of 25
First low frequency all-sky search for continuous gravitational wave signals
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
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
M. S. Kehl,
63
D. Keitel,
10
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
PHYSICAL REVIEW D
93,
042007 (2016)
2470-0010
=
2016
=
93(4)
=
042007(25)
042007-1
© 2016 American Physical Society
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
S. Mastrogiovanni,
75,25
F. Matichard,
12
L. Matone,
35
N. Mavalvala,
12
N. Mazumder,
50
G. Mazzolo,
10
R. McCarthy,
33
D. E. McClelland,
72
S. McCormick,
6
S. C. McGuire,
111
G. McIntyre,
1
J. McIver,
95
S. T. McWilliams,
97
D. Meacher,
47
G. D. Meadors,
10
M. Mehmet,
10
J. Meidam,
11
M. Meinders,
10
A. Melatos,
80
G. Mendell,
33
R. A. Mercer,
16
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,
5
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,
81
K. Mossavi,
10
B. Mours,
8
C. M. Mow-Lowry,
39
C. L. Mueller,
5
G. Mueller,
5
A. Mukherjee,
15
S. Mukherjee,
81
A. Mullavey,
6
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,
6
M. E. N. Normandin,
81
L. K. Nuttall,
16
E. Ochsner,
16
J. O
Dell,
115
E. Oelker,
12
G. H. Ogin,
116
J. J. Oh,
117
S. H. Oh,
117
F. Ohme,
7
M. Okounkova,
70
P. Oppermann,
10
R. Oram,
6
B. O
Reilly,
6
W. E. Ortega,
85
R. O
Shaughnessy,
118
C. D. Ott,
70
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,
42
J. R. Palamos,
54
O. Palashov,
103
C. Palomba,
25
A. Pal-Singh,
10
H. Pan,
68
Y. Pan,
57
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,
9
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,
81
E. A. Quintero,
1
R. Quitzow-James,
54
F. J. Raab,
33
D. S. Rabeling,
72
I. Rácz,
83
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
J. D. Romano,
81
R. Romano,
3,4
G. Romanov,
112
J. H. Romie,
6
D. Rosi
ń
ska,
120,37
S. Rowan,
32
A. Rüdiger,
10
P. Ruggi,
30
K. Ryan,
33
S. Sachdev,
1
T. Sadecki,
33
L. Sadeghian,
16
M. Saleem,
101
F. Salemi,
10
L. Sammut,
80
E. Sanchez,
1
V. Sandberg,
33
J. R. Sanders,
65
I. Santiago-Prieto,
32
B. Sassolas,
59
B. S. Sathyaprakash,
7
P. R. Saulson,
31
R. Savage,
33
A. Sawadsky,
17
P. Schale,
54
R. Schilling,
10
P. Schmidt,
1
R. Schnabel,
10
R. M. S. Schofield,
54
A. Schönbeck,
10
E. Schreiber,
10
D. Schuette,
10
B. F. Schutz,
7
J. Scott,
32
S. M. Scott,
72
D. Sellers,
6
D. Sentenac,
30
V. Sequino,
66,67
A. Sergeev,
103
G. Serna,
22
A. Sevigny,
33
D. A. Shaddock,
72
P. Shaffery,
108
S. Shah,
11,46
M. S. Shahriar,
102
M. Shaltev,
10
Z. Shao,
1
B. Shapiro,
20
P. Shawhan,
57
D. H. Shoemaker,
12
T. L. Sidery,
39
K. Siellez,
47
X. Siemens,
16
D. Sigg,
33
A. D. Silva,
13
D. Simakov,
10
A. Singer,
1
L. P. Singer,
62
R. Singh,
2
A. M. Sintes,
60
B. J. J. Slagmolen,
72
J. R. Smith,
22
N. D. Smith,
1
R. J. E. Smith,
1
E. J. Son,
117
B. Sorazu,
32
T. Souradeep,
14
A. K. Srivastava,
93
A. Staley,
35
M. Steinke,
10
J. Steinlechner,
32
S. Steinlechner,
32
D. Steinmeyer,
10
B. C. Stephens,
16
S. Steplewski,
50
S. P. Stevenson,
39
R. Stone,
81
K. A. Strain,
32
N. Straniero,
59
N. A. Strauss,
73
S. Strigin,
43
