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### Please be advised that this information was generated on 2017-12-05 and may be subject to

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### 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,}18,19 _{J. C. Batch,}37 _{C. Baune,}8 _{V. Bavigadda,}34 _{M. Bazzan,}41,42

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,}8,17 _{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,9R. Bork,1V. Boschi,18,19 S. Bose,56,14 Y. Bouffanais,30 A. Bozzi,34 C. Bradaschia,19P. R. Brady,16
V. B. Braginsky,49 _{M. Branchesi,}57,58 _{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,61,9 _{A. Buonanno,}29,62 _{D. Buskulic,}7 _{C. Buy,}30 _{R. L. Byer,}40 _{L. Cadonati,}63 _{G. Cagnoli,}64,65

C. Cahillane,1_{J. Calder´}_{on Bustillo,}66,63 _{T. Callister,}1 _{E. Calloni,}67,4 _{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,}25,13 _{S. Caudill,}16

M. Cavagli`a,21 _{F. Cavalier,}23 _{R. Cavalieri,}34 _{G. Cella,}19 _{C. B. Cepeda,}1_{L. Cerboni Baiardi,}57,58 _{G. Cerretani,}18,19

E. Cesarini,25,13 R. Chakraborty,1 T. Chalermsongsak,1 S. J. Chamberlin,72M. Chan,36 S. Chao,73P. 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,20N. Christensen,78,53 Q. Chu,51 S. Chua,60S. Chung,51 G. Ciani,5F. Clara,37J. A. Clark,63
F. Cleva,53 _{E. Coccia,}25,12,13 _{P.-F. Cohadon,}60 _{A. Colla,}79,28 _{C. G. Collette,}80_{L. Cominsky,}81_{M. Constancio Jr.,}11

A. Conte,79,28 _{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,}53 _{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,36L. Cunningham,36E. Cuoco,34 T. Dal Canton,8 S. L. Danilishin,36S. D’Antonio,13
K. Danzmann,17,8 _{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,67,4 S. Del´eglise,60
W. Del Pozzo,45_{T. Denker,}8,17 _{T. Dent,}8 _{H. Dereli,}53 _{V. Dergachev,}1 _{R. T. DeRosa,}6_{R. De Rosa,}67,4 _{R. DeSalvo,}87

S. Dhurandhar,14_{M. C. D´ıaz,}85 _{L. Di Fiore,}4_{M. Di Giovanni,}79,28 _{A. Di Lieto,}18,19 _{S. Di Pace,}79,28 _{I. Di Palma,}29,8

A. Di Virgilio,19 _{G. Dojcinoski,}88 _{V. Dolique,}65 _{F. Donovan,}10 _{K. L. Dooley,}21 _{S. Doravari,}6,8 _{R. Douglas,}36

T. P. Downes,16 _{M. Drago,}8,89,90 _{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,25,13,12 H. Fair,35S. Fairhurst,91 X. Fan,70 Q. Fang,51 S. Farinon,47 B. Farr,75W. M. Farr,45 M. Favata,88
M. Fays,91 _{H. Fehrmann,}8 _{M. M. Fejer,}40 _{I. Ferrante,}18,19 _{E. C. Ferreira,}11 _{F. Ferrini,}34 _{F. Fidecaro,}18,19 _{I. Fiori,}34

D. Fiorucci,30 _{R. P. Fisher,}35 _{R. Flaminio,}65,92 _{M. Fletcher,}36 _{J.-D. Fournier,}53 _{S. Franco,}23 _{S. Frasca,}79,28

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,}32,33 _{S. G. Gaonkar,}14 _{F. Garufi,}67,4 _{A. Gatto,}30

G. Gaur,94,95 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,}52,9 _{J. A. Giaime,}2,6 _{K. D. Giardina,}6 _{A. Giazotto,}19 _{K. Gill,}97

A. Glaefke,36E. Goetz,98 R. Goetz,5 L. Gondan,54 G. Gonz´alez,2 J. M. Gonzalez Castro,18,19 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,}57,58 _{A. C. Green,}45 _{P. Groot,}52 _{H. Grote,}8

