All-sky search for long-duration gravitational wave transients
with initial LIGO
B. P. Abbott,
1
R. Abbott,
1
T. D. Abbott,
2
M. R. Abernathy,
1
F. Acernese,
3,4
K. Ackley,
5
C. Adams,
6
T. Adams,
7
P. Addesso,
8
R. X. Adhikari,
1
V. B. Adya,
9
C. Affeldt,
9
M. Agathos,
10
K. Agatsuma,
10
N. Aggarwal,
11
O. D. Aguiar,
12
A. Ain,
13
P. Ajith,
14
B. Allen,
9,15,16
A. Allocca,
17,18
D. V. Amariutei,
5
S. B. Anderson,
1
W. G. Anderson,
15
K. Arai,
1
M. C. Araya,
1
C. C. Arceneaux,
19
J. S. Areeda,
20
N. Arnaud,
21
K. G. Arun,
22
G. Ashton,
23
M. Ast,
24
S. M. Aston,
6
P. Astone,
25
P. Aufmuth,
16
C. Aulbert,
9
S. Babak,
26
P. T. Baker,
27
F. Baldaccini,
28,29
G. Ballardin,
30
S. W. Ballmer,
31
J. C. Barayoga,
1
S. E. Barclay,
32
B. C. Barish,
1
D. Barker,
33
F. Barone,
3,4
B. Barr,
32
L. Barsotti,
11
M. Barsuglia,
34
D. Barta,
35
J. Bartlett,
33
I. Bartos,
36
R. Bassiri,
37
A. Basti,
17,18
J. C. Batch,
33
C. Baune,
9
V. Bavigadda,
30
M. Bazzan,
38,39
B. Behnke,
26
M. Bejger,
40
C. Belczynski,
41
A. S. Bell,
32
C. J. Bell,
32
B. K. Berger,
1
J. Bergman,
33
G. Bergmann,
9
C. P. L. Berry,
42
D. Bersanetti,
43,44
A. Bertolini,
10
J. Betzwieser,
6
S. Bhagwat,
31
R. Bhandare,
45
I. A. Bilenko,
46
G. Billingsley,
1
J. Birch,
6
R. Birney,
47
S. Biscans,
11
A. Bisht,
9,16
M. Bitossi,
30
C. Biwer,
31
M. A. Bizouard,
21
J. K. Blackburn,
1
C. D. Blair,
48
D. Blair,
48
R. M. Blair,
33
S. Bloemen,
10,49
O. Bock,
9
T. P. Bodiya,
11
M. Boer,
50
G. Bogaert,
50
C. Bogan,
9
A. Bohe,
26
P. Bojtos,
51
C. Bond,
42
F. Bondu,
52
R. Bonnand,
7
R. Bork,
1
V. Boschi,
18,17
S. Bose,
53,13
A. Bozzi,
30
C. Bradaschia,
18
P. R. Brady,
15
V. B. Braginsky,
46
M. Branchesi,
54,55
J. E. Brau,
56
T. Briant,
57
A. Brillet,
50
M. Brinkmann,
9
V. Brisson,
21
P. Brockill,
15
A. F. Brooks,
1
D. A. Brown,
31
D. Brown,
5
D. D. Brown,
42
N. M. Brown,
11
C. C. Buchanan,
2
A. Buikema,
11
T. Bulik,
41
H. J. Bulten,
58,10
A. Buonanno,
26,59
D. Buskulic,
7
C. Buy,
34
R. L. Byer,
37
L. Cadonati,
60
G. Cagnoli,
61
C. Cahillane,
1
J. Calderón Bustillo,
62,60
T. Callister,
1
E. Calloni,
63,4
J. B. Camp,
64
K. C. Cannon,
65
J. Cao,
66
C. D. Capano,
9
E. Capocasa,
34
F. Carbognani,
30
S. Caride,
67
J. Casanueva Diaz,
21
C. Casentini,
68,69
S. Caudill,
15
M. Cavaglià,
19
F. Cavalier,
21
R. Cavalieri,
30
G. Cella,
18
C. Cepeda,
1
L. Cerboni Baiardi,
54,55
G. Cerretani,
17,18
E. Cesarini,
68,69
R. Chakraborty,
1
T. Chalermsongsak,
1
S. J. Chamberlin,
15
M. Chan,
32
S. Chao,
70
P. Charlton,
71
E. Chassande-Mottin,
34
H. Y. Chen,
72
Y. Chen,
73
C. Cheng,
70
A. Chincarini,
44
A. Chiummo,
30
H. S. Cho,
74
M. Cho,
59
J. H. Chow,
75
N. Christensen,
76
Q. Chu,
48
S. Chua,
57
S. Chung,
48
G. Ciani,
5
F. Clara,
33
J. A. Clark,
60
F. Cleva,
50
E. Coccia,
68,77
P.-F. Cohadon,
57
A. Colla,
78,25
C. G. Collette,
79
M. Constancio, Jr.,
12
A. Conte,
78,25
L. Conti,
39
D. Cook,
33
T. R. Corbitt,
2
N. Cornish,
27
A. Corsi,
80
S. Cortese,
30
C. A. Costa,
12
M. W. Coughlin,
76
S. B. Coughlin,
81
J.-P. Coulon,
50
S. T. Countryman,
36
P. Couvares,
1
D. M. Coward,
48
M. J. Cowart,
6
D. C. Coyne,
1
R. Coyne,
80
K. Craig,
32
J. D. E. Creighton,
15
J. Cripe,
2
S. G. Crowder,
82
A. Cumming,
32
L. Cunningham,
32
E. Cuoco,
30
T. Dal Canton,
9
S. L. Danilishin,
32
S. D
’
Antonio,
69
K. Danzmann,
16,9
N. S. Darman,
83
V. Dattilo,
30
I. Dave,
45
H. P. Daveloza,
84
M. Davier,
21
G. S. Davies,
32
E. J. Daw,
85
R. Day,
30
D. DeBra,
37
G. Debreczeni,
35
J. Degallaix,
61
M. De Laurentis,
63,4
S. Deléglise,
57
W. Del Pozzo,
42
T. Denker,
9,16
T. Dent,
9
H. Dereli,
50
V. Dergachev,
1
R. DeRosa,
6
R. De Rosa,
63,4
R. DeSalvo,
8
S. Dhurandhar,
13
M. C. Díaz,
84
L. Di Fiore,
4
M. Di Giovanni,
78,25
A. Di Lieto,
17,18
I. Di Palma,
26,9
A. Di Virgilio,
18
G. Dojcinoski,
86
V. Dolique,
61
F. Donovan,
11
K. L. Dooley,
19
S. Doravari,
6
R. Douglas,
32
T. P. Downes,
15
M. Drago,
9,87,88
R. W. P. Drever,
1
J. C. Driggers,
33
Z. Du,
66
M. Ducrot,
7
S. E. Dwyer,
33
T. B. Edo,
85
M. C. Edwards,
76
A. Effler,
6
H.-B. Eggenstein,
9
P. Ehrens,
1
J. M. Eichholz,
5
S. S. Eikenberry,
5
W. Engels,
73
R. C. Essick,
11
T. Etzel,
1
M. Evans,
11
T. M. Evans,
6
R. Everett,
89
M. Factourovich,
36
V. Fafone,
68,69,77
H. Fair,
31
S. Fairhurst,
81
X. Fan,
66
Q. Fang,
48
S. Farinon,
44
B. Farr,
72
W. M. Farr,
42
M. Favata,
86
M. Fays,
81
H. Fehrmann,
9
M. M. Fejer,
37
I. Ferrante,
17,18
E. C. Ferreira,
12
F. Ferrini,
30
F. Fidecaro,
17,18
I. Fiori,
30
R. P. Fisher,
31
R. Flaminio,
61
M. Fletcher,
32
J.-D. Fournier,
50
S. Franco,
21
S. Frasca,
78,25
F. Frasconi,
18
Z. Frei,
51
A. Freise,
42
