of 13
arXiv:astro-ph/0703419v2 19 Apr 2007
LIGO-P040055-01-Z
Search for gravitational wave radiation associated with th
e 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,
14,6
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,
36, 2
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. D ́ıaz,
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. Gonz ́alez,
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. L ̈uck,
36, 2
B. Machenschalk,
1
M. MacInnis,
17
M. Mageswaran,
14
K. Mailand,
14
M. Malec,
36
V. Mandic,
14
S. Marano,
45
S. M ́arka,
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. M ̈uller-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. R ̈udiger,
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,
14, 6
D. Sigg,
15
S. Sinha,
30
A. M. Sintes,
35, 1
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. Th ̈uring,
36
K. V. Tokmakov,
40
C. Torres,
33
C. Torrie,
40
2
G. Traylor,
16
M. Trias,
35
W. Tyler,
14
D. Ugolini,
34
C. Ungarelli,
38
K. Urbanek,
30
H. Vahlbruch,
36
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,
36, 2
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 M ̈uhlen,
36
and J. Zweizig
14
(The LIGO Scientific Collaboration, http://www.ligo.org)
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, CF2 3YB, 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
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
3
We have searched for Gravitational Waves (GWs) associated w
ith 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
Quasi-Periodic Oscillations (QPOs) in the 30
2000 Hz frequency range, most of which coincides
with the bandwidth of the LIGO detectors. These QPOs, with we
ll-characterized frequencies, can
plausibly be attributed to seismic modes of the neutron star
which could emit GWs. Our search
targeted potential quasi-monochromatic GWs lasting for te
ns of seconds and emitted at the QPO
frequencies. We have observed no candidate signals above a p
re-determined 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% confide
nce) 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 emissio
n 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 electro
magnetic spectrum. This result provides
a means to probe the energy reservoir of the source with the be
st upper limit on the GW waveform
strength published and represents the first broadband aster
oseismology measurement using a GW
detector.
PACS numbers: 04.80.Nn, 07.05.Kf, 95.85.Sz, 04.30.Db, 95.
55.Ym, 04.40.Dg, 97.60.Jd, 97.10.Sj
I. INTRODUCTION
Soft Gamma-ray Repeaters (SGRs) are objects that
emit short-duration X and gamma-ray bursts at irregu-
lar 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, 3, 4]) with peak elec-
tromagnetic luminosities reaching 10
47
erg
/
s [5]. Pulsa-
tions in the light curve tail reveal the neutron star spin
period.
Quasi-Periodic Oscillations (QPOs) [6, 7, 8, 9, 10] in
the pulsating 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, 7, 8].
Prompted by these observations, the RXTE data from
the SGR 1900 + 14 giant flare of 27 August 1998 was
revisited [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 process 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
rearrangement 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 ob-
served QPOs [6, 7, 8, 15], which leads us to investigate
a possible emission of Gravitational Waves (GWs) asso-
ciated with them. There are several classes of non-radial
neutron star seismic modes with characteristic frequen-
cies 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, 7, 8, 17]), though these modes
may be poor GW emitters. However, crust modes could
magnetically couple to the core’s modes, possibly gen-
erating a GW signal accessible with today’s technology
(see [18, 19, 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 the-
ory, be stronger GW emitters (see for example [21, 22]).
In addition, it has been noted [23] that a normal neu-
tron star can only store a crustal elastic energy of up to
10
44
erg before breaking. An alternative to the con-
ventional neutron star model, that of a solid quark star,
has also been proposed in several versions [23, 24, 25, 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 compara-
ble 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
[4, 28, 29, 30] and the availability of precisely measured
QPO frequencies and bandwidths [6, 7, 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.
4
Observation Frequency FWHM Period Satellite References
[Hz]
[Hz]
[s]
a
17.9
±
0.1 1.9
±
0.2 60-230 RHESSI
[7]
b
25.7
±
0.1 3.0
±
0.2 60-230 RHESSI
[7]
c
29.0
±
0.4 4.1
±
0.5 190-260 RXTE
[8]
d
92.5
±
0.2 1
.
