of 30
arXiv:0704.0943v3 [gr-qc] 9 Oct 2007
Search for gravitational-wave bursts in LIGO data
from the fourth science run
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Search for gravitational-wave bursts in LIGO data
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, B F Schutz
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Search for gravitational-wave bursts in LIGO data
3
P Schwinberg
15
, S M Scott
4
, A C Searle
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, B Sears
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, A Weidner
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, A Weinstein
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, R Weiss
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, K Wette
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, D M Whitbeck
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, S E Whitcomb
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, I Wilmut
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, A G Wiseman
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, G Woan
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, H zur M ̈uhlen
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and J Zweizig
14
(LIGO Scientific Collaboration)
1
Albert-Einstein-Institut, Max-Planck-Institut f ̈ur Gra
vitationsphysik, D-14476
Golm, Germany
2
Albert-Einstein-Institut, Max-Planck-Institut f ̈ur Gra
vitationsphysik, D-30167
Hannover, Germany
3
Andrews University, Berrien Springs, MI 49104 USA
4
Australian National University, Canberra, 0200, Australi
a
5
California Institute of Technology, Pasadena, CA 91125, US
A
6
Caltech-CaRT, Pasadena, CA 91125, USA
7
Cardiff University, Cardiff, CF24 3AA, United Kingdom
8
Carleton College, Northfield, MN 55057, USA
9
Charles Sturt University, Wagga Wagga, NSW 2678, Australia
10
Columbia University, New York, NY 10027, USA
11
Embry-Riddle Aeronautical University, Prescott, AZ 86301
USA
12
Hobart and William Smith Colleges, Geneva, NY 14456, USA
13
Inter-University Centre for Astronomy and Astrophysics, P
une - 411007, India
14
LIGO - California Institute of Technology, Pasadena, CA 911
25, USA
15
LIGO Hanford Observatory, Richland, WA 99352, USA
16
LIGO Livingston Observatory, Livingston, LA 70754, USA
17
LIGO - Massachusetts Institute of Technology, Cambridge, M
A 02139, USA
18
Louisiana State University, Baton Rouge, LA 70803, USA
19
Louisiana Tech University, Ruston, LA 71272, USA
20
Loyola University, New Orleans, LA 70118, USA
21
Moscow State University, Moscow, 119992, Russia
22
NASA/Goddard Space Flight Center, Greenbelt, MD 20771, USA
23
National Astronomical Observatory of Japan, Tokyo 181-858
8, Japan
24
Northwestern University, Evanston, IL 60208, USA
25
Rochester Institute of Technology, Rochester, NY 14623, US
A
26
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OX1
1 0QX United
Kingdom
Search for gravitational-wave bursts in LIGO data
4
27
San Jose State University, San Jose, CA 95192, USA
28
Southeastern Louisiana University, Hammond, LA 70402, USA
29
Southern University and A&M College, Baton Rouge, LA 70813,
USA
30
Stanford University, Stanford, CA 94305, USA
31
Syracuse University, Syracuse, NY 13244, USA
32
The Pennsylvania State University, University Park, PA 168
02, USA
33
The University of Texas at Brownsville and Texas Southmost C
ollege,
Brownsville, TX 78520, USA
34
Trinity University, San Antonio, TX 78212, USA
35
Universitat de les Illes Balears, E-07122 Palma de Mallorca
, Spain
36
Universit ̈at Hannover, D-30167 Hannover, Germany
37
University of Adelaide, Adelaide, SA 5005, Australia
38
University of Birmingham, Birmingham, B15 2TT, United King
dom
39
University of Florida, Gainesville, FL 32611, USA
40
University of Glasgow, Glasgow, G12 8QQ, United Kingdom
41
University of Maryland, College Park, MD 20742 USA
42
University of Michigan, Ann Arbor, MI 48109, USA
43
University of Oregon, Eugene, OR 97403, USA
44
University of Rochester, Rochester, NY 14627, USA
45
University of Salerno, 84084 Fisciano (Salerno), Italy
46
University of Sannio at Benevento, I-82100 Benevento, Ital
y
47
University of Southampton, Southampton, SO17 1BJ, United K
ingdom
48
University of Strathclyde, Glasgow, G1 1XQ, United Kingdom
49
University of Washington, Seattle, WA, 98195
50
University of Western Australia, Crawley, WA 6009, Austral
ia
51
University of Wisconsin-Milwaukee, Milwaukee, WI 53201, U
SA
52
Washington State University, Pullman, WA 99164, USA
E-mail:
pshawhan@umd.edu
Abstract.
