Search for gravitational wave radiation associated with the pulsating tail
of the SGR
1806
20
hyperflare of 27 December 2004 using LIGO
B. Abbott,
14
R. Abbott,
14
R. Adhikari,
14
J. Agresti,
14
P. Ajith,
2
B. Allen,
2,51
R. Amin,
18
S. B. Anderson,
14
W. G. Anderson,
51
M. Arain,
39
M. Araya,
14
H. Armandula,
14
M. Ashley,
4
S. Aston,
38
P. Aufmuth,
36
C. Aulbert,
1
S. Babak,
1
S. Ballmer,
14
H. Bantilan,
8
B. C. Barish,
14
C. Barker,
15
D. Barker,
15
B. Barr,
40
P. Barriga,
50
M. A. Barton,
40
K. Bayer,
17
K. Belczynski,
24
J. Betzwieser,
17
P. T. Beyersdorf,
27
B. Bhawal,
14
I. A. Bilenko,
21
G. Billingsley,
14
R. Biswas,
51
E. Black,
14
K. Blackburn,
14
L. Blackburn,
17
D. Blair,
50
B. Bland,
15
J. Bogenstahl,
40
L. Bogue,
16
R. Bork,
14
V. Boschi,
14
S. Bose,
52
P. R. Brady,
51
V. B. Braginsky,
21
J. E. Brau,
43
M. Brinkmann,
2
A. Brooks,
37
D. A. Brown,
6,14
A. Bullington,
30
A. Bunkowski,
2
A. Buonanno,
41
O. Burmeister,
2
D. Busby,
14
R. L. Byer,
30
L. Cadonati,
17
G. Cagnoli,
40
J. B. Camp,
22
J. Cannizzo,
22
K. Cannon,
51
C. A. Cantley,
40
J. Cao,
17
L. Cardenas,
14
M. M. Casey,
40
G. Castaldi,
46
C. Cepeda,
14
E. Chalkey,
40
P. Charlton,
9
S. Chatterji,
14
S. Chelkowski,
2
Y. Chen,
1
F. Chiadini,
45
D. Chin,
42
E. Chin,
50
J. Chow,
4
N. Christensen,
8
J. Clark,
40
P. Cochrane,
2
T. Cokelaer,
7
C. N. Colacino,
38
R. Coldwell,
39
R. Conte,
45
D. Cook,
15
T. Corbitt,
17
D. Coward,
50
D. Coyne,
14
J. D. E. Creighton,
51
T. D. Creighton,
14
R. P. Croce,
46
D. R. M. Crooks,
40
A. M. Cruise,
38
A. Cumming,
40
J. Dalrymple,
31
E. D’Ambrosio,
14
K. Danzmann,
2,36
G. Davies,
7
D. DeBra,
30
J. Degallaix,
50
M. Degree,
30
T. Demma,
46
V. Dergachev,
42
S. Desai,
32
R. DeSalvo,
14
S. Dhurandhar,
13
M. Dı
́
az,
33
J. Dickson,
4
A. Di Credico,
31
G. Diederichs,
36
A. Dietz,
7
E. E. Doomes,
29
R. W. P. Drever,
5
J.-C. Dumas,
50
R. J. Dupuis,
14
J. G. Dwyer,
10
P. Ehrens,
14
E. Espinoza,
14
T. Etzel,
14
M. Evans,
14
T. Evans,
16
S. Fairhurst,
7,14
Y. Fan,
50
D. Fazi,
14
M. M. Fejer,
30
L. S. Finn,
32
V. Fiumara,
45
N. Fotopoulos,
51
A. Franzen,
36
K. Y. Franzen,
39
A. Freise,
38
R. Frey,
43
T. Fricke,
44
P. Fritschel,
17
V. V. Frolov,
16
M. Fyffe,
16
V. Galdi,
46
J. Garofoli,
15
I. Gholami,
1
J. A. Giaime,
16,18
S. Giampanis,
44
K. D. Giardina,
16
K. Goda,
17
E. Goetz,
42
L. Goggin,
14
G. Gonza
́
lez,
18
S. Gossler,
4
A. Grant,
40
S. Gras,
50
C. Gray,
15
M. Gray,
4
J. Greenhalgh,
26
A. M. Gretarsson,
11
R. Grosso,
33
H. Grote,
2
S. Grunewald,
1
M. Guenther,
15
R. Gustafson,
42
B. Hage,
36
D. Hammer,
51
C. Hanna,
18
J. Hanson,
16
J. Harms,
2
G. Harry,
17
E. Harstad,
43
T. Hayler,
26
J. Heefner,
14
I. S. Heng,
40
A. Heptonstall,
40
M. Heurs,
2
M. Hewitson,
2
S. Hild,
36
E. Hirose,
31
D. Hoak,
16
D. Hosken,
37
J. Hough,
40
E. Howell,
50
D. Hoyland,
38
S. H. Huttner,
40
D. Ingram,
15
E. Innerhofer,
17
M. Ito,
43
Y. Itoh,
51
A. Ivanov,
14
D. Jackrel,
30
B. Johnson,
15
W. W. Johnson,
18
D. I. Jones,
47
G. Jones,
7
R. Jones,
40
L. Ju,
50
P. Kalmus,
10
V. Kalogera,
24
S. Kamat,
10
D. Kasprzyk,
38
E. Katsavounidis,
17
K. Kawabe,
15
S. Kawamura,
23
F. Kawazoe,
23
W. Kells,
14
D. G. Keppel,
14
F. Ya. Khalili,
21
C. Kim,
24
P. King,
14
J. S. Kissel,
18
S. Klimenko,
39
K. Kokeyama,
23
V. Kondrashov,
14
R. K. Kopparapu,
18
D. Kozak,
14
B. Krishnan,
1
P. Kwee,
36
P. K. Lam,
4
M. Landry,
15
B. Lantz,
30
A. Lazzarini,
14
B. Lee,
50
M. Lei,
14
J. Leiner,
52
V. Leonhardt,
23
I. Leonor,
43
K. Libbrecht,
14
P. Lindquist,
14
N. A. Lockerbie,
48
M. Longo,
45
M. Lormand,
16
M. Lubinski,
15
H. Lu
̈
ck,
2,36
B. Machenschalk,
1
M. MacInnis,
17
M. Mageswaran,
14