R. Sturani,
113
A. L. Stuver,
6
T. Z. Summerscales,
121
L. Sun,
80
P. J. Sutton,
7
B. L. Swinkels,
30
M. J. Szczepanczyk,
53
M. Tacca,
34
D. Talukder,
54
D. B. Tanner,
5
M. Tápai,
91
S. P. Tarabrin,
10
A. Taracchini,
26
R. Taylor,
1
T. Theeg,
10
M. P. Thirugnanasambandam,
1
M. Thomas,
6
P. Thomas,
33
K. A. Thorne,
6
K. S. Thorne,
70
E. Thrane,
107
S. Tiwari,
74
V. Tiwari,
5
K. V. Tokmakov,
100
C. Tomlinson,
82
M. Tonelli,
36,19
C. V. Torres,
81
C. I. Torrie,
1
F. Travasso,
28,29
G. Traylor,
6
D. Trifirò,
21
M. C. Tringali,
86,87
M. Tse,
12
M. Turconi,
47
D. Ugolini,
122
C. S. Unnikrishnan,
92
A. L. Urban,
16
S. A. Usman,
31
H. Vahlbruch,
10
G. Vajente,
1
G. Valdes,
81
M. Vallisneri,
70
N. van Bakel,
11
M. van Beuzekom,
11
J. F. J. van den Brand,
56,11
C. van den Broeck,
11
L. van der Schaaf,
11
M. V. van der Sluys,
11,46
J. van Heijningen,
11
A. A. van Veggel,
32
M. Vardaro,
123,77
S. Vass,
1
M. Vasúth,
83
R. Vaulin,
12
A. Vecchio,
39
G. Vedovato,
77
J. Veitch,
39
P. J. Veitch,
96
K. Venkateswara,
124
D. Verkindt,
8
F. Vetrano,
51,52
A. Viceré,
51,52
J.-Y. Vinet,
47
S. Vitale,
12
T. Vo,
31
H. Vocca,
28,29
C. Vorvick,
33
W. D. Vousden,
39
S. P. Vyatchanin,
43
A. R. Wade,
72
J. AASI
et al.
PHYSICAL REVIEW D
93,
042007 (2016)
042007-2
M. Wade,
16
L. E. Wade IV,
16
M. Walker,
2
L. Wallace,
1
S. Walsh,
16
G. Wang,
74
H. Wang,
39
M. Wang,
39
X. Wang,
64
R. L. Ward,
72
J. Warner,
33
M. Was,
8
B. Weaver,
33
L.-W. Wei,
47
M. Weinert,
10
A. J. Weinstein,
1
R. Weiss,
12
T. Welborn,
6
L. Wen,
45
P. Weßels,
10
T. Westphal,
10
K. Wette,
10
J. T. Whelan,
118,10
S. E. Whitcomb,
1
D. J. White,
82
B. F. Whiting,
5
K. J. Williams,
111
L. Williams,
5
R. D. Williams,
1
A. R. Williamson,
7
J. L. Willis,
125
B. Willke,
17,10
M. H. Wimmer,
10
W. Winkler,
10
C. C. Wipf,
1
H. Wittel,
10
G. Woan,
32
J. Worden,
33
J. Yablon,
102
I. Yakushin,
6
W. Yam,
12
H. Yamamoto,
1
C. C. Yancey,
57
M. Yvert,
8
A. Zadro
ż
ny,
105
L. Zangrando,
77
M. Zanolin,
53
J.-P. Zendri,
77
Fan Zhang,
12
L. Zhang,
1
M. Zhang,
112
Y. Zhang,
118
C. Zhao,
45
M. Zhou,
102
X. J. Zhu,
45
M. E. Zucker,
12
S. E. Zuraw,
95
and J. Zweizig
1
(LIGO Scientific Collaboration and Virgo Collaboration)
1
LIGO
California Institute of Technology, Pasadena, California 91125, USA
2
Louisiana State University, Baton Rouge, Louisiana 70803, USA
3
Università di Salerno, Fisciano, I-84084 Salerno, Italy
4
INFN, Sezione di Napoli, Complesso Universitario di Monte S. Angelo, I-80126 Napoli, Italy
5
University of Florida, Gainesville, Florida 32611, USA
6
LIGO Livingston Observatory, Livingston, Louisiana 70754, USA
7
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 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, Sao 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
FIRST LOW FREQUENCY ALL-SKY SEARCH FOR
...
PHYSICAL REVIEW D
93,
042007 (2016)
042007-3
46
Department of Astrophysics/IMAPP, Radboud University Nijmegen,
P.O. Box 9010, 6500 GL Nijmegen, Netherlands
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, 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
J. AASI
et al.