7
+0
.
7
0
.
4
170-220 RXTE
[6]
e
150-260
[8]
a
f
92.7
±
0.1 2.3
±
0.2 150-260 RHESSI
[7]
g
92.9
±
0.2 2.4
±
0.3 190-260 RXTE
[8]
h
150.3
±
1.6 17
±
5 10-350 RXTE
[8]
i
626.46
±
0.02 0.8
±
0.1 50-200 RHESSI
[7]
l
625.5
±
0.2 1.8
±
0.4 190-260 RXTE
[8]
m
1837
±
0.8 4.7
±
1.2 230-245 RXTE
[8]
a
Ref. [8] makes an adjustment to the observation period of Ref
.
[6]
TABLE I: Summary of the most significant QPOs observed in the p
ulsating tail of SGR 1806
20 during the 27 December
2004 hyperflare (from Ref. [8]). The period of observation fo
r the QPO transient is measured with respect to the flare peak,
the frequencies are given from the Lorenzian fits of the data a
nd the width corresponds to the Full-Width-at-Half-Maximu
m
(FWHM) of the given QPO band.
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, 29, 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
.
5 Hz. Using RHESSI, Watts and Strohmayer [7]
confirmed the QPO observations of Israel
et al.
reveal-
ing additional frequencies at
26 Hz and
626
.
5 Hz
associated with a different rotational phase. Closer in-
spection of the RXTE data by Strohmayer and Watts [8]
revealed a richer presence of QPOs, identifying signifi-
cant components at
150 and
1840 Hz as well. Table
I is taken from Ref. [8] and summarizes the properties
of the most significant 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 Observa-
tory (LIGO) [42] consists of three detectors, two located
at Hanford, WA (referred to as H1 and H2) and a third
located in Livingston, LA (referred to as L1). Each of
the detectors consists of a long-baseline interferometer
in a Michelson configuration with Fabry-Perot arms (see
Ref. [31] 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
16384 Hz to produce a time series which we refer to as
the GW channel.
To calibrate the GW channel in physical units, the in-
terferometer response function is frequently measured by
generating known differential arm length changes. The
uninterrupted monitoring of the response function is en-
5
sured with the addition of continuous sinusoidal excita-
tions referred to as
calibration lines
.
The interferometer sensitivity to ∆
L
enables to mea-
sure a strain
h
defined as
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
frequencies in the 50 Hz to 7 kHz range.
LIGO has dedicated science runs when good and re-
liable coincidence data is available, alternating with pe-
riods of commissioning to improve the sensitivity of the
instrument. In order to cover times when an astrophys-
ically notable event might occur, such as the 27 Decem-
ber 2004 event of this analysis, data from times when
commissioning activities do not disable the machine is
archived by a program referred to as
Astrowatch
[32].
Due to the nature of the time period, the detector’s con-
figuration 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 inter-
ferometers in a high-sensitivity configuration compatible
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 is 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 [43], vari-
ants of which are described in Ref. [33, 34, 35]. In this
analysis we compare time-frequency slices at the time
of the observations with neighboring ones. The algo-
rithm used analyzes a single data stream at multiple fre-
quency bands and can easily be expanded to handle coin-
cident 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 [44] and 2936 [45] at time corre-
sponding to 21:30:26.65 UTC of 2004-12-27.
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 spec-
trum 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 Tab. 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 emis-
sion associated with the proposed seismic modes from
the received trigger time of the event. In addition, we
chose to examine arbitrary selected frequency bands, re-
ferred 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
flexibility to estimate the sensitivity to low significance
QPOs not addressed here (see Ref. [8]) as well as future
observations/exotic models of GW emission yet to come.