S. Grunewald,29 _{G. M. Guidi,}57,58 _{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

2
C. Hanna,72 M. D. Hannam,91 J. Hanson,6 T. Hardwick,2 J. Harms,57,58 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,}5,6 _{H. Heitmann,}53

P. Hello,23G. Hemming,34 M. Hendry,36 I. S. Heng,36 J. Hennig,36 A. W. Heptonstall,1 M. Heurs,8,17 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,}103,82 _{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,104S. Jawahar,105F. Jim´enez-Forteza,66W. W. Johnson,2 D. I. Jones,26R. Jones,36 R. J. G. Jonker,9
L. Ju,51 _{Haris K,}106 _{C. V. Kalaghatgi,}24,91 _{V. Kalogera,}82_{S. Kandhasamy,}21 _{G. Kang,}77 _{J. B. Kanner,}1_{S. Karki,}59

M. Kasprzack,2,23,34 E. Katsavounidis,10 W. Katzman,6 S. Kaufer,17 T. Kaur,51K. Kawabe,37 F. Kawazoe,8,17
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,110,111
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,113A. Lazzarini,1 C. Lazzaro,63,42 P. Leaci,29,79,28 S. Leavey,36 E. O. Lebigot,30,70
C. H. Lee,108 _{H. K. Lee,}109 _{H. M. Lee,}114 _{K. Lee,}36 _{A. Lenon,}35 _{M. Leonardi,}89,90 _{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,12,13 V. Loriette,116 M. Lormand,6 G. Losurdo,58
J. D. Lough,8,17 _{H. L¨}_{uck,}17,8 _{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,}25,13 _{N. Man,}53 _{I. Mandel,}45 _{V. Mandic,}83 _{V. Mangano,}36 _{G. L. Mansell,}20

M. Manske,16 M. Mantovani,34 F. Marchesoni,117,33 F. Marion,7 S. M´arka,39 Z. M´arka,39 A. S. Markosyan,40
E. Maros,1 _{F. Martelli,}57,58 _{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,56G. Mazzolo,8 R. McCarthy,37D. E. McClelland,20S. McCormick,6S. C. McGuire,118G. McIntyre,1
J. McIver,1 _{D. J. McManus,}20_{S. T. McWilliams,}103 _{D. Meacher,}72 _{G. D. Meadors,}29,8 _{J. Meidam,}9 _{A. Melatos,}84

G. Mendell,37D. 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,}28,79 _{H. Miao,}45 _{C. Michel,}65 _{H. Middleton,}45 _{E. E. Mikhailov,}119

L. Milano,67,4 _{J. Miller,}10 _{M. Millhouse,}31 _{Y. Minenkov,}13 _{J. Ming,}29,8 _{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,57,58 _{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,45C. L. Mueller,5 G. Mueller,5 A. W. Muir,91 Arunava Mukherjee,15D. Mukherjee,16
S. Mukherjee,85 _{N. Mukund,}14 _{A. Mullavey,}6 _{J. Munch,}102 _{D. J. Murphy,}39 _{P. G. Murray,}36 _{A. Mytidis,}5

I. Nardecchia,25,13 L. Naticchioni,79,28 R. K. Nayak,122 V. Necula,5K. Nedkova,101G. Nelemans,52,9 M. Neri,46,47
A. Neunzert,98 _{G. Newton,}36 _{T. T. Nguyen,}20 _{A. B. Nielsen,}8_{S. Nissanke,}52,9 _{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,48J. R. Palamos,59O. Palashov,107C. Palomba,28A. Pal-Singh,27 H. Pan,73C. Pankow,82F. Pannarale,91
B. C. Pant,48 _{F. Paoletti,}34,19 _{A. Paoli,}34 _{M. A. Papa,}29,16,8 _{H. R. Paris,}40 _{W. Parker,}6 _{D. Pascucci,}36

A. Pasqualetti,34R. Passaquieti,18,19D. Passuello,19B. Patricelli,18,19Z. Patrick,40B. 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,16J. Qin,51 V. Quetschke,85E. 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,82M. Shaltev,8 Z. Shao,1B. Shapiro,40P. Shawhan,62A. 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,78S. Strigin,49 R. Sturani,120 A. L. Stuver,6T. 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,105C. 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,8J. T. Whelan,112,8 D. J. White,86B. 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,6J. Yablon,82 W. Yam,10 H. Yamamoto,1 C. C. Yancey,62 M. J. Yap,20H. 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

