Upper Limits on the Stochastic Gravitational-Wave Background from Advanced LIGO's First Observing Run
LIGO Scientific Collaboration, Virgo Collaboration, B. P. Abbott, R. Abbott, T. D. Abbott, M. R. Abernathy, F. Acernese, K. Ackley, C. Adams, T. Adams, P. Addesso, R. X. Adhikari, V. B. Adya, C. Affeldt, M. Agathos, K. Agatsuma, N. Aggarwal, O. D. Aguiar, L. Aiello, A. Ain, P. Ajith, B. Allen, A. Allocca, P. A. Altin, A. Ananyeva, S. B. Anderson, W. G. Anderson, S. Appert, K. Arai, M. C. Araya, J. S. Areeda, N. Arnaud, K. G. Arun, S. Ascenzi, G. Ashton, M. Ast, S. M. Aston, P. Astone, P. Aufmuth, C. Aulbert, A. Avila-Alvarez, S. Babak, P. Bacon, M. K. M. Bader, P. T. Baker, F. Baldaccini, G. Ballardin, S. W. Ballmer, J. C. Barayoga, S. E. Barclay, B. C. Barish, D. Barker, F. Barone, B. Barr, L. Barsotti, M. Barsuglia, D. Barta, J. Bartlett, I. Bartos, R. Bassiri, A. Basti, J. C. Batch, C. Baune, V. Bavigadda, M. Bazzan, C. Beer, M. Bejger, I. Belahcene, M. Belgin, A. S. Bell, B. K. Berger, G. Bergmann, C. P. L. Berry, D. Bersanetti, A. Bertolini, J. Betzwieser, S. Bhagwat, R. Bhandare, I. A. Bilenko, G. Billingsley, C. R. Billman, J. Birch, R. Birney, O. Birnholtz, S. Biscans, A. S. Biscoveanu, A. Bisht, M. Bitossi, C. Biwer, M. A. Bizouard, J. K. Blackburn, J. Blackman, C. D. Blair, D. G. Blair, R. M. Blair, S. Bloemen, O. Bock, M. Boer, G. Bogaert, A. Bohe, et al. (895 additional authors not shown)
UUpper Limits on the Stochastic Gravitational-Wave Background fromAdvanced LIGO’s First Observing Run
B. P. Abbott, R. Abbott, T. D. Abbott, M. R. Abernathy, F. Acernese, , K. Ackley, C. Adams, T. Adams, P. Addesso, R. X. Adhikari, V. B. Adya, C. Affeldt, M. Agathos, K. Agatsuma, N. Aggarwal, O. D. Aguiar, L. Aiello, , A. Ain, P. Ajith, B. Allen, , , A. Allocca, , P. A. Altin, A. Ananyeva, S. B. Anderson, W. G. Anderson, S. Appert, K. Arai, M. C. Araya, J. S. Areeda, N. Arnaud, K. G. Arun, S. Ascenzi, , G. Ashton, M. Ast, S. M. Aston, P. Astone, P. Aufmuth, C. Aulbert, A. Avila-Alvarez, S. Babak, P. Bacon, M. K. M. Bader, P. T. Baker, F. Baldaccini, , G. Ballardin, S. W. Ballmer, J. C. Barayoga, S. E. Barclay, B. C. Barish, D. Barker, F. Barone, , B. Barr, L. Barsotti, M. Barsuglia, D. Barta, J. Bartlett, I. Bartos, R. Bassiri, A. Basti, , J. C. Batch, C. Baune, V. Bavigadda, M. Bazzan, , C. Beer, M. Bejger, I. Belahcene, M. Belgin, A. S. Bell, B. K. Berger, G. Bergmann, C. P. L. Berry, D. Bersanetti, , A. Bertolini, J. Betzwieser, S. Bhagwat, R. Bhandare, I. A. Bilenko, G. Billingsley, C. R. Billman, J. Birch, R. Birney, O. Birnholtz, S. Biscans, , A. S. Biscoveanu, A. Bisht, M. Bitossi, C. Biwer, M. A. Bizouard, J. K. Blackburn, J. Blackman, C. D. Blair, D. G. Blair, R. M. Blair, S. Bloemen, O. Bock, M. Boer, G. Bogaert, A. Bohe, F. Bondu, R. Bonnand, B. A. Boom, R. Bork, V. Boschi, , S. Bose, , Y. Bouffanais, A. Bozzi, C. Bradaschia, P. R. Brady, V. B. Braginsky ∗ , M. Branchesi, , J. E. Brau, T. Briant, A. Brillet, M. Brinkmann, V. Brisson, P. Brockill, J. E. Broida, A. F. Brooks, D. A. Brown, D. D. Brown, N. M. Brown, S. Brunett, C. C. Buchanan, A. Buikema, T. Bulik, H. J. Bulten, , A. Buonanno, , D. Buskulic, C. Buy, R. L. Byer, M. Cabero, L. Cadonati, G. Cagnoli, , C. Cahillane, J. Calder´on Bustillo, T. A. Callister, E. Calloni, , J. B. Camp, W. Campbell,
M. Canepa, , K. C. Cannon, H. Cao, J. Cao, C. D. Capano, E. Capocasa, F. Carbognani, S. Caride, J. Casanueva Diaz, C. Casentini, , S. Caudill, M. Cavagli`a, F. Cavalier, R. Cavalieri, G. Cella, C. B. Cepeda, L. Cerboni Baiardi, , G. Cerretani, , E. Cesarini, , S. J. Chamberlin, M. Chan, S. Chao, P. Charlton, E. Chassande-Mottin, B. D. Cheeseboro, H. Y. Chen, Y. Chen, H.-P. Cheng, A. Chincarini, A. Chiummo, T. Chmiel, H. S. Cho, M. Cho, J. H. Chow, N. Christensen, Q. Chu, A. J. K. Chua, S. Chua, S. Chung, G. Ciani, F. Clara, J. A. Clark, F. Cleva, C. Cocchieri, E. Coccia, , P.-F. Cohadon, A. Colla, , C. G. Collette, L. Cominsky, M. Constancio Jr., L. Conti, S. J. Cooper, T. R. Corbitt, N. Cornish, A. Corsi, S. Cortese, C. A. Costa, E. Coughlin, M. W. Coughlin, S. B. Coughlin, J.