Search of the Orion spur for continuous gravitational waves using a loosely
coherent algorithm on data from LIGO interferometers
J. Aasi,
1
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,
7,8
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
A. Ain,
14
P. Ajith,
15
B. Allen,
10,16,17
A. Allocca,
18,19
D. V. Amariutei,
5
M. Andersen,
20
S. B. Anderson,
1
W. G. Anderson,
16
K. Arai,
1
M. C. Araya,
1
C. C. Arceneaux,
21
J. S. Areeda,
22
N. Arnaud,
23
G. Ashton,
24
S. M. Aston,
6
P. Astone,
25
P. Aufmuth,
17
C. Aulbert,
10
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,
12
M. Barsuglia,
34
J. Bartlett,
33
M. A. Barton,
33
I. Bartos,
35
R. Bassiri,
20
A. Basti,
36,19
J. C. Batch,
33
C. Baune,
10
V. Bavigadda,
30
B. Behnke,
26
M. Bejger,
37
C. Belczynski,
38
A. S. Bell,
32
B. K. Berger,
1
J. Bergman,
33
G. Bergmann,
10
C. P. L. Berry,
39
D. Bersanetti,
40,41
A. Bertolini,
11
J. Betzwieser,
6
S. Bhagwat,
31
R. Bhandare,
42
I. A. Bilenko,
43
G. Billingsley,
1
J. Birch,
6
R. Birney,
44
S. Biscans,
12
M. Bitossi,
30
C. Biwer,
31
M. A. Bizouard,
23
J. K. Blackburn,
1
C. D. Blair,
45
D. Blair,
45
S. Bloemen,
11,46
O. Bock,
10
T. P. Bodiya,
12
M. Boer,
47
G. Bogaert,
47
P. Bojtos,
48
C. Bond,
39
F. Bondu,
49
R. Bonnand,
8
R. Bork,
1
M. Born,
10
V. Boschi,
19,36
Sukanta Bose,
14,50
C. Bradaschia,
19
P. R. Brady,
16
V. B. Braginsky,
43
M. Branchesi,
51,52
V. Branco,
53
J. E. Brau,
54
T. Briant,
55
A. Brillet,
47
M. Brinkmann,
10
V. Brisson,
23
P. Brockill,
16
A. F. Brooks,
1
D. A. Brown,
31
D. Brown,
5
D. D. Brown,
39
N. M. Brown,
12
C. C. Buchanan,
2
A. Buikema,
12
T. Bulik,
38
H. J. Bulten,
56,11
A. Buonanno,
57,26
D. Buskulic,
8
C. Buy,
34
R. L. Byer,
20
L. Cadonati,
58
G. Cagnoli,
59
J. Calderón Bustillo,
60
E. Calloni,
61,4
J. B. Camp,
62
K. C. Cannon,
63
J. Cao,
64
C. D. Capano,
10
E. Capocasa,
34
F. Carbognani,
30
S. Caride,
65
J. Casanueva Diaz,
23
C. Casentini,
66,67
S. Caudill,
16
M. Cavaglià,
21
F. Cavalier,
23
R. Cavalieri,
30
C. Celerier,
20
G. Cella,
19
C. Cepeda,
1
L. Cerboni Baiardi,
51,52
G. Cerretani,
36,19
E. Cesarini,
66,67
R. Chakraborty,
1
T. Chalermsongsak,
1
S. J. Chamberlin,
16
S. Chao,
68
P. Charlton,
69
E. Chassande-Mottin,
34
X. Chen,
55,45
Y. Chen,
70
C. Cheng,
68
A. Chincarini,
41
A. Chiummo,
30
H. S. Cho,
71
M. Cho,
57
J. H. Chow,
72
N. Christensen,
73
Q. Chu,
45
S. Chua,
55
S. Chung,
45
G. Ciani,
5
F. Clara,
33
J. A. Clark,
58
F. Cleva,
47
E. Coccia,
66,74
P.-F. Cohadon,
55
A. Colla,
75,25
C. G. Collette,
76
M. Colombini,
29
M. Constancio, Jr.,
13
A. Conte,
75,25
L. Conti,
77
D. Cook,
33
T. R. Corbitt,
2
N. Cornish,
27
A. Corsi,
78
C. A. Costa,
13
M. W. Coughlin,
73
S. B. Coughlin,
7
J.-P. Coulon,
47
S. T. Countryman,
35
P. Couvares,
31
D. M. Coward,
45
M. J. Cowart,
6
D. C. Coyne,
1
R. Coyne,
78
K. Craig,
32
J. D. E. Creighton,
16
T. Creighton,
81
J. Cripe,
2
S. G. Crowder,
79
A. Cumming,
32
L. Cunningham,
32
E. Cuoco,
30
T. Dal Canton,
10
M. D. Damjanic,
10
S. L. Danilishin,
45
S. D
’
Antonio,
67
K. Danzmann,
17,10
N. S. Darman,
80
V. Dattilo,
30
I. Dave,
42
H. P. Daveloza,
81
M. Davier,
23
G. S. Davies,
32
E. J. Daw,
82
R. Day,
30
D. DeBra,
20
G. Debreczeni,
83
J. Degallaix,
59
M. De Laurentis,
61,4
S. Deléglise,
55
W. Del Pozzo,
39
T. Denker,
10
T. Dent,
10
H. Dereli,
47
V. Dergachev,
1
R. De Rosa,
61,4
R. T. DeRosa,
2
R. DeSalvo,
9
S. Dhurandhar,
14
M. C. Díaz,
81
L. Di Fiore,
4
M. Di Giovanni,
75,25
A. Di Lieto,
36,19
I. Di Palma,
26
A. Di Virgilio,
19
G. Dojcinoski,
84
V. Dolique,
59
E. Dominguez,
85
F. Donovan,
12
K. L. Dooley,
1,21
S. Doravari,
6
R. Douglas,
32
T. P. Downes,
16
M. Drago,
86,87
R. W. P. Drever,
1
J. C. Driggers,
1
Z. Du,
64
M. Ducrot,
8
S. E. Dwyer,
33
T. B. Edo,
82
M. C. Edwards,
73
M. Edwards,
7
A. Effler,
2
H.-B. Eggenstein,
10
P. Ehrens,
1
J. M. Eichholz,
5
S. S. Eikenberry,
5
R. C. Essick,
12
T. Etzel,
1
M. Evans,
12
T. M. Evans,
6
R. Everett,
88
M. Factourovich,
35
V. Fafone,
66,67,74
S. Fairhurst,
7
Q. Fang,
45
S. Farinon,
41
B. Farr,
89
W. M. Farr,
39
M. Favata,
84
M. Fays,
7
H. Fehrmann,
10
M. M. Fejer,
20
D. Feldbaum,
5,6
I. Ferrante,
36,19
E. C. Ferreira,
13
F. Ferrini,
30
F. Fidecaro,
36,19
I. Fiori,
30
R. P. Fisher,
31
R. Flaminio,
59
J.-D. Fournier,
47
S. Franco,
23
S. Frasca,
75,25
F. Frasconi,
19
M. Frede,
10
Z. Frei,
48
A. Freise,
39
R. Frey,
54
T. T. Fricke,
10
P. Fritschel,
12
V. V. Frolov,
6
P. Fulda,
5
M. Fyffe,
6
H. A. G. Gabbard,
21
J. R. Gair,
90
L. Gammaitoni,
28,29
S. G. Gaonkar,
14
F. Garufi,
61,4
A. Gatto,
34
N. Gehrels,
62
G. Gemme,
41
B. Gendre,
47
E. Genin,
30
A. Gennai,
19
L. Á. Gergely,
91
V. Germain,
8
A. Ghosh,
15
S. Ghosh,
11,46
J. A. Giaime,
2,6
K. D. Giardina,
6
A. Giazotto,
19
J. R. Gleason,
5
E. Goetz,
10,65
R. Goetz,
5
L. Gondan,
48
G. González,
2
J. Gonzalez,
36,19
A. Gopakumar,
92
N. A. Gordon,
32
M. L. Gorodetsky,
43
S. E. Gossan,
70
M. Gosselin,
30
S. Goßler,
10
R. Gouaty,
8
C. Graef,
32
P. B. Graff,
62,57
M. Granata,
59
A. Grant,
32
S. Gras,
12
C. Gray,
33
G. Greco,
51,52
P. Groot,
46
H. Grote,
10
K. Grover,
39
S. Grunewald,
26
G. M. Guidi,
51,52
C. J. Guido,
6
X. Guo,
64
A. Gupta,
14
M. K. Gupta,
93
K. E. Gushwa,
1
E. K. Gustafson,
1
R. Gustafson,
65
J. J. Hacker,
22
B. R. Hall,
50
E. D. Hall,
1
D. Hammer,
16
G. Hammond,
32
M. Haney,
92
M. M. Hanke,
10
J. Hanks,
33
C. Hanna,
88
M. D. Hannam,
7
J. Hanson,
6
T. Hardwick,
2
J. Harms,
51,52
G. M. Harry,
94
I. W. Harry,
26
M. J. Hart,
32
M. T. Hartman,
5
C.-J. Haster,
39
K. Haughian,
32
A. Heidmann,
55
M. C. Heintze,
5,6
H. Heitmann,
47
P. Hello,
23
G. Hemming,
30
M. Hendry,
32
I. S. Heng,
32
J. Hennig,
32
A. W. Heptonstall,
1
M. Heurs,
10
S. Hild,
32
D. Hoak,
95
K. A. Hodge,
1
J. Hoelscher-Obermaier,
17
D. Hofman,
59
S. E. Hollitt,
96
K. Holt,
6
P. Hopkins,
7
D. J. Hosken,
96
J. Hough,
32
E. A. Houston,
32
E. J. Howell,
45
Y. M. Hu,
32
S. Huang,
68
E. A. Huerta,
97
D. Huet,
23
B. Hughey,
53
S. Husa,
60
S. H. Huttner,
32
M. Huynh,
16
T. Huynh-Dinh,
6
A. Idrisy,
88
N. Indik,
10
D. R. Ingram,
33
R. Inta,
78
G. Islas,
22
J. C. Isler,
31
T. Isogai,
12
B. R. Iyer,
15
K. Izumi,
33
M. B. Jacobson,
1
H. Jang,
98
P. Jaranowski,
99
S. Jawahar,
100
Y. Ji,
64
F. Jiménez-Forteza,
60
W. W. Johnson,
2
D. I. Jones,
24
R. Jones,
32
R. J. G. Jonker,
11
L. Ju,
45
K. Haris,
101
V. Kalogera,
102
S. Kandhasamy,
21
G. Kang,
98
J. B. Kanner,
1
S. Karki,
54
J. L. Karlen,
95
M. Kasprzack,
23,30
E. Katsavounidis,
12
W. Katzman,
6
S. Kaufer,
17
T. Kaur,
45
K. Kawabe,
33
F. Kawazoe,
10
F. Kéfélian,
47
PHYSICAL REVIEW D
93,
042006 (2016)
2470-0010
=
2016
=
93(4)
=
042006(14)
042006-1
© 2016 American Physical Society
M. S. Kehl,
63
D. Keitel,
10
N. Kelecsenyi,
48
D. B. Kelley,
31
W. Kells,
1
J. Kerrigan,
95
J. S. Key,
81
F. Y. Khalili,
43
Z. Khan,
93
E. A. Khazanov,
103
N. Kijbunchoo,
33
C. Kim,
98