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

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 ΩGW(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 5.1σ [3]. The observed signal is consis-tent with a binary black hole waveform with component masses of m1 =36+5−4 M and m2 =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−3yr−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]: ΩGW(f ) = f ρc dρGW df , (1)

where dρGW is the energy density in the frequency

in-terval f to f + df , ρc = 3H02c2/8πG is the critical

en-ergy density required to close the Universe, and H0 =

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 θk, merge at a rate

Rm(z; θk) per unit comoving volume Vc per unit source

time, then the total gravitational-wave energy density spectrum is given by (see, e.g. [6–13]):

ΩGW(f ; θk) = f ρcH0 Z zmax 0 dzRm(z, θk) dEGW dfs (fs, θk) (1 + z)E(ΩM, ΩΛ, z) , (2) and the total energy density spectrum is the sum of ΩGW(f ; θk) from each class.1 In Eq. 2, dEGW/dfs(fs, θk)

is the spectral energy density of a source of class k at the frequency fs = f (1 + z), which depends on the source

parameters θk; E(ΩM, ΩΛ, z) =pΩM(1 + z)3+ ΩΛ

cap-tures the dependence of the comoving volume on redshift for the standard flat cosmology model, with ΩM = 0.31

and ΩΛ = 1 − ΩM. 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 zmax corresponds to the time of the first

coalescences. We set zmax = 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.

sources above z ∼ 5 contribute very little to the total background (see, e.g., [6–13]).

The merger rate Rm(z; θk) is a convolution of the

bi-nary formation rate Rf(z; θk) with the distribution of

the time delays P (td; θk) between binary black hole

for-mation and merger (see e.g., [18]

Rm(z; θk) =

Z tmax

tmin

Rf(zf; θk)P (td; θk)dtd, (3)

where td is the time delay, zf is the redshift at the

for-mation time tf = t(z) − td, 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 dEGW/dfs 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 dEGW/dfs 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 χeff, 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 Zc = 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 (td) ∝ tαd, with α = −1 for td > tmin[18, 27–33], where

tmin = 50 Myr is the minimum delay time for a massive

binary to evolve until coalescence [e.g., 34], and a maxi-mum time delay tmax equal to the Hubble time.

The rest of the Fiducial model parameters corre-spond to the median inferred parameters of GW150914: the chirp mass Mc = 28 M, the symmetric mass ratio

η ∼ 0.25, and the effective spin parameter χeff = −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−3yr−1_{[15].}

Results — We plot ΩGW(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 ΩGW(f =

25 Hz) = 1.1+2.7_{−0.9}× 10−9_{. The spectrum is well }

approxi-mated by a power law ΩGW(f ) ∝ f2/3 at low frequencies

where the contribution from the inspiral phase is dom-inant and the spectral energy density is dEGW/dfs =

[(Gπ)2/3_{/3]M}5/3

c fs−1/3. 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 ΩGW(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 AdAd-vanced 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 ΩGW ∼

f2/3_{. 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 1σ sensitivity of the standard cross-correlation search [5] to power-law gravitational-wave backgrounds, of which the ΩGW(f ) ∝ f2/3

101 102 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 10−1 100 101

Observation time (months)

SNR 5σ 3σ 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 1σ 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 = 3H
2
0
10π2
√
2T
Z ∞
0
df
n
X
i=1
X
j>i
γ2
ij(f )Ω2GW(f )
f6_{P}
i(f )Pj(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, Pi(f ) and Pj(f ) are the one-sided strain noise power

spectral densities of two detectors; γij(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

TABLE I. Different phases in the evolution of the aLIGO–AdVirgo detector network over the next several years. The aLIGO and AdVirgo noise curves corresponding to high-sensitivity versions of “Early”, “Mid”, “Late”, and “Design” spectra are taken from [35]. Note that AdVirgo did not participate in the O1 observing run, so is not included in the first phase. “Duration” refers to the planned calendar time as opposed to the amount of accumulated data, for which we assume a duty cycle of 33% for O1 (actual) and 50% for all other runs (predicted).

