Search for continuous gravitational waves from neutron stars
in globular cluster NGC 6544
B. P. Abbott,
1
R. Abbott,
1
T. D. Abbott,
2
M. R. Abernathy,
3
F. Acernese,
4,5
K. Ackley,
6
C. Adams,
7
T. Adams,
8
P. Addesso,
9
R. X. Adhikari,
1
V. B. Adya,
10
C. Affeldt,
10
M. Agathos,
11
K. Agatsuma,
11
N. Aggarwal,
12
O. D. Aguiar,
13
L. Aiello,
14,15
A. Ain,
16
B. Allen,
10,18,19
A. Allocca,
20,21
P. A. Altin,
22
S. B. Anderson,
1
W. G. Anderson,
18
K. Arai,
1
M. C. Araya,
1
C. C. Arceneaux,
23
J. S. Areeda,
24
N. Arnaud,
25
K. G. Arun,
26
S. Ascenzi,
27,15
G. Ashton,
28
M. Ast,
29
S. M. Aston,
7
P. Astone,
30
P. Aufmuth,
19
C. Aulbert,
10
S. Babak,
31
P. Bacon,
32
M. K. M. Bader,
11
P. T. Baker,
33
F. Baldaccini,
34,35
G. Ballardin,
36
S. W. Ballmer,
37
J. C. Barayoga,
1
S. E. Barclay,
38
B. C. Barish,
1
D. Barker,
39
F. Barone,
4,5
B. Barr,
38
L. Barsotti,
12
M. Barsuglia,
32
D. Barta,
40
J. Bartlett,
39
I. Bartos,
41
R. Bassiri,
42
A. Basti,
20,21
J. C. Batch,
39
C. Baune,
10
V. Bavigadda,
36
M. Bazzan,
43,44
M. Bejger,
45
A. S. Bell,
38
B. K. Berger,
1
G. Bergmann,
10
C. P. L. Berry,
46
D. Bersanetti,
47,48
A. Bertolini,
11
J. Betzwieser,
7
S. Bhagwat,
37
R. Bhandare,
49
I. A. Bilenko,
50
G. Billingsley,
1
J. Birch,
7
R. Birney,
51
S. Biscans,
12
A. Bisht,
10,19
M. Bitossi,
36
C. Biwer,
37
M. A. Bizouard,
25
J. K. Blackburn,
1
C. D. Blair,
52
D. G. Blair,
52
R. M. Blair,
39
S. Bloemen,
53
O. Bock,
10
M. Boer,
54
G. Bogaert,
54
C. Bogan,
10
A. Bohe,
31
C. Bond,
46
F. Bondu,
55
R. Bonnand,
8
B. A. Boom,
11
R. Bork,
1
V. Boschi,
20,21
S. Bose,
56,16
Y. Bouffanais,
32
A. Bozzi,
36
C. Bradaschia,
21
P. R. Brady,
18
V. B. Braginsky,
50
,*
M. Branchesi,
57,58
J. E. Brau,
59
T. Briant,
60
A. Brillet,
54
M. Brinkmann,
10
V. Brisson,
25
P. Brockill,
18
J. E. Broida,
61
A. F. Brooks,
1
D. A. Brown,
37
D. D. Brown,
46
N. M. Brown,
12
S. Brunett,
1
C. C. Buchanan,
2
A. Buikema,
12
T. Bulik,
62
H. J. Bulten,
63,11
A. Buonanno,
31,64
D. Buskulic,
8
C. Buy,
32
R. L. Byer,
42
M. Cabero,
10
L. Cadonati,
65
G. Cagnoli,
66,67
C. Cahillane,
1
J. Calderón Bustillo,
65
T. Callister,
1
E. Calloni,
68,5
J. B. Camp,
69
K. C. Cannon,
70
J. Cao,
71
C. D. Capano,
10
E. Capocasa,
32
F. Carbognani,
36
S. Caride,
72
J. Casanueva Diaz,
25
C. Casentini,
27,15
S. Caudill,
18
M. Cavaglià,
23
F. Cavalier,
25
R. Cavalieri,
36
G. Cella,
21
C. B. Cepeda,
1
L. Cerboni Baiardi,
57,58
G. Cerretani,
20,21
E. Cesarini,
27,15
S. J. Chamberlin,
73
M. Chan,
38
S. Chao,
74
P. Charlton,
75
E. Chassande-Mottin,
32
B. D. Cheeseboro,
76
H. Y. Chen,
77
Y. Chen,
78
C. Cheng,
74
A. Chincarini,
48
A. Chiummo,
36
H. S. Cho,
79
M. Cho,
64
J. H. Chow,
22
N. Christensen,
61
Q. Chu,
52
S. Chua,
60
S. Chung,
52
G. Ciani,
6
F. Clara,
39
J. A. Clark,
65
F. Cleva,
54
E. Coccia,
27,14
P.-F. Cohadon,
60
A. Colla,
80,30
C. G. Collette,
81
L. Cominsky,
82
M. Constancio, Jr.,
13
A. Conte,
80,30
L. Conti,
44
D. Cook,
39
T. R. Corbitt,
2
N. Cornish,
33
A. Corsi,
72
S. Cortese,
36
C. A. Costa,
13
M. W. Coughlin,
61
S. B. Coughlin,
83
J.-P. Coulon,
54
S. T. Countryman,
41
P. Couvares,
1
E. E. Cowan,
65
D. M. Coward,
52
M. J. Cowart,
7
D. C. Coyne,
1
R. Coyne,
72
K. Craig,
38
J. D. E. Creighton,
18
T. Creighton,
88
J. Cripe,
2
S. G. Crowder,
84
A. Cumming,
38
L. Cunningham,
38
E. Cuoco,
36
T. Dal Canton,
10
S. L. Danilishin,
38
S. D
’
Antonio,
15
K. Danzmann,
19,10
N. S. Darman,
85
A. Dasgupta,
86
C. F. Da Silva Costa,
6
V. Dattilo,
36
I. Dave,
49
M. Davier,
25
G. S. Davies,
38
E. J. Daw,
87
R. Day,
36
S. De,
37
D. DeBra,
42
G. Debreczeni,
40
J. Degallaix,
66
M. De Laurentis,
68,5
S. Deléglise,
60
W. Del Pozzo,
46
T. Denker,
10
T. Dent,
10
V. Dergachev,
1
R. De Rosa,
68,5
R. T. DeRosa,
7
R. DeSalvo,
9
R. C. Devine,
76
S. Dhurandhar,
16
M. C. Díaz,
88
L. Di Fiore,
5
M. Di Giovanni,
89,90
T. Di Girolamo,
68,5
A. Di Lieto,
20,21
S. Di Pace,
80,30
I. Di Palma,
31,80,30
A. Di Virgilio,
21
V. Dolique,
66
F. Donovan,
12
K. L. Dooley,
23
S. Doravari,
10
R. Douglas,
38
T. P. Downes,
18
M. Drago,
10
R. W. P. Drever,
1
J. C. Driggers,
39
M. Ducrot,
8
S. E. Dwyer,
39
T. B. Edo,
87
M. C. Edwards,
61
A. Effler,
7
H.-B. Eggenstein,
10
P. Ehrens,
1
J. Eichholz,
6,1
S. S. Eikenberry,
6
W. Engels,
78
R. C. Essick,
12
T. Etzel,
1
M. Evans,
12
T. M. Evans,
7
R. Everett,
73
M. Factourovich,
41
V. Fafone,
27,15
H. Fair,
37
X. Fan,
71
Q. Fang,
52
S. Farinon,
48
B. Farr,
77
W. M. Farr,
46
M. Favata,
92
M. Fays,
91
H. Fehrmann,
10
M. M. Fejer,
42
E. Fenyvesi,
93
I. Ferrante,
20,21
E. C. Ferreira,
13
F. Ferrini,
36
F. Fidecaro,
20,21
I. Fiori,
36
D. Fiorucci,
32
R. P. Fisher,
37
R. Flaminio,
66,94
M. Fletcher,
38
J.-D. Fournier,
54
S. Frasca,
80,30
F. Frasconi,
21
Z. Frei,
93
A. Freise,
46
R. Frey,
59
V. Frey,
25
P. Fritschel,
12
V. V. Frolov,
7
P. Fulda,
6
M. Fyffe,
7
H. A. G. Gabbard,
23
J. R. Gair,
95
L. Gammaitoni,
34
S. G. Gaonkar,
16
F. Garufi,
68,5
G. Gaur,
96,86
N. Gehrels,
69
G. Gemme,
48
P. Geng,
88
E. Genin,
36
A. Gennai,
21
J. George,
49
L. Gergely,
97
V. Germain,
8
Abhirup Ghosh,
17
Archisman Ghosh,
17
S. Ghosh,
53,11
J. A. Giaime,
2,7
K. D. Giardina,
7
A. Giazotto,
21
K. Gill,
98
A. Glaefke,
38
E. Goetz,
39
R. Goetz,
6
L. Gondan,
93
G. González,
2
J. M. Gonzalez Castro,
20,21
A. Gopakumar,
99
N. A. Gordon,
38
M. L. Gorodetsky,
50
S. E. Gossan,
1
M. Gosselin,
36
R. Gouaty,
8
A. Grado,
100,5
C. Graef,
38
P. B. Graff,
64
M. Granata,
66
A. Grant,
38
S. Gras,
12
C. Gray,
39
G. Greco,
57,58
A. C. Green,
46
P. Groot,
53
H. Grote,
10
S. Grunewald,
31
G. M. Guidi,
57,58
X. Guo,
71
A. Gupta,
16
M. K. Gupta,
86
K. E. Gushwa,
1
E. K. Gustafson,
1
R. Gustafson,
101
J. J. Hacker,
24
B. R. Hall,
56
E. D. Hall,
1
G. Hammond,
38
M. Haney,
99
M. M. Hanke,
10
J. Hanks,
39
C. Hanna,
73
J. Hanson,
7