-P. Coulon, S. T. Countryman, P. Couvares, P. B. Covas, E. E. Cowan, D. M. Coward, M. J. Cowart, D. C. Coyne, R. Coyne, J. D. E. Creighton, T. D. Creighton, J. Cripe, S. G. Crowder, T. J. Cullen, A. Cumming, L. Cunningham, E. Cuoco, T. Dal Canton, S. L. Danilishin, S. D’Antonio, K. Danzmann, , A. Dasgupta, C. F. Da Silva Costa, V. Dattilo, I. Dave, M. Davier, G. S. Davies, D. Davis, E. J. Daw, B. Day, R. Day, S. De, D. DeBra, G. Debreczeni, J. Degallaix, M. De Laurentis, , S. Del´eglise, W. Del Pozzo, T. Denker, T. Dent, V. Dergachev, R. De Rosa, , R. T. DeRosa, R. DeSalvo, J. Devenson, R. C. Devine, S. Dhurandhar, M. C. D´ıaz, L. Di Fiore, M. Di Giovanni, , T. Di Girolamo, , A. Di Lieto, , S. Di Pace, , I. Di Palma, , , A. Di Virgilio, Z. Doctor, V. Dolique, F. Donovan, K. L. Dooley, S. Doravari, I. Dorrington, R. Douglas, M. Dovale ´Alvarez, T. P. Downes, M. Drago, R. W. P. Drever, J. C. Driggers, Z. Du, M. Ducrot, S. E. Dwyer, T. B. Edo, M. C. Edwards, A. Effler, H.-B. Eggenstein, P. Ehrens, J. Eichholz, S. S. Eikenberry, R. C. Essick, Z. Etienne, T. Etzel, M. Evans, T. M. Evans, R. Everett, M. Factourovich, V. Fafone, , , H. Fair, S. Fairhurst, X. Fan, S. Farinon, B. Farr, W. M. Farr, E. J. Fauchon-Jones, M. Favata, M. Fays, H. Fehrmann, M. M. Fejer, A. Fern´andez Galiana, I. Ferrante, , E. C. Ferreira, F. Ferrini, F. Fidecaro, , I. Fiori, D. Fiorucci, R. P. Fisher, R. Flaminio, , M. Fletcher, H. Fong, S. S. Forsyth, J.-D. Fournier, S. Frasca, , F. Frasconi, Z. Frei, A. Freise, R. Frey, V. Frey, E. M. Fries, P. Fritschel, V. V. Frolov, P. Fulda, , M. Fyffe, H. Gabbard, B. U. Gadre, S. M. Gaebel, J. R. Gair, L. Gammaitoni, S. G. Gaonkar, F. Garufi, , G. Gaur,
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M. L. Gorodetsky, S. E. Gossan, M. Gosselin, a r X i v : . [ g r- q c ] J u l R. Gouaty, A. Grado, , C. Graef, M. Granata, A. Grant, S. Gras, C. Gray, G. Greco, , A. C. Green, P. Groot, H. Grote, S. Grunewald, G. M. Guidi, , X. Guo, A. Gupta, M. K. Gupta, K. E. Gushwa, E. K. Gustafson, R. Gustafson,
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Whansun Kim,
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C. Zhao, M. Zhou, Z. Zhou, S. J. Zhu, , X. J. Zhu, M. E. Zucker, , and J. Zweizig (LIGO Scientific Collaboration and Virgo Collaboration) ∗ Deceased, March 2016. LIGO, California Institute of Technology, Pasadena, CA 91125, USA Louisiana State University, Baton Rouge, LA 70803, USA American University, Washington, D.C. 20016, USA Universit`a di Salerno, Fisciano, I-84084 Salerno, Italy INFN, Sezione di Napoli, Complesso Universitario di Monte S.Angelo, I-80126 Napoli, Italy University of Florida, Gainesville, FL 32611, USA LIGO Livingston Observatory, Livingston, LA 70754, USA Laboratoire d’Annecy-le-Vieux de Physique des Particules (LAPP),Universit´e Savoie Mont Blanc, CNRS/IN2P3, F-74941 Annecy-le-Vieux, France University of Sannio at Benevento, I-82100 Benevento,Italy and INFN, Sezione di Napoli, I-80100 Napoli, Italy Albert-Einstein-Institut, Max-Planck-Institut f¨ur Gravitationsphysik, D-30167 Hannover, Germany Nikhef, Science Park, 1098 XG Amsterdam, The Netherlands LIGO, Massachusetts Institute of Technology, Cambridge, MA 02139, USA Instituto Nacional de Pesquisas Espaciais, 12227-010 S˜ao Jos´e dos Campos, S˜ao Paulo, Brazil INFN, Gran Sasso Science Institute, I-67100 L’Aquila, Italy INFN, Sezione di Roma Tor Vergata, I-00133 Roma, Italy Inter-University Centre for Astronomy and Astrophysics, Pune 411007, India International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India University of Wisconsin-Milwaukee, Milwaukee, WI 53201, USA Leibniz Universit¨at Hannover, D-30167 Hannover, Germany Universit`a di Pisa, I-56127 Pisa, Italy INFN, Sezione di Pisa, I-56127 Pisa, Italy Australian National University, Canberra, Australian Capital Territory 0200, Australia California State University Fullerton, Fullerton, CA 92831, USA LAL, Univ. Paris-Sud, CNRS/IN2P3, Universit´e Paris-Saclay, F-91898 Orsay, France Chennai Mathematical Institute, Chennai 603103, India Universit`a di Roma Tor Vergata, I-00133 Roma, Italy Universit¨at Hamburg, D-22761 Hamburg, Germany INFN, Sezione di Roma, I-00185 Roma, Italy Albert-Einstein-Institut, Max-Planck-Institut f¨ur Gravitationsphysik, D-14476 Potsdam-Golm, Germany 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 West Virginia University, Morgantown, WV 26506, USA Universit`a di Perugia, I-06123 Perugia, Italy INFN, Sezione di Perugia, I-06123 Perugia, Italy European Gravitational Observatory (EGO), I-56021 Cascina, Pisa, Italy Syracuse University, Syracuse, NY 13244, USA SUPA, University of Glasgow, Glasgow G12 8QQ, United Kingdom LIGO Hanford Observatory, Richland, WA 99352, USA Wigner RCP, RMKI, H-1121 Budapest, Konkoly