GW150914: Implications for the stochastic gravitational-wave background from
binary black holes
B. P. Abbott,
1
R. Abbott,
1
T. D. Abbott,
2
M. R. Abernathy,
1
F. Acernese,
3
,
4
K. Ackley,
5
C. Adams,
6
T. Adams,
7
P. Addesso,
3
R. X. Adhikari,
1
V. B. Adya,
8
C. Affeldt,
8
M. Agathos,
9
K. Agatsuma,
9
N. Aggarwal,
10
O. D. Aguiar,
11
L. Aiello,
12
,
13
A. Ain,
14
P. Ajith,
15
B. Allen,
8
,
16
,
17
A. Allocca,
18
,
19
P. A. Altin,
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
K. G. Arun,
24
S. Ascenzi,
25
,
13
G. Ashton,
26
M. Ast,
27
S. M. Aston,
6
P. Astone,
28
P. Aufmuth,
8
C. Aulbert,
8
S. Babak,
29
P. Bacon,
30
M. K. M. Bader,
9
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,
3
,
4
B. Barr,
36
L. Barsotti,
10
M. Barsuglia,
30
D. Barta,
38
J. Bartlett,
37
I. Bartos,
39
R. Bassiri,
40
A. Basti,
18
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19
J. C. Batch,
37
C. Baune,
8
V. Bavigadda,
34
M. Bazzan,
41
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42
B. Behnke,
29
M. Bejger,
43
C. Belczynski,
44
A. S. Bell,
36
C. J. Bell,
36
B. K. Berger,
1
J. Bergman,
37
G. Bergmann,
8
C. P. L. Berry,
45
D. Bersanetti,
46
,
47
A. Bertolini,
9
J. Betzwieser,
6
S. Bhagwat,
35
R. Bhandare,
48
I. A. Bilenko,
49
G. Billingsley,
1
J. Birch,
6
R. Birney,
50
S. Biscans,
10
A. Bisht,
8
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17
M. Bitossi,
34
C. Biwer,
35
M. A. Bizouard,
23
J. K. Blackburn,
1
C. D. Blair,
51
D. G. Blair,
51
R. M. Blair,
37
S. Bloemen,
52
O. Bock,
8
T. P. Bodiya,
10
M. Boer,
53
G. Bogaert,
53
C. Bogan,
8
A. Bohe,
29
P. Bojtos,
54
C. Bond,
45
F. Bondu,
55
R. Bonnand,
7
B. A. Boom,
9
R. Bork,
1
V. Boschi,
18
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19
S. Bose,
56
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14
Y. Bouffanais,
30
A. Bozzi,
34
C. Bradaschia,
19
P. R. Brady,
16
V. B. Braginsky,
49
M. Branchesi,
57
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58
J. E. Brau,
59
T. Briant,
60
A. Brillet,
53
M. Brinkmann,
8
V. Brisson,
23
P. Brockill,
16
A. F. Brooks,
1
D. D. Brown,
45
N. M. Brown,
10
C. C. Buchanan,
2
A. Buikema,
10
T. Bulik,
44
H. J. Bulten,
61
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9
A. Buonanno,
29
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62
D. Buskulic,
7
C. Buy,
30
R. L. Byer,
40
L. Cadonati,
63
G. Cagnoli,
64
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65
C. Cahillane,
1
J. Calder ́on Bustillo,
66
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63
T. Callister,
1
E. Calloni,
67
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4
J. B. Camp,
68
K. C. Cannon,
69
J. Cao,
70
C. D. Capano,
8
E. Capocasa,
30
F. Carbognani,
34
S. Caride,
71
J. Casanueva Diaz,
23
C. Casentini,
25
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13
S. Caudill,
16
M. Cavagli`a,
21
F. Cavalier,
23
R. Cavalieri,
34
G. Cella,
19
C. B. Cepeda,
1
L. Cerboni Baiardi,
57
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58
G. Cerretani,
18
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19
E. Cesarini,
25
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13
R. Chakraborty,
1
T. Chalermsongsak,
1
S. J. Chamberlin,
72
M. Chan,
36
S. Chao,
73
P. Charlton,
74
E. Chassande-Mottin,
30
H. Y. Chen,
75
Y. Chen,
76
C. Cheng,
73
A. Chincarini,
47
A. Chiummo,
34
H. S. Cho,
77
M. Cho,
62
J. H. Chow,
20
N. Christensen,
78
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53
Q. Chu,
51
S. Chua,
60
S. Chung,
51
G. Ciani,
5
F. Clara,
37
J. A. Clark,
63
F. Cleva,
53
E. Coccia,
25
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12
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13
P.-F. Cohadon,
60
A. Colla,
79
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28
C. G. Collette,
80
L. Cominsky,
81
M. Constancio Jr.,
11
A. Conte,
79
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28
L. Conti,
42
D. Cook,
37
T. R. Corbitt,
2
N. Cornish,
31
A. Corsi,
71
S. Cortese,
34
C. A. Costa,
11
M. W. Coughlin,
78
S. B. Coughlin,
82
J.-P. Coulon,
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S. T. Countryman,
39
P. Couvares,
1
E. E. Cowan,
63
D. M. Coward,
51
M. J. Cowart,
6
D. C. Coyne,
1
R. Coyne,
71
K. Craig,
36
J. D. E. Creighton,
16
J. Cripe,
2
S. G. Crowder,
83
A. Cumming,
36
L. Cunningham,
36
E. Cuoco,
34
T. Dal Canton,
8
S. L. Danilishin,
36
S. D’Antonio,
13
K. Danzmann,
17
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8
N. S. Darman,
84
V. Dattilo,
34
I. Dave,
48
H. P. Daveloza,
85
M. Davier,
23
G. S. Davies,
36
E. J. Daw,
86
R. Day,
34
D. DeBra,
40
G. Debreczeni,
38
J. Degallaix,
65
M. De Laurentis,
67
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4
S. Del ́eglise,
60
W. Del Pozzo,
45
T. Denker,
8
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17
T. Dent,
8
H. Dereli,
53
V. Dergachev,
1
R. T. DeRosa,
6
R. De Rosa,
67
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4
R. DeSalvo,