K. Mailand,
14
M. Malec,
36
V. Mandic,
14
S. Marano,
45
S. Ma
́
rka,
10
J. Markowitz,
17
E. Maros,
14
I. Martin,
40
J. N. Marx,
14
K. Mason,
17
L. Matone,
10
V. Matta,
45
N. Mavalvala,
17
R. McCarthy,
15
D. E. McClelland,
4
S. C. McGuire,
29
M. McHugh,
20
K. McKenzie,
4
J. W. C. McNabb,
32
S. McWilliams,
22
T. Meier,
36
A. Melissinos,
44
G. Mendell,
15
R. A. Mercer,
39
S. Meshkov,
14
E. Messaritaki,
14
C. J. Messenger,
40
D. Meyers,
14
E. Mikhailov,
17
S. Mitra,
13
V. P. Mitrofanov,
21
G. Mitselmakher,
39
R. Mittleman,
17
O. Miyakawa,
14
S. Mohanty,
33
G. Moreno,
15
K. Mossavi,
2
C. MowLowry,
4
A. Moylan,
4
D. Mudge,
37
G. Mueller,
39
S. Mukherjee,
33
H. Mu
̈
ller-Ebhardt,
2
J. Munch,
37
P. Murray,
40
E. Myers,
15
J. Myers,
15
T. Nash,
14
G. Newton,
40
A. Nishizawa,
23
K. Numata,
22
B. O’Reilly,
16
R. O’Shaughnessy,
24
D. J. Ottaway,
17
H. Overmier,
16
B. J. Owen,
32
Y. Pan,
41
M. A. Papa,
1,51
V. Parameshwaraiah,
15
P. Patel,
14
M. Pedraza,
14
S. Penn,
12
V. Pierro,
46
I. M. Pinto,
46
M. Pitkin,
40
H. Pletsch,
2
M. V. Plissi,
40
F. Postiglione,
45
R. Prix,
1
V. Quetschke,
39
F. Raab,
15
D. Rabeling,
4
H. Radkins,
15
R. Rahkola,
43
N. Rainer,
2
M. Rakhmanov,
32
K. Rawlins,
17
S. Ray-Majumder,
51
V. Re,
38
H. Rehbein,
2
S. Reid,
40
D. H. Reitze,
39
L. Ribichini,
2
R. Riesen,
16
K. Riles,
42
B. Rivera,
15
N. A. Robertson,
14,40
C. Robinson,
7
E. L. Robinson,
38
S. Roddy,
16
A. Rodriguez,
18
A. M. Rogan,
52
J. Rollins,
10
J. D. Romano,
7
J. Romie,
16
R. Route,
30
S. Rowan,
40
A. Ru
̈
diger,
2
L. Ruet,
17
P. Russell,
14
K. Ryan,
15
S. Sakata,
23
M. Samidi,
14
L. Sancho de la Jordana,
35
V. Sandberg,
15
V. Sannibale,
14
S. Saraf,
25
P. Sarin,
17
B. S. Sathyaprakash,
7
S. Sato,
23
P. R. Saulson,
31
R. Savage,
15
P. Savov,
6
S. Schediwy,
50
R. Schilling,
2
R. Schnabel,
2
R. Schofield,
43
B. F. Schutz,
1,7
P. Schwinberg,
15
S. M. Scott,
4
A. C. Searle,
4
B. Sears,
14
F. Seifert,
2
D. Sellers,
16
A. S. Sengupta,
7
P. Shawhan,
41
D. H. Shoemaker,
17
A. Sibley,
16
J. A. Sidles,
49
X. Siemens,
6,14
D. Sigg,
15
S. Sinha,
30
A. M. Sintes,
1,35
B. J. J. Slagmolen,
4
J. Slutsky,
18
J. R. Smith,
2
M. R. Smith,
14
K. Somiya,
2,1
K. A. Strain,
40
D. M. Strom,
43
A. Stuver,
32
T. Z. Summerscales,
3
K.-X. Sun,
30
M. Sung,
18
P. J. Sutton,
14
H. Takahashi,
1
D. B. Tanner,
39
M. Tarallo,
14
R. Taylor,
14
R. Taylor,
40
J. Thacker,
16
K. A. Thorne,
32
K. S. Thorne,
6
A. Thu
̈
ring,
36
M. Tinto,
14
K. V. Tokmakov,
40
C. Torres,
33
C. Torrie,
40
G. Traylor,
16
M. Trias,
35
W. Tyler,
14
D. Ugolini,
34
C. Ungarelli,
38
K. Urbanek,
30
H. Vahlbruch,
36
PHYSICAL REVIEW D
76,
062003 (2007)
1550-7998
=
2007
=
76(6)
=
062003(12)
062003-1
©
2007 The American Physical Society
M. Vallisneri,
6
C. Van Den Broeck,
7
M. Varvella,
14
S. Vass,
14
A. Vecchio,
38
J. Veitch,
40
P. Veitch,
37
A. Villar,
14
C. Vorvick,
15
S. P. Vyachanin,
21
S. J. Waldman,
14
L. Wallace,
14
H. Ward,
40
R. Ward,
14
K. Watts,
16
D. Webber,
14
A. Weidner,
2
M. Weinert,
2
A. Weinstein,
14
R. Weiss,
17
S. Wen,
18
K. Wette,
4
J. T. Whelan,
1
D. M. Whitbeck,
32
S. E. Whitcomb,
14
B. F. Whiting,
39
C. Wilkinson,
15
P. A. Willems,
14
L. Williams,
39
B. Willke,
2,36
I. Wilmut,
26
W. Winkler,
2
C. C. Wipf,
17
S. Wise,
39
A. G. Wiseman,
51
G. Woan,
40
D. Woods,
51
R. Wooley,
16
J. Worden,
15
W. Wu ,
39
I. Yakushin,
16
H. Yamamoto,
14
Z. Yan,
50
S. Yoshida,
28
N. Yunes,
32
M. Zanolin,
17
J. Zhang,
42
L. Zhang,
14
C. Zhao,
50
N. Zotov,
19
M. Zucker,
17
H. zur Mu
̈
hlen,
36
and J. Zweizig
14
(LIGO Scientific Collaboration)
*
1
Albert-Einstein-Institut, Max-Planck-Institut fu
̈
r Gravitationsphysik, D-14476 Golm, Germany
