I
NSTITUTE OF
P
HYSICS
P
UBLISHING
C
LASSICAL AND
Q
UANTUM
G
RAVITY
Class. Quantum Grav.
23
(2006) S29–S39
doi:10.1088/0264-9381/23/8/S05
Search for gravitational-wave bursts in LIGO’s third
science run
B Abbott
1
, R Abbott
1
, R Adhikari
1
, J Agresti
1
,PAjith
2
, B Allen
3
,
J Allen
4
,RAmin
5
, S B Anderson
1
, W G Anderson
3
, M Araya
1
,
H Armandula
1
, M Ashley
6
, C Aulbert
7
, S Babak
7
, R Balasubramanian
8
,
S Ballmer
4
, H Bantilan
9
, B C Barish
1
, C Barker
10
, D Barker
10
,
M A Barton
1
,KBayer
4
, K Belczynski
11,
42
, J Betzwieser
4
, B Bhawal
1
,
I A Bilenko
12
, G Billingsley
1
, E Black
1
, K Blackburn
1
, L Blackburn
4
,
B Bland
10
, L Bogue
13
, R Bork
1
,SBose
14
, P R Brady
3
, V B Braginsky
12
,
J E Brau
15
,DABrown
1
, A Buonanno
16
,DBusby
1
,WEButler
17
,
L Cadonati
4
, G Cagnoli
18
,JBCamp
19
, J Cannizzo
19
, K Cannon
3
,JCao
4
,
L Cardenas
1
, K Carter
13
, M M Casey
18
, P Charlton
1,
43
, S Chatterji
1
,
Y Chen
7
,DChin
20
, N Christensen
9
, T Cokelaer
8
, C N Colacino
21
,
R Coldwell
22
, D Cook
10
, T Corbitt
4
, D Coyne
1
, J D E Creighton
3
,
T D Creighton
1
, J Dalrymple
23
, E D’Ambrosio
1
, K Danzmann
2,24
,
GDavies
8
,DDeBra
25
, V Dergachev
20
,SDesai
6
, R DeSalvo
1
,
S Dhurandar
35
,MD
́
ıaz
26
, A Di Credico
23
,RWPDrever
27
, R J Dupuis
1
,
P Ehrens
1
, T Etzel
1
, M Evans
1
, T Evans
13
, S Fairhurst
3
,LSFinn
6
,
K Y Franzen
22
,REFrey
15
, P Fritschel
4
,VVFrolov
13
, M Fyffe
13
,
K S Ganezer
28
,JGarofoli
10
, I Gholami
7
, J A Giaime
5
, K Goda
4
,
L Goggin
1
, G Gonz
́
alez
5
, C Gray
10
, A M Gretarsson
29
, D Grimmett
1
,
HGrote
2
, S Grunewald
7
, M Guenther
10
, R Gustafson
20
, W O Hamilton
5
,
C Hanna
5
, J Hanson
13
, C Hardham
25
, G Harry
4
, J Heefner
1
, I S Heng
18
,
MHewitson
2
, N Hindman
10
, P Hoang
1
, J Hough
18
,WHua
25
, M Ito
15
,
YItoh
3
, A Ivanov
1
, B Johnson
10
, W W Johnson
5
, D I Jones
6,
44
, G Jones
8
,
L Jones
1
, V Kalogera
11
, E Katsavounidis
4
, K Kawabe
10
, S Kawamura
30
,
W Kells
1
, A Khan
13
,CKim
11
,PKing
1
, S Klimenko
22
, S Koranda
3
,
D Kozak
1
, B Krishnan
7
, M Landry
10
, B Lantz
25
, A Lazzarini
1
,MLei
1
,
I Leonor
15
, K Libbrecht
1
, P Lindquist
1
,SLiu
1
, M Lormand
13
,
M Lubinski
10
,HL
̈
uck
2
, M Luna
31
, B Machenschalk
7
, M MacInnis
4
,
M Mageswaran
1
, K Mailand
1
, M Malec
24
, V Mandic
1
,SM
́
arka
32
,
E Maros
1
, K Mason
4
, L Matone
32
, N Mavalvala
4
, R McCarthy
10
,
D E McClelland
33
, M McHugh
34
,JWCMcNabb
6
, A Melissinos
17
,
G Mendell
10
, R A Mercer
21
, S Meshkov
1
, E Messaritaki
3
, C Messenger
21
,
E Mikhailov
4
, S Mitra
35
, V P Mitrofanov
12
, G Mitselmakher
22
,
R Mittleman
4
, O Miyakawa
1
, S Mohanty
26
, G Moreno
10
, K Mossavi
2
,
G Mueller
22
, S Mukherjee
26
, E Myers
36
, J Myers
10
,TNash
1
, F Nocera
1
,
J S Noel
14
, B O’Reilly
13
, R O’Shaughnessy
11
, D J Ottaway
4
,
H Overmier
13
, B J Owen
6
,YPan
37
, M A Papa
7
, V Parameshwaraiah
10
,
42
Present address: New Mexico State University, USA.