K. Kim,
104
N. G. Kim,
98
N. Kim,
20
Y.-M. Kim,
71
E. J. King,
96
P. J. King,
33
D. L. Kinzel,
6
J. S. Kissel,
33
S. Klimenko,
5
J. T. Kline,
16
S. M. Koehlenbeck,
10
K. Kokeyama,
2
S. Koley,
11
V. Kondrashov,
1
M. Korobko,
10
W. Z. Korth,
1
I. Kowalska,
38
D. B. Kozak,
1
V. Kringel,
10
B. Krishnan,
10
A. Królak,
105,106
C. Krueger,
17
G. Kuehn,
10
A. Kumar,
93
P. Kumar,
63
L. Kuo,
68
A. Kutynia,
105
B. D. Lackey,
31
M. Landry,
33
B. Lantz,
20
P. D. Lasky,
80,107
A. Lazzarini,
1
C. Lazzaro,
58,77
P. Leaci,
26,75
S. Leavey,
32
E. O. Lebigot,
34,64
C. H. Lee,
71
H. K. Lee,
104
H. M. Lee,
108
J. Lee,
104
J. P. Lee,
12
M. Leonardi,
86,87
J. R. Leong,
10
N. Leroy,
23
N. Letendre,
8
Y. Levin,
107
B. M. Levine,
33
J. B. Lewis,
1
T. G. F. Li,
1
A. Libson,
12
A. C. Lin,
20
T. B. Littenberg,
102
N. A. Lockerbie,
100
V. Lockett,
22
D. Lodhia,
39
J. Logue,
32
A. L. Lombardi,
95
M. Lorenzini,
74
V. Loriette,
109
M. Lormand,
6
G. Losurdo,
52
J. D. Lough,
31,10
M. J. Lubinski,
33
H. Lück,
17,10
A. P. Lundgren,
10
J. Luo,
73
R. Lynch,
12
Y. Ma,
45
J. Macarthur,
32
E. P. Macdonald,
7
T. MacDonald,
20
B. Machenschalk,
10
M. MacInnis,
12
D. M. Macleod,
2
D. X. Madden-Fong,
20
F. Magaña-Sandoval,
31
R. M. Magee,
50
M. Mageswaran,
1
E. Majorana,
25
I. Maksimovic,
109
V. Malvezzi,
66,67
N. Man,
47
I. Mandel,
39
V. Mandic,
79
V. Mangano,
75,25,32
N. M. Mangini,
95
G. L. Mansell,
72
M. Manske,
16
M. Mantovani,
30
F. Marchesoni,
110,29
F. Marion,
8
S. Márka,
35
Z. Márka,
35
A. S. Markosyan,
20
E. Maros,
1
F. Martelli,
51,52
L. Martellini,
47
I. W. Martin,
32
R. M. Martin,
5
D. V. Martynov,
1
J. N. Marx,
1
K. Mason,
12
A. Masserot,
8
T. J. Massinger,
31
F. Matichard,
12
L. Matone,
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N. Mavalvala,
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N. Mazumder,
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G. Mazzolo,
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R. McCarthy,
33
D. E. McClelland,
72
S. McCormick,
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S. C. McGuire,
111
G. McIntyre,
1
J. McIver,
95
S. T. McWilliams,
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D. Meacher,
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G. D. Meadors,
10
M. Mehmet,
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J. Meidam,
11
M. Meinders,
10
A. Melatos,
80
G. Mendell,
33
R. A. Mercer,
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M. Merzougui,
47
S. Meshkov,
1
C. Messenger,
32
C. Messick,
88
P. M. Meyers,
79
F. Mezzani,
25,75
H. Miao,
39
C. Michel,
59
H. Middleton,
39
E. E. Mikhailov,
112
L. Milano,
61,4
J. Miller,
12
M. Millhouse,
27
Y. Minenkov,
67
J. Ming,
26
S. Mirshekari,
113
C. Mishra,
15
S. Mitra,
14
V. P. Mitrofanov,
43
G. Mitselmakher,
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R. Mittleman,
12
B. Moe,
16
A. Moggi,
19
M. Mohan,
30
S. R. P. Mohapatra,
12
M. Montani,
51,52
B. C. Moore,
84
D. Moraru,
33
G. Moreno,
33
S. R. Morriss,
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K. Mossavi,
10
B. Mours,
8
C. M. Mow-Lowry,
39
C. L. Mueller,
5
G. Mueller,
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A. Mukherjee,
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S. Mukherjee,
81
A. Mullavey,
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J. Munch,
96
D. J. Murphy IV,
35
P. G. Murray,
32
A. Mytidis,
5
M. F. Nagy,
83
I. Nardecchia,
66,67
L. Naticchioni,
75,25
R. K. Nayak,
114
V. Necula,
5
K. Nedkova,
95
G. Nelemans,
11,46
M. Neri,
40,41
G. Newton,
32
T. T. Nguyen,
72
A. B. Nielsen,
10
A. Nitz,
31
F. Nocera,
30
D. Nolting,
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M. E. N. Normandin,
81
L. K. Nuttall,
16
E. Ochsner,
16
J. O
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E. Oelker,
12
G. H. Ogin,
116
J. J. Oh,
117
S. H. Oh,
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F. Ohme,
7
M. Okounkova,
70
P. Oppermann,
10
R. Oram,
6
B. O
’
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W. E. Ortega,
85
R. O
’
Shaughnessy,
118
D. J. Ottaway,
96
R. S. Ottens,
5
H. Overmier,
6
B. J. Owen,
78
C. T. Padilla,
22
A. Pai,
101
S. A. Pai,
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J. R. Palamos,
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O. Palashov,
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C. Palomba,
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A. Pal-Singh,
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H. Pan,
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Y. Pan,
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C. Pankow,
16
F. Pannarale,
7
B. C. Pant,
42
F. Paoletti,
30,19
M. A. Papa,
26,16
H. R. Paris,
20
A. Pasqualetti,
30
R. Passaquieti,
36,19
D. Passuello,
19
Z. Patrick,
20
M. Pedraza,
1
L. Pekowsky,
31
A. Pele,
6
S. Penn,
119
A. Perreca,
31
M. Phelps,
32
O. Piccinni,
75,25
M. Pichot,
47
M. Pickenpack,
10
F. Piergiovanni,
51,52
V. Pierro,
9
G. Pillant,
30
L. Pinard,
59
I. M. Pinto,
9
M. Pitkin,
32
J. H. Poeld,
10
R. Poggiani,
36,19
A. Post,
10
J. Powell,
32
J. Prasad,
14
V. Predoi,
7
S. S. Premachandra,
107
T. Prestegard,
79
L. R. Price,
1
M. Prijatelj,
30
M. Principe,
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S. Privitera,
26
R. Prix,
10
G. A. Prodi,
86,87
L. Prokhorov,
43
O. Puncken,
81,10
M. Punturo,
29
P. Puppo,
25
M. Pürrer,
7
J. Qin,
45
V. Quetschke,
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E. A. Quintero,
1
R. Quitzow-James,
54
F. J. Raab,
33
D. S. Rabeling,
72
I. Rácz,
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H. Radkins,
33
P. Raffai,
48
S. Raja,
42
M. Rakhmanov,
81
P. Rapagnani,
75,25
V. Raymond,
26
M. Razzano,
36,19
V. Re,
66,67
C. M. Reed,
33
T. Regimbau,
47
L. Rei,
41
S. Reid,
44
D. H. Reitze,
1,5
F. Ricci,
75,25
K. Riles,
65
N. A. Robertson,
1,32
R. Robie,
32
F. Robinet,
23
A. Rocchi,
67
A. S. Rodger,
32
L. Rolland,
8
J. G. Rollins,
1
V. J. Roma,
54
R. Romano,
3,4
G. Romanov,
112
J. H. Romie,
6
D. Rosi
ń
ska,
120,37
S. Rowan,
32
A. Rüdiger,
10
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30
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33
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1
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33
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16
M. Saleem,
101
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10
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1
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33
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65
I. Santiago-Prieto,
32
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59
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31
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33
A. Sawadsky,
17
P. Schale,
54
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10