PHYSICAL REVIEW D
93,
042007 (2016)
042007-4
100
SUPA, University of Strathclyde, Glasgow G1 1XQ, United Kingdom
101
IISER-TVM, CET Campus, Trivandrum Kerala 695016, India
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, Sao Paulo, Sao Paulo 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
(Received 22 October 2015; published 25 February 2016)
In this paper we present the results of the first low frequency all-sky search of continuous gravitational
wave signals conducted on Virgo VSR2 and VSR4 data. The search covered the full sky, a frequency range
between 20 and 128 Hz with a range of spin-down between
1
.
0
×
10
10
and
þ
1
.
5
×
10
11
Hz
=
s, and was
based on a hierarchical approach. The starting point was a set of short fast Fourier transforms, of length
8192 s, built from the calibrated strain data. Aggressive data cleaning, in both the time and frequency
domains, has been done in order to remove, as much as possible, the effect of disturbances of instrumental
origin. On each data set a number of candidates has been selected, using the FrequencyHough transform in
an incoherent step. Only coincident candidates among VSR2 and VSR4 have been examined in order to
strongly reduce the false alarm probability, and the most significant candidates have been selected. The
criteria we have used for candidate selection and for the coincidence step greatly reduce the harmful effect
of large instrumental artifacts. Selected candidates have been subject to a follow-up by constructing a new
set of longer fast Fourier transforms followed by a further incoherent analysis, still based on the
FrequencyHough transform. No evidence for continuous gravitational wave signals was found, and
therefore we have set a population-based joint VSR2-VSR4 90% confidence level upper limit on the
dimensionless gravitational wave strain in the frequency range between 20 and 128 Hz. This is the first
all-sky search for continuous gravitational waves conducted, on data of ground-based interferometric
detectors, at frequencies below 50 Hz. We set upper limits in the range between about
10
24
and
2
×
10
23
at most frequencies. Our upper limits on signal strain show an improvement of up to a factor of
2
with
respect to the results of previous all-sky searches at frequencies below 80 Hz.
DOI:
10.1103/PhysRevD.93.042007
I. INTRODUCTION
Continuous gravitational wave signals (CW) emitted by
asymmetric spinning neutron stars are among the
sources currently sought in the data of interferometric
gravitational wave detectors. The search for signals
emitted by spinning neutron stars with no electromagnetic
counterpart requires the exploration of a large portion
of the source parameter space, consisting of the source
position, signal frequency, and signal frequency time
derivative (spin-down). This kind of search, called all-
sky, cannot be based on fully coherent methods, as in
targeted searches for known pulsars, see, e.g., Refs.
[1,2]
,
FIRST LOW FREQUENCY ALL-SKY SEARCH FOR
...
PHYSICAL REVIEW D
93,
042007 (2016)
042007-5
because of the huge computational resources that would be
required.
For this reason various hierachical analysis pipelines,
based on the alternation of coherent and incoherent steps,
have been developed
[3
7]
. They allow us to dramatically
reduce the computational burden of the analysis, at the cost
of a small sensitivity loss. In this paper we present the
results of the first all-sky search for CW signals using the
data of Virgo science runs VSR2 and VSR4 (discussed in
Sec.
III
). The analysis has been carried out on the frequency
band 20
128 Hz, using an efficient hierarchical analysis
pipeline, based on the FrequencyHough transform
[7]
.No
detection was made, so we established upper limits on
signal strain amplitude as a function of the frequency.
Frequencies below 50 Hz have never been considered in
all-sky searches for CW signals, and the estimated joint
sensitivity of Virgo VSR2 and VSR4 data is better than that
of data from LIGO science runs S5 and S6 below about
60
70 Hz. Moreover, lower frequencies could potentially
offer promising sources. Higher frequency signals would
be in principle easier to detect because of their high signal
amplitudes at fixed distance and ellipticity [see Eq.
(5)
]. On
the other hand, neutron stars with no electromagnetic
counterpart, which are the main target of an all-sky search,
could have a spin rate distribution significantly different
with respect to standard pulsars. Then, we cannot exclude
that a substantial fraction of neutron stars emits gravita-
tional waves with frequency in the range between 20 and
about 100 Hz. This is particularly true when considering
young, unrecycled, neutron stars, which could be more
distorted than older objects. Below about 20 Hz, the
detector sensitivity significantly worsens, and the noise
is highly nonstationary making the analysis pointless. A
search at low frequency, as described below, could detect
signals from a potentially significant population of nearby
neutron stars.
The plan of the paper is as follows. In Sec.
II
,we
describe the kind of gravitational wave (GW) signal we are
searching for. In Sec.
III
, we discuss the Virgo detector
performance during the VSR2 and VSR4 runs. In Sec.