T. Hardwick,
2
J. Harms,
57,58
G. M. Harry,
3
I. W. Harry,
31
M. J. Hart,
38
M. T. Hartman,
6
C.-J. Haster,
46
K. Haughian,
38
A. Heidmann,
60
M. C. Heintze,
7
H. Heitmann,
54
P. Hello,
25
G. Hemming,
36
M. Hendry,
38
I. S. Heng,
38
J. Hennig,
38
J. Henry,
102
A. W. Heptonstall,
1
M. Heurs,
10,19
S. Hild,
38
D. Hoak,
36
D. Hofman,
66
K. Holt,
7
D. E. Holz,
77
P. Hopkins,
91
J. Hough,
38
E. A. Houston,
38
E. J. Howell,
52
Y. M. Hu,
10
S. Huang,
74
E. A. Huerta,
103
D. Huet,
25
B. Hughey,
98
S. Husa,
104
S. H. Huttner,
38
T. Huynh-Dinh,
7
N. Indik,
10
D. R. Ingram,
39
R. Inta,
72
H. N. Isa,
38
J.-M. Isac,
60
M. Isi,
1
T. Isogai,
12
PHYSICAL REVIEW D
95,
082005 (2017)
2470-0010
=
2017
=
95(8)
=
082005(15)
082005-1
© 2017 American Physical Society
B. R. Iyer,
17
K. Izumi,
39
T. Jacqmin,
60
H. Jang,
79
K. Jani,
65
P. Jaranowski,
105
S. Jawahar,
106
L. Jian,
52
F. Jiménez-Forteza,
104
W. W. Johnson,
2
D. I. Jones,
28
R. Jones,
38
R. J. G. Jonker,
11
L. Ju,
52
Haris K.,
107
C. V. Kalaghatgi,
91
V. Kalogera,
83
S. Kandhasamy,
23
G. Kang,
79
J. B. Kanner,
1
S. J. Kapadia,
10
S. Karki,
59
K. S. Karvinen,
10
M. Kasprzack,
36,2
E. Katsavounidis,
12
W. Katzman,
7
S. Kaufer,
19
T. Kaur,
52
K. Kawabe,
39
F. Kéfélian,
54
M. S. Kehl,
108
D. Keitel,
104
D. B. Kelley,
37
W. Kells,
1
R. Kennedy,
87
J. S. Key,
88
F. Y. Khalili,
50
I. Khan,
14
S. Khan,
91
Z. Khan,
86
E. A. Khazanov,
109
N. Kijbunchoo,
39
Chi-Woong Kim,
79
Chunglee Kim,
79
J. Kim,
110
K. Kim,
111
N. Kim,
42
W. Kim,
112
Y.-M. Kim,
110
S. J. Kimbrell,
65
E. J. King,
112
P. J. King,
39
J. S. Kissel,
39
B. Klein,
83
L. Kleybolte,
29
S. Klimenko,
6
S. M. Koehlenbeck,
10
S. Koley,
11
V. Kondrashov,
1
A. Kontos,
12
M. Korobko,
29
W. Z. Korth,
1
I. Kowalska,
62
D. B. Kozak,
1
V. Kringel,
10
B. Krishnan,
10
A. Królak,
113,114
C. Krueger,
19
G. Kuehn,
10
P. Kumar,
108
R. Kumar,
86
L. Kuo,
74
A. Kutynia,
113
B. D. Lackey,
37
M. Landry,
39
J. Lange,
102
B. Lantz,
42
P. D. Lasky,
115
M. Laxen,
7
C. Lazzaro,
44
P. Leaci,
80,30
S. Leavey,
38
E. O. Lebigot,
32,71
C. H. Lee,
110
H. K. Lee,
111
H. M. Lee,
116
K. Lee,
38
A. Lenon,
37
M. Leonardi,
89,90
J. R. Leong,
10
N. Leroy,
25
N. Letendre,
8
Y. Levin,
115
J. B. Lewis,
1
T. G. F. Li,
117
A. Libson,
12
T. B. Littenberg,
118
N. A. Lockerbie,
106
A. L. Lombardi,
119
L. T. London,
91
J. E. Lord,
37
M. Lorenzini,
14,15
V. Loriette,
120
M. Lormand,
7
G. Losurdo,
58
J. D. Lough,
10,19
H. Lück,
19,10
A. P. Lundgren,
10
R. Lynch,
12
Y. Ma,
52
B. Machenschalk,
10
M. MacInnis,
12
D. M. Macleod,
2
F. Magaña-Sandoval,
37
L. Magaña Zertuche,
37
R. M. Magee,
56
E. Majorana,
30
I. Maksimovic,
120
V. Malvezzi,
27,15
N. Man,
54
V. Mandic,
84
V. Mangano,
38
G. L. Mansell,
22
M. Manske,
18
M. Mantovani,
36
F. Marchesoni,
121,35
F. Marion,
8
S. Márka,
41
Z. Márka,
41
A. S. Markosyan,
42
E. Maros,
1
F. Martelli,
57,58
L. Martellini,
54
I. W. Martin,
38
D. V. Martynov,
12
J. N. Marx,
1
K. Mason,
12
A. Masserot,
8
T. J. Massinger,
37
M. Masso-Reid,
38
S. Mastrogiovanni,
80,30
F. Matichard,
12
L. Matone,
41
N. Mavalvala,
12
N. Mazumder,
56
R. McCarthy,
39
D. E. McClelland,
22
S. McCormick,
7
S. C. McGuire,
122
G. McIntyre,
1
J. McIver,
1
D. J. McManus,
22
T. McRae,
22
S. T. McWilliams,
76
D. Meacher,
73
G. D. Meadors,
31,10
J. Meidam,
11
A. Melatos,
85
G. Mendell,
39
R. A. Mercer,
18
E. L. Merilh,
39
M. Merzougui,
54
S. Meshkov,
1
C. Messenger,
38
C. Messick,
73
R. Metzdorff,
60
P. M. Meyers,
84
F. Mezzani,
30,80
H. Miao,
46
C. Michel,
66
H. Middleton,
46
E. E. Mikhailov,
123
L. Milano,
68,5
A. L. Miller,
6,80,30
A. Miller,
83
B. B. Miller,
83
J. Miller,
12
M. Millhouse,
33
Y. Minenkov,
15
J. Ming,
31
S. Mirshekari,
124
C. Mishra,
17
S. Mitra,
16
V. P. Mitrofanov,
50
G. Mitselmakher,
6
R. Mittleman,
12
A. Moggi,
21
M. Mohan,
36
S. R. P. Mohapatra,
12
M. Montani,
57,58
B. C. Moore,
92
C. J. Moore,
125
D. Moraru,
39
G. Moreno,
39
S. R. Morriss,
88
K. Mossavi,
10
B. Mours,
8
C. M. Mow-Lowry,
46
G. Mueller,
6
A. W. Muir,
91
Arunava Mukherjee,
17
D. Mukherjee,
18
S. Mukherjee,
88
N. Mukund,
16
A. Mullavey,
7
J. Munch,
112
D. J. Murphy,
41
P. G. Murray,
38
A. Mytidis,
6
I. Nardecchia,
27,15
L. Naticchioni,
80,30
R. K. Nayak,
126
K. Nedkova,
119
G. Nelemans,
53,11
T. J. N. Nelson,
7
M. Neri,
47,48
A. Neunzert,
101
G. Newton,
38
T. T. Nguyen,
22
A. B. Nielsen,
10
S. Nissanke,
53,11
A. Nitz,
10
F. Nocera,
36
D. Nolting,
7
M. E. N. Normandin,
88
L. K. Nuttall,
37
J. Oberling,
39
E. Ochsner,
18
J. O
’
Dell,
127
E. Oelker,
12
G. H. Ogin,
128
J. J. Oh,
129
S. H. Oh,
129
F. Ohme,
91
M. Oliver,
104
P. Oppermann,
10
Richard J. Oram,
7
B. O
’
Reilly,
7
R. O
’
Shaughnessy,
102
D. J. Ottaway,
112
H. Overmier,
7
B. J. Owen,
72
A. Pai,
107
S. A. Pai,
49
J. R. Palamos,
59
O. Palashov,
109
C. Palomba,
30
A. Pal-Singh,
29
H. Pan,
74
C. Pankow,
83
F. Pannarale,
91
B. C. Pant,
49
F. Paoletti,
36,21
A. Paoli,
36
M. A. Papa,
31,18,10
H. R. Paris,
42
W. Parker,
7
D. Pascucci,
38
A. Pasqualetti,
36
R. Passaquieti,
20,21
D. Passuello,
21
P. Patel,
1
B. Patricelli,
20,21
Z. Patrick,
42
B. L. Pearlstone,
38
M. Pedraza,
1
R. Pedurand,
66,130
L. Pekowsky,
37
A. Pele,
7
S. Penn,
131
A. Perreca,
1
L. M. Perri,
83
M. Phelps,
38
O. J. Piccinni,
80,30
M. Pichot,
54
F. Piergiovanni,
57,58
V. Pierro,
9
G. Pillant,
36
L. Pinard,
66
I. M. Pinto,
9
M. Pitkin,
38
M. Poe,
18
R. Poggiani,
20,21
P. Popolizio,
36
A. Post,
10
J. Powell,
38
J. Prasad,
16
V. Predoi,
91
T. Prestegard,
84
L. R. Price,
1
M. Prijatelj,
10,36
M. Principe,
9
S. Privitera,
31
R. Prix,
10
G. A. Prodi,
89,90
L. Prokhorov,
50
O. Puncken,
10
M. Punturo,
35
P. Puppo,
30
M. Pürrer,
31
H. Qi,
18
J. Qin,
52
S. Qiu,
115
V. Quetschke,
88
E. A. Quintero,
1
R. Quitzow-James,
59
F. J. Raab,
39
D. S. Rabeling,
22
H. Radkins,
39
P. Raffai,