2
Albert-Einstein-Institut, Max-Planck-Institut fu
̈
r Gravitationsphysik, D-30167 Hannover, Germany
3
Andrews University, Berrien Springs, Michigan 49104 USA
4
Australian National University, Canberra, 0200, Australia
5
California Institute of Technology, Pasadena, California 91125, USA
6
Caltech-CaRT, Pasadena, California 91125, USA
7
Cardiff University, Cardiff, CF2 3YB, United Kingdom
8
Carleton College, Northfield, Minnesota 55057, USA
9
Charles Sturt University, Wagga Wagga, NSW 2678, Australia
10
Columbia University, New York, New York 10027, USA
11
Embry-Riddle Aeronautical University, Prescott, Arizona 86301 USA
12
Hobart and William Smith Colleges, Geneva, New York 14456, USA
13
Inter-University Centre for Astronomy and Astrophysics, Pune - 411007, India
14
LIGO —California Institute of Technology, Pasadena, California 91125, USA
15
LIGO Hanford Observatory, Richland, Washington 99352, USA
16
LIGO Livingston Observatory, Livingston, Louisiana 70754, USA
17
LIGO —Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
18
Louisiana State University, Baton Rouge, Louisiana 70803, USA
19
Louisiana Tech University, Ruston, Louisiana 71272, USA
20
Loyola University, New Orleans, Louisiana 70118, USA
21
Moscow State University, Moscow, 119992, Russia
22
NASA/Goddard Space Flight Center, Greenbelt, Maryland 20771, USA
23
National Astronomical Observatory of Japan, Tokyo 181-8588, Japan
24
Northwestern University, Evanston, Illinois 60208, USA
25
Rochester Institute of Technology, Rochester, New York 14623, USA
26
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OX11 0QX United Kingdom
27
San Jose State University, San Jose, California 95192, USA
28
Southeastern Louisiana University, Hammond, Louisiana 70402, USA
29
Southern University and A&M College, Baton Rouge, Louisiana 70813, USA
30
Stanford University, Stanford, California 94305, USA
31
Syracuse University, Syracuse, New York 13244, USA
32
The Pennsylvania State University, University Park, Pennsylvania 16802, USA
33
The University of Texas at Brownsville and Texas Southmost College, Brownsville, Texas 78520, USA
34
Trinity University, San Antonio, Texas 78212, USA
35
Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain
36
Universita
̈
t Hannover, D-30167 Hannover, Germany
37
University of Adelaide, Adelaide, SA 5005, Australia
38
University of Birmingham, Birmingham, B15 2TT, United Kingdom
39
University of Florida, Gainesville, Florida 32611, USA
40
University of Glasgow, Glasgow, G12 8QQ, United Kingdom
41
University of Maryland, College Park, Maryland 20742 USA
42
University of Michigan, Ann Arbor, Michigan 48109, USA
43
University of Oregon, Eugene, Oregon 97403, USA
44
University of Rochester, Rochester, New York 14627, USA
45
University of Salerno, 84084 Fisciano (Salerno), Italy
46
University of Sannio at Benevento, I-82100 Benevento, Italy
*
http://www.ligo.org
B. ABBOTT
et al.
PHYSICAL REVIEW D
76,
062003 (2007)
062003-2
47
University of Southampton, Southampton, SO17 1BJ, United Kingdom
48
University of Strathclyde, Glasgow, G1 1XQ, United Kingdom
49
University of Washington, Seattle, Washington, 98195, USA
50
University of Western Australia, Crawley, WA 6009, Australia
51
University of Wisconsin-Milwaukee, Milwaukee, Wisconsin 53201, USA
52
Washington State University, Pullman, Washington 99164, USA
(Received 9 April 2007; published 27 September 2007)
We have searched for gravitational waves (GWs) associated with the SGR
1806
20
hyperflare of 27
December 2004. This event, originating from a Galactic neutron star, displayed exceptional energetics.