IV
,
we briefly recap the analysis procedure, referring the reader
to Ref.
[7]
for more details. Section
V
is focused on the
cleaning steps applied at different stages of the analysis.
Section
VI
is dedicated to candidate selection and Sec.
VII
to their clustering and coincidences. Section
VIII
deals with
the follow-up of candidates surviving the coincidence step.
Section
IX
is dedicated to validation tests of the analysis
pipeline, by using hardware-injected signals in VSR2 and
VSR4 data. In Sec.
X
, a joint upper limit on signal strain
amplitude is derived as a function of the search frequency.
Conclusions and future prospects are presented in Sec.
XI
.
Appendix
A
contains a list of the 108 candidates for which
the follow-up has been done, along with their main
parameters. Appendix
B
is devoted to a deeper analysis
of the three outliers found. Appendix
C
contains the list of
frequency intervals excluded from the computation of the
upper limits.
II. SIGNAL
The expected quadrupolar GW signal from a nonax-
isymmetric neutron star steadily spinning around one of its
principal axes has a frequency
f
0
twice the rotation
frequency
f
rot
, with a strain at the detector of
[7,8]
h
ð
t
Þ¼
H
0
ð
H
þ
A
þ
þ
H
×
A
×
Þ
e
|
ð
ω
ð
t
Þ
t
þ
Φ
0
Þ
;
ð
1
Þ
where taking the real part is understood and where
Φ
0
is an
initial phase. The signal
s time-dependent angular fre-
quency
ω
ð
t
Þ
will be discussed below. The two complex
amplitudes
H
þ
and
H
×
are given, respectively, by
H
þ
¼
cos
2
ψ
|
η
sin
2
ψ
ffiffiffiffiffiffiffiffiffiffiffiffiffi
1
þ
η
2
p
;
ð
2
Þ
H
×
¼
sin
2
ψ
þ
|
η
cos
2
ψ
ffiffiffiffiffiffiffiffiffiffiffiffiffi
1
þ
η
2
p
;
ð
3
Þ
in which
η
is the ratio of the polarization ellipse semiminor
to semimajor axis and the polarization angle
ψ
defines the
direction of the major axis with respect to the celestial
parallel of the source (counterclockwise). The parameter
η
varies in the range
½
1
;
1

, where
η
¼
0
for a linearly
polarized wave, while
η
¼
1
for a circularly polarized
wave (
η
¼
1
if the circular rotation is counterclockwise).
The functions
A
þ
;
×
describe the detector response as a
function of time, with a periodicity of one and two sidereal
periods, and depend on the source position, detector
position and orientation on the Earth
[8]
.
As discussed in Ref.
[1]
, the strain described by Eq.
(1)
is
equivalent to the standard expression (see, e.g., Ref.
[9]
)
h
ð
t
Þ¼
1
2
F
þ
ð
t;
ψ
Þ
h
0
ð
1
þ
cos
2
ι
Þ
cos
Φ
ð
t
Þ
þ
F
×
ð
t;
ψ
Þ
h
0
cos
ι
sin
Φ
ð
t
Þ
:
ð
4
Þ
Here,
F
þ
;F
×
are the standard beam-pattern functions, and
ι
is the angle between the star
s rotation axis and the line of
sight. The amplitude parameter
h
0
¼
4
π
2
G
c
4
I
zz
ε
f
2
0
d
ð
5
Þ
depends on the signal frequency
f
0
and on the source
distance
d
;on
I
zz
, the star
s moment of inertia with respect
to the principal axis aligned with the rotation axis; and on
ε
,
which is the fiducial equatorial ellipticity expressed in
terms of principal moments of inertia as
J. AASI
et al.
PHYSICAL REVIEW D
93,
042007 (2016)
042007-6
ε
¼
I
xx
I
yy
I
zz
:
ð
6
Þ
It must be stressed that it is not the fiducial ellipticity but
the quadrupole moment
Q
22
I
zz
ε
that, in case of detec-
tion, can be measured independently of any assumption
about the star
s equation of state and moment of inertia
(assuming the source distance can be also estimated). There
exist estimates of the maximum ellipticity a neutron star
can sustain from both elastic and magnetic deformations. In
the elastic case, these maxima depend strongly on the
breaking strain of the solid portion sustaining the defor-
mation (see, e.g., Refs.
[10]
and
[11]
for calculations for the
crust) as well as on the star
s structure and equation of state
and the possible presence of exotic phases in the stars
interior (like in hybrid or strange quark stars; see, e.g.,
Ref.