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1
R. Schnabel,
10
R. M. S. Schofield,
54
A. Schönbeck,
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10
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7
J. Scott,
32
S. M. Scott,
72
D. Sellers,
6
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30
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66,67
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22
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D. A. Shaddock,
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P. Shaffery,
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PHYSICAL REVIEW D
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and J. Zweizig
1
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
Cardiff University, Cardiff CF24 3AA, United Kingdom
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 Gravi-ta-tions-physik, D-30167 Hannover, Germany
11
Nikhef, Science Park, 1098 XG Amsterdam, The 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
Inter-University Centre for Astronomy and Astrophysics, Pune 411007, India
15
International Centre for Theoretical Sciences, Tata Institute of Fundamental Research,
Bangalore 560012, India
16
University of Wisconsin-Milwaukee, Milwaukee, Wisconsin 53201, USA
17
Leibniz Universität Hannover, D-30167 Hannover, Germany
18
Università di Siena, I-53100 Siena, Italy
19
INFN, Sezione di Pisa, I-56127 Pisa, Italy
20
Stanford University, Stanford, California 94305, USA
21
The University of Mississippi, University, Mississippi 38677, USA
22
California State University Fullerton, Fullerton, California 92831, USA
23
LAL, Université Paris-Sud, IN2P3/CNRS, F-91898 Orsay, France
24
University of Southampton, Southampton SO17 1BJ, United Kingdom
25
INFN, Sezione di Roma, I-00185 Roma, Italy
26
Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-14476 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
Columbia University, New York, New York 10027, USA
36
Università di Pisa, I-56127 Pisa, Italy
37
CAMK-PAN, 00-716 Warsaw, Poland
38
Astronomical Observatory Warsaw University, 00-478 Warsaw, Poland
39
University of Birmingham, Birmingham B15 2TT, United Kingdom
40
Università degli Studi di Genova, I-16146 Genova, Italy
41
INFN, Sezione di Genova, I-16146 Genova, Italy
42
RRCAT, Indore, Madhya Pradesh 452013, India
43
Faculty of Physics, Lomonosov Moscow State University, Moscow 119991, Russia
44
SUPA, University of the West of Scotland, Paisley PA1 2BE, United Kingdom
45
University of Western Australia, Crawley, Western Australia 6009, Australia
46
Department of Astrophysics/IMAPP, Radboud University Nijmegen,
P.O. Box 9010, 6500 GL Nijmegen, The Netherlands
SEARCH OF THE ORION SPUR FOR CONTINUOUS
...
PHYSICAL REVIEW D
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47
ARTEMIS, Université Nice-Sophia-Antipolis, CNRS and Observatoire de la Côte d
’
Azur,
F-06304 Nice, France
48
MTA Eötvös University,
“
Lendulet
”
Astrophysics Research Group, Budapest 1117, Hungary
49
Institut de Physique de Rennes, CNRS, Université de Rennes 1, F-35042 Rennes, France
50
Washington State University, Pullman, Washington 99164, USA
51
Università degli Studi di Urbino
’
Carlo Bo
’
, I-61029 Urbino, Italy
52
INFN, Sezione di Firenze, I-50019 Sesto Fiorentino, Firenze, Italy
53
Embry-Riddle Aeronautical University, Prescott, Arizona 86301, USA
54
University of Oregon, Eugene, Oregon 97403, USA
55
Laboratoire Kastler Brossel, UPMC-Sorbonne Universités, CNRS, ENS-PSL Research University,
Collège de France, F-75005 Paris, France
56
VU University Amsterdam, 1081 HV Amsterdam, The Netherlands
57
University of Maryland, College Park, Maryland 20742, USA
58
Center for Relativistic Astrophysics and School of Physics, Georgia Institute of Technology,
Atlanta, Georgia 30332, USA
59
Laboratoire des Matériaux Avancés (LMA), IN2P3/CNRS, Université de Lyon,
F-69622 Villeurbanne, Lyon, France
60
Universitat de les Illes Balears
—
IEEC, E-07122 Palma de Mallorca, Spain
61
Università di Napoli
’
Federico II
’
, Complesso Universitario di Monte S. Angelo, I-80126 Napoli, Italy
62
NASA/Goddard Space Flight Center, Greenbelt, Maryland, 20771, USA
63
Canadian Institute for Theoretical Astrophysics, University of Toronto,
Toronto, Ontario M5S 3H8, Canada
64
Tsinghua University, Beijing 100084, China
65
University of Michigan, Ann Arbor, Michigan 48109, USA
66
Università di Roma Tor Vergata, I-00133 Roma, Italy
67
INFN, Sezione di Roma Tor Vergata, I-00133 Roma, Italy
68
National Tsing Hua University, Hsinchu Taiwan 300
69
Charles Sturt University, Wagga Wagga, New South Wales 2678, Australia
70
Caltech
—
CaRT, Pasadena, California 91125, USA
71
Pusan National University, Busan 609-735, Korea
72
Australian National University, Canberra, Australian Capital Territory 0200, Australia
73
Carleton College, Northfield, Minnesota 55057, USA
74
INFN, Gran Sasso Science Institute, I-67100 L
’
Aquila, Italy
75
Università di Roma
’
La Sapienza
’
, I-00185 Roma, Italy
76
University of Brussels, Brussels 1050, Belgium
77
INFN, Sezione di Padova, I-35131 Padova, Italy
78
Texas Tech University, Lubbock, Texas 79409, USA
79
University of Minnesota, Minneapolis, Minnesota 55455, USA
80
The University of Melbourne, Parkville, Victoria 3010, Australia
81
The University of Texas at Brownsville, Brownsville, Texas 78520, USA
82
The University of Sheffield, Sheffield S10 2TN, United Kingdom
83
Wigner RCP, RMKI, H-1121 Budapest, Konkoly Thege Miklós út 29-33, Hungary
84
Montclair State University, Montclair, New Jersey, 07043, USA
85
Argentinian Gravitational Wave Group, Cordoba Cordoba 5000, Argentina
86
Università di Trento, Dipartimento di Fisica, I-38123 Povo, Trento, Italy
87
INFN, Trento Institute for Fundamental Physics and Applications, I-38123 Povo, Trento, Italy
88
The Pennsylvania State University, University Park, Pennsylvania 16802, USA
89
University of Chicago, Chicago, Illinois 60637, USA
90
University of Cambridge, Cambridge CB2 1TN, United Kingdom
91
University of Szeged, Dóm tér 9, Szeged 6720, Hungary
92
Tata Institute for Fundamental Research, Mumbai 400005, India
93
Institute for Plasma Research, Bhat, Gandhinagar 382428, India
94
American University, Washington, D.C. 20016, USA
95
University of Massachusetts-Amherst, Amherst, Massachusetts 01003, USA
96
University of Adelaide, Adelaide, South Australia 5005, Australia
97
West Virginia University, Morgantown, West Virginia 26506, USA
98
Korea Institute of Science and Technology Information, Daejeon 305-806, Korea
99
University of Bia
ł
ystok, 15-424 Bia
ł
ystok, Poland
100
SUPA, University of Strathclyde, Glasgow G1 1XQ, United Kingdom
101
IISER-TVM, CET Campus, Trivandrum Kerala 695016, India
J. AASI
et al.