43
Present address: Charles Sturt University, Australia.
44
Present address: University of Southampton, UK.
0264-9381/06/080029+11$30.00 © 2006 IOP Publishing Ltd Printed in the UK
S29
S30
B Abbott
et al
(LIGO Scientific Collaboration)
C Parameswariah
13,
45
, M Pedraza
1
, S Penn
38
,MPitkin
18
,RPrix
7
,
V Quetschke
22
, F Raab
10
, H Radkins
10
, R Rahkola
15
, M Rakhmanov
22
,
K Rawlins
4,
46
, S Ray-Majumder
3
,VRe
21
, T Regimbau
8,
47
,DHReitze
22
,
RRiesen
13
, K Riles
20
, B Rivera
10
, D I Robertson
18
, N A Robertson
18,25
,
C Robinson
8
, S Roddy
13
, A Rodriguez
5
, J Rollins
32
, J D Romano
8
,
JRomie
1
, S Rowan
18
,AR
̈
udiger
2
, L Ruet
4
, P Russell
1
, K Ryan
10
,
V Sandberg
10
, G H Sanders
1,
48
, V Sannibale
1
, P Sarin
4
,
B S Sathyaprakash
8
, P R Saulson
23
, R Savage
10
, A Sazonov
22
,
R Schilling
2
, R Schofield
15
, B F Schutz
7
, P Schwinberg
10
, S M Scott
33
,
S E Seader
14
, A C Searle
33
, B Sears
1
, D Sellers
13
, A S Sengupta
8
,
P Shawhan
1
, D H Shoemaker
4
, A Sibley
13
, X Siemens
3
, D Sigg
10
,
A M Sintes
7,31
,JSmith
2
,MRSmith
1
, O Spjeld
13
, K A Strain
18
,
DMStrom
15
, A Stuver
6
, T Summerscales
6
, M Sung
5
, P J Sutton
1
,
D B Tanner
22
, M Tarallo
1
, R Taylor
1
, K A Thorne
6
, K S Thorne
37
,
K V Tokmakov
12
, C Torres
26
, C Torrie
1
, G Traylor
13
,WTyler
1
,
D Ugolini
39
, C Ungarelli
21
, M Vallisneri
37
,MvanPutten
4
,SVass
1
,
A Vecchio
21
,JVeitch
18
,CVorvick
10
, S P Vyachanin
12
, L Wallace
1
,
H Ward
18
, R Ward
1
,KWatts
13
, D Webber
1
, U Weiland
24
,AWeinstein
1
,
RWeiss
4
,SWen
5
,KWette
33
, J T Whelan
34
, S E Whitcomb
1
,
B F Whiting
22
, S Wiley
28
, C Wilkinson
10
, P A Willems
1
, B Willke
2,24
,
A Wilson
1
, W Winkler
2
,SWise
22
, A G Wiseman
3
, G Woan
18
, D Woods
3
,
R Wooley
13
, J Worden
10
, I Yakushin
13
, H Yamamoto
1
,SYoshida
40
,
M Zanolin
4
, L Zhang
1
,NZotov
41
, M Zucker
13
and J Zweizig
1
(LIGO
Scientific Collaboration)
1
LIGO—California Institute of Technology, Pasadena, CA 91125, USA
2
Albert-Einstein-Institut, Max-Planck-Institut f
̈
ur Gravitationsphysik, D-30167 Hannover,
Germany
3
University of Wisconsin-Milwaukee, Milwaukee, WI 53201, USA
4
LIGO—Massachusetts Institute of Technology, Cambridge, MA 02139, USA
5
Louisiana State University, Baton Rouge, LA 70803, USA
6
The Pennsylvania State University, University Park, PA 16802, USA
7
Albert-Einstein-Institut, Max-Planck-Institut f
̈
ur Gravitationsphysik, D-14476 Golm, Germany
8
Cardiff University, Cardiff CF2 3YB, UK
9
Carleton College, Northfield, MN 55057, USA
10
LIGO Hanford Observatory, Richland, WA 99352, USA
11
Northwestern University, Evanston, IL 60208, USA
12
Moscow State University, Moscow 119992, Russia
13
LIGO Livingston Observatory, Livingston, LA 70754, USA
14
Washington State University, Pullman, WA 99164, USA
15
University of Oregon, Eugene, OR 97403, USA
16
University of Maryland, College Park, MD 20742 USA
17
University of Rochester, Rochester, NY 14627, USA
18
University of Glasgow, Glasgow G12 8QQ, UK
19
NASA
/
Goddard Space Flight Center, Greenbelt, MD 20771, USA
20
University of Michigan, Ann Arbor, MI 48109, USA
21
University of Birmingham, Birmingham B15 2TT, UK
22
University of Florida, Gainesville, FL 32611, USA
23
Syracuse University, Syracuse, NY 13244, USA
45
Present address: New Mexico Institute of Mining and Technology
/
Magdalena Ridge Observatory Interferometer,
USA.