[12]
). In the magnetic case, the deformation depends
on the strength and configuration of the star
s internal
magnetic field (see, e.g., Ref.
[13]
). However, the actual
ellipticity of a given neutron star is unknown
the best we
have are observational upper limits. The relations between
H
0
;
η
and
h
0
;
ι
are given, e.g., in Ref.
[8]
. In Eq.
(1)
, the
signal angular frequency
ω
ð
t
Þ
is a function of time, and
therefore the signal phase
Φ
ð
t
Þ¼
Z
t
t
0
ω
ð
t
0
Þ
dt
0
ð
7
Þ
is not that of a simple monochromatic signal. It depends
on the rotational frequency and frequency derivatives of
the neutron star, as well as on Doppler and propagation
effects. In particular, the received Doppler-shifted fre-
quency
f
ð
t
Þ
is related to the emitted frequency
f
0
ð
t
Þ
by
the well-known relation (valid in the nonrelativistic
approximation)
f
ð
t
Þ¼
1
2
π
d
Φ
ð
t
Þ
dt
¼
f
0
ð
t
Þ

1
þ
~
v
ð
t
Þ
·
ˆ
n
c

;
ð
8
Þ
where
~
v
is the detector velocity with respect to the Solar
System barycenter (SSB),
ˆ
n
is the unit vector in the
direction to the source from the SSB, and
c
is the light
speed. A smaller relativistic effect, namely the
Einstein
delay
, is not relevant for the incoherent step of the search
described in Sec.
IV
, due to the use of short length fast
Fourier transforms (FFTs), and has been therefore
neglected. On the contrary, it has been taken into account
in the candidate follow-up, described in Sec.
VIII
,spe-
cifically when a coherent analysis using candidate param-
eters is done.
The intrinsic signal frequency
f
0
ð
t
Þ
slowly decreases in
time due to the source
s spin-down, associated with the
rotational energy loss following emission of electromag-
netic and/or gravitational radiation. The spin-down can be
described through a series expansion
f
0
ð
t
Þ¼
f
0
þ
_
f
0
ð
t
t
0
Þþ
̈
f
0
2
ð
t
t
0
Þ
2
þð
9
Þ
In general, the frequency evolution of a CW depends on
3
þ
s
parameters: position, frequency, and
s
spin-down
parameters. In the all-sky search described in this paper, we
need to take into account only the first spin-down (
s
¼
1
)
parameter (see Sec.
IV
).
III. INSTRUMENTAL PERFORMANCE DURING
VSR2 AND VSR4 RUNS
Interferometric GW detectors, such as LIGO
[14]
,
Virgo
[15]
,andGEO
[16]
, have collected years of data,
from 2002 to 2011. For the analysis described in this
paper, we have used calibrated data from the Virgo VSR2
and VSR4 science runs. The VSR3 run was characterized
by a diminished sensitivity level and poor data quality
(highly nonstationary data, large glitch rate) and so was
not included in this analysis. The VSR2 run began on July
7, 2009 (21:00 UTC) and ended on January 8, 2010 (22:00
UTC). The duty cycle was 80.4%, resulting in a total of
149
days of
science mode
data, divided among 361
segments. The data used in the analysis have been
produced using the most up-to-date calibration parameters
and reconstruction procedure. The associated systematic
error amounts to 5.5% in amplitude and
50
mrad in
phase
[17]
.
The VSR4 run extended from June 3, 2011 (10:27
UTC) to September 5, 2011 (13:26 UTC), with a duty
factor of about 81%, corresponding to an effective
duration of 76 days. Calibration uncertainties amounted
to 7.5% in amplitude and
ð
40
þ
50
f
kHz
Þ
mrad in phase up
to 500 Hz, where
f
kHz
is the frequency in kilohertz
[18]
.
The uncertainty on the amplitude contributes to the
uncertainty on the upper limit on the signal amplitude,
together with that coming from the finite size of the
Monte Carlo simulation used to compute it (see Sec.
X
). A
calibration error on the phase of this size can be shown to
have a negligible impact on the analysis
[1]
. The low-
frequency sensitivity of VSR4 was significantly better, up
to a factor of 2, than that of previous Virgo runs, primarily
due to the use of monolithic mirror suspensions, and
nearly in agreement with the design sensitivity of the
initial Virgo interferometer
[15]
.Thisrepresentsaremark-
able improvement considering that, with the gravitational
wave strain being proportional to the inverse of the
distance to the source, a factor of 2 in sensitivity
corresponds to an increase of a factor of 8 in the accessible
volume of space (assuming a homogeneous source dis-
tribution). We show in Fig.