Thege Mikl´os ´ut 29-33, Hungary Columbia University, New York, NY 10027, USA Stanford University, Stanford, CA 94305, USA Universit`a di Padova, Dipartimento di Fisica e Astronomia, I-35131 Padova, Italy INFN, Sezione di Padova, I-35131 Padova, Italy Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, 00-716, Warsaw, Poland Center for Relativistic Astrophysics and School of Physics,Georgia Institute of Technology, Atlanta, GA 30332, USA University of Birmingham, Birmingham B15 2TT, United Kingdom Universit`a degli Studi di Genova, I-16146 Genova, Italy INFN, Sezione di Genova, I-16146 Genova, Italy RRCAT, Indore MP 452013, India Faculty of Physics, Lomonosov Moscow State University, Moscow 119991, Russia SUPA, University of the West of Scotland, Paisley PA1 2BE, United Kingdom Caltech CaRT, Pasadena, CA 91125, USA University of Western Australia, Crawley, Western Australia 6009, Australia Department of Astrophysics/IMAPP, Radboud University Nijmegen,P.O. 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University of Adelaide, Adelaide, South Australia 5005, Australia Tsinghua University, Beijing 100084, China Texas Tech University, Lubbock, TX 79409, USA The University of Mississippi, University, MS 38677, USA The Pennsylvania State University, University Park, PA 16802, USA National Tsing Hua University, Hsinchu City, 30013 Taiwan, Republic of China Charles Sturt University, Wagga Wagga, New South Wales 2678, Australia University of Chicago, Chicago, IL 60637, USA Kenyon College, Gambier, OH 43022, USA Korea Institute of Science and Technology Information, Daejeon 305-806, Korea University of Cambridge, Cambridge CB2 1TN, United Kingdom Universit`a di Roma ’La Sapienza’, I-00185 Roma, Italy University of Brussels, Brussels 1050, Belgium Sonoma State University, Rohnert Park, CA 94928, USA Montana State University, Bozeman, MT 59717, USA Center for Interdisciplinary Exploration & Research in Astrophysics (CIERA),Northwestern University, Evanston, IL 60208, USA Universitat de les Illes Balears, IAC3—IEEC, E-07122 Palma de Mallorca, Spain The University of Texas Rio Grande Valley, Brownsville, TX 78520, USA Bellevue College, Bellevue, WA 98007, USA Institute for Plasma Research, Bhat, Gandhinagar 382428, India The University of Sheffield, Sheffield S10 2TN, United Kingdom California State University, Los Angeles, 5154 State University Dr, Los Angeles, CA 90032, USA Universit`a di Trento, Dipartimento di Fisica, I-38123 Povo, Trento, Italy INFN, Trento Institute for Fundamental Physics and Applications, I-38123 Povo, Trento, Italy Cardiff University, Cardiff CF24 3AA, United Kingdom Montclair State University, Montclair, NJ 07043, USA National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan Canadian Institute for Theoretical Astrophysics,University of Toronto, Toronto, Ontario M5S 3H8, Canada MTA E¨otv¨os University, “Lendulet” Astrophysics Research Group, Budapest 1117, Hungary School of Mathematics, University of Edinburgh, Edinburgh EH9 3FD, United Kingdom
University and Institute of Advanced Research, Gandhinagar, Gujarat 382007, India
IISER-TVM, CET Campus, Trivandrum Kerala 695016, India
University of Szeged, D´om t´er 9, Szeged 6720, Hungary
Embry-Riddle Aeronautical University, Prescott, AZ 86301, USA
Tata Institute of Fundamental Research, Mumbai 400005, India
INAF, Osservatorio Astronomico di Capodimonte, I-80131, Napoli, Italy
University of Michigan, Ann Arbor, MI 48109, USA
Rochester Institute of Technology, Rochester, NY 14623, USA
NCSA, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
University of Bia(cid:32)lystok, 15-424 Bia(cid:32)lystok, Poland
SUPA, University of Strathclyde, Glasgow G1 1XQ, United Kingdom
University of Southampton, Southampton SO17 1BJ, United Kingdom
University of Washington Bothell, 18115 Campus Way NE, Bothell, WA 98011, USA
Institute of Applied Physics, Nizhny Novgorod, 603950, Russia
Seoul National University, Seoul 151-742, Korea
Inje University Gimhae, 621-749 South Gyeongsang, Korea
National Institute for Mathematical Sciences, Daejeon 305-390, Korea
Pusan National University, Busan 609-735, Korea
NCBJ, 05-400 ´Swierk-Otwock, Poland
Institute of Mathematics, Polish Academy of Sciences, 00656 Warsaw, Poland
The School of Physics & Astronomy, Monash University, Clayton 3800, Victoria, Australia
Hanyang University, Seoul 133-791, Korea
The Chinese University of Hong Kong, Shatin, NT, Hong Kong
