because of this, we exclude SNe 2008ax and
2008bk from the analysis presented in the rest of this paper.
SN 2011dh exploded a few days before the start of the
S6E/VSR4 run during which the V1 and G1 interferom-
eters were operating (cf. Table
II
). G1 was operating in
GEO-HF mode
[131]
, which improved its high-frequency
(
f
1
kHz) sensitivity to within a factor of 2 of V1
s
sensitivity. While not officially in a science run during the
SN 2011dh on-source window, both G1 and V1 were
operating and collecting data that passed the data quality
standards necessary for being classified as science-quality
data (e.g., Refs.
[132
134]
). The coincident G1V1 duty
factor is 37% for SN 2011dh.
In Fig.
2
, we plot the one-side noise amplitude spectral
densities of each detector averaged over the on-source
windows of SNe 2007gr and 2011dh. In order to demon-
strate the high-frequency improvement in the 2011 G1
detector, we also plot the G1 noise spectral density for SN
2008ax for comparison.
IV. SEARCH METHODOLOGY
Two search algorithms are employed in this study:
X-P
IPELINE
[61,135]
and Coherent WaveBurst (
C
WB)
[136]
. Neither algorithm requires detailed assumptions
about the GW morphology, and both look for subsecond
GW transients in the frequency band 60
2000 Hz. This is
the most sensitive band of the detector network, where the
amplitude of the noise spectrum of the most sensitive
detector is within about an order of magnitude of its
minimum. This band also encompasses most models for
GW emission from CCSNe (cf. Refs.
[36,37,137]
). The
benefit of having two independent algorithms is that they
can act as a cross-check for outstanding events.
Furthermore, sensitivity studies using simulated GWs show
some complementarity in the signals detected by each
pipeline; this is discussed further in Sec.
V
.
The two algorithms process the data independently to
identify potential GW events for each supernova and
network combination. Each algorithm assigns a
loudness
measure to each event; these are described in more detail
below. The two algorithms also evaluate measures of signal
consistency across different interferometers and apply
thresholds on these measures (called coherence tests) to
reject background noise events. The internal thresholds of
each algorithm are chosen to obtain robust performance
across a set of signal morphologies of interest. We also
reject events that occur at times of environmental noise
disturbances that are known to be correlated with transients
in the GW data via well-established physical mechanisms;
these so-called
category 2
data quality cuts are described
in Ref.
[58]
.
The most important measure of an event
s significance is
its false alarm rate (FAR): the rate at which the background
noise produces events of equal or higher loudness than
events that pass all coherent tests and data quality cuts.
Each pipeline estimates the FAR using background events
generated by repeating the analysis on time-shifted data
the data from the different detectors are offset in time, in
typical increments of
1
s. The shifts remove the chance of
drawing a subsecond GW transient into the background
sample, since the largest time of flight between the LIGO
and Virgo sites is 27 milliseconds (between H1 and V1). To
accumulate a sufficient sampling of rare background
events, this shifting procedure is performed thousands of
times without repeating the same relative time shifts among
detectors. Given a total duration
T
off
of off-source (time-
shifted) data, the smallest false alarm rate that can be
measured is
1
=T
off
.
On-source events from each combination of CCSN,
detector network, and pipeline are assigned a FAR using
the time-slide background from that combination only. The
event lists from the different CCSNe, detector networks,
and pipelines are then combined and the events ranked by
their FAR. The event with lowest FAR is termed the
loudest event
.
In order for the loudest event to be considered as a GW
detection, it must have a false alarm probability (FAP) low
enough that it is implausible to have been caused by
background noise. Given a FAR value
R
, the probability
p
ð
R
Þ
of noise producing one or more events of FAR less
than or equal to
R
during one or more CCSN on-source
windows of total duration
T
on
is
FIG. 2. Noise amplitude spectral densities of the GW interfer-
ometers whose data are analyzed for SNe 2007gr and 2011dh (see
Sec.
III
). The curves are the results of averaging
1
=S
ð
f
Þ
over the
on-source windows of the SNe (see Table
I
). We plot the G1 noise
spectrum also for SN 2008ax to demonstrate the improvement in
high-frequency sensitivity due to GEO-HF
[131]
for SN 2011dh.