87
S. Dhurandhar,
14
M. C. D ́ıaz,
85
L. Di Fiore,
4
M. Di Giovanni,
79
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28
A. Di Lieto,
18
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19
S. Di Pace,
79
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28
I. Di Palma,
29
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8
A. Di Virgilio,
19
G. Dojcinoski,
88
V. Dolique,
65
F. Donovan,
10
K. L. Dooley,
21
S. Doravari,
6
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8
R. Douglas,
36
T. P. Downes,
16
M. Drago,
8
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89
,
90
R. W. P. Drever,
1
J. C. Driggers,
37
Z. Du,
70
M. Ducrot,
7
S. E. Dwyer,
37
T. B. Edo,
86
M. C. Edwards,
78
A. Effler,
6
H.-B. Eggenstein,
8
P. Ehrens,
1
J. Eichholz,
5
S. S. Eikenberry,
5
W. Engels,
76
R. C. Essick,
10
T. Etzel,
1
M. Evans,
10
T. M. Evans,
6
R. Everett,
72
M. Factourovich,
39
V. Fafone,
25
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13
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12
H. Fair,
35
S. Fairhurst,
91
X. Fan,
70
Q. Fang,
51
S. Farinon,
47
B. Farr,
75
W. M. Farr,
45
M. Favata,
88
M. Fays,
91
H. Fehrmann,
8
M. M. Fejer,
40
I. Ferrante,
18
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19
E. C. Ferreira,
11
F. Ferrini,
34
F. Fidecaro,
18
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19
I. Fiori,
34
D. Fiorucci,
30
R. P. Fisher,
35
R. Flaminio,
65
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92
M. Fletcher,
36
J.-D. Fournier,
53
S. Franco,
23
S. Frasca,
79
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28
F. Frasconi,
19
Z. Frei,
54
A. Freise,
45
R. Frey,
59
V. Frey,
23
T. T. Fricke,
8
P. Fritschel,
10
V. V. Frolov,
6
P. Fulda,
5
M. Fyffe,
6
H. A. G. Gabbard,
21
J. R. Gair,
93
L. Gammaitoni,
32
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33
S. G. Gaonkar,
14
F. Garufi,
67
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4
A. Gatto,
30
G. Gaur,
94
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95
N. Gehrels,
68
G. Gemme,
47
B. Gendre,
53
E. Genin,
34
A. Gennai,
19
J. George,
48
L. Gergely,
96
V. Germain,
7
Archisman Ghosh,
15
S. Ghosh,
52
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9
J. A. Giaime,
2
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6
K. D. Giardina,
6
A. Giazotto,
19
K. Gill,
97
A. Glaefke,
36
E. Goetz,
98
R. Goetz,
5
L. Gondan,
54
G. Gonz ́alez,
2
J. M. Gonzalez Castro,
18
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19
A. Gopakumar,
99
N. A. Gordon,
36
M. L. Gorodetsky,
49
S. E. Gossan,
1
M. Gosselin,
34
R. Gouaty,
7
C. Graef,
36
P. B. Graff,
62
M. Granata,
65
A. Grant,
36
S. Gras,
10
C. Gray,
37
G. Greco,
57
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58
A. C. Green,
45
P. Groot,
52
H. Grote,
8
S. Grunewald,
29
G. M. Guidi,
57
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58
X. Guo,
70
A. Gupta,
14
M. K. Gupta,
95
K. E. Gushwa,
1
E. K. Gustafson,
1
R. Gustafson,
98
J. J. Hacker,
22
B. R. Hall,
56
E. D. Hall,
1
G. Hammond,
36
M. Haney,
99
M. M. Hanke,
8
J. Hanks,
37
arXiv:1602.03847v2 [gr-qc] 20 Mar 2016
2
C. Hanna,
72
M. D. Hannam,
91
J. Hanson,
6
T. Hardwick,
2
J. Harms,
57
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58
G. M. Harry,
100
I. W. Harry,
29
M. J. Hart,
36
M. T. Hartman,
5
C.-J. Haster,
45
K. Haughian,
36
A. Heidmann,
60
M. C. Heintze,
5
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6
H. Heitmann,
53
P. Hello,
23
G. Hemming,
34
M. Hendry,
36
I. S. Heng,
36
J. Hennig,
36
A. W. Heptonstall,
1
M. Heurs,
8
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17
S. Hild,
36
D. Hoak,
101
K. A. Hodge,
1
D. Hofman,
65
S. E. Hollitt,
102
K. Holt,
6
D. E. Holz,
75
P. Hopkins,
91
D. J. Hosken,
102
J. Hough,
36
E. A. Houston,
36
E. J. Howell,
51
Y. M. Hu,
36
S. Huang,
73
E. A. Huerta,
103
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D. Huet,
23
B. Hughey,
97
S. Husa,
66
S. H. Huttner,
36
T. Huynh-Dinh,
6
A. Idrisy,
72
N. Indik,
8
D. R. Ingram,
37
R. Inta,
71
H. N. Isa,
36
J.-M. Isac,
60
M. Isi,
1
G. Islas,
22
T. Isogai,
10
B. R. Iyer,
15
K. Izumi,
37
T. Jacqmin,
60
H. Jang,
77
K. Jani,
63
P. Jaranowski,
104
S. Jawahar,
105
F. Jim ́enez-Forteza,
66
W. W. Johnson,
2
D. I. Jones,
26
R. Jones,
36
R. J. G. Jonker,
9
L. Ju,
51
Haris K,
106
C. V. Kalaghatgi,
24
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91
V. Kalogera,
82
S. Kandhasamy,
21
G. Kang,
77
J. B. Kanner,
1
S. Karki,
59
M. Kasprzack,
2
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23
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34
E. Katsavounidis,
10
W. Katzman,
6
S. Kaufer,
17
T. Kaur,
51
K. Kawabe,
37
F. Kawazoe,
8
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17
F. K ́ef ́elian,
53
M. S. Kehl,
69
D. Keitel,
8
,
66
D. B. Kelley,
35
W. Kells,
1
R. Kennedy,
86
J. S. Key,
85
A. Khalaidovski,
8
F. Y. Khalili,
49
I. Khan,
12
S. Khan,
91
Z. Khan,
95
E. A. Khazanov,