University of Alabama in Huntsville, Huntsville, AL 35899, USA
ESPCI, CNRS, F-75005 Paris, France
University of Minnesota, Minneapolis, MN 55455, USA
Universit`a di Camerino, Dipartimento di Fisica, I-62032 Camerino, Italy
Southern University and A&M College, Baton Rouge, LA 70813, USA
The University of Melbourne, Parkville, Victoria 3010, Australia
College of William and Mary, Williamsburg, VA 23187, USA
Instituto de F´ısica Te´orica, University Estadual Paulista/ICTP SouthAmerican Institute for Fundamental Research, S˜ao Paulo SP 01140-070, Brazil
Whitman College, 345 Boyer Avenue, Walla Walla, WA 99362 USA
Universit´e de Lyon, F-69361 Lyon, France
Hobart and William Smith Colleges, Geneva, NY 14456, USA
Janusz Gil Institute of Astronomy, University of Zielona G´ora, 65-265 Zielona G´ora, Poland
King’s College London, University of London, London WC2R 2LS, United Kingdom
IISER-Kolkata, Mohanpur, West Bengal 741252, India
Indian Institute of Technology, Gandhinagar Ahmedabad Gujarat 382424, India
Andrews University, Berrien Springs, MI 49104, USA
Universit`a di Siena, I-53100 Siena, Italy
Trinity University, San Antonio, TX 78212, USA
University of Washington, Seattle, WA 98195, USA
Abilene Christian University, Abilene, TX 79699, USA
A wide variety of astrophysical and cosmological sources are expected to contribute to a stochasticgravitational-wave background. Following the observations of GW150914 and GW151226, the rateand mass of coalescing binary black holes appear to be greater than many previous expectations. Asa result, the stochastic background from unresolved compact binary coalescences is expected to beparticularly loud. We perform a search for the isotropic stochastic gravitational-wave backgroundusing data from Advanced LIGO’s first observing run. The data display no evidence of a stochasticgravitational-wave signal. We constrain the dimensionless energy density of gravitational waves tobe Ω < . × − with 95% confidence, assuming a flat energy density spectrum in the mostsensitive part of the LIGO band (20 −
86 Hz). This is a factor of ∼
33 times more sensitive thanprevious measurements. We also constrain arbitrary power-law spectra. Finally, we investigate theimplications of this search for the background of binary black holes using an astrophysical modelfor the background.
Introduction. — Many astrophysical and cosmologicalphenomena are expected to contribute to a stochasticgravitational-wave background, henceforth, simply ref-ered to as a “background”. These include unresolvedcompact binary coalescences of both black holes and neu-tron stars [1–5], rotating neutron stars [6–8], supernovae[9–12], cosmic strings [13–16], inflationary models [17–24], phase transitions [25–27], and the pre-Big Bang sce-nario [28–31]. The variety of mechanisms potentially con-tributing to the background provides the opportunity tostudy a number of different environments within the Uni-verse.The recent detections of binary black hole (BBH) coa-lescences by Advanced LIGO [32, 33] suggest that theUniverse may be rich with coalescing BBHs. Whileevents like GW150914 and GW151226 are loud enoughto be clearly detected, we expect there to be manymore events that are too far away to be individuallyresolved and that contribute to the background. Sincethis BBH population originates from sources that aretoo distant to be individually detected, the stochasticsearch probes a distinct population of binaries comparedto nearby sources [34]. The background from these bina-ries provides complementary information to individuallyresolved binary coalescences [35].In this Letter, we report on the search for an isotropicbackground using data from Advanced LIGO’s first ob-serving run O1. We search for the background by cross-correlating data streams from the two separate LIGOdetectors and looking for a coherent signal. We find noevidence for the background and place the best upperlimits to date on the energy density of the backgroundin the LIGO frequency band. We also update the impli- cations for a BBH background using all the data fromO1.
Data. —Before this analysis, the best limits on thebackground from Initial LIGO and Virgo data were ob-tained using 2009–2010 [36] and 2005–2007 data [37]. Inthis work we use data from the upgraded Advanced LIGOobservatories in Hanford, WA (H1) and Livingston, LA(L1) [38]. We analyze O1 data from September 18, 201515:00 UTC-January 12, 2016 16:00 UTC.