The fourth science run of the LIGO and GEO 600 gravitational-
wave
detectors, carried out in early 2005, collected data with si
gnificantly lower noise
than previous science runs. We report on a search for short-d
uration gravitational-
wave bursts with arbitrary waveform in the 64–1600 Hz freque
ncy range appearing
in all three LIGO interferometers. Signal consistency test
s, data quality cuts, and
auxiliary-channel vetoes are applied to reduce the rate of s
purious triggers. No
gravitational-wave signals are detected in 15.5 days of liv
e observation time; we
set a frequentist upper limit of 0.15 per day (at 90% confidenc
e level) on the rate
of bursts with large enough amplitudes to be detected reliab
ly. The amplitude
sensitivity of the search, characterized using Monte Carlo
simulations, is several
times better than that of previous searches. We also provide
rough estimates
of the distances at which representative supernova and bina
ry black hole merger
signals could be detected with 50% efficiency by this analysis
.
PACS numbers: 04.80.Nn, 95.30.Sf, 95.85.Sz
Submitted to
Classical and Quantum Gravity
1. Introduction
Large interferometers are now being used to search for gravi
tational waves with
sufficient sensitivity to be able to detect signals from dista
nt astrophysical sources.
At present, the three detectors of the Laser Interferometer
Gravitational-wave
Observatory (LIGO) project [1] have achieved strain sensit
ivities consistent with their
design goals, while the GEO 600 [2] and Virgo [3] detectors ar
e in the process of being
commissioned and are expected to reach comparable sensitiv
ities. Experience gained
with these detectors, TAMA300 [4], and several small protot
ype interferometers has
Search for gravitational-wave bursts in LIGO data
5
nurtured advanced designs for future detector upgrades and
new facilities, including
Advanced LIGO [5], Advanced Virgo [6], and the Large-scale C
ryogenic Gravitational-
wave Telescope (LCGT) proposed to be constructed in Japan [7
]. The LIGO Scientific
Collaboration (LSC) carries out the analysis of data collec
ted by the LIGO and
GEO 600 gravitational-wave detectors, and has begun to purs
ue joint searches with
other collaborations (see, for example, [8]) as the network
of operating detectors
evolves.
As the exploration of the gravitational-wave sky can now be c
arried out with
greater sensitivity than ever before, it is important to sea
rch for all plausible signals
in the data. In addition to well-modeled signals such as thos
e from binary inspirals [9]
and spinning neutron stars [10], some astrophysical system
s may emit gravitational
waves which are modeled imperfectly (if at all) and therefor
e cannot reliably be
searched for using matched filtering. Examples of such imper
fectly-modeled systems
include binary mergers (despite recent advances in the fidel
ity of numerical relativity
calculations for at least some cases; see, for example, [11]
) and stellar core collapse
events. For the latter, several sets of simulations have bee
n carried out in the past
(see, for example, [12] and [13]), but more recent simulatio
ns have suggested a new
resonant core oscillation mechanism, driven by in-falling
material, which appears to
power the supernova explosion and also to emit strong gravit
ational waves [14, 15].
Given the current uncertainties regarding gravitational w
ave emission by systems such
as these, as well as the possibility of detectable signals fr
om other astrophysical sources
which are unknown or for which no attempt has been made to mode
l gravitational
wave emission, it is desirable to cast a wide net.
In this article, we report the results of a search for gravita
tional-wave “bursts”
that is designed to be able to detect short-duration (
1 s) signals of arbitrary form
as long as they have significant signal power in the most sensi
tive frequency band
of LIGO, considered here to be 64–1600 Hz. This analysis uses
LIGO data from
the fourth science run carried out by the LSC, called S4, and u
ses the same basic
methods as previous LSC burst searches [17, 18] that were per
formed using data from
the S2 and S3 science runs. (A burst search was performed usin
g data from the S1
science run using different methods [16].) We briefly describ
e the instruments and
data collection in section 2. In sections 3 and 4 we review the
two complementary
signal processing methods—one based on locating signal pow
er in excess of the baseline
noise and the other based on cross-correlating data streams
—that are used together
to identify gravitational-wave event candidates. We note w
here the implementations
have been improved relative to the earlier searches and desc
ribe the signal consistency
tests which are based on the outputs from these tools. Sectio
n 5 describes additional
selection criteria which are used to “clean up” the data samp
le, reducing the average
rate of spurious triggers in the data. The complete analysis
“pipeline” finds no event
candidates that pass all of the selection criteria, so we pre
sent in section 6 an upper
limit on the rate of gravitational-wave events which would b
e detected reliably by our
pipeline.