Recent investigations of the x-ray light curve’s pulsating tail revealed the presence of quasiperiodic
oscillations (QPOs) in the 30 – 2000 Hz frequency range, most of which coincides with the bandwidth of
the LIGO detectors. These QPOs, with well-characterized frequencies, can plausibly be attributed to
seismic modes of the neutron star which could emit GWs. Our search targeted potential quasimonochro-
matic GWs lasting for tens of seconds and emitted at the QPO frequencies. We have observed no
candidate signals above a predetermined threshold, and our lowest upper limit was set by the 92.5 Hz QPO
observed in the interval from 150 s to 260 s after the start of the flare. This bound corresponds to a (90%
confidence) root-sum-squared amplitude
h
90%
rss
-
det
4
:
5
10
22
strain
Hz
1
=
2
on the GW waveform
strength in the detectable polarization state reaching our Hanford (WA) 4 km detector. We illustrate
the astrophysical significance of the result via an estimated characteristic energy in GW emission that we
would expect to be able to detect. The above result corresponds to
7
:
7
10
46
erg
(
4
:
3
10
8
M
c
2
),
which is of the same order as the total (isotropic) energy emitted in the electromagnetic spectrum. This
result provides a means to probe the energy reservoir of the source with the best upper limit on the GW
waveform strength published and represents the first broadband asteroseismology measurement using a
GW detector.
DOI:
10.1103/PhysRevD.76.062003
PACS numbers: 04.80.Nn, 04.30.Db, 07.05.Kf, 95.85.Sz
I. INTRODUCTION
Soft gamma-ray repeaters (SGRs) are objects that emit
short-duration x-ray and gamma-ray bursts at irregular
intervals (see [
1
] for a review). These recurrent bursts
generally have durations of the order of
100 ms
and
luminosities in the
10
39
–
10
42
erg
=
s
range. At times,
though rarely, these sources emit giant flares lasting hun-
dreds of seconds (see, for example, [
2
–
4
]) with peak
electromagnetic luminosities reaching
10
47
erg
=
s
[
5
]. Pul-
sations in the light curve tail reveal the neutron star spin
period.
Quasiperiodic oscillations (QPOs) [
6
–
10
] in the pulsat-
ing tail of giant flares were first observed for the 27
December 2004 event of SGR
1806
20
by the
Rossi X-
Ray Timing Explorer (RXTE)
and
Ramaty High Energy
Solar Spectroscopic Imager (RHESSI)
satellites [
6
–
8
].
Prompted by these observations, the RXTE data from the
SGR
1900
14
giant flare of 27 August 1998 were revis-
ited [
11
]. Transient QPOs were found in the light curve
pulsating tail at similar frequencies to the SGR
1806
20
event, suggesting that the same fundamental physical pro-
cess is likely taking place.
Several characteristics of SGRs can be explained by the
magnetar
model [
12
], in which the object is a neutron star
with a high magnetic field (
B
10
15
G
). In this model the
giant flares are generated by the catastrophic rearrange-
ment of the neutron star’s crust and magnetic field, a
starquake
[
13
,
14
].
It has been suggested that the star’s seismic modes,
excited by this catastrophic event, might drive the observed
QPOs [
6
–
8
,
15
], which leads us to investigate a possible
emission of gravitational waves (GWs) associated with
them. There are several classes of nonradial neutron star
seismic modes with characteristic frequencies in the
10
–
2000 Hz
range [
16
]. Toroidal modes of the neutron
star crust are expected to be excited by large crustal
fracturing (see [
6
–
8
,
17
]), though these modes may be
poor GW emitters. However, crust modes could magneti-
cally couple to the core’s modes, possibly generating a GW
signal accessible with today’s technology (see [
18
–
20
]).
Other modes with expected frequencies in the observed
range are crustal interface modes, crustal spheroidal
modes, crust/core interface modes, or perhaps
p
modes,
g
modes, or
f
modes. The latter should, in theory, be
stronger GW emitters (see, for example, [
21
,
22
]).
In addition, it has been noted [
23
] that a normal neutron
star can only store a crustal elastic energy of up to
10
44
erg
before breaking. An alternative to the conven-
tional neutron star model, that of a solid quark star, has also
been proposed in several versions [
23
–
26
]. In this case an
energy of
10
46
erg
(as observed for this flare) is feasible,
and thus the mechanical energy in the GW-emitting crust
oscillations could be comparable to the energy released
electromagnetically. This was also noted by Horvath
[
27
], who, in addition, estimated that LIGO might be
able to detect a GW burst of comparable energy to the
electromagnetic energy (this was before the QPOs were
discovered).
The exceptional energetics of the SGR
1806
20
hyperflare [
4
,
14
], the close proximity of the source
SEARCH FOR GRAVITATIONAL WAVE RADIATION
...
PHYSICAL REVIEW D
76,
062003 (2007)
062003-3
[
4
,
28
–
30
], and the availability of precisely measured QPO
frequencies and bandwidths [
6
–
8
] made SGR
1806
20
attractive for study as a possible GW emitter.
In this paper we make use of the LIGO Hanford (WA)
4 km detector (H1), the only LIGO detector collecting low
noise data at the time of the flare, to search for or to place
an upper bound on the GW emission associated with the
observed QPO phenomena of SGR
1806
20
. At the time
of the event the GEO600 detector was also collecting data.
However, due to its significantly lower sensitivity at the
frequencies of interest, it was not used in this analysis.
As will be shown, the 92.5 Hz QPO upper bounds can
be cast into a characteristic GW energy release in the
8
10
46
3
10
47
erg
(
4
10
8
2
10
7
M
c
2
) range.