46
Present address: University of Alaska Anchorage, USA.
47
Present address: Observatoire de la C
̃
ote d’Azur, France.
48
Present address: Thirty Meter Telescope Project, Caltech, USA.
Search for gravitational-wave bursts in LIGO’s third science run
S31
24
Universit
̈
at Hannover, D-30167 Hannover, Germany
25
Stanford University, Stanford, CA 94305, USA
26
The University of Texas at Brownsville and Texas Southmost College, Brownsville, TX 78520,
USA
27
California Institute of Technology, Pasadena, CA 91125, USA
28
California State University Dominguez Hills, Carson, CA 90747, USA
29
Embry-Riddle Aeronautical University, Prescott, AZ 86301, USA
30
National Astronomical Observatory of Japan, Tokyo 181-8588, Japan
31
Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain
32
Columbia University, New York, NY 10027, USA
33
Australian National University, Canberra 0200, Australia
34
Loyola University, New Orleans, LA 70118, USA
35
Inter-University Centre for Astronomy and Astrophysics, Pune 411007, India
36
Vassar College, Poughkeepsie, NY 12604, USA
37
Caltech-CaRT, Pasadena, CA 91125, USA
38
Hobart and William Smith Colleges, Geneva, NY 14456, USA
39
Trinity University, San Antonio, TX 78212, USA
40
Southeastern Louisiana University, Hammond, LA 70402, USA
41
Louisiana Tech University, Ruston, LA 71272, USA
Received 14 October 2005, in final form 29 November 2005
Published 22 March 2006
Online at
stacks.iop.org/CQG/23/S29
Abstract
We report on a search for gravitational-wave bursts in data from the three LIGO
interferometric detectors during their third science run. The search targets sub-
second bursts in the frequency range 100–1100 Hz for which no waveform
model is assumed and has a sensitivity in terms of the
root-sum-square
(rss)
strain amplitude of
h
rss
∼
10
−
20
Hz
−
1
/
2
. No gravitational-wave signals were
detected in the eight days of analysed data.
PACS numbers: 04.80.Nn, 07.05.Kf, 95.30.Sf, 95.85.Sz
1. Introduction
Gravitational-wave bursts are generally described as time-varying strain signals that are of
very short duration. Within the context of LIGO data analysis, this term describes primarily
sub-second duration signals with significant power in the instruments’ sensitive frequency
band. Typical sources of this kind of radiation include astrophysical systems for which the
resulting burst waveforms are either poorly modelled or are completely unknown. These
include the core collapse of massive stars, the merger phase of binary black-hole systems and
the astrophysical engines that power gamma-ray bursts. Other sources of gravitational-wave
bursts exist for which their waveforms are well modelled. These include black-hole ringdowns
and bursts resulting from cosmic string cusps and kinks. Gravitational-wave bursts may also
result from sources that are completely unknown or not anticipated.
The Laser Interferometer Gravitational wave Observatory (LIGO) is a network of
interferometric detectors aiming to make direct observations of gravitational waves [
1
]. LIGO
is composed of three interferometers at two sites. Two interferometers, one of 4 km (H1) and
another of 2 km arm length (H2), are co-located at Hanford, WA. A third instrument of 4 km
arm length (L1) is located at Livingston, LA. Each detector is a power-recycled Michelson
S32
B Abbott
et al
(LIGO Scientific Collaboration)
10
1
10
2
10
3
10
-23
10
-22
10
-21
10
-20
10
-19
10
-18
10
-17
10
-16
Frequency [Hz]
Strain spectral density [strain Hz
−
1/2
]
Best sensitivity achieved in each LIGO science run
1st science run
2nd science run
3rd science run
4th science run
4 km design
10
1
10
2
10
3
10
-23
10
-22
10
-21
10
-20
10
-19
10
-18
10
-17
10
-16
Frequency [Hz]
Strain spectral density [strain Hz
−
1/2
]
Best sensitivities achieved during the 3rd science run
Hanford 2 km
Hanford 4 km
Livingston 4 km
4 km design
Figure 1.