Another aspect of the satellite observations is the
quasi-periodic 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 quasi-periodic
waveforms with fairly narrow bandwidths while short
bursts are strongly discriminated 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 Net-
work (GCN) reports provide the trigger for the analy-
sis. The
on
and
off
-source data regions are then selected
where the former corresponds to the QPO observation
periods, as shown in Tab. I. The
off
-source data region
begins at the end of the six minute long QPO tail (set to
400 s after the flare peak) lasting to ten minutes prior to
the end of the stable H1 lock stretch for a total of
2 h
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
) 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 non-
overlapping segments, each of duration ∆
t
=
t
end
t
start
.
To provide an estimate of the search sensitivity, an ar-
bitrary 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 is band-pass filtered to select the three frequency
bands of interest: the QPO band as shown in Tab. I
and the two adjacent frequency bands. Using the inter-
ferometer response function at the time of the event, the
data is calibrated into units of strain and a data-quality
procedure, as described below, is applied to the data set.
6
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 detecto
r at the time of the hyperflare, the fourth and fifth science run
s (S4,
S5), and its design sensitivity.
FIG. 2: A block diagram of the analysis sketching the signal
flow.
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,
the standard Feldman-Cousins [36] statistical approach is
used to place an upper limit based on the loudest signal.
The data processing can be validated against analyt-
ical expectations by replacing the off-source region with
simulated data.
B. Data conditioning
The conditioning procedure consists of zero-phase fil-
tering of the data with three different band-pass Butter-
worth filters. The first band-pass filters the data around
the QPO frequency of interest with a predefined band-
width. This bandwidth depends on the observed QPO
width (see Tab. I) and on the fact that the QPOs have
been observed to evolve in frequency. For the QPOs ad-
dressed here, the bandwidth is set to 10 Hz (well above
the measured FWHM shown in Tab. I with the excep-
tion 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 exception to this is the 150
.
3 Hz second harmonic
which is within one 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 reason, the effective bandwidth is 30 Hz.
The data is also filtered to select the two adjacent fre-
7
quency bands with identical bandwidths of the chosen
QPO band. Using the adjacent frequency bands allows
us to discriminate against common non-stationary broad-
band 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. Fur-
thermore, 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 interferom-
eter response to a differential arm length change.
The conditioning procedure ends with the identifi-
cation of periods of significant sensitivity degradation.
These periods are selected by monitoring the power in
each of the three frequency bands in data segment dura-
tions, 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 ques-
tion 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 hun-
dreds of seconds long. 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
σ
, 3
σ
and 4
σ
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 tak-
ing the difference in power between a band centered at
a frequency
f
qpo
and the average of the two frequency
bands adjacent to the QPO frequency band, also of band-
width ∆
f
, typically centered at
f
±
=
f
qpo
±
f
.
After band-pass filtering, we are left with three chan-
nels for each QPO:
c
qpo
(
t
),
c
+
(
t
), and
c
(
t
). The power
for the QPO interval is for each of these channels:
P
qpo
,
±
=
t
end
t
start
(
c
qpo
,
±
)
2
dt
(2)
where tiles that were vetoed are excluded from the inte-
gral. 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
=
t
1
+∆
t
t
1
|
h
det
(
t
)
|
2
dt
(4)
integrated over the interval ∆
t
, as described in Sec. IV A,
where
t
1
indicates the start of a segment in the back-
ground 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 di-
rectly 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 Tab. I) is shown in Fig. 3
where the band center frequencies, bandwidths and signal
durations were set to
f
qpo
= 92
.
5 Hz,
f
= 82
.
5 Hz,
f
+
= 102
.
5 Hz, ∆
f
= 10 Hz and ∆
t
= 50 s.
SG waveforms are parameterized as follows
h
det
(
t
) =
A
sin (2
πf
c
t
+
φ
)
e
(
t
t
0
)
2
2
(5)
where
A
is the waveform peak amplitude,
f
c
is the wave-
form central frequency,
Q
=
2
πτ f
c
is the quality factor,
τ
is the 1
/e
decay time,
φ
is an arbitrary phase and
t
0
indicates the waveform peak time. In the case of
Q
→∞
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,
indicating that the analysis is most sensitive to SG wave-
forms with quality factors in the range
Q
[
10
3
:
].
