Search for gravitational-wave bursts associated with gamma-ray bursts using data from LIGO Science Run 5 and Virgo Science Run 1

Abstract

We present the results of a search for gravitational-wave bursts associated
with 137 gamma-ray bursts (GRBs) that were detected by satellite-based
gamma-ray experiments during the fifth LIGO science run and first Virgo science
run. The data used in this analysis were collected from 2005 November 4 to 2007
October 1, and most of the GRB triggers were from the Swift satellite. The
search uses a coherent network analysis method that takes into account the
different locations and orientations of the interferometers at the three
LIGO-Virgo sites. We find no evidence for gravitational-wave burst signals
associated with this sample of GRBs. Using simulated short-duration (<1 s)
waveforms, we set upper limits on the amplitude of gravitational waves
associated with each GRB. We also place lower bounds on the distance to each
GRB under the assumption of a fixed energy emission in gravitational waves,
with typical limits of D ~ 15 Mpc (E_GW^iso / 0.01 M_o c^2)^1/2 for emission at
frequencies around 150 Hz, where the LIGO-Virgo detector network has best
sensitivity. We present astrophysical interpretations and implications of these
results, and prospects for corresponding searches during future LIGO-Virgo
runs.

Full text

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Draft version April 8, 2010
Preprint typeset using LATEX style emulateapj v. 11/10/09
SEARCH FOR GRAVITATIONAL-WAVE BURSTS ASSOCIATED WITH GAMMA-RAY BURSTS USING DATA
FROM LIGO SCIENCE RUN 5 AND VIRGO SCIENCE RUN 1
B. P. Abbott28, R. Abbott28, F. Acernese18ac, R. Adhikari28, P. Ajith2, B. Allen2,75, G. Allen51,
M. Alshourbagy20ab, R. S. Amin33, S. B. Anderson28, W. G. Anderson75, F. Antonucci21a, S. Aoudia42a,
M. A. Arain63, M. Araya28, H. Armandula28, P. Armor75, K. G. Arun25, Y. Aso28, S. Aston62, P. Astone21a,
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arXiv:0908.3824v2 [astro-ph.HE] 7 Apr 2010

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1Albert-Einstein-Institut, Max-Planck-Institut f¨ ur Gravitationsphysik, D-14476 Golm, Germany
2Albert-Einstein-Institut, Max-Planck-Institut f¨ ur Gravitationsphysik, D-30167 Hannover, Germany
3Andrews University, Berrien Springs, MI 49104 USA
4AstroParticule et Cosmologie (APC), CNRS: UMR7164-IN2P3-Observatoire de Paris-Universit´ e Denis Diderot-Paris VII - CEA :
DSM/IRFU
5Australian National University, Canberra, 0200, Australia
6California Institute of Technology, Pasadena, CA 91125, USA
7Caltech-CaRT, Pasadena, CA 91125, USA
8Cardiff University, Cardiff, CF24 3AA, United Kingdom
9Carleton College, Northfield, MN 55057, USA
77Charles Sturt University, Wagga Wagga, NSW 2678, Australia
10Columbia University, New York, NY 10027, USA
11European Gravitational Observatory (EGO), I-56021 Cascina (Pi), Italy
12Embry-Riddle Aeronautical University, Prescott, AZ 86301 USA
13E¨ otv¨ os University, ELTE 1053 Budapest, Hungary
14ESPCI, CNRS, F-75005 Paris, France
15Hobart and William Smith Colleges, Geneva, NY 14456, USA
16INFN, Sezione di Firenze, I-50019 Sesto Fiorentinoa; Universit` a degli Studi di Firenze, I-50121b, Firenze; Universit` a degli Studi di
Urbino ’Carlo Bo’, I-61029 Urbinoc, Italy
17INFN, Sezione di Genova; I-16146 Genova, Italy
18INFN, sezione di Napolia; Universit` a di Napoli ’Federico II’bComplesso Universitario di Monte S.Angelo, I-80126 Napoli; Universit` a
di Salerno, Fisciano, I-84084 Salernoc, Italy
19INFN, Sezione di Perugiaa; Universit` a di Perugiab, I-6123 Perugia,Italy
20INFN, Sezione di Pisaa; Universit` a di Pisab; I-56127 Pisa; Universit` a di Siena, I-53100 Sienac, Italy
21INFN, Sezione di Romaa; Universit` a ’La Sapienza’b, I-00185 Roma, Italy
22INFN, Sezione di Roma Tor Vergataa; Universit` a di Roma Tor Vergatab, Istituto di Fisica dello Spazio Interplanetario (IFSI) INAFc,
I-00133 Roma; Universit` a dell’Aquila, I-67100 L’Aquilad, Italy
23Institute of Applied Physics, Nizhny Novgorod, 603950, Russia
24Inter-University Centre for Astronomy and Astrophysics, Pune - 411007, India
25LAL, Universit´ e Paris-Sud, IN2P3/CNRS, F-91898 Orsay, France
26Laboratoire d’Annecy-le-Vieux de Physique des Particules (LAPP), IN2P3/CNRS, Universit´ e de Savoie, F-74941 Annecy-le-Vieux,
France
27Leibniz Universit¨ at Hannover, D-30167 Hannover, Germany
28LIGO - California Institute of Technology, Pasadena, CA 91125, USA
29LIGO - Hanford Observatory, Richland, WA 99352, USA
30LIGO - Livingston Observatory, Livingston, LA 70754, USA
31LIGO - Massachusetts Institute of Technology, Cambridge, MA 02139, USA
32Laboratoire des Mat´ eriaux Avanc´ es (LMA), IN2P3/CNRS, F-69622 Villeurbanne, Lyon, France

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Search for GWBs associated with GRBs using LIGO and Virgo3
33Louisiana State University, Baton Rouge, LA 70803, USA
34Louisiana Tech University, Ruston, LA 71272, USA
35Loyola University, New Orleans, LA 70118, USA
36Montana State University, Bozeman, MT 59717, USA
37Moscow State University, Moscow, 119992, Russia
38NASA/Goddard Space Flight Center, Greenbelt, MD 20771, USA
39National Astronomical Observatory of Japan, Tokyo 181-8588, Japan
40Nikhef, National Institute for Subatomic Physics, P.O. Box 41882, 1009 DB Amsterdam, The Netherlandsa; VU University
Amsterdam, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlandsb
41Northwestern University, Evanston, IL 60208, USA
42Departement Artemis, Observatoire de la Cˆ ote d’Azur, CNRS, F-06304 Nicea; Institut de Physique de Rennes, CNRS, Universit´ e de
Rennes 1, 35042 Rennesb; France
43INFN, Gruppo Collegato di Trentoaand Universit` a di Trentob, I-38050 Povo, Trento, Italy; INFN, Sezione di Padovacand Universit` a
di Padovad, I-35131 Padova, Italy
44IM-PAN 00-956 Warsawa; Warsaw Univ. 00-681b; Astro. Obs. Warsaw Univ. 00-478c; CAMK-PAM 00-716 Warsawd; Bialystok Univ.
15-424e; IPJ 05-400 Swierk-Otwockf; Inst. of Astronomy 65-265 Zielona Gorag, Poland
45Rochester Institute of Technology, Rochester, NY 14623, USA
46Rutherford Appleton Laboratory, HSIC, Chilton, Didcot, Oxon OX11 0QX United Kingdom
47San Jose State University, San Jose, CA 95192, USA
48Sonoma State University, Rohnert Park, CA 94928, USA
49Southeastern Louisiana University, Hammond, LA 70402, USA
50Southern University and A&M College, Baton Rouge, LA 70813, USA
51Stanford University, Stanford, CA 94305, USA
52Syracuse University, Syracuse, NY 13244, USA
53The Pennsylvania State University, University Park, PA 16802, USA
54The University of Melbourne, Parkville VIC 3010, Australia
55The University of Mississippi, University, MS 38677, USA
56The University of Sheffield, Sheffield S10 2TN, United Kingdom
57The University of Texas at Austin, Austin, TX 78712, USA
58The University of Texas at Brownsville and Texas Southmost College, Brownsville, TX 78520, USA
59Trinity University, San Antonio, TX 78212, USA
60Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain
61University of Adelaide, Adelaide, SA 5005, Australia
62University of Birmingham, Birmingham, B15 2TT, United Kingdom
63University of Florida, Gainesville, FL 32611, USA
64University of Glasgow, Glasgow, G12 8QQ, United Kingdom
65University of Maryland, College Park, MD 20742 USA
66University of Massachusetts - Amherst, Amherst, MA 01003, USA
67University of Michigan, Ann Arbor, MI 48109, USA
68University of Minnesota, Minneapolis, MN 55455, USA
69University of Oregon, Eugene, OR 97403, USA
70University of Rochester, Rochester, NY 14627, USA
71University of Sannio at Benevento, I-82100 Benevento, Italy
72University of Southampton, Southampton, SO17 1BJ, United Kingdom
73University of Strathclyde, Glasgow, G1 1XQ, United Kingdom
74University of Western Australia, Crawley, WA 6009, Australia
75University of Wisconsin-Milwaukee, Milwaukee, WI 53201, USA and
76Washington State University, Pullman, WA 99164, USA
Draft version April 8, 2010
ABSTRACT
We present the results of a search for gravitational-wave bursts associated with 137 gamma-ray
bursts (GRBs) that were detected by satellite-based gamma-ray experiments during the fifth LIGO
science run and first Virgo science run. The data used in this analysis were collected from 2005
November 4 to 2007 October 1, and most of the GRB triggers were from the Swift satellite. The
search uses a coherent network analysis method that takes into account the different locations and
orientations of the interferometers at the three LIGO-Virgo sites. We find no evidence for gravitational-
wave burst signals associated with this sample of GRBs. Using simulated short-duration (< 1 s)
waveforms, we set upper limits on the amplitude of gravitational waves associated with each GRB.
We also place lower bounds on the distance to each GRB under the assumption of a fixed energy
emission in gravitational waves, with a median limit of D ∼ 12 Mpc (Eiso
at frequencies around 150 Hz, where the LIGO-Virgo detector network has best sensitivity.
present astrophysical interpretations and implications of these results, and prospects for corresponding
searches during future LIGO-Virgo runs.
Subject headings: gamma-ray bursts – gravitational waves – compact object mergers – soft gamma-ray
repeaters
GW/0.01M?c2)1/2for emission
We
1. INTRODUCTION
Gamma-ray bursts (GRBs) are intense flashes of γ-rays
which occur approximately once per day and are isotrop-
ically distributed over the sky (see, e.g.: M´ esz´ aros 2006,
and references therein). The variability of the bursts on
time scales as short as a millisecond indicates that the
sources are very compact, while the identification of host
galaxies and the measurement of redshifts for more than