107
N. Kijbunchoo,
37
C. Kim,
77
J. Kim,
108
K. Kim,
109
Nam-Gyu Kim,
77
Namjun Kim,
40
Y.-M. Kim,
108
E. J. King,
102
P. J. King,
37
D. L. Kinzel,
6
J. S. Kissel,
37
L. Kleybolte,
27
S. Klimenko,
5
S. M. Koehlenbeck,
8
K. Kokeyama,
2
S. Koley,
9
V. Kondrashov,
1
A. Kontos,
10
M. Korobko,
27
W. Z. Korth,
1
I. Kowalska,
44
D. B. Kozak,
1
V. Kringel,
8
A. Kr ́olak,
110
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111
C. Krueger,
17
G. Kuehn,
8
P. Kumar,
69
L. Kuo,
73
A. Kutynia,
110
B. D. Lackey,
35
M. Landry,
37
J. Lange,
112
B. Lantz,
40
P. D. Lasky,
113
A. Lazzarini,
1
C. Lazzaro,
63
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42
P. Leaci,
29
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79
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28
S. Leavey,
36
E. O. Lebigot,
30
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70
C. H. Lee,
108
H. K. Lee,
109
H. M. Lee,
114
K. Lee,
36
A. Lenon,
35
M. Leonardi,
89
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90
J. R. Leong,
8
N. Leroy,
23
N. Letendre,
7
Y. Levin,
113
B. M. Levine,
37
T. G. F. Li,
1
A. Libson,
10
T. B. Littenberg,
115
N. A. Lockerbie,
105
J. Logue,
36
A. L. Lombardi,
101
J. E. Lord,
35
M. Lorenzini,
12
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13
V. Loriette,
116
M. Lormand,
6
G. Losurdo,
58
J. D. Lough,
8
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17
H. L ̈uck,
17
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8
A. P. Lundgren,
8
J. Luo,
78
R. Lynch,
10
Y. Ma,
51
T. MacDonald,
40
B. Machenschalk,
8
M. MacInnis,
10
D. M. Macleod,
2
F. Maga ̃na-Sandoval,
35
R. M. Magee,
56
M. Mageswaran,
1
E. Majorana,
28
I. Maksimovic,
116
V. Malvezzi,
25
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13
N. Man,
53
I. Mandel,
45
V. Mandic,
83
V. Mangano,
36
G. L. Mansell,
20
M. Manske,
16
M. Mantovani,
34
F. Marchesoni,
117
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33
F. Marion,
7
S. M ́arka,
39
Z. M ́arka,
39
A. S. Markosyan,
40
E. Maros,
1
F. Martelli,
57
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L. Martellini,
53
I. W. Martin,
36
R. M. Martin,
5
D. V. Martynov,
1
J. N. Marx,
1
K. Mason,
10
A. Masserot,
7
T. J. Massinger,
35
M. Masso-Reid,
36
F. Matichard,
10
L. Matone,
39
N. Mavalvala,
10
N. Mazumder,
56
G. Mazzolo,
8
R. McCarthy,
37
D. E. McClelland,
20
S. McCormick,
6
S. C. McGuire,
118
G. McIntyre,
1
J. McIver,
1
D. J. McManus,
20
S. T. McWilliams,
103
D. Meacher,
72
G. D. Meadors,
29
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8
J. Meidam,
9
A. Melatos,
84
G. Mendell,
37
D. Mendoza-Gandara,
8
R. A. Mercer,
16
E. Merilh,
37
M. Merzougui,
53
S. Meshkov,
1
C. Messenger,
36
C. Messick,
72
P. M. Meyers,
83
F. Mezzani,
28
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79
H. Miao,
45
C. Michel,
65
H. Middleton,
45
E. E. Mikhailov,
119
L. Milano,
67
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4
J. Miller,
10
M. Millhouse,
31
Y. Minenkov,
13
J. Ming,
29
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8
S. Mirshekari,
120
C. Mishra,
15
S. Mitra,
14
V. P. Mitrofanov,
49
G. Mitselmakher,
5
R. Mittleman,
10
A. Moggi,
19
M. Mohan,
34
S. R. P. Mohapatra,
10
M. Montani,
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B. C. Moore,
88
C. J. Moore,
121
D. Moraru,
37
G. Moreno,
37
S. R. Morriss,
85
K. Mossavi,
8
B. Mours,
7
C. M. Mow-Lowry,
45
C. L. Mueller,
5
G. Mueller,
5
A. W. Muir,
91
Arunava Mukherjee,
15
D. Mukherjee,
16
S. Mukherjee,
85
N. Mukund,
14
A. Mullavey,
6
J. Munch,
102
D. J. Murphy,
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P. G. Murray,
36
A. Mytidis,
5
I. Nardecchia,
25
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13
L. Naticchioni,
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28
R. K. Nayak,
122
V. Necula,
5
K. Nedkova,
101
G. Nelemans,
52
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9
M. Neri,
46
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47
A. Neunzert,
98
G. Newton,
36
T. T. Nguyen,
20
A. B. Nielsen,
8
S. Nissanke,
52
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9
A. Nitz,
8
F. Nocera,
34
D. Nolting,
6
M. E. N. Normandin,
85
L. K. Nuttall,
35
J. Oberling,
37
E. Ochsner,
16
J. O’Dell,
123
E. Oelker,
10
G. H. Ogin,
124
J. J. Oh,
125
S. H. Oh,
125
F. Ohme,
91
M. Oliver,
66
P. Oppermann,
8
Richard J. Oram,
6
B. O’Reilly,
6
R. O’Shaughnessy,
112
C. D. Ott,
76
D. J. Ottaway,
102
R. S. Ottens,
5
H. Overmier,
6
B. J. Owen,
71
A. Pai,
106
S. A. Pai,
48
J. R. Palamos,
59
O. Palashov,
107
C. Palomba,
28
A. Pal-Singh,
27
H. Pan,
73
C. Pankow,
82
F. Pannarale,
91
B. C. Pant,
48
F. Paoletti,
34
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19
A. Paoli,
34
M. A. Papa,
29
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16
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8
H. R. Paris,
40
W. Parker,
6
D. Pascucci,
36
A. Pasqualetti,
34
R. Passaquieti,
18
,
19
D. Passuello,