B. P. ABBOTT
et al.
PHYSICAL REVIEW D
94,
102001 (2016)
102001-6
p
¼
1
exp
ð
RT
on
Þ
:
ð
1
Þ
The smallest such false alarm probability (FAP) that can be
measured given an off-source (time-shifted) data duration
T
off
is approximately
T
on
=T
off
. Several thousand time shifts
are therefore sufficient to measure FAP values of
O
ð
10
3
Þ
.
We require a FAP below 0.001, which exceeds
3
σ
con-
fidence, in order to consider an event to be a possible GW
detection candidate. Figure
3
shows examples of the FAP as
a function of event loudness for
C
WB and X-P
IPELINE
for
the H1H2L1V1 network during the SN 2007gr on-source
window.
The loudest surviving events of the current search are
reported in Table
III
. In practice, none of these events has a
FAP low enough to be considered a GW candidate (see
Sec.
V
for further discussion). We therefore set upper limits
on the strength of possible GW emission by the CCSNe.
This is done by adding to the data simulated GW signals of
various amplitudes (or equivalently sources at various
distances) and repeating the analysis. For each amplitude
or distance, we measure the fraction of simulations that
produce an event in at least one pipeline with FAP lower
than the loudest on-source event, and which survive our
coherence tests and data quality cuts; this fraction is the
detection efficiency
of the search.
A. Coherent WaveBurst
The
C
WB
[136]
analysis is performed as described in
Ref.
[57]
, and it is based on computing a constrained
likelihood function. In brief, each detector data stream is
decomposed into six different wavelet decompositions
(each one with different time and frequency resolutions).
The data are whitened, and the largest 0.1% of wavelet
magnitudes in each frequency bin and decomposition for
each interferometer are retained (we call these
black
pixels
). We also retain
halo
pixels, which are those that
surround each black pixel. In order to choose pixels that are
more likely related to a GW transient (
candidate event
), we
identify clusters of them. Once all of the wavelet decom-
positions are projected into the same time-frequency plane,
clusters are defined as sets of contiguous retained pixels
(black or halo). Only the pixels involved in a cluster are
used in the subsequent calculation of the likelihood. These
clusters also need to be consistent between interferometers
for the tested direction of arrival. For each cluster of
wavelets, a Gaussian likelihood function is computed,
where the unknown GW is reconstructed with a maxi-
mum-likelihood estimator.
The likelihood analysis is repeated over a grid of sky
positions covering the range of possible directions to the
GW source. Since the sky location of each of the analyzed
CCSNe is well known, we could choose to apply this
procedure only for the known CCSN sky location.
FIG. 3. False Alarm Probability [FAP, Equation
(1)
] distributions of the background events for SN 2007gr and the H1H2L1V1
detector network (cf. Section
III
). The FAP indicates the probability that an event of a given
loudness
(significance) is consistent with
background noise. The left panel shows the FAP distribution determined by the
C
WB pipeline as a function of its loudness measure,
ρ
,
(see
[136]
for details). The right panel depicts the same for X-P
IPELINE
as a function of its loudness measure,
Λ
c
, (see
[61,135]
for
details). The shaded regions indicate
1
σ
error estimates for the FAP.
TABLE III. False alarm rate (FAR) of the loudest event found
by each pipeline for each detector network. No on-source events
survived the coherent tests and data quality cuts for the
C
WB
analysis of the H1H2L1 and H1H2 networks for SN 2007gr. The
lowest FAR,
1
.
7
×
10
6
Hz, corresponds to a FAP of 0.77, where
the total live time analyzed was
T
on
¼
873461
s.
Network
C
WB
X-P
IPELINE
H1H2L1V1
1
.
7
×
10
6
Hz
2
.
5
×
10
6
Hz
H1H2L1
no events
1
.
1
×
10
5
Hz
H1H2V1
1
.
2
×
10
5
Hz
5
.
3
×
10
6
Hz
H1H2
no events
7
.
1
×
10
5
Hz
L1V1
4
.
8
×
10
5
Hz
4
.
1
×
10
3
Hz
G1V1
1
.