The detectability of a given type of burst, and thus the effect
ive rate limit for a
particular astrophysical source model, depends on the sign
al waveform and amplitude;
in general, the detection efficiency (averaged over sky posit
ions and arrival times) is less
than unity. We do not attempt a comprehensive survey of possi
ble astrophysical signals
in this paper, but use a Monte Carlo method with a limited numb
er of ad-hoc simulated
signals to evaluate the amplitude sensitivity of our pipeli
ne, as described in section 7.
Overall, this search has much better sensitivity than previ
ous searches, mostly due to
Search for gravitational-wave bursts in LIGO data
6
Mode Cleaner
Smoothes out fluctuations
of the input beam,
passes only fundamental
Gaussian beam mode
Pre-
Stabilized
Laser
Power Recycling Mirror
(2.7% transmission)
Increases the stored power
by a factor of ~45, reducing
the photostatistics noise
Fabry-Perot Arm Cavity
Increases the sensitivity
to small length changes by
a factor of ~140
Photodiode
Input Mirror
End Mirror
Beam Splitter
(50% transmission)
2 km or 4 km
Figure 1.
Simplified optical layout of a LIGO interferometer.
using lower-noise data and partly due to improvements in the
analysis pipeline. In
section 8 we estimate the amplitude sensitivity for certain
modeled signals of interest
and calculate approximate distances at which those signals
could be detected with 50%
efficiency. This completed S4 search sets the stage for burst s
earches now underway
using data from the S5 science run of the LIGO and GEO 600 detec
tors, which benefit
from much longer observation time and will be able to detect e
ven weaker signals.
2. Instruments and data collection
LIGO comprises two observatory sites in the United States wi
th a total of three
interferometers. As shown schematically in figure 1, the opt
ical design is a Michelson
interferometer augmented with additional partially-tran
smitting mirrors to form
Fabry-Perot cavities in the arms and to “recycle” the outgoi
ng beam power by
interfering it with the incoming beam. Servo systems are use
d to “lock” the mirror
positions to maintain resonance in the optical cavities, as
well as to control the mirror
orientations, laser frequency and intensity, and many othe
r degrees of freedom of the
apparatus. Interference between the two beams recombining
at the beam splitter is
detected by photodiodes, providing a measure of the differen
ce in arm lengths that
would be changed by a passing gravitational wave. The large m
irrors which direct
the laser beams are suspended from wires, with the support st
ructures isolated from
ground vibrations using stacks of inertial masses linked by
damped springs. Active
feed-forward and feedback systems provide additional supp
ression of ground vibrations
for many of the degrees of freedom. The beam path of the interf
erometer, excluding
the laser light source and the photodiodes, is entirely encl
osed in a vacuum system.
The LIGO Hanford Observatory in Washington state has two int
erferometers within
the same vacuum system, one with arms 4 km long (called H1) and
the other with
arms 2 km long (called H2). The LIGO Livingston Observatory i
n Louisiana has a
single interferometer with 4 km long arms, called L1.
The response of an interferometer to a gravitational wave ar
riving at local time
Search for gravitational-wave bursts in LIGO data
7
t
depends on the dimensionless strain amplitude and polariza
tion of the wave and its
arrival direction with respect to the arms of the interferom
eter. In the low-frequency
limit, the differential strain signal detected by the interf
erometer (effective arm length
difference divided by the length of an arm) can be expressed as
a projection of the
two polarization components of the gravitational wave,
h
+
(
t
) and
h
×
(
t
), with antenna
response factors
F
+
(
α, δ, t
) and
F
×
(
α, δ, t
):
h
det
(
t
) =
F
+
(
α, δ, t
)
h
+
(
t
) +
F
×
(
α, δ, t
)
h
×
(
t
)
,
(1)
where
α
and
δ
are the right ascension and declination of the source.
F
+
and
F
×
are
distinct for each interferometer site and change slowly wit
h
t
over the course of a
sidereal day as the Earth’s rotation changes the orientatio
n of the interferometer with
respect to the source location.
The electrical signal from the photodiode is filtered and dig
itized continuously at a
rate of 16 384 Hz. The time series of digitized values, referr
ed to as the “gravitational-
wave channel” (GW channel), is recorded in a computer file, al
ong with a timestamp
derived from the Global Positioning System (GPS) and additi
onal information. The
relationship between a given gravitational-wave signal an
d the digitized time series is
measured
in situ
by imposing continuous sinusoidal position displacements
of known
amplitude on some of the mirrors. These are called “calibrat
ion lines” because they
appear as narrow line features in a spectrogram of the GW chan
nel.