19
B. Patricelli,
18
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19
Z. Patrick,
40
B. L. Pearlstone,
36
M. Pedraza,
1
R. Pedurand,
65
L. Pekowsky,
35
A. Pele,
6
S. Penn,
126
A. Perreca,
1
M. Phelps,
36
O. Piccinni,
79
,
28
M. Pichot,
53
F. Piergiovanni,
57
,
58
V. Pierro,
87
G. Pillant,
34
L. Pinard,
65
I. M. Pinto,
87
M. Pitkin,
36
R. Poggiani,
18
,
19
P. Popolizio,
34
A. Post,
8
J. Powell,
36
J. Prasad,
14
V. Predoi,
91
S. S. Premachandra,
113
T. Prestegard,
83
L. R. Price,
1
M. Prijatelj,
34
M. Principe,
87
S. Privitera,
29
G. A. Prodi,
89
,
90
L. Prokhorov,
49
O. Puncken,
8
M. Punturo,
33
P. Puppo,
28
M. P ̈urrer,
29
H. Qi,
16
J. Qin,
51
V. Quetschke,
85
E. A. Quintero,
1
R. Quitzow-James,
59
F. J. Raab,
37
D. S. Rabeling,
20
H. Radkins,
37
P. Raffai,
54
S. Raja,
48
M. Rakhmanov,
85
P. Rapagnani,
79
,
28
V. Raymond,
29
M. Razzano,
18
,
19
V. Re,
25
J. Read,
22
C. M. Reed,
37
T. Regimbau,
53
L. Rei,
47
S. Reid,
50
D. H. Reitze,
1
,
5
H. Rew,
119
S. D. Reyes,
35
F. Ricci,
79
,
28
K. Riles,
98
N. A. Robertson,
1
,
36
R. Robie,
36
F. Robinet,
23
A. Rocchi,
13
3
L. Rolland,
7
J. G. Rollins,
1
V. J. Roma,
59
J. D. Romano,
85
R. Romano,
3
,
4
G. Romanov,
119
J. H. Romie,
6
D. Rosi ́nska,
127
,
43
S. Rowan,
36
A. R ̈udiger,
8
P. Ruggi,
34
K. Ryan,
37
S. Sachdev,
1
T. Sadecki,
37
L. Sadeghian,
16
L. Salconi,
34
M. Saleem,
106
F. Salemi,
8
A. Samajdar,
122
L. Sammut,
84
,
113
E. J. Sanchez,
1
V. Sandberg,
37
B. Sandeen,
82
J. R. Sanders,
98
,
35
B. Sassolas,
65
B. S. Sathyaprakash,
91
P. R. Saulson,
35
O. Sauter,
98
R. L. Savage,
37
A. Sawadsky,
17
P. Schale,
59
R. Schilling
†
,
8
J. Schmidt,
8
P. Schmidt,
1
,
76
R. Schnabel,
27
R. M. S. Schofield,
59
A. Sch ̈onbeck,
27
E. Schreiber,
8
D. Schuette,
8
,
17
B. F. Schutz,
91
,
29
J. Scott,
36
S. M. Scott,
20
D. Sellers,
6
D. Sentenac,
34
V. Sequino,
25
,
13
A. Sergeev,
107
G. Serna,
22
Y. Setyawati,
52
,
9
A. Sevigny,
37
D. A. Shaddock,
20
S. Shah,
52
,
9
M. S. Shahriar,
82
M. Shaltev,
8
Z. Shao,
1
B. Shapiro,
40
P. Shawhan,
62
A. Sheperd,
16
D. H. Shoemaker,
10
D. M. Shoemaker,
63
K. Siellez,
53
,
63
X. Siemens,
16
D. Sigg,
37
A. D. Silva,
11
D. Simakov,
8
A. Singer,
1
L. P. Singer,
68
A. Singh,
29
,
8
R. Singh,
2
A. Singhal,
12
A. M. Sintes,
66
B. J. J. Slagmolen,
20
J. R. Smith,
22
N. D. Smith,
1
R. J. E. Smith,
1
E. J. Son,
125
B. Sorazu,
36
F. Sorrentino,
47
T. Souradeep,
14
A. K. Srivastava,
95
A. Staley,
39
M. Steinke,
8
J. Steinlechner,
36
S. Steinlechner,
36
D. Steinmeyer,
8
,
17
B. C. Stephens,
16
R. Stone,
85
K. A. Strain,
36
N. Straniero,
65
G. Stratta,
57
,
58
N. A. Strauss,
78
S. Strigin,
49
R. Sturani,
120
A. L. Stuver,
6
T. Z. Summerscales,
128
L. Sun,
84
P. J. Sutton,
91
B. L. Swinkels,
34
M. J. Szczepa ́nczyk,
97
M. Tacca,
30
D. Talukder,
59
D. B. Tanner,
5
M. T ́apai,
96
S. P. Tarabrin,
8
A. Taracchini,
29
R. Taylor,
1
T. Theeg,
8
M. P. Thirugnanasambandam,
1
E. G. Thomas,
45
M. Thomas,
6
P. Thomas,
37
K. A. Thorne,
6
K. S. Thorne,
76
E. Thrane,
113
S. Tiwari,
12
V. Tiwari,
91
K. V. Tokmakov,
105
C. Tomlinson,
86
M. Tonelli,
18
,
19
C. V. Torres
‡
,
85
C. I. Torrie,
1
D. T ̈oyr ̈a,
45
F. Travasso,
32
,
33
G. Traylor,
6
D. Trifir`o,
21
M. C. Tringali,
89
,
90
L. Trozzo,
129
,
19
M. Tse,
10
M. Turconi,
53
D. Tuyenbayev,
85
D. Ugolini,
130
C. S. Unnikrishnan,
99
A. L. Urban,
16
S. A. Usman,
35
H. Vahlbruch,
17
G. Vajente,
1
G. Valdes,
85
N. van Bakel,
9
M. van Beuzekom,
9
J. F. J. van den Brand,
61
,
9
C. Van Den Broeck,
9
D. C. Vander-Hyde,
35
,
22
L. van der Schaaf,
9
J. V. van Heijningen,
9
A. A. van Veggel,
36
M. Vardaro,
41
,
42
S. Vass,
1
M. Vas ́uth,
38
R. Vaulin,
10
A. Vecchio,
45
G. Vedovato,
42
J. Veitch,
45
P. J. Veitch,
102
K. Venkateswara,
131
D. Verkindt,
7
F. Vetrano,
57
,
58
A. Vicer ́e,
57
,
58
S. Vinciguerra,
45
D. J. Vine,
50
J.-Y. Vinet,
53
S. Vitale,
10
T. Vo,
35
H. Vocca,
32
,
33
C. Vorvick,
37
D. Voss,
5
W. D. Vousden,
45
S. P. Vyatchanin,
49
A. R. Wade,
20
L. E. Wade,
132
M. Wade,
132
M. Walker,
2
L. Wallace,
1
S. Walsh,
16
,
8
,
29
G. Wang,
12
H. Wang,
45
M. Wang,
45
X. Wang,
70
Y. Wang,
51
R. L. Ward,
20
J. Warner,
37
M. Was,
7
B. Weaver,
37
L.-W. Wei,
53
M. Weinert,
8
A. J. Weinstein,
1
R. Weiss,
10
T. Welborn,
6
L. Wen,
51
P. Weßels,
8
T. Westphal,
8
K. Wette,
8
J. T. Whelan,
112
,
8
D. J. White,
86
B. F. Whiting,
5
R. D. Williams,
1
A. R. Williamson,
91
J. L. Willis,
133
B. Willke,
17
,
8
M. H. Wimmer,
8
,
17
W. Winkler,
8
C. C. Wipf,
1
H. Wittel,
8
,
17
G. Woan,
36
J. Worden,
37
J. L. Wright,
36
G. Wu,
6
J. Yablon,
82
W. Yam,
10
H. Yamamoto,
1
C. C. Yancey,
62
M. J. Yap,
20
H. Yu,
10
M. Yvert,
7
A. Zadro ̇zny,
110
L. Zangrando,
42
M. Zanolin,
97
J.-P. Zendri,
42
M. Zevin,
82
F. Zhang,
10
L. Zhang,
1
M. Zhang,
119
Y. Zhang,
112
C. Zhao,
51
M. Zhou,
82
Z. Zhou,
82
X. J. Zhu,
51
M. E. Zucker,
1
,
10
S. E. Zuraw,
101
and J. Zweizig
1
(LIGO Scientific Collaboration and Virgo Collaboration)
†
Deceased, May 2015.