R. Frey,
56
V. Frey,
21
T. T. Fricke,
9
P. Fritschel,
11
V. V. Frolov,
6
P. Fulda,
5
M. Fyffe,
6
H. A. G. Gabbard,
19
J. R. Gair,
90
L. Gammaitoni,
28,29
S. G. Gaonkar,
13
F. Garufi,
63,4
A. Gatto,
34
G. Gaur,
91,92
N. Gehrels,
64
G. Gemme,
44
B. Gendre,
50
E. Genin,
30
A. Gennai,
18
J. George,
45
L. Gergely,
93
V. Germain,
7
A. Ghosh,
14
S. Ghosh,
10,49
J. A. Giaime,
2,6
K. D. Giardina,
6
A. Giazotto,
18
K. Gill,
94
A. Glaefke,
32
E. Goetz,
67
R. Goetz,
5
L. Gondan,
51
G. González,
2
J. M. Gonzalez Castro,
17,18
A. Gopakumar,
95
N. A. Gordon,
32
M. L. Gorodetsky,
46
S. E. Gossan,
1
M. Gosselin,
30
R. Gouaty,
7
C. Graef,
32
P. B. Graff,
64,59
M. Granata,
61
A. Grant,
32
S. Gras,
11
C. Gray,
33
G. Greco,
54,55
A. C. Green,
42
P. Groot,
49
H. Grote,
9
S. Grunewald,
26
G. M. Guidi,
54,55
X. Guo,
66
A. Gupta,
13
M. K. Gupta,
92
K. E. Gushwa,
1
E. K. Gustafson,
1
R. Gustafson,
67
J. J. Hacker,
20
B. R. Hall,
53
E. D. Hall,
1
G. Hammond,
32
M. Haney,
95
M. M. Hanke,
9
J. Hanks,
33
C. Hanna,
89
M. D. Hannam,
81
J. Hanson,
6
T. Hardwick,
2
J. Harms,
54,55
G. M. Harry,
96
I. W. Harry,
26
M. J. Hart,
32
M. T. Hartman,
5
C.-J. Haster,
42
K. Haughian,
32
A. Heidmann,
57
M. C. Heintze,
5,6
H. Heitmann,
50
P. Hello,
21
G. Hemming,
30
M. Hendry,
32
I. S. Heng,
32
J. Hennig,
32
A. W. Heptonstall,
1
M. Heurs,
9,16
S. Hild,
32
D. Hoak,
97
K. A. Hodge,
1
D. Hofman,
61
S. E. Hollitt,
98
K. Holt,
6
D. E. Holz,
72
P. Hopkins,
81
D. J. Hosken,
98
J. Hough,
32
E. A. Houston,
32
E. J. Howell,
48
Y. M. Hu,
32
S. Huang,
70
E. A. Huerta,
99
D. Huet,
21
B. Hughey,
94
S. Husa,
62
S. H. Huttner,
32
T. Huynh-Dinh,
6
A. Idrisy,
89
N. Indik,
9
D. R. Ingram,
33
R. Inta,
80
H. N. Isa,
32
J.-M. Isac,
57
M. Isi,
1
G. Islas,
20
T. Isogai,
11
B. R. Iyer,
14
K. Izumi,
33
T. Jacqmin,
57
H. Jang,
74
K. Jani,
60
P. Jaranowski,
100
S. Jawahar,
101
F. Jiménez-Forteza,
62
W. W. Johnson,
2
D. I. Jones,
23
R. Jones,
32
R. J. G. Jonker,
10
L. Ju,
48
K. Haris,
102
C. V. Kalaghatgi,
22
V. Kalogera,
103
S. Kandhasamy,
19
G. Kang,
74
J. B. Kanner,
1
S. Karki,
56
M. Kasprzack,
2,21,30
E. Katsavounidis,
11
W. Katzman,
6
S. Kaufer,
16
T. Kaur,
48
K. Kawabe,
33
F. Kawazoe,
9
F. Kéfélian,
50
M. S. Kehl,
65
PHYSICAL REVIEW D
93,
042005 (2016)
2470-0010
=
2016
=
93(4)
=
042005(19)
042005-1
© 2016 American Physical Society
D. Keitel,
9
D. B. Kelley,
31
W. Kells,
1
R. Kennedy,
85
J. S. Key,
84
A. Khalaidovski,
9
F. Y. Khalili,
46
S. Khan,
81
Z. Khan,
92
E. A. Khazanov,
104
N. Kijbunchoo,
33
C. Kim,
74
J. Kim,
105
K. Kim,
106
N. Kim,
74
N. Kim,
37
Y.-M. Kim,
105
E. J. King,
98
P. J. King,
33
D. L. Kinzel,
6
J. S. Kissel,
33
L. Kleybolte,
24
S. Klimenko,
5
S. M. Koehlenbeck,
9
K. Kokeyama,
2
S. Koley,
10
V. Kondrashov,
1
A. Kontos,
11
M. Korobko,
24
W. Z. Korth,
1
I. Kowalska,
41
D. B. Kozak,
1
V. Kringel,
9
B. Krishnan,
9
A. Królak,
107,108
C. Krueger,
16
G. Kuehn,
9
P. Kumar,
65
L. Kuo,
70
A. Kutynia,
107
B. D. Lackey,
31
M. Landry,
33
J. Lange,
109
B. Lantz,
37
P. D. Lasky,
110
A. Lazzarini,
1
C. Lazzaro,
60,39
P. Leaci,
26,78,25
S. Leavey,
32
E. Lebigot,
34,66
C. H. Lee,
105
H. K. Lee,
106
H. M. Lee,
111
K. Lee,
32
M. Leonardi,
87,88
J. R. Leong,
9
N. Leroy,
21
N. Letendre,
7
Y. Levin,
110
B. M. Levine,
33
T. G. F. Li,
1
A. Libson,
11
T. B. Littenberg,
103
N. A. Lockerbie,
101
J. Logue,
32
A. L. Lombardi,
97
J. E. Lord,
31
M. Lorenzini,
77
V. Loriette,
112
M. Lormand,
6
G. Losurdo,
55
J. D. Lough,
9,16
H. Lück,
16,9
A. P. Lundgren,
9
J. Luo,
76
R. Lynch,
11
Y. Ma,
48
T. MacDonald,
37
B. Machenschalk,
9
M. MacInnis,
11
D. M. Macleod,
2
F. Magaña-Sandoval,
31
R. M. Magee,
53
M. Mageswaran,
1
E. Majorana,
25
I. Maksimovic,
112
V. Malvezzi,
68,69
N. Man,
50
I. Mandel,
42
V. Mandic,
82
V. Mangano,
78,25,32
G. L. Mansell,
75
M. Manske,
15
M. Mantovani,
30
F. Marchesoni,
113,29
F. Marion,
7
S. Márka,
36
Z. Márka,
36
A. S. Markosyan,
37
E. Maros,
1
F. Martelli,
54,55
L. Martellini,
50
I. W. Martin,
32
R. M. Martin,
5
D. V. Martynov,
1
J. N. Marx,
1
K. Mason,
11
A. Masserot,
7
T. J. Massinger,
31
M. Masso-Reid,
32
F. Matichard,
11
L. Matone,
36
N. Mavalvala,
11
N. Mazumder,
53
G. Mazzolo,
9
R. McCarthy,
33
D. E. McClelland,
75
S. McCormick,
6
S. C. McGuire,
114
G. McIntyre,
1
J. McIver,
97
S. T. McWilliams,
99
D. Meacher,
50
G. D. Meadors,
26,9
J. Meidam,
10
A. Melatos,
83
G. Mendell,
33
D. Mendoza-Gandara,
9
R. A. Mercer,
15
M. Merzougui,
50
S. Meshkov,
1
C. Messenger,
32
C. Messick,
89
P. M. Meyers,
82
F. Mezzani,
25,78
H. Miao,
42
C. Michel,
61
H. Middleton,
42
E. E. Mikhailov,
115
L. Milano,
63,4
J. Miller,
11
M. Millhouse,
27
