of 14
Upper Limits on the Stochastic Gravitational-Wave Background from
Advanced LIGO’s First Observing Run
B. P. Abbott,
1
R. Abbott,
1
T. D. Abbott,
2
M. R. Abernathy,
3
F. Acernese,
4
,
5
K. Ackley,
6
C. Adams,
7
T. Adams,
8
P. Addesso,
9
R. X. Adhikari,
1
V. B. Adya,
10
C. Affeldt,
10
M. Agathos,
11
K. Agatsuma,
11
N. Aggarwal,
12
O. D. Aguiar,
13
L. Aiello,
14
,
15
A. Ain,
16
P. Ajith,
17
B. Allen,
10
,
18
,
19
A. Allocca,
20
,
21
P. A. Altin,
22
A. Ananyeva,
1
S. B. Anderson,
1
W. G. Anderson,
18
S. Appert,
1
K. Arai,
1
M. C. Araya,
1
J. S. Areeda,
23
N. Arnaud,
24
K. G. Arun,
25
S. Ascenzi,
26
,
15
G. Ashton,
10
M. Ast,
27
S. M. Aston,
7
P. Astone,
28
P. Aufmuth,
19
C. Aulbert,
10
A. Avila-Alvarez,
23
S. Babak,
29
P. Bacon,
30
M. K. M. Bader,
11
P. T. Baker,
31
F. Baldaccini,
32
,
33
G. Ballardin,
34
S. W. Ballmer,
35
J. C. Barayoga,
1
S. E. Barclay,
36
B. C. Barish,
1
D. Barker,
37
F. Barone,
4
,
5
B. Barr,
36
L. Barsotti,
12
M. Barsuglia,
30
D. Barta,
38
J. Bartlett,
37
I. Bartos,
39
R. Bassiri,
40
A. Basti,
20
,
21
J. C. Batch,
37
C. Baune,
10
V. Bavigadda,
34
M. Bazzan,
41
,
42
C. Beer,
10
M. Bejger,
43
I. Belahcene,
24
M. Belgin,
44
A. S. Bell,
36
B. K. Berger,
1
G. Bergmann,
10
C. P. L. Berry,
45
D. Bersanetti,
46
,
47
A. Bertolini,
11
J. Betzwieser,
7
S. Bhagwat,
35
R. Bhandare,
48
I. A. Bilenko,
49
G. Billingsley,
1
C. R. Billman,
6
J. Birch,
7
R. Birney,
50
O. Birnholtz,
10
S. Biscans,
12
,
1
A. S. Biscoveanu,
74
A. Bisht,
19
M. Bitossi,
34
C. Biwer,
35
M. A. Bizouard,
24
J. K. Blackburn,
1
J. Blackman,
51
C. D. Blair,
52
D. G. Blair,
52
R. M. Blair,
37
S. Bloemen,
53
O. Bock,
10
M. Boer,
54
G. Bogaert,
54
A. Bohe,
29
F. Bondu,
55
R. Bonnand,
8
B. A. Boom,
11
R. Bork,
1
V. Boschi,
20
,
21
S. Bose,
56
,
16
Y. Bouffanais,
30
A. Bozzi,
34
C. Bradaschia,
21
P. R. Brady,
18
V. B. Braginsky
,
49
M. Branchesi,
57
,
58
J. E. Brau,
59
T. Briant,
60
A. Brillet,
54
M. Brinkmann,
10
V. Brisson,
24
P. Brockill,
18
J. E. Broida,
61
A. F. Brooks,
1
D. A. Brown,
35
D. D. Brown,
45
N. M. Brown,
12
S. Brunett,
1
C. C. Buchanan,
2
A. Buikema,
12
T. Bulik,
62
H. J. Bulten,
63
,
11
A. Buonanno,
29
,
64
D. Buskulic,
8
C. Buy,
30
R. L. Byer,
40
M. Cabero,
10
L. Cadonati,
44
G. Cagnoli,
65
,
66
C. Cahillane,
1
J. Calder ́on Bustillo,
44
T. A. Callister,
1
E. Calloni,
67
,
5
J. B. Camp,
68
W. Campbell,
120
M. Canepa,
46
,
47
K. C. Cannon,
69
H. Cao,
70
J. Cao,
71
C. D. Capano,
10
E. Capocasa,
30
F. Carbognani,
34
S. Caride,
72
J. Casanueva Diaz,
24
C. Casentini,
26
,
15
S. Caudill,
18
M. Cavagli`a,
73
F. Cavalier,
24
R. Cavalieri,
34
G. Cella,
21
C. B. Cepeda,
1
L. Cerboni Baiardi,
57
,
58
G. Cerretani,
20
,
21
E. Cesarini,
26
,
15
S. J. Chamberlin,
74
M. Chan,
36
S. Chao,
75
P. Charlton,
76
E. Chassande-Mottin,
30
B. D. Cheeseboro,
31
H. Y. Chen,
77
Y. Chen,
51
H.-P. Cheng,
6
A. Chincarini,
47
A. Chiummo,
34
T. Chmiel,
78
H. S. Cho,
79
M. Cho,
64
J. H. Chow,
22
N. Christensen,
61
Q. Chu,
52
A. J. K. Chua,
80
S. Chua,
60
S. Chung,
52
G. Ciani,
6
F. Clara,
37
J. A. Clark,
44
F. Cleva,
54
C. Cocchieri,
73
E. Coccia,
14
,
15
P.-F. Cohadon,
60
A. Colla,
81
,
28
C. G. Collette,
82
L. Cominsky,
83
M. Constancio Jr.,
13
L. Conti,
42
S. J. Cooper,
45
T. R. Corbitt,
2
N. Cornish,
84
A. Corsi,
72
S. Cortese,
34
C. A. Costa,
13
E. Coughlin,
61
M. W. Coughlin,
61
S. B. Coughlin,
85
J.-P. Coulon,
54
S. T. Countryman,
39
P. Couvares,
1
P. B. Covas,
86
E. E. Cowan,
44
D. M. Coward,
52
M. J. Cowart,
7
D. C. Coyne,
1
R. Coyne,
72
J. D. E. Creighton,
18
T. D. Creighton,
87
J. Cripe,
2
S. G. Crowder,
88
T. J. Cullen,
23
A. Cumming,
36
L. Cunningham,
36
E. Cuoco,
34
T. Dal Canton,
68
S. L. Danilishin,
36
S. D’Antonio,
15
K. Danzmann,
19
,
10
A. Dasgupta,
89
C. F. Da Silva Costa,
6
V. Dattilo,
34
I. Dave,
48
M. Davier,
24
G. S. Davies,
36
D. Davis,
35
E. J. Daw,
90
B. Day,
44
R. Day,
34
S. De,
35
D. DeBra,
40
G. Debreczeni,
38
J. Degallaix,
65
M. De Laurentis,
67
,
5
S. Del ́eglise,
60
W. Del Pozzo,
45
T. Denker,
10
T. Dent,
10
V. Dergachev,
29
R. De Rosa,
67
,
5
R. T. DeRosa,
7
R. DeSalvo,
91
J. Devenson,
50
R. C. Devine,
31
S. Dhurandhar,
16
M. C. D ́ıaz,