93
S. Raja,
49
C. Rajan,
49
M. Rakhmanov,
88
P. Rapagnani,
80,30
V. Raymond,
31
M. Razzano,
20,21
V. Re,
27
J. Read,
24
C. M. Reed,
39
T. Regimbau,
54
L. Rei,
48
S. Reid,
51
D. H. Reitze,
1,6
H. Rew,
123
S. D. Reyes,
37
F. Ricci,
80,30
K. Riles,
101
M. Rizzo,
102
N. A. Robertson,
1,38
R. Robie,
38
F. Robinet,
25
A. Rocchi,
15
L. Rolland,
8
J. G. Rollins,
1
V. J. Roma,
59
R. Romano,
4,5
G. Romanov,
123
J. H. Romie,
7
D. Rosi
ń
ska,
132,45
S. Rowan,
38
A. Rüdiger,
10
P. Ruggi,
36
K. Ryan,
39
S. Sachdev,
1
T. Sadecki,
39
L. Sadeghian,
18
M. Sakellariadou,
133
L. Salconi,
36
M. Saleem,
107
F. Salemi,
10
A. Samajdar,
126
L. Sammut,
115
E. J. Sanchez,
1
V. Sandberg,
39
B. Sandeen,
83
J. R. Sanders,
37
B. Sassolas,
66
P. R. Saulson,
37
O. E. S. Sauter,
101
R. L. Savage,
39
A. Sawadsky,
19
P. Schale,
59
R. Schilling,
10
,*
J. Schmidt,
10
P. Schmidt,
1,78
R. Schnabel,
29
R. M. S. Schofield,
59
A. Schönbeck,
29
E. Schreiber,
10
D. Schuette,
10,19
B. F. Schutz,
91,31
J. Scott,
38
S. M. Scott,
22
D. Sellers,
7
A. S. Sengupta,
96
D. Sentenac,
36
V. Sequino,
27,15
A. Sergeev,
109
Y. Setyawati,
53,11
D. A. Shaddock,
22
T. Shaffer,
39
M. S. Shahriar,
83
M. Shaltev,
10
B. Shapiro,
42
P. Shawhan,
64
A. Sheperd,
18
D. H. Shoemaker,
12
D. M. Shoemaker,
65
K. Siellez,
65
X. Siemens,
18
M. Sieniawska,
45
D. Sigg,
39
A. D. Silva,
13
A. Singer,
1
L. P. Singer,
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A. Singh,
31,10,19
R. Singh,
2
A. Singhal,
14
A. M. Sintes,
104
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22
J. R. Smith,
24
N. D. Smith,
1
R. J. E. Smith,
1
E. J. Son,
129
B. Sorazu,
38
F. Sorrentino,
48
T. Souradeep,
16
A. K. Srivastava,
86
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41
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10
J. Steinlechner,
38
B. P. ABBOTT
et al.
PHYSICAL REVIEW D
95,
082005 (2017)
082005-2
S. Steinlechner,
38
D. Steinmeyer,
10,19
B. C. Stephens,
18
R. Stone,
88
K. A. Strain,
38
N. Straniero,
66
G. Stratta,
57,58
N. A. Strauss,
61
S. Strigin,
50
R. Sturani,
124
A. L. Stuver,
7
T. Z. Summerscales,
134
L. Sun,
85
S. Sunil,
86
P. J. Sutton,
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M. J. Szczepa
ń
czyk,
98
M. Tacca,
32
D. Talukder,
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97
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31
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1
T. Theeg,
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1
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46
M. Thomas,
7
P. Thomas,
39
K. A. Thorne,
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E. Thrane,
115
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14,90
V. Tiwari,
91
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106
K. Toland,
38
C. Tomlinson,
87
M. Tonelli,
20,21
Z. Tornasi,
38
C. V. Torres,
88
,*
C. I. Torrie,
1
D. Töyrä,
46
F. Travasso,
34,35
G. Traylor,
7
D. Trifirò,
23
M. C. Tringali,
89,90
L. Trozzo,
135,21
M. Tse,
12
M. Turconi,
54
D. Tuyenbayev,
88
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136
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99
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18
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37
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19
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1
G. Valdes,
88
N. van Bakel,
11
M. van Beuzekom,
11
J. F. J. van den Brand,
63,11
C. Van Den Broeck,
11
D. C. Vander-Hyde,
37
L. van der Schaaf,
11
J. V. van Heijningen,
11
A. A. van Veggel,
38
M. Vardaro,
43,44
S. Vass,
1
M. Vasúth,
40
R. Vaulin,
12
A. Vecchio,
46
G. Vedovato,
44
J. Veitch,
46
P. J. Veitch,
112
K. Venkateswara,
137
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8
F. Vetrano,
57,58
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57,58
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46
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51
J.-Y. Vinet,
54
S. Vitale,
12
T. Vo,
37
H. Vocca,
34,35
C. Vorvick,
39
D. V. Voss,
6
W. D. Vousden,
46
S. P. Vyatchanin,
50
A. R. Wade,
22
L. E. Wade,
138
M. Wade,
138
M. Walker,
2
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1
S. Walsh,
31,10
G. Wang,
14,58
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46
M. Wang,
46
X. Wang,
71
Y. Wang,
52
R. L. Ward,
22
J. Warner,
39
M. Was,
8
B. Weaver,
39
L.-W. Wei,
54
M. Weinert,
10
A. J. Weinstein,
1
R. Weiss,
12
L. Wen,
52
P. Weßels,
10
T. Westphal,
10
K. Wette,
10
J. T. Whelan,
102
B. F. Whiting,
6
R. D. Williams,
1
A. R. Williamson,
91
J. L. Willis,
139
B. Willke,
19,10
M. H. Wimmer,
10,19
W. Winkler,
10
C. C. Wipf,
1
H. Wittel,
10,19
G. Woan,
38
J. Woehler,
10
J. Worden,
39
J. L. Wright,
38
D. S. Wu,
10
G. Wu,
7
J. Yablon,
83
W. Yam,
12
H. Yamamoto,
1
C. C. Yancey,
64
H. Yu,
12
M. Yvert,
8
A. Zadro
ż
ny,
113
L. Zangrando,
44
M. Zanolin,
98
J.-P. Zendri,
44
M. Zevin,
83
L. Zhang,
1
M. Zhang,
123
Y. Zhang,
102
C. Zhao,
52
M. Zhou,
83
Z. Zhou,
83
X. J. Zhu,
52
M. E. Zucker,
1,12
S. E. Zuraw,
119
J. Zweizig,
1
(LIGO Scientific Collaboration and Virgo Collaboration) and S. Sigurdsson
73
1
LIGO, California Institute of Technology, Pasadena, California 91125, USA
2
Louisiana State University, Baton Rouge, Louisiana 70803, USA
3
American University, Washington, D.C. 20016, USA
4
Università di Salerno, Fisciano, I-84084 Salerno, Italy
5
INFN, Sezione di Napoli, Complesso Universitario di Monte S.Angelo, I-80126 Napoli, Italy
6
University of Florida, Gainesville, Florida 32611, USA
7
LIGO Livingston Observatory, Livingston, Louisiana 70754, USA
8
Laboratoire d
’
Annecy-le-Vieux de Physique des Particules (LAPP), Université Savoie Mont Blanc,
CNRS/IN2P3, F-74941 Annecy-le-Vieux, France
9
University of Sannio at Benevento, I-82100 Benevento, Italy