PHYSICAL REVIEW D
93,
042006 (2016)
042006-4
102
Northwestern University, Evanston, Illinois 60208, USA
103
Institute of Applied Physics, Nizhny Novgorod, 603950, Russia
104
Hanyang University, Seoul 133-791, Korea
105
NCBJ, 05-400
Ś
wierk-Otwock, Poland
106
IM-PAN, 00-956 Warsaw, Poland
107
Monash University, Victoria 3800, Australia
108
Seoul National University, Seoul 151-742, Korea
109
ESPCI, CNRS, F-75005 Paris, France
110
Università di Camerino, Dipartimento di Fisica, I-62032 Camerino, Italy
111
Southern University and A&M College, Baton Rouge, Louisiana 70813, USA
112
College of William and Mary, Williamsburg, Virginia 23187, USA
113
Instituto de Física Teórica, University Estadual Paulista/ICTP South American Institute
for Fundamental Research, São Paulo SP 01140-070, Brazil
114
IISER-Kolkata, Mohanpur, West Bengal 741252, India
115
Rutherford Appleton Laboratory, HSIC, Chilton, Didcot, Oxon OX11 0QX, United Kingdom
116
Whitman College, 280 Boyer Ave, Walla Walla, Washington 9936, USA
117
National Institute for Mathematical Sciences, Daejeon 305-390, Korea
118
Rochester Institute of Technology, Rochester, New York 14623, USA
119
Hobart and William Smith Colleges, Geneva, New York 14456, USA
120
Institute of Astronomy, 65-265 Zielona Góra, Poland
121
Andrews University, Berrien Springs, Michigan 49104, USA
122
Trinity University, San Antonio, Texas 78212, USA
123
Università di Padova, Dipartimento di Fisica e Astronomia, I-35131 Padova, Italy
124
University of Washington, Seattle, Washington 98195, USA
125
Abilene Christian University, Abilene, Texas 79699, USA
126
Emory University, Atlanta, Georgia 30322, USA
(Received 25 October 2015; published 17 February 2016)
We report results of a wideband search for periodic gravitational waves from isolated neutron stars
within the Orion spur towards both the inner and outer regions of our Galaxy. As gravitational waves
interact very weakly with matter, the search is unimpeded by dust and concentrations of stars. One search
disk (A) is 6.87° in diameter and centered on
20
h
10
m
54
.
71
s
þ
33
°
33
0
25
.
29
00
, and the other (B) is 7.45° in
diameter and centered on
8
h
35
m
20
.
61
s
−
46
°
49
0
25
.
151
00
. We explored the frequency range of 50
–
1500 Hz
and frequency derivative from 0 to
−
5
×
10
−
9
Hz
=
s. A multistage,
loosely coherent
search program
allowed probing more deeply than before in these two regions, while increasing coherence length with
every stage. Rigorous follow-up parameters have winnowed the initial coincidence set to only 70
candidates, to be examined manually. None of those 70 candidates proved to be consistent with an isolated
gravitational-wave emitter, and 95% confidence level upper limits were placed on continuous-wave strain
amplitudes. Near 169 Hz we achieve our lowest 95% C.L. upper limit on the worst-case linearly polarized
strain amplitude
h
0
of
6
.
3
×
10
−
25
, while at the high end of our frequency range we achieve a worst-case
upper limit of
3
.
4
×
10
−
24
for all polarizations and sky locations.
DOI:
10.1103/PhysRevD.93.042006
I. INTRODUCTION
In this paper we report the results of a deep search along
the Orion spur for continuous, nearly monochromatic
gravitational waves in data from LIGO
’
s sixth science
(S6) run. The search covered frequencies from 50 through
1500 Hz and frequency derivatives from 0 through
−
5
×
10
−
9
Hz
=
s.
Our Solar System is located in the Orion spur
—
a spoke-
like concentration of stars connecting the Sagittarius and
Perseus arms of our Galaxy. Since known pulsars tend to be
found in concentrations of stars such as galactic arms and
globular clusters
[1,2]
, the Orion spur offers a potential
target. This search explores a portion of the Orion spur
towards the inner regions of our Galaxy as well as a nearly
opposite direction covering the Vela nebula.
A number of searches have been carried out previously
on LIGO data
[3
–
11]
, including coherent searches for
gravitational waves from known radio and x-ray pulsars.
An Einstein@Home search running on the BOINC infra-
structure
[12]
has performed blind all-sky searches on data
from LIGO
’
s S4 and S5 science runs
[13
–
15]
.
The results in this paper were produced with the
PowerFlux search code. It was first described in Ref.
[3]
together with two other semicoherent search pipelines
(Hough, Stackslide). The sensitivities of all three methods
were compared, with PowerFlux showing better results in
SEARCH OF THE ORION SPUR FOR CONTINUOUS
...
PHYSICAL REVIEW D
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042006 (2016)
042006-5
frequency bands lacking severe spectral artifacts. A sub-
sequent article
[5]
based on the data from the S5 run
featured improved upper limits and a systematic follow-
up detection search based on the
loosely coherent
algorithm
[16]
.
In this paper we establish the most sensitive wideband
upper limits to date in the frequency band 50
–
1500 Hz.
Near 169 Hz our strain sensitivity to a neutron star with the
most unfavorable sky location and orientation (
“
worst
case
”
) yields a 95% confidence level upper limit in the
intrinsic strain amplitude of
6
.
3
×
10
−
25
, while at the high
end of our frequency range we achieve a worst-case upper
limit of
3
.
4
×
10
−
24
.
Starting from 94 000 outliers surviving the first stage of
the pipeline, only 70 survived the fourth and final stage of
the automated search program and were then examined
manually for instrumental contamination. Of the 70 outliers
found, several do not have an easily identifiable instru-
mental cause.
Deeper follow-ups of the outliers do not lead to increased
statistical significance, as would be expected for a gravi-
tational-wave-emitting isolated neutron star. Accurate esti-
mation of the probability for a statistical fluctuation to lead
to the loudest of these outliers, using simulation of the
search on independent data sets, is computationally infea-
sible, but a rough (conservative) estimate (described in
Sec.