87
L. Di Fiore,
5
M. Di Giovanni,
92
,
93
T. Di Girolamo,
67
,
5
A. Di Lieto,
20
,
21
S. Di Pace,
81
,
28
I. Di Palma,
29
,
81
,
28
A. Di Virgilio,
21
Z. Doctor,
77
V. Dolique,
65
F. Donovan,
12
K. L. Dooley,
73
S. Doravari,
10
I. Dorrington,
94
R. Douglas,
36
M. Dovale
́
Alvarez,
45
T. P. Downes,
18
M. Drago,
10
R. W. P. Drever,
1
J. C. Driggers,
37
Z. Du,
71
M. Ducrot,
8
S. E. Dwyer,
37
T. B. Edo,
90
M. C. Edwards,
61
A. Effler,
7
H.-B. Eggenstein,
10
P. Ehrens,
1
J. Eichholz,
1
S. S. Eikenberry,
6
R. C. Essick,
12
Z. Etienne,
31
T. Etzel,
1
M. Evans,
12
T. M. Evans,
7
R. Everett,
74
M. Factourovich,
39
V. Fafone,
26
,
15
,
14
H. Fair,
35
S. Fairhurst,
94
X. Fan,
71
S. Farinon,
47
B. Farr,
77
W. M. Farr,
45
E. J. Fauchon-Jones,
94
M. Favata,
95
M. Fays,
94
H. Fehrmann,
10
M. M. Fejer,
40
A. Fern ́andez Galiana,
12
I. Ferrante,
20
,
21
E. C. Ferreira,
13
F. Ferrini,
34
F. Fidecaro,
20
,
21
I. Fiori,
34
D. Fiorucci,
30
R. P. Fisher,
35
R. Flaminio,
65
,
96
M. Fletcher,
36
H. Fong,
97
S. S. Forsyth,
44
J.-D. Fournier,
54
S. Frasca,
81
,
28
F. Frasconi,
21
Z. Frei,
98
A. Freise,
45
R. Frey,
59
V. Frey,
24
E. M. Fries,
1
P. Fritschel,
12
V. V. Frolov,
7
P. Fulda,
6
,
68
M. Fyffe,
7
H. Gabbard,
10
B. U. Gadre,
16
S. M. Gaebel,
45
J. R. Gair,
99
L. Gammaitoni,
32
S. G. Gaonkar,
16
F. Garufi,
67
,
5
G. Gaur,
100
V. Gayathri,
101
N. Gehrels,
68
G. Gemme,
47
E. Genin,
34
A. Gennai,
21
J. George,
48
L. Gergely,
102
V. Germain,
8
S. Ghonge,
17
Abhirup Ghosh,
17
Archisman Ghosh,
11
,
17
S. Ghosh,
53
,
11
J. A. Giaime,
2
,
7
K. D. Giardina,
7
A. Giazotto,
21
K. Gill,
103
A. Glaefke,
36
E. Goetz,
10
R. Goetz,
6
L. Gondan,
98
G. Gonz ́alez,
2
J. M. Gonzalez Castro,
20
,
21
A. Gopakumar,
104
M. L. Gorodetsky,
49
S. E. Gossan,
1
M. Gosselin,
34
arXiv:1612.02029v2 [gr-qc] 30 Jan 2017
2
R. Gouaty,
8
A. Grado,
105
,
5
C. Graef,
36
M. Granata,
65
A. Grant,
36
S. Gras,
12
C. Gray,
37
G. Greco,
57
,
58
A. C. Green,
45
P. Groot,
53
H. Grote,
10
S. Grunewald,
29
G. M. Guidi,
57
,
58
X. Guo,
71
A. Gupta,
16
M. K. Gupta,
89
K. E. Gushwa,
1
E. K. Gustafson,
1
R. Gustafson,
106
J. J. Hacker,
23
B. R. Hall,
56
E. D. Hall,
1
G. Hammond,
36
M. Haney,
104
M. M. Hanke,
10
J. Hanks,
37
C. Hanna,
74
M. D. Hannam,
94
J. Hanson,
7
T. Hardwick,
2
J. Harms,
57
,
58
G. M. Harry,
3
I. W. Harry,
29
M. J. Hart,
36
M. T. Hartman,
6
C.-J. Haster,
45
,
97
K. Haughian,
36
J. Healy,
107
A. Heidmann,
60
M. C. Heintze,
7
H. Heitmann,
54
P. Hello,
24
G. Hemming,
34
M. Hendry,
36
I. S. Heng,
36
J. Hennig,
36
J. Henry,
107
A. W. Heptonstall,
1
M. Heurs,
10
,
19
S. Hild,
36
D. Hoak,
34
D. Hofman,
65
K. Holt,
7
D. E. Holz,
77
P. Hopkins,
94
J. Hough,
36
E. A. Houston,
36
E. J. Howell,
52
Y. M. Hu,
10
E. A. Huerta,
108
D. Huet,
24
B. Hughey,
103
S. Husa,
86
S. H. Huttner,
36
T. Huynh-Dinh,
7
N. Indik,
10
D. R. Ingram,
37
R. Inta,
72
H. N. Isa,
36
J.-M. Isac,
60
M. Isi,
1
T. Isogai,
12
B. R. Iyer,
17
K. Izumi,
37
T. Jacqmin,
60
K. Jani,
44
P. Jaranowski,
109
S. Jawahar,
110
F. Jim ́enez-Forteza,
86
W. W. Johnson,
2
D. I. Jones,
111
R. Jones,
36
R. J. G. Jonker,
11
L. Ju,
52
J. Junker,
10
C. V. Kalaghatgi,
94
V. Kalogera,
85
S. Kandhasamy,
73
G. Kang,
79
J. B. Kanner,
1
S. Karki,
59
K. S. Karvinen,
10
M. Kasprzack,
2
E. Katsavounidis,
12
W. Katzman,
7
S. Kaufer,
19
T. Kaur,
52
K. Kawabe,
37
F. K ́ef ́elian,
54
D. Keitel,
86
D. B. Kelley,
35
R. Kennedy,
90
J. S. Key,
112
F. Y. Khalili,
49
I. Khan,
14
S. Khan,
94
Z. Khan,
89
E. A. Khazanov,
113
N. Kijbunchoo,
37
Chunglee Kim,
114
J. C. Kim,
115
Whansun Kim,
116
W. Kim,
70
Y.-M. Kim,
117
,
114
S. J. Kimbrell,
44
E. J. King,
70
P. J. King,
37
R. Kirchhoff,
10
J. S. Kissel,
37
B. Klein,
85
L. Kleybolte,
27
S. Klimenko,
6
P. Koch,
10
S. M. Koehlenbeck,
10
S. Koley,
11
V. Kondrashov,
1
A. Kontos,
12
M. Korobko,
27
W. Z. Korth,
1
I. Kowalska,
62
D. B. Kozak,
1
C. Kr ̈amer,
10
V. Kringel,
10
A. Kr ́olak,
118
,
119
G. Kuehn,
10
P. Kumar,
97
R. Kumar,
89
L. Kuo,
75
A. Kutynia,
118
B. D. Lackey,
29
,
35
M. Landry,
37
R. N. Lang,
18
J. Lange,
107
B. Lantz,
40
R. K. Lanza,
12
A. Lartaux-Vollard,
24
P. D. Lasky,
120
M. Laxen,
7
A. Lazzarini,