and INFN, Sezione di Napoli, I-80100 Napoli, Italy
10
Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-30167 Hannover, Germany
11
Nikhef, Science Park, 1098 XG Amsterdam, Netherlands
12
LIGO, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
13
Instituto Nacional de Pesquisas Espaciais, 12227-010 São José dos Campos, São Paulo, Brazil
14
INFN, Gran Sasso Science Institute, I-67100 L
’
Aquila, Italy
15
INFN, Sezione di Roma Tor Vergata, I-00133 Roma, Italy
16
Inter-University Centre for Astronomy and Astrophysics, Pune 411007, India
17
International Centre for Theoretical Sciences, Tata Institute of Fundamental Research,
Bangalore 560012, India
18
University of Wisconsin-Milwaukee, Milwaukee, Wisconsin 53201, USA
19
Leibniz Universität Hannover, D-30167 Hannover, Germany
20
Università di Pisa, I-56127 Pisa, Italy
21
INFN, Sezione di Pisa, I-56127 Pisa, Italy
22
Australian National University, Canberra, Australian Capital Territory 0200, Australia
23
The University of Mississippi, University, Mississippi 38677, USA
24
California State University Fullerton, Fullerton, California 92831, USA
25
LAL, University of Paris-Sud, CNRS/IN2P3, Université Paris-Saclay, F-91898 Orsay, France
26
Chennai Mathematical Institute, Chennai 603103, India
27
Università di Roma Tor Vergata, I-00133 Roma, Italy
28
University of Southampton, Southampton SO17 1BJ, United Kingdom
29
Universität Hamburg, D-22761 Hamburg, Germany
30
INFN, Sezione di Roma, I-00185 Roma, Italy
31
Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-14476 Potsdam-Golm, Germany
32
APC, AstroParticule et Cosmologie, Université Paris Diderot, CNRS/IN2P3, CEA/Irfu,
Observatoire de Paris, Sorbonne Paris Cité, F-75205 Paris Cedex 13, France
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33
Montana State University, Bozeman, Montana 59717, USA
34
Università di Perugia, I-06123 Perugia, Italy
35
INFN, Sezione di Perugia, I-06123 Perugia, Italy
36
European Gravitational Observatory (EGO), I-56021 Cascina, Pisa, Italy
37
Syracuse University, Syracuse, New York 13244, USA
38
SUPA, University of Glasgow, Glasgow G12 8QQ, United Kingdom
39
LIGO Hanford Observatory, Richland, Washington 99352, USA
40
Wigner RCP, RMKI, H-1121 Budapest, Konkoly Thege Miklós út 29-33, Hungary
41
Columbia University, New York, New York 10027, USA
42
Stanford University, Stanford, California 94305, USA
43
Università di Padova, Dipartimento di Fisica e Astronomia, I-35131 Padova, Italy
44
INFN, Sezione di Padova, I-35131 Padova, Italy
45
CAMK-PAN, 00-716 Warsaw, Poland
46
University of Birmingham, Birmingham B15 2TT, United Kingdom
47
Università degli Studi di Genova, I-16146 Genova, Italy
48
INFN, Sezione di Genova, I-16146 Genova, Italy
49
RRCAT, Indore MP 452013, India
50
Faculty of Physics, Lomonosov Moscow State University, Moscow 119991, Russia
51
SUPA, University of the West of Scotland, Paisley PA1 2BE, United Kingdom
52
University of Western Australia, Crawley, Western Australia 6009, Australia
53
Department of Astrophysics/IMAPP, Radboud University Nijmegen,
P.O. Box 9010, 6500 GL Nijmegen, Netherlands
54
Artemis, Université Côte d
’
Azur, CNRS, Observatoire Côte d
’
Azur, CS 34229, Nice cedex 4, France
55
Institut de Physique de Rennes, CNRS, Université de Rennes 1, F-35042 Rennes, France
56
Washington State University, Pullman, Washington 99164, USA
57
Università degli Studi di Urbino
“
Carlo Bo
”
, I-61029 Urbino, Italy
58
INFN, Sezione di Firenze, I-50019 Sesto Fiorentino, Firenze, Italy
59
University of Oregon, Eugene, Oregon 97403, USA
60
Laboratoire Kastler Brossel, UPMC-Sorbonne Universités, CNRS, ENS-PSL Research University,
Collège de France, F-75005 Paris, France
61
Carleton College, Northfield, Minnesota 55057, USA
62
Astronomical Observatory Warsaw University, 00-478 Warsaw, Poland
63
VU University Amsterdam, 1081 HV Amsterdam, Netherlands
64
University of Maryland, College Park, Maryland 20742, USA
65
Center for Relativistic Astrophysics and School of Physics, Georgia Institute of Technology,
Atlanta, Georgia 30332, USA
66
Laboratoire des Matériaux Avancés (LMA), CNRS/IN2P3, F-69622 Villeurbanne, France
67
Université Claude Bernard Lyon 1, F-69622 Villeurbanne, France
68
Università di Napoli
“
Federico II
”
, Complesso Universitario di Monte S.Angelo, I-80126 Napoli, Italy
69
NASA/Goddard Space Flight Center, Greenbelt, Maryland 20771, USA
70
RESCEU, University of Tokyo, Tokyo, 113-0033, Japan
71
Tsinghua University, Beijing 100084, China
72
Texas Tech University, Lubbock, Texas 79409, USA
73
The Pennsylvania State University, University Park, Pennsylvania 16802, USA
74
National Tsing Hua University, Hsinchu City, 30013 Taiwan, Republic of China
75
Charles Sturt University, Wagga Wagga, New South Wales 2678, Australia
76
West Virginia University, Morgantown, West Virginia 26506, USA
77
University of Chicago, Chicago, Illinois 60637, USA
78
Caltech CaRT, Pasadena, California 91125, USA
79
Korea Institute of Science and Technology Information, Daejeon 305-806, Korea
80
Università di Roma
“
La Sapienza
”
, I-00185 Roma, Italy
81
University of Brussels, Brussels 1050, Belgium
82
Sonoma State University, Rohnert Park, California 94928, USA
83
Center for Interdisciplinary Exploration & Research in Astrophysics (CIERA), Northwestern University,
Evanston, Illinois 60208, USA
84
University of Minnesota, Minneapolis, Minnesota 55455, USA
85
The University of Melbourne, Parkville, Victoria 3010, Australia
86
Institute for Plasma Research, Bhat, Gandhinagar 382428, India
87
The University of Sheffield, Sheffield S10 2TN, United Kingdom
88
The University of Texas Rio Grande Valley, Brownsville, Texas 78520, USA
B. P. ABBOTT
et al.