2
×
10
5
Hz
2
.
7
×
10
5
Hz
TARGETED SEARCH FOR GRAVITATIONAL-WAVE BURSTS
...
PHYSICAL REVIEW D
94,
102001 (2016)
102001-7
However, the detector noise occasionally forces the
C
WB
likelihood to peak in a sky location away from the true sky
location. As a consequence, some real GW events could be
assigned a smaller likelihood value, lowering the capability
to detect them. Because of this, we consider triggers that
fall within an error region of 0.4° of the known CCSN sky
location and that pass the significance threshold, even if
they are not at the peak of the
C
WB reconstructed sky
position likelihood. The 0.4° region is determined empiri-
cally by trade-off studies between detection efficiency
and FAR.
For SN 2011dh, the noise spectra were very different for
the G1 and V1 detectors, with the consequence that the
networkeffectivelyhadonlyonedetectoratfrequenciesupto
several hundred Hz, and therefore location reconstruction
was very poor. As a consequence, we decided to scan the
entire sky for candidate events for this CCSN.
The events reported for a given network configuration
are internally ranked for detection purposes by
C
WB using
the coherent network amplitude statistic
ρ
defined in
Ref.
[138]
. Other constraints related to the degree of
similarity of the reconstructed signal across different
interferometers [the
network correlation coefficient
(
cc
)] and the ability of the network to reconstruct both
polarizations of the GW signal (called
regulators
) are
applied to reject background events; these are also
described in Ref.
[138]
.
B. X-P
IPELINE
In the X-P
IPELINE
[61,135,139]
analysis, the detector data
are first whitened, then Fourier-transformed. A total energy
map is made by summing the spectrogram for each detector,
and
hot
pixels are identified as the 1% in each detector with
the largesttotal energy.Hot pixelsthat shareanedgeorvertex
(nearest neighbors and next-nearest neighbors) are clustered.
For each cluster, the raw time-frequency maps are recom-
bined in a number of linear combinations designed to give
maximum-likelihood estimates of various GW polarizations
given the known sky position of the CCSN. The energy
in each combination is recorded for each cluster, along
with various time-frequency properties of the cluster.
The procedure is repeated using a series of Fourier-transform
lengths from
1
=
4
s
;
1
=
8
s
;
...
1
=
128
s. Clusters are ranked
internally using a Bayesian-inspired estimate
Λ
c
of the
likelihood ratio for a circularly polarized GW, marginalized
over the unknown GW amplitude
σ
h
with a Jeffreys (loga-
rithmic) prior
σ
1
h
; see Refs.
[135,140,141]
for details.
When clusters from different Fourier-transform lengths
overlap in time-frequency, the cluster with the largest
likelihood
Λ
c
is retained and the rest are discarded.
Finally, a postprocessing algorithm tunes and applies a
series of pass/fail tests to reject events due to background
noise; these tests are based on measures of correlation
between the detectors for each cluster. The tuning of these
tests is described in detail in Ref.
[61]
. For more details, see
also Ref.
[73]
.
C. Simulated signals and search sensitivity
An important aspect of the GW search presented in this
study is to understand how sensitive the GW detector
networks are to GWs emitted by the considered CCSNe.
We establish sensitivity via Monte Carlo simulation in the
following way:
(1) We determine the loudest event in the on-source
window that is consistent with the CCSN location
(and the angular uncertainty of the search algorithms).
(2) We
inject
(add) theoretical waveforms scaled to a
specific distance (or emitted GWenergy) every 100 s
plus a randomly selected time in
½
10
;
10

s into the
time-shifted background data. We compare the
loudness of the recovered injections with the loudest
on-source event and record the fraction of the
injections that passed the coherent tests and data
quality cuts and were louder than the loudest on-
source event. This fraction is the
detection efficiency
.
(3) We repeat step 2 for a range of distances (or emitted
GW energies) to determine the detection efficiency
as a function of distance (or emitted GW energy).
We refer the reader to Ref.
[73]
for more details on the
injection procedure.