Observing run Epoch Duration (months) aLIGO sensitivity AdVirgo sensitivity

O1 2015–2016 4 Early —

O2 2016–2017 6 Mid Early

O3 2017–2018 9 Late Mid

O4 2019 12 Design Late

O5 2020+ – Design Design

to be proportional to the SFR, with no metallic-ity threshold. We also considered the Madau & Dickinson SFR [24], and found that it produces an energy density spectrum that is essentially indis-tinguishable from the Fiducial model.

• LongDelay is identical to the Fiducial model but assumes a significantly longer minimum time delay tmin = 5 Gyr, potentially consistent with binary

black hole formation via the chemically homoge-neous evolution of rapidly rotating massive stars in very tight binaries [45].

• LowMetallicity is the same as Fiducial, but as-sumes that a significantly lower metallicity is re-quired to form heavy black holes, with a threshold of Zc= Z/10 [14].

• FlatDelay assumes a flat time delay distribution, α = 0, with tmin = 50 Myr and tmax = 1 Gyr.

This is inspired by the supposition that dynami-cal formation of the most massive binaries is likely to happen fairly early in the history of the host environment.

• ConstRate follows the assumption of [3] in consid-ering a redshift-independent merger rate, Rm(z) =

16 Gpc−3_{yr}−1_{.}

• LowMass is the same as the Fiducial model except we add a second class of binary black hole sources corresponding to lower-mass systems with a smaller range for individual detections during O1. As an example, we assume a chirp mass of half the mass of GW150914, Mc = 15 M (corresponding to the

second most significant trigger in the compact bi-nary coalescence search [38]) and a local merger rate of 60 Gpc−3 yr−1, about 4 times larger than the rate of GW150914. We assume here that the metallicity threshold is Zc= Z.

Figure 2 shows the impact of alternative models de-scribed above. The differences in the spectra of alter-native models are not negligible. However, all models

considered here fall within the range of statistical uncer-tainty in the local merger rate estimate relative to the Fiducial model in the sensitive frequency band.

The impact of an alternative star formation rate, as ex-amined through model AltSFR, is particularly small, in-dicating that the accuracy of SFR models is not a signifi-cant source of systematic error in predicting the strength of the gravitational-wave background.

Relative to the Fiducial model, the LongDelay, FlatDelay, and ConstRate models all predict fewer bi-naries at z > 0, even though all of these models are constrained to have the same local merger rate (z = 0). These latter three models consequently yield a lower energy density. The LowMetallicity model is charac-terized by a greater high-redshift merger rate than the Fiducial model, with significant merger rates extend-ing out to z ∼ 5 − 6. This is because very little of the local Universe has the required low metallicity, so the local mergers come from the long time-delay tail of a large high-redshift population. Consequently, the LowMetallicity model has a higher overall normaliza-tion, as well as a different spectral shape at frequencies above 100 Hz due to the redshifting of the dominant high-z contribution to the gravitational-wave background to lower frequencies.

Relative to the Fiducial model, the LowMass model shows a greater energy density at all frequencies, partic-ularly at high frequencies due to the signals from lower-mass binaries. This model indicates that if there is a sig-nificant rate of mergers of binaries with smaller masses than GW150914, their contribution to the gravitational-wave energy density spectrum could be significant. The delta-function mass distributions assumed in all models are motivated by the observed candidates, but are not realistic. We have analyzed two alternative broad mass distributions considered in [15], flat in the log-mass of the component black holes and a Salpeter-like mass function for the larger black hole with a flat mass ratio; these yield broadly consistent energy densities. We have not carried out a systematic study of black hole spin. Mea-surements of GW150914 prefer small values of spin in the

101 102 10−10 10−9 10−8 10−7 Frequency (Hz) Ω GW O5:2020−22 Fiducial AltSFR LongDelay LowMass LowMetallicity ConstRate FlatDelay Poisson

FIG. 2. Energy density spectra for the different models summarized in the text. The pink shaded region “Poisson” shows the 90% CL statistical uncertainty propagated from the local rate measurement, on the Fiducial model. The black dashed curve shows the design sensitivity of the network of Advanced LIGO [1, 2] and Virgo [36, 37]; see Tab. I. If the astrophysical background spectrum intersects with the dashed black line, it has expected SNR ≥ 1.

direction of orbital momentum, but spins in the orbital plane are not constrained. Preliminary studies suggest that ΩGW(f ) could change by a factor of . 2 for models

including spin.