Method. — We define the background energy densityspectrum as [39] Ω GW ( f ) = fρ c dρ GW df , (1)where f is the frequency, ρ c = 3 c H / (8 πG ) is the crit-ical energy density to close the Universe (numerically, ρ c = 7 . × − erg / cm using the Hubble constant H = 68 km s − Mpc − from [40, 41]), and dρ GW is thegravitational-wave energy density in the frequency rangefrom f to f + df . For the LIGO frequency band, mosttheoretical models for Ω GW ( f ) can be approximated asa power law in frequency [39, 42, 43]:Ω GW ( f ) = Ω α (cid:18) ff ref (cid:19) α . (2)Following [35], we assume a reference frequency of 25 Hz,which corresponds to the most sensitive band of theLIGO stochastic search for a detector network operat-ing at design sensitivity. The variable Ω α characterizesthe background amplitude across the sensitive frequencyband. Past analyses have used α = 0 and α = 3 to repre-sent cosmologically and astrophysically motivated back-ground models respectively [36, 42–45]. In this analysiswe use these two spectral indices but also include limitson the background spectrum assuming α = 2 /
3, whichdescribes the background dominated by compact binaryinspirals [35, 46]. This choice of spectral index is espe-cially interesting given the loud background from BBHsinferred from recent Advanced LIGO detections in O1[32, 33, 35, 47].Our search uses a cross-correlation method optimizedto search for the background using the pair of LIGOdetectors [39]. As discussed for instance in [48], cross-correlation is preferred to auto-correlation methods be-cause the noise variances in each detector are not knownsufficiently well to perform subtraction of the noise auto-power. We define the estimatorˆ Y α = (cid:90) ∞−∞ df (cid:90) ∞−∞ df (cid:48) δ T ( f − f (cid:48) )˜ s ∗ ( f )˜ s ( f (cid:48) ) ˜ Q α ( f (cid:48) ) (3)with variance σ Y ≈ T (cid:90) ∞ df P ( f ) P ( f ) | ˜ Q α ( f ) | , (4)where ˜ s , ( f ) are the Fourier transforms of the straintime series data from the two detectors, δ T ( f − f (cid:48) ) isa finite-time approximation to the Dirac delta function, T is the observation time, P , are the one-sided powerspectral densities for the detectors, and ˜ Q α ( f ) is a filterfunction to optimize the search [49],˜ Q α ( f ) = λ α γ ( f ) H f P ( f ) P ( f ) (cid:18) ff ref (cid:19) α . (5)The spatial separation and relative orientation of the twodetectors are accounted for in the overlap reduction func-tion, γ ( f ) [50] and the normalization constant λ α is cho-sen such that (cid:104) ˆ Y α (cid:105) = Ω α . Data Quality. —For this analysis, the strain time se-ries data are down-sampled to 4096 Hz from 16384 Hzand separated into 50%-overlapping 192 s segments, asin [42]. The segments are Hann-windowed and high-passfiltered with a 16 th order Butterworth digital filter withknee frequency of 11 Hz. The data are coarse-grainedto a frequency resolution of 0 .
031 Hz. This is a finerfrequency resolution than was used in previous analysesdue to the need to remove many finely spaced lines atlow frequencies.We apply cuts in the time and frequency domains, fol-lowing [36]. The total live time after all time domainvetoes have been applied was 29.85 days. These cuts re-move 35% of the time-series data. The frequency domaincuts remove 21% of the observing band. In the Supple-mentary Matrial [51], which includes Refs. [52–55], wediscuss in more detail the removed times and frequencies,the recovery of hardware and software injections, and ananalysis of correlated noise due to geophysical Schumannresonances.
20 30 40 50 60 70 80−6−4−20246 x 10 −5 Frequency (Hz) Ω Ω ± σ Ω FIG. 1. We show the estimator for Ω in each frequency bin,along with ± σ error bars, in the frequency band that con-tains 99% of the sensitivity for α = 0. The loss of sensitivity ataround 65 Hz is due to a zero in the overlap reduction func-tion. There are several lines associated with known instru-mental artifacts which do not lead to excess cross-correlation.The data are consistent with Gaussian noise, as described inthe Results section. Results. —Our search finds no evidence of the back-ground, and the data are consistent with statistical fluc-tuations, assuming Gaussian noise. The integrand ofEquation 3, multiplied by df = 0 .
031 Hz, gives an es-timator for Ω in each frequency bin. We plot this quan-tity, along with ± σ error bars, in Figure 6. To checkfor Gaussianity, we employ a noise model that the esti-mator in each frequency bin is drawn from a Gaussiandistribution with zero mean with the standard deviationof that frequency bin. We obtain a χ per degree of free-dom of 0.92, indicating that the data are consistent withGaussian noise.Consequently, we are able to place upper bounds onthe energy density present in the background. For α = 0,we place the bound Ω < . × − at 95% confidence,where 99% of the sensitivity comes in the frequency band20 −
86 Hz. This is a factor of 33 times more sensitivethan the previous best limit at these frequencies [36].Following [56], we show 95% confidence contours in theΩ α − α plane in Figure 2 by computing the joint posteriorfor Ω α and α . In addition, in Table I, we report upperlimits on the energy density for specific fixed values of thespectral index, marginalizing over amplitude calibrationuncertainty [57] using the conservative estimates of 11 . .