In this paper, we employ three classes of GW signals for
our Monte Carlo studies: (1) representative waveforms
from detailed multidimensional (2D axisymmetric or 3D)
CCSN simulations; (2) semianalytic phenomenological
waveforms of plausible but extreme emission scenarios;
and (3)
ad hoc
waveform models with tuneable frequency
content and amplitude to establish upper limits on the
energy emitted in GWs at a fixed CCSN distance.
We briefly summarize the nature of these waveforms below.
We list all employed waveforms in Tables
IV
and
V
and
summarize their key emission metrics. In particular, we
provide the angle-averaged root-sum-squared GW strain,
h
rss
¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Z
h
h
2
þ
ð
t
Þþ
h
2
×
ð
t
Þi
Ω
d
t
s
;
ð
2
Þ
and the energy
E
GW
emitted in GWs, using the expressions
given in Ref.
[73]
.
1. Waveforms from multidimensional CCSN simulations
Rotation leads to a natural axisymmetric quadrupole
(oblate) deformation of the collapsing core. The tremen-
dous acceleration at core bounce and protoneutron star
formation results in a strong linearly polarized burst of
GWs followed by a ringdown signal. Rotating core collapse
is the most extensively studied GW emission process in the
CCSN context (see, e.g., Refs.
[20,27,145
150]
and
Refs.
[36,37,137]
for reviews). For the purpose of this
B. P. ABBOTT
et al.
PHYSICAL REVIEW D
94,
102001 (2016)
102001-8
study, we select three representative rotating core-collapse
waveforms from the 2D general-relativistic study of
Dimmelmeier
et al.
[27]
. The simulations producing these
waveforms used the core of a
15
M
progenitor star and the
Lattimer-Swesty nuclear equation of state
[151]
. The
waveforms are enumerated by Dim1
Dim3 prefixes and
are listed in Table
IV
. They span the range from moderate
rotation (Dim1-s15A2O05ls) to extremely rapid rotation
(Dim3-s15A3O15ls). See Ref.
[27]
for details on the
collapse dynamics and GW emission.
In nonrotating or slowly rotating CCSNe, neutrino-
driven convection and the standing accretion shock insta-
bility (SASI) are expected to dominate the GW emission.
GWs from convection/SASI have also been extensively
studied in 2D (e.g., Refs.
[28,31,35,152
157]
) and more
recently also in 3D
[30,33]
. For the present study, we select
a waveform from a 2D Newtonian (
þ
relativistic correc-
tions) radiation-hydrodynamics simulation of a CCSN in a
15
M
progenitor by Yakunin
et al.
[28]
. This waveform
also captures the frequency content of more recent 3D
waveforms
[158,159]
. This waveform and its key emission
metrics are listed as Yakunin-s15 in Table
IV
. Note that
since the simulation producing this waveform was axisym-
metric, only the
þ
polarization is available.
CCSNe in nature are 3D and produce both GW polar-
izations (
h
þ
and
h
×
). Only a few GW signals from 3D
simulations are presently available. We draw three wave-
forms from the work of Müller
et al.
[30]
. These and their
key GW emission characteristics are listed with Müller1
Müller3 prefixes in Table
IV
. Waveforms Müller1-L15-3
and Müller2-W15-4 are from simulations using two differ-
ent progenitor models for a
15
M
star. Waveform Müller2-
N20-2 is from a simulation of a CCSN in a
20
M
star. Note
that the simulations of Müller
et al.
[30]
employed an
ad hoc
inner boundary at multiple tens of kilometers. This
prevented decelerating convective plumes from reaching
TABLE V. Injection waveforms from phenomenological and
ad hoc
emission models described in the text. For each waveform, we
give the emission type, journal reference, waveform identifier, angle-averaged root-sum-squared strain
h
rss
, the frequency
f
peak
at which
the GW energy spectrum peaks, the emitted GW energy
E
GW
, and available polarizations. See Refs.
[73,142]
for details. As sine-
Gaussian waveforms are
ad hoc
, they can be rescaled arbitrarily and do not have a defined physical distance or
E
GW
value.
h
rss
f
peak
E
GW
Emission Type
Ref.
Waveform Identifier
½
10
20
@10
kpc

[Hz]
½
M
c
2

Polarizations
Long-lasting bar mode
[143]
LB1-M0.2L60R10f400t100
1.480
800
2
.