The response is also shown as a function of a 2
σ
and
4
σ
data quality cut on the off-source RMS distribution
calculated for 125 ms long tiles. The more aggressive
2
σ
cut yields significantly better results and was chosen
for the 92
.
5 Hz QPO analysis. This band in particular is
significantly more problematic than the others exhibiting
a high-degree of non-stationarity as well as a relatively
high glitch rate.
8
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 an
d for different data quality cuts. The cuts are relative to the
off-
source RMS distribution calculated in segments 125 ms long a
nd for 2
σ
cuts (dark gray crosses) and 4
σ
cuts (light gray crosses).
Top left: SG waveforms injections as a function of quality fa
ctor Q varied from
Q
= 600 to
Q
= 10
6
. 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
σ
cut. Top right: 40 s long WNBs waveform injections as a functi
on of burst bandwidth ranging from 1 Hz to 11 Hz. Within
the parameter space explored the sensitivity is essentiall
y constant. Bottom left and right: PM and AM waveform injecti
ons
as a function of modulation depth for a modulation frequency
of 100 mHz.
The decline in sensitivity as the Q decreases originates
from the data quality procedure. As parameter Q takes
smaller values, the waveform energy begins to concen-
trate in shorter time scales and the conditioning pro-
cedure identifies and removes intervals of the injection
which are above threshold. In the 2
σ
case, the sensitiv-
ity 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
δt
, defined as the interval for which the wave-
form amplitude is above
A/e
, is
δt
2
Q/πf
c
24 s,
appropriate for the targeted search as shown in Tab. I.
The top right panel of Fig. 3 plots the sensitivity to a
large population of 40 s long WNBs injections of band-
widths ranging from 1 Hz to 11 Hz. The waveform is gen-
erated by band-passing white noise through a 2
nd
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
σ
cut
outperforms the 4
σ
and no significant departure in sen-
sitivity is seen for bandwidths up to 10 Hz. It is worth
noting that WNBs would correspond to incoherent mo-
tion 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
πf
c
t
+
k
mod
x
(
t
) +
φ
)
(6)
where
A
is the waveform amplitude,
f
c
is the carrier fre-
quency,
φ
is an arbitrary phase,
k
mod
is a modulation
depth constant and
x
(
t
) is the modulation signal
x
(
t
) = sin (2
πf
mod
t
)
(7)
It can be shown that the instantaneous frequency
ˆ
f
is
ˆ
f
(
t
) =
f
c
+ ∆
f
mod
cos(2
πf
mod
t
)
(8)
where ∆
f
mod
=
k
mod
f
mod
. From Fig. 3 the PM sen-
sitivity is essentially constant within modulation depths
in the range ∆
f
mod
[1 : 5] Hz.
9
The AM injection is parameterized as
h
det
(
t
) =
A
(
t
) cos (2
πf
c
t
)
(9)
where
A
(
t
) = A
0
sin(2
πf
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
→ ∞
, the
modulation depth parameter
R
0, no modulation is
applied and the waveform is a sinusoid of constant am-
plitude. As
k
mod
1, the modulation depth is maximal
(
R
= 1) and the amplitude
A
(
t
) is also sinusoidal in na-
ture. From Fig. 3 the AM sensitivity is essentially con-
stant within modulation depths in the range
R
[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 wave-
forms considered.
It is also possible to estimate the theoretical search sen-
sitivity to a sinusoidal injection. Assuming white gaus-
sian stationary noise for the detector output, we can de-
rive (see Ref. [35]) the following expression for the search
sensitivity
h
theo
rss
det
1
.
25
S
1
/
2
h
(
f
)
(
f
t
)
1
/
4
(12)
where
S
1
/
2
h
(
f
) is the strain-equivalent amplitude spectral
density of the detector noise at frequency
f
, in units of
strain Hz
1
/
2
, and ∆
f
and ∆
t
are the bandwidth and
duration of the segment in question, in units of Hz and s.
The order-of-unity factor (1.25) stems from the 90% sen-
sitivity definition as previously discussed and from taking
the difference in power between bands.