1
C. Lazzaro,
42
P. Leaci,
81
,
28
S. Leavey,
36
E. O. Lebigot,
30
C. H. Lee,
117
H. K. Lee,
121
H. M. Lee,
114
K. Lee,
36
J. Lehmann,
10
A. Lenon,
31
M. Leonardi,
92
,
93
J. R. Leong,
10
N. Leroy,
24
N. Letendre,
8
Y. Levin,
120
T. G. F. Li,
122
A. Libson,
12
T. B. Littenberg,
123
J. Liu,
52
N. A. Lockerbie,
110
A. L. Lombardi,
44
L. T. London,
94
J. E. Lord,
35
M. Lorenzini,
14
,
15
V. Loriette,
124
M. Lormand,
7
G. Losurdo,
21
J. D. Lough,
10
,
19
G. Lovelace,
23
H. L ̈uck,
19
,
10
A. P. Lundgren,
10
R. Lynch,
12
Y. Ma,
51
S. Macfoy,
50
B. Machenschalk,
10
M. MacInnis,
12
D. M. Macleod,
2
F. Maga ̃na-Sandoval,
35
E. Majorana,
28
I. Maksimovic,
124
V. Malvezzi,
26
,
15
N. Man,
54
V. Mandic,
125
V. Mangano,
36
G. L. Mansell,
22
M. Manske,
18
M. Mantovani,
34
F. Marchesoni,
126
,
33
F. Marion,
8
S. M ́arka,
39
Z. M ́arka,
39
A. S. Markosyan,
40
E. Maros,
1
F. Martelli,
57
,
58
L. Martellini,
54
I. W. Martin,
36
D. V. Martynov,
12
K. Mason,
12
A. Masserot,
8
T. J. Massinger,
1
M. Masso-Reid,
36
S. Mastrogiovanni,
81
,
28
A. Matas,
125
F. Matichard,
12
,
1
L. Matone,
39
N. Mavalvala,
12
N. Mazumder,
56
R. McCarthy,
37
D. E. McClelland,
22
S. McCormick,
7
C. McGrath,
18
S. C. McGuire,
127
G. McIntyre,
1
J. McIver,
1
D. J. McManus,
22
T. McRae,
22
S. T. McWilliams,
31
D. Meacher,
54
,
74
G. D. Meadors,
29
,
10
J. Meidam,
11
A. Melatos,
128
G. Mendell,
37
D. Mendoza-Gandara,
10
R. A. Mercer,
18
E. L. Merilh,
37
M. Merzougui,
54
S. Meshkov,
1
C. Messenger,
36
C. Messick,
74
R. Metzdorff,
60
P. M. Meyers,
125
F. Mezzani,
28
,
81
H. Miao,
45
C. Michel,
65
H. Middleton,
45
E. E. Mikhailov,
129
L. Milano,
67
,
5
A. L. Miller,
6
,
81
,
28
A. Miller,
85
B. B. Miller,
85
J. Miller,
12
M. Millhouse,
84
Y. Minenkov,
15
J. Ming,
29
S. Mirshekari,
130
C. Mishra,
17
S. Mitra,
16
V. P. Mitrofanov,
49
G. Mitselmakher,
6
R. Mittleman,
12
A. Moggi,
21
M. Mohan,
34
S. R. P. Mohapatra,
12
M. Montani,
57
,
58
B. C. Moore,
95
C. J. Moore,
80
D. Moraru,
37
G. Moreno,
37
S. R. Morriss,
87
B. Mours,
8
C. M. Mow-Lowry,
45
G. Mueller,
6
A. W. Muir,
94
Arunava Mukherjee,
17
D. Mukherjee,
18
S. Mukherjee,
87
N. Mukund,
16
A. Mullavey,
7
J. Munch,
70
E. A. M. Muniz,
23
P. G. Murray,
36
A. Mytidis,
6
K. Napier,
44
I. Nardecchia,
26
,
15
L. Naticchioni,
81
,
28
G. Nelemans,
53
,
11
T. J. N. Nelson,
7
M. Neri,
46
,
47
M. Nery,
10
A. Neunzert,
106
J. M. Newport,
3
G. Newton,
36
T. T. Nguyen,
22
A. B. Nielsen,
10
S. Nissanke,
53
,
11
A. Nitz,
10
A. Noack,
10
F. Nocera,
34
D. Nolting,
7
M. E. N. Normandin,
87
L. K. Nuttall,
35
J. Oberling,
37
E. Ochsner,
18
E. Oelker,
12
G. H. Ogin,
131
J. J. Oh,
116
S. H. Oh,
116
F. Ohme,
94
,
10
M. Oliver,
86
P. Oppermann,
10
Richard J. Oram,
7
B. O’Reilly,
7
R. O’Shaughnessy,
107
D. J. Ottaway,
70
H. Overmier,
7
B. J. Owen,
72
A. E. Pace,
74
J. Page,
123
A. Pai,
101
S. A. Pai,
48
J. R. Palamos,
59
O. Palashov,
113
C. Palomba,
28
A. Pal-Singh,
27
H. Pan,
75
C. Pankow,
85
F. Pannarale,
94
B. C. Pant,
48
F. Paoletti,
34
,
21
A. Paoli,
34
M. A. Papa,
29
,
18
,
10
H. R. Paris,
40
W. Parker,
7
D. Pascucci,
36
A. Pasqualetti,
34
R. Passaquieti,
20
,
21
D. Passuello,
21
B. Patricelli,
20
,
21
B. L. Pearlstone,
36
M. Pedraza,
1
R. Pedurand,
65
,
132
L. Pekowsky,
35
A. Pele,
7
S. Penn,
133
C. J. Perez,
37
A. Perreca,
1
L. M. Perri,
85
H. P. Pfeiffer,
97
M. Phelps,
36
O. J. Piccinni,
81
,
28
M. Pichot,
54
F. Piergiovanni,
57
,
58
V. Pierro,
9
G. Pillant,
34
L. Pinard,
65
I. M. Pinto,
9
M. Pitkin,
36
M. Poe,
18
R. Poggiani,
20
,
21
P. Popolizio,
34
A. Post,
10
J. Powell,
36
J. Prasad,
16
J. W. W. Pratt,
103
V. Predoi,
94
T. Prestegard,
125
,
18
M. Prijatelj,
10
,
34
M. Principe,
9
S. Privitera,
29
3
G. A. Prodi,
92
,
93
L. G. Prokhorov,
49
O. Puncken,
10
M. Punturo,
33
P. Puppo,
28
M. P ̈urrer,
29
H. Qi,
18
J. Qin,
52
S. Qiu,
120
V. Quetschke,
87
E. A. Quintero,
1
R. Quitzow-James,
59
F. J. Raab,
37
D. S. Rabeling,
22
H. Radkins,
37
P. Raffai,
98
S. Raja,
48
C. Rajan,
48
M. Rakhmanov,
87
P. Rapagnani,
81
,
28
V. Raymond,
29
M. Razzano,
20
,
21
V. Re,
26
J. Read,
23
T. Regimbau,
54
L. Rei,
47
S. Reid,
50
D. H. Reitze,
1
,
6
H. Rew,
129