984
×
10
4
þ
Long-lasting bar mode
[143]
LB2-M0.2L60R10f400t1000
4.682
800
2
.
979
×
10
3
þ
Long-lasting bar mode
[143]
LB3-M0.2L60R10f800t100
5.920
1600
1
.
902
×
10
2
þ
Long-lasting bar mode
[143]
LB4-M1.0L60R10f400t100
7.398
800
7
.
459
×
10
3
þ
Long-lasting bar mode
[143]
LB5-M1.0L60R10f400t1000
23.411
800
7
.
448
×
10
2
þ
Long-lasting bar mode
[143]
LB6-M1.0L60R10f800t25
14.777
1601
1
.
184
×
10
1
þ
Torus fragmentation instability
[50]
Piro1-M
5
.
0
η
0
.
3
2.550
2035
6
.
773
×
10
4
þ
Torus fragmentation instability
[50]
Piro2-M
5
.
0
η
0
.
6
9.936
1987
1
.
027
×
10
2
þ
Torus fragmentation instability
[50]
Piro3-M
10
.
0
η
0
.
3
7.208
2033
4
.
988
×
10
3
þ
Torus fragmentation instability
[50]
Piro4-M
10
.
0
η
0
.
6
28.084
2041
7
.
450
×
10
2
þ
sine-Gaussian
[144]
SG1-235HzQ8d9linear

235

þ
sine-Gaussian
[144]
SG2-1304HzQ8d9linear

1304

þ
sine-Gaussian
[144]
SG3-235HzQ8d9elliptical

235

þ
sine-Gaussian
[144]
SG4-1304HzQ8d9elliptical

1304

þ
TABLE IV. Injection waveforms from detailed multidimensional CCSN simulations described in the text. For each waveform, we give
the emission type, journal reference, waveform identifier, angle-averaged root-sum-squared strain
h
rss
, the frequency
f
peak
at which the
GW energy spectrum peaks, the emitted GW energy
E
GW
, and available polarizations. See Refs.
[73,142]
for details.
h
rss
f
peak
E
GW
Emission Type
Ref.
Waveform Identifier
½
10
22
@10
kpc

[Hz]
½
10
9
M
c
2

Polarizations
Rotating core collapse
[27]
Dim1-s15A2O05ls
1.052
774
7.685
þ
Rotating core collapse
[27]
Dim2-s15A2O09ls
1.803
753
27.873
þ
Rotating core collapse
[27]
Dim3-s15A3O15ls
2.690
237
1.380
þ
2D convection and SASI
[28]
Yakunin-s15
1.889
888
9.079
þ
3D convection and SASI
[30]
Müller1-L15-3
1.655
150
3
.
741
×
10
2
þ
3D convection and SASI
[30]
Müller2-N20-2
3.852
176
4
.
370
×
10
2
þ
3D convection and SASI
[30]
Müller3-W15-4
1.093
204
3
.
247
×
10
2
þ
Protoneutron star pulsations
[36]
Ott-s15
5.465
971
429.946
þ
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PHYSICAL REVIEW D
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small radii and high velocities. As a consequence, the
overall GW emission in these simulations peaks at lower
frequencies than in simulations that do not employ an inner
boundary (cf. Refs.
[28,31,33,35]
). For example, the
expected signal-to-noise ratios of waveforms from the
simulations of Ref.
[33]
are 2
3 times higher than those
of Müller
et al.
, so their detectable range should be larger
by approximately the same factor.
We also do not include any waveforms from 3D rotating
core collapse. However, the study in Ref.
[160]
, which used
X-P
IPELINE
and realistic LIGO noise, did include wave-
forms from the 3D Newtonian magnetohydrodynamical
simulations of Scheidegger
et al.
[161]
. The two selected
waveforms were for a
15
M
progenitor star with the
Lattimer-Swesty equation of state. These simulations
exhibited stronger GW emission, and the detectable range
was typically 2
3 times further than for the 2D
Dimmelmeier
et al.
waveforms.