Left plot: sensitivity progress of the LIGO 4 km interferometers. The traces show
the best sensitivity achieved by either of the LIGO interferometers during each of the four LIGO
science runs, along with the 4 km design sensitivity in the LIGO Science Requirements Document.
Right plot: best sensitivity achieved by each LIGO interferometer during the third science run.
interferometer with Fabry–Perot cavities in each of its orthogonal arms. These interferometers
are sensitive to quadrupolar oscillations in the spacetime metric due to passing gravitational
waves.
LIGO commissioning has been interspersed with the collection of data under stable
operating conditions in order to perform astrophysical gravitational-wave searches. The first
science run, called S1, took place in the summer of 2002 (23 August–9 September), while
two additional runs, S2 and S3, collected data in 2003 (S2: 14 February–14 April; S3: 31
October 2003–9 January 2004). A fourth science run, S4, took place at the beginning of 2005
(22 February–23 March). As of May 2005, the instruments are to within a factor of 2 of their
design expectation in their most sensitive frequency band.
Three searches for gravitational-wave bursts were performed using data collected by
the LIGO instruments in S1 and S2 [
2
–
4
]. These include the first
untriggered
search using
35.5 h of S1 data [
2
] and the first
triggered
search for gravitational-wave bursts in coincidence
with one of the brightest GRBs, 030329, which fortuitously occurred during LIGO’s S2
run [
3
]. In the most recent publication [
4
], the analysis of 239.5 h of data taken while the
three LIGO detectors were in simultaneous operation during S2 was reported. As in the
previous burst searches with the LIGO detectors, no final candidate events were observed and
the search results were interpreted as an upper limit of 0.26 events per day on the rate of
gravitational-wave bursts at the instruments at the 90% confidence level. The all-sky averaged
sensitivity of the S2 search for bursts with significant power in the LIGO sensitivity band (100–
1000 Hz) lies in the range of
h
rss
∼
10
−
20
–10
−
19
Hz
−
1
/
2
root-sum-square (rss) strain amplitude
[
4
]. In this analysis we use data from the S3 run of the LIGO detectors in order to search for
gravitational-wave bursts. The S3 run provided data with improved sensitivity with respect to
the previous data taking, as can be seen in figure
1
.
2. Search pipeline overview
The burst search pipeline for the S3 analysis follows closely the procedure used for the S2
search [
4
]. As in S2, the search is restricted to burst signals that are detectable above the noise
in all three LIGO detectors at once. Therefore, we begin with times when the three detectors
Search for gravitational-wave bursts in LIGO’s third science run
S33
are operating in ‘science mode’ simultaneously. This ‘triple-coincident’ data set is further
reduced by removing periods of data taking when instrumental artefacts or environmental
conditions have been shown to degrade the search.
The Waveburst [
5
] algorithm is used to identify coincident clusters of excess power in
the wavelet domain across the three gravitational-wave data streams. The triggers generated
by Waveburst are checked for amplitude consistency and then passed to the
r
-statistic [
6
]
waveform consistency test, which uses a normalized cross-correlation statistic to check for
consistent waveform morphology between pairs of detectors.
We estimate the background event rate from accidental noise sources (i.e., anything
not
directly causing a simultaneous event in the three detectors) by running the pipeline over
time-shifted data where the gravitational-wave data stream from the Livingston detector is
artificially shifted in time with respect to the two Hanford detectors. It is assumed that the
time-shifted noise has similar characteristics to the unshifted noise, and that the instrumental
behaviour is approximately stationary over the range of time shifts (up to 2 min). To check
this assumption, we verify that the distribution of event counts at the various nonzero time
shifts is consistent with a Poisson process. Detection efficiencies for a variety of ad hoc and
model-based waveforms are measured by running the pipeline over the real detector data, with
software injections added to the time series. The efficiencies measured are checked against
those of physical hardware injections carried out during the run.
We tune the parameters of the search algorithms with the goal of maximizing detection
efficiency over the simulated events while maintaining a very low false event rate. Unlike the
S2 analysis, time-shifted data over the entire run is used for tuning instead of a random subset of
‘playground’ data set aside purely for such studies. This procedure avoids removing a valuable
fraction of the data from the analysis result and reduces the chance that the playground data is
unrepresentative of the entire data set. Once the thresholds and parameters of the search are
decided, we run the pipeline over a new set of time shifts to estimate the background rate, as
well as the unshifted data to search for candidate gravitational-wave events.
3. Data selection
There are 265.1 h of data with all three detectors operating simultaneously in science mode,
giving a triple-coincident duty cycle of 16% over the S3 run. From these, 14.0 h (5.3%) are
removed due to data-acquisition problems: unwritten data, data-acquisition overflows, and
timing and synchronization errors.