Y. Minenkov,
69
J. Ming,
26,9
S. Mirshekari,
116
C. Mishra,
14
S. Mitra,
13
V. P. Mitrofanov,
46
G. Mitselmakher,
5
R. Mittleman,
11
A. Moggi,
18
S. R. P. Mohapatra,
11
M. Montani,
54,55
B. C. Moore,
86
C. J. Moore,
90
D. Moraru,
33
G. Moreno,
33
S. R. Morriss,
84
K. Mossavi,
9
B. Mours,
7
C. M. Mow-Lowry,
42
C. L. Mueller,
5
G. Mueller,
5
A. W. Muir,
81
Arunava Mukherjee,
14
D. Mukherjee,
15
S. Mukherjee,
84
A. Mullavey,
6
J. Munch,
98
D. J. Murphy,
36
P. G. Murray,
32
A. Mytidis,
5
I. Nardecchia,
68,69
L. Naticchioni,
78,25
R. K. Nayak,
117
V. Necula,
5
K. Nedkova,
97
G. Nelemans,
10,49
M. Neri,
43,44
A. Neunzert,
67
G. Newton,
32
T. T. Nguyen,
75
A. B. Nielsen,
9
S. Nissanke,
49,10
A. Nitz,
31
F. Nocera,
30
D. Nolting,
6
M. E. N. Normandin,
84
L. K. Nuttall,
31
J. Oberling,
33
E. Ochsner,
15
J. O
’
Dell,
118
E. Oelker,
11
G. H. Ogin,
119
J. J. Oh,
120
S. H. Oh,
120
F. Ohme,
81
M. Oliver,
62
P. Oppermann,
9
Richard J. Oram,
6
B. O
’
Reilly,
6
R. O
’
Shaughnessy,
109
C. D. Ott,
73
D. J. Ottaway,
98
R. S. Ottens,
5
H. Overmier,
6
B. J. Owen,
80
A. Pai,
102
S. A. Pai,
45
J. R. Palamos,
56
O. Palashov,
104
C. Palomba,
25
A. Pal-Singh,
24
H. Pan,
70
C. Pankow,
15,103
F. Pannarale,
81
B. C. Pant,
45
F. Paoletti,
30,18
A. Paoli,
30
M. A. Papa,
26,15,9
H. R. Paris,
37
W. Parker,
6
D. Pascucci,
32
A. Pasqualetti,
30
R. Passaquieti,
17,18
D. Passuello,
18
Z. Patrick,
37
B. L. Pearlstone,
32
M. Pedraza,
1
R. Pedurand,
61
L. Pekowsky,
31
A. Pele,
6
S. Penn,
121
R. Pereira,
36
A. Perreca,
1
M. Phelps,
32
O. Piccinni,
78,25
M. Pichot,
50
F. Piergiovanni,
54,55
V. Pierro,
8
G. Pillant,
30
L. Pinard,
61
I. M. Pinto,
8
M. Pitkin,
32
R. Poggiani,
17,18
A. Post,
9
J. Powell,
32
J. Prasad,
13
V. Predoi,
81
S. S. Premachandra,
110
T. Prestegard,
82
L. R. Price,
1
M. Prijatelj,
30
M. Principe,
8
S. Privitera,
26
G. A. Prodi,
87,88
L. Prokhorov,
46
M. Punturo,
29
P. Puppo,
25
M. Pürrer,
81
H. Qi,
15
J. Qin,
48
V. Quetschke,
84
E. A. Quintero,
1
R. Quitzow-James,
56
F. J. Raab,
33
D. S. Rabeling,
75
H. Radkins,
33
P. Raffai,
51
S. Raja,
45
M. Rakhmanov,
84
P. Rapagnani,
78,25
V. Raymond,
26
M. Razzano,
17,18
V. Re,
68,69
J. Read,
20
C. M. Reed,
33
T. Regimbau,
50
L. Rei,
44
S. Reid,
47
D. H. Reitze,
1,5
H. Rew,
115
F. Ricci,
78,25
K. Riles,
67
N. A. Robertson,
1,32
R. Robie,
32
F. Robinet,
21
A. Rocchi,
69
L. Rolland,
7
J. G. Rollins,
1
V. J. Roma,
56
J. D. Romano,
84
R. Romano,
3,4
G. Romanov,
115
J. H. Romie,
6
D. Rosi
ń
ska,
122,40
S. Rowan,
32
A. Rüdiger,
9
P. Ruggi,
30
K. Ryan,
33
S. Sachdev,
1
T. Sadecki,
33
L. Sadeghian,
15
M. Saleem,
102
F. Salemi,
9
A. Samajdar,
117
L. Sammut,
83
E. J. Sanchez,
1
V. Sandberg,
33
B. Sandeen,
103
J. R. Sanders,
67
B. Sassolas,
61
P. R. Saulson,
31
O. Sauter,
67
R. Savage,
33
A. Sawadsky,
16
P. Schale,
56
R. Schilling,
9
,*
J. Schmidt,
9
P. Schmidt,
1,73
R. Schnabel,
24
R. M. S. Schofield,
56
A. Schönbeck,
24
E. Schreiber,
9
D. Schuette,
9,16
B. F. Schutz,
81
J. Scott,
32
S. M. Scott,
75
D. Sellers,
6
D. Sentenac,
30
V. Sequino,
68,69
A. Sergeev,
104
G. Serna,
20
Y. Setyawati,
49,10
A. Sevigny,
33
D. A. Shaddock,
75
S. Shah,
10,49
M. S. Shahriar,
103
M. Shaltev,
9
Z. Shao,
1
B. Shapiro,
37
P. Shawhan,
59
A. Sheperd,
15
D. H. Shoemaker,
11
D. M. Shoemaker,
60
K. Siellez,
50
X. Siemens,
15
D. Sigg,
33
A. D. Silva,
12
D. Simakov,
9
A. Singer,
1
L. P. Singer,
64
A. Singh,
26,9
R. Singh,
2
A. M. Sintes,
62
B. J. J. Slagmolen,
75
J. R. Smith,
20
N. D. Smith,
1
R. J. E. Smith,
1
E. J. Son,
120
B. Sorazu,
32
F. Sorrentino,
44
T. Souradeep,
13
A. K. Srivastava,
92
A. Staley,
36
M. Steinke,
9
J. Steinlechner,
32
S. Steinlechner,
32
D. Steinmeyer,
9,16
B. C. Stephens,
15
R. Stone,
84
K. A. Strain,
32
N. Straniero,
61
G. Stratta,
54,55
N. A. Strauss,
76
S. Strigin,
46
R. Sturani,
116
A. L. Stuver,
6
T. Z. Summerscales,
123
L. Sun,
83
P. J. Sutton,
81
B. L. Swinkels,
30
M. J. Szczepanczyk,
94
M. Tacca,
34
D. Talukder,
56
D. B. Tanner,
5
M. Tápai,
93
S. P. Tarabrin,
9
A. Taracchini,
26
R. Taylor,
1
T. Theeg,
9
M. P. Thirugnanasambandam,
1
E. G. Thomas,
42
M. Thomas,
6
P. Thomas,
33
K. A. Thorne,
6
K. S. Thorne,
73
E. Thrane,
110
S. Tiwari,
77
V. Tiwari,
81
C. Tomlinson,
85
M. Tonelli,
17,18
C. V. Torres,
84
,*
C. I. Torrie,
1
D. Töyrä,
42
F. Travasso,
28,29
G. Traylor,
6
D. Trifirò,
19
M. C. Tringali,
87,88
L. Trozzo,
124,18
M. Tse,
11
M. Turconi,
50
D. Tuyenbayev,
84
D. Ugolini,
125
C. S. Unnikrishnan,
95
A. L. Urban,
15
S. A. Usman,
31
H. Vahlbruch,
16
G. Vajente,
1
G. Valdes,
84
N. van Bakel,
10
M. van Beuzekom,
10
J. F. J. van den Brand,
58,10
C. van den Broeck,