S. D. Reyes,
35
E. Rhoades,
103
F. Ricci,
81
,
28
K. Riles,
106
M. Rizzo,
107
N. A. Robertson,
1
,
36
R. Robie,
36
F. Robinet,
24
A. Rocchi,
15
L. Rolland,
8
J. G. Rollins,
1
V. J. Roma,
59
J. D. Romano,
87
R. Romano,
4
,
5
J. H. Romie,
7
D. Rosi ́nska,
134
,
43
S. Rowan,
36
A. R ̈udiger,
10
P. Ruggi,
34
K. Ryan,
37
S. Sachdev,
1
T. Sadecki,
37
L. Sadeghian,
18
M. Sakellariadou,
135
L. Salconi,
34
M. Saleem,
101
F. Salemi,
10
A. Samajdar,
136
L. Sammut,
120
L. M. Sampson,
85
E. J. Sanchez,
1
V. Sandberg,
37
J. R. Sanders,
35
B. Sassolas,
65
B. S. Sathyaprakash,
74
,
94
P. R. Saulson,
35
O. Sauter,
106
R. L. Savage,
37
A. Sawadsky,
19
P. Schale,
59
J. Scheuer,
85
S. Schlassa,
61
E. Schmidt,
103
J. Schmidt,
10
P. Schmidt,
1
,
51
R. Schnabel,
27
R. M. S. Schofield,
59
A. Sch ̈onbeck,
27
E. Schreiber,
10
D. Schuette,
10
,
19
B. F. Schutz,
94
,
29
S. G. Schwalbe,
103
J. Scott,
36
S. M. Scott,
22
D. Sellers,
7
A. S. Sengupta,
137
D. Sentenac,
34
V. Sequino,
26
,
15
A. Sergeev,
113
Y. Setyawati,
53
,
11
D. A. Shaddock,
22
T. J. Shaffer,
37
M. S. Shahriar,
85
B. Shapiro,
40
P. Shawhan,
64
A. Sheperd,
18
D. H. Shoemaker,
12
D. M. Shoemaker,
44
K. Siellez,
44
X. Siemens,
18
M. Sieniawska,
43
D. Sigg,
37
A. D. Silva,
13
A. Singer,
1
L. P. Singer,
68
A. Singh,
29
,
10
,
19
R. Singh,
2
A. Singhal,
14
A. M. Sintes,
86
B. J. J. Slagmolen,
22
B. Smith,
7
J. R. Smith,
23
R. J. E. Smith,
1
E. J. Son,
116
B. Sorazu,
36
F. Sorrentino,
47
T. Souradeep,
16
A. P. Spencer,
36
A. K. Srivastava,
89
A. Staley,
39
M. Steinke,
10
J. Steinlechner,
36
S. Steinlechner,
27
,
36
D. Steinmeyer,
10
,
19
B. C. Stephens,
18
S. P. Stevenson,
45
R. Stone,
87
K. A. Strain,
36
N. Straniero,
65
G. Stratta,
57
,
58
S. E. Strigin,
49
R. Sturani,
130
A. L. Stuver,
7
T. Z. Summerscales,
138
L. Sun,
128
S. Sunil,
89
P. J. Sutton,
94
B. L. Swinkels,
34
M. J. Szczepa ́nczyk,
103
M. Tacca,
30
D. Talukder,
59
D. B. Tanner,
6
D. Tao,
61
M. T ́apai,
102
A. Taracchini,
29
R. Taylor,
1
T. Theeg,
10
E. G. Thomas,
45
M. Thomas,
7
P. Thomas,
37
K. A. Thorne,
7
E. Thrane,
120
T. Tippens,
44
S. Tiwari,
14
,
93
V. Tiwari,
94
K. V. Tokmakov,
110
K. Toland,
36
C. Tomlinson,
90
M. Tonelli,
20
,
21
Z. Tornasi,
36
C. I. Torrie,
1
D. T ̈oyr ̈a,
45
F. Travasso,
32
,
33
G. Traylor,
7
D. Trifir`o,
73
J. Trinastic,
6
M. C. Tringali,
92
,
93
L. Trozzo,
139
,
21
M. Tse,
12
R. Tso,
1
M. Turconi,
54
D. Tuyenbayev,
87
D. Ugolini,
140
C. S. Unnikrishnan,
104
A. L. Urban,
1
S. A. Usman,
94
H. Vahlbruch,
19
G. Vajente,
1
G. Valdes,
87
N. van Bakel,
11
M. van Beuzekom,
11
J. F. J. van den Brand,
63
,
11
C. Van Den Broeck,
11
D. C. Vander-Hyde,
35
L. van der Schaaf,
11
J. V. van Heijningen,
11
A. A. van Veggel,
36
M. Vardaro,
41
,
42
V. Varma,
51
S. Vass,
1
M. Vas ́uth,
38
A. Vecchio,
45
G. Vedovato,
42
J. Veitch,
45
P. J. Veitch,
70
K. Venkateswara,
141
G. Venugopalan,
1
D. Verkindt,
8
F. Vetrano,
57
,
58
A. Vicer ́e,
57
,
58
A. D. Viets,
18
S. Vinciguerra,
45
D. J. Vine,
50
J.-Y. Vinet,
54
S. Vitale,
12
T. Vo,
35
H. Vocca,
32
,
33
C. Vorvick,
37
D. V. Voss,
6
W. D. Vousden,
45
S. P. Vyatchanin,
49
A. R. Wade,
1
L. E. Wade,
78
M. Wade,
78
M. Walker,
2
L. Wallace,
1
S. Walsh,
29
,
10
G. Wang,
14
,
58
H. Wang,
45
M. Wang,
45
Y. Wang,
52
R. L. Ward,
22
J. Warner,
37
M. Was,
8
J. Watchi,
82
B. Weaver,
37
L.-W. Wei,
54
M. Weinert,
10
A. J. Weinstein,
1
R. Weiss,
12
L. Wen,
52
P. Weßels,
10
T. Westphal,
10
K. Wette,
10
J. T. Whelan,
107
B. F. Whiting,
6
C. Whittle,
120
D. Williams,
36
R. D. Williams,
1
A. R. Williamson,
94
J. L. Willis,
142
B. Willke,
19
,
10
M. H. Wimmer,
10
,
19
W. Winkler,
10
C. C. Wipf,
1
H. Wittel,
10
,
19
G. Woan,
36
J. Woehler,
10
J. Worden,
37
J. L. Wright,
36
D. S. Wu,
10
G. Wu,
7
W. Yam,
12
H. Yamamoto,
1
C. C. Yancey,
64
M. J. Yap,
22
Hang Yu,
12
Haocun Yu,
12
M. Yvert,
8
A. Zadro ̇zny,
118
L. Zangrando,
42
M. Zanolin,
103
J.-P. Zendri,
42
M. Zevin,
85
L. Zhang,
1
M. Zhang,
129
T. Zhang,
36
Y. Zhang,
107
C. Zhao,
52
M. Zhou,
85
Z. Zhou,
85
S. J. Zhu,
29
,
10
X. J. Zhu,
52
M. E. Zucker,
1
,
12
and J. Zweizig
1
(LIGO Scientific Collaboration and Virgo Collaboration)
Deceased, March 2016.