Referring to Fig. 1, the strain sensitivity at
f
=
92
.
5 Hz is
S
1
/
2
h
(
f
)
9
×
10
23
strain Hz
1
/
2
. Using
f
= 10 Hz and ∆
t
= 50 s, the expected sensitivity is
h
theo
rss
det
5
.
3
×
10
22
strain Hz
1
/
2
(13)
in good agreement with the average response of
h
sens
rss
det
= 5
.
1
×
10
22
strain Hz
1
/
2
shown in Fig. 3.
VI. RESULTS
Inspection of the on-source data segments revealed no
significant departure from the off-source distribution and
we cast the results of this analysis in terms of upper
bounds on GW signals. These limits are found to be
well below the maximum allowed upper bounds in the
non-detection regime, which we refer to as non-detection
threshold, assuming a continuous observation of SGR
1806
20 and requiring an accidental rate of one event
in one-hundred years (see Tab. II).
We used the unified approach of Feldman-Cousins [36],
which provides upper confidence limits for null results,
two-sided confidence intervals for non-null results and
treats confidence limits with constraints on a physical re-
gion. In view of the fact that at the time of the hyperflare
event only one of the three LIGO detectors was collecting
data and that the full detector diagnostic capability was
not fully exploited, the lower bounds on the confidence
intervals was set to zero (i.e. no detection claim based
purely on the statistical analysis was allowed).
Table X of Ref. [36] was used to place the upper limits
of this search. The excess power distribution for the off-
source region of each QPO transient was parameterized
with a Gaussian Probability Density function (PDF), and
the mean
μ
, standard deviation
σ
and their relative errors
is estimated. The on-source excess power measure and
the lookup table were then used to set 90% confidence
intervals.
Table II presents the results of this search, for both
the control and QPO frequencies, in terms of 90% upper
bounds on the GW waveform strength, h
90%
rss
det
, mea-
sured at the time of the observation. The first column
of the table indicates the observation we address, with
reference to the original measurements shown in Tab. I.
The second, third, fourth and fifth columns indicate the
center frequency, bandwidth, period, and duration used
in the search. The sixth column, labeled as non-detection
threshold, lists the maximum upper bound allowed in the
non-detection regime. A data quality flag was used for
the 92
.
5 Hz QPO observation only, with a power thresh-
old set at the 2
σ
level relative to tiles 125 ms long.
The last column, labeled h
90%
rss
det
, presents the results
where the contributions due to the different uncertainties
are shown separately. The first of these, the first number
in superscript, shows the 90% upper bound arising from
the statistical uncertainties in the off-source estimation
.
These uncertainties are generated using a Monte-Carlo
simulation: a set of means ˆ
μ
and standard deviations
ˆ
σ
are extracted from Gaussian distributed populations
of standard deviation
σ
ˆ
μ
and
σ
ˆ
σ
corresponding to the
fit parameter uncertainties. For each (ˆ
μ,
ˆ
σ
) combination
and the same on-source excess power measure we used
the lookup table in Ref. [36] to generate 90% confidence
intervals for the quoted upper limit.
The second uncertainty quoted is statistical and arises
from errors in the detector response function to GW ra-
diation via the calibration procedure. We placed a con-
servative estimate of the calibration accuracy to a one
standard deviation of 20%. The third uncertainty is a
systematic error of 6% also arising from the calibration
procedure.
10
Observation Frequency Bandwidth Interval Duration Thresh
old
non
det
h
90
%
rss
det
[Hz]
[Hz]
[s]
[s]
[
10
22
strain Hz
1
/
2
]
[
10
22
strain Hz
1
/
2
]
e,f
92.5
10
150-260
110
18
.
0
2
.
75
+0
.
47 +0
.
70 +0
.
16 +0
.
77
= 4
.
53
g
190-260
70
15
.
7
2
.
90
+0
.
43 +0
.
74 +0
.
17 +0
.
75
= 4
.
67
d
170-220
50
14
.
4
5
.
15
+0
.
35 +1
.
32 +0
.
31 +0
.