‡
Deceased, March 2015.
1
LIGO, California Institute of Technology, Pasadena, CA 91125, USA
2
Louisiana State University, Baton Rouge, LA 70803, USA
3
Universit`a 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, FL 32611, USA
6
LIGO Livingston Observatory, Livingston, LA 70754, USA
7
Laboratoire d’Annecy-le-Vieux de Physique des Particules (LAPP),
Universit ́e Savoie Mont Blanc, CNRS/IN2P3, F-74941 Annecy-le-Vieux, France
8
Albert-Einstein-Institut, Max-Planck-Institut f ̈ur Gravitationsphysik, D-30167 Hannover, Germany
9
Nikhef, Science Park, 1098 XG Amsterdam, The Netherlands
10
LIGO, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
11
Instituto Nacional de Pesquisas Espaciais, 12227-010 S ̃ao Jos ́e dos Campos, SP, Brazil
12
INFN, Gran Sasso Science Institute, I-67100 L’Aquila, Italy
13
INFN, Sezione di Roma Tor Vergata, I-00133 Roma, Italy
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, WI 53201, USA
17
Leibniz Universit ̈at Hannover, D-30167 Hannover, Germany
18
Universit`a di Pisa, I-56127 Pisa, Italy
19
INFN, Sezione di Pisa, I-56127 Pisa, Italy
20
Australian National University, Canberra, Australian Capital Territory 0200, Australia
21
The University of Mississippi, University, MS 38677, USA
4
22
California State University Fullerton, Fullerton, CA 92831, USA
23
LAL, Univ. Paris-Sud, CNRS/IN2P3, Universit ́e Paris-Saclay, Orsay, France
24
Chennai Mathematical Institute, Chennai, India
25
Universit`a di Roma Tor Vergata, I-00133 Roma, Italy
26
University of Southampton, Southampton SO17 1BJ, United Kingdom
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
Montana State University, Bozeman, MT 59717, 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
CAMK-PAN, 00-716 Warsaw, Poland
44
Astronomical Observatory Warsaw University, 00-478 Warsaw, Poland
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
University of Western Australia, Crawley, Western Australia 6009, Australia
52
Department of Astrophysics/IMAPP, Radboud University Nijmegen,
P.O. Box 9010, 6500 GL Nijmegen, The Netherlands
53
Artemis, Universit ́e Cˆote d’Azur, CNRS, Observatoire Cˆote d’Azur, CS 34229, Nice cedex 4, France
54
MTA E ̈otv ̈os University, “Lendulet” Astrophysics Research Group, Budapest 1117, Hungary
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
VU University Amsterdam, 1081 HV Amsterdam, The Netherlands
62
University of Maryland, College Park, MD 20742, USA
63
Center for Relativistic Astrophysics and School of Physics,
Georgia Institute of Technology, Atlanta, GA 30332, USA
64
Institut Lumi`ere Mati`ere, Universit ́e de Lyon, Universit ́e Claude
Bernard Lyon 1, UMR CNRS 5306, 69622 Villeurbanne, France
65
Laboratoire des Mat ́eriaux Avanc ́es (LMA), IN2P3/CNRS,
Universit ́e de Lyon, F-69622 Villeurbanne, Lyon, France
66
Universitat de les Illes Balears, IAC3—IEEC, E-07122 Palma de Mallorca, Spain
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
Canadian Institute for Theoretical Astrophysics,
University of Toronto, Toronto, Ontario M5S 3H8, Canada
70
Tsinghua University, Beijing 100084, China
71
Texas Tech University, Lubbock, TX 79409, USA
72
The Pennsylvania State University, University Park, PA 16802, USA
73
National Tsing Hua University, Hsinchu City, Taiwan 30013, R.O.C.