This energy approaches the total energy emitted in the
electromagnetic spectrum and offers the opportunity to
explore the energy reservoir of the source. In the event
of a similar Galactic hyperflare coinciding with LIGO’s
fifth science run (S5), the energy sensitivity involved at
100 Hz
would probe the
2
10
45
erg
(
10
9
M
c
2
)
regime.
II. SATELLITE OBSERVATIONS
SGR
1806
20
is a Galactic x-ray star thought to be at a
distance in the 6 to 15 kpc range [
4
,
28
–
30
]. The total
(isotropic) electromagnetic flare energy for the 27
December 2004 record flare was measured to be
10
46
ergs
[
4
,
14
] assuming a distance of 10 kpc.
QPOs in the pulsating tail of the SGR
1806
20
hyper-
flare were first observed by Israel
et al.
[
6
] using RXTE,
and revealed oscillations centered at
18
,
30
, and
92
:
5Hz
. Using RHESSI, Watts and Strohmayer [
7
] con-
firmed the QPO observations of Israel
et al.
, revealing
additional frequencies at
26 Hz
and
626
:
5Hz
associ-
ated with a different rotational phase. Closer inspection of
the RXTE data by Strohmayer and Watts [
8
] revealed a
richer presence of QPOs, identifying significant compo-
nents at
150
and
1840 Hz
as well. Table
I
is taken from
Ref. [
8
] and summarizes the properties of the most signifi-
cant QPOs detected in the x-ray light curve tail of the SGR
1806
20
giant flare.
III. THE LIGO DETECTORS
The
Laser
Interferometer
Gravitational
Wave
Observatory (LIGO) [
31
] consists of three detectors, two
located at Hanford, Washington (referred to as H1 and H2)
and a third located in Livingston, Louisiana (referred to as
L1). Each of the detectors consists of a long-baseline
interferometer in a Michelson configuration with Fabry-
Perot arms (see Ref. [
32
] for details). The passage of a GW
induces a differential arm length change
L
which is
converted to a photocurrent by a photosensitive element
monitoring the interference pattern of the detector. This
electrical signal is then amplified, filtered, and digitized at
a rate of 16 384 Hz to produce a time series which we refer
to as the GW channel.
To calibrate the GW channel in physical units, the
interferometer response function is frequently measured
by generating known differential arm length changes.
The uninterrupted monitoring of the response function is
ensured with the addition of continuous sinusoidal excita-
tions referred to as
calibration lines
.
The interferometer sensitivity to
L
enables us to mea-
sure a strain
h
defined as
TABLE I. Summary of the most significant QPOs observed in the pulsating tail of SGR
1806
20
during the 27 December 2004 hyperflare (from Ref. [
8
]). The period of observation
for the QPO transient is measured with respect to the flare peak, the frequencies are given from
the Lorenzian fits of the data, and the width corresponds to the full-width-at-half-maximum
(FWHM) of the given QPO band.
Observation
Frequency
FWHM (Hz)
Period (s)
Satellite
References
a
17
:
9
0
:
11
:
9
0
:
2
60 – 230
RHESSI
[
7
]
b
25
:
7
0
:
13
:
0
0
:
2
60 – 230
RHESSI
[
7
]
c
29
:
0
0
:
44
:
1
0
:
5
190 – 260
RXTE
[
8
]
d
92
:
5
0
:
21
:
7
0
:
7
0
:
4
170 – 220
RXTE
[
6
]
e
92
:
5
0
:
21
:
7
0
:
7
0
:
4
150 – 260
RXTE
[
8
]
a
f
92
:
7
0
:
12
:
3
0
:
2
150 – 260
RHESSI
[
7
]
g
92
:
9
0
:
22
:
4
0
:
3
190 – 260
RXTE
[
8
]
h
150
:
3
1
:
617
5
10 – 350
RXTE
[
8
]
i
626
:
46
0
:
02
0
:
8
0
:
1
50 – 200
RHESSI
[
7
]
l
625
:
5
0
:
21
:
8
0
:
4
190 – 260
RXTE
[
8
]
m
1837
0
:
84
:
7
1
:
2
230 – 245
RXTE
[
8
]
a
Reference [
8
] makes an adjustment to the observation period of Ref. [
6
].
B. ABBOTT
et al.
PHYSICAL REVIEW D
76,
062003 (2007)
062003-4
h
L
L
(1)
where
L
denote the mean of the two arm lengths. The target
frequency range of interest is the audio band with frequen-
cies in the 50 Hz to 7 kHz range.
LIGO has dedicated science runs when good and reliable
coincidence data are available, alternating with periods of
commissioning to improve the sensitivity of the instru-
ment. In order to cover times when an astrophysically
notable event might occur, such as the 27 December
2004 event of this analysis, data from times when com-
missioning activities do not disable the machine are ar-
chived by a program referred to as
Astrowatch
[
33
].
Because of the nature of the time period, the detector’s
configuration was continuously evolving and was not as
well characterized as the dedicated science runs. On the
other hand, there was a deliberate attempt to place the
interferometers in a high-sensitivity configuration compat-
ible with the commissioning modifications of the epoch.
At the time of this event two of the LIGO detectors were
undergoing commissioning in preparation for the fourth
science run (S4). Only data from H1 are available for the
analysis of this event.
Figure
1
plots the best strain-equivalent noise spectra of
H1 during the S4 and S5 data-taking periods (light gray
curves). The average noise spectra at the time of the flare is
shown by the dark gray curve and the dashed line describes
the design sensitivity.