A number of additional instrumental issues were discovered during the analysis and
accounted for in the final data selection. First, we ignore the 10 s just before loss of optical
cavity resonance in any of the interferometers, as such loss is often preceded by a sudden
growth in instrument instability. Also, periods of excessive levels of dust at any of the output
optical tables of the interferometers are removed from the analysis. Large transients in the
gravitational-wave channel were found to occur during large fluctuations in the light level
stored in the arm cavities; such periods are identified and removed. We implement two event-
by-event vetoes that are used to remove single events that can be identified with observed
instrumental artefacts. The first is a veto applied to all three detectors on events caused by a
calibration line drop-out. The second is a veto for events occurring simultaneously with a large
excursion in the power-recycling servo loop control signal for H2. Details on the selection
and safety of the event-by-event vetoes can be found in the S3 data quality and veto paper [
7
].
In total, these cuts reduce the data set by an additional 16.8%.
The presence of a remaining environmental event at the end of the S2 burst analysis [
4
]
underscored the need to monitor environmental disturbances. In the case of the S2 event,
S34
B Abbott
et al
(LIGO Scientific Collaboration)
strong coherent signals were acoustically coupled into the co-located H1 and H2 detectors
when a propeller airplane flew overhead. Although the acoustic coupling was reduced for S3,
airplane signals in the gravitational-wave channel were still observed during our investigations.
To automate a search for these acoustical disturbances, we identify periods in many of the
microphone channels with large RMS noise in the 62–100 Hz range. Periods of high acoustic
activity are removed from the analysis at both sites. A similar RMS-based monitor is used on
seismic data from the Hanford site to identify periods of high seismic activity at frequencies
with large coupling to the mirrors. These two environmental cuts further reduce the data set
by 1.5%.
The above data quality cuts remove 62.5 h from the original 265.1 h of triple-coincident
livetime. The Waveburst algorithm is able to analyse 95% of the remaining 202.6 h, with some
loss due to data stream segmentation and boundary effects of the wavelet transform, resulting
in an effective S3 livetime of 192.2 h for this burst analysis.
4. Event generation
4.1. Trigger generation
The Waveburst algorithm [
5
], also used for the S2 analysis [
8
], generates triggers on coincident
excess power in the wavelet domain across the raw gravitational-wave data streams. The data
first undergo a complete wavelet packet decomposition, giving for each detector a uniform
time–frequency map of the signal indexed in time by
i
and in frequency by
j
. Significant tiles
in each decomposition are defined by the largest 10% of wavelet coefficients at each effective
frequency. They are assigned a
significance
according to their energy-determined rank within
the set of tiles at fixed frequency
j
:
y
ij
=−
ln
(R
ij
/N ),
(1)
where the rank,
R
ij
, is equal to 1 for the most energetic and
N
for the least energetic of the
selected
N
tiles. The significant tiles with closely matching tiles in time and frequency across
the three data streams are determined to be ‘in coincidence’, and a clustering routine clusters
nearby tiles from the set of coincident tiles for each detector separately.
These single-detector clusters are thus built from the triple-coincident energy in the
wavelet domain. Each cluster of
k
tiles,
C(k)
, is characterized by its
cluster significance
,
z
,
given by
z
=
Y
−
ln
(
k
−
1
∑
m
=
0
Y
m
m
!
)
,
where
Y
=
∑
i,j
∈
C(k)
y
ij
,
(2)
which has an exponential distribution regardless of cluster size. The
trigger significance
,
Z
g
,
is calculated as the geometric average of the cluster significances for a particular H1
/
H2
/
L1
coincident triplet of clusters.
Z
g
provides a measure of the confidence of each triple-coincident
event trigger and is used for future thresholding.
The Waveburst implementation used for S3 has two major improvements over the S2
version. For S2, Waveburst operated on just two data streams, meaning that for triple-
coincidence analysis, the final triggers from the three detector pairs were subject to yet
another coincidence stage. For S3, Waveburst is able to analyse an arbitrary number of data
streams at once, allowing a tighter triple-coincidence stage prior to clustering. Also during
the S2 analysis, Waveburst searched the wavelet time–frequency map at a fixed resolution of
1
/
128 s
×
64 Hz. While this was well tuned for a region of the parameter space of interest,
other regions suffered from poor matching of the wavelet basis to simulated bursts, particularly
Search for gravitational-wave bursts in LIGO’s third science run
S35
10
−
22
10
−
21
10
−
20
10
−
19
10
−
18
10
−
17
10
−
22
10
−
21
10
−
20
10
−
19
10
−
18
10
−
17
h
rss
at H2
h
rss
at H1
injections
noise events
0
1
2
3
0
0.2
0.4
0.6
0.8
1
|log
10
(
h
rss
at H1/
h
rss
at H2)|
fraction of events
injections
noise events
threshold
Figure 2.