74
Charles Sturt University, Wagga Wagga, New South Wales 2678, Australia
75
University of Chicago, Chicago, IL 60637, USA
76
Caltech CaRT, Pasadena, CA 91125, USA
77
Korea Institute of Science and Technology Information, Daejeon 305-806, Korea
5
78
Carleton College, Northfield, MN 55057, USA
79
Universit`a di Roma ’La Sapienza’, I-00185 Roma, Italy
80
University of Brussels, Brussels 1050, Belgium
81
Sonoma State University, Rohnert Park, CA 94928, USA
82
Northwestern University, Evanston, IL 60208, USA
83
University of Minnesota, Minneapolis, MN 55455, USA
84
The University of Melbourne, Parkville, Victoria 3010, Australia
85
The University of Texas Rio Grande Valley, Brownsville, TX 78520, USA
86
The University of Sheffield, Sheffield S10 2TN, United Kingdom
87
University of Sannio at Benevento, I-82100 Benevento,
Italy and INFN, Sezione di Napoli, I-80100 Napoli, Italy
88
Montclair State University, Montclair, NJ 07043, USA
89
Universit`a di Trento, Dipartimento di Fisica, I-38123 Povo, Trento, Italy
90
INFN, Trento Institute for Fundamental Physics and Applications, I-38123 Povo, Trento, Italy
91
Cardiff University, Cardiff CF24 3AA, United Kingdom
92
National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan
93
School of Mathematics, University of Edinburgh, Edinburgh EH9 3FD, United Kingdom
94
Indian Institute of Technology, Gandhinagar Ahmedabad Gujarat 382424, India
95
Institute for Plasma Research, Bhat, Gandhinagar 382428, India
96
University of Szeged, D ́om t ́er 9, Szeged 6720, Hungary
97
Embry-Riddle Aeronautical University, Prescott, AZ 86301, USA
98
University of Michigan, Ann Arbor, MI 48109, USA
99
Tata Institute of Fundamental Research, Mumbai 400005, India
100
American University, Washington, D.C. 20016, USA
101
University of Massachusetts-Amherst, Amherst, MA 01003, USA
102
University of Adelaide, Adelaide, South Australia 5005, Australia
103
West Virginia University, Morgantown, WV 26506, USA
104
University of Bia lystok, 15-424 Bia lystok, Poland
105
SUPA, University of Strathclyde, Glasgow G1 1XQ, United Kingdom
106
IISER-TVM, CET Campus, Trivandrum Kerala 695016, India
107
Institute of Applied Physics, Nizhny Novgorod, 603950, Russia
108
Pusan National University, Busan 609-735, Korea
109
Hanyang University, Seoul 133-791, Korea
110
NCBJ, 05-400
́
Swierk-Otwock, Poland
111
IM-PAN, 00-956 Warsaw, Poland
112
Rochester Institute of Technology, Rochester, NY 14623, USA
113
Monash University, Victoria 3800, Australia
114
Seoul National University, Seoul 151-742, Korea
115
University of Alabama in Huntsville, Huntsville, AL 35899, USA
116
ESPCI, CNRS, F-75005 Paris, France
117
Universit`a di Camerino, Dipartimento di Fisica, I-62032 Camerino, Italy
118
Southern University and A&M College, Baton Rouge, LA 70813, USA
119
College of William and Mary, Williamsburg, VA 23187, USA
120
Instituto de F ́ısica Te ́orica, University Estadual Paulista/ICTP South
American Institute for Fundamental Research, S ̃ao Paulo SP 01140-070, Brazil
121
University of Cambridge, Cambridge CB2 1TN, United Kingdom
122
IISER-Kolkata, Mohanpur, West Bengal 741252, India
123
Rutherford Appleton Laboratory, HSIC, Chilton, Didcot, Oxon OX11 0QX, United Kingdom
124
Whitman College, 345 Boyer Ave, Walla Walla, WA 99362 USA
125
National Institute for Mathematical Sciences, Daejeon 305-390, Korea
126
Hobart and William Smith Colleges, Geneva, NY 14456, USA
127
Janusz Gil Institute of Astronomy, University of Zielona G ́ora, 65-265 Zielona G ́ora, Poland
128
Andrews University, Berrien Springs, MI 49104, USA
129
Universit`a di Siena, I-53100 Siena, Italy
130
Trinity University, San Antonio, TX 78212, USA
131
University of Washington, Seattle, WA 98195, USA
132
Kenyon College, Gambier, OH 43022, USA
133
Abilene Christian University, Abilene, TX 79699, USA
(Dated: March 22, 2016)
The LIGO detection of the gravitational wave transient GW150914, from the inspiral and merger
of two black holes with masses
&
30 M
, suggests a population of binary black holes with relatively
high mass. This observation implies that the stochastic gravitational-wave background from binary
black holes, created from the incoherent superposition of all the merging binaries in the Universe,
could be higher than previously expected. Using the properties of GW150914, we estimate the
energy density of such a background from binary black holes. In the most sensitive part of the
Advanced LIGO/Virgo band for stochastic backgrounds (near 25 Hz), we predict Ω
GW
(
f
= 25 Hz) =
1
.
1
+2
.
7
−
0
.
9
×
10
−
9
with 90% confidence. This prediction is robustly demonstrated for a variety of
formation scenarios with different parameters. The differences between models are small compared
to the statistical uncertainty arising from the currently poorly constrained local coalescence rate.
We conclude that this background is potentially measurable by the Advanced LIGO/Virgo detectors
operating at their projected final sensitivity.
PACS numbers: 04.80.Nn, 04.25.dg, 95.85.Sz, 97.80.-d
Introduction
— On September 14, 2015 the Advanced
LIGO [1, 2] Hanford and Livingston detectors observed
the gravitational-wave event GW150914 with a signifi-
cance in excess of 5
.
1
σ
[3]. The observed signal is consis-
tent with a binary black hole waveform with component
masses of
m
1
=36
+5
−
4
M
and
m
2
=29
+4
−
4
M
, as mea-
sured in the source frame, and coalescing at a luminosity
distance of 410
+160
−
180
Mpc, corresponding to a redshift of
z
= 0
.
09
+0
.
03
−
0
.
04
[3, 4].
For every event like GW150914 observed by advanced
gravitational-wave detectors, there are many more too
distant to be resolved. The gravitational waves from
these unresolvable events combine to create a stochas-
tic background, which can be detected by correlating
the signals from two or more gravitational-wave detec-
tors [5]. While it has long been known that the advanced
detectors could observe such a background, the detection
of GW150914 suggests that the binary black hole back-
ground level is likely to be at the higher end of previous
predictions (see, e.g., [6–13]).
Heavy black holes like GW150914 are predicted to form
in low-metallicity stellar environments, lower than about
half of solar metallicity, and in the presence of relatively
weak massive-star winds [14]. These masses are also
larger than the masses inferred from reliable dynamical
measurements in black-hole X-ray binaries. More mas-
sive binaries emit more energy in gravitational waves.
Hence, the measurement of the component masses of
GW150914 favors a higher amplitude of the correspond-
ing gravitational-wave background.
In addition, the coalescence rate of binary black holes
like GW150914 in the local Universe is estimated to be
16
+38
−
13
Gpc
−
3
yr
−
1
[15] median with 90% credible interva.
This rate excludes the lower end of pre-detection rate es-
timates [14], while being consistent with the higher end.
A higher coalescence rate also implies a brighter stochas-
tic background.
There are currently two possible formation channels
that are consistent with the GW150914 event [14]. Bi-
nary black holes may be formed from isolated binaries of
massive stars in galactic fields, or through dynamical in-
teractions in dense stellar environments such as globular
clusters [14]. The evolution of the merger rate with red-
shift depends in part on the assumed formation scenario.