In some 2D CCSN simulations
[162,163]
, strong exci-
tations of an
l
¼
1
g
-mode (an oscillation mode with
gravity as its restoring force) were observed. These
oscillations were found to be highly nonlinear and to
couple to GW-emitting
l
¼
2
modes. The result is a strong
burst of GWs that lasts for the duration of the large-
amplitude mode excitation, possibly for hundreds of
milliseconds
[36,48]
. More recent simulations do not find
such strong
g
-mode excitations (e.g., Refs.
[31,164]
). We
nevertheless include here one waveform from the simu-
lations of Ref.
[163]
that was reported by Ott
[36]
. This
waveform is from a simulation with a
15
M
progenitor and
is denoted as Ott-s15 in Table
IV
.
2. Phenomenological waveform models
In the context of rapidly rotating core collapse, various
nonaxisymmetric instabilities can deform the protoneutron
star into a triaxial (
bar
) shape (e.g., Refs.
[150,158,
165
169]
), potentially leading to extended (
10
ms
fews)
and energetic GW emission. This emission occurs at twice
the protoneutron star spin frequency, with a 90° phase shift
between the plus and cross modes (similar to the wave-
forms from some more realistic 3D simulations), and with
amplitude dependent on the magnitude of the bar defor-
mation
[49,150,158]
. We use the simple phenomenological
bar model described in Ref.
[143]
. Its parameters are the
length of the bar deformation,
L
, in km; its radius,
R
,
in km; the mass,
M
,in
M
, involved in the deformation;
and the spin frequency,
f
, and the duration,
t
, of the
deformation. We select six waveforms as representa-
tive examples. We sample the potential parameter space
by chosing
M
¼f
0
.
2
;
1
.
0
g
M
,
f
¼f
400
;
800
g
Hz, and
t
¼f
25
;
100
;
1000
g
ms. We list these waveforms as
long-lasting bar mode
in Table
V
and enumerate them
as LB1
LB6. The employed model parameters are encoded
in the full waveform name. One notes from Table
V
that the
strength of the bar-mode GW emission is orders of
magnitude greater than that of any of the waveforms
computed from detailed multidimensional simulations
listed in Table
IV
. We emphasize that the phenomenological
bar-mode waveforms should be considered as being at
the extreme end of plausible GW emission scenarios.
Theoretical considerations (e.g., Ref.
[36]
) suggest that
such strong emission is unlikely to obtain in CCSNe.
Observationally, however, having this emission in one or all
of the CCSNe has not been ruled out.
We also consider the phenomenological waveform model
proposed by Piro and Pfahl
[50]
. They considered the
formation of a dense self-gravitating
M
-scale fragment in
a thick accretion torus around a black hole in the context of
collapsar-type gamma-ray bursts. The fragment is driven
toward the black hole by a combination of viscous torques
and energetic GWemission. This is an extreme but plausible
scenario. We generate injection waveforms from this model
using the implementation described in Ref.
[170]
. The
model has the following parameters: mass
M
BH
of the black
hole in
M
, a spatially constant geometrical parameter
controlling the torus thickness,
η
¼
H=r
, where
H
is the
disk scale height and
r
is the local radius, a scale factor for
the fragment mass (fixed at 0.2), the value of the phenom-
enological
α
viscosity (fixed at
α
¼
0
.
1
), and a starting
radius that we fix to be
100
r
g
¼
100
GM
BH
=c
2
. We employ
four waveforms, probing black hole masses
M
BH
¼
f
5
;
10
g
M
and geometry factors
η
¼f
0
.
3
;
0
.
6
g
. The
resulting waveforms and their key emission metrics are
listed as
torus fragmentation instability
and enumerated
by Piro1
Piro4 in Table
V
. The full waveform names encode
the particular parameter values used. As in the case of the
bar-mode emission model, we emphasize that the torus
fragmentation instability also represents an extreme GW
emission scenario for CCSNe. It may be unlikely based on
theoretical considerations (e.g., Refs.
[36,170]
), but has not
been ruled out observationally.