1
LIGO, California Institute of Technology, Pasadena, CA 91125, USA
2
Louisiana State University, Baton Rouge, LA 70803, USA
3
American University, Washington, D.C. 20016, USA
4
Universit`a di Salerno, Fisciano, I-84084 Salerno, Italy
5
INFN, Sezione di Napoli, Complesso Universitario di Monte S.Angelo, I-80126 Napoli, Italy
6
University of Florida, Gainesville, FL 32611, USA
7
LIGO Livingston Observatory, Livingston, LA 70754, USA
8
Laboratoire d’Annecy-le-Vieux de Physique des Particules (LAPP),
Universit ́e 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 f ̈ur Gravitationsphysik, D-30167 Hannover, Germany
11
Nikhef, Science Park, 1098 XG Amsterdam, The Netherlands
4
12
LIGO, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
13
Instituto Nacional de Pesquisas Espaciais, 12227-010 S ̃ao Jos ́e dos Campos, S ̃ao Paulo, Brazil
14
INFN, Gran Sasso Science Institute, I-67100 L’Aquila, Italy
15
INFN, Sezione di Roma Tor Vergata, I-00133 Roma, Italy
16
Inter-University Centre for Astronomy and Astrophysics, Pune 411007, India
17
International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India
18
University of Wisconsin-Milwaukee, Milwaukee, WI 53201, USA
19
Leibniz Universit ̈at Hannover, D-30167 Hannover, Germany
20
Universit`a di Pisa, I-56127 Pisa, Italy
21
INFN, Sezione di Pisa, I-56127 Pisa, Italy
22
Australian National University, Canberra, Australian Capital Territory 0200, Australia
23
California State University Fullerton, Fullerton, CA 92831, USA
24
LAL, Univ. Paris-Sud, CNRS/IN2P3, Universit ́e Paris-Saclay, F-91898 Orsay, France
25
Chennai Mathematical Institute, Chennai 603103, India
26
Universit`a di Roma Tor Vergata, I-00133 Roma, Italy
27
Universit ̈at Hamburg, D-22761 Hamburg, Germany
28
INFN, Sezione di Roma, I-00185 Roma, Italy
29
Albert-Einstein-Institut, Max-Planck-Institut f ̈ur Gravitationsphysik, D-14476 Potsdam-Golm, Germany
30
APC, AstroParticule et Cosmologie, Universit ́e Paris Diderot,
CNRS/IN2P3, CEA/Irfu, Observatoire de Paris,
Sorbonne Paris Cit ́e, F-75205 Paris Cedex 13, France
31
West Virginia University, Morgantown, WV 26506, USA
32
Universit`a di Perugia, I-06123 Perugia, Italy
33
INFN, Sezione di Perugia, I-06123 Perugia, Italy
34
European Gravitational Observatory (EGO), I-56021 Cascina, Pisa, Italy
35
Syracuse University, Syracuse, NY 13244, USA
36
SUPA, University of Glasgow, Glasgow G12 8QQ, United Kingdom
37
LIGO Hanford Observatory, Richland, WA 99352, USA
38
Wigner RCP, RMKI, H-1121 Budapest, Konkoly Thege Mikl ́os ́ut 29-33, Hungary
39
Columbia University, New York, NY 10027, USA
40
Stanford University, Stanford, CA 94305, USA
41
Universit`a di Padova, Dipartimento di Fisica e Astronomia, I-35131 Padova, Italy
42
INFN, Sezione di Padova, I-35131 Padova, Italy
43
Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, 00-716, Warsaw, Poland
44
Center for Relativistic Astrophysics and School of Physics,
Georgia Institute of Technology, Atlanta, GA 30332, USA
45
University of Birmingham, Birmingham B15 2TT, United Kingdom
46
Universit`a degli Studi di Genova, I-16146 Genova, Italy
47
INFN, Sezione di Genova, I-16146 Genova, Italy
48
RRCAT, Indore MP 452013, India
49
Faculty of Physics, Lomonosov Moscow State University, Moscow 119991, Russia
50
SUPA, University of the West of Scotland, Paisley PA1 2BE, United Kingdom
51
Caltech CaRT, Pasadena, CA 91125, USA
52
University of Western Australia, Crawley, Western Australia 6009, Australia
53
Department of Astrophysics/IMAPP, Radboud University Nijmegen,
P.O. Box 9010, 6500 GL Nijmegen, The Netherlands
54
Artemis, Universit ́e Cˆote d’Azur, CNRS, Observatoire Cˆote d’Azur, CS 34229, F-06304 Nice Cedex 4, France
55
Institut de Physique de Rennes, CNRS, Universit ́e de Rennes 1, F-35042 Rennes, France
56
Washington State University, Pullman, WA 99164, USA
57
Universit`a degli Studi di Urbino ’Carlo Bo’, I-61029 Urbino, Italy
58
INFN, Sezione di Firenze, I-50019 Sesto Fiorentino, Firenze, Italy
59
University of Oregon, Eugene, OR 97403, USA
60
Laboratoire Kastler Brossel, UPMC-Sorbonne Universit ́es, CNRS,
ENS-PSL Research University, Coll`ege de France, F-75005 Paris, France
61
Carleton College, Northfield, MN 55057, USA
62
Astronomical Observatory Warsaw University, 00-478 Warsaw, Poland
63
VU University Amsterdam, 1081 HV Amsterdam, The Netherlands
64
University of Maryland, College Park, MD 20742, USA
65
Laboratoire des Mat ́eriaux Avanc ́es (LMA), CNRS/IN2P3, F-69622 Villeurbanne, France
66
Universit ́e Claude Bernard Lyon 1, F-69622 Villeurbanne, France
67
Universit`a di Napoli ’Federico II’, Complesso Universitario di Monte S.Angelo, I-80126 Napoli, Italy
68
NASA/Goddard Space Flight Center, Greenbelt, MD 20771, USA
69
RESCEU, University of Tokyo, Tokyo, 113-0033, Japan.
70
University of Adelaide, Adelaide, South Australia 5005, Australia
5
71
Tsinghua University, Beijing 100084, China
72
Texas Tech University, Lubbock, TX 79409, USA
73
The University of Mississippi, University, MS 38677, USA
74
The Pennsylvania State University, University Park, PA 16802, USA
75
National Tsing Hua University, Hsinchu City, 30013 Taiwan, Republic of China
76
Charles Sturt University, Wagga Wagga, New South Wales 2678, Australia
77
University of Chicago, Chicago, IL 60637, USA
78
Kenyon College, Gambier, OH 43022, USA
79
Korea Institute of Science and Technology Information, Daejeon 305-806, Korea
80
University of Cambridge, Cambridge CB2 1TN, United Kingdom
81
Universit`a di Roma ’La Sapienza’, I-00185 Roma, Italy
82
University of Brussels, Brussels 1050, Belgium
83
Sonoma State University, Rohnert Park, CA 94928, USA
84
Montana State University, Bozeman, MT 59717, USA
85
Center for Interdisciplinary Exploration & Research in Astrophysics (CIERA),
Northwestern University, Evanston, IL 60208, USA
86
Universitat de les Illes Balears, IAC3—IEEC, E-07122 Palma de Mallorca, Spain
87
The University of Texas Rio Grande Valley, Brownsville, TX 78520, USA
88
Bellevue College, Bellevue, WA 98007, USA
89
Institute for Plasma Research, Bhat, Gandhinagar 382428, India
90
The University of Sheffield, Sheffield S10 2TN, United Kingdom
91
California State University, Los Angeles, 5154 State University Dr, Los Angeles, CA 90032, USA
92
Universit`a di Trento, Dipartimento di Fisica, I-38123 Povo, Trento, Italy
93
INFN, Trento Institute for Fundamental Physics and Applications, I-38123 Povo, Trento, Italy
94
Cardiff University, Cardiff CF24 3AA, United Kingdom
95
Montclair State University, Montclair, NJ 07043, USA
96
National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan
97
Canadian Institute for Theoretical Astrophysics,
University of Toronto, Toronto, Ontario M5S 3H8, Canada
98
MTA E ̈otv ̈os University, “Lendulet” Astrophysics Research Group, Budapest 1117, Hungary
99
School of Mathematics, University of Edinburgh, Edinburgh EH9 3FD, United Kingdom
100
University and Institute of Advanced Research, Gandhinagar, Gujarat 382007, India
101
IISER-TVM, CET Campus, Trivandrum Kerala 695016, India
102
University of Szeged, D ́om t ́er 9, Szeged 6720, Hungary
103
Embry-Riddle Aeronautical University, Prescott, AZ 86301, USA
104
Tata Institute of Fundamental Research, Mumbai 400005, India
105
INAF, Osservatorio Astronomico di Capodimonte, I-80131, Napoli, Italy
106
University of Michigan, Ann Arbor, MI 48109, USA
107
Rochester Institute of Technology, Rochester, NY 14623, USA
108
NCSA, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
109
University of Bia lystok, 15-424 Bia lystok, Poland
110
SUPA, University of Strathclyde, Glasgow G1 1XQ, United Kingdom
111
University of Southampton, Southampton SO17 1BJ, United Kingdom
112
University of Washington Bothell, 18115 Campus Way NE, Bothell, WA 98011, USA
113
Institute of Applied Physics, Nizhny Novgorod, 603950, Russia
114
Seoul National University, Seoul 151-742, Korea
115
Inje University Gimhae, 621-749 South Gyeongsang, Korea