Wave bu r s t
h
rss
amplitude consistency between H1 and H2 for injections of simulated
signals and for time-shifted events. On the left is a scatter plot showing the recorded amplitudes
at both detectors for each event. On the right is a histogram of the absolute value of the logarithm
of the ratio of recorded amplitudes, with a dotted line showing the threshold chosen for an
h
rss
consistency within a factor of 2.
at low frequencies where the choice of simulated bursts included many waveforms longer
than 1
/
128 s. For S3, Waveburst operates on several additional time–frequency resolutions,
essentially running a separate analysis at each resolution and combining the results at the end.
This allows for better matching of the time–frequency tiles to a much larger parameter space.
4.2. Amplitude consistency
Because the orientations of the two Hanford interferometers are identical, we expect to observe
the same strain waveform at the two detectors. Simulations show that the accuracy of signal-
energy reconstruction by Waveburst of a gravitational-wave burst is sufficient to use amplitude
consistency to rule out spurious events. Based on the performance over simulated signals
shown in figure
2
, we require the observed
h
rss
amplitudes in the two Hanford detectors to
agree within a factor of 2. This allows us to reject 76% of the time-shifted events while
maintaining a false rejection rate of just 0.4% for simulated bursts.
4.3. Waveform consistency
We use the
r
-statistic test [
6
] to check for waveform consistency across the three detectors.
The test is run over time intervals triggered by Waveburst as a means of further reducing the
background rate. The test measures the normalized cross-correlation,
r
=
∑
i
(x
i
−
̄
x)(y
i
−
̄
y)
√
∑
i
(x
i
−
̄
x)
2
√
∑
i
(y
i
−
̄
y)
2
,
(3)
between two whitened gravitational-wave strain data time series
{
x
i
}
and
{
y
i
}
with mean
values
̄
x
and
̄
y
. For uncorrelated white noise of sufficient length
N
p
such that the central limit
theorem applies, we expect the
r
-statistic values obtained to follow a normal distribution with
zero mean and
σ
p
=
1
/
√
N
p
. Any coherent component in the two sequences will cause
r
to
deviate from the normal distribution.
To compute the
r
-statistic for unknown waveform duration and sky position, we use
integration lengths
N
p
corresponding to 20, 50 and 100 ms, which have been shown to cover
well the burst durations of interest. The integration windows scan over a region surrounding
the Waveburst trigger central time, calculating
r
using rectangular windows centred at each
S36
B Abbott
et al
(LIGO Scientific Collaboration)
time
j
. Furthermore, the two data streams may be shifted by a small amount,
k
,priorto
calculating the
r
-statistic. For the H1–H2 pair,
k
is
±
1 ms to account for a small timing
error, while for Hanford–Livingston pairs
k
takes on values up to
±
11 ms to account for all
possible physical light travel times between the sites. For each pair of detectors, the maximum
logarithmic confidence is obtained:
C
=
max
{
−
log
10
[
erfc
(
∣
∣
r
k
pj
∣
∣
√
N
p
2
)]}
.
(4)
The parameter
is then defined as the arithmetic average of the three values of
C
from
the three detector pairs. This single parameter is used for thresholding to cut events with
low confidence. A final requirement is that the sign of
r
at maximum confidence between
H1 and H2 must be positive. Otherwise the trigger is discarded since a negative value would
imply opposite phase. Because L1 is not precisely aligned with the Hanford detectors, it will
be sensitive to different gravitational-wave polarizations and thus different waveforms. We
therefore do not expect the signals to be 100% correlated between the sites. This is taken into
account, in a waveform-dependent way, in our simulations.
5. Search results
Preliminary studies over time-shifted S3 data led us to set thresholds on the Waveburst
Z
g
7.39 and
r
-statistic
10. To estimate the background rate at these thresholds, we run
through the pipeline 50 additional time shifts of the data using 5 s steps. One time-shifted
event survives, giving an expected background of 0.02 events per S3 livetime. No events pass
all the analysis cuts in the unshifted data (figure
3
).
6. Simulations
The efficiency of the analysis pipeline is defined as the fraction of events that would be
successfully detected by the pipeline, as a function of waveform and characteristic amplitude.
Preliminary detection efficiency studies were completed over a randomly selected 10% subset
of the S3 data. Our simulations include 58 waveforms of various morphologies: short and
long duration sine-Gaussians, Gaussians, cosmic string cusps [
9
], Gaussian windowed band-
passed white noise, rising whistles, black-hole merger simulations [
10
] and supernova core
collapse simulations [
11
–
13
]. In total,
∼
100 000 events were injected over the S3 livetime
with durations between 0.1 and 100 ms and time–frequency area
tf
between 1 and 100,
where unity time–frequency area corresponds to a minimal-uncertainty waveform.