37
= 7
.
19
0-260
260
22
.
5
5
.
06
+1
.
42 +1
.
30 +0
.
30 +2
.
21
= 9
.
50
control freq.
185.0
8
150-260
110
19
.
0
9
.
48
+0
.
51 +2
.
43 +0
.
57 +0
.
27
= 12
.
8
190-260
70
17
.
6
8
.
17
+0
.
40 +2
.
09 +0
.
49 +0
.
17
= 11
.
0
170-220
50
16
.
5
8
.
03
+0
.
30 +2
.
06 +0
.
48 +0
.
24
= 10
.
8
0-260
260
24
.
1
11
.
4
+1
.
06 +2
.
91 +0
.
68 +0
.
00
= 15
.
1
h
150.3
17
0-350
350
30
.
2
12
.
4
+1
.
78 +3
.
16 +0
.
74 +0
.
00
= 16
.
7
control freq.
300.6
30
0-350
350
70
.
3
26
.
4
+4
.
46 +6
.
75 +1
.
58 +0
.
00
= 36
.
0
i
626.5
10
50-200
150
53
.
4
25
.
6
+1
.
76 +6
.
56 +1
.
54 +0
.
00
= 33
.
9
l
190-260
70
47
.
4
19
.
4
+1
.
23 +4
.
97 +1
.
17 +0
.
00
= 25
.
7
0-260
260
60
.
1
28
.
2
+2
.
70 +7
.
22 +1
.
69 +0
.
00
= 37
.
6
control freq.
1253.0
10
50-200
150
114
49
.
4
+4
.
10 +12
.
64 +2
.
96 +0
.
00
= 65
.
6
190-260
70
89
.
0
30
.
6
+2
.
69 +7
.
84 +1
.
84 +0
.
00
= 40
.
7
0-260
260
107
53
.
5
+4
.
50 +13
.
71 +3
.
21 +0
.
00
= 71
.
2
m
1837.0
10
230-245
15
94
.
7
34
.
6
+1
.
26 +8
.
86 +2
.
08 +0
.
00
= 45
.
6
0-245
245
192
54
.
9
+11
.
72 +14
.
05 +3
.
29 +0
.
00
= 76
.
5
TABLE II: List of frequencies and observation times used in t
his analysis with the corresponding results. The first colum
n
describes the addressed QPO observation, labeled by letter
s as they appear in Tab. I. A wider range of the detector’s sens
itivity
can be explored using the frequency bands here labeled as con
trol frequencies (see text). The second, third, fourth and fi
fth
columns indicate the center frequency, bandwidth, interva
l, and duration used in the search. The sixth column provides
the
non-detection threshold. The last column presents the resu
lts where the contributions due to the different uncertainti
es are
shown separately. The first two numbers in superscript repre
sent the statistical uncertainty in the off-source estimati
on and
calibration procedure respectively. The third one shows th
e contribution of a systematic uncertainty of 6% due to the ca
libration
procedure. The last uncertainty is a systematic arising fro
m the off-source data modeling which depends on the presence o
f
outliers (see text for details). To produce the upper bound h
90%
rss
det
statistical contributions are added in quadrature while th
e
systematic contributions are added linearly.
The occasional presence of tails in the off-source seg-
ments, consisting typically of a few large excess power
measurements in the off-source data of each QPO intro-
duces a bias in the upper bounds which is presented as
a source of systematic uncertainty (represented by the
fourth number in superscript). This bias is quantified by
including and excluding the off-source distribution
±
3
σ
outliers from the fitting procedure and the difference in
the upper bounds,
δh
syst
rss
det
=
h
with
rss
det
h
without
rss
det
is shown
in the column in question.
In order to fold in the different uncertainties we sum in
quadrature the statistical uncertainties shown (originat
-
ing from the off-source estimation and the calibration)
and we increase the bound by the two systematic errors.