10
L. van der Schaaf,
10
M. V. van der Sluys,
10,49
J. V. van Heijningen,
10
A. A. van Veggel,
32
M. Vardaro,
38,39
S. Vass,
1
M. Vasúth,
35
R. Vaulin,
11
B. P. ABBOTT
et al.
PHYSICAL REVIEW D
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042005 (2016)
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A. Vecchio,
42
G. Vedovato,
39
J. Veitch,
42
P. J. Veitch,
98
K. Venkateswara,
126
D. Verkindt,
7
F. Vetrano,
54,55
A. Viceré,
54,55
S. Vinciguerra,
42
J.-Y. Vinet,
50
S. Vitale,
11
T. Vo,
31
H. Vocca,
28,29
C. Vorvick,
33
W. D. Vousden,
42
S. P. Vyatchanin,
46
A. R. Wade,
75
L. E. Wade,
15
M. Wade,
15
M. Walker,
2
L. Wallace,
1
S. Walsh,
15
G. Wang,
77
H. Wang,
42
M. Wang,
42
X. Wang,
66
Y. Wang,
48
R. L. Ward,
75
J. Warner,
33
M. Was,
7
B. Weaver,
33
L.-W. Wei,
50
M. Weinert,
9
A. J. Weinstein,
1
R. Weiss,
11
T. Welborn,
6
L. Wen,
48
P. Weßels,
9
T. Westphal,
9
K. Wette,
9
J. T. Whelan,
109,9
D. J. White,
85
B. F. Whiting,
5
R. D. Williams,
1
A. R. Williamson,
81
J. L. Willis,
127
B. Willke,
16,9
M. H. Wimmer,
9,16
W. Winkler,
9
C. C. Wipf,
1
H. Wittel,
9,16
G. Woan,
32
J. Worden,
33
J. L. Wright,
32
G. Wu,
6
J. Yablon,
103
W. Yam,
11
H. Yamamoto,
1
C. C. Yancey,
59
H. Yu,
11
M. Yvert,
7
A. Zadro
ż
ny,
107
L. Zangrando,
39
M. Zanolin,
94
J.-P. Zendri,
39
M. Zevin,
103
F. Zhang,
11
L. Zhang,
1
M. Zhang,
115
Y. Zhang,
109
C. Zhao,
48
M. Zhou,
103
Z. Zhou,
103
X. J. Zhu,
48
M. E. Zucker,
11
S. E. Zuraw,
97
and J. Zweizig
1
(The LIGO Scientific Collaboration and the Virgo Collaboration)
†
1
LIGO, California Institute of Technology, Pasadena, California 91125, USA
2
Louisiana State University, Baton Rouge, Louisiana 70803, USA
3
Università di Salerno, Fisciano, I-84084 Salerno, Italy
4
INFN, Sezione di Napoli, Complesso Universitario di Monte S.Angelo, I-80126 Napoli, Italy
5
University of Florida, Gainesville, Florida 32611, USA
6
LIGO Livingston Observatory, Livingston, Louisiana 70754, USA
7
Laboratoire d
’
Annecy-le-Vieux de Physique des Particules (LAPP), Université Savoie Mont Blanc,
CNRS/IN2P3, F-74941 Annecy-le-Vieux, France
8
University of Sannio at Benevento, I-82100 Benevento, Italy
and INFN, Sezione di Napoli, I-80100 Napoli, Italy
9
Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-30167 Hannover, Germany
10
Nikhef, Science Park, 1098 XG Amsterdam, Netherlands
11
LIGO, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
12
Instituto Nacional de Pesquisas Espaciais, 12227-010 São José dos Campos, SP, Brazil
13
Inter-University Centre for Astronomy and Astrophysics, Pune 411007, India
14
International Centre for Theoretical Sciences, Tata Institute of Fundamental Research,
Bangalore 560012, India
15
University of Wisconsin-Milwaukee, Milwaukee, Wisconsin 53201, USA
16
Leibniz Universität Hannover, D-30167 Hannover, Germany
17
Università di Pisa, I-56127 Pisa, Italy
18
INFN, Sezione di Pisa, I-56127 Pisa, Italy
19
The University of Mississippi, University, Mississippi 38677, USA
20
California State University Fullerton, Fullerton, California 92831, USA
21
LAL, Univ Paris-Sud, CNRS/IN2P3, Orsay, France
22
Chennai Mathematical Institute, Chennai, India
23
University of Southampton, Southampton SO17 1BJ, United Kingdom
24
Universität Hamburg, D-22761 Hamburg, Germany
25
INFN, Sezione di Roma, I-00185 Roma, Italy
26
Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-14476 Potsdam-Golm, Germany
27
Montana State University, Bozeman, Montana 59717, USA
28
Università di Perugia, I-06123 Perugia, Italy
29
INFN, Sezione di Perugia, I-06123 Perugia, Italy
30
European Gravitational Observatory (EGO), I-56021 Cascina, Pisa, Italy
31
Syracuse University, Syracuse, New York 13244, USA
32
SUPA, University of Glasgow, Glasgow G12 8QQ, United Kingdom
33
LIGO Hanford Observatory, Richland, Washington 99352, USA
34
APC, AstroParticule et Cosmologie, Université Paris Diderot, CNRS/IN2P3, CEA/Irfu,
Observatoire de Paris, Sorbonne Paris Cité, F-75205 Paris Cedex 13, France
35
Wigner RCP, RMKI, H-1121 Budapest, Konkoly Thege Miklós út 29-33, Hungary
36
Columbia University, New York, New York 10027, USA
37
Stanford University, Stanford, California 94305, USA
38
Università di Padova, Dipartimento di Fisica e Astronomia, I-35131 Padova, Italy
39
INFN, Sezione di Padova, I-35131 Padova, Italy
40
CAMK-PAN, 00-716 Warsaw, Poland
41
Astronomical Observatory Warsaw University, 00-478 Warsaw, Poland
42
University of Birmingham, Birmingham B15 2TT, United Kingdom
43
Università degli Studi di Genova, I-16146 Genova, Italy
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...