PHYSICAL REVIEW D
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89
Università di Trento, Dipartimento di Fisica, I-38123 Povo, Trento, Italy
90
INFN, Trento Institute for Fundamental Physics and Applications, I-38123 Povo, Trento, Italy
91
Cardiff University, Cardiff CF24 3AA, United Kingdom
92
Montclair State University, Montclair, New Jersey 07043, USA
93
MTA Eötvös University,
“
Lendulet
”
Astrophysics Research Group, Budapest 1117, Hungary
94
National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan
95
School of Mathematics, University of Edinburgh, Edinburgh EH9 3FD, United Kingdom
96
Indian Institute of Technology, Gandhinagar Ahmedabad Gujarat 382424, India
97
University of Szeged, Dóm tér 9, Szeged 6720, Hungary
98
Embry-Riddle Aeronautical University, Prescott, Arizona 86301, USA
99
Tata Institute of Fundamental Research, Mumbai 400005, India
100
INAF, Osservatorio Astronomico di Capodimonte, I-80131 Napoli, Italy
101
University of Michigan, Ann Arbor, Michigan 48109, USA
102
Rochester Institute of Technology, Rochester, New York 14623, USA
103
NCSA, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
104
Universitat de les Illes Balears, IAC3
—
IEEC, E-07122 Palma de Mallorca, Spain
105
University of Bia
ł
ystok, 15-424 Bia
ł
ystok, Poland
106
SUPA, University of Strathclyde, Glasgow G1 1XQ, United Kingdom
107
IISER-TVM, CET Campus, Trivandrum, Kerala 695016, India
108
Canadian Institute for Theoretical Astrophysics, University of Toronto,
Toronto, Ontario M5S 3H8, Canada
109
Institute of Applied Physics, Nizhny Novgorod 603950, Russia
110
Pusan National University, Busan 609-735, Korea
111
Hanyang University, Seoul 133-791, Korea
112
University of Adelaide, Adelaide, South Australia 5005, Australia
113
NCBJ, 05-400
Ś
wierk-Otwock, Poland
114
IM-PAN, 00-956 Warsaw, Poland
115
Monash University, Victoria 3800, Australia
116
Seoul National University, Seoul 151-742, Korea
117
The Chinese University of Hong Kong, Shatin, NT, Hong Kong SAR, China
118
University of Alabama in Huntsville, Huntsville, Alabama 35899, USA
119
University of Massachusetts-Amherst, Amherst, Massachusetts 01003, USA
120
ESPCI, CNRS, F-75005 Paris, France
121
Università di Camerino, Dipartimento di Fisica, I-62032 Camerino, Italy
122
Southern University and A&M College, Baton Rouge, Louisiana 70813, USA
123
College of William and Mary, Williamsburg, Virginia 23187, USA
124
Instituto de Física Teórica, University Estadual Paulista/ICTP South American Institute for
Fundamental Research, São Paulo, São Paulo 01140-070, Brazil
125
University of Cambridge, Cambridge CB2 1TN, United Kingdom
126
IISER-Kolkata, Mohanpur, West Bengal 741252, India
127
Rutherford Appleton Laboratory, HSIC, Chilton, Didcot, Oxon OX11 0QX, United Kingdom
128
Whitman College, 345 Boyer Avenue, Walla Walla, Washington 99362 USA
129
National Institute for Mathematical Sciences, Daejeon 305-390, Korea
130
Université de Lyon, F-69361 Lyon, France
131
Hobart and William Smith Colleges, Geneva, New York 14456, USA
132
Janusz Gil Institute of Astronomy, University of Zielona Góra, 65-265 Zielona Góra, Poland
133
King
’
s College London, University of London, London WC2R 2LS, United Kingdom
134
Andrews University, Berrien Springs, Michigan 49104, USA
135
Università di Siena, I-53100 Siena, Italy
136
Trinity University, San Antonio, Texas 78212, USA
137
University of Washington, Seattle, Washington 98195, USA
138
Kenyon College, Gambier, Ohio 43022, USA
139
Abilene Christian University, Abilene, Texas 79699, USA
(Received 12 July 2016; published 19 April 2017)
We describe a directed search for continuous gravitational waves in data from the sixth initial LIGO
science run. The target was the nearby globular cluster NGC 6544 at a distance of
≈
2
.
7
kpc. The search
*
Deceased.
SEARCH FOR CONTINUOUS GRAVITATIONAL WAVES
...
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covered a broad band of frequencies along with first and second frequency derivatives for a fixed sky
position. The search coherently integrated data from the two LIGO interferometers over a time span of
9.2 days using the matched-filtering
F
-statistic. We found no gravitational-wave signals and set
95% confidence upper limits as stringent as
6
.
0
×
10
−
25
on intrinsic strain and
8
.
5
×
10
−
6
on fiducial
ellipticity. These values beat the indirect limits from energy conservation for stars with characteristic spin-
down ages older than 300 years and are within the range of theoretical predictions for possible neutron-star
ellipticities. An important feature of this search was use of a barycentric resampling algorithm which
substantially reduced computational cost; this method is used extensively in searches of Advanced LIGO
and Virgo detector data.
DOI:
10.1103/PhysRevD.95.082005
I. INTRODUCTION
The LIGO Scientific Collaboration and Virgo
Collaboration have undertaken numerous searches for
continuous gravitational waves (GW). None has yet
detected a signal, but many have placed interesting upper
limits (ULs) on possible sources. These searches have
generally been drawn from one of three types.
Targeted searches are aimed at a single known
pulsar, with a known precise timing solution. The first
search for continuous waves, using data from the first
initial LIGO science run (S1), was of this type
[1]
,and
subsequent searches have probed the Crab and Vela
pulsars, among others
[2
–
7]
. A number of these most
recent searches have been able to set direct upper limits
on GW emission comparable to or stricter than the
indirect
“
spin-down limits
”
(derived from energy con-
servation, as well as the distance from Earth of the target,
its gravitational-wave frequency, and the frequency
’
sfirst
derivative, the spin down) for a few of the pulsars
searched.
All-sky searches, as their name suggests, survey the
entire sky for neutron stars not seen as pulsars. These are
very computationally costly, searching over wide frequency
bands and covering large ranges of spin-down parameters
[8
–
17]
. The latest of these have incorporated new tech-
niques to cover possible binary parameters as well
[18]
.
Recent all-sky searches have set direct upper limits close to
indirect upper limits derived from galactic neutron-star
population simulations
[19]
.
Directed searches sit between these two extremes.
As in the all-sky case, their targets are neutron stars not
seen as pulsars, so that the frequency and other
parameters are unknown. They focus, however, on a
known sky location (and therefore a known detector-
frame Doppler modulation). This directionality allows
for searching over a wide range of frequencies and
frequency derivatives while remaining much cheaper
computationally than an all-sky search without sacri-
ficing sensitivity. This approach was first used in a
search for the accreting neutron star in the low-mass
x-ray binary Sco X-1
[9,20,21]
.
The search for the central compact object in the super-
nova remnant Cassiopeia A (Cas A)
[22]
was the first
directed search for a young neutron star without electro-
magnetically detected pulsation, motivated by the idea that
young neutron stars might be promising emitters of
continuous GW. The Cas A search
[22]
set upper limits
on GW strain which beat an indirect limit derived from
energy conservation and the age of the remnant
[23]
over a
wide frequency band. Other directed searches have since
followed in its footsteps, using different data analysis
methods, for supernova 1987A and unseen neutron stars
near the galactic Center
[21,24]
. Most methodologically
similar to this search and the S5 Cas A search was a recent
search for nine supernova remnants
[25]
, which also used
fully coherent integration over observation times on the
order of 10 days.
In this article, we describe a search of data from the sixth
initial LIGO science run (S6) for potential young isolated
neutron stars with no observed electromagnetic pulsations
in the nearby (
d
≈
2
.
7
kpc) globular cluster NGC 6544.
Globular clusters are unlikely to contain young neutron
stars, but in these dense environments older neutron stars
may be subject to debris accretion (see Sec.
II C
) or other
events which could render them detectable as gravitational-
wave sources. This particular globular cluster was chosen
so that a computationally feasible coherent search similar
to
[22]
could beat the age-based indirect limits on GW
emission.