116
National Institute for Mathematical Sciences, Daejeon 305-390, Korea
117
Pusan National University, Busan 609-735, Korea
118
NCBJ, 05-400
́
Swierk-Otwock, Poland
119
Institute of Mathematics, Polish Academy of Sciences, 00656 Warsaw, Poland
120
The School of Physics & Astronomy, Monash University, Clayton 3800, Victoria, Australia
121
Hanyang University, Seoul 133-791, Korea
122
The Chinese University of Hong Kong, Shatin, NT, Hong Kong
123
University of Alabama in Huntsville, Huntsville, AL 35899, USA
124
ESPCI, CNRS, F-75005 Paris, France
125
University of Minnesota, Minneapolis, MN 55455, USA
126
Universit`a di Camerino, Dipartimento di Fisica, I-62032 Camerino, Italy
127
Southern University and A&M College, Baton Rouge, LA 70813, USA
128
The University of Melbourne, Parkville, Victoria 3010, Australia
129
College of William and Mary, Williamsburg, VA 23187, USA
130
Instituto de F ́ısica Te ́orica, University Estadual Paulista/ICTP South
American Institute for Fundamental Research, S ̃ao Paulo SP 01140-070, Brazil
131
Whitman College, 345 Boyer Avenue, Walla Walla, WA 99362 USA
6
132
Universit ́e de Lyon, F-69361 Lyon, France
133
Hobart and William Smith Colleges, Geneva, NY 14456, USA
134
Janusz Gil Institute of Astronomy, University of Zielona G ́ora, 65-265 Zielona G ́ora, Poland
135
King’s College London, University of London, London WC2R 2LS, United Kingdom
136
IISER-Kolkata, Mohanpur, West Bengal 741252, India
137
Indian Institute of Technology, Gandhinagar Ahmedabad Gujarat 382424, India
138
Andrews University, Berrien Springs, MI 49104, USA
139
Universit`a di Siena, I-53100 Siena, Italy
140
Trinity University, San Antonio, TX 78212, USA
141
University of Washington, Seattle, WA 98195, USA
142
Abilene Christian University, Abilene, TX 79699, USA
(Dated: February 1, 2017)
A wide variety of astrophysical and cosmological sources are expected to contribute to a stochastic
gravitational-wave background. Following the observations of GW150914 and GW151226, the rate
and mass of coalescing binary black holes appear to be greater than many previous expectations. As
a result, the stochastic background from unresolved compact binary coalescences is expected to be
particularly loud. We perform a search for the isotropic stochastic gravitational-wave background
using data from Advanced LIGO’s first observing run. The data display no evidence of a stochastic
gravitational-wave signal. We constrain the dimensionless energy density of gravitational waves to
be Ω
0
<
1
.
7
×
10
7
with 95% confidence, assuming a flat energy density spectrum in the most
sensitive part of the LIGO band (20
86 Hz). This is a factor of
33 times more sensitive than
previous measurements. We also constrain arbitrary power-law spectra. Finally, we investigate the
implications of this search for the background of binary black holes using an astrophysical model
for the background.
Introduction.
— Many astrophysical and cosmological
phenomena are expected to contribute to a stochastic
gravitational-wave background, henceforth, simply ref-
ered to as a “background”. These include unresolved
compact binary coalescences of both black holes and neu-
tron stars [1–5], rotating neutron stars [6–8], supernovae
[9–12], cosmic strings [13–16], inflationary models [17–
24], phase transitions [25–27], and the pre-Big Bang sce-
nario [28–31]. The variety of mechanisms potentially con-
tributing to the background provides the opportunity to
study a number of different environments within the Uni-
verse.
The recent detections of binary black hole (BBH) coa-
lescences by Advanced LIGO [32, 33] suggest that the
Universe may be rich with coalescing BBHs.
While
events like GW150914 and GW151226 are loud enough
to be clearly detected, we expect there to be many
more events that are too far away to be individually
resolved and that contribute to the background. Since
this BBH population originates from sources that are
too distant to be individually detected, the stochastic
search probes a distinct population of binaries compared
to nearby sources [34]. The background from these bina-
ries provides complementary information to individually
resolved binary coalescences [35].
In this Letter, we report on the search for an isotropic
background using data from Advanced LIGO’s first ob-
serving run O1. We search for the background by cross-
correlating data streams from the two separate LIGO
detectors and looking for a coherent signal. We find no
evidence for the background and place the best upper
limits to date on the energy density of the background
in the LIGO frequency band. We also update the impli-
cations for a BBH background using all the data from
O1.
Data.
—Before this analysis, the best limits on the
background from Initial LIGO and Virgo data were ob-
tained using 2009–2010 [36] and 2005–2007 data [37]. In
this work we use data from the upgraded Advanced LIGO
observatories in Hanford, WA (H1) and Livingston, LA
(L1) [38]. We analyze O1 data from September 18, 2015
15:00 UTC-January 12, 2016 16:00 UTC.
Method.
— We define the background energy density
spectrum as [39]
GW
(
f
) =
f
ρ
c
GW
df
,
(1)
where
f
is the frequency,
ρ
c
= 3
c
2
H
2
0
/
(8
πG
) is the crit-
ical energy density to close the Universe (numerically,
ρ
c
= 7
.
8
×
10
9
erg
/
cm
3
using the Hubble constant
H
0
= 68 km s
1
Mpc
1
from [40, 41]), and
GW
is the
gravitational-wave energy density in the frequency range
from
f
to
f
+
df
. For the LIGO frequency band, most
theoretical models for Ω
GW
(
f
) can be approximated as
a power law in frequency [39, 42, 43]:
GW
(
f
) = Ω
α
(
f
f
ref
)
α
.
(2)
Following [35], we assume a reference frequency of 25 Hz,
which corresponds to the most sensitive band of the
LIGO stochastic search for a detector network operat-
ing at design sensitivity. The variable Ω
α
characterizes
the background amplitude across the sensitive frequency
7
band. Past analyses have used
α
= 0 and
α
= 3 to repre-
sent cosmologically and astrophysically motivated back-
ground models respectively [36, 42–45]. In this analysis
we use these two spectral indices but also include limits
on the background spectrum assuming
α
= 2
/
3, which
describes the background dominated by compact binary
inspirals [35, 46]. This choice of spectral index is espe-
cially interesting given the loud background from BBHs
inferred from recent Advanced LIGO detections in O1
[32, 33, 35, 47].
Our search uses a cross-correlation method optimized
to search for the background using the pair of LIGO
detectors [39]. As discussed for instance in [48], cross-
correlation is preferred to auto-correlation because the
noise in each detector is not sufficiently well modelled to
perform subtraction of the noise auto-power. We define
the estimator
ˆ
Y
α
=
−∞
df
−∞
df
δ
T
(
f
f
) ̃
s
1
(
f
) ̃
s
2
(
f
)
̃
Q
α
(
f
) (3)
with variance
σ
2
Y
T
2
0
df P
1
(
f
)
P
2
(
f
)
|
̃
Q
α
(
f
)
|
2
,
(4)
where ̃
s
1
,
2
(
f
) are the Fourier transforms of the strain
time series data from the two detectors,
δ
T
(
f
f
) is
a finite-time approximation to the Dirac delta function,
T
is the observation time,
P
1
,
2
are the one-sided power
spectral densities for the detectors, and
̃
Q
α
(
f
) is a filter
function to optimize the search [49],
̃
Q
α
(
f
) =
λ
α
γ
(
f
)
H
2
0
f
3
P
1
(
f
)
P
2
(
f
)
(
f
f
ref
)
α
.
(5)
The spatial separation and relative orientation of the two
detectors are accounted for in the overlap reduction func-
tion,
γ
(
f
) [50] and the normalization constant
λ
α
is cho-
sen such that
ˆ
Y
α
= Ω
α
.
Data Quality.
—For this analysis, the strain time se-
ries data are down-sampled to 4096 Hz from 16384 Hz
and separated into 50%-overlapping 192 s segments, as
in [42]. The segments are Hann-windowed and high-pass
filtered with a 16
th
order Butterworth digital filter with
knee frequency of 11 Hz. The data are coarse-grained
to a frequency resolution of 0
.