4% for L1. Phase calibration uncertaintiesare negligible.We also compare our results with the limits placed athigh frequencies from the two co-located detectors at the
Spectral index α Frequency band with 99% sensitivity Amplitude Ω α
95% CL upper limit Previous limits [36]0 20 − . . ± . × − . × − . × − / − . . ± . × − . × − –3 20 −
305 Hz (3 . ± . × − . × − . × − TABLE I. The frequency band with 99% of the sensitivity are shown, along with the point estimate and standard deviation forthe amplitude of the background, and 95% confidence level upper limits using O1 data for three values of the spectral index, α = 0 , / ,
3. We also show the previous upper limits using Initial LIGO-Virgo data. −5 −4 −3 −2 −1 0 1 2 3 4 510 −12 −11 −10 −9 −8 −7 −6 −5 −4 −3 α Ω α Initial LIGO−VirgoaLIGO O1Design
FIG. 2. Following [56], we present 95 % confidence contours inthe Ω α − α plane. The region above these curves is excludedat 95% confidence. We show the constraints coming fromthe final science run of Initial LIGO-Virgo [36] and from O1data. Finally, we display the projected (not observed) designsensitivity to Ω α and α for Advanced LIGO and Virgo [58]. Hanford site (H1 and H2). In [37], the limit Ω < . × − in the frequency band 460 − α = 3 and f ref = 900 Hz. Usingthis same frequency band, and using the cross-correlateddata between the Hanford and Livingston detectors, weplace a limit Ω < . × − for f ref = 900 Hz. Thisis about a factor of 22 larger than the limit from the co-located detectors, in part due to the loss in sensitivityof a stochastic search from cross-correlating detectors atdifferent spatial locations.In Figure 3, we show the constraints from this analysisand from previous analyses using other detectors, theo-retical predictions, and the expected sensitivity of futuremeasurements by LIGO-Virgo and by the Laser Inter-ferometer Space Antenna (LISA). Where applicable, weshow constraints using power-law integrated curves (PIcurves) [59], which account for the broadband nature ofthe search by integrating a range of power-law signalsover the sensitive frequency band of the detector. Byconstruction, any power-law spectrum which crosses aPI curve is detectable with SNR ≥
2. The blue curve labeled ‘aLIGO O1’ in Figure 3 showsthe measured O1 PI curve. We also display the PI curvefor the final science run of Initial LIGO and Virgo [36],H1-H2 [37], as well as the projected design sensitivityfor the advanced detector network. The curve labeled‘Design’ assumes 2 years of co-incident data taken withboth Advanced LIGO and Virgo operating at design sen-sitivity, using the projections in [58]. For the sake ofcomparison, the measured O1 PI curve at α = 0 is 1.6times larger than the projected PI curve at α = 0 usingthe projections in [58] and 29.85 days of live time, whichis fairly good agreement between predicted and achievedsensitivity. Finally, in red we present the projected sen-sitivity of a space-based detector with similar sensitivityto LISA, using the PI curve presented in [59] computedusing the projections in [64, 65].We compare these constraints with direct limits fromthe ringing of Earth’s normal modes [63], indirect lim-its from the Cosmic Microwave Background (CMB) andBig Bang Nucleosynthesis (BBN) [61], and limits frompulsar timing arrays [62] and CMB measurements at lowmultipole moments [60].In addition, we give examples of several models whichcan contribute to the background. We show the back-ground expected from slow-roll inflation with a tensor-to-scalar-ratio r = 0 .
11 (the upper limit allowed by Planck[40]). We also show examples of the BBH coalescencemodel, and the binary neutron star (BNS) coalescencemodel, which we describe below. As noted in [66], LISAis likely to be able to detect the BBH background of thesize considered here.