Commissioning the LIGO interferometers has required sever
al years of effort and
was the primary activity through late 2005. Beginning in 200
0, a series of short data
collection runs was begun to establish operating procedure
s, test the detector systems
with stable configurations, and provide data for the develop
ment of data analysis
techniques. The first data collection run judged to have some
scientific interest,
science run S1, was conducted in August-September 2002 with
detector noise more
than two orders of magnitude higher than the design goal. Sci
ence runs S2 and S3
followed in 2003 with steadily improving detector noise, bu
t with a poor duty cycle
for L1 due primarily to low-frequency, large-amplitude gro
und motion from human
activities and weather. During 2004, a hydraulic pre-isola
tion system was installed
and commissioned at the Livingston site to measure the groun
d motion and counteract
it with a relative displacement between the external and int
ernal support structures
for the optical components, keeping the internal component
s much closer to an inertial
frame at frequencies above 0
.
1 Hz. At the same time, several improvements were made
to the H1 interferometer at Hanford to allow the laser power t
o be increased to the
full design power of 10 W.
The S4 science run, which lasted from 22 February to 23 March 2
005, featured
good overall “science mode” duty cycles of 80
.
5%, 81
.
4%, and 74
.
5% for H1, H2,
and L1, respectively, corresponding to observation times o
f 570, 576, and 528 hours.
Thanks to the improvements made after the S3 run, the detecto
r noise during S4 was
within a factor of two of the design goal over most of the frequ
ency band, as shown in
figure 2. The GEO 600 interferometer also collected data thro
ughout the S4 run, but
was over a factor of 100 less sensitive than the LIGO interfer
ometers at 200 Hz and
a factor of few at and above the 1 kHz frequency range. The anal
ysis approach used
in this article effectively requires a gravitational-wave s
ignal to be distinguishable
above the noise in each of a fixed set of detectors, so it uses on
ly the three LIGO
interferometers and not GEO 600. There are a total of 402 hour
s of S4 during which
all three LIGO interferometers were simultaneously collec
ting science-mode data.
Search for gravitational-wave bursts in LIGO data
8
100
1000
10
−23
10
−22
10
−21
10
−20
10
−19
10
−18
LIGO Detector Sensitivities During S4 Science Run
Frequency (Hz)
Strain noise amplitude spectral density (Hz
−1/2
)
H2
L1
H1
LIGO SRD goal (4 km)
Figure 2.
Best achieved detector noise for the three LIGO interferome
ters during
the S4 science run, in terms of equivalent gravitational wav
e strain amplitude
spectral density. “LIGO SRD goal” is the sensitivity goal fo
r the 4-km LIGO
interferometers set forth in the 1995 LIGO Science Requirem
ents Document [19].
3. Trigger generation
The first stage of the burst search pipeline is to identify tim
es when the GW channels
of the three interferometers appear to contain signal power
in excess of the baseline
noise; these times, along with parameters derived from the d
ata, are called “triggers”
and are used as input to later processing stages. As in previo
us searches [17, 18],
the WaveBurst algorithm [20] is used for this purpose; it wil
l only be summarized
here [21].
WaveBurst performs a linear wavelet packet decomposition,
using the symlet
wavelet basis [22], on short intervals of gravitational-wa
ve data from each
interferometer. This decomposition produces a time-frequ
ency map of the data similar
to a windowed Fourier transformation. A time-frequency dat
a sample is referred to as a
pixel. Pixels containing significant excess signal power ar
e selected in a non-parametric
way by ranking them with other pixels at nearby times and freq
uencies. As in the S3
analysis, WaveBurst has been configured for S4 to use six diffe
rent time resolutions
and corresponding frequency resolutions, ranging from 1
/
16 s by 8 Hz to 1
/
512 s by
256 Hz, to be able to closely match the natural time-frequenc
y properties of a variety
of burst signals. The wavelet decomposition is restricted t
o 64–2048 Hz. At any
given resolution, significant pixels from the three detecto
r data streams are compared
and coincident pixels are selected; these are used to constr
uct “clusters”, potentially
spanning many pixels in time and/or frequency, within which
there is evidence for
a common signal appearing in the different detector data stre
ams. These coincident
clusters form the basis for triggers, each of which is charac
terized by a central time,
Search for gravitational-wave bursts in LIGO data
9
Entries 8325975
Mean
2.583
RMS
0.9666
g
Z
0
5
10
15
20
25
30
35
40
triggers
1
10
2
10
3
10
4
10
5
10
6
10
Figure 3.