031 Hz. This is a finer
frequency resolution than was used in previous analyses
due to the need to remove many finely spaced lines at
low frequencies.
We apply cuts in the time and frequency domains, fol-
lowing [36]. The total live time after all time domain
vetoes have been applied was 29.85 days. These cuts re-
move 35% of the time-series data. The frequency domain
cuts remove 21% of the observing band. In the technical
supplement to this paper [51], we discuss in more de-
tail the removed times and frequencies, the recovery of
20
30
40
50
60
70
80
−3
−2
−1
0
1
2
3
x 10
−5
Frequency (Hz)
0
0
±
2
σ
0
FIG. 1. We show the estimator for Ω
0
in each frequency bin,
along with
±
2
σ
error bars, in the frequency band that con-
tains 99% of the sensitivity for
α
= 0. The loss of sensitivity at
around 65 Hz is due to a zero in the overlap reduction func-
tion. There are several lines associated with known instru-
mental artifacts which do not lead to excess cross-correlation.
The data are consistent with Gaussian noise, as described in
the Results section.
hardware and software injections, and an analysis of cor-
related noise due to geophysical Schumann resonances.
Results.
—Our search finds no evidence of the back-
ground, and the data are consistent with statistical fluc-
tuations, assuming Gaussian noise. The integrand of
Equation 3, multiplied by
df
= 0
.
031 Hz, gives an es-
timator for Ω
0
in each frequency bin. We plot this quan-
tity, along with
±
2
σ
error bars, in Figure 6. To check
for Gaussianity, we employ a noise model that the esti-
mator in each frequency bin is drawn from a Gaussian
distribution with zero mean with the standard deviation
of that frequency bin. We obtain a
χ
2
per degree of free-
dom of 0.92, indicating that the data are consistent with
Gaussian noise.
Consequently, we are able to place upper bounds on
the energy density present in the background. For
α
= 0,
we place the bound Ω
0
<
1
.
7
×
10
7
at 95% confidence,
where 99% of the sensitivity comes in the frequency band
20
86 Hz. This is a factor of 33 times more sensitive
than the previous best limit at these frequencies [36].
Following [52], we show 95% confidence contours in the
α
α
plane in Figure 2 by computing the joint posterior
for Ω
α
and
α
. In addition, in Table I, we report upper
limits on the energy density for specific fixed values of the
spectral index, marginalizing over amplitude calibration
uncertainty [53] using the conservative estimates of 11
.
8%
for H1 and 13
.
4% for L1. Phase calibration uncertainties
are negligible.
8
Spectral index
α
Frequency band with 99% sensitivity
Amplitude Ω
α
95% CL upper limit
Previous limits [36]
0
20
85
.
8 Hz
(4
.
4
±
5
.
9)
×
10
8
1
.
7
×
10
7
5
.
6
×
10
6
2
/
3
20
98
.
2 Hz
(3
.
5
±
4
.
4)
×
10
8
1
.
3
×
10
7
3
20
305 Hz
(3
.
7
±
6
.
5)
×
10
9
1
.
7
×
10
8
7
.
6
×
10
8
TABLE I. The frequency band with 99% of the sensitivity are shown, along with the point estimate and standard deviation for
the amplitude of the background, and 95% confidence level upper limits using O1 data for three values of the spectral index,
α
= 0
,
2
/
3
,
3. We also show the previous upper limits using Initial LIGO-Virgo data.
−5
−4
−3
−2
−1
0
1
2
3
4
5
10
−12
10
−11
10
−10
10
−9
10
−8
10
−7
10
−6
10
−5
10
−4
10
−3
α
α
Initial LIGO−Virgo
aLIGO O1
Design
FIG. 2. Following [52], we present 95 % confidence contours in
the Ω
α
α
plane. The region above these curves is excluded
at 95% confidence. We show the constraints coming from
the final science run of Initial LIGO-Virgo [36] and from O1
data. Finally, we display the projected (not observed) design
sensitivity to Ω
α
and
α
for Advanced LIGO and Virgo [54].
We also compare our results with the limits placed at
high frequencies from the two co-located detectors at the
Hanford site (H1 and H2). In [37], the limit Ω
3
<
7
.
7
×
10
4
in the frequency band 460
1000 Hz was obtained
for the spectral index
α
= 3 and
f
ref
= 900 Hz. Using
this same frequency band, and using the cross-correlated
data between the Hanford and Livingston detectors, we
place a limit Ω
3
<
1
.
7
×
10
2
for
f
ref
= 900 Hz. This
is about a factor of 22 larger than the limit from the co-
located detectors, in part due to the loss in sensitivity
of a stochastic search from cross-correlating detectors at
different spatial locations.
In Figure 3, we show the constraints from this analysis
and from previous analyses using other detectors, theo-
retical predictions, and the expected sensitivity of future
measurements by LIGO-Virgo and by the Laser Inter-
ferometer Space Antenna (LISA). Where applicable, we
show constraints using power-law integrated curves (PI
curves) [55], which account for the broadband nature of
the search by integrating a range of power-law signals
over the sensitive frequency band of the detector. By
construction, any power-law spectrum which crosses a
PI curve is detectable with SNR
2.
The blue curve labeled ‘aLIGO O1’ in Figure 3 shows
the measured O1 PI curve. We also display the PI curve
for the final science run of Initial LIGO and Virgo [36],
H1-H2 [37], as well as the projected design sensitivity
for the advanced detector network. The curve labeled
‘Design’ assumes 2 years of co-incident data taken with
both Advanced LIGO and Virgo operating at design sen-
sitivity, using the projections in [54]. For the sake of
comparison, the measured O1 PI curve at
α
= 0 is 1.6
times larger than the projected PI curve at
α
= 0 using
the projections in [54] and 29.85 days of live time, which
is fairly good agreement between predicted and achieved
sensitivity. Finally, in red we present the projected sen-
sitivity of a space-based detector with similar sensitivity
to LISA, using the PI curve presented in [55] computed
using the projections in [60, 61].
We compare these constraints with direct limits from
the ringing of Earth’s normal modes [59], indirect lim-
its from the Cosmic Microwave Background (CMB) and
Big Bang Nucleosynthesis (BBN) [57], and limits from
pulsar timing arrays [58] and CMB measurements at low
multipole moments [56].
In addition, we give examples of several models which
can contribute to the background. We show the back-
ground expected from slow-roll inflation with a tensor-to-
scalar-ratio
r
= 0
.
11 (the upper limit allowed by Planck
[40]). We also show examples of the BBH coalescence
model, and the binary neutron star (BNS) coalescence
model, which we describe below. As noted in [62], LISA
is likely to be able to detect the BBH background of the
size considered here.
Astrophysical Implications.