In this paper we discuss the detectability of the
stochastic background produced by binary black holes
throughout the Universe based on the measured proper-
ties of GW150914.
Binary black hole background
— The energy density spec-
trum of gravitational waves is described by the following
dimensionless quantity [5]:
Ω
GW
(
f
) =
f
ρ
c
dρ
GW
df
,
(1)
where
dρ
GW
is the energy density in the frequency in-
terval
f
to
f
+
df
,
ρ
c
= 3
H
2
0
c
2
/
8
πG
is the critical en-
ergy density required to close the Universe, and
H
0
=
67
.
8
±
0
.
9 km
/
s
/
Mpc [16].
A population of binary black holes is characterized by
the distribution of the intrinsic source parameters
θ
(usu-
ally the component masses and spin). Since this distri-
bution is unknown at present, following [15] and [17] we
divide the distribution into distinct classes correspond-
ing to the observed candidates. If binary black holes in
some class
k
, with source parameters
θ
k
, merge at a rate
R
m
(
z
;
θ
k
) per unit comoving volume
V
c
per unit source
time, then the total gravitational-wave energy density
spectrum is given by (see, e.g. [6–13]):
Ω
GW
(
f
;
θ
k
) =
f
ρ
c
H
0
∫
z
max
0
dz
R
m
(
z,θ
k
)
dE
GW
df
s
(
f
s
,θ
k
)
(1 +
z
)
E
(Ω
M
,
Ω
Λ
,z
)
,
(2)
and the total energy density spectrum is the sum of
Ω
GW
(
f
;
θ
k
) from each class.
1
In Eq. 2,
dE
GW
/df
s
(
f
s
,θ
k
)
is the spectral energy density of a source of class
k
at the
frequency
f
s
=
f
(1 +
z
), which depends on the source
parameters
θ
k
;
E
(Ω
M
,
Ω
Λ
,z
) =
√
Ω
M
(1 +
z
)
3
+ Ω
Λ
cap-
tures the dependence of the comoving volume on redshift
for the standard flat cosmology model, with Ω
M
= 0
.
31
and Ω
Λ
= 1
−
Ω
M
. The (1 +
z
) factor in the denom-
inator of Eq. 2 corrects for the cosmic expansion, con-
verting time in the source frame to the detector frame.
The parameter
z
max
corresponds to the time of the first
coalescences. We set
z
max
= 10, noting, however, that
1
When the distribution of the source parameters is better under-
stood after multiple detections, the discrete sum can be replaced
by a continuous integral.
6
sources above
z
∼
5 contribute very little to the total
background (see, e.g., [6–13]).
The merger rate
R
m
(
z
;
θ
k
) is a convolution of the bi-
nary formation rate
R
f
(
z
;
θ
k
) with the distribution of
the time delays
P
(
t
d
;
θ
k
) between binary black hole for-
mation and merger (see e.g., [18]
R
m
(
z
;
θ
k
) =
∫
t
max
t
min
R
f
(
z
f
;
θ
k
)
P
(
t
d
;
θ
k
)
dt
d
,
(3)
where
t
d
is the time delay,
z
f
is the redshift at the for-
mation time
t
f
=
t
(
z
)
−
t
d
, and
t
(
z
) is the age of the
Universe at merger.
Inference on GW150914 [4], along with expectations
that gravitational-wave emission is efficient in circular-
izing the orbit [14], allows us to restrict our models for
dE
GW
/df
s
to circular orbits. Measurements do not con-
strain the component spins in the orbital plane [4]; we
therefore restrict our model to spins (anti-)aligned with
the orbital angular momentum, and use the functional
form of
dE
GW
/df
s
derived in [19]. In addition to the
component masses, this model depends on the effective
spin parameter along the direction of the orbital angu-
lar momentum
χ
eff
, which takes values between
−
1 (in
which both black holes have maximal spins anti-aligned
with respect to the orbital angular momentum) and +1
(assuming maximally aligned spins) [4].
Fiducial Model
— The GW150914 event appears consis-
tent with both the dynamic and field formation chan-
nels [14]; however the field channel is currently better
described in the stochastic background literature. Thus
our
Fiducial
model is inspired by population synthesis
studies of field binaries (see [13]).
We assume that the binary black hole formation rate is
proportional to the star formation rate (SFR) at metal-
licity
Z
≤
Z
/
2 [14], where
Z
is the solar metallicity.
That is, to compute the binary black hole formation rate,
the SFR is multiplied by the fraction of star formation
occurring below the metallicity threshold
Z
c
=
Z
/
2.
For the SFR, we use the recent model [20], referred to
here as “Vangioni”, based on the gamma-ray burst rate
of [21] and on the normalization described in [22, 23].
We adopt the mean metallicity–redshift relation of [24],
rescaled upwards by a factor of 3 to account for local
observations [20, 25]. In addition, we assume the metal-
licity is log
10
-normally distributed with a standard devi-
ation of 0.5 around the mean at each redshift [26]. We
further assume that the time delay distribution follows
P
(
t
d
)
∝
t
α
d
, with
α
=
−
1 for
t
d
> t
min
[18, 27–33], where
t
min
= 50 Myr is the minimum delay time for a massive
binary to evolve until coalescence [e.g., 34], and a maxi-
mum time delay
t
max
equal to the Hubble time.
The rest of the
Fiducial
model parameters corre-
spond to the median inferred parameters of GW150914:
the chirp mass
M
c
= 28 M
, the symmetric mass ratio
η
∼
0
.
25, and the effective spin parameter
χ
eff
=
−
0
.
06.
We normalize the overall merger rate so that the local
merger rate at
z
= 0 matches the most conservative me-
dian inferred rate, 16
+38
−
13
Gpc
−
3
yr
−
1
[15].
Results
— We plot Ω
GW
(
f
) for the
Fiducial
model
as a solid blue curve in Fig. 1a. The curve is shown
against the pink shaded region, which represents the
90% credible interval statistical uncertainty in the local
rate. Considering this uncertainty, we predict Ω
GW
(
f
=
25 Hz) = 1
.
1
+2
.
7
−
0
.
9
×
10
−
9
. The spectrum is well approxi-
mated by a power law Ω
GW
(
f
)
∝
f
2
/
3
at low frequencies
where the contribution from the inspiral phase is dom-
inant and the spectral energy density is
dE
GW
/df
s
=
[(
Gπ
)
2
/
3
/
3]
M
5
/
3
c
f
−
1
/
3
s
. This power law remains a good
approximation until the spectrum reaches a maximum
at
f
∼
100 Hz. The shape is in agreement with previous
predictions (see, e.g., [7–13]), except that the maximum
is shifted to lower frequencies, due to the higher mass
considered.