3. Ad hoc waveforms: Sine-Gaussians
Following previous GW searches, we also employ
ad hoc
sine-Gaussian waveforms to establish frequency-dependent
upper limits on the emitted energy in GWs. This also allows
us to compare the sensitivity of our targeted search with
results from previous all-sky searches for GW bursts (e.g.,
Refs.
[57
59]
).
Sine-Gaussian waveforms are, as the name implies,
sinusoids in a Gaussian envelope. They are analytic and
given by
h
þ
ð
t
Þ¼
A
1
þ
α
2
2
exp
ð
t
2
=
τ
2
Þ
sin
ð
2
π
f
0
t
Þ
;
ð
3
Þ
h
×
ð
t
Þ¼
A
α
exp
ð
t
2
=
τ
2
Þ
cos
ð
2
π
f
0
t
Þ
:
ð
4
Þ
Here,
A
is an amplitude scale factor,
α
¼
cos
ι
is the
ellipticity of the waveform with
ι
being the inclination
B. P. ABBOTT
et al.
PHYSICAL REVIEW D
94,
102001 (2016)
102001-10
angle,
f
0
is the central frequency, and
τ
¼
Q=
ð
ffiffiffi
2
p
π
f
0
Þ
,
where
Q
is the quality factor controlling the width of the
Gaussian and thus the duration of the signal. Since the
focus of our study is more on realistic and phenomeno-
logical waveforms, we limit the set of sine-Gaussian
waveforms to four, enumerated SG1
SG4 in Table
V
.
We fix
Q
¼
8
.
9
and study linearly polarized (cos
ι
¼
0
)
and elliptically polarized (cos
ι
sampled uniformly on
½
1
;
1

) waveforms at
f
¼f
235
;
1304
g
Hz. We choose
this quality factor and these particular frequencies for
comparison with Refs.
[57
59]
.
D. Systematic uncertainties
Our efficiency estimates are subject to a number of
uncertainties. The most important of these are calibration
uncertainties in the strain data recorded at each detector,
and Poisson uncertainties due to the use of a finite number
of injections (Monte Carlo uncertainties). We account for
each of these uncertainties in the sensitivities reported in
this paper.
We account for Poisson uncertainties from the finite
number of injections using the Bayesian technique
described in Ref.
[171]
. Specifically, given the total number
of injections performed at some amplitude and the number
detected, we compute the 90% credible lower bound on
the efficiency assuming a uniform prior on [0, 1] for the
efficiency. All efficiency curves reported in this paper are
therefore actually 90%-confidence-level lower bounds on
the efficiency.
Calibration uncertainties are handled by rescaling quoted
h
rss
and distance values following the method in Ref.
[56]
.
The dominant effect is from the uncertainties in the
amplitude calibration; these are estimated at approximately
10% for G1, H1, and H2; 14% for L1; and 6%
8% for V1
at the times of the two CCSNe studied
[172,173]
. The
individual detector amplitude uncertainties are combined
into a single uncertainty by calculating a combined root-
sum-square signal-to-noise ratio and propagating the indi-
vidual uncertainties assuming each error is independent
(the signal-to-noise ratio is used as a proxy for the loudness
measures the two pipelines use for ranking events). This
combination depends upon the relative sensitivity of each
detector, which is a function of frequency, so we compute
the total uncertainty at a range of frequencies across our
analysis band for each CCSN and select the largest result,
7.6%, as a conservative estimate of the total
1
σ
uncertainty.
This
1
σ
uncertainty is then scaled by a factor of 1.28 (to
9.7%) to obtain the factor by which our amplitude and
distance limits must be rescaled in order to obtain values
consistent with a 90%-confidence-level upper limit.
V. SEARCH RESULTS
As discussed in Sec.
IV
, on-source events from each
combination of CCSN, detector network, and pipeline are
assigned a false alarm rate by comparing to time-slide
background events. Table
III
lists the FAR values of the
loudest event found by each pipeline for each network and
CCSN. The lowest FAR,
1
.
7
×
10
6
Hz, was reported by
C
WB for the analysis of SN 2007gr with the H1H2L1V1
network. This rate can be converted to a false alarm
probability (FAP) using Eq.