1
the average experimental
strain amplitude spectral density for VSR2 and VSR4, in
the frequency range 20
128Hz,obtainedbymakingan
average of the periodograms (squared modulus of the
FFTs) stored in the short FFT database (see the next
section).
FIRST LOW FREQUENCY ALL-SKY SEARCH FOR
...
PHYSICAL REVIEW D
93,
042007 (2016)
042007-7
IV. ANALYSIS PROCEDURE
All-sky searches are intractable using completely coher-
ent methods because of the huge size of the parameter
space, which poses challenging computational problems
[19,20]
. Moreover, a completely coherent search would not
be robust against unpredictable phase variations of the
signal during the observation time.
For these reasons, hierarchical schemes have been
developed. The hierarchical scheme we have used for this
analysis has been described in detail in Ref.
[7]
. In this
section, we briefly recall the main steps. The analysis starts
from the detector calibrated data, sampled at 4096 Hz. The
first step consists of constructing a database of
short
discrete Fourier transforms
(SFDBs)
[21]
, computed
through the FFT algorithm [the FFT is just an efficient
algorithm to compute discrete Fourier transforms (DFTs),
but for historical reasons and for consistency with previous
papers, we will use the term FFT instead of DFT). Each
FFT covers the frequency range from 20 to 128 Hz and is
built from a data chunk of duration (
coherence time
) short
enough such that if a signal is present, its frequency
(modified by Doppler and spin-down) does not shift more
than a frequency bin. The FFT duration for this search is
8192 sec. This corresponds to a natural frequency reso-
lution
δ
f
¼
1
.
22
×
10
4
Hz. The FFTs are interlaced by
half and windowed with a Tukey window with a width
parameter
α
¼
0
.
5
[22]
. Before constructing the SFDB,
short strong time-domain disturbances are removed from
the data. This is the first of several cleaning steps applied to
the data (see Sec.
V
). The total number of FFTs for the
VSR2 run is 3896 and for the VSR4 run is 1978.
From the SFDB, we create a time-frequency map, called
the
peakmap
[23]
. This is obtained by selecting the most
significant local maxima (which we call
peaks
) of the
square root of equalized periodograms, obtained by divid-
ing the periodogram by an autoregressive average spectrum
estimation. The threshold for peak selection has been
chosen equal to
ffiffiffiffiffiffiffi
2
.
5
p
¼
1
.
58
[7]
which, in the ideal case
of Gaussian noise, would correspond to a probability of
selecting a peak of 0.0755. The peakmap is cleaned by
removing peaks clearly due to disturbances, as explained in
Sec.
V
. The peakmap is then corrected for the Doppler shift
for the different sky directions, by shifting the frequency of
the peaks by an amount corresponding to the variation the
frequency of a signal coming from a given direction would
be subject to at a given time. A
coarse
grid in the sky is
used in this stage of the analysis. The grid is built using
ecliptic coordinates, as described in Ref.
[7]
. Figure
2
shows the number of sky points (
patches
) as a function of
the frequency (in steps of 1 Hz), for both VSR2 and VSR4
analyses. The number of patches increases with the
square of the frequency and ranges from 2492 at 20 Hz
to 81244 at 128 Hz. The total number of sky patches
is
N
sky
3
.
5
×
10
6
.
Each corrected peakmap is the input of the incoherent
step, based on the FrequencyHough transform
[7,24]
. This
is a very efficient implementation of the Hough transform
(see Ref.
[24]
for efficiency tests and comparison with a
different implementation) which, for every sky position,
maps the points of the peakmap into the signal frequency/
spin-down plane. In the FrequencyHough transform, we
take into account slowly varying nonstationarity in the
noise and the varying detector sensitivity caused by the
time-dependent radiation pattern
[25,26]
. Furthermore,
the frequency/spin-down plane is discretized by building
a suitable grid
[7]
. As the transformation from the peakmap
to the Hough plane is not computationally bounded by the
size of the frequency bin (which only affects the size of the
Hough map), we have increased the frequency resolution
by a factor of 10, with respect to the natural step size
δ
f
,in
order to reduce the digitalization loss, so that the actual
resolution is
δ
f
H
¼
δ
f=
10
¼
1
.
22
×
10
5
Hz.
20
40
60
80
100
120
0
1
2
3
4
5
6
7
8
9
x 10
4
Frequency [Hz]
Number of sky patches
FIG. 2. Number of sky patches in every 1 Hz band, from 20 up
to 128 Hz. The frequency on the abscissa axis indicates the
beginning frequency of each band. The number of patches
increases with the square of the frequency and is fixed by the
highest frequency of each 1 Hz band.