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44
INFN, Sezione di Genova, I-16146 Genova, Italy
45
RRCAT, Indore MP 452013, India
46
Faculty of Physics, Lomonosov Moscow State University, Moscow 119991, Russia
47
SUPA, University of the West of Scotland, Paisley PA1 2BE, United Kingdom
48
University of Western Australia, Crawley, Western Australia 6009, Australia
49
Department of Astrophysics/IMAPP, Radboud University Nijmegen,
P.O. Box 9010, 6500 GL Nijmegen, Netherlands
50
ARTEMIS, Université Côte d
’
Azur, CNRS and Observatoire de la Côte d
’
Azur, F-06304 Nice, France
51
MTA Eötvös University,
“
Lendulet
”
Astrophysics Research Group, Budapest 1117, Hungary
52
Institut de Physique de Rennes, CNRS, Université de Rennes 1, F-35042 Rennes, France
53
Washington State University, Pullman, Washington 99164, USA
54
Università degli Studi di Urbino
“
Carlo Bo,
”
I-61029 Urbino, Italy
55
INFN, Sezione di Firenze, I-50019 Sesto Fiorentino, Firenze, Italy
56
University of Oregon, Eugene, Oregon 97403, USA
57
Laboratoire Kastler Brossel, UPMC-Sorbonne Universités, CNRS, ENS-PSL Research University,
Collège de France, F-75005 Paris, France
58
VU University Amsterdam, 1081 HV Amsterdam, Netherlands
59
University of Maryland, College Park, Maryland 20742, USA
60
Center for Relativistic Astrophysics and School of Physics, Georgia Institute of Technology,
Atlanta, Georgia 30332, USA
61
Laboratoire des Matériaux Avancés (LMA), IN2P3/CNRS, Université de Lyon,
F-69622 Villeurbanne, Lyon, France
62
Universitat de les Illes Balears
–
IEEC, E-07122 Palma de Mallorca, Spain
63
Università di Napoli
“
Federico II,
”
Complesso Universitario di Monte S.Angelo, I-80126 Napoli, Italy
64
NASA/Goddard Space Flight Center, Greenbelt, Maryland 20771, USA
65
Canadian Institute for Theoretical Astrophysics, University of Toronto, Toronto,
Ontario M5S 3H8, Canada
66
Tsinghua University, Beijing 100084, China
67
University of Michigan, Ann Arbor, Michigan 48109, USA
68
Università di Roma Tor Vergata, I-00133 Roma, Italy
69
INFN, Sezion e di Roma Tor Vergata, I-00133 Roma, Italy
70
National Tsing Hua University, Hsinchu City 30013, Taiwan, Republic of China
71
Charles Sturt University, Wagga Wagga, New South Wales 2678, Australia
72
University of Chicago, Chicago, Illinois 60637, USA
73
Caltech CaRT, Pasadena, California 91125, USA
74
Korea Institute of Science and Technology Information, Daejeon 305-806, Korea
75
Australian National University, Canberra, Australian Capital Territory 0200, Australia
76
Carleton College, Northfield, Minnesota 55057, USA
77
INFN, Gran Sasso Science Institute, I-67100 L
’
Aquila, Italy
78
Università di Roma
“
La Sapienza,
”
I-00185 Roma, Italy
79
University of Brussels, Brussels 1050, Belgium
80
Texas Tech University, Lubbock, Texas 79409, USA
81
Cardiff University, Cardiff CF24 3AA, United Kingdom
82
University of Minnesota, Minneapolis, Minnesota 55455, USA
83
The University of Melbourne, Parkville, Victoria 3010, Australia
84
The University of Texas Rio Grande Valley, Brownsville, Texas 78520, USA
85
The University of Sheffield, Sheffield S10 2TN, United Kingdom
86
Montclair State University, Montclair, New Jersey 07043, USA
87
Università di Trento, Dipartimento di Fisica, I-38123 Povo, Trento, Italy
88
INFN, Trento Institute for Fundamental Physics and Applications, I-38123 Povo, Trento, Italy
89
The Pennsylvania State University, University Park, Pennsylvania 16802, USA
90
University of Cambridge, Cambridge CB2 1TN, United Kingdom
91
Indian Institute of Technology, Gandhinagar Ahmedabad Gujarat 382424, India
92
Institute for Plasma Research, Bhat, Gandhinagar 382428, India
93
University of Szeged, Dóm tér 9, Szeged 6720, Hungary
94
Embry-Riddle Aeronautical University, Prescott, Arizona 86301, USA
95
Tata Institute for Fundamental Research, Mumbai 400005, India
96
American University, Washington, D.C. 20016, USA
97
University of Massachusetts-Amherst, Amherst, Massachusetts 01003, USA
98
University of Adelaide, Adelaide, South Australia 5005, Australia
B. P. ABBOTT
et al.