The search did not find a GW signal, and hence the
main result is a set of upper limits on strain amplitude,
fiducial ellipticity, and
r
-mode amplitude
α
, similar to those
presented in
[22]
. An important new feature of the search
described here was use of a barycentric resampling algo-
rithm which substantially reduced computational cost,
allowing a search over a larger parameter space using a
longer coherence time (see Sec.
II D
). This barycentric
resampling method is used extensively in searches of
Advanced LIGO and Virgo detector data.
This article is structured as follows: In Sec.
II
we present
the method, implementation, and results of the search. The
upper limits set in the absence of a signal are presented in
Sec.
III
, and the results are discussed in Sec.
IV
.
B. P. ABBOTT
et al.
PHYSICAL REVIEW D
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II. SEARCHES
A. Data selection
The sixth initial LIGO science run (S6) extended from
July 7, 2009 21
∶
00:00 UTC (GPS 931035615) to October
21, 2010 00
∶
00:00 UTC (GPS 971654415) and included
two initial LIGO detectors with 4-km arm lengths, H1 at
LIGO Hanford Observatory near Hanford, Washington and
L1 at LIGO Livingston Observatory near Livingston,
Louisiana.
After optimization at fixed computing cost determined
an optimum coherence time of 9.2 days (see Sec.
II D
), two
different methods were used to determine which data would
be searched, producing two different 9.2-day stretches.
Both were searched, allowing for the comparison of search
results between them.
The first method was to look for the most sensitive
average data from S6. This was done by taking nine week-
long data samples from each detector spaced roughly
55 days apart, giving nine evenly spaced weeks throughout
the duration of S6. The data samples used are shown in
Table
I
. We chose four representative frequencies (100,
200, 400, and 600 Hz) and generated joint-detector strain
noise power spectral densities (PSDs) in 1-Hz bands about
these frequencies, using 0.01-Hz binning. The sensitivity
h
sens
was then taken to be
h
j
sens
¼
0
B
@
1
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ð
1
=
100
Þ
·
P
100
i
¼
0
ð
S
i
h
ð
f
i
ÞÞ
−
1
q
1
C
A
j
ð
1
Þ
where
S
i
h
ð
f
Þ
represents the PSD value of the
i
th bin, at
frequency
f
i
, and the index
j
runs from 1 through 4 and
represents the four representative frequencies (note that
this is not an actual estimate of detectable strain). At all
four frequencies, detector sensitivity improved as the run
progressed. Using this figure of merit, it was found that the
final nine days of S6 yielded the most sensitive data stretch
for all four frequencies: October 11
–
20, 2010 (GPS
970840605
–
971621841).
An alternate data selection scheme
[22,25]
, which takes
detector duty cycle into account, is to maximize the figure
of merit
X
k;f
1
S
h
ð
f
Þ
ð
2
Þ
where
S
h
ð
f
Þ
represents the strain noise power spectral
density at frequency
f
in the
k
th short Fourier transform
(SFT), and the sum is taken across all frequencies
f
in the
search band and all SFTs in a given 9.2-day (see Sec.
II D
below) observation time. The SFT format is science-mode
detector data split into 1800s segments, band-pass filtered
from 40
–
2035 Hz, Tukey windowed in the time domain,
and Fourier transformed. This method favored a different
data stretch: July 24
–
August 2, 2010 (GPS 964007133
–
964803598). This second data stretch had slightly worse
average sensitivity than the first, but a higher detector
livetime: our first (October) data set contained 374 SFTs
(202 from Hanford and 172 from Livingston) with average
sensitivity
h
200
Hz
sens
¼
1
.
92
×
10
−
23
; the second (July
–
August) data set contained 642 SFTs (368 from Hanford
and 274 from Livingston) with average sensitivity
h
200
Hz
sens
¼
1
.
95
×
10
−
23
.
B. Analysis method
The analysis was based on matched filtering, the optimal
method for detecting signals of known functional form.
To obtain that form we assumed that the potential target
neutron star did not glitch (suffer an abrupt frequency
jump) or have significant timing noise (additional, possibly
stochastic, time dependence of the frequency)
[26]
during
the observation. We also neglected third and higher
derivatives of the GW frequency, based on the time span
and range of
_
f
and
̈
f
(the first two derivatives) covered. The
precise expression for the interferometer strain response
h
ð
t
Þ
to an incoming continuous GW also includes ampli-
tude and phase modulation by the changing of the beam
patterns as the interferometer rotates with the Earth. It
depends on the source
’
s sky location and orientation angles,
as well as on the parameters of the interferometer. The full
expression can be found in
[27]
.
The detection statistic used was the multi-interferometer
F
-statistic
[28]
, based on the single-interferometer
F
-statistic
[27]
. This combines the results of matched
filters for the signal in a way that is computationally
fast and nearly optimal
[29]
. Assuming Gaussian noise,
2
F
is drawn from a
χ
2
distribution with 4 degrees of
freedom.
We used the implementation of the
F
-statistic in
the LALSuite package
[30]
. In particular most of the
computing power of the search was spent in the
TABLE I. The weeks sampled to find the most sensitive S6
data. Times are given both in GPS and UTC calendar dates.
S6 sampling times
Label
GPS start GPS end
Dates (UTC)
Week 1 931053000 931657800
Jul 8
–
15, 2009
Week 2 936053000 936657800
Sep 3
–
10, 2009
Week 3 941053000 941657800
Oct 31
–
Nov 7, 2009
Week 4 946053000 946657800 Dec 28, 2009
–
Jan 4, 2010
Week 5 951053000 951657800
Feb 24
–
Mar 3, 2010
Week 6 956053000 956657800
Apr 23
–
30, 2010
Week 7 961053000 961657800
Jun 20
–
27, 2010
Week 8 966053000 966657800
Aug 17
–
24, 2010
Week 9 971053000 971657800
Oct 14
–
21, 2010
SEARCH FOR CONTINUOUS GRAVITATIONAL WAVES
...
PHYSICAL REVIEW D
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082005 (2017)
082005-7
ComputeFStatistic_v2
program. Unlike the version
used in preceding methodologically similar searches
[22,25]
, this one implements an option to use a barycentric
resampling algorithm which significantly speeds up the
analysis.
The method of efficiently computing the
F
-statistic by
barycentering and fast-Fourier transforming the data was
first proposed in
[27]
. Various implementations of this
method have been developed and used in previous
searches, such as
[31
–
33]
. Here we are using a new
LALSuite
[30]
implementation of this method, which
evolved out of
[33]
, and which will be described in more
detail in a future publication. It converts the input data into
a heterodyned, down-sampled time series weighted by
antenna-pattern coefficients, and then resamples this time
series at the Solar System barycenter using an interpolation
technique. The resampled time series is then Fourier
transformed to return to the frequency domain, and from
there the
F
-statistic is calculated. For this search, both
single-detector and multidetector
F
-statistics were calcu-
lated (see the vetoes section below).
Timing tests run on a modern processor (ca. 2011)
showed that the resampling code was more than 24 times
faster in terms of seconds per template per SFT. This
improvement, by more than an order of magnitude, was
used to perform a deeper search over a wider parameter
space than previously possible for the computational cost
incurred (see target selection and search parameters below).
C. Target selection
Unlike previous directed searches, this one targets a
globular cluster. Since stars in globular clusters are very
old, it is unlikely that a young neutron star will be found in
such an environment. However, some neutron stars are
known to be accompanied by debris disks
[34]
and even
planets
[35
–
37]
. In the densely populated core of a globular
cluster, close encounters may stimulate bombardment
episodes as debris orbits are destabilized, akin to cometary
bombardments in our Solar System when the Oort cloud is
perturbed
[38]
. A neutron star which has recently accreted
debris could have it funneled by the magnetic field into
mountains which relax on time scales of
10
5
–
10
8
years
[39]
and emit gravitational waves for that duration. Other
mechanisms are likely to last a few years at most
[40]
.
Hence an old neutron star could be a good gravitational-
wave source with a low spin-down age.