—In order to model the
background from binary systems we will follow the ap-
proach of [35]. We divide the compact binary population
into classes labeled by
k
[63, 64]. Each class has distinct
values of source parameters (for example the masses),
which we denote by
θ
k
. The total astrophysical back-
ground is a sum over the contributions in each class. The
contribution of class
k
to the background may be written
in terms of an integral over the redshift
z
as [1, 5, 65–70]
GW
(
f
;
θ
k
) =
f
ρ
c
H
0
z
max
0
dz
R
m
(
z
;
θ
k
)
dE
GW
df
(
f
s
;
θ
k
)
(1 +
z
)
E
(Ω
M
,
Λ
,z
)
,
(6)
9
FIG. 3. Presented here are constraints on the background in PI form [55], as well as some representative models, across many
decades in frequency. We compare the limits from ground-based interferometers from the final science run of Initial LIGO-Virgo,
the co-located detectors at Hanford (H1-H2), Advanced LIGO (aLIGO) O1, and the projected design sensitivity of the advanced
detector network assuming two years of coincident data, with constraints from other measurements: CMB measurements at low
multipole moments [56], indirect limits from the Cosmic Microwave Background (CMB) and Big-Bang Nucleosynthesis [57, 58],
pulsar timing [58], and from the ringing of Earth’s normal modes [59]. We also show projected limits from a space-based
detector such as LISA [55, 60, 61], following the assumptions of [55]. We extend the BNS and BBH distributions using an
f
2
/
3
power-law down to low frequencies, with a low-frequency cut-off imposed where the inspiral time-scale is of order the Hubble
scale. In Figure 5, we show the region in the black box in more detail.
where
R
m
(
z
;
θ
k
) is the binary merger rate per unit co-
moving volume per unit time,
dE
GW
/df
(
f
s
k
) is the
energy spectrum emitted by a single binary evaluated
in terms of the source frequency
f
s
= (1 +
z
)
f
, and
E
(Ω
M
,
Λ
,z
) =
M
(1 +
z
)
3
+ Ω
Λ
accounts for the de-
pendence of comoving volume on cosmology. We use
cosmological parameters from Planck [40], and Ω
M
=
1
Λ
= 0
.
308.
The energy spectrum
dE
GW
/df
is determined from the
strain waveform of the binary system. The dominant
contribution to the background comes from the inspiral
phase, however for BBH we include the merger and ring-
down phases using the waveforms from [5, 71] with the
modifications from [72]. We choose to cut off the red-
shift integral at
z
max
= 10. Redshifts larger than five
contribute little to the integral due to the small number
of stars formed at such high redshift [1, 5, 34, 65–70].
To compute the binary merger rate
R
m
(
z
;
θ
k
), we use
the same assumptions as in [35], unless stated otherwise.
For the BNS case, we assume that the minimal time be-
tween the formation and the coalescence of the binary is
t
min
= 20 Myr, following for instance [46]. This is to be
compared to
t
min
= 50 Myr for BBH [35, 73].
As was emphasized in [74], heavy stellar mass black
holes are expected to form in regions of low metallicity,
which are associated with weaker stellar winds. To ac-
count for this effect, following [35], for binary systems
with chirp masses larger than 30
M
, we use only the
fraction of stars that form in an environment with metal-
licity
Z < Z
/
2. For BBH (and BNS) systems with
smaller masses, we do not use a cutoff. However, we note
that it makes little difference whether or not the cutoff
is applied to high masses.
With the model defined above, the free parameters are
the local merger rate
R
local
=
R
m
(0;
θ
k
) and the average
chirp mass
M
c
. The distribution of the chirp mass has
little effect on the spectrum for a fixed average chirp mass
[5].
We place upper limits at 95% confidence in the
M
c
R
local
plane, which are shown in Figure 4. Alongside
the O1 results, we show the limits using Initial LIGO-
Virgo data, as well as projected sensitivity of the ad-
vanced detector network. The limits presented here are
about 10 times more sensitive than those placed with
Initial LIGO-Virgo data. Furthermore, the future runs
of the advanced detectors are expected to yield another
factor of 100 improvement in sensitivity in
R
local
for a
given average chirp mass. We also show the local rate
and chirp mass inferred from direct detections of BBH
mergers during O1 [47, 64]. Comparing the projected
design sensitivity on
R
local
and
M
c
, with the values in-
ferred from BBH observations in O1, suggests that it may
be possible for the advanced detector network to detect
the astrophysical BBH background.
Finally, instead of treating the chirp mass and local
merger rate as free parameters, we can use the informa-
tion from individually observed BBHs to compute the
corresponding background, see Figure 5. To do this, we
use the same model described above and we adopt the
three rate models described in [47]. Specifically, we con-
sider the three-events-based, power-law, and flat-log dis-
tributions of component masses. In each case, the rate at
10
10
0
10
1
10
2
10
0
10
2
10
4
10
6
M
c
(M
solar
)
R
local
(Gpc
−3
yr
−1
)
BNS
BBH
Flat
Power
Initial LIGO−VIRGO
aLIGO O1
Design
FIG. 4. Displayed here are the 95% confidence contours on
the local rate and average chirp mass parameters, using the
model described in the Astrophysical Implications section. In
addition to the constraint from Advanced LIGO (aLIGO) O1
data, we show the constraint from the final science run of
Initial LIGO-Virgo, and the projected design sensitivity of
Advanced LIGO-Virgo. We also show the median rate with
90% uncertainty inferred from O1 data for the power-law and
flat-log mass distributions [47], along with the band contain-
ing 68% of the chirp mass for each distribution. The gray
band separates BNS from BBH backgrounds. The dip at 30
M
is due to the metallicity cutoff, as described in the As-
trophysical Implications section.
redshift
z
= 0 is normalized to the local rate derived from
the O1 detections. With these assumptions we compute
the background, including statistical uncertainty bands
showing the 90% uncertainty in the local rate. The three
rate models agree well in the sensitive frequency band of
advanced detectors (10-100 Hz). Note also that the final
sensitivity of the advanced detectors may be sufficient to
detect this background.
Conclusions.
—The results presented here represent the
first search for the stochastic gravitational-wave back-
ground made with the Advanced LIGO detectors. With
no evidence of a stochastic signal, we place an upper limit
of Ω
0
<
1
.
7
×
10
7
on the GW energy density, for a spec-
tral index
α
= 0. This is
33 times more sensitive than
previous direct measurements in this frequency band. We
also constrain the binary coalescence parameters of chirp
mass and local merger rate. For fixed chirp mass be-
low the high mass threshold of 30
M
, the constraint on
the merger rate is improved by a factor of
24, while
for fixed merger rate, the constraint on the chirp mass
is improved by a factor of
7, as can be seen from Fig-
ure 4. Finally, we update the background predictions due
to BBH coalescences using data from O1. In this work
we have focused the implications of our results for an as-
trophysical BBH background, as this provides the most
promising candidate for first detecting the background.
The implications of our search for other astrophysical and
cosmological models can be seen in Figure 3. There is also
an upcoming publication that will study implications for
cosmic string models in more detail.
These O1 results are a glimpse of the improvements
in sensitivity to be seen in upcoming years. As the ad-
vanced detectors reach design sensitivity, there is a rea-
sonable possibility of detecting the background due to
BBHs. Even if no detection is made with these future
searches, the searches will be able to constrain impor-
tant cosmological and astrophysical background models.
FIG. 5. We present a range of potential spectra for a BBH
background, using the flat-log, power-law, and 3-delta mass
distribution models described in [47, 74], with the local rate
inferred from the O1 detections [47]. For the flat-log and
power-law distributions, we show the 90% Poisson uncertainty
band due to the uncertainty in the local rate measurement.
In addition, we show the measured O1 PI curve and the pro-
jected PI curve for Advanced LIGO-Virgo operating at design
sensitivity.
Acknowledgments.
— The authors gratefully acknowl-
edge the support of the United States National Science
Foundation (NSF) for the construction and operation of
the LIGO Laboratory and Advanced LIGO as well as
the Science and Technology Facilities Council (STFC)
of the United Kingdom, the Max-Planck-Society (MPS),
and the State of Niedersachsen/Germany for support of
the construction of Advanced LIGO and construction
and operation of the GEO600 detector. Additional sup-
port for Advanced LIGO was provided by the Australian
Research Council. The authors gratefully acknowledge
the Italian Istituto Nazionale di Fisica Nucleare (INFN),
the French Centre National de la Recherche Scientifique
(CNRS) and the Foundation for Fundamental Research
on Matter supported by the Netherlands Organisation
for Scientific Research, for the construction and opera-
tion of the Virgo detector and the creation and support
of the EGO consortium. The authors also gratefully ac-
knowledge research support from these agencies as well