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4 Abbott et al.
100 bursts have shown that GRBs are of extra-galactic
origin.
GRBs are grouped into two broad classes by their char-
acteristic duration and spectral hardness (Kouveliotou
et al. 1993; Gehrels et al. 2006). The progenitors of most
short GRBs (? 2 s, with hard spectra) are widely thought
to be mergers of neutron star binaries or neutron star-
black hole binaries; see for example Nakar (2007); Shi-
bata & Taniguchi (2008); Liu et al. (2008); Anderson
et al. (2008); Etienne et al. (2009). A small fraction (up
to ?15%) of short-duration GRBs are also thought to
be due to giant flares from a local distribution of soft-
gamma repeaters (SGRs) (Duncan & Thompson 1992;
Tanvir et al. 2005; Nakar et al. 2006; Chapman et al.
2009). Long GRBs (? 2 s, with soft spectra), on the
other hand, are associated with core-collapse supernovae
(Galama et al. 1998; Hjorth et al. 2003; Malesani et al.
2004; Campana et al. 2006). Both the merger and super-
nova scenarios result in the formation of a stellar-mass
black hole with accretion disk (Fryer et al. 1999; Can-
nizzo & Gehrels 2009), and the emission of gravitational
radiation is expected in this process.
To date, several searches for gravitational-wave bursts
(GWBs) associated with gamma-ray bursts (GRBs) have
been performed using data from LIGO or Virgo. Data
from the second LIGO science run were used to search for
a gravitational-wave signal from GRB 030329/SN 2003dh
(Abbott et al. 2005), a bright GRB and associated su-
pernova located at a redshift of z = 0.1685. This was
followed by a search for GWBs coincident with 39 GRBs
which were detected during the second, third, and fourth
LIGO science runs (Abbott et al. 2008b). Data from the
Virgo detector were used to search for a GWB associated
with GRB 050915a (Acernese et al. 2007, 2008a). Most
recently, data from the fifth LIGO science run was ana-
lyzed to search for a GWB or binary coalescence inspi-
ral signal from GRB 070201 (Abbott et al. 2008a). This
short-duration GRB had a position error box overlapping
the Andromeda galaxy (M31), located at a distance of
770 kpc. No evidence for a gravitational-wave signal was
found in these searches. In the case of GRB 070201, the
non-detection of associated gravitational waves provided
important information about its progenitor, ruling out a
compact-object binary in M31 with high confidence.
In this paper, we present the results of a search for
gravitational-wave bursts associated with 137 GRBs that
were detected by satellite-based gamma-ray experiments
during the fifth LIGO science run (S5) and first Virgo
science run (VSR1), which collectively spanned the pe-
riod from 2005 November 4 to 2007 October 1. This
is the first joint search for gravitational waves by LIGO
and Virgo; it also uses improved methods compared to
previous searches, and is thus able to achieve better sen-
sitivity.
We search for GWBs from both short- and long-
duration GRBs. Since the precise nature of the radiation
depends on the somewhat-unknown progenitor model,
and we analyse both short and long GRBs, the search
methods presented in this paper do not require specific
knowledge of the gravitational waveforms. Instead, we
look for unmodelled burst signals with duration ? 1 s
and frequencies in the LIGO/Virgo band, approximately
60 Hz − 2000 Hz. The results of a template-based search
specifically targeting binary inspiral gravitational-wave
signals associated with short GRBs are presented sepa-
rately (Abbott et al. 2010).
Although it is expected that most GRB progeni-
tors will be at distances too large for the resulting
gravitational-wave signals to be detectable by LIGO and
Virgo (Berger et al. 2005), it is possible that a few GRBs
could be located nearby. For example, the smallest ob-
served redshift of an optical GRB afterglow is z = 0.0085
(? 36Mpc), for GRB 980425 (Kulkarni et al. 1998;
Galama et al. 1998; Iwamoto et al. 1998); this would be
within the LIGO-Virgo detectable range for some progen-
itor models. Recent studies (Liang et al. 2007; Chapman
et al. 2007) indicate the existence of a local population of
under-luminous long GRBs with an observed rate density
(number per unit volume per unit time) approximately
103times that of the high-luminosity population. Also,
observations seem to suggest that short-duration GRBs
tend to have smaller redshifts than long GRBs (Guetta
& Piran 2005; Fox et al. 2005), and this has led to fairly
optimistic estimates (Nakar et al. 2006; Guetta & Piran
2006; Guetta & Stella 2009; Leonor et al. 2009) for de-
tecting associated gravitational-wave emission in an ex-
tended LIGO science run. Approximately 70% of the
GRBs in our sample do not have measured redshifts, so
it is possible that one or more could be much closer than
the typical Gpc distance of GRBs.
The paper is organized as follows. Section 2 describes
the LIGO and Virgo detectors, and Sec. 3 describes the
GRB sample during LIGO Science Run 5 / Virgo Sci-
ence Run 1. We summarize the analysis procedure in
Sec. 4. Two independent analysis “pipelines” are used
to search for GWBs. Section 5 details the results of the
search. No significant signal is found in association with
any of the 137 GRBs studied. A statistical analysis of the
collective GRB sample also shows no sign of a collective
signature of weak GWBs. In Sec. 6 we place upper limits
on the amplitude of gravitational waves associated with
each GRB. We also set lower limits on the distance to
each GRB assuming a fixed energy emission in gravita-
tional waves. We conclude in Sec. 7 with some comments
on the astrophysical significance of these results and the
prospects for future GRB searches.
2. LIGO SCIENCE RUN 5 & VIRGO SCIENCE RUN 1
The LIGO detectors are kilometer-scale power-recycled
Michelson interferometers with orthogonal Fabry-Perot
arms (Abbott et al. 2004, 2009a). They are designed to
detect gravitational waves with frequencies ranging from
∼ 40 Hz to several kHz. The interferometers’ maximum
sensitivity occurs near 150 Hz. There are two LIGO ob-
servatories: one located at Hanford, WA and the other
at Livingston, LA. The Hanford site houses two interfer-
ometers: one with 4 km arms (H1), and the other with 2
km arms (H2). The Livingston observatory has one 4 km
interferometer (L1). The observatories are separated by
a distance of 3000 km, corresponding to a time-of-flight
separation of 10 ms.
The Virgo detector (V1) is in Cascina near Pisa, Italy.
It is a 3 km long power-recycled Michelson interferom-
eter with orthogonal Fabry-Perot arms (Acernese et al.
2008b). During VSR1, the Virgo detector had sensitivity
similar to the LIGO 4 km interferometers above approx-
imately 500 Hz. The time-of-flight separation between
the Virgo and Hanford observatories is 27 ms, and be-

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Search for GWBs associated with GRBs using LIGO and Virgo5
10
2
10
3
10
−23
10
−22
10
−21
10
−20
10
−19
frequency (Hz)
noise amplitude (Hz−1/2)


LIGO Hanford 4km 2007−03−18
LIGO Hanford 2km 2007−05−14
LIGO Livingston 4km 2007−08−30
Virgo 3km 2007−09−05
Fig. 1.— Best strain noise spectra from the LIGO and Virgo
detectors during S5-VSR1.
tween Virgo and Livingston it is 25 ms.
A gravitational wave is a spacetime metric perturba-
tion that is manifested as a time-varying quadrupolar
strain, with two polarization components.
each interferometer record the length difference of the
arms and, when calibrated, measure the strain induced
by a gravitational wave. These data are in the form of
a time series, digitized at a sample rate of 16384 s−1
(LIGO) or 20000 s−1(Virgo). The response of an inter-
ferometer to a given strain is measured by injecting si-
nusoidal excitations with known amplitude into the test
mass control systems and tracking the resulting signals
at the measurement point throughout each run.
result is a measurement of the time-varying, frequency-
dependent response function of each interferometer.
The fifth LIGO science run (S5) was held from 2005
November 4 to 2007 October 1. During this run, over one
year of science-quality data was collected with all three
LIGO interferometers in simultaneous operation. The
LIGO interferometers operated at their design sensitiv-
ity, with duty factors of 75%, 76%, and 65% for the H1,
H2, and L1 interferometers. The Virgo detector started
its first science run (VSR1) on 2007 May 18. The Virgo
duty cycle over VSR1 was 78%. Figure 1 shows the best
sensitivities, in terms of noise spectral density, of the
LIGO and Virgo interferometers during the run. All of
the instruments ran together continuously until 2007 Oc-
tober 1, amounting to about 4.5 months of joint data
taking.
The GEO 600 detector (Grote et al. 2008), located near
Hannover, Germany, was also operational during the S5-
VSR1 run, though with a lower sensitivity than LIGO
and Virgo. We do not use the GEO data in this search as
the modest gains in the sensitivity to gravitational wave
signals would not have offset the increased complexity of
the analysis.
Data from
The
3. GRB SAMPLE
The GRB triggers that were contemporaneous with
the S5-VSR1 run came mostly from the Swift satellite
(Gehrels et al. 2004), but several triggers also came
from other IPN satellites (Hurley et al. 2009), including
HETE-2 (Ricker et al. 2003), and INTEGRAL (Winkler
et al. 2003). We obtained our GRB triggers through the
Gamma-ray Burst Coordinates Network (GCN 2007).
During the S5-VSR1 run, there were a total of 212
GRBs reported by these satellite-based gamma-ray ex-
periments. Of these, 33 were short-duration GRBs, and
59 had associated redshift measurements. All but 4 of
these GRBs had well-defined positions.
Only LIGO and Virgo data which are of science-mode
quality are analyzed. These are data collected when the
interferometers are in a stable, resonant configuration.
Additionally, data segments which are flagged as being
of poor quality are not included in the analysis. A full
analysis (detection search and upper limit calculation) is
performed for all GRBs which have well-defined positions
and for which at least two interferometers have science-
mode data passing quality requirements. There are 137
such GRBs, of which 21 are short-duration bursts, and 35
have measured redshifts. A list of the GRBs and relevant
information are given in Table 1 in Appendix A.
4. SEARCH PROCEDURE
4.1. Overview
The basic search procedure follows that used in re-
cent LIGO GRB searches (Abbott et al. 2008a,b). All
GRBs are treated identically, without regard to their
duration, redshift (if known), or fluence.
interval from 120 s before each GRB trigger time to 60 s
after as the window in which to search for an associated
gravitational-wave burst. This conservative window is
large enough to take into account most reasonable time
delays between a gravitational-wave signal from a pro-
genitor and the onset of the gamma-ray signal. For ex-
ample, it is much larger than the O(10) s delay of the
gamma-ray signal resulting from the sub-luminal propa-
gation of the jet to the surface of the star in the collapsar
model for long GRBs (see for example Aloy et al. 2000;
Zhang et al. 2003; Wang & Meszaros 2007; Lazzati et al.
2009). It is also much longer than the ? 1 s delay which
may occur in the binary neutron star merger scenario for
short GRBs if a hypermassive neutron star is formed (see
for example Liu et al. 2008; Baiotti et al. 2008; Kiuchi
et al. 2009). Our window is also safely larger than any
uncertainty in the definition of the measured GRB trig-
ger time. The data in this search window are called the
on-source data.
The on-source data are scanned by an algorithm de-
signed to detect transients that may have been caused
by a gravitational-wave burst. In this search, two algo-
rithms are used: the cross-correlation algorithm used in
previous LIGO searches (Abbott et al. 2008b), and X-
Pipeline1, a new coherent analysis package (Chatterji
et al. 2006; Sutton et al. 2009). The cross-correlation
algorithm correlates the data between pairs of detectors,
while X-Pipeline combines data from arbitrary sets of
detectors, taking into account the antenna response and
noise level of each detector to improve the search sensi-
tivity.
Thedataareanalysed
Pipelineandthecross-correlation
produce lists of transients, or events, that may be
candidate gravitational-wave signals.
characterised by a measure of significance, based on
We use the
independentlybyX-
to algorithm
Each event is
1https://geco.phys.columbia.edu/xpipeline/browser?rev=2634