VII. ASTROPHYSICAL INTERPRETATION
In this section we provide a characteristic GW en-
ergy
E
iso
GW
associated with the measured upper bounds
h
90%
rss
det
, shown in Tab. II, cast in terms of a simple
source model. In this model we assume that the emission
is isotropic, that the plus and cross polarization states ar
e
uncorrelated but have equal power.
Under these assumptions (equal uncorrelated power ra-
diated in the plus and cross polarizations) the strain in
the detector can be related to the GW flux incident on
the Earth via
h
2
rss
det
=
1
2
(
F
2
+
+
F
2
×
)
h
2
rss
(14)
11
where
h
2
rss
=
−∞
[
h
2
+
(
t
) +
h
2
×
(
t
)]
dt
(15)
and
F
+
and
F
×
are antenna response functions that de-
pend on (i) the right-ascension and declination of the
source, (ii) the time of the flare, (iii) the location and
orientation of the detector, and (iv) a polarization an-
gle defining the plus and cross polarizations. The depen-
dence on this polarization angle vanishes in the combina-
tion
F
2
+
+
F
2
×
, which is a quantity ranging from 0 to 1; the
Hanford detector’s antenna response to SGR 1806
20
at the time of the hyperflare was
F
2
+
+
F
2
×
= 0
.
174
(16)
This shows that the source was not particularly well sit-
uated in the detectors antenna pattern. Under our as-
sumption of isotropic emission, the energy released by
the source is related to the gravitational wave flux at the
Earth by
E
iso
GW
=
π
2
c
3
r
2
f
2
qpo
G
h
2
rss
(17)
In terms of the upper limits presented, the equivalent
bound on the gravitational wave emission corresponding
to a particular QPO is
E
iso
,
90%
GW
= 4
.
29
×
10
8
M
c
2
×
(18)
(
r
10kpc
)
2
(
f
qpo
92
.
5Hz
)
2
(
h
90%
rss
det
4
.
53
×
10
22
strain Hz
1
/
2
)
2
(here the values of the best QPO strain bound are used).
It is worth noting that the best energy upper bound is
comparable to the energy emitted in the electromagnetic
spectrum (see for example Ref. [4]).
VIII. CONCLUSION
Quasi-Periodic Oscillations have been observed in the
pulsating X-ray tail of the SGR 1806
20 hyperflare of
27 December 2004 by the RXTE and RHESSI satellites.
The present consensus interprets the event as a dramatic
re-configuration of the star’s crust and/or magnetic field.
In turn, this
starquake
could plausibly excite the star’s
global seismic modes and the observed QPOs could po-
tentially be driven by the seismic modes. The energetics
of the event, the close proximity of the source, and the
availability of observed QPO frequencies and bandwidths
provided a unique opportunity to measure GWs associ-
ated with this phenomenon.
Upper limits in the gamma and high-energy neutrino
flux were recently measured by the AMANDA-II detec-
tor [37]. However the only other published GW search
associated with the SGR 1806
20 hyperflare used the
AURIGA bar detector [38] to place upper limits on the
GW waveform strength emitted for frequencies around
900 Hz. At the time of the event, H1’s strain noise
equivalent in the
900 Hz region is a factor
5 lower
than AURIGA’s.
The AURIGA search targeted different physics, there-
fore the comparison to our results is not possible. Expo-
nentially decaying sinusoids of decay time 100 ms were
searched for by measuring the power in time and fre-
quency slices of ∆
t
= 201
.
5 ms and ∆
f
= 5 Hz respec-
tively in the 855 Hz to 945 Hz range. A set of 95%
upper bounds on the waveform strength were placed in
the
h
95%
rss
det
= 1
.
4
×
10
21
strain Hz
1
/
2
to
h
95%
rss
det
=
3
.
5
×
10
21
strain Hz
1
/
2
range.
At the time of the event one of the three LIGO de-
tectors was in operation under the
Astrowatch
program.
Under this program, data is collected at times of com-
missioning when the interferometers are not undergoing
adjustments. Only
2 h of data was available for this
analysis.