(1)
. The total duration of data
processed by
C
WB or X-P
IPELINE
for the two CCSNe was
T
on
¼
873461
s. Equation
(1)
then yields a false alarm
probability of 0.77 for the loudest event; this is consistent
with the event being due to background noise. We conclude
that none of the events has a FAP low enough to be
considered as a candidate GW detection.
We note that the loudest events reported by
C
WB and
X-P
IPELINE
are both from the analysis of SN 2007gr with
the H1H2L1V1 network; this is consistent with chance, as
this network combination accounted for more than 60%
of the data processed. In addition, the times of the loudest
X-P
IPELINE
and
C
WB events differ by more than a day, so
they are not due to a common physical trigger.
A. Detection efficiency vs distance
Given the loudest event, we can compute detection
efficiencies for the search following the procedure detailed
in Sec.
IV C
. In brief, we measure the fraction of simulated
signals that produce events surviving the coherent tests and
data quality cuts and which have a FAR (or equivalently,
FAP) lower than the loudest event.
Figures
4
and
5
show the efficiency as a function of
distance for the CCSN waveforms from multidimensional
simulations and the phenomenological waveforms dis-
cussed in Sec.
IV C
and summarized in Tables
IV
and
V
.
For SN 2007gr, the maximum distance reach is of order
1 kpc for waveforms from detailed multidimensional
CCSN simulations, and from
100
kpc to
1
Mpc for
GWs from the phenomenological models (torus fragmen-
tation instability and long-lived rotating bar mode). The
variation in distance reach is due to the different peak
emission frequencies of the models and the variation in
detector sensitivities with frequency, and is easily under-
stood in terms of the expected signal-to-noise ratio of each
waveform relative to the noise spectra of Fig.
2
.For
example, the distance reach for the Yakunin waveform is
similar to those of the Müller waveforms even though the
Yakunin energy emission is more than 2 orders of magni-
tude higher; this is due to the emission being at a much
higher frequency, where the detectors are less sensitive.
Similarly, of the three Müller waveforms, the distance reach
is largest for Müller1 because the peak frequency is 150 Hz,
where the LIGO detectors have the best sensitivity.
The distance reaches for SN 2011dh are lower by a factor
of several than those for SN 2007gr; this is due to the
difference in sensitivity of the operating detectors, as is also
evident in Fig.
2
. Finally, we note that at small distances,
the efficiencies asymptote to the fraction of the on-source
TARGETED SEARCH FOR GRAVITATIONAL-WAVE BURSTS
...
PHYSICAL REVIEW D
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102001 (2016)
102001-11
FIG. 4. SN 2007gr detection efficiency versus distance for the waveforms from multidimensional CCSN simulations (left) and the
phenomenological waveforms (right) described in Tables
IV
and
V
. Simulated GW signals are added into detector data with a range of
amplitudes corresponding to different source distances. A simulated signal is considered to be detected if
C
WB or X-P
IPELINE
reports an
event that survives the coherent tests and data quality cuts with a FAR value lower than that of the loudest event from the SN 2007gr and
SN 2011dh on-source windows. These efficiencies are averaged over all detector network combinations for SN 2007gr. The efficiencies
are limited to
93%
at small distances due to the fact that this was the duty cycle for coincident observation over the SN 2007gr on-
source window. The numbers in brackets for each model are the distances at which the efficiency equals 50% of the asymptotic value at
small distances.
FIG. 5. SN 2011dh detectionefficiencyvsdistanceforthephenomenologicalwaveformsdescribedinTable
V
.SimulatedGWsignalsare
added into detector data with a range of amplitudes corresponding to different source distances. A simulated signal is considered to be
detected if either
C
WB or X-P
IPELINE
reports an event that survives the coherent tests and data quality cuts with a FAR value lower than that
of the loudest event from the SN 2007gr and SN 2011dh on-sourcewindows. The efficiencies are limited to
37%
at small distances due to
the fact that this was the duty cycle for coincident observation over the SN 2011dh on-sourcewindow; some simulations are also vetoed by
data quality cuts. The numbers in the brackets are the distances at which the efficiency equals 50% of its maximum value for each model.
B. P. ABBOTT
et al.
PHYSICAL REVIEW D
94,
102001 (2016)
102001-12