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6 Abbott et al.
energy (X-Pipeline) or correlation between detectors
(cross-correlation algorithm).
non-stationary background noise, the list of candidate
events is subjected to checks that “veto” events overlap-
ping in time with known instrumental or environmental
disturbances (Abbott et al. 2009b).
applies additional consistency tests based on the cor-
relations between the detectors to further reduce the
number of background events.
with the largest significance is taken to be the best
candidate for a gravitational-wave signal for that GRB;
it is referred to as the loudest event (Brady et al. 2004;
Biswas et al. 2009).
To estimate the expected distribution of the loudest
events under the null hypothesis, the pipelines are also
applied to all coincident data within a 3 h period sur-
rounding the on-source data. This data for background
estimation is called the off-source data. Its proximity
to the on-source data makes it likely that the estimated
background will properly reflect the noise properties in
the on-source segment. The off-source data are processed
identically to the on-source data; in particular, the same
data-quality cuts and consistency tests are applied, and
the same sky position relative to the Earth is used. To in-
crease the off-source distribution statistics, multiple time
shifts are applied to the data streams from different de-
tector sites (or between the H1 and H2 streams for GRBs
occurring when only those two detectors were operat-
ing), and the off-source data are re-analysed for each time
shift. For each 180 s segment of off-source data, the loud-
est surviving event is determined. The distribution of
significances of the loudest background events, C(Smax),
thus gives us an empirical measure of the expected distri-
bution of the significance of the loudest on-source event
Son
To determine if a GWB is present in the on-source
data, the loudest on-source event is compared to the
background distribution. If the on-source significance is
larger than that of the loudest event in 95% of the off-
source segments (i.e., if C(Son
is considered as a candidate gravitational-wave signal.
Candidate signals are subjected to additional “detection
checklist” studies to try to determine the physical ori-
gin of the event; these studies may lead to rejecting the
event as being of terrestrial origin, or they may increase
our degree of confidence in it being due to a gravitational
wave.
Regardless of whether a statistically significant signal
is present, we also set a frequentist upper limit on the
strength of gravitational waves associated with the GRB.
For a given gravitational-wave signal model, we define
the 90% confidence level upper limit on the signal ampli-
tude as the minimum amplitude for which there is a 90%
or greater chance that such a signal, if present in the
on-source region, would have produced an event with
significance larger than the largest value Son
measured. The signal models simulated are discussed in
Sec. 6.1.
Since X-Pipeline was found to be more sensitive to
GWBs than the cross-correlation pipeline (by about a
factor of 2 in amplitude), we decided in advance to set the
upper limits using the X-Pipeline results. The cross-
correlation pipeline is used as a detection-only search.
Since it was used previously for the analysis of a large
To reduce the effect of
X-Pipeline also
The surviving event
maxunder the null hypothesis.
max) ≥ 0.95), then the event
maxactually
number of GRBs during S2-S4, and for GRB070201 dur-
ing S5, including the cross-correlation pipeline provides
continuity with past GRB searches and allows compar-
ison of X-Pipeline with the technique used for these
past searches.
4.2. X-Pipeline
X-Pipeline is a matlab-based software package
for performing coherent searches for gravitational-wave
bursts in data from arbitrary networks of detectors.
Since X-Pipeline has not previously been used in a
published LIGO or Virgo search, in this section we give
a brief overview of the main steps followed in a GRB-
triggered search. For more details on X-Pipeline, see
Sutton et al. (2009).
Coherent techniques for GWB detection (see for ex-
ample Gursel & Tinto 1989; Flanagan & Hughes 1998;
Anderson et al. 2001; Klimenko et al. 2005, 2006; Mo-
hanty et al. 2006; Rakhmanov 2006; Chatterji et al. 2006;
Summerscales et al. 2008) combine data from multiple
detectors before scanning it for candidate events. They
naturally take into account differences in noise spectrum
and antenna response of the detectors in the network.
X-Pipeline constructs several different linear combina-
tions of the data streams: those that maximize the ex-
pected signal-to-noise ratio for a GWB of either polariza-
tion from a given sky position (referred to as the d+and
d×streams), and those in which the GWB signal cancels
(referred to as the dnullstreams). It then looks for tran-
sients in the d+and d×streams. Later, the energies in
the d+, d×, and dnullstreams are compared to attempt to
discriminate between true GWBs and background noise
fluctuations.
4.2.1. Event Generation
X-Pipeline processes data in 256 s blocks. First, it
whitens the data from each detector using linear predic-
tor error filters (Chatterji et al. 2004). It then time-shifts
each stream according to the time-of-flight for a gravita-
tional wave incident from the sky position of the GRB, so
that a gravitational-wave signal will be simultaneous in
all the data streams after the shifting. The data are di-
vided into 50% overlapping segments and Fourier trans-
formed. X-Pipeline then coherently sums and squares
these Fourier series to produce time-frequency maps of
the energy in the d+, d×, and dnullcombinations. Specifi-
cally, we define the noise-weighted antenna response vec-
tors f+,DPFand f×,DPFfor the network, with compo-
nents
(θ,φ,f)=F+
f+,DPF
α
α(θ,φ,ψDPF)
?Sα(f)
α(θ,φ,ψDPF)
?Sα(f)
, (1)
f×,DPF
α
(θ,φ,f)=F×
.(2)
Here (θ,φ) is the direction to the GRB, ψDPFis the po-
larization angle specifying the orientation of the plus and
cross polarizations, F+
α∈ [−1,1] are the antenna
response factors to the plus and cross polarizations (An-
derson et al. 2001, see also Sec. 6.1), and Sαis the noise
power spectrum of detector α. DPF stands for the dom-
inant polarization frame; this is a frequency-dependent
α, F×