V
) is O(10%). Given this modest improbability and
given the inconsistency of deep follow-up results with the
isolated signal model, we conclude that statistical fluctua-
tions are a likely explanation for these outliers.
As the deeper follow-up searches assumed a tight
coherence length, this leaves open a narrow window for
the outliers to be caused by a neutron star with an additional
frequency modulation such as would be observed if it were
in long-period orbit. The enlargement of parameter space
needed to cover this possibility makes it impractical to test
this hypothesis with S6 data.
II. LIGO INTERFEROMETERS
AND S6 SCIENCE RUN
The LIGO gravitational-wave network consists of two
observatories, one in Hanford, Washington and the other in
Livingston, Louisiana, separated by a 3000-km baseline.
During the S6 run each site housed one suspended
interferometer with 4-km long arms.
Although the sixth science run spanned a data acquis-
ition period of more than one year, the analysis in this paper
used data only from GPS 951534120 (March 2, 2010,
03:01:45 UTC) through GPS 971619922 (October 20,
2010, 14:25:07 UTC), selected for good strain sensitivity
and noise stationarity. Since interferometers sporadically
fall out of operation (
“
lose lock
”
) due to environmental or
instrumental disturbances or for scheduled maintenance
periods, the data set is not contiguous. For the time span
used in the search the Hanford interferometer H1 had a duty
factor of 53%, while the Livingston interferometer L1 had a
duty factor of 51%. The strain sensitivity in the search band
was not uniform, exhibiting a
∼
50%
daily variation from
anthropogenic activity as well as gradual improvement
toward the end of the run
[17,18]
.
A thorough description of instruments and data can be
found in Ref.
[19]
.
III. SEARCH REGION
All-sky searches for continuous gravitational waves in
data produced by modern interferometers are computation-
ally limited, with the established upper limits an order of
magnitude away from what is theoretically possible given
impractically large computational resources. This limita-
tion arises from the rapid increase in computational cost
with coherence time of the search, because of both the
necessarily finer gridding of the sky and the need to search
over higher-order derivatives of the signal frequency.
Hence there is a trade-off between searching the largest
sky area with the reduced sensitivity of an all-sky search,
and pushing for sensitivity in a smaller region.
The loosely coherent search program was initially
developed for follow-up of outliers from an all-sky semi-
coherent search
[5]
. For this search we have chosen to
isolate two small regions and take advantage of the
enhanced sensitivity of the loosely coherent search.
Besides the gain from increasing coherence length we also
benefit from search regions (listed in Table
I
) with strong
Doppler-modulated frequency evolution and greater rejec-
tion of instrumental artifacts.
Known radio pulsars tend to cluster along the spiral arms,
in globular clusters, and in other star-forming regions.
To increase the chances of discovering a continuous-
wave gravitational source we selected regions where one
can expect a clustering of neutron star sources in
TABLE I. Area of sky covered by this search.
RA
DEC
Radius
RA
DEC
Radius
Search region
rad
rad
rad
hours
deg
deg
A
5.283600
0.585700
0.060
20
h
10
m
54
.
715
s
33
°
33
0
29
.
297
00
3.438
B
2.248610
−
0
.
788476
0.065
8
h
35
m
20
.
607
s
−
46
°
49
0
25
.
151
00
3.724
J. AASI
et al.
PHYSICAL REVIEW D
93,
042006 (2016)
042006-6
line-of-sight cones determined by the search area and
sensitivity reach of the detector.
The positions of known pulsars from the ATNF catalog
(
[20,21]
, retrieved 2015 Jan 29) and the expected reach of
semicoherent searches are illustrated in Fig.
1
on the
Galactic background
[22]
. Only pulsars with Galactic
latitude less than 0.06 rad are shown in the figure. We
observe loose association with galactic arms, which is
skewed by observational bias. In particular, the area
searched by the Parkes survey marked as a blue sector
contains many more pulsars than elsewhere on the map.
The expected reach of the all-sky search in S6 data,
assuming a neutron star ellipticity of
10
−
6
, is illustrated by
the pink circle. A computationally feasible spotlight search
can reach twice as far, but the globular clusters and galactic
center remain out of its reach in the S6 data set.
A closer alternative is to look in the local neighborhood
of the Sun along the Orion spur
—
a grouping of stars that
connects the Perseus and Sagittarius arms of our Galaxy.
For this search we have chosen two regions (Table
I
),
exploring two nearly opposite directions along the Orion
spur.
Region A was chosen to point near Cygnus X, with
region B pointing toward the Vela nebula I. A recent study
of OB stars and their ramifications for local supernova rates
support these two directions as potentially promising, along
with several other star-forming regions
[2]
. The choice of
sky area to search for region B is more ambiguous because
of the larger extent of the Orion spur
—
Fig.
1
shows two
grouping of stars towards the Vela Molecular Ridge and
Perseus transit directions. We have chosen the direction
towards Vela as it coincides with a star-forming region with
several known neutron stars. In order to better cover the
Vela nebula the region B search radius is slightly larger than
that of region A.
IV. SEARCH ALGORITHM
The results presented in this paper were obtained with
the loosely coherent search, implemented as part of the
PowerFlux program. We have used the follow-up procedure
developed for the all-sky S6 search, but where the first
loosely coherent stage is applied directly to the entire A and
B regions. A detailed description of the loosely coherent
code can be found in Refs.
[5,16]
.
Mathematically, we transform the input data to the Solar
System barycentric reference frame, correct for putative
signal evolution given by frequency, spin-down and polari-
zation parameters, and then apply a low-pass filter whose
bandwidth determines the coherence length of the search.
The total power in the computed time series is then
compared to the power obtained for nearby frequency bins
in a 0.25 Hz interval.
A signal-to-noise ratio (SNR) and an upper limit are
derived for each frequency bin using a universal statistic
method
[23]
that establishes a 95% C.L. upper limit for an
arbitrary underlying noise distribution. If the noise is
Gaussian distributed the upper limits are close to optimal
values that would be produced with the assumption of
Gaussianity. For non-Gaussian noise the upper limits are
conservatively correct.
Maxima of the SNR and upper limits over marginalized
search parameters are presented in the Figs.
2
,
3
and
4
.
The search results described in this paper assume a
classical model of a spinning neutron star with a fixed,
nonaxisymmetric mass quadrupole that produces circularly
polarized gravitational waves along the rotation axis and
linearly polarized radiation in the directions perpendicular
to the rotation axis.
The assumed signal model is thus
h
ð
t
Þ¼
h
0
F
þ
ð
t;
α
;
δ
;
ψ
Þ
1
þ
cos
2
ð
ι
Þ
2
cos
ð
Φ
ð
t
ÞÞ
þ
F
×
ð
t;
α
;
δ
;
ψ
Þ
cos
ð
ι
Þ
sin
ð
Φ
ð
t
ÞÞ
;
ð
1
Þ
FIG. 1. Distribution of known pulsars in the Milky Way galaxy.
The Orion spur region (marked by dashed rectangle) connects the
Perseus and Sagittarius galactic arms and includes regions
marked A and B. The ranges shown for gravitational-wave
searches correspond to a 1500 Hz frequency and an ellipticity
of
10
−
6
. The arc shown for the PARKES survey
[1]
shows the
search area, not the range. The green stars show locations of
pulsars from the ATNF database (retrieved on January 29, 2015
[20]
) with Galactic latitude Gb below 0.06 radians. The back-
ground image is due to R. Hurt
[22]
.
SEARCH OF THE ORION SPUR FOR CONTINUOUS
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PHYSICAL REVIEW D
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042006 (2016)
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where
F
þ
and
F
×
characterize the detector responses to
signals with
“
þ
”
and
“
×
”
quadrupolar polarizations, the
sky location is described by right ascension
α
and decli-
nation
δ
,
ι
describes the inclination of the source rotation
axis to the line of sight, and the phase evolution of the
signal is given by the formula
Φ
ð
t
Þ¼
2
π
ð
f
source
ð
t
−
t
0
Þþ
f
ð
1
Þ
ð
t
−
t
0
Þ
2
=
2
Þþ
φ
;
ð
2
Þ
with
f
source
being the source frequency and
f
ð
1
Þ
denoting
the first frequency derivative (for which we also use the
abbreviation
spin-down
).