Astrophysical Implications. —In order to model thebackground from binary systems we will follow the ap-proach of [35]. We divide the compact binary populationinto classes labeled by k [67, 68]. Each class has distinctvalues of source parameters (for example the masses),which we denote by θ k . The total astrophysical back-ground is a sum over the contributions in each class. Thecontribution of class k to the background may be writtenin terms of an integral over the redshift z as [1, 5, 69–74]Ω GW ( f ; θ k ) = fρ c H (cid:90) z max dz R m ( z ; θ k ) dE GW df ( f s ; θ k )(1 + z ) E (Ω M , Ω Λ , z ) , (6)where R m ( z ; θ k ) is the binary merger rate per unit co-moving volume per unit time, dE GW /df ( f s , θ k ) is the FIG. 3. Presented here are constraints on the background in PI form [59], as well as some representative models, across manydecades in frequency. We compare the limits from ground-based interferometers from the final science run of Initial LIGO-Virgo,the co-located detectors at Hanford (H1-H2), Advanced LIGO (aLIGO) O1, and the projected design sensitivity of the advanceddetector network assuming two years of coincident data, with constraints from other measurements: CMB measurements at lowmultipole moments [60], indirect limits from the Cosmic Microwave Background (CMB) and Big-Bang Nucleosynthesis [61, 62],pulsar timing [62], and from the ringing of Earth’s normal modes [63]. We also show projected limits from a space-baseddetector such as LISA [59, 64, 65], following the assumptions of [59]. We extend the BNS and BBH distributions using an f / power-law down to low frequencies, with a low-frequency cut-off imposed where the inspiral time-scale is of order the Hubblescale. In Figure 5, we show the region in the black box in more detail. energy spectrum emitted by a single binary evaluatedin terms of the source frequency f s = (1 + z ) f , and E (Ω M , Ω Λ , z ) = (cid:112) Ω M (1 + z ) + Ω Λ accounts for the de-pendence of comoving volume on cosmology. We usecosmological parameters from Planck [40], and Ω M =1 − Ω Λ = 0 . dE GW /df is determined from thestrain waveform of the binary system. The dominantcontribution to the background comes from the inspiralphase, however for BBH we include the merger and ring-down phases using the waveforms from [5, 75] with themodifications from [76]. We choose to cut off the red-shift integral at z max = 10. Redshifts larger than fivecontribute little to the integral due to the small numberof stars formed at such high redshift [1, 5, 34, 69–74].To compute the binary merger rate R m ( z ; θ k ), we usethe same assumptions as in [35], unless stated otherwise.For the BNS case, we assume that the minimal time be-tween the formation and the coalescence of the binary is t min = 20 Myr, following for instance [46]. This is to becompared to t min = 50 Myr for BBH [35, 77].As was emphasized in [78], heavy stellar mass blackholes are expected to form in regions of low metallicity,which are associated with weaker stellar winds. To ac-count for this effect, following [35], for binary systemswith chirp masses larger than 30 M (cid:12) , we use only thefraction of stars that form in an environment with metal-licity Z < Z (cid:12) /
2. For BBH (and BNS) systems withsmaller masses, we do not use a cutoff. However, we notethat it makes little difference whether or not the cutoffis applied to high masses. With the model defined above, the free parameters arethe local merger rate R local = R m (0; θ k ) and the averagechirp mass M c . The distribution of the chirp mass haslittle effect on the spectrum for a fixed average chirp mass[5].We place upper limits at 95% confidence in the M c − R local plane, which are shown in Figure 4. Alongsidethe O1 results, we show the limits using Initial LIGO-Virgo data, as well as projected sensitivity of the ad-vanced detector network. The limits presented here areabout 10 times more sensitive than those placed withInitial LIGO-Virgo data. Furthermore, the future runsof the advanced detectors are expected to yield anotherfactor of 100 improvement in sensitivity in R local for agiven average chirp mass. We also show the local rateand chirp mass inferred from direct detections of BBHmergers during O1 [47, 68]. Comparing the projecteddesign sensitivity on R local and M c , with the values in-ferred from BBH observations in O1, suggests that it maybe possible for the advanced detector network to detectthe astrophysical BBH background.Finally, instead of treating the chirp mass and localmerger rate as free parameters, we can use the informa-tion from individually observed BBHs to compute thecorresponding background, see Figure 5. To do this, weuse the same model described above and we adopt thethree rate models described in [47]. Specifically, we con-sider the three-events-based, power-law, and flat-log dis-tributions of component masses. In each case, the rate atredshift z = 0 is normalized to the local rate derived fromthe O1 detections. With these assumptions we compute0 M c (M solar ) R l o c a l ( G p c − y r − ) BNS BBH
FlatPower
Initial LIGO−VIRGOaLIGO O1Design
FIG. 4. Displayed here are the 95% confidence contours onthe local rate and average chirp mass parameters, using themodel described in the Astrophysical Implications section. Inaddition to the constraint from Advanced LIGO (aLIGO) O1data, we show the constraint from the final science run ofInitial LIGO-Virgo, and the projected design sensitivity ofAdvanced LIGO-Virgo. We also show the median rate with90% uncertainty inferred from O1 data for the power-law andflat-log mass distributions [47], along with the band contain-ing 68% of the chirp mass for each distribution. The grayband separates BNS from BBH backgrounds. The dip at 30 M (cid:12) is due to the metallicity cutoff, as described in the As-trophysical Implications section. the background, including statistical uncertainty bandsshowing the 90% uncertainty in the local rate. The threerate models agree well in the sensitive frequency band ofadvanced detectors (10-100 Hz). Note also that the finalsensitivity of the advanced detectors may be sufficient todetect this background. Conclusions. —The results presented here represent thefirst search for the stochastic gravitational-wave back-ground made with the Advanced LIGO detectors. Withno evidence of a stochastic signal, we place an upper limitof Ω < . × − on the GW energy density, for a spec-tral index α = 0. This is ∼
33 times more sensitive thanprevious direct measurements in this frequency band. Wealso constrain the binary coalescence parameters of chirpmass and local merger rate. For fixed chirp mass be-low the high mass threshold of 30 M (cid:12) , the constraint onthe merger rate is improved by a factor of ∼
24, whilefor fixed merger rate, the constraint on the chirp massis improved by a factor of ∼
7, as can be seen from Fig-ure 4. Finally, we update the background predictions dueto BBH coalescences using data from O1. In this workwe have focused the implications of our results for an as-trophysical BBH background, as this provides the mostpromising candidate for first detecting the background.The implications of our search for other astrophysical and cosmological models can be seen in Figure 3. There is alsoan upcoming publication that will study implications forcosmic string models in more detail.These O1 results are a glimpse of the improvementsin sensitivity to be seen in upcoming years. As the ad-vanced detectors reach design sensitivity, there is a rea-sonable possibility of detecting the background due toBBHs. Even if no detection is made with these futuresearches, the searches will be able to constrain impor-tant cosmological and astrophysical background models.