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Search for GWBs associated with GRBs using LIGO and Virgo7
polarization basis ψDPF(f) such that f+,DPF·f×,DPF=
0 and |f+,DPF| ≥ |f×,DPF| (Klimenko et al. 2005). With
this choice of basis, the d+stream is defined as the pro-
jection
d+≡f+,DPF· d
|f+,DPF|
where d is the set of whitened data streams from the in-
dividual detectors. The “signal energy” E+≡ |d+|2can
be shown to be the sum-squared signal-to-noise ratio in
the network corresponding to the least-squares estimate
of the h+ polarization of the gravitational wave in the
dominant polarization frame. The d× stream and en-
ergy E×are defined analogously. The sum E++ E×is
then the maximum sum-squared signal-to-noise at that
frequency that is consistent with a GWB arriving from
the given sky position at that time.
The projections of the data orthogonal to f+,DPF,
f×,DPFyield the null streams, in which the contri-
butions of a real gravitational wave incident from the
given sky position will cancel. The null stream energy
Enull≡ |dnull|2should therefore be consistent with back-
ground noise. (The definition of the null streams is in-
dependent of the polarization basis used.) The number
of independent data combinations yielding null streams
depends on the geometry of the network. Networks con-
taining both the H1 and H2 interferometers have one null
stream combination. Networks containing L1, V1, and
at least one of H1 or H2 have a second null stream. For
the H1-H2-L1-V1 network there are two independent null
streams; in this case we sum the null energy maps from
the two streams to yield a single null energy.
Events are selected by applying a threshold to the
E++E×map, so that the pixels with the 1% highest val-
ues are marked as black pixels. Nearest-neighbor black
pixels are grouped together into clusters (Sylvestre 2002).
These clusters are our events. Each event is assigned an
approximate statistical significance S based on a χ2dis-
tribution; for Gaussian noise in the absence of a signal,
2(E++E×) is χ2-distributed with 4Npixdegrees of free-
dom, where Npixis the number of pixels in the event clus-
ter. This significance is used when comparing different
clusters to determine which is the “loudest”. The vari-
ous coherent energies (E+, E×, Enull) are summed over
the component pixels of the cluster, and other properties
such as duration and bandwidth of the cluster are also
recorded.
The analysis of time shifting, FFTing, and clus-
ter identification is repeated for FFT lengths of
(1/8,1/16,1/32,1/64,1/128,1/256) s, to cover a range
of possible GWB durations. Clusters produced by dif-
ferent FFT lengths that overlap in time and frequency
are compared. The cluster with the largest significance
is kept; the others are discarded. Finally, only clusters
with central time in the on-source window of 120 s be-
fore the GRB time to 60 s after are considered as possible
candidate events.
, (3)
4.2.2. Glitch Rejection
Real detector noise contains glitches, which are short
transients of excess strain noise that can masquerade as
GWB signals. As shown in Chatterji et al. (2006), one
can construct tests that are effective at rejecting glitches.
Specifically, each coherent energy E+, E×, Enull has a
corresponding “incoherent” energy I+, I×, Inull that is
formed by discarding the cross-correlation terms (dαd∗
when computing E+= |d+|2, etc. For large-amplitude
background noise glitches the coherent and incoherent
energies are strongly correlated, E ∼ I ±√I. For strong
gravitational-wave signals one expects either E+ > I+
and E×< I×or E+< I+and E×> I×depending on
the signal polarization content, and Enull< Inull.
X-Pipeline uses the incoherent energies to apply a
pass/fail test to each event. A nonlinear curve is fit to the
measured distribution of background events used for tun-
ing (discussed below); specifically, to the median value of
I as a function of E. Each event is assigned a measure
of how far it is above or below the median:
β)
σ ≡ (I − Imed(E))/I1/2. (4)
For (Inull,Enull), an event is passed if σnull> rnull, where
rnullis some threshold. For (I+,E+) and (I×,E×), the
event passes if |σ+| > r+and |σ×| > r×. (For the H1-
H2 network, which contains only aligned interferometers,
the conditions are σ+< r+and σnull> rnull.) An event
may be tested for one, two, or all three of the pairs
(Inull,Enull), (I+,E+), and (I×,E×), depending on the
GRB. The choice of which energy pairs are tested and
the thresholds applied are determined independently for
each of the 137 GRBs. X-Pipeline makes the selection
automatically by comparing simulated GWBs to back-
ground noise events, as discussed below. In addition,
the criterion Inull≥ 1.2Enullwas imposed for all H1-H2
GRBs, as this was found to be effective at removing loud
background glitches without affecting simulated gravita-
tional waves.
In addition to the coherent glitch vetoes, events may
also be rejected because they overlap data quality flags
or vetoes, as mentioned in Sec. 4.1. The flags and vetoes
used are discussed in Abbott et al. (2009b). To avoid
excessive dead time due to poor data quality, we impose
minimum criteria for a detector to be included in the
network for a given GRB. Specifically, at least 95% of
the 180 s of on-source data must be free of data quality
flags and vetoes, and all of the 6 s spanning the interval
from -5 to +1 s around the GRB trigger must be free of
flags and vetoes.
4.2.3. Pipeline Tuning
To detect a gravitational wave, X-Pipeline compares
the largest significance of all events in the on-source time
after application of vetoes, Son
tribution C(Smax) of loudest significances measured in
each off-source segment. If C(Son
the event for follow-up study.
To maximize the sensitivity of X-Pipeline, we tune
the coherent glitch test thresholds r+,r×,rnull for each
GRB to optimize the trade-off between glitch rejection
and signal acceptance. We do this using the off-source
data and data containing simulated GWB signals (injec-
tions, discussed in Sec. 6.1), but not the on-source data.
This blind tuning avoids the possibility of biasing the
upper limit.
The procedure is simple. The off-source segments and
injections are divided randomly into two equal sets: half
for tuning, and half for sensitivity and background esti-
max, to the cumulative dis-
max) ≥ 0.95, we consider

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8Abbott et al.
mation. Each of r+,r×, and rnull are tested with trial
thresholds of [0,0.5,1,1.5,...,5], where a value of 0 is
treated as not testing that energy type. For each of the
113= 1331 possible combinations of trial thresholds, the
loudest surviving event in each tuning off-source segment
is found. The injection amplitude required for 90% of the
injections to be louder than the 95thpercentile of Smaxis
computed for each waveform type. The set of thresholds
giving the lowest required injection amplitude over all
waveforms is selected as optimal (at least one of r+,r×,
and rnullis required to be non-zero). To get an unbiased
estimate of the expected sensitivity and background, we
apply the tuned vetoes to the second set of off-source
segments and injections, that were not used for tuning.
For more details, see Sutton et al. (2009).
4.3. Cross-Correlation Pipeline
The cross-correlation pipeline has been used in two pre-
vious LIGO searches (Abbott et al. 2008b,a) for GWBs
associated with GRBs, and is described in detail in these
references. We therefore give only a brief summary of
the pipeline here.
In the present search, the cross-correlation pipeline is
applied to the LIGO detectors only. (The different ori-
entation and noise spectrum shape of Virgo relative to
the LIGO detectors is more easily accounted for in a
coherent analysis.) The 180 s on-source time series for
each interferometer is whitened as described in Abbott
et al. (2008b) and divided into time bins, then the cross-
correlation for each interferometer pair and time bin is
calculated. The cross-correlation cc of two timeseries s1
and s2is defined as
?m
cc =
i=1[s1(i) − µ1][s2(i) − µ2]
??m
j=1[s1(j) − µ1]2??m
k=1[s2(k) − µ2]2, (5)
where µ1and µ2are the corresponding means, and m is
the number of samples in the bin. Cross-correlation bins
of lengths 25 ms and 100 ms are used to target short-
duration GW signals with durations of ∼ 1 ms to ∼ 100
ms. The bins are overlapped by half a bin width to avoid
loss of signals occurring near a bin boundary. Each LHO-
LLO pair of 180 s on-source segments is shifted in time
relative to each other to account for the time-of-flight
between the detector sites for the known sky position of
the GRB before the cross-correlations are calculated.
The cross-correlation is calculated for each interferom-
eter pair and time bin for each bin length used.
an H1-H2 search the largest cross-correlation value ob-
tained within the 180 s search window is considered the
most significant measurement. For an H1-L1 or H2-L1
search, the largest absolute value of the cross-correlation
is taken as the most significant measurement. This was
done to take into account the possibility that signals at
LHO and LLO could be anticorrelated depending on the
(unknown) polarization of the gravitational wave.
For
5. SEARCH RESULTS
5.1. Per-GRB Results
The results of the search for each of the 137 GRBs anal-
ysed by X-Pipeline are shown in Table 1, Appendix A.
The seventh column in this table lists the local probability
p ≡ 1−C(Son
max) for the loudest on-source event, defined
as the fraction of background trials that produced a more
significant event (a “−” indicates no event survived all
cuts). Five GRBs had events passing the threshold of
p = 0.05 to become candidate signals.
Since the local probability is typically estimated using
approximately 150 off-source segments, small p values
are subject to relatively large uncertainty from Poisson
statistics. We therefore applied additional time-shifts to
the off-source data to obtain a total of 18000 off-source
segments for each candidate which were processed to im-
prove the estimate of p. The 5 GRBs and their refined
local probabilities are 060116 (p = 0.0402), 060510B
(0.0124), 060807 (0.00967), 061201 (0.0222), and 070529
(0.0776). (Note that for GRB 070529, the refined local
probability from the extra off-source segments was larger
than the threshold of 0.05 for candidate signals.)
Considering that we analysed 137 GRBs, these num-
bers are consistent with the null hypothesis that no
gravitational-wave burst signal is associated with any of
the GRBs tested. In addition, three of these GRBs have
large measured redshift: GRB 060116 (z = 6.6), 060510B
(z = 4.9), and 070529 (z = 2.5), making it highly
unlikely a priori that we would expect to see a GWB
in these cases. Nevertheless, each event has been sub-
jected to follow-up examinations. These include checks of
the consistency of the candidate with background events
(such as in coherent energies, and frequency), checks of
detector performance at the time as indicated by mon-
itoring programs and operator logs, and scans of data
from detector and environmental monitoring equipment
to look for anomalous behavior. In each case, the candi-
date event appears consistent with the coherent energy
distributions of background events, lying just outside the
coherent glitch rejection thresholds. The frequency of
each event is also typical of background events for their
respective GRBs. Some of these GRBs occurred during
periods of elevated background noise, and one occurred
during a period of glitchy data in H1. In two cases scans
of data from monitoring equipment indicate a possible
physical cause for the candidate event: one from non-
stationarity in a calibration line, and another due to up-
conversion of low-frequency noise in H1.
All but two of the GRBs processed by X-Pipeline are
also analysed by the cross-correlation pipeline.
cross-correlation pipeline produces a local probability for
each detector pair and for each bin length (25 ms and 100
ms), for a total of 646 measurements from 135 GRBs.
The threshold on the cross-correlation local probability
corresponding to the 5% threshold for X-Pipeline is
therefore 5%×135/646 ? 1%. A total of 7 GRBs have
p < 1% from cross-correlation: 060306 (0.00833), 060719
(0.00669), 060919 (0.00303), 061110 (0.00357), 070704
(0.00123), and 070810 (0.00119). These results are also
consistent with the null hypothesis. Furthermore, none
of these GRBs are among those that had a low p value
from X-Pipeline. This is further indication that the
candidate events detected by each pipeline are due to
background noise rather than GWBs. Specifically, X-
Pipeline and the cross-correlation pipeline use different
measures of significance of candidate events. Whereas
a strong GWB should be detected by both, any given
background noise fluctuation may have very different sig-
nificance in the two pipelines.
We conclude that we have not identified a plausible
The