Conclusions and discussion — The detection of gravita-tional waves from GW150914 is consistent with the ex-istence of high-mass binary black hole mergers with a coalescence rate of tens per Gpc3 per year. As a con-sequence, the stochastic background from binary black holes is expected to be at the higher end of previous predictions (see, e.g., [7–13]). We have shown that, for the Fiducial field model, the energy density spectrum is ΩGW(f = 25 Hz) = 1.1+2.7−0.9 × 10−9 with 90%

confi-dence. This, in turn, implies that the background may be measured by the network of advanced LIGO and Virgo detectors operating at or near their final sensitivity. The uncertainty in this prediction arises from the statistical uncertainty in the local merger rate estimate.

Our predictions are subject to statistical fluctuations in the observed ΩGW(f ) due to random realizations of the

binaries that coalesce during the observing run. These fluctuations are much smaller than the current local merger uncertainty [43]. The predictions may also be conservative. Throughout, we have assumed the use of the standard cross-correlation statistic, which is known to be sub-optimal for non-Gaussian backgrounds [46]. The development of more sensitive non-Gaussian pipelines may hasten the detection of the binary black hole back-ground [47–49].

We have examined several alternative models for the merger rate evolution with redshift, representative of the uncertainties in the formation channels for high-mass bi-nary black holes. We find that all of these variations lie within the envelope of the uncertain local rate normal-ization in the 10–50 Hz band, as illustrated in Fig. 2. The power-law slope of the spectrum in this frequency band is not expected to deviate from 2/3 unless there is a significant contribution from sources with high total mass merging at high redshift, M (1 + z) & 200M. This

illustrates the robustness of the predicted amplitude and power-law slope of the energy density spectrum.

However, this also implies that the stochastic back-ground measurement with Advanced LIGO and Virgo detectors can only constrain the amplitude of the back-ground power law in the 10–50 Hz sensitive frequency band. The sensitivity of this search at the 2σ level will correspond to ΩGW ∼ 10−9 at 25 Hz with the

full-sensitivity network of the Advanced LIGO/Virgo detec-tors. Therefore, the stochastic search alone will not be able to distinguish between different model variations that have a similar effect on the spectrum in the 10-50 Hz band. Future measurements of individual binary coa-lescences will help break at least some of these degenera-cies, by providing a better estimate of the local merger rate and chirp mass distribution. Combining the two types of measurements (stochastic and individual coales-cence event) could therefore help distinguish between dif-ferent astrophysical formation scenarios for binary black holes [50], but the full potential of this approach may only be reached using third generation of gravitational-wave detectors.

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 creaopera-tion and support of the EGO consortium. The authors also gratefully ac-knowledge research support from these agencies as well as by the Council of Scientific and Industrial Research of India, Department of Science and Technology, India, Science & Engineering Research Board (SERB), India, Ministry of Human Resource Development, India, the

Spanish Ministerio de Econom´ıa y Competitividad, the Conselleria d’Economia i Competitivitat and Conselleria d’Educaci´o, Cultura i Universitats of the Govern de les Illes Balears, the National Science Centre of Poland, the European Commission, the Royal Society, the Scottish Funding Council, the Scottish Universities Physics Al-liance, the Hungarian Scientific Research Fund (OTKA), the Lyon Institute of Origins (LIO), the National Re-search Foundation of Korea, Industry Canada and the Province of Ontario through the Ministry of Economic Development and Innovation, the Natural Science and Engineering Research Council Canada, Canadian Insti-tute for Advanced Research, the Brazilian Ministry of Science, Technology, and Innovation, Russian Founda-tion for Basic Research, the Leverhulme Trust, the Re-search Corporation, Ministry of Science and Technology (MOST), Taiwan and the Kavli Foundation. The au-thors gratefully acknowledge the support of the NSF, STFC, MPS, INFN, CNRS and the State of Niedersach-sen/Germany for provision of computational resources.

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