PHYSICAL REVIEW D
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99
West Virginia University, Morgantown, West Virginia 26506, USA
100
University of Bia
ł
ystok, 15-424 Bia
ł
ystok, Poland
101
SUPA, University of Strathclyde, Glasgow G1 1XQ, United Kingdom
102
IISER-TVM, CET Campus, Trivandrum Kerala 695016, India
103
Northwestern University, Evanston, Illinois 60208, USA
104
Institute of Applied Physics, Nizhny Novgorod, 603950, Russia
105
Pusan National University, Busan 609-735, Korea
106
Hanyang University, Seoul 133-791, Korea
107
NCBJ, 05-400
Ś
wierk-Otwock, Poland
108
IM-PAN, 00-956 Warsaw, Poland
109
Rochester Institute of Technology, Rochester, New York 14623, USA
110
Monash University, Victoria 3800, Australia
111
Seoul National University, Seoul 151-742, Korea
112
ESPCI, CNRS, F-75005 Paris, France
113
Università di Camerino, Dipartimento di Fisica, I-62032 Camerino, Italy
114
Southern University and A&M College, Baton Rouge, Louisiana 70813, USA
115
College of William and Mary, Williamsburg, Virginia 23187, USA
116
Instituto de Física Teórica, University Estadual Paulista/ICTP South American Institute for
Fundamental Research, São Paulo, São Paulo 01140-070, Brazil
117
IISER-Kolkata, Mohanpur, West Bengal 741252, India
118
Rutherford Appleton Laboratory, HSIC, Chilton, Didcot, Oxon OX11 0QX, United Kingdom
119
Whitman College, 280 Boyer Ave, Walla Walla, Washington 9936, USA
120
National Institute for Mathematical Sciences, Daejeon 305-390, Korea
121
Hobart and William Smith Colleges, Geneva, New York 14456, USA
122
Institute of Astronomy, 65-265 Zielona Góra, Poland
123
Andrews University, Berrien Springs, Michigan 49104, USA
124
Università di Siena, I-53100 Siena, Italy
125
Trinity University, San Antonio, Texas 78212, USA
126
University of Washington, Seattle, Washington 98195, USA
127
Abilene Christian University, Abilene, Texas 79699, USA
(Received 30 November 2015; published 12 February 2016)
We present the results of a search for long-duration gravitational wave transients in two sets of data
collected by the LIGO Hanford and LIGO Livingston detectors between November 5, 2005 and September
30, 2007, and July 7, 2009 and October 20, 2010, with a total observational time of 283.0 days and 132.9
days, respectively. The search targets gravitational wave transients of duration 10
–
500 s in a frequency
band of 40
–
1000 Hz, with minimal assumptions about the signal waveform, polarization, source direction,
or time of occurrence. All candidate triggers were consistent with the expected background; as a result we
set 90% confidence upper limits on the rate of long-duration gravitational wave transients for different
types of gravitational wave signals. For signals from black hole accretion disk instabilities, we set upper
limits on the source rate density between
3
.
4
×
10
−
5
and
9
.
4
×
10
−
4
Mpc
−
3
yr
−
1
at 90% confidence. These
are the first results from an all-sky search for unmodeled long-duration transient gravitational waves.
DOI:
10.1103/PhysRevD.93.042005
I. INTRODUCTION
The goal of the Laser Interferometer Gravitational-
Wave Observatory (LIGO)
[1]
and the Virgo detectors
[2]
is to directly detect and study gravitational waves
(GWs). The direct detection of GWs holds the promise
of testing general relativity in the strong-field regime, of
providing a new probe of objects such as black holes
and neutron stars, and of uncovering unanticipated new
astrophysics.
LIGO and Virgo have jointly acquired data that have
been used to search for many types of GW signals:
unmodeled bursts of short duration (
<
1
s)
[3
–
7]
, well-
modeled chirps emitted by binary systems of compact
objects
[8
–
12]
, continuous signals emitted by asymmetric
neutron stars
[13
–
20]
, as well as a stochastic background of
GWs
[21
–
24]
. For a complete review, see Ref.
[25]
. While
no GW sources have been observed by the first-generation
network of detectors, first detections are expected with the
next generation of ground-based detectors: advanced LIGO
[26]
, advanced Virgo
[27]
, and the cryogenic detector
KAGRA
[28]
. It is expected that the advanced detectors,
*
Deceased.
†
publication@ligo.org; publication@ego-gw.it
ALL-SKY SEARCH FOR LONG-DURATION
...
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operating at design sensitivity, will be capable of detecting
approximately 40 neutron star binary coalescences per year,
although significant uncertainties exist
[29]
.
Previous searches for unmodeled bursts of GWs
[3
–
5]
targeted source objects such as core-collapse supernovae
[30]
, neutron-star-to-black-hole collapse
[31]
, cosmic
string cusps
[32]
, binary black hole mergers
[33
–
35]
,
star-quakes in magnetars
[36]
, pulsar glitches
[37]
, and
signals associated with gamma-ray bursts (GRBs)
[38]
.
These burst searches typically look for signals of duration
1 s or shorter.
At the other end of the spectrum, searches for
persistent, unmodeled (stochastic) GW backgrounds have
also been conducted, including isotropic
[21]
, anisotropic
and point-source backgrounds
[22]
. This leaves the
parameter space of unmodeled transient GWs not fully
explored; indeed, multiple proposed astrophysical scenar-
ios predict long-duration GW transients lasting from a
few seconds to hundreds of seconds, or even longer, as
described in Sec.
II
. The first search for unmodeled long-
duration GW transients was conducted using LIGO data
from the S5 science run, in association with long GRBs
[39]
. In this paper, we apply a similar technique
[40]
in
order to search for long-lasting transient GW signals over
all sky directions and for all times. We utilize LIGO data
from the LIGO Hanford and Livingston detectors from
the S5 and S6 science runs, lasting from November 5,
2005 to September 30, 2007 and from July 7, 2009 to
October 20, 2010, respectively.
The organization of the paper is as follows: In Sec.
II
,we
summarize different types of long-duration transient signals
which may be observable by LIGO and Virgo. In Sec.
III
,
we describe the selection of the LIGO S5 and S6 science
run data that have been used for this study. We discuss the
search algorithm, background estimation, and data quality
methods in Sec.
IV
. In Sec.
V
, we evaluate the sensitivity of
the search to simulated GW waveforms. The results of the
search are presented in Sec.
VI
. We conclude with possible
improvements for a long-transient GW search using data
from the advanced LIGO and Virgo detectors in Sec.
VII
.
II. ASTROPHYSICAL SOURCES OF LONG
GW TRANSIENTS
Some of the most compelling astrophysical sources of
long GW transients are associated with extremely complex
dynamics and hydrodynamic instabilities following the
collapse of a massive star
’
s core in the context of core-
collapse supernovae and long GRBs
[30,40,41]
. Soon after
core collapse and the formation of a protoneutron star,
convective and other fluid instabilities (including standing
accretion shock instability
[42]
) may develop behind the
supernova shock wave as it transitions into an accretion
shock. In progenitor stars with rapidly rotating cores,
long-lasting, nonaxisymmetric rotational instabilities can
be triggered by corotation modes
[43
–
46]
. Long-duration
GW signals are expected from these violently aspherical
dynamics, following within tens of milliseconds of the
short-duration GW burst signal from core bounce and
protoneutron star formation. Given the turbulent and
chaotic nature of postbounce fluid dynamics, one expects
a stochastic GW signal that could last from a fraction of a
second to multiple seconds, and possibly even longer
[30,40,47
–
50]
.