This calculation of Ω
GW
(
f
) captures the total energy
density in gravitational waves generated by binary black
hole coalescences. In practice, some of these sources will
be individually detected as resolved binaries. We define
“the residual background” as the energy density spec-
trum that excludes potentially resolvable binaries. While
the total background is a property of the Universe, the
residual background is detector-dependent. As sensitiv-
ity improves, the surveyed volume increases, more bina-
ries are resolved and the residual background decreases.
The dashed blue curve in Fig. 1a represents the resid-
ual background calculated for the network of the Ad-
vanced LIGO [1, 2] and Advanced Virgo [36, 37] detec-
tors at final sensitivity, assuming that a binary black hole
signal is detected if it is associated with a single-detector
matched filter signal-to-noise ratio of
ρ >
8 in at least two
detectors [38]. The difference between the two curves is
about 30% in the sensitive frequency band (10–50 Hz),
indicating that the residual background carries comple-
mentary information about the binary black hole pop-
ulation. Binaries with the same component masses as
GW150914 can be detected at a redshift up to
z
.
1
.
3
by advanced detectors operating at design sensitivity if
optimally located and oriented (see Fig. 4 of [14]). How-
ever, most sources at
z
&
0
.
4 will not be individually
resolvable because of unfavorable location and orienta-
tion.
The sensitive frequency band of the Advanced LIGO-
Virgo network to a gravitational-wave background pro-
duced by binary black holes is 10–50 Hz, where Ω
GW
∼
f
2
/
3
. It corresponds to more than 95% of the accumu-
lated sensitivity [12, 13, 39]. The black curves shown
in Fig. 1a are
power-law integrated curves
[40], which
represent the expected 1
σ
sensitivity of the standard
cross-correlation search [5] to power-law gravitational-
wave backgrounds, of which the Ω
GW
(
f
)
∝
f
2
/
3
spec-
7
10
1
10
2
10
−
10
10
−
9
10
−
8
10
−
7
Frequency (Hz)
Ω
GW
O1:2015
−
16
O2:2016
−
17
O5:2020
−
22
Total
Residual
Poisson
0
20
40
60
80
100
10
−
2
10
−
1
10
0
10
1
Observation time (months)
SNR
5
σ
3
σ
σ
O1
O2
O3
O4
O5
total
residual
Poisson
FIG. 1. Expected sensitivity of the network of advanced LIGO and Virgo detectors to the
Fiducial
field model. Left panel:
Energy density spectra are shown in blue (solid for the total background; dashed for the residual background, excluding resolved
sources, assuming final advanced LIGO and Virgo [1, 2] sensitivity). The pink shaded region “Poisson” shows the 90% CL
statistical uncertainty, propagated from the local rate measurement, on the total background. The black power-law integrated
curves show the 1
σ
sensitivity of the network expected for the two first observing runs O1 and O2, and for 2 years at the design
sensitivity in O5. (O3 and O4 are not significantly different than O5; see Table I.) If the astrophysical background spectrum
intersects a black line, it has expected SNR
≥
1. In both panels we assume a coincident duty cycle of 33% for O1 (actual) and
50% for all other runs (predicted). Right panel: Predicted SNR as a function of total observing time. The blue lines and pink
shaded region have the same interpretation as in the left panel. Each observing run is indicated by an improvement in the
LIGO-Virgo network sensitivity [35], which results in a discontinuity in the slope. The thresholds for SNR = 1, 3 (false-alarm
probability
<
3
×
10
−
3
) and 5 (false-alarm probability
<
6
×
10
−
7
) are indicated by horizontal lines.
trum for binary inspirals is an example. A power-law in-
tegrated curve is calculated by taking the locus of power-
law spectra that have expected SNR = 1, where [5]:
SNR =
3
H
2
0
10
π
2
√
2
T
∫
∞
0
df
n
∑
i
=1
∑
j>i
γ
2
ij
(
f
)Ω
2
GW
(
f
)
f
6
P
i
(
f
)
P
j
(
f
)
1
/
2
,
(4)
for a network of detectors
i
= 1
,
2
,
···
,n
. Hence, if
the spectrum of an astrophysical background intersects
a black curve, then it has an expected SNR
≥
1. In Eq.
4,
P
i
(
f
) and
P
j
(
f
) are the one-sided strain noise power
spectral densities of two detectors;
γ
ij
(
f
) is the normal-
ized isotropic overlap reduction function [41, 42]; and
T
is the accumulated coincident observation time. While
Eq. 4 is derived by assuming a Gaussian background [5],
it can also be applied to non-Gaussian backgrounds (with
signals that are clearly separated in time) such as the bi-
nary black hole background considered here [43]. The
different black curves shown in this plot illustrate the
improvement in expected sensitivity in the coming years.
Following [35, 39], we consider five different phases, de-
noted O1 to O5, corresponding to the first five observing
runs, summarized in Table I. For clarity, we show only
the O1, O2, and O5 power-law integrated curves since
the differences between the projected sensitivities for O3,
O4, and O5 are relatively small. In Fig. 1b, we plot the
expected accumulated SNR for the
Fiducial
model as
a function of total observation time. For both the sen-
sitivity curves and the accumulated SNR, we assume a
coincident duty cycle for each pair of detectors of 33% for
O1 (actual) and 50% for all other runs (predicted). The
total background associated with the
Fiducial
model
could be identified with SNR = 3, corresponding to false
alarm probability
<
3
×
10
−
3
, after approximately 6 years
of observing. In the most optimistic scenario given by
statistical uncertainties, the total background could be
identified after 1.5 years with SNR = 3 and after approx-
imatively 2 years with SNR = 5, which is even before
design sensitivity is reached. It would take about 2 years
of observing to achieve SNR = 3 and about 3.5 years for
SNR = 5 for the optimistic residual background. The
most pessimistic case considered here is out of reach of
the advanced detector network but is in the scope of third
generation detectors.
Alternative Models
— We now investigate the impact of
possible variations on the
Fiducial
model. We consider
the following alternatives:
•
AltSFR
differs from the
Fiducial
model in as-
suming a different SFR proposed by Tornatore et
al. [44], who combined observations and simulations
at higher redshift; the formation rate is assumed
8