Here we report detection efficiencies of the search pipeline for Gaussian injections of the
form
h(t
+
t
0
)
=
h
0
exp
(
−
t
2
/τ
2
)
, with
τ
equal to 0.1 ms, and sine-Gaussian injections of the
form
h(t
+
t
0
)
=
h
0
sin
(
2
πf
0
t)
exp
(
−
t
2
/τ
2
)
, where
τ
is chosen according to
τ
=
Q/(
√
2
πf
0
)
with
Q
=
8
.
9 and
f
0
assumes values of 235, 554 and 849 Hz. These simulated events are
generated according to a random, isotropic sky distribution and have waveforms of purely
linear polarization with random polarization angle. The strengths of the injected events are
quantified by their
root-sum-square
(rss) amplitudes
at the Earth
(without folding in the
antenna pattern of a detector) defined by
h
rss
≡
√
∫
(
|
h
+
(t)
|
2
+
|
h
×
(t)
|
2
)
d
t.
(5)
Search for gravitational-wave bursts in LIGO’s third science run
S37
Waveburst significance
Z
g
r
−
statistic confidence
Γ
10
20
30
40
0
10
20
30
40
0
5
10
15
0.1
1
10
r
−
statistic confidence
Γ
number of events
unshifted
background
rms
spread
Figure 3.
Left plot: measured Waveburst
Z
g
and
r
-statistic
values for each time-shifted
event (black dots) and unshifted event (white dots). The time-shifted events used to estimate the
background of our search are generated over 50 time shifts of the entire S3 data set using 5.0 s
steps. Dotted lines represent the thresholds on
Z
g
and
chosen in advance to maintain a low
background event rate while preserving detection efficiency for simulated events, whose density is
represented by the logarithmically weighted 2D histogram. In the past, the Waveburst significance
has been occasionally shown in its log
10
representation:
Z
g
/
ln
(
10
)
. Here we follow the convention
used in the S2 paper [
4
]. Right plot: histogram (circles) of
values for unshifted events with
Z
g
>
7
.
39. The most significant event has
=
7
.
34, below our threshold of 10; thus, no events
from the analysis at zero time shift remain after all analysis cuts. Stair-step curve: estimated
mean background per bin normalized to an observation time equal to that of the unshifted analysis.
The black error bars indicate the statistical uncertainty on the mean background. The shaded
bars represent the expected root-mean-square statistical fluctuations on the number of unshifted
background events in each bin.
Ta b l e 1 .
Summary of the S3 pipeline sensitivity to ad hoc waveforms. Shown are the 50%
detection efficiencies in terms of
h
rss
(
strain
/
√
Hz
)
and in terms of the dimensionless
signal-to-
noise ratio
(SNR) in the least sensitive detector. These values are averages over random sky position
and polarization angle. The equivalent
h
rss
values for 50% detection efficiency at a comparable
expected background event rate for the same waveforms in the S2 search were 1.5, 2.3, 3.9 and
4.3
×
10
−
20
strain
/
√
Hz [
4
].
At 50% detection efficiency
Waveform
h
rss
Minimum SNR
sine-Gaussian
f
0
=
235 Hz,
Q
=
8
.
90.9
×
10
−
20
6.0
sine-Gaussian
f
0
=
554 Hz,
Q
=
8
.
91.3
×
10
−
20
5.8
sine-Gaussian
f
0
=
849 Hz,
Q
=
8
.
92.3
×
10
−
20
7.5
Gaussian
τ
=
0
.
1ms
1.8
×
10
−
20
8.4
For linearly polarized signals
(h
×
(t)
=
0
)
, this is simply the root-sum-square amplitude of
the measured strain for an optimally oriented detector. For a non-optimal orientation, the
measured signal energy is diminished by an antenna factor.
The simulated events are created at constant
h
rss
and converted into detector-specific
ADC counts using the known calibration response function and antenna pattern for each
interferometer. Efficiencies at different
h
rss
values are evaluated by multiplying the ADC(
t
)
time series by the appropriate factor, adding it to the raw detector data and running the
combined time series through the search pipeline. Table
1
shows
h
rss
corresponding to 50%
detection efficiency for the four reported waveforms. We find a factor of
∼
2 improvement in
overall sensitivity compared to the S2 search.