After the launch of an at least initially successful
explosion, fallback accretion onto the newborn
neutron star may spin it up, leading to nonaxisymmetric
deformation and a characteristic upward chirp signal
(700 Hz
–
few kHz) as the spin frequency of the neutron
star increases over tens to hundreds of seconds
[51,52]
.
GW emission may eventually terminate when the neutron
star collapses to a black hole. The collapse process
and formation of the black hole itself will also produce
a short-duration GW burst
[53,54]
.
In the collapsar model for long GRBs
[55]
, a stellar-mass
black hole forms, surrounded by a massive, self-gravitating
accretion disk. This disk may be susceptible to various
nonaxisymmetric hydrodynamic and magnetohydrody-
namic instabilities which may lead to fragmentation and
inspiral of fragments into the central black hole (e.g.,
Refs.
[56,57]
). In an extreme scenario of such accretion
disk instabilities (ADIs), magnetically
“
suspended accre-
tion
”
is thought to extract spin energy from the black hole
and dissipate it via GW emission from nonaxisymmetric
disk modes and fragments
[58,59]
. The associated GW
signal is potentially long lasting (10
–
100 s) and predicted to
exhibit a characteristic downward chirp.
Finally, in magnetar models for long and short
GRBs (e.g., Refs.
[60,61]
), a long-lasting post-GRB GW
transient may be emitted by a magnetar undergoing
rotational or magnetic nonaxisymmetric deformation
(e.g., Refs.
[62,63]
).
III. DATA SELECTION
During the fifth LIGO science run (S5, November
5, 2005 to September 30, 2007), the 4 km and 2 km
detectors at Hanford, Washington (H1 and H2), and the
4 km detector at Livingston, Louisiana (L1), recorded data
for nearly two years. They were joined on May 18, 2007
by the Virgo detector (V1) in Pisa, Italy, which was
beginning its first science run. After a two-year period
of upgrades to the detectors and the decommissioning of
H2, the sixth LIGO and second and third Virgo scientific
runs were organized jointly from July 7, 2009 to October
10, 2010.
Among the four detectors, H1 and L1 achieved the
best strain sensitivity, reaching
≈
2
×
10
−
23
=
ffiffiffiffiffiffi
Hz
p
around
150 Hz in 2010
[64,65]
. Because of its reduced arm length,
H2 sensitivity was at least a factor of 2 lower than H1 on
average. V1 sensitivity varied over time, but was always
lower than the sensitivity of H1 and L1 by a factor between
B. P. ABBOTT
et al.
PHYSICAL REVIEW D
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1.5 and 5 at frequencies higher than 60 Hz. Moreover, the
H1-L1 pair live time was at least a factor 2 longer than the
live time of the H1-V1 and L1-V1 pairs added together.
Using Virgo data, however, could help with sky localization
of source candidates; unfortunately, the sky localization
was not implemented at the time of this search.
Consequently, including Virgo data in this analysis would
have increased the overall search sensitivity by only a few
percent or less at the cost of analyzing two additional pairs
of detectors. As a result, we have analyzed only S5 and
S6 data from the H1-L1 pair for this search.
In terms of frequency content, we restrict the analysis to
the 40
–
1000 Hz band. The lower limit is constrained by
seismic noise, which steeply increases at lower frequencies
in LIGO data. The upper limit is set to include the most
likely regions of frequency space for long-transient GWs,
while keeping the computational requirements of the search
at an acceptable level. We note that the frequency range of
our analysis includes the most sensitive band of the LIGO
detectors, namely 100
–
200 Hz.
Occasionally, the detectors are affected by instrumental
problems (data acquisition failures, misalignment of optical
cavities, etc.) or environmental conditions (bad weather,
seismic motion, etc.) that decrease their sensitivity and
increase the rate of data artifacts, or glitches. Most of these
periods have been identified and can be discarded from
the analysis using data quality flags
[66
–
69]
. These are
classified by each search into different categories depend-
ing on how the GW search is affected.
Category 1 data quality flags are used to define periods
when the data should not be searched for GW signals
because of serious problems, like invalid calibration. To
search for GW signals, the interferometers should be
locked and there should be no evidence of environmental
noise transients corrupting the measured signal. For this
search, we have used the category 1 data quality flags used
by searches for an isotropic stochastic background of GWs
[21,23]
. This list of flags is almost identical to what has
been used by the unmodeled all-sky searches for short-
duration GW transients
[3,4]
. We also discard times when
simulated signals are injected into the detectors through the
application of a differential force onto the mirrors.
Category 2 data quality flags are used to discard triggers
which pass all selection cuts in a search, but are clearly
associated with a detector malfunction or an environmental
condition
[68]
. In Sec.
IV C
, we explain which category 2
flags have been selected and how we use them in this
search.
Overall, we discard 5.8% and 2.2% of H1-L1 coincident
data with our choices of category 1 data quality flags for S5
and S6, respectively. The remaining coincident strain time
series are divided into 500 s intervals with 50% overlap.
Intervals smaller than 500 s are not considered. For the
H1-L1 pair, this results in a total observation time of
283.0 days during S5 and 132.9 days for S6.
IV. LONG TRANSIENT GW SEARCH PIPELINE
A. Search algorithm
The search algorithm we employ is based on the cross-
correlation of data from two GW detectors, as described in
Ref.
[40]
. This algorithm builds a frequency-time map
(
ft
-map) of the cross power computed from the strain time
series of two spatially separated detectors. A pattern
recognition algorithm is then used to identify clusters of
above-threshold pixels in the map, thereby defining candi-
date triggers. A similar algorithm has been used to search for
long-lasting GW signals in coincidence with long GRBs in
LIGO data
[39]
. Here we extend the method to carry out an
untriggered (all-sky, all-time) search, considerably increas-
ing the parameter space covered by previous searches.
Following Ref.
[40]
, each 500 s interval of coincident
data is divided into 50% overlapping, Hann-windowed,
1 s long segments. Strain data from each detector in the
given 1 s segment are then Fourier transformed, allowing
formation of
ft
-maps with a pixel size of
1
s×
1
Hz.