Page 9

Search for GWBs associated with GRBs using LIGO and Virgo9
gravitational-wave burst signal associated with any of
the 137 GRBs tested.
5.2. Binomial Test
Gravitational-wave signals from individual GRBs are
likely to be very weak in most cases due to the cosmo-
logical distances involved. Therefore, besides searching
for GWB signals from each GRB, we also test for a cu-
mulative signature associated with a sample of several
GRBs (Finn et al. 1999). This approach has been used
in Astone et al. (2002, 2005) to analyze resonant mass
detector data using triggers from the BATSE and Bep-
poSAX missions, and more recently in the LIGO search
for GRBs during the S2, S3, and S4 science runs (Abbott
et al. 2008b).
Under the null hypothesis (no GWB signal), the local
probability for each GRB is expected to be uniformly
distributed on [0,1]. Moderately strong GWBs associ-
ated with one or more of the GRBs will cause the low-
p tail of the distribution to deviate from that expected
under the null hypothesis. We apply the binomial test
used in Abbott et al. (2008b) to search for a statistically
significant deviation, applying it to the 5% × 137 ? 7
least probable (lowest p) on-source results in the GRB
distribution. Briefly, we sort the 7 smallest local prob-
abilities in increasing order, p1,p2,...,p7. For each pi
we compute the binomial probability P≥i(pi) of getting
i or more events out of 137 at least as significant as pi.
The smallest P≥i(pi) is selected as the most significant
deviation from the null hypothesis. To account for the
trials factor from testing 7 values of i, we repeat the
test many times using 137 fake local probabilities drawn
from uniform discrete distributions corresponding to the
number of off-source segments for each GRB (18000 for
our refined p estimates). The probability associated with
the actual smallest P≥i(pi) is defined as the fraction of
Monte Carlo trials that gave binomial probabilities as
small or smaller. Note that this procedure also automat-
ically handles the case of a single loud GWB.
In addition to the 5 “candidate” GRBs, extra time-
shifted off-source segments were analysed for the 2 GRBs
with the next smallest local probabilities, GRB 060428B
(0.0139) and 060930 (p = 0.0248). (By chance, for both
of these GRBs the refined local probabilities from the ex-
tra off-source segments are smaller than the threshold of
0.05 for candidate signals, though the original estimates
were larger.) Together with the 5 candidates, this gives
the 7 refined local probabilities 0.00967, 0.0124, 0.0139,
0.0222, 0.0248, 0.0402, 0.0776. The associated smallest
binomial probability is P≥5(0.0248) = 0.259. Approxi-
mately 56% of Monte Carlo trials give binomial probabil-
ities this small or smaller, hence we conclude that there
is no significant deviation of the measured local probabil-
ities from the null hypothesis. For comparison, Figure 2
shows the distribution of local probabilities for all GRBs,
as well as the values that would need to be observed to
give only 1% consistency with the null hypothesis.
Similar results are found when restricting the test to
GRBs without measured redshift. In this case the small-
est binomial probability is P≥4(0.0248) = 0.252 with 48%
of Monte Carlo trials yielding binomial probabilities this
small or smaller. Analysis of the cross-correlation local
probabilities also shows no significant deviation. Com-
bining the local probabilities from the 25 ms and 100 ms
10
−3
10
−2
10
−1
10
0
10
0
10
1
10
2
local probability p
number of GRBs


data
expected
needed for 1% CL
Fig. 2.—
from the search of 137 GRBs with X-Pipeline. The most signif-
icant excess is indicated by the arrow. The expected distribution
under the null hypothesis is indicated by the diagonal dashed line.
The excess needed for a 1% confidence in the null hypothesis is
indicated by the solid line. The maximum excess indicated by this
line is 7 events because only the 7 most significant events in the ac-
tual distribution are tested. The buildup of GRBs at p = 1 occurs
because approximately half of the GRBs do not have any event
surviving all the analysis cuts.
analyses, we find the smallest binomial probability to be
P≥2(0.00123) = 0.190 with 52% of Monte Carlo trials
yielding binomial probabilities this small or smaller.
Cumulative local probability distribution resulting
6. UPPER LIMITS
The sensitivity of the search to gravitational waves is
determined by a Monte Carlo analysis. For each GRB,
we add (or “inject”) simulated GWB signals into the
detector data and repeat the analysis. We count an in-
jected signal as “detected” if it produces an event that is
louder than the loudest on-source event within 100 ms of
the injection time. (When tuning, we do not know the
significance of the loudest on-source event. We therefore
count an injection as detected if it is louder than the me-
dian background loudest event from the off-source tuning
segments; i.e., louder than the 50thpercentile of the sam-
ple of Smaxvalues.) For a given waveform morphology,
we define the 90% confidence level upper limit on the sig-
nal amplitude as the minimum amplitude for which the
detection probability is 0.9 or greater.
We discuss the signal models in Sec. 6.1, their system-
atic uncertainties in Sec. 6.2, and the upper limit results
in Sec. 6.3.
6.1. Simulations
The antenna response of an interferometer to a gravi-
tational wave with polarization strains h+(t) and h×(t)
depends on the polarization basis angle ψ and the direc-
tion (θ,φ) to the source as
h(t) = F+(θ,φ,ψ)h+(t) + F×(θ,φ,ψ)h×(t).
Here F+(θ,φ,ψ), F×(θ,φ,ψ) are the plus and cross an-
tenna factors introduced in Sec. 4.2; see Anderson et al.
(2001) for explicit definitions.
(6)

Page 10

10Abbott et al.
A convenient measure of the gravitational-wave ampli-
tude is the root-sum-square amplitude,
??
The energy flux (power per unit area) of the wave is
(Isaacson 1968)
hrss=
(|h+(t)|2+ |h×(t)|2) dt .(7)
FGW=
c3
16πG?(˙h+)2+ (˙h×)2?, (8)
where the angle brackets denote an average over several
periods. The total energy emitted assuming isotropic
emission is then
Eiso
GW= 4πD2
?
dtFGW, (9)
where D is the distance to the source.
The forms of h+(t) and h×(t) depend on the type of
simulated waveform. It is likely that many short GRBs
are produced by the merger of neutron-star–neutron-star
or black-hole–neutron-star binaries. The gravitational-
wave signal from inspiralling binaries is fairly well un-
derstood (Blanchet 2006; Aylott et al. 2009). Progress
is being made on modelling the merger phase; recent
numerical studies of the merger of binary neutron star
systems and gravitational-wave emission have been per-
formed by Shibata et al. (2005); Shibata & Taniguchi
(2006); Baiotti et al. (2008, 2009); Yamamoto et al.
(2008); Read et al. (2009); Kiuchi et al. (2009); Rez-
zolla et al. (2010). Preliminary explorations of the im-
pact of magnetic fields have also been made by Ander-
son et al. (2008); Liu et al. (2008); Giacomazzo et al.
(2009). The merger of black-hole–neutron-star binaries
have been studied by Shibata & Ury¯ u (2006, 2007); Shi-
bata & Taniguchi (2008); Etienne et al. (2008); Duez
et al. (2008); Yamamoto et al. (2008); Shibata et al.
(2009); Etienne et al. (2009); Duez et al. (2009). For
other progenitor types, particularly for long GRBs, there
are no robust models for the gravitational-wave emission
(see for example Fryer et al. 2002; Kobayashi & Meszaros
2003; van Putten et al. 2004; Ott 2009, for possible sce-
narios). Since our detection algorithm is designed to be
sensitive to generic gravitational-wave bursts, we choose
simple ad hoc waveforms for tuning and testing. Specif-
ically, we use sine-Gaussian and cosine-Gaussian wave-
forms:
h+(t + t0)= h+,0sin(2πf0t)exp
?−(2πf0t)2
?−(2πf0t)2
2Q2
?
?
, (10)
h×(t + t0) = h×,0cos(2πf0t)exp
2Q2
, (11)
where t0is the central time, f0is the central frequency,
h+,0and h×,0are the amplitude parameters of the two
polarizations, and Q is a dimensionless constant which
represents roughly the number of cycles with which the
waveform oscillates with more than half of the peak am-
plitude. For Q ? 3, the root-sum-squared amplitude of
this waveform is
?
hrss≈
Q(h2
+,0+ h2
4π1/2f0
×,0)
(12)
and the energy in gravitational waves is
Eiso
GW≈π2c3
G
D2f2
0h2
rss.(13)
Using these waveforms for h+(t) and h×(t), we simu-
late circularly polarized GW waves by setting the sine-
Gaussian and cosine-Gaussian amplitudes equal to each
other, h+,0= h×,0. To simulate linearly polarized waves,
we set h×,0= 0.
The peak time of the simulated signals is distributed
uniformly through the on-source interval. We use Q =
23/2π = 8.9, a standard choice in LIGO burst searches.
The polarization angle ψ for which h+, h×take the forms
in equations (10) and (11) is uniform on [0,π), and the
sky position used is that of the GRB (fixed in right as-
cension and declination). We simulate signals at discrete
log-spaced amplitudes, with 500 injections of each wave-
form for each amplitude.
Early tests of the search algorithms used the central
frequencies f0= (100,150,250,554,1000,1850) Hz, and
both linearly and circularly polarized injections. The fi-
nal X-Pipeline tuning (performed after implementation
of an improved data-whitening procedure) uses 150 Hz
and 1000 Hz injections of both polarizations.
6.2. Statistical and Systematic Errors
Our upper limit on gravitational-wave emission by a
GRB is h90%
rss, the amplitude at which there is a 90% or
greater chance that such a signal, if present in the on-
source region, would have produced an event with signi-
cance larger than the largest actually measured. There
are several sources of error, both statistical and system-
atic, that can affect our limits. These are calibration
uncertainties (amplitude and phase response of the de-
tectors, and relative timing errors), uncertainty in the
sky position of the GRB, and uncertainty in the mea-
surement of h90%
rss
due to the finite number of injections
and the use of a discrete set of amplitudes.
To estimate the effect of these errors on our upper
limits, we repeat the Monte Carlo runs for a subset
of the GRBs, simulating all three of these types of er-
rors. Specifically, the amplitude, phase, and time de-
lays for each injection in each detector are perturbed
by Gaussian-distributed corrections matching the cali-
bration uncertainties for each detector. The sky posi-
tion is perturbed in a random direction by a Gaussian-
distributed angle with standard deviation of 3 arcmin.
Finally, the discrete amplitudes used are offset by those
in the standard analysis by a half-step in amplitude. The
perturbed injections are then processed, and the open-
box upper limit produced using the same coherent consis-
tency test tuning as in the actual open-box search. The
typical difference between the upper limits for perturbed
injections and unperturbed injections then gives an esti-
mate of the impact of the errors on our upper limits.
For low-frequency injections (at 150 Hz) we find that
the ratio of the upper limit for perturbed injections to un-
perturbed injections is 1.03 with a standard deviation of
0.06. We therefore increase the estimated upper limits at
100 Hz by a factor of 1.03+1.28×0.06 = 1.10 as a conser-
vative allowance for statistical and systematic errors (the
factor 1.28 comes from the 90% upper limit for a Gaus-
sian distribution). The dominant contribution is due to