IV. DATA ANALYSIS
This analysis relies on an
excess power
search [
34
],
variants of which are described in Refs. [
35
–
37
]. In this
analysis we compare time-frequency slices at the time of
the observations with neighboring ones. The algorithm
used analyzes a single data stream at multiple-frequency
bands and can easily be expanded to handle coincident data
streams from multiple detectors. The trigger provided for
the analysis corresponds to the flare’s x-ray peak as
provided by the GRB Coordinate Network (GCN) reports
2920 [
38
] and 2936 [
39
] at time corresponding to
21:30:26.65 UTC (Coordinate Universal Time) of 2004
December 27.
In the absence of reliable theoretical models of GW
emission from magnetars, we keep the GW search as broad
and sensitive as possible. The search follows the QPO
signatures observed in the electromagnetic spectrum both
in frequency and time interval. In particular, we measure
the power (in terms of detector strain) for the intervals at
the observed QPO frequencies (as shown in Table
I
) for a
given bandwidth (typically 10 Hz) and we compare it to the
power measured in adjacent frequency bands not related to
the QPO. The excess power is then calculated for each
time-frequency volume of interest.
Although QPOs are not observed in x rays until some
time after the flare, the magnetar model suggests that the
seismic modes would be excited at the time of the flare
itself. For this reason, we also search for GW emission
associated with the proposed seismic modes from the
received trigger time of the event. In addition, we chose
to examine arbitrarily selected frequency bands, referred to
as control bands, whose center frequency is set to twice the
QPO frequency and processed identically to the QPO
bands. This allowed us to cover a wider range of the
detector’s sensitivity while allowing the reader the flexi-
bility to estimate the sensitivity to low significance QPOs
not addressed here (see Ref. [
8
]) as well as future obser-
vations/exotic models of GW emission yet to come.
Another aspect of the satellite observations is the qua-
siperiodic nature of the emitted electromagnetic waveform
with a possible slow drift in frequency. Since there is no
knowledge of the GW waveforms that would be associated
with this type of event, we tune our search algorithm to be
most sensitive to long quasiperiodic waveforms with fairly
narrow bandwidths while short bursts are strongly discri-
minated against. The waveform set used in testing the
sensitivity of the algorithm by adding simulated data in
the analysis software is chosen in line with this argument.
A. Pipeline
A block diagram of the analysis pipeline is shown in
Fig.
2
where the Gamma-Ray Bursts Coordinates Network
(GCN) reports provide the trigger for the analysis. The
on
-
and
off
-source data regions are then selected where the
former corresponds to the QPO observation periods, as
shown in Table
I
. The
off
-source data region begins at the
end of the 6 min long QPO tail (set to 400 s after the flare
peak) lasting to 10 min prior to the end of the stable H1
lock stretch for a total of
2h
of data.
The on-source region consists of a single segment. This
segment either starts at the moment of the flare (
t
start
t
0
)
10
2
10
3
10
−23
10
−22
10
−21
10
−20
10
−19
Frequency (Hz)
Strain−equivalent noise (Hz
−1/2
)
flare
S4
S5
H1 design
FIG. 1. The strain-equivalent sensitivity of the H1 detector at
the time of the hyperflare, the fourth and fifth science runs (S4,
S5), and its design sensitivity.
SEARCH FOR GRAVITATIONAL WAVE RADIATION
...
PHYSICAL REVIEW D
76,
062003 (2007)
062003-5
or at the beginning of the QPO observation (
t
start
t
QPO
)
and lasts until the end of the observation (
t
end
). The off-
source region consists of numerous nonoverlapping seg-
ments, each of duration
t
t
end
t
start
.
To provide an estimate of the search sensitivity, an
arbitrary simulated gravitational waveform can be added
(or
injected
) to each off-source data segment. All of the
segments (
on
or
off
source) are processed identically. In the
procedure described by the conditioning block, the data are
bandpass filtered to select the three frequency bands of
interest: the QPO band as shown in Table
I
and the two
adjacent frequency bands. Using the interferometer re-
sponse function at the time of the event, the data are
calibrated into units of strain and a data-quality procedure,
as described below, is applied to the data set.
After the conditioning procedure is complete, the data
stream is pushed through the search algorithm, which
computes the power in each segment for the three fre-
quency bands of interest and then the excess power in the
segment. Finally, on- and off-source excesses are com-
pared, and in the case of no significant on-source signals,
an upper limit interval is constructed using the Feldman
and Cousins [
40
] method modified, as will be discussed in
Sec. VI, by assigning the lower bound to zero.
The data processing can be validated against analytical
expectations by replacing the off-source region with simu-
lated data.
B. Data conditioning
The conditioning procedure consists of zero-phase filter-
ing of the data with three different bandpass Butterworth
filters. The first bandpass filters the data around the QPO
frequency of interest with a predefined bandwidth. This
bandwidth depends on the observed QPO width (see
Table
I
) and on the fact that the QPOs have been observed
to evolve in frequency. For the QPOs addressed here, the
bandwidth is set to 10 Hz (well above the measured
FWHM shown in Table
I
) with the exception of the
150.3 Hz oscillation where the bandwidth was set to the
measured FWHM, 17 Hz.
The bandwidth for the control bands is also set to 10 Hz
which is still above twice the measured FWHM. An ex-
ception to this is the 150.3 Hz second harmonic which is
within 1 Hz away from the fifth harmonic of the 60 Hz
power line. The bandwidth in this case is set to twice the
measured FWHM (
2
17 Hz
34 Hz
) but a 4 Hz wide
notch at 300 Hz is included to suppress the significant
sensitivity degradation provided by the line. For this rea-
son, the effective bandwidth is 30 Hz.