An estimator for GW power can be formed
[40]
:
ˆ
Y
ð
t
;
f
;
ˆ
Ω
Þ¼
2
N
Re
½
Q
IJ
ð
t
;
f
;
ˆ
Ω
Þ
~
s
⋆
I
ð
t
;
f
Þ
~
s
J
ð
t
;
f
Þ
:
ð
1
Þ
Here
t
is the start time of the pixel,
f
is the frequency of the
pixel,
ˆ
Ω
is the sky direction,
N
is a window normalization
factor, and
~
s
I
and
~
s
J
are the discrete Fourier transforms
of the strain data from GW detectors
I
and
J
. We use
the LIGO H1 and L1 detectors as the
I
and
J
detectors,
respectively. The optimal filter
Q
IJ
takes into account the
phase delay due to the spatial separation of the two
detectors,
Δ
~
x
IJ
, and the direction-dependent efficiency of
the detector pair,
ε
IJ
ð
t
;
ˆ
Ω
Þ
:
Q
IJ
ð
t
;
f
;
ˆ
Ω
Þ¼
e
2
π
if
Δ
~
x
IJ
·
ˆ
Ω
=c
ε
IJ
ð
t
;
ˆ
Ω
Þ
:
ð
2
Þ
The pair efficiency is defined by
ε
IJ
ð
t
;
ˆ
Ω
Þ¼
1
2
X
A
F
A
I
ð
t
;
ˆ
Ω
Þ
F
A
J
ð
t
;
ˆ
Ω
Þ
;
ð
3
Þ
where
F
A
I
ð
t
;
ˆ
Ω
Þ
is the antenna factor for detector
I
and
A
is
the polarization state of the incoming GW
[40]
.An
estimator for the variance of the
ˆ
Y
ð
t
;
f;
ˆ
Ω
Þ
statistic is then
given by
ˆ
σ
2
Y
ð
t
;
f
;
ˆ
Ω
Þ¼
1
2
j
Q
IJ
ð
t
;
f
;
ˆ
Ω
Þj
2
P
adj
I
ð
t
;
f
Þ
P
adj
J
ð
t
;
f
Þ
;
ð
4
Þ
where
P
adj
I
ð
t
;
f
Þ
is the average one-sided power spectrum
for detector
I
, calculated by using the data in eight
nonoverlapping segments on each side of time segment
t
[40]
. We can then define the cross-correlation signal-to-
noise ratio (SNR) in a single pixel,
ρ
:
ALL-SKY SEARCH FOR LONG-DURATION
...
PHYSICAL REVIEW D
93,
042005 (2016)
042005-7
ρ
ð
t
;
f
;
ˆ
Ω
Þ¼
ˆ
Y
ð
t
;
f
;
ˆ
Ω
Þ
=
ˆ
σ
Y
ð
t
;
f
;
ˆ
Ω
Þ
:
ð
5
Þ
Because this is proportional to strain squared, it is an
energy SNR, rather than an amplitude SNR.
This statistic is designed such that true GW signals
should induce positive definite
ρ
when the correct filter is
used (i.e., the sky direction
ˆ
Ω
is known). Consequently,
using a wrong sky direction in the filter results in reduced or
even negative
ρ
for real signals. Figure
1
shows an example
ft
-map of
ρ
containing a simulated GW signal with a
known sky position.
Next, a seed-based clustering algorithm
[70]
is applied
to the
ρ
ft
-map to identify significant clusters of pixels.
In particular, the clustering algorithm applies a threshold
of
j
ρ
j
≥
1
to identify seed pixels, and then groups these
seed pixels that are located within a fixed distance
(two pixels) of each other into a cluster. These parameters
were determined through empirical testing with simulated
long-transient GW signals similar to those used in this
search (discussed further in Sec.
VA
). The resulting
clusters (denoted
Γ
) are ranked using a weighted sum of
the individual pixel values of
ˆ
Y
and
ˆ
σ
Y
:
SNR
Γ
ð
ˆ
Ω
Þ¼
P
t
;
f
∈
Γ
ˆ
Y
ð
t
;
f
;
ˆ
Ω
Þ
ˆ
σ
−
2
Y
ð
t
;
f
;
ˆ
Ω
Þ
ð
P
t
;
f
∈
Γ
ˆ
σ
−
2
Y
ð
t
;
f
;
ˆ
Ω
ÞÞ
1
=
2
:
ð
6
Þ
SNR
Γ
ð
ˆ
Ω
Þ
represents the signal-to-noise ratio of the
cluster
Γ
.
In principle, this pattern recognition algorithm could be
applied for every sky direction
ˆ
Ω
, since each sky direction
is associated with a different filter
Q
IJ
ð
t
;
f
;
ˆ
Ω
Þ
. However,
this procedure is prohibitively expensive from a computa-
tional standpoint. We have therefore modified the seed-
based clustering algorithm to cluster both pixels with
positive
ρ
and those with negative
ρ
(arising when an
incorrect sky direction is used in the filter). Since the sky
direction is not known in an all-sky search, this modifica-
tion allows for the recovery of some of the power that
would normally be lost due to a suboptimal choice of sky
direction in the filter.
The algorithm is applied to each
ft
-map a certain number
of times, each iteration corresponding to a different sky
direction. The sky directions are chosen randomly, but are
fixed for each stretch ofuninterrupted science data. Different
methods for choosing the sky directions were studied,
including using only sky directions where the detector
network had high sensitivity and choosing the set of sky
directions to span the set of possible signal time delays. The
results indicated that sky-direction choice did not have a
significant impact on the sensitivity of the search.
We also studied the effect that the number of sky
directions used had on the search sensitivity. We found
that the search sensitivity increased approximately loga-
rithmically with the number of sky directions, while the
computational time increased linearly with the number of
sky directions. The results of our empirical studies indi-
cated that using five sky directions gave the optimal
balance between computational time and search sensitivity.
This clustering strategy results in a loss of sensitivity of
≈
10%
–
20%
for the waveforms considered in this search
as compared to a strategy using hundreds of sky directions
and clustering only positive pixels. However, this strategy
increases the computational speed of the search by a factor
of 100 and is necessary to make the search computationally
feasible.
We also apply two data-cleaning techniques concurrently
with the data processing. First, we remove frequency bins
that are known to be contaminated by instrumental and
environmental effects. This includes the violin resonance
modes of the suspensions, power line harmonics, and
sinusoidal signals injected for calibration purposes. In total,
we removed 47 1 Hz
–
wide frequency bins from the S5 data,
and 64 1 Hz
–
wide frequency bins from the S6 data. Second,
we require the waveforms observed by the two detectors to
be consistent with each other, so as to suppress instrumental
artifacts (glitches) that affect onlyone of the detectors. This is
achieved by the use of a consistency-check algorithm
[71]
which compares the power spectra from each detector, taking
into account the antenna factors.
B. Background estimation
An important aspect of any GW search is understanding
the background of accidental triggers due to detector noise;
this is crucial for preventing false identification of noise
triggers as GW candidates. To estimate the false alarm rate
(FAR), i.e. the rate of accidental triggers due to detector
Time [s]
Frequency [Hz]
20
40
60
80
100
150
200
250
ρ
−5
0
5
FIG. 1.
ft
-map of
ρ
(cross-correlation signal-to-noise ratio)
using simulated Gaussian data. A simulated GW signal from
an accretion disk instability
[58,59]
(model waveform ADI-E, see
Table
I
) with known sky position is added to the data stream and
is visible as a bright, narrow-band track. Blurring around the track
is due to the usage of adjacent time segments in estimating
ˆ
σ
Y
;
the estimate of
ˆ
σ
Y
in these bins is affected by the presence of the
GW signal.
B. P. ABBOTT
et al.
PHYSICAL REVIEW D
93,
042005 (2016)
042005-8