20
30
40
50
60
70
80
90
100
110
120
130
10
−22
10
−21
Frequency [Hz]
Strain amplitude spectral density [Hz
−1/2
]
FIG. 1. VSR2 (darker, black in the color version) and VSR4
(lighter, red in the color version) average strain amplitude spectral
density in the frequency range from 20 up to 128 Hz.
J. AASI
et al.
PHYSICAL REVIEW D
93,
042007 (2016)
042007-8
We have searched approximately over the spin-down
range
½
1
.
0
×
10
10
;
þ
1
.
5
×
10
11

Hz
=
s. This choice has
been dictated by the need to not increase too much the
computational load of the analysis while, at the same time,
covering a range of spin-down values including the values
measured for most known pulsars. Given the spin-down bin
width scales as
T
1
obs
(
δ
_
f
¼
δ
f=T
obs
), this implies a different
number of spin-down values for the two data sets:
N
sd
¼
16
for VSR2 with a resolution of
δ
_
f
¼
7
.
63
×
10
12
Hz
=
s and
N
sd
¼
9
for VSR4 with a resolution of
δ
_
f
¼
1
.
5
×
10
11
Hz
=
s.
The corresponding minimum gravitational-wave spin-
down age, defined as
τ
min
ð
f
Þ¼
f=
4
N
sd
δ
_
f
(where
4
N
sd
δ
_
f
is the absolute value of the maximum spin-down we have
searched over), is a function of the frequency, going from
1600
to
10200
yr for VSR2 and from
1500
to
9700
yr for VSR4. These values are large enough that
only the first order spin-down is needed in the analysis
[7]
.
In Table
I
, some quantities referring to the FFTs and
peakmaps of VSR2 and VSR4 data sets are given. Table
II
contains a summary of the main parameters of the coarse
step, among which is the exact spin-down range considered
for VSR2 and VSR4 analyses.
For a given sky position, the result of the
FrequencyHough transform is a histogram in the signal
frequency/spin-down plane, called the Hough map. The
most significant candidates, i.e., the bins of the Hough map
with the highest amplitude, are then selected using an
effective way to avoid being blinded by particularly
disturbed frequency bands (see Sec.
VI
and Ref.
[7]
).
For each coarse (or
raw
) candidate, a refined search, still
based on the FrequencyHough, is run again on the
neighborhood of the candidate parameters, and the final
first-level
refined candidates are selected. The refinement
results in a reduction of the digitalization effects, that is the
sensitivity loss due to the use of a discrete grid in the
parameter space. With regard to the frequency, which was
already refined at the coarse step, no further over-resolution
occurs. For the spin-down, we have used an over-resolution
factor
K
_
f
¼
6
; i.e., the coarse interval between the spin-
down of each candidate and the next value (on both sides) is
divided in six pieces. The refined search range includes
2
K
_
f
¼
12
bins on the left of the coarse original value and
ð
2
K
_
f
1
Þ¼
11
bins on the right, so that two coarse bins
are covered on both sides. This choice is dictated by the fact
that the refinement is also done in parallel for the position
of the source, and because of parameter correlation, a
coarse candidate could be found with a refined spin-
down value outside the original coarse bin. Using an
over-resolution factor
K
_
f
¼
6
is a compromise between
the reduction of digitization effects and the increase of
computational load.
The refinement in the sky position for every candidate is
performed by using a rectangular region centered at the
candidate coordinates. The distance between the estimated
latitude (longitude) and the next latitude (longitude) point
in the coarse grid is divided into
K
sky
¼
5
points, so that 25
sky points are considered in total; see the discussion in
Sec. IX-C of Ref.
[7]
.
From a practical point of view, the incoherent step of the
analysis has been done by splitting the full parameter space
to be explored in several independent jobs. Each job
covered a frequency band of 5 Hz, the full spin-down
range, and a portion of the sky (the extent of which
depended on the frequency band and was chosen to
maintain balanced job durations). The full set of jobs
was run on the European Grid Infrastructure (
http://www
.egi.eu/
). Overall, about 7000 jobs were run, with a total
computational load of about 22,000 CPU hours.
Candidates found in the analysis of VSR2 and VSR4
data are then
clustered
, grouping together those occupying
nearby points in the parameter space. This is done to
improve the computational efficiency of the next steps of
the analysis. In order to significantly reduce the false alarm
probability,
coincidences
are required among clusters of
candidates obtained from the two data sets. The most
significant coincident candidates are subject to a
follow-up
with greater coherence time, in order to confirm or discard
them. Candidate selection and analysis are described in
some detail in Secs.