Page 11

Search for GWBs associated with GRBs using LIGO and Virgo11
the finite number of injections. For the high-frequency
(1000 Hz) injections the factor is 1.10+1.28×0.12 = 1.25.
In addition to finite-number statistics, the calibration un-
certainties are more important at high frequencies and
make a significant contribution to this factor. All limits
reported in this paper include these allowance factors.
6.3. Limits on Strain and Distance
The upper limits on GWB amplitude and lower limits
on the distance for each of the GRBs analysed are given
in Table 1 in Appendix A. These limits are computed for
circularly polarized 150 Hz and 1000 Hz sine-Gaussian
waveforms. We compute the distance limits by assuming
the source emitted Eiso
of energy isotropically in gravitational waves and use
equation (13) to infer a lower limit on D. We choose
Eiso
one might expect to be emitted in the LIGO-Virgo band
by various progenitor models. For example, mergers of
neutron-star binaries or neutron-star–black-hole binaries
(the likely progenitors of most short GRBs) will have
isotropic-equivalent emission of order (0.01 − 0.1) M?c2
in the 100-200 Hz band. For long GRBs, fragmentation
of the accretion disk (Davies et al. 2002; King et al. 2005;
Piro & Pfahl 2007) could produce inspiral-like chirps
with (0.001 − 0.01) M?c2emission.
accretion model (van Putten et al. 2004) also predicts
an energy emission of up to (0.01 − 0.1)M?c2in this
band. For other values of Eiso
GWthe distance limit scales
as D ∝ (Eiso
As can be seen from Table 1, the strongest limits are on
gravitational-wave emission at 150 Hz, where the sensi-
tivity of the detectors is best (see Figure 1). Figure 3
shows a histogram of the distance limits for the 137
GRBs tested.The typical limits at 150 Hz from the
X-Pipeline analysis are (5−20) Mpc. The best upper
limits are for GRBs later in S5-VSR1, when the detec-
tor noise levels tended to be lowest (and when the most
detectors were operating), and for GRBs that occurred
at sky positions for which the detector antenna responses
F+, F×were best. The strongest limits obtained were for
GRB 070429B: h90%
Mpc at 150 Hz. For comparison, the smallest measured
redshift in our GRB sample is for 060614, which had
z = 0.125 (Price et al. 2006) or D ? 578 Mpc (Wright
2006). (Though GRB 060218 at z = 0.0331 (Mirabal
et al. 2006) occurred during S5, unfortunately, the LIGO-
Hanford and Virgo detectors were not operating at the
time.)
A GRB of particular interest is 070201. This short-
duration GRB had a position error box overlapping
M31 (see Mazets et al. 2008, and references therein),
which is at a distance of only 770 kpc.
of LIGO data from this time was presented in Abbott
et al. (2008a). GRB 070201 was included in the present
search using the new X-Pipeline search package. Our
new upper limits on the amplitude of a GWB associ-
ated with GRB 070201 are h90%
at 150 Hz, and h90%
rss
= 27.8 × 10−22Hz−1/2at 1000
Hz. These are approximately a factor of 2 lower than
those placed by the cross-correlation algorithm. For a
source at 770 kpc, the energy limit from equation (13)
GW= 0.01M?c2= 1.8 × 1052erg
GW= 0.01M?c2because this is a reasonable value
The suspended
GW)1/2.
rss = 1.75×10−22Hz−1/2, D90%= 26.2
An analysis
rss
= 6.38 × 10−22Hz−1/2
05 1015 20 2530 35
0
5
10
15
20
25
30
35
40
45
50
number of GRBs
distance (Mpc)
Fig. 3.— Histogram of lower limits on the distance to each of
the 137 GRBs studied, assuming that the GRB progenitors emit
0.01M?c2= 1.8 × 1052erg of energy in circularly polarized gravi-
tational waves at 150 Hz.
is Eiso
a factor of 4 lower than the GWB limit presented in
Abbott et al. (2008a), this is still several orders of mag-
nitude away from being able to test the hypothesis that
this GRB’s progenitor was a soft-gamma repeater in M31
(Mazets et al. 2008).
GW= 1.15 × 10−4M?c2at 150 Hz. While about
7. SUMMARY AND CONCLUSION
We have presented the results of a search for
gravitational-wave bursts associated with 137 GRBs that
occurred during the LIGO Science Run 5 – Virgo Science
Run 1, from 2005 November 4 to 2007 October 1. The
search used two independent data-analysis pipelines to
scan for unmodelled transient signals consistent with the
known time and sky position of each GRB. No plausi-
ble gravitational-wave signals were identified. Assum-
ing isotropic gravitational-wave emission by the progen-
itor, we place lower limits on the distance to each GRB.
The median limit is D ∼ 12 Mpc (Eiso
for emission at frequencies around 150 Hz, where the
LIGO-Virgo detector network has best sensitivity.
It is informative to compare this result to the rate den-
sity of GRBs (see, for example, Leonor et al. 2009). For
long GRBs, a commonly used estimate of the local rate
density (the rate of observable GRBs per unit volume)
is Robs
Le & Dermer 2007). We therefore estimate the a priori
expected number of long GRBs being observed within a
distance D during a two-year science run as
?4
where T is the total observation time with two or more
gravitational-wave detectors operating, and Ω is the field
of view of the satellite’s GRB detector. Most of the S5-
VSR1 GRBs were detected by Swift, with Ω = 1.4 sr.
The coincident observation time was approximately 1.3
yr. These give
GW/0.01M?c2)1/2
long∼ 0.5 Gpc−3yr−1(Sokolov 2001; Schmidt 2001;
?Nlong??Robs
long
3πD3
?
TΩ
4π,
(14)
?Nlong??1 × 10−6
Robs
long
0.5 Gpc−3yr−1
?
Eiso
GW
0.01M?c2
?3/2
. (15)

Page 12

12Abbott et al.
Recent studies (Liang et al. 2007; Chapman et al. 2007)
have indicated that there exists a local population of
under-luminous long GRBs with an observed rate den-
sity approximately 103times that of the high-luminosity
population. For this population we have
?Nlocal??1 × 10−3
Robs
local
500 Gpc−3yr−1
?
Eiso
GW
0.01M?c2
?3/2
. (16)
For short GRBs the estimated local rate density is of
order Robs
Nakar et al. 2006). We therefore estimate the a priori
expected number of short GRBs being observed during
S5-VSR1 as
short∼ 10 Gpc−3yr−1(Guetta & Piran 2006;
?Nshort??2 × 10−5
Robs
short
10 Gpc−3yr−1
?
Eiso
GW
0.01M?c2
?3/2
. (17)
There is also evidence of a high-density local population
of short GRBs (Tanvir et al. 2005; Nakar et al. 2006;
Chapman et al. 2009), but these are thought to be due
to extra-galactic SGRs, which are not so promising as
GW sources.
It is clear that the detection of gravitational-wave emis-
sion associated with either a short or long GRB with the
current LIGO-Virgo network is unlikely, though not im-
possible. Looking ahead, the enhanced LIGO and Virgo
detectors have recently begun their next data-taking run,
S6-VSR2. Furthermore, the Fermi satellite is now oper-
ating, with a field of view of approximately Ω = 9.5 sr.
Assuming a similar observation time and sensitivity for
S6-VSR2, the expected number of detections scales to
?Nlong??7 × 10−6
?Nlocal??7 × 10−3
?Nshort??1 × 10−4,
(18)
(19)
(20)
where we use the nominal values for Robs, Eiso
equations (15)–(17). Further in the future (c.2015),
GWas in
the planned advanced LIGO (Abbott et al. 2007) and
advanced Virgo (Acernese et al. 2006) detectors will
have amplitude sensitivities about an order of magni-
tude greater than the current detectors. Since the search
volume scales as D3, there is a very good chance that
we will be able to detect gravitational waves associated
with one or more GRBs during an extended science run
of the advanced detectors.
We are indebted to the observers of the electromag-
netic events and the GCN for providing us with valu-
able data. The authors gratefully acknowledge the sup-
port of the United States National Science Foundation
for the construction and operation of the LIGO Labo-
ratory, the Science and Technology Facilities Council of
the United Kingdom, the Max-Planck-Society, and the
State of Niedersachsen/Germany for support of the con-
struction and operation of the GEO600 detector, and
the Italian Istituto Nazionale di Fisica Nucleare and the
French Centre National de la Recherche Scientifique for
the construction and operation of the Virgo detector.
The authors also gratefully acknowledge the support of
the research by these agencies and by the Australian
Research Council, the Council of Scientific and Indus-
trial Research of India, the Istituto Nazionale di Fisica
Nucleare of Italy, the Spanish Ministerio de Educaci´ on
y Ciencia, the Conselleria d’Economia Hisenda i Inno-
vaci´ o of the Govern de les Illes Balears, the Founda-
tion for Fundamental Research on Matter supported by
the Netherlands Organisation for Scientific Research, the
Royal Society, the Scottish Funding Council, the Scottish
Universities Physics Alliance, The National Aeronautics
and Space Administration, the Carnegie Trust, the Lev-
erhulme Trust, the David and Lucile Packard Founda-
tion, the Research Corporation, and the Alfred P. Sloan
Foundation.This document has been assigned LIGO
Laboratory document number LIGO-P0900023-v16.
APPENDIX
GRB SAMPLE AND SEARCH RESULTS
Table 1 lists the 137 GRBs analyzed in this analysis, including the GRB name, time, sky position, and redshift (when
known). In addition, for each GRB we display the results of the X-Pipeline search for an associated GWB: the set
of detectors used, the local probability of the loudest on-source event, and 90% confidence limits on the gravitational-
wave amplitude and the distance to the progenitor. For approximately half of the GRBs there was no surviving event
and hence no local probability. The limits are computed for circularly polarized 150 Hz and 1000 Hz sine-Gaussian
waveforms. The distances are lower limits, assuming isotropic emission of 0.01M?c2= 1.8 × 1053erg of energy in
gravitational waves. These limits include allowances for statistical and systematic errors as discussed in Sec. 6.2.
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Page 13