The data are also filtered to select the two adjacent
frequency bands with identical bandwidths of the chosen
QPO band. Using the adjacent frequency bands allows us
to discriminate against common nonstationary broadband
noise, thereby increasing the search sensitivity, as will be
described in Sec. IV C.
A gap between frequency bands was introduced for
some of the QPO frequencies in order to minimize the
power
contribution
of
known
instrumental
lines.
Furthermore, 60 Hz harmonics which landed in the bands
of interest were strongly suppressed using narrow notch
filters.
The three data streams are calibrated in units of strain
using a transfer function which describes the interferome-
ter response to a differential arm length change.
The conditioning procedure ends with the identification
of periods of significant sensitivity degradation. These
periods are selected by monitoring the power in each of
the three frequency bands in data segment durations, or
tiles
, 125 ms and 1 s long. If the power is above a set
threshold in any of the three bands, the tile in question
identifies a period of noise increase. This abrupt power
change in a second-long time frame (or less) does not
correspond to a GW candidate lasting tens to hundreds of
seconds. For this reason, the full data set contained in the
identified tile is disregarded and short-duration GW bursts,
not among the targeted signals, would be excluded by this
analysis.
To set a particular threshold we first determined the
variance of the resulting power distribution which was
calculated by removing outliers iteratively. As will be
described in Sec. V, we used
2
,
3
, and
4
cuts and
we injected different waveform families to optimize the
search sensitivity.
C. The search algorithm
The algorithm at the root of the search consists of taking
the difference in power between a band centered at a
frequency
f
QPO
and the average of the two frequency bands
FIG. 2.
A block diagram of the analysis sketching the signal
flow.
B. ABBOTT
et al.
PHYSICAL REVIEW D
76,
062003 (2007)
062003-6
adjacent to the QPO frequency band, also of bandwidth
f
, typically centered at
f
f
QPO
f
.
After bandpass filtering, we are left with three channels
for each QPO:
c
QPO
t
,
c
t
, and
c
t
. The power for
each of these channels is
P
QPO
;
Z
t
end
t
start
c
QPO
;
2
dt
(2)
where tiles that were vetoed are excluded from the integral.
The excess power is then defined as
P
P
QPO
P
avg
(3)
where
P
avg
P
P
=
2
is the average of the adjacent
bands. We refer to the resulting set of
P
calculated over
the off-source region as the
background
, while the on-
source region provides a single excess power measurement
of duration
t
for the period from
t
start
to
t
end
.
V. SENSITIVITY OF THE SEARCH
In order to estimate the sensitivity of the search, differ-
ent sets of more or less astrophysically motivated wave-
forms, or in some cases completely
ad-hoc
waveforms, are
injected in the off-source region and the resulting excess
power is computed.
The strength of the injected strain (at the detector)
h
det
t
is defined by its
root-sum-square
(rss) amplitude, or
h
rss
-
det
Z
t
1
t
t
1
j
h
det
t
j
2
dt
s
(4)
integrated over the interval
t
, as described in Sec. IVA,
where
t
1
indicates the start of a segment in the background
region. The search sensitivity to a particular waveform,
h
sens
rss
-
det
, is defined as the injected amplitude
h
rss
-
det
such
that 90% of the resulting
P
is above the off-source
median. This choice of definition provides a
characteristic
waveform strength which, on average, should not be far
from a 90% upper bound.
We injected various waveform families [namely, sine-
Gaussians (SG), white noise bursts (WNB), amplitude
(AM), and phase modulated (PM) waveforms] in the off-
source region to quantify the sensitivity of the search to
these types of waveforms. Each waveform was added
directly to the raw data segments and the search sensitivity
was explored as a function of the various parameters. As
previously mentioned, we designed the algorithm to be
sensitive to arbitrary waveforms with a preset small fre-
quency range while discriminating against any type of
short-duration signals.
The result of the sensitivity study for the case of the
92.5 Hz QPO (observation d of Table
I
) is shown in Fig.
3
where the band center frequencies, bandwidths, and signal
durations were set to
f
QPO
92
:
5Hz
,
f
82
:
5Hz
,
f
102
:
5Hz
,
f
10 Hz
, and
t
50 s
.
SG waveforms are parametrized as follows:
h
det
t
A
sin
2
f
c
t
e
t
t
0
2
=
2
(5)
where
A
is the waveform peak amplitude,
f
c
is the wave-
form central frequency,
Q
2
p
f
c
is the quality factor,
is the
1
=e
decay time,
is an arbitrary phase, and
t
0
indicates the waveform peak time. In the case of
Q
!1
the waveform approaches the form of a pure sinusoid. The
top left panel of Fig.
3
plots the search sensitivity versus
the quality factor
Q
of the injected SG waveform, indicat-
ing that the analysis is most sensitive to SG waveforms
with quality factors in the range
Q
2
10
3
:
1
. The
response is also shown as a function of a
2
and
4
data-quality cut on the off-source RMS distribution calcu-
lated for 125 ms long tiles. The more aggressive
2
cut
yields significantly better results and was chosen for the
92.5 Hz QPO analysis. This band, in particular, is signifi-
cantly more problematic than the others exhibiting a high
degree of nonstationarity as well as a relatively high glitch
rate.