The first step in picking a globular cluster is a figure of
merit based on that for directed searches for supernova
remnants
[23]
, an indirect upper limit on gravitational-wave
strain based on energy conservation and the age of the
object. Here the inverse of the object age is replaced by the
interaction rate of the globular cluster, which scales like
density
ð
3
=
2
Þ
times core radius
2
[38,41]
, reflecting the mean
time since the last bombardment. It is hard to know when
the most recent bombardment episode was, and thus the
constant factor out in front, but globular clusters can be
ranked with respect to each other by a maximum-strain-
type figure of merit
h
0
∝
ρ
3
=
4
c
r
c
=d;
ð
3
Þ
where
ρ
c
is the globular cluster core density,
r
c
is the core
radius,
d
is the distance to the cluster, and thus
r
c
=d
is the
angular radius of the core. We ranked the Harris catalog of
globular clusters
[42,43]
by this figure of merit and looked
at the top few choices, which were mainly nearby core-
collapsed clusters. The closest is NGC 6397 at
≈
2
.
2
kpc,
but it is at high declination. This lessens the Doppler
modulation of any gravitational-wave signal, making it
harder to distinguish from stationary spectral line artifacts,
which tend to contaminate searches at high declination near
the ecliptic pole. Hence we chose the next closest, NGC
6544, which is at a declination of less than 30 degrees and
only slightly further away at
≈
2
.
7
kpc.
We restrict the search described below to sources for
which the bombardment history corresponds to a character-
istic spin-down age older than 300 years. The figure of
300 years is mainly a practical consideration: the cost of a
search rises steeply for lower spin-down ages, and 300 years
proved tractable for the Cas A search
[22]
.
D. Search parameter space
An iterative method was used to generate the parameter
space to be searched. Starting with an (assumed) spin-
down age no younger than 300 years, a braking index
n
¼
5
(see below), and the known distance to the globular
cluster, we calculated the age-based indirect upper
limit. This is an optimistic limit on the gravitational-wave
strain
h
0
which assumes that all energy lost as the target
neutron star spins down is radiated away as gravitational
waves
[23]
,
h
0
≤
1
d
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
5
GI
2
c
3
τ
ð
n
−
1
Þ
s
:
ð
4
Þ
Here
d
is the distance to the target,
τ
the assumed age of
the target object, and
I
a fiducial moment of inertia for a
neutron star (
10
38
kg · m
2
).
G
and
c
are the gravitational
constant and the speed of light, respectively. This age-based
limit was then superimposed on a curve of expected upper
limits in the absence of signal for the LIGO detectors,
obtained from the noise PSD harmonically averaged over
all of S6 and both interferometers. A running median with a
16-Hz window was further applied to smooth the curve.
The curve is given by
h
95%
0
¼
Θ
ffiffiffiffiffiffiffiffiffi
S
h
T
data
s
ð
5
Þ
B. P. ABBOTT
et al.
PHYSICAL REVIEW D
95,
082005 (2017)
082005-8
where
S
h
is the harmonically averaged noise,
T
data
is the
coherence time (the total data livetime searched coherently),
initially estimated at two weeks, and
Θ
is a sensitivity factor
that includes a trials factor, or number of templates searched,
and uncertainty in the source orientation
[23]
. For a directed
search like ours,
Θ
is approximately 35
[23,44]
. The
intersection of this coherence-time adjusted upper limit
curve and our indirect limit [Eq.
(4)
] gives an initial
frequency band over which the indirect limit can be beaten.
The braking index is related to the frequency parameters by
the definition,
n
¼
f
̈
f
_
f
2
:
ð
6
Þ
Assuming a braking index
n
between 2 and 7 covers
most accepted neutron-star models (
n
¼
5
, the neutron star
radiating all energy as gravitational waves via the mass
quadrupole, is used to obtain the indirect limit). We allow
the braking indices in these expressions to range from 2 to 7
independently, to reflect the fact that in general multiple
processes are operating and
_
f
is not a simple power law.
This constraint on the braking indices then produces limits
on the frequency derivatives given by
[23]
f
τ
≤−
_
f
≤
f
6
τ
ð
7
Þ
for the spin down at each frequency and
2
_
f
2
f
≤
̈
f
≤
7
_
f
2
f
ð
8
Þ
for the second spin down at each
ð
f;
_
f
Þ
. The step sizes
for frequency and its derivatives are given by the
equations
[33,45,46]
df
¼
2
ffiffiffiffiffiffiffi
3
m
p
π
1
T
data
;
ð
9
Þ
d
_
f
¼
12
ffiffiffiffiffiffiffi
5
m
p
π
1
T
2
data
;
ð
10
Þ
and
d
̈
f
¼
20
ffiffiffiffiffiffiffi
7
m
p
π
1
T
3
data
;
ð
11
Þ
where
m
is the mismatch parameter, the maximum loss of
2
F
due to discretization of the frequency and derivatives
[47,48]
. This search used a mismatch parameter
m
¼
0
.
2
at
all stages.
From these relations the total number of templates
(points in frequency parameter space) to be searched can
be calculated, and with knowledge of the per-template
time taken by the code (obtained from timing tests), the
total computing time can be obtained. Limiting the target
computing time, in our case to 1000 core months, then
allows us to solve for the coherence time
T
data
, which we
then feed back into Eq.
(5)
to begin the process anew until it
iteratively converges on a parameter space and accompa-
nying coherence time. The iterative algorithm thus balances
the computational gains from resampling between the
use of a longer coherence time (giving better sensitivity)
and the expansion of the parameter space over which the
indirect limit can be beaten (caused by the improved
sensitivity). The result for the globular cluster NGC
6544 is a search over the frequency range 92.5 to
675 Hz, with a coherence time of 9.2 days.
The peculiar velocities of globular clusters are negli-
gible, as they represent an essentially constant Doppler shift
of order
1
×
10
−
3
; so is velocity dispersion, which is an
order of magnitude smaller. Since we search down to
300-year time scales, the acceleration of the cluster is also
not an issue
[49]
.
E. Implementation
All searches were run on the LIGO-Caltech Computing
Cluster at the California Institute of Technology in
Pasadena, California, under the control of the Condor
queuing system for parallel processing. The search process
was split into 5825 individual Condor jobs, each of which
searched over a 0.1-Hz sub-band and corresponding
swathes of
ð
_
f;
̈
f
Þ
. The number of templates searched by
each job thus varied as a function of frequency.
Each search job produced three distinct outputs. First, a
record was made of all candidates with
2
F
above 45.0, a
choice of recording different from the fifth initial LIGO
science run (S5) search which recorded the loudest 0.01%
of events. This was needed because of the contamination
of the S6 noise by detector artifacts, as well as limits on
the disk space available and the input/output capability of
the cluster file system. Second, a histogram of
2
F
values
for all templates searched was produced to verify that
the data matched the expected chi-square distribution
(described in Sec.
II B
above). Last, each job produced
a record of the loudest (highest-
2
F
-valued) candidate in
its 0.1-Hz band, regardless of threshold. This data were
used in the setting and validation of upper limits (see
Sec.
III
below).
F. Vetoes
A high value of
2
F
is not enough to claim a detection,
since instrumental artifacts lead to non-Gaussian and/or
nonstationary noise in many narrow frequency bands.
A variety of veto techniques was used to trim down the
initial list of candidates and arrive at a final list of
outliers.
SEARCH FOR CONTINUOUS GRAVITATIONAL WAVES
...
PHYSICAL REVIEW D
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Six 0.1 Hz sub-bands [see Table (
II
)] had to be manually
aborted in both searches, with a seventh aborted in the
July
–
August search, as even with the threshold in place,
they produced an excessive number of candidates. Each of
these sub-bands was compared to records of known noise
artifacts and disturbances in the detector, and in each case a
known instrumental line was confirmed. These sub-bands
were later rerun with the record of candidates disabled in
order to produce histograms and loudest-outlier files for
upper limit validation.
To protect against spurious noise lines, a second veto
based on the
F
-statistic consistency veto introduced in
[15]
was used. This uses the fact that an astrophysical signal
should have a higher joint value of
2
F
(combining data
from the two interferometers) than in either interferometer
alone. Recorded candidates that violate this inequality were
vetoed. This is a simpler version of the more recent line
veto
[50]
.
Finally, to enforce coincidence between detectors, a
single-detector threshold was employed. Since a true
astrophysical signal should be present in both detectors
at a significant level, any candidates passing the initial
joint-detector detection criteria (see Sec.
II G
) also had to
pass an additional threshold on the individual-detector
values of
2
F
.