Search for GWBs associated with GRBs using LIGO and Virgo13
TABLE 1
GRB Sample and Search Results
150 Hz 1000 Hz
UTC
time
RA
(deg)
Dec
(deg)
DD
GRBz networkphrss
(Mpc)hrss
(Mpc)
051114‡
051117
051117B
051210‡
051211‡
051211B
051213
051221B
060102
060105
060108
060110
060111
060114
060115
060116
060121‡
060202
060203
060206
060211B
060223
060306
060312
060313‡
060319
060323
060403
060418
060427
060427B‡
060428
060428B
060429‡
060501
060510
060510B
060515
060516
060526
060605
060607
060607B
060614
060707
060712
060714
060719
060804
060805
060807
060813
060814
060825
060904
060904B
060906
060908
060919
060923
060923C
060927
060928
–
–
–
–
–
–
–
–
–
–
04:11:30
10:51:20
13:22:54
05:46:21
02:50:05.4
22:05:44
07:13:04
20:03:20
21:17:28
06:49:28
14:39:11.76
08:01:17
04:23:06
12:39:44
13:08:00
08:37:27
22:24:54.5
08:40:55
23:55:35
04:46:53
15:55:15
06:04:23
00:49:10
01:36:12
00:12:06
00:55:42
14:32:36
13:12:17
03:06:08
11:43:10
23:51:55
03:22:48
08:54:38
12:19:51.00
08:14:58
07:43:27
08:22:14
02:27:52
06:43:34
16:28:30
18:15:44
05:12:13
23:32:44
12:43:48
21:30:19
21:07:43
15:12:00
06:50:36
07:28:19
04:47:49
14:41:35
22:50:22
23:02:19
02:59:57
01:03:21
02:31:03
08:32:46
08:57:22
07:48:38
05:12:15
13:33:02
14:07:35
01:17:01.00
15h5m4s
15h13m36s
5h40m45s
22h0m47s
6h56m13s
23h2m45s
16h48m19s
20h49m26s
21h55m20s
19h49m57s
9h48m4s
4h50m57s
18h24m47s
13h1m7s
3h36m1s
5h38m48s
9h9m57s
2h23m17s
6h54m0s
13h31m44s
5h0m18s
3h40m45s
2h44m23s
3h3m6s
4h26m30s
11h45m28s
11h37m39s
18h49m21s
15h45m43s
8h16m42s
6h33m53s
8h14m8s
15h41m31s
7h42m3s
21h53m32s
6h23m25s
15h56m52s
8h29m11s
4h44m40s
15h31m21s
21h28m38s
21h58m51s
2h48m12s
21h23m31s
23h48m18s
12h16m16s
15h11m25s
1h13m40s
7h28m52s
14h43m42s
16h50m1s
7h27m34s
14h45m21s
1h12m31s
15h50m55s
3h52m52s
2h42m50s
2h7m17s
18h27m36s
16h58m30s
23h4m29s
21h58m11s
8h30m27s
60◦9?
30◦52?
−19◦17?
−57◦37?
32◦41?
55◦5?
−59◦14?
53◦2?
−1◦50?
46◦22?
31◦56?
28◦26?
37◦36?
−4◦45?
17◦20?
−5◦27?
45◦40?
38◦23?
71◦50?
35◦3?
14◦57?
−17◦8?
−2◦9?
12◦49?
−10◦52?
60◦2?
50◦0?
8◦20?
−3◦39?
62◦39?
21◦21?
−37◦10?
62◦2?
−24◦57?
43◦60?
−1◦10?
78◦36?
73◦34?
−18◦6?
0◦18?
−6◦3?
−22◦30?
14◦45?
−53◦2?
−17◦54?
35◦32?
−6◦33?
−48◦23?
−27◦14?
12◦35?
31◦36?
−29◦51?
20◦36?
55◦48?
44◦59?
0◦44?
30◦21?
0◦20?
−50◦60?
12◦20?
3◦57?
5◦22?
−42◦44?
H1H2
H1H2
H1H2L1
H1H2
H1H2L1
H1H2L1
H1H2L1
H1H2
H1H2
H1H2L1
H1H2L1
H1H2L1
H1H2L1
H1H2L1
H1L1
H1H2L1
H1H2
H1H2
H1H2
H1H2L1
H1H2
H1H2L1
H1H2L1
H1H2L1
H1H2
H1H2
H1H2
H1H2
H1H2L1
H1H2L1
H1H2L1
H1H2
H1H2L1
H1H2
H1H2
H1H2L1
H1H2L1
H1H2L1
H1H2L1
H1H2L1
H1H2
H1H2L1
H1H2L1
H2L1
H1H2L1
H1H2
H1H2
H1H2L1
H1H2L1
H1H2L1
H1H2L1
H1H2L1
H2L1
H1H2
H1H2L1
H1H2
H1H2L1
H1H2L1
H1H2L1
H1H2
H1H2
H1H2
H1H2
– (162)7.98
8.12
6.77
6.60
4.83
3.12
2.62
4.91
6.84
5.44
4.92
3.58
4.97
3.51
4.56
5.11
35.32
9.20
6.00
4.94
8.67
4.88
3.45
3.14
4.92
4.90
5.26
3.66
7.01
4.60
2.44
18.52
2.39
3.36
5.72
3.36
2.89
2.36
2.09
2.56
10.63
4.88
9.49
26.59
2.53
4.89
3.88
3.46
2.34
3.34
4.70
3.49
3.21
5.06
1.82
3.57
2.30
2.34
3.26
5.11
37.92
4.79
2.96
5.7
5.6
6.8
6.9
9.5
14.7
17.5
9.3
6.7
8.4
9.3
12.8
9.2
13.0
10.0
9.0
1.3
5.0
7.6
9.3
5.3
9.4
13.3
14.6
9.3
9.3
8.7
12.5
6.5
9.9
18.7
2.5
19.2
13.6
8.0
13.6
15.9
19.4
21.9
17.9
4.3
9.4
4.8
1.7
18.1
9.4
11.8
13.2
19.5
13.7
9.7
13.1
14.2
9.1
25.1
12.8
19.9
19.6
14.0
9.0
1.2
9.6
15.5
29.9
31.0
28.3
27.0
21.2
13.2
11.3
20.6
27.8
23.6
20.4
15.5
21.1
15.4
20.7
26.9
143.6
34.3
21.9
21.9
29.0
21.0
15.1
11.8
20.5
20.8
22.1
15.3
34.1
20.5
10.6
79.7
10.8
14.5
24.0
15.1
14.7
10.6
10.4
11.7
43.3
21.9
41.2
118.8
11.2
19.9
15.6
15.3
10.8
14.9
21.2
15.8
13.5
21.9
8.1
15.3
10.6
10.9
15.1
22.3
164.5
21.1
11.7
0.229
0.221
0.242
0.254
0.324
0.519
0.609
0.334
0.247
0.291
0.336
0.444
0.325
0.444
0.332
0.255
0.048
0.200
0.313
0.313
0.237
0.327
0.454
0.581
0.335
0.331
0.311
0.450
0.201
0.334
0.649
0.086
0.637
0.472
0.286
0.455
0.466
0.650
0.657
0.587
0.158
0.314
0.167
0.058
0.612
0.344
0.440
0.447
0.635
0.462
0.323
0.434
0.507
0.313
0.843
0.447
0.647
0.631
0.456
0.308
0.042
0.325
0.587
0.184 (250)
– (57)
– (191)
– (190)
– (105)
0.0769 (104)
– (82)
– (147)
– (128)
– (89)
– (135)
– (131)
– (118)
– (117)
0.0402 (18000)
2.03
–
–
–
3.53
6.6
–
–
–
4.045
–
4.41
–
–
<1.7
–
–
–
1.49
–
–
–
–
–
–
–
4.9
–
–
3.21
3.8
–
–
0.125
3.43
–
2.71
–
–
–
–
–
0.84
–
–
0.703
3.685
2.43
–
–
–
5.6
–
– (159)
– (207)
– (174)
0.444 (187)
– (149)
0.321 (162)
0.102 (186)
– (196)
– (186)
– (187)
– (84)
– (207)
0.681 (141)
– (168)
0.228 (114)
– (207)
0.0139 (18000)
– (166)
– (172)
– (114)
0.0124 (18000)
0.509 (57)
0.221 (140)
0.731 (52)
– (201)
0.0945 (201)
– (135)
– (61)
– (188)
– (65)
– (162)
– (127)
– (109)
0.569 (195)
0.00967 (18000)
0.297 (185)
0.0741 (135)
– (163)
– (146)
0.391 (179)
– (187)
0.487 (189)
0.130 (138)
– (142)
– (199)
0.576 (184)
0.228 (114)