φ
denotes the initial phase with
respect to the reference time
t
0
.
t
is time in the Solar System
barycenter frame. When expressed as a function of the local
time of ground-based detectors it includes the sky-position-
dependent Doppler shift. We use
ψ
to denote the polari-
zation angle of the projected source rotation axis in the
sky plane.
As a first step, individual SFTs (short Fourier trans-
forms) with high noise levels or large spikes in the
underlying data are removed from the analysis. For a
typical well-behaved frequency band, we can exclude
8% of the SFTs while losing only 4% of the accumulated
statistical weight. For a band with large detector artifacts
(such as instrumental lines arising from resonant vibration
of mirror suspension wires), however, we can end up
removing most, if not all, SFTs. As such bands are not
expected to have any sensitivity of physical interest they
were excluded from the upper limit analysis (Table
II
).
The detection pipeline used in this search was developed
for an S6 all-sky analysis and is an extension of the
pipeline described in Ref.
[5]
. It consists of several stages
employing a loosely coherent
[16]
search algorithm with
progressively stricter coherence requirements. The param-
eters of the pipeline are described in Table
III
.
Unlike in the all-sky analysis the first stage is used to
establish upper limits. In effect, instead of investigating all-
sky outliers we have simply pointed the follow-up pipeline
along the direction of the Orion spur. This allowed us to
increase the sensitivity by a factor of 2. The rest of the
pipeline is unmodified.
The frequency refinement parameter is specified relative
to the
1
=
1800
Hz frequency bin width used in SFTs that
serve as input to the analysis. Thus at the last stage of
follow-up our frequency resolution is
ð
1800
s·
32
Þ
−
1
¼
17
μ
Hz. However, because of the degeneracy between
frequency, sky position and spin-down, the accuracy is
not as good and the frequency can deviate by up to
50
μ
Hz
in 95% of injections. This degeneracy is mostly due to
Doppler shifts from Earth orbital motion and is thus
common to both interferometers.
The phase coherence parameter
δ
is described in detail
in Ref.
[16]
. It represents the amount of allowed phase
variation over a 1800 s interval. We are thus sensitive both
to the expected sources with ideal frequency evolution
[Eq.
(2)
] and unexpected sources with a small amount of
frequency modulation.
The sky refinement parameter is relative to the sky
resolution sufficient for the plain semicoherent PowerFlux
mode and was necessary because the improved frequency
resolution made the search more sensitive to Doppler shift.
Stages 1 and 2 used the same parameters, with the only
difference being that data acquired at nearby times by
different interferometers were combined without regard to
phase in stage 1, but we took phase into account in stage 2.
In the ideal situation, when both detectors are operational at
the same time and at the same sensitivity, one would expect
an increase in the SNR by
ffiffiffi
2
p
by including phase
information. In practice, the duty cycle did not overlap
perfectly and, most importantly, it was quite common for
one interferometer to be more sensitive than another. Thus,
to keep an outlier, we only required that the SNR did not
decrease when transitioning to stage 2.
Subsequent stages used longer coherence times, with
correspondingly finer sky and frequency resolutions.
The analysis data set was partitioned in time into seven
parts of equal duration numbered 0 through 6. As an
intermediate product we have obtained upper limits and
TABLE II. Frequency regions excluded from upper limit
analysis. These are separated into power line artifacts and
harmonics of
“
violin modes
”
(resonant vibrations of the wires
which suspend the many mirrors of the interferometer).
Category
Description
60 Hz line
59.75
–
60.25 Hz
Violin modes
343.25
–
343.75 Hz, 347 Hz
Second harmonic of violin modes
687.00
–
687.50 Hz
Third harmonic of violin modes
1031.00
–
1031.25 Hz
TABLE III. Analysis pipeline parameters. All stages used the loosely coherent algorithm for demodulation. The sky and frequency
refinement parameters are relative to values used in the semicoherent PowerFlux search.
Phase coherence Spin-down step
SNR increase
Stage Instrument sum
rad
Hz/s
Sky refinement Frequency refinement
%
1
Incoherent
π
=
21
.
0
×
10
−
10
1
=
41
=
8
NA
2
Coherent
π
=
25
.
0
×
10
−
11
1
=
41
=
8
0
3
Coherent
π
=
42
.
5
×
10
−
11
1
=
81
=
16
12
4
Coherent
π
=
85
.
0
×
10
−
12
1
=
16
1
=
32
12
J. AASI
et al.
PHYSICAL REVIEW D
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042006 (2016)
042006-8
outliers of each contiguous sequence of parts. For example,
a segment [1,5] would consist of the middle
5
=
7
of the
entire data set. This allowed us to identify outliers that
exhibited an enhanced SNR on a subset of data and thus
were more likely to be induced by instrumental artifacts
(Tables
V
and
VI
).
V. GAUSSIAN FALSE ALARM EVENT RATE
The computation of the false alarm rate for the outliers
passing all stages of the pipeline is complicated by the fact
that most outliers are caused by instrumental artifacts for
which we do not know the underlying probability distri-
bution. In principle, one could repeat the analysis many
times using nonphysical frequency shifts (which would
exclude picking up a real signal by accident) in order to
obtain estimates of the false alarm rate, but this approach
incurs prohibitive computational cost. Even assuming a
perfect Gaussian background, it is difficult to model the
pipeline in every detail to obtain an accurate estimate of the
false alarm rate, given the gaps in interferometer operations
and nonstationary noise.
Instead, we compute a figure of merit that overestimates
the actual Gaussian false alarm event rate. We simplify the
problem by assuming that the entire analysis was carried
out with the resolution of the very last stage of follow-up
and we are merely triggering on the SNR value of the last
stage. This is extremely conservative as we ignore the
consistency requirements that allow the outlier to proceed
from one stage of the pipeline to the next, so the actual false
alarm rate could be lower.
The SNR of each outlier is computed relative to the
loosely coherent power sum for 501 frequency bins spaced
at
1
=
1800
Hz intervals (including the outlier) but with all
the other signal parameters held constant. The spacing
assures that any sub-bin leakage does not affect the
statistics of the power sum.
As the power sums are weighted, the statistics should
follow a weighted
χ
2
distribution, the exact shape of which
is difficult to characterize analytically because the weights
depend on sky position, gaps in acquired data, background
noise in the SFTs and the polarization parameters of the
outlier.
To simplify computation we assume that we are dealing
with a simple
χ
2
distribution with the number of degrees of
freedom given by the timebase divided by the coherence
length and multiplied by a conservative duty factor reflect-
ing interferometer uptime and the worst-case weights from
linearly polarized signals.
Thus to find the number of degrees of freedom we will
use the formula
N
≈
timebase ·
δ
· duty factor
1800
s·
2
π
ð
3
Þ
with the duty factor taken to be 0.125 and
δ
giving the
phase coherence parameter of the loosely coherent search.
The duty factor was chosen to allow for only 50%
interferometer uptime and only one quarter of the data
receiving high weights from our weighting scheme, which
weights the contribution of data inversely as the square of
the estimated noise
[24,25]
.
The number of search templates that would be needed if
the last stage of follow-up were used on the entire search
region is conservatively (over)estimated as
K
¼
5
.
8
×
10
7
f
3
1
−
f
3
0
1400
.
25
3
−
1400
3
ð
4
Þ
where
f
0
and
f
1
(in Hz) describe the frequency band of
interest. For any particular 0.25 Hz search band the number
of templates scales quadratically in frequency due to the
linearly growing influence of Doppler shifts. Thus the
integrated frequency dependence is cubic. The scaling
factor
5
.
8
×
10
7
was obtained by counting the number of
templates for a particular PowerFlux instance that searched
from 1400 to 1400.25 Hz. For the entire analysis
f
0
¼
50
Hz and
f
1
¼
1500
Hz, which yields
K
¼
1
.
3
×
10
11
templates, without accounting for template overlap.
Thus we define the outlier figure of merit describing the
Gaussian false alarm event rate (GFA) as
GFA
¼
K
·
P
χ
2
ð
N
þ
SNR ·
ffiffiffiffiffiffiffi
2
N
p
;
N
Þð
5
Þ
where
N
defines the number of degrees of freedom as given
by Eq.
(3)
,
P
χ
2
ð
x
;
N
Þ
gives the probability for a
χ
2
distribution with
N
degrees of freedom to exceed
x
, and
K
describes the estimated number of templates.