VI
VIII
.
V. DATA CLEANING
Time and frequency domain disturbances in detector data
affect the search and, if not properly removed, can
TABLE I. Some quantities referring to FFTs and peakmaps. For
each run,
T
obs
is the run duration,
T
start
is the run start epoch,
expressed by Modified Julian Date (MJD),
T
FFT
is the FFT time
length, and
N
peaks
is the number of peaks in the peakmap, after
applying all the vetoing procedures.
Run
T
obs
(days)
T
start
(MJD)
T
FFT
(s)
N
peaks
(after vetoes)
VSR2
185
55 112
8192
191 771 835
VSR4
95
55 762
8192
93 896 752
TABLE II. Summary of the main parameters for the coarse step of the analysis.
δ
f
H
is the frequency bin,
N
f
is the number of
frequency bins in the analyzed band,
δ
_
f
is the spin-down bin,
N
sd
is the number of spin-down steps,
Δ
_
f
is the range of spin-down
covered in the analysis,
τ
min
is the corresponding minimum spin-down age, and
N
sky
is the total number of sky patches.
Run
δ
f
H
(Hz)
N
f
δ
_
f
( Hz/s)
N
sd
Δ
_
f
(Hz/s)
τ
min
(yr)
N
sky
VSR2
1
.
22
×
10
5
8 847 360
7
.
63
×
10
12
16
½
9
.
91
;
1
.
52

×
10
11
1600
10200
3 528 767
VSR4
1
.
22
×
10
5
8 847 360
1
.
50
×
10
11
9
½
10
.
5
;
1
.
50

×
10
11
1500
9700
3 528 767
FIRST LOW FREQUENCY ALL-SKY SEARCH FOR
...
PHYSICAL REVIEW D
93,
042007 (2016)
042007-9
significantly degrade the search sensitivity, in the worst
case blinding the search at certain times or in certain
frequency bands. The effects can vary depending on the
nature and amplitude of the disturbance. As described in
Ref.
[7]
, we apply cleaning procedures to safely remove
such disturbances or reduce their effect, without contami-
nating a possible CW signal. The disturbances can be
cataloged as
time-domain glitches,
which enhance the
noise level of the detector in a wide frequency band:
spectral lines of constant frequency,
in most cases of
known origin, like calibration lines or lines of which the
origin has been discovered by studying the behavior of the
detector and the surrounding environment, or
spectral
wandering lines,
where the frequency of the disturbance
changes in time (often of unknown origin and present only
for a few days or even hours). Time-domain glitches are
removed during the construction of the SFDB.
Spectral wandering lines and spectral lines of constant
frequency are removed from the peakmaps
[7]
. Removal of
spectral wandering lines (composed by peaks occurring at
varying frequencies) is based on the construction of a
histogram of low resolution (both in time and in frequency)
peakmap entries, which we call the
gross histogram.
Based on a study on VSR2 and VSR4 data, we have chosen
a time resolution of 12 h and a frequency resolution of
0.01 Hz. In this way, any true CW signal of plausible
strength would be completely confined within one bin but
would not significantly contribute to the histogram, avoid-
ing veto. As an example, Fig.
3
shows the time-frequency
plot of the peaks removed by the gross histogram cleaning
procedure on VSR2 and VSR4 data, and Fig.
4
shows the
histogram of the removed peaks, using a 10 mHz bin width,
again both for VSR2 and VSR4 data.
A second veto, aimed at removing lines of constant
frequency, is based on the
persistency
analysis of the
peakmaps, defined as the ratio between the number of FFTs
in which a given line was present and the total number of
analyzed FFTs. The vetoing procedure consisted of histo-
gramming the frequency bins and setting a reasonable
threshold to select lines to be removed. To evaluate the veto
FIG. 3. Time-frequency plot of the peaks removed by the gross histogram cleaning procedure for VSR2 (left) and VSR4 (right).
20
40
60
80
100
120
0
1000
2000
3000
4000
5000
6000
7000
Frequency [Hz]
Histogram
20
40
60
80
100
120
0
500
1000
1500
2000
2500
3000
3500
Frequency [Hz]
Histogram
FIG. 4. Histogram of the peaks removed by the gross histogram veto for VSR2 (left) and VSR4 (right). The size of the bins in the
histogram is 10 mHz.
J. AASI
et al.
PHYSICAL REVIEW D
93,
042007 (2016)
042007-10