S38
B Abbott
et al
(LIGO Scientific Collaboration)
Alternatively, the efficiency can be evaluated as a function of the signal energy
received
by a given detector, taking the antenna factor into account. This can be expressed in terms of
the
signal-to-noise ratio
(SNR) that would be measured by an optimal filter,
SNR
2
=
4
∫
∞
0
d
f
|
F
+
̃
h
+
(f )
+
F
×
̃
h
×
(f )
|
2
S(f )
,
(6)
where
̃
h
+
(f )
and
̃
h
×
(f )
are the
two
-sided Fourier transforms of the two polarization
components of the signal,
F
+
and
F
×
represent the antenna factors and
S(f )
is the
one
-sided
power spectral density of the noise. Table
1
shows the SNR in the
least
sensitive detector
(calculated event by event using the best noise power spectrum for each detector during the
run) which yields 50% detection efficiency. The majority of the other simulated waveforms
maintain 50% detection efficiency at 5–9 SNR, giving us confidence in the generality of our
search pipeline with respect to match-filtering for known waveforms.
The systematic uncertainty that results from measuring the efficiency over a randomly
selected 10% instead of the full data set is not expected to be large. Furthermore, a higher
overlap window (finer increments in time for
j
and
k
)forthe
r
-statistic waveform consistency
test was adopted in the analysis of the full data and not implemented in the efficiency studies,
implying that the efficiencies reported may be underestimated.
7. Conclusions
No gravitational-wave burst event was observed during the eight days of LIGO’s S3 data that
we analyse. Several improvements in the search methodology are introduced in this analysis.
The waveform amplitude consistency test and the tighter
r
-statistic requirements for H1 and
H2 both make use of the co-location and common orientation of the two Hanford detectors;
information not exploited in the S2 search [
4
]. Additionally, the new ability of Waveburst
to search at multiple time–frequency resolutions allows us to maintain sensitivity to a much
larger signal space than before. These improvements are expected to be part of our future burst
searches. The sensitivity of the S3 search in terms of the
root-sum-square
(rss) strain amplitude
is
h
rss
∼
10
−
20
Hz
−
1
/
2
and reflects the most sensitive broadband search for untriggered and
unmodelled gravitational-wave bursts to date.
A first interpretation of our burst upper limits within an astrophysical source context
was performed in the analysis of the S2 data [
4
]. That analysis set the order-of-magnitude
distance reach to plausible systems emitting astrophysical burst waveforms during the S2 run.
Although we did not repeat this interpretation in the S3 analysis reported here, we plan to
invoke astrophysical burst source population and waveform models in future searches.
Acknowledgments
The authors gratefully acknowledge the support of the United States National Science
Foundation for the construction and operation of the LIGO Laboratory, and the Particle
Physics and Astronomy Research Council of the United Kingdom, the Max-Planck-Society
and the State of Niedersachsen
/
Germany for support of the construction and operation of the
GEO600 detector. The authors also gratefully acknowledge the support of the research by
these agencies and by the Australian Research Council, the Natural Sciences and Engineering
Research Council of Canada, the Council of Scientific and Industrial Research of India,
the Department of Science and Technology of India, the Spanish Ministerio de Educacion
y Ciencia, the John Simon Guggenheim Foundation, the Leverhulme Trust, the David and
Search for gravitational-wave bursts in LIGO’s third science run
S39
Lucile Packard Foundation, the Research Corporation and the Alfred P Sloan Foundation.
This paper has been assigned LIGO Laboratory document number P050043-A-R.
References
[1] Abbott B
et al
(LSC) 2004
Nucl. Instrum. Methods
A
517
154
[2] Abbott B
et al
(LSC) 2004
Phys. Rev.
D
69
102001
[3] Abbott B
et al
(LSC) 2005
Phys. Rev.
D
72
042002
[4] Abbott B
et al
(LSC) 2005
Phys. Rev.
D
72
062001
[5] Klimenko S and Mitselmakher G 2004
Class. Quantum Grav.
21
S1819
[6] Cadonati L 2004
Class. Quantum Grav.
21
S1695
[7] Di Credico A (LSC) 2005
Class. Quantum Grav.
22
S1051
[8] Klimenko S, Yakushin I, Rakhmanov M and Mitselmakher G 2004
Class. Quantum Grav.
21
S1685
[9] Damour T and Vilenkin A 2005
Phys. Rev.
D
71
063510
[10] Baker J, Campanelli M, Lousto C O and Takahashi R 2004
Phys. Rev.
D
69
027505
[11] Zwerger T and M
̈
uller E 1997
Astron. Astrophys.
320
209
[12] Dimmelmeier H, Font J A and M
̈
uller E 2001
Astrophys. J. Lett.
560
L163
[13] Ott C D, Burrows A, Livne E and Walder R 2004
Astrophys. J.
600
834