The decline in sensitivity as the
Q
decreases originates
from the data-quality procedure. As parameter
Q
takes
smaller values, the waveform energy concentrates in
shorter time scales and the conditioning procedure identi-
fies and removes intervals of the injection which are above
threshold. In the
2
case, the sensitivity is relatively flat for
Q>
5
10
3
and the average value is
h
sens
rss
-
det
5
:
1
10
22
strain
Hz
1
=
2
, also shown in the plot by the
dashed line. The corresponding waveform duration
t
,
defined as the interval for which the waveform amplitude
is above
A=e
,is
t
2
p
Q=f
c
’
24 s
, appropriate for
the targeted search as shown in Table
I
.
The top right panel of Fig.
3
plots the sensitivity to a
large population of 40 s long WNB injections of band-
widths ranging from 1 Hz to 11 Hz. The waveform is
generated by bandpassing white noise through a 2nd order
Butterworth filter with bandwidth defined at the
3dB
cutoff point and burst duration set by a Tukey window. As
shown in the SG case, the most aggressive
2
cut outper-
forms the
4
, and no significant departure in sensitivity is
seen for bandwidths up to 10 Hz. It is worth noting that
WNBs would correspond to incoherent motion of the
source and may not be physical. However, the purpose of
this study is to quantify the robustness of the search to a
variety of waveforms.
The bottom two panels of Fig.
3
plot the sensitivity to
PM and AM waveforms versus modulation depth, where
the modulation frequency is set to
f
mod
100 mHz
for
both cases. These waveforms are used to investigate QPO
amplitude and frequency evolutions. For the PM case, the
waveform is described as
h
det
t
A
cos
2
f
c
t
k
mod
x
t
(6)
where
A
is the waveform amplitude,
f
c
is the carrier
frequency,
is an arbitrary phase,
k
mod
is a modulation
SEARCH FOR GRAVITATIONAL WAVE RADIATION
...
PHYSICAL REVIEW D
76,
062003 (2007)
062003-7
depth constant, and
x
t
is the modulation signal,
x
t
sin
2
f
mod
t
:
(7)
It can be shown that the instantaneous frequency
^
f
is
^
f
t
f
c
f
mod
cos
2
f
mod
t
(8)
where
f
mod
k
mod
f
mod
. From Fig.
3
the PM sensitivity
is essentially constant within modulation depths in the
range
f
mod
2
1:5
Hz
.
The AM injection is parametrized as
h
det
t
A
t
cos
2
f
c
t
(9)
where
A
t
A
0
sin
2
f
mod
t
k
mod
1
k
mod
(10)
with waveform constant amplitude
A
0
,
k
mod
modulation
constant, and
f
c
carrier frequency. The search sensitivity to
this waveform family can be expressed in terms of the
modulation depth
R
defined as
R
1
1
k
mod
1
k
mod
2
1
k
mod
:
(11)
The bottom right panel of Fig.
3
plots the sensitivity of
this waveform as a function of
R
.As
k
mod
!1
, the
modulation depth parameter
R
!
0
, no modulation is ap-
plied, and the waveform is a sinusoid of constant ampli-
tude. As
k
mod
!
1
, the modulation depth is maximal
(
R
1
) and the amplitude
A
t
is also sinusoidal in nature.
From Fig.
3
the AM sensitivity is essentially constant
within modulation depths in the range
R
2
0:1
. The
average response to SG, as shown in the top left panel of
Fig.
3
, is also shown in the other three panels for
comparison.
The results shown in Fig.
3
indicate that the search
sensitivity is approximately the same for all the waveforms
considered.
It is also possible to estimate the theoretical search
sensitivity to a sinusoidal injection. Assuming white
Gaussian stationary noise for the detector output, the ex-
cess power statistic is a noncentral
2
distribution with
2
f
t
degrees of freedom and noncentral parameter
,
2
h
2
rss
-
det
S
h
f
(12)
where
S
h
f
is the power spectral density of the detector
noise floor at frequency
f
, in units
Hz
1
, and
f
and
t
are the bandwidth and duration of the segment in question,
in units of Hz and s (see Ref. [
37
]).
10
3
10
4
10
5
10
6
5
6
7
8
Sine−Gaussian
Quality Factor Q
h
rss−det
sens
(10
−22
strain Hz
−1/2
)
0
2
4
6
8
10
12
5
6
7
8
White−Noise−Bursts
Bandwidth (Hz)
h
rss−det
sens
(10
−22
strain Hz
−1/2
)
0
2
4
6
5
6
7
8
Phase−Modulated
Modulation Depth
∆
f
mod
(Hz
peak
)
h
rss−det
sens
(10
−22
strain Hz
−1/2
)
0
0.2
0.4
0.6
0.8
1
5
6
7
8
Amplitude−Modulated
Modulation Depth R
h
rss−det
sens
(10
−22
strain Hz
−1/2
)
2
σ
4
σ
5.1
FIG. 3.
Search sensitivity to different waveform families and for different data-quality cuts. The cuts are relative to the off-source
RMS distribution calculated in segments 125 ms long and for
2
cuts (dark gray crosses) and
4
cuts (light gray crosses). Top left
panel: SG waveform injections as a function of quality factor
Q
varied from
Q
600
to
Q
10
6
. The dashed line represents the
average sensitivity (
5
:
1
10
22
strain
Hz
1
=
2
) for injections with
Q>
5
10
3
(where the sensitivity is essentially flat) and a
2
cut.
Top right panel: 40 s long WNB waveform injections as a function of burst bandwidth ranging from 1 Hz to 11 Hz. Within the
parameter space explored, the sensitivity is essentially constant. Bottom left and right panels: PM and AM waveform injections as a
function of modulation depth for a modulation frequency of 100 mHz.
B. ABBOTT
et al.
PHYSICAL REVIEW D
76,
062003 (2007)
062003-8