Distribution of
Z
g
values for all WaveBurst triggers. The arrow shows
the location of the initial significance cut,
Z
g
>
6
.
7.
duration, central frequency, frequency range, and overall
significance
Z
g
as defined
in [23].
Z
g
is calculated from the pixels in the cluster and is roughly pr
oportional to
the geometric average of the excess signal power measured in
the three interferometers,
relative to the average noise in each interferometer at the r
elevant frequency. Thus,
a large value of
Z
g
indicates that the signal power in those pixels is highly unl
ikely
to have resulted from usual instrumental noise fluctuations
. In addition, the absolute
strength of the signal detected by each interferometer with
in the sensitive frequency
band of the search is estimated in terms of the root-sum-squa
red amplitude of the
detected strain,
h
rss
det
=
|
h
det
(
t
)
|
2
d
t .
(2)
WaveBurst was run on time intervals during which all three LI
GO interferometers
were in science mode, but omitting periods when simulated si
gnals were injected into
the interferometer hardware, any photodiode readout exper
ienced an overflow, or the
data acquisition system was not operating. In addition, the
last 30 seconds of each
science-mode data segment were omitted because it was obser
ved that loss of “lock”
is sometimes preceded by a period of instability. These sele
ction criteria reduced the
amount of data processed by WaveBurst from 402 hours to 391 ho
urs.
For this analysis, triggers found by WaveBurst are initiall
y required to have a
frequency range which overlaps 64–1600 Hz. An initial signi
ficance cut,
Z
g
6
.
7, is
applied to reject the bulk of the triggers and limit the numbe
r passed along to later
stages of the analysis. Figure 3 shows the distribution of
Z
g
prior to applying this
significance cut.
Besides identifying truly simultaneous signals in the thre
e data streams,
WaveBurst applies the same pixel matching and cluster coinc
idence tests to the three
data streams with many discrete relative time shifts impose
d between the Hanford
and Livingston data streams, each much larger than the maxim
um light travel time
between the sites and the duration of the signals targeted by
this search. The time-
shifted triggers found in this way provide a large sample to a
llow the “background”
(spurious triggers produced in response to detector noise i
n the absence of gravitational
waves) to be studied, under the assumption that the detector
noise properties do not
Search for gravitational-wave bursts in LIGO data
10
−150
−100
−50
0
50
100
150
20
30
40
50
60
70
Mean = 41.1
χ
2
= 130.5
d.o.f. = 97
WaveBurst trigger rate versus time shift
Time shift (s)
Trigger rate (
μ
Hz)
Figure 4.
WaveBurst trigger rate as a function of the relative time shi
ft applied
between the Hanford and Livingston data streams. The horizo
ntal line is a fit to
a constant value, yielding a
χ
2
of 130
.
5 for 97 degrees of freedom.
vary much over the span of a few minutes and are independent at
the two sites.
The two Hanford data streams are
not
shifted relative to one another, so that any
local environmental effects which influence both detectors a
re preserved. In fact,
some correlation in time is observed between noise transien
ts in the H1 and H2 data
streams.
Initially, WaveBurst found triggers for 98 time shifts in mu
ltiples of 3
.
125 s
between
156
.
25 and
6
.
25 s and between +6
.
25 and +156
.
25 s. These 5119 triggers,
called the “tuning set”, were used to choose the parameters o
f the signal consistency
tests and additional selection criteria described in the fo
llowing two sections. As
shown in figure 4, the rate of triggers in the tuning set is roug
hly constant for all time
shifts, with a marginal
χ
2
value but without any gross dependence on time shift. The
unshifted triggers were kept hidden throughout the tuning p
rocess, in order to avoid
the possibility of human bias in the choice of analysis param
eters.
4. Signal consistency tests
The WaveBurst algorithm requires only a rough consistency a
mong the different
detector data streams—namely, some apparent excess power i
n the same pixels
in the wavelet decomposition—to generate a trigger. This se
ction describes more
sophisticated consistency tests based on the detailed cont
ent of the GW channels.
These tests succeed in eliminating most WaveBurst triggers
in the data, while keeping
essentially all triggers generated in response to simulate
d gravitational-wave signals
added to the data streams. (The simulation method is describ
ed in section 7.) Similar
tests were also used in the S3 search [18].