The 0.1 Hz band between 200 and 200.1 Hz was
arbitrarily chosen as a test band. The joint-detector
2
F
values were taken from the loudest-candidate files and used
to semianalytically compute
[51]
an estimate of the 95%
upper limit for that sub-band using the SFTs employed by
the search. Sets of 1,000 software injections were per-
formed with strengths of 100%, 80%, 60%, 40% and 20%
of this estimated upper limit. The results were used to set a
threshold of
2
F
≥
20
in each individual detector, leading to
an additional false dismissal rate of 1.5% of injections at the
95% confidence upper limit estimate (ULE). Candidates
failing to meet this criterion were vetoed.
G. Detection criteria and results
The results of a mock data challenge (MDC) were used
to set a detection criterion for the joint-detector
2
F
value.
The mock data challenge consisted of a set of 1577 artificial
continuous wave (CW) signals injected into a set of real
detector data from S6, which were then searched for using
the same resampled
F
-statistic used in the search. A survey
of the loudest joint-detector
2
F
value reported for back-
ground sub-bands known to be free of injected signals for
the band between 200 and 240 Hz (used in a pilot MDC
run) gave a mean loudest joint detector
2
F
≈
55
. While we
cannot be sure there were zero true signals in these sub-
bands, the fact that no true CW signal has ever been
reported in the S6 data implies that the odds that real signals
were present, in high enough number and strength to
significantly alter that mean, are very low. This threshold
was confirmed to be appropriate for other bands as well, via
visual examination of distributions of the detection statistic
in a large sampling of 0.1 Hz bins throughout the full search
band and via examination of the loudest detection statistic
from each 0.1 Hz sub-band for all 0.1 Hz sub-bands. Given
this background level, the detection criterion was chosen to
be joint detector
2
F
≥
60
to maintain high efficiency and
low false-alarm rate (the false-alarm rate was 3.17% in
these pilot sub-bands).
With these detection criteria, a search was carried out in
S6 data. The lists of all templates with joint detector
2
F
greater than 45.0 were filtered for the individual detector
threshold and the consistency veto, both singly and in
tandem. If the loudest template failed either check, the list
was used to move to the next-loudest template until the
loudest template passing all thresholds and vetoes was
identified. This created three sets of results (threshold only,
veto only, and threshold
þ
veto) which could all be queried
independently.
The joint
2
F
values for the loudest single template
(passing all thresholds and vetoes) in each 0.1 Hz sub-band
were collated into lists spanning 10 Hz (100 joint
2
F
values per list). These lists were then parsed, and any joint
2
F
values greater than the joint
2
F
threshold of 60 were
identified. Each such entry
’
s corresponding template was
then added to a list of outliers. This method produced a list
of 168 outliers for the entirety of the search band in the
October data, and a list of 155 outliers for the entirety of the
search band in the July
–
August data.
These outliers were then tested using time shifts and
extended looks. In a time shift, the frequency parameters
of the outliers from each data stretch (October and July
–
August) were evolved forwards or backwards in time, as
appropriate, and sought in the opposite data stretch, under
the assumption that a true astrophysical signal should be
present in both data sets for the implicitly long lived CW
signals searched for here. A set of 1000 software injections
(simulated signals with randomly generated parameters)
underwent the same treatment to provide a baseline
2
F
TABLE II. Search sub-bands that, due to the identified dis-
turbances, produced an excessive number of candidates and were
aborted. The 580.0 Hz sub-band had to be stopped only for the
July
–
August run; the other six bands were vetoed in both
searches.
Band
job minimum
and maximum
frequency (Hz)
Note
370.1
370.1
370.2
L1 output mode
cleaner (OMC) jitter line
393.1
393.1
393.2
H1 calibration line
396.7
396.7
396.8
L1 calibration line
400.2
400.2
400.3
H1 OMC quad
photodiode (QPD) line
403.8
403.8
403.9
L1 OMC QPD line
417.1
417.1
417.2
H1 OMC QPD line
580.0
580.0
580.1
L1 2 Hz Harmonic
B. P. ABBOTT
et al.
PHYSICAL REVIEW D
95,
082005 (2017)
082005-10
threshold for signal detection, and outliers surpassing the
threshold were considered present.
In an extended look, each outlier was sought in an
expanded 20-day coherence time encompassing the origi-
nal nine-day coherence time; the same assumption of signal
continuity would predict, roughly, a doubling of the
2
F
value for a doubling of coherence time. These cases as well
were tested with software injections to determine a
threshold.
In both time shifts and extended looks, the searches were
conducted over a parameter space envelope obtained by
starting at the outlier frequency parameters
ð
f;
_
f;
̈
f
Þ
2
bins, and evolving those ranges backwards or forwards in
time using the extremum values of the next derivative (e.g.,
f
evolved at maximum
_
f
,
_
f
evolved at maximum
̈
f
)to
achieve a conservatively wide envelope.
Outliers detected in time shifts and extended looks with
joint
2
F
greater than the threshold established by the
software injections were labeled candidates. The time shift
and extended look tests were not cumulative; an outlier
needed only to survive any one test, not all of them, to
persist as a candidate. The software injection threshold
for both types of test was placed at a value for joint
2
F
yielding 80% injection recovery; because each outlier
would receive further consideration if it passed either test,
the false dismissal probability for the first follow-up stage
was
≈
4%
. The combined 323 outliers produced only seven
candidates, listed in Table
III
.
These seven candidates were subject to manual follow
up. They were compared to strain histograms of run-
averaged (i.e., over all of S6) spectra from each detector,
to identify instrumental noise lines which could be respon-
sible. In five of the seven cases, the strain histograms gave
clear evidence of an instrumental noise line responsible
for the candidate, and in these cases records of prior
detector characterization studies were consulted to provide
explanations for the noise artifacts. In those cases the
artifact is listed in Table
III
as well. Two of the artifacts
arose from hardware injections located at other points in the
sky, used to test interferometer response
[25]
.
The final remaining two candidates, which were not
associated with known instrumental lines, were given
another subsequent round of follow up: a time shift and
extended look performed in data from June 2010, the
farthest removed (in the time domain) available data of
comparable sensitivity. The large time separation creates a
large difference in the Doppler corrections needed to
reconstruct an astrophysical source, making these correc-
tions unlikely to reinforce instrumental or environmental
artifacts. Both outliers failed to pass the
2
F
thresholds
established by software injections in any of their June tests.
The loudest
2
F
value expected in the absence of signal
depends on the number of templates searched
[51]
1
;
for our search, the largest expected
2
F
value lies in the
range
72
≤
2
F
≤
80
with 90% confidence. The
2
F
values
associated with the two remaining candidates, outliers
79 and 131, were joint detector
2
F
¼
61
.
3
and joint
detector
2
F
¼
61
.
9
, respectively. The final two candidates
’
failure to pass the June tests and their marginal
2
F
values
led us to dismiss them as noise fluctuations.
For ease of understanding, Table
IV
illustrates the
successive stages of follow up, and the number of remain-
ing candidates after each step.
Thus no credible gravitational-wave signals were
detected by our search. In the absence of a detection, we
can set upper limits on the possible strength of gravitational
waves in our data.
TABLE III. The seven candidates that passed the first round of outlier follow up. The columns give, respectively, the outlier
’
s
identifying number; the frequency of the outlier in the search; the frequency of the outlier in the follow-up data set in which it appeared;
the
2
F
value of the outlier in the search; the
2
F
value of the outlier in the follow-up data set in which it appeared; the explanation, if any,
provided by comparison with run-averaged strain histograms in conjunction with detector characterization records. For outliers due to
random noise and for many instrumental artifacts, we expect the follow-up
2
F
to be smaller than the originally obtained
2
F
, in contrast
to true signals for which
2
F
should increase with observation time.
July
–
August data
Outlier
Search
f
(Hz)
Follow-up
f
(Hz)
Search
2
F
J
Follow-up
2
F
J
Artifact, if any
27
192.4907
192.4956
612.969
300.712
Hardware injection
74
392.2232
392.2315
189.903
173.787
Clock noise
77
394.0231
394.0307
228.268
197.300
Digital line
October data
27
192.4195
192.4313
875.575
484.254
Hardware injection
79
403.6424
403.8612
114.626
61.331
—
–
85
417.0394
417.1384
60.309
176.200
H1 output mode cleaner line
131
575.9658
576.5057
61.943
53.805
—
–
1
The
N
T
templates used in our searches are not completely
independent, but can be represented by
N
statistically indepen-
dent templates where
N
≈
0
.
88
N
T
. See Sec. 8.7 of
[51]
.
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