An algorithm was designed to measure the
excess
power
deposited in the machine at the time of the
event. This algorithm exploits power measures in mul-
tiple bands to reject common mode noise sources, such
as broadband noise. Power measures in time scales less
than 1s are also monitored to reject
fast
signatures in-
consistent with the scope of this analysis.
The design was driven by the desire to repeat this mea-
surement for future flares with the ability to use multiple
data streams from multiple detectors, focusing on mod-
ularity, flexibility, and simplicity.
Signals were software-injected into the raw data stream
to study the analysis sensitivity to a variety of waveform
families and parameters. A large astrophysical motivated
parameter space was explored under which the search
sensitivity is essentially constant.
At the time of the event, the strain-equivalent ampli-
tude spectral density of the detector output was a fac-
tor of a few away from the one corresponding to the
fourth science run. Under this condition, the best up-
per limit that we place corresponds to the 92
.
5 Hz QPO
observed 150 s to 260 s seconds after the flare. In terms
of waveform strength, we place a 90% upper bound of
h
90%
rss
det
= 4
.
53
×
10
22
strain Hz
1
/
2
on the GW wave-
form strength in the detectable polarization state reach-
ing our Hanford (WA) detector, which, in terms of a
simple source model, provides a characteristic energy
E
iso
,
90%
GW
= 7
.
67
×
10
46
erg (4
.
29
×
10
8
M
c
2
). This
is the best upper limit published on the GW waveform
strength on this type of source and represents the first
multiple-frequency asteroseismology measurement using
a GW detector. It is also worth noting that this en-
ergy estimate is of the same order as the isotropic energy
estimate measured electromagnetically, providing the op-
portunity to probe the energy reservoir of the source.
The limits presented here represent GW strength ob-
tained by the LIGO detectors in late 2004. At the
time of this writing, LIGO is undergoing a data-taking
12
period, referred to as the fifth science run S5, where
all three interferometers have reached design sensitiv-
ity, [39]. The improvement at 150 Hz corresponds to
a decrease in strain-equivalent noise of
3 in terms of
GW energetics. This estimate excludes the sensitivity
increase that can be achieved by cross-correlating data
streams from the multiple LIGO detectors. A follow-up
of this analysis will certainly examine the various SGR
1806
20/SGR 1900 + 14 outbursts, which occurred in
the 2005 - 2006 period, exploring GW energetics which
probe the
2
×
10
45
erg (
10
9
M
c
2
) regime.
At the end of the S5 data-taking period, the initial
LIGO detectors will be upgraded to an enhanced state
[40] which we refer to as Enhanced LIGO. The foreseen
improvement will be a factor of
2 in strain-equivalent
noise for frequencies above 100 Hz. The future GEO-
HF [41] detector will provide a significant high-frequency
improvement in sensitivity providing an opportunity to
study future high-frequency QPOs.
Advanced LIGO [46] will provide an increase in strain-
equivalent sensitivity of
10 with respect to the initial
LIGO detectors while opening up the low (10
50 Hz)
frequency range. This offers a particularly interesting
opportunity because a lower frequency search would be
feasible. For hyperflare events occurring at the time of
its operation, the observable GW energetics at 100 Hz
would lie in the
2
×
10
43
erg (
10
11
M
c
2
) regime.
IX. ACKNOWLEDGMENTS
We are indebted to Gianluca Israel and Anna Watts
for frequent and fruitful discussions. The authors grate-
fully acknowledge the support of the United States Na-
tional Science Foundation for the construction and oper-
ation of the LIGO Laboratory and the Particle Physics
and Astronomy Research Council of the United King-
dom, the Max-Planck-Society and the State of Nieder-
sachsen/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 Coun-
cil of Canada, the Council of Scientific and Industrial
Research of India, the Department of Science and Tech-
nology of India, the Spanish Ministerio de Educacion y
Ciencia, The National Aeronautics and Space Adminis-
tration, the John Simon Guggenheim Foundation, the
Alexander von Humboldt Foundation, the Leverhulme
Trust, the David and Lucile Packard Foundation, the Re-
search Corporation, the Alfred P. Sloan Foundation and
Columbia University in the City of New York.
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