We point out that the GFA is overly conservative when
applied to frequency bands with Gaussian noise, but is only
loosely applicable to bands with detector artifacts, which
can affect both the estimate of the degrees of freedom of the
underlying distribution and the assumption of uncorrelated
underlying noise.
VI. RESULTS
PowerFlux produces 95% confidence level upper limits
for individual templates, where each template represents a
particular value of frequency, spin-down, sky location and
polarization. The results are maximized over several
parameters, and a correction factor is applied to account
for possible mismatches between a true signal and sampled
parameters. Figure
2
shows the resulting upper limits
maximized over the analyzed spin-down range, over the
search regions and, for the upper curve, over all sampled
polarizations. The lower curve shows the upper limit for
circular polarized signals alone.
The numerical data for this plot can be obtained
separately
[26]
.
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...
PHYSICAL REVIEW D
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The regions near harmonics of the 60 Hz power mains
frequency are shown as circles.
Figure
3
provides an easy way to judge the astrophysical
range of the search. We have computed the implied
spin-down solely due to gravitational emission at various
distances, as well as corresponding ellipticity curves,
assuming a circularly polarized signal. This follows for-
mulas in Ref.
[3]
. For example, at the highest frequency
sampled, assuming an ellipticity of
5
×
10
−
7
(which is well
under the maximum limit in Refs.
[27,28]
) we can see as far
as 1000 parsecs.
In each search band, including regions with detector
artifacts, the follow-up pipeline was applied to outliers
satisfying the initial coincidence criteria. The outlier
statistics are given in Table
IV
. The outliers that passed
all stages of the automated pipeline are listed in Table
V
for
the A direction and Table
VI
for the B direction. Each of
these outliers was inspected manually and tested against
further criteria to determine whether it was convincingly
due to a source in the targeted astrophysical population.
Tables
V
and
VI
list the outlier index (an identifier used
during follow-up), signal-to-noise ratio, decimal logarithm
of Gaussian false alarm as computed by Eq.
(5)
, the
contiguous segment of data where the outlier had the
highest SNR (see below), frequency, spin-down, right
ascension and declination, as well as a summary of manual
follow-up conclusions.
FIG. 2. S6 95% C.L. upper limits on the signal strain amplitude. The upper (green) curve shows worst-case upper limits in the
analyzed 0.25 Hz bands (see Table
II
for list of excluded bands). The lower (grey) curve shows upper limits assuming a circularly
polarized source. The values of solid points and circles (marking power line harmonics for circularly and linearly polarized sources) are
not considered reliable. They are shown to indicate contaminated bands.
FIG. 3. Range of the PowerFlux search for neutron stars
spinning down solely due to gravitational waves. This is a
superposition of two contour plots. The grey and red solid lines
are contours of the maximum distance at which a neutron star in
optimum orientation could be detected as a function of gravita-
tional-wave frequency
f
and its derivative
_
f
. The dashed lines are
contours of the corresponding ellipticity
ε
ð
f;
_
f
Þ
. The fine dotted
line marks the maximum spindown searched. Together these
quantities tell us the maximum range of the search in terms of
various populations (see text for details). In particular, at 1500 Hz
we are sensitive to stars with an ellipticity of
5
×
10
−
7
up to
1 kpc away.
TABLE IV. Outlier counts found at each stage of follow-up.
Stage
Region A
Region B
1
43884
51027
2
7921
9152
3
510
566
43733
J. AASI
et al.
PHYSICAL REVIEW D
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042006-10
The segment column describes the persistence of the
outlier throughout the analysis. The data to be analyzed was
divided into seven equal-duration segments labeled 0
through 6. For a continuous signal, the maximum SNR
is achieved by integrating all segments: this is indicated by
the notation [0,6]. For a transient artifact
[29]
, one can
achieve a higher SNR by analyzing only those segments
when it was on. This case is indicated by noting the
continuous set of segments that gives the largest SNR, e.g.
[1,5] if a higher SNR is achieved by dropping the first and
last segment. Note, however, that an astrophysical signal
such as a long-period binary may also appear more strongly
in some segments than others, and thus could have a
segment notation other than [0,6]. The same will be true of
a strong signal outside of the search area on the sky, whose
Doppler shifts happen to align with the target area
’
s over
some segment of time. This occurs, for instance, with
outliers A1 and A3, which were generated by a strong
simulated signal outside of the search area.
For a low SNR continuous signal it is also possible for
the background noise to randomly align in such a way that
the SNR over the [0,6] segment is slightly lower than on a
smaller subset. Our simulations show that 98.5% of
injections achieve a maximum SNR over one of the
[0,6], [0,5] or [1,6] segments.
Outliers marked as non-Gaussian were found to lie in
bands whose statistics deviated from Gaussian noise,
according to the following criterion: the excess kurtosis
of 501 bins around the outlier was smaller than
−
1
.
05
. The
probability of a Gaussian sample having this excess
kurtosis is smaller than
10
−
6
.
If manual inspection of an outlier indicated that it
overlaps with a strong spectral disturbance in one of the
detectors, this is noted in the tables. Disturbances might be
TABLE V. Outliers that passed the full detection pipeline from region A. Only the highest-SNR outlier is shown for each 0.1 Hz
frequency region. Outliers marked with
“
line
”
had strong narrowband disturbance identified near the outlier location. Outliers marked as
“
non-Gaussian
”
were identified as having a non-Gaussian statistic in their power sums, often due to a very steeply sloping spectrum.
Idx SNR log
10
ð
GFA
Þ
Segment
Frequency Spin-down RA
J
2000
DEC
J
2000
Description
Hz
nHz/s degrees degrees
1 194.1
−
188
.
8
½
0
;
0
108.83151
−
3
.
090
323.755 37.114 Induced by loud hardware injection 3
3
32.1
−
27
.
3
½
0
;
1
192.55507
−
0
.
585
306.480 34.197 Induced by loud hardware injection 8
4
31.3
−
36
.
8
½
2
;
5
69.73917
−
2
.
885
313.580 16.478 Line in L1, non-Gaussian
6
14.7
−
7
.
3
½
2
;
5
988.82017
0.215 307.682 33.630 Line in H1, non-Gaussian
7
11.4
−
2
.
9
½
2
;
6
648.74939
−
5
.
000
299.622 33.315 Line in H1
8
10.8
−
1
.
2
½
2
;
5
1143.32783
−
0
.
995
300.553 32.632 Strong disturbance in H1
9
10.2
1.4
½
0
;
1
481.96422
−
0
.
105
301.872 34.275 Line in L1, disturbed background in H1 and L1
10 10.2
0.5
½
2
;
4
99.14832
−
1
.
100
318.949 27.088 Disturbed background in L1
11
9.8
0.3
½
1
;
4
897.63729
−
2
.
215
303.190 35.780 Non-Gaussian
12
9.8
1.0
½
2
;
4
956.74358
−
4
.
115
302.033 34.395 Disturbed background in H1, non-Gaussian
13
9.8
−
0
.
7
½
1
;
6
1138.50993
0.090 299.389 34.748 Disturbed background in H1+L1, non-Gaussian
14
9.7
−
0
.
9
½
0
;
6
1404.89226
−
1
.
205
303.637 36.819
15
9.6
−
0
.
8
½
0
;
6
799.42915
−
0
.
840
300.724 31.062 Line in H1, non-Gaussian
16
9.5
0.1
½
1
;
5
1368.77913
−
3
.
560
304.484 30.949 Lines in H1
17
9.4
2.4
½
1
;
2
1308.96651
−
1
.
670
304.436 30.232 Non Gaussian
18
9.4
0.8
½
2
;
5
1386.45871
−
0
.
510
304.398 34.228 Line in H1 at 1386.5 Hz, non-Gaussian
21
9.2
2.6
½
5
;
6
1170.98217
−
4
.
395
304.353 34.829 Non-Gaussian
22
9.0
4.1
½
2
;
2
1191.26642
−
0
.
455
300.720 31.494
23
8.9
2.1
½
0
;
2
829.72137
−
2
.
900
305.831 33.090
24
8.9
0.4
½
0
;
6
1321.56703
−
1
.