Page 14

14 Abbott et al.
TABLE 1
− Continued
150 Hz1000 Hz
UTC
time
RA
(deg)
Dec
(deg)
DD
GRBz networkphrss
(Mpc)hrss
(Mpc)
060930
061002
061006‡
061007
061021
061027
061102
061110
061122
061126
061201‡
061217‡
061218
061222
061222B
070103
070107
070110
070129
070201‡
070208
070209‡
070219
070223
070309
070311
070318
070330
070402
070411
070412
070419
070419B
070420
070427
070429
070429B‡
070506
070508
070518
070520
070520B
070521
070529
070531
070611
070612
070612B
070615
070616
070621
070626
070628
070704
070707‡
070714‡
070714B‡
070721
070721B
070724‡
070724B
070729‡
070731
–
–
–
09:04:09
01:03:29
16:45:50
10:08:08
15:39:07
10:15:02
01:00:31
11:47:21
07:56:49
08:47:56
15:58:36
03:40:08
04:05:05
03:28:52
04:11:02
20:46:39.41
12:05:18
07:22:41
23:35:10
15:23:10.78
09:10:34
03:33:41
01:10:16
01:15:00
10:01:03
01:52:35
07:28:56
22:51:31
15:48:35.00
20:12:33
01:27:03
09:59:26
10:44:05
06:18:13
08:31:08
01:35:10
03:09:04
05:35:58
04:18:17
14:26:21
13:05:10
17:44:53
06:51:10
12:48:28
02:10:17
01:57:13
02:38:45
06:21:17
02:20:35
16:29:33
23:17:39
04:05:33
14:41:02
20:05:57
16:08:38
03:20:31
04:59:29
10:01:08
10:33:48
10:53:50
23:25:09
00:25:53
09:33:22
20h18m9s
14h41m25s
7h23m60s
3h5m12s
9h40m35s
18h3m58s
9h53m34s
22h25m8s
20h15m21s
5h46m28s
22h8m19s
10h41m40s
9h56m57s
23h53m2s
7h1m24s
23h30m20s
10h37m41s
0h3m44s
2h28m0s
0h44m21s
13h11m35s
3h4m51s
17h20m53s
10h13m49s
17h34m44s
5h50m10s
3h13m57s
17h58m8s
20h44m44s
7h9m23s
12h6m6s
12h11m1s
21h2m50s
8h4m59s
1h55m29s
19h50m47s
21h52m1s
23h8m49s
20h51m20s
16h56m53s
12h53m1s
8h7m33s
16h10m38s
18h54m54s
0h26m53s
0h8m1s
8h5m25s
17h26m52s
2h57m14s
2h8m23s
21h35m13s
9h25m25s
7h41m5s
23h38m50s
17h51m0s
2h51m44s
3h51m25s
0h12m35s
2h12m31s
1h51m18s
1h10m31s
3h45m11s
21h54m19s
−23◦38?
48◦44?
−79◦12?
−50◦30?
−21◦57?
−82◦14?
−17◦0?
−2◦15?
15◦31?
64◦12?
−74◦34?
−21◦9?
−35◦13?
46◦32?
−25◦52?
26◦49?
−53◦12?
−52◦59?
11◦44?
42◦18?
61◦57?
−47◦23?
69◦21?
43◦8?
−37◦57?
3◦23?
−42◦57?
−63◦48?
27◦24?
H1L1
H1H2L1
H1H2
H1H2L1
H1H2L1
H1H2
H1H2L1
H1H2L1
H1H2L1
H1H2
H1H2
H1L1
H1H2L1
H1H2
H1H2L1
H1H2
H1H2L1
H1H2L1
H1H2
H1H2
H1H2L1
H1H2L1
H1L1
H1H2L1
H1H2L1
H1H2L1
H1H2L1
H1H2L1
H1H2L1
H2L1
H1H2L1
H1H2L1
H1H2
H1H2L1
H1H2L1
H1L1
H1H2L1
H1H2L1
H1H2L1
H1H2
H1H2V1
L1V1
H1H2V1
H1H2L1V1
L1V1
H1H2L1
L1V1
H1H2L1V1
H1H2L1V1
H1H2V1
H1L1V1
H1L1V1
H1V1
H1H2L1
L1V1
H1H2L1V1
H1H2L1V1
H1H2L1V1
H1H2L1V1
H1H2L1V1
H1H2L1V1
H1H2L1V1
H1H2L1V1
0.0248 (18000)6.95
2.49
3.61
9.70
4.32
4.42
2.38
3.12
4.36
2.79
3.53
3.32
3.67
4.85
6.50
5.37
15.57
2.50
3.50
6.38
1.87
11.24
3.61
3.36
3.92
2.35
2.14
1.87
2.24
18.35
2.49
2.75
6.14
3.58
2.02
1.79
1.75
3.17
2.37
3.48
4.20
22.37
2.62
2.86
11.47
1.80
13.85
2.62
2.57
2.79
1.79
4.96
9.88
3.66
36.04
5.04
5.46
4.29
3.49
4.76
4.85
2.33
4.97
6.6
18.3
12.7
4.7
10.6
10.4
19.2
14.6
10.5
16.4
13.0
13.8
12.5
9.4
7.0
8.5
2.9
18.3
13.1
7.2
24.5
4.1
12.7
13.6
11.7
19.5
21.4
24.5
20.5
2.5
18.4
16.6
7.4
12.8
22.6
25.6
26.2
14.4
19.3
13.1
10.9
2.0
17.5
16.0
4.0
25.4
3.3
17.5
17.8
16.4
25.6
9.2
4.6
12.5
1.3
9.1
8.4
10.7
13.1
9.6
9.4
19.6
9.2
36.9
11.2
18.8
42.7
19.8
15.4
10.7
14.1
20.6
11.0
16.8
15.8
15.9
15.9
28.0
21.4
60.2
11.1
14.8
27.8
10.4
52.6
20.6
15.3
18.6
10.9
10.1
10.2
10.3
75.3
11.1
12.8
24.9
18.8
10.1
10.6
8.0
15.3
10.7
15.1
16.2
30.0
12.1
13.0
18.4
8.5
68.3
14.4
11.2
10.8
10.0
18.6
43.7
15.1
85.5
26.0
20.7
15.2
15.3
19.2
19.9
10.7
16.7
0.186
0.615
0.365
0.161
0.347
0.446
0.639
0.486
0.334
0.622
0.408
0.433
0.431
0.430
0.245
0.321
0.114
0.618
0.462
0.247
0.658
0.131
0.334
0.448
0.370
0.631
0.680
0.671
0.667
0.091
0.621
0.535
0.276
0.365
0.679
0.647
0.862
0.450
0.642
0.453
0.424
0.229
0.569
0.528
0.372
0.805
0.100
0.477
0.614
0.636
0.689
0.368
0.157
0.455
0.080
0.264
0.331
0.450
0.450
0.357
0.344
0.639
0.410
– (193)
0.310 (184)
0.775 (160)
0.979 (94)
– (193)
– (113)
0.214 (168)
0.575 (73)
– (144)
0.0222 (18000)
1.261
<2.0
–
–
0.757
–
<1.5
–
0.827
–
–
3.355
–
–
2.352
–
–
1.165
–
–
–
–
–
0.836
–
–
2.954
–
0.97
–
–
–
–
–
2.31
<2.3
–
–
–
–
2.4996
–
2.04
0.617
–
–
–
–
–
–
–
–
–
0.92
–
3.626
0.457
–
–
–
– (187)
– (169)
– (207)
0.444 (180)
– (207)
– (186)
0.609 (207)
0.261 (207)
0.0791 (177)
0.0847 (177)
0.605 (185)
0.192 (104)
0.219 (137)
0.357 (196)
0.447 (188)
0.873 (166)
0.134 (201)
0.299 (87)
0.0733 (150)
0.915 (177)
0.715 (123)
– (193)
0.805 (133)
– (150)
– (152)
0.443 (194)
0.811 (122)
0.147 (184)
0.525 (120)
– (180)
0.487 (195)
– (167)
0.0776 (18000)
0.533 (184)
1◦3?
40◦8?
39◦54?
−31◦16?
−45◦34?
−27◦36?
−32◦25?
−38◦51?
10◦43?
−78◦23?
55◦17?
75◦0?
57◦35?
30◦16?
20◦39?
74◦19?
−29◦45?
37◦15?
−8◦45?
−4◦24?
56◦57?
−24◦49?
−39◦52?
−20◦17?
66◦15?
−68◦53?
30◦14?
28◦18?
−28◦32?
−2◦12?
−18◦37?
57◦40?
−39◦20?
−15◦44?
– (172)
0.174 (207)
0.129 (124)
0.219 (169)
0.633 (166)
0.652 (69)
– (86)
0.767 (133)
0.237 (80)
0.799 (184)
– (114)
0.965 (141)
– (138)
0.492 (118)
0.191 (110)
– (164)
– (155)
– (84)

Page 15

Search for GWBs associated with GRBs using LIGO and Virgo 15
TABLE 1
− Continued
150 Hz 1000 Hz
UTC
time
RA
(deg)
Dec
(deg)
DD
GRBznetworkphrss
(Mpc)hrss
(Mpc)
070802
070805
070809‡
070810
070810B‡
070821
070911
070917
070920
070920B
070923‡
2.45
–
–
2.17
–
–
–
–
–
–
–
07:07:25
19:55:45
19:22:17
02:11:52
15:19:17
12:49:24.00
05:57:44
07:33:56
04:00:13
21:04:32
19:15:23
2h27m37s
16h20m14s
13h35m4s
12h39m47s
0h35m48s
6h22m6s
1h43m17s
19h35m42s
6h43m52s
0h0m30s
12h18m30s
−55◦31?
−59◦57?
−22◦7?
10◦45?
8◦49?
−63◦51?
−33◦29?
2◦25?
72◦15?
−34◦51?
−38◦18?
H1H2
H1H2L1
H1H2V1
H1H2L1V1
H1H2L1
H1H2L1V1
H1H2L1V1
H1H2V1
H1H2L1V1
H1H2L1V1
H1H2L1
– (161) 3.56
2.51
9.20
4.48
4.80
3.96
4.74
4.23
3.54
2.26
4.91
12.8
18.2
5.0
10.2
9.5
11.6
9.6
10.8
12.9
20.2
9.3
15.4
13.9
38.6
15.4
21.4
14.7
17.7
15.6
15.6
10.4
26.0
0.445
0.493
0.178
0.446
0.321
0.467
0.387
0.439
0.441
0.659
0.264
0.193 (207)
– (183)
– (120)
0.239 (180)
0.303 (119)
0.512 (160)
0.295 (193)
– (123)
0.600 (60)
– (196)
Note. —
are GRB name, redshift (if known), time, and sky position (right ascension and declination). The remaining columns
display the results of the X-Pipeline search for an associated GWB: the set of detectors used, the local probability p of the
loudest on-source event, and 90% confidence limits on the gravitational-wave amplitude and the distance to the progenitor.
A p value of “−” indicates no event survived all cuts. The number in parentheses after the p value is the number of
off-source segments used to estimate p. The limits are computed for circularly polarized 150 Hz and 1000 Hz sine-Gaussian
waveforms. The hrss amplitudes are in units of 10−22Hz−1/2. The distances are lower limits, assuming isotropic emission
of Eiso
for systematics as discussed in Sec. 6.2. A double dagger (‡) following the GRB name indicates that it was also included
in the template-based search for binary inspiral gravitational-wave signals presented in Abbott et al. (2010).
Information and limits on associated GWB emission for each of the GRBs studied. The first five columns
GW= 0.01M?c2= 1.8 × 1052erg in gravitational waves, and scale as D ∝ (Eiso
GW)1/2. These limits include allowances
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