FIG. 5. We present a range of potential spectra for a BBHbackground, using the flat-log, power-law, and 3-delta massdistribution models described in [47, 78], with the local rateinferred from the O1 detections [47]. For the flat-log andpower-law distributions, we show the 90% Poisson uncertaintyband due to the uncertainty in the local rate measurement.In addition, we show the measured O1 PI curve and the pro-jected PI curve for Advanced LIGO-Virgo operating at designsensitivity.
Acknowledgments. — The authors gratefully acknowl-edge the support of the United States National ScienceFoundation (NSF) for the construction and operation ofthe LIGO Laboratory and Advanced LIGO as well asthe Science and Technology Facilities Council (STFC)of the United Kingdom, the Max-Planck-Society (MPS),and the State of Niedersachsen/Germany for support ofthe construction of Advanced LIGO and constructionand operation of the GEO600 detector. Additional sup-port for Advanced LIGO was provided by the AustralianResearch Council. The authors gratefully acknowledgethe Italian Istituto Nazionale di Fisica Nucleare (INFN),the French Centre National de la Recherche Scientifique(CNRS) and the Foundation for Fundamental Researchon Matter supported by the Netherlands Organisationfor Scientific Research, for the construction and opera-tion of the Virgo detector and the creation and supportof the EGO consortium. The authors also gratefully ac-knowledge research support from these agencies as wellas by the Council of Scientific and Industrial Researchof India, Department of Science and Technology, India,1Science & Engineering Research Board (SERB), India,Ministry of Human Resource Development, India, theSpanish Ministerio de Econom´ıa y Competitividad, theConselleria d’Economia i Competitivitat and Conselleriad’Educaci´o, Cultura i Universitats of the Govern de lesIlles Balears, the National Science Centre of Poland, theEuropean Commission, the Royal Society, the ScottishFunding 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 theProvince of Ontario through the Ministry of EconomicDevelopment and Innovation, the Natural Science andEngineering Research Council Canada, Canadian Insti-tute for Advanced Research, the Brazilian Ministry ofScience, Technology, and Innovation, Funda¸c˜ao de Am-paro `a Pesquisa do Estado de S˜ao Paulo (FAPESP),Russian Foundation for Basic Research, the LeverhulmeTrust, the Research Corporation, Ministry of Scienceand Technology (MOST), Taiwan and the Kavli Foun-dation. 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In this supplement we describe in more detail how thedata in the main text are analyzed. Data used in theanalysis are from times when both detectors are in alow-noise observing mode. We exclude certain times andfrequencies based on auxiliary channels that establishedthem as instrumental effects within the detectors.We remove times due to known instrumental artifacts,such as radio frequency (RF) glitching and electronicssaturations [52], or due to simulated signals (referred toas hardware injections) generated by coherently movingthe interferometer mirrors [53]. We also exclude segmentsassociated with detections of gravitational waves. Dataare also excluded when the detectors’ noise power spectravary by more than 20% over the course of three 192s seg-ments. This cut is performed to remove non-stationarynoise, and has been used in previous analyses [36]. Adedicated study has verified that removing variations of20% provides a close-to-optimal balance between the falsepositive and false negative rates. The total live time withall vetoes applied, for 192s segments, is 29.85 days. Thesecuts remove 35% of the time-series data.We exclude frequencies known to be associated with in-strumental artifacts, such as vibrations of the test masssuspensions and calibration lines. We also remove fre-quencies that are known to be instrumentally correlatedbetween the two LIGO detectors. As an example, wedetected a comb-like structure (a series of lines evenlyspaced in frequency) at half Hz frequencies with 1 Hzseparation. This structure was coherent between thetwo sites and subsequently observed in auxiliary chan-nels. The contributing frequency bins were not includedin the analysis. The frequency domain cuts remove 21%of the observing band within each segment.To verify the data analysis cuts described above, weintroduce an artificial time shift of 1 s between the twosites. This effectively blinds the analysis by removing cor-relations due to a broadband gravitational-wave signal,while maintaining instrumental correlations with coher-ence times greater than 1 s. This method also allows usto identify additional instrumental artifacts that are notidentified using the cuts above, without biasing our anal-ysis of the data. Upon studying the time-shifted datawith the analysis cuts described above, we find no excesscorrelation, which is consistent with statistical expecta-tions of uncorrelated Gaussian noise.As a test of the detectors and the analysis pipeline,we simulate a strong stochastic signal both by a hard-ware injection and by a software injection (made byadding a coherent signal to the data streams). The in-jected background signals were isotropic and Gaussian,with an amplitude of Ω = 8 . × − and a duration3of 600 s. Both types of injections were successfully re-covered within 1 σ uncertainty: the hardware injectionmeasured (8 . ± . × − and the software injectionmeasured (9 . ± . × − .Finally, we study the possibility of correlated noise be-tween H1 and L1 so that we may be confident that thesystematic error in our measurements is negligible. Afteraccounting for narrowband correlation detector artifactsarising from digital systems, we estimate the contamina-tion from the environment. Previous investigations haveidentified geophysical Schumann resonances as the mostlikely source of correlated environmental noise [54, 55].Excitations in the spherical shell cavity formed betweenthe surface of the Earth and the ionosphere cause mag-netic fields to be correlated over great distances, compa-rable to the separation between H1 and L1. The magneticfields, in turn, can couple mechanically to the test massthrough the suspension system or electronically [55]