820
304.707 32.001 Non-Gaussian
25
8.9
2.9
½
4
;
5
1058.43325
−
3
.
600
300.356 31.068
26
8.9
1.6
½
1
;
4
1302.65337
−
2
.
250
299.854 34.786
27
8.8
0.9
½
0
;
5
1474.94224
−
2
.
050
303.295 32.273
28
8.8
0.6
½
0
;
6
990.76130
−
2
.
705
299.638 33.235 Disturbed background in H1
29
8.7
1.1
½
1
;
6
1429.67892
−
2
.
010
303.739 32.845
30
8.6
0.9
½
0
;
6
1325.50969
−
4
.
325
300.291 34.313 Disturbed background in L1, non-Gaussian
31
8.5
3.4
½
5
;
6
1177.15326
−
0
.
040
307.054 32.374
32
8.4
1.5
½
1
;
6
1330.69434
−
3
.
285
300.625 34.037 Disturbed background in H1, non-Gaussian
33
8.4
1.5
½
0
;
5
1456.26611
0.195 302.336 33.628 L1 SNR is inconsistent with background level
34
8.3
2.0
½
2
;
6
995.14313
−
1
.
400
302.428 31.768 Disturbed background in L1
35
8.1
1.8
½
0
;
6
1286.17215
−
1
.
185
305.624 35.126 Line in H1, non-Gaussian
36
8.0
2.8
½
2
;
5
1386.02201
0.050 304.242 36.465 Line in H1 at 1385.9 Hz, non-Gaussian
37
7.8
4.2
½
1
;
2
1359.72387
−
1
.
745
298.903 32.885 Instrumental contamination in L1
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PHYSICAL REVIEW D
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either narrow lines, or steep slopes or edges characteristic
of wandering lines or the wings of nearby spectral features.
When such contamination is manifestly obvious under
visual inspection, it is likely that the outlier was due to that
artifact rather than an astrophysical signal. Outliers with
identified contamination are marked with comments in
Tables
V
and
VI
.
Two of the outliers were induced by very loud simulated
hardware injections. The true parameters of these signals
are listed in Table
VII
.
VII. MANUAL OUTLIER FOLLOW-UP
To determine whether or not any of the outliers in
Tables
V
and
VI
indicated a credible gravitational-wave
detection, each outlier was subjected to manual inspection,
after which several criteria were used to eliminate those not
likely due to the target astrophysical population. First, we
discarded any candidate with a segment other than [0,6],
[0,5], or [1,6]: as noted, this would eliminate less than 1.5%
of true signals from our population. Next, we disregard
those signals marked as
“
non-Gaussian.
”
This criterion has
a more substantial false dismissal probability: roughly 20%
of the search band was so marked. Nonetheless, we would
be unable to claim with any confidence that a candidate
from such a band was
not
simply a non-Gaussian instru-
mental outlier. Finally, we disregard outliers in bands with
visually obvious spectral disturbances: this has a similar
false dismissal rate, but has substantial overlap with the
non-Gaussian bands.
TABLE VI. Outliers that passed the full detection pipeline from region B. Only the highest-SNR outlier is shown for each 0.1 Hz
frequency region. Outliers marked with
“
line
”
had strong narrowband disturbance identified near the outlier location. Outliers marked as
“
non-Gaussian
”
were identified as having a non-Gaussian statistic in their power sums, often due to a very steeply sloping spectrum.
Idx SNR log
10
ð
GFA
Þ
Segment
Frequency Spin-down RA
J
2000
DEC
J
2000
Description
Hz
nHz/s degrees degrees
1 41.3
−
55
.
9
½
1
;
4
243.27113
−
3
.
675
134.486
−
35
.
443
Line in H1
3 19.8
−
20
.
9
½
0
;
6
69.74870
−
4
.
130
111.634
−
36
.
471
Line in L1, non-Gaussian
4 15.3
−
6
.
8
½
1
;
3
268.96658
−
5
.
065
135.288
−
46
.
431
Line in H1
5 11.7
−
2
.
5
½
2
;
5
170.84304
−
2
.
725
124.589
−
48
.
321
H1 SNR is larger than coherent sum
6 11.3
0.2
½
2
;
3
108.07698
−
0
.
115
122.585
−
48
.
207
Disturbed background in H1
7 10.9
−
2
.
0
½
1
;
5
158.39427
−
3
.
550
122.974
−
49
.
793
Line in H1
8 10.8
2.5
½
0
;
0
1111.39559
−
0
.
345
131.270
−
44
.
537
9 10.8
2.5
½
3
;
3
956.81519
−
0
.
905
129.372
−
44
.
282
Disturbed background in H1
10 10.6
2.7
½
3
;
3
950.80278
−
1
.
900
128.821
−
45
.
115
Disturbed background in H1
11 10.5
2.8
½
0
;
0
611.12967
0.255 130.848
−
49
.
230
Non Gaussian
12 10.0
−
0
.
6
½
2
;
6
1076.04377
−
3
.
250
133.282
−
47
.
130
Line in L1 at 1076 Hz, non-Gaussian
13 9.9
3.3
½
3
;
3
1118.06896
−
2
.
645
128.952
−
47
.
992
Disturbed background in L1
14 9.6
0.0
½
2
;
6
1498.30429
−
2
.
000
131.393
−
48
.
022
Disturbed background in L1
15 9.6
−
0
.
7
½
0
;
6
613.26132
−
3
.
950
125.353
−
42
.
144
Non-Gaussian
16 9.3
0.4
½
2
;
6
1498.73031
−
0
.
195
125.668
−
42
.
539
Non-Gaussian
17 9.3
0.0
½
0
;
5
933.33823
0.100 127.556
−
48
.
783
Non-Gaussian
18 9.1
1.3
½
0
;
3
1313.24312
−
5
.
000
127.562
−
47
.
859
Disturbed background in H1
19 8.9
1.6
½
0
;
3
1458.79267
−
2
.
425
125.394
−
43
.
661
20 8.9
0.8
½
1
;
6
1249.43835
−
1
.
550
128.846
−
46
.
928
Disturbed background in H1+L1, non-Gaussian
21 8.7
1.1
½
1
;
6
880.40175
−
2
.
865
130.890
−
47
.
472
Disturbed background in H1, non-Gaussian
22 8.6
2.5
½
2
;
4
1254.11705
−
1
.
295
128.862
−
41
.
615
Line in L1, non-Gaussian
23 8.6
1.3
½
1
;
6
1333.27906
−
1
.
650
128.265
−
47
.
879
Non-Gaussian
24 8.6
3.3
½
1
;
2
1497.14217
−
2
.
210
129.202
−
46
.
366
Line in H1, non-Gaussian
25 8.6
3.3
½
2
;
3
1333.83095
−
4
.
445
124.636
−
46
.
522
Non-Gaussian
26 8.4
1.8
½
0
;
4
1336.24255
−
0
.
005
126.374
−
42
.
633
Non-Gaussian
27 8.3
4.7
½
1
;
1
1370.69201
−
3
.
375
130.199
−
41
.
568
28 8.3
2.1
½
1
;
5
1316.98962
−
1
.
025
130.853
−
47
.
324
Non-Gaussian
29 8.2
4.9
½
2
;
2
795.42245
−
3
.
855
131.083
−
47
.
536
30 8.2
1.6
½
0
;
6
1458.53648
−
3
.
800
131.684
−
43
.
218
Line in H1
31 8.1
2.0
½
0
;
5
1119.11347
−
3
.
975
125.384
−
43
.
551
Disturbed background in L1
32 7.9
3.0
½
2
;
5
1331.56844
−
4
.
210
128.647
−
46
.
135
Disturbed background in H1
33 7.6
3.8
½
3
;
5
1334.83602
−
4
.
700
129.188
−
41
.
911
TABLE VII. Parameters of hardware-injected simulated signals
detected by PowerFlux (epoch GPS 846885755).
Name
Frequency
Spin-down
RA
J
2000
DEC
J
2000
Hz
Hz/s
degrees
degrees
ip3
108.85716
−
1
.
46
×
10
−
17
178.37
−
33
.
44
ip8
193.48479
−
8
.
65
×
10
−
09
351.39
−
33
.
42
J. AASI
et al.
PHYSICAL REVIEW D
93,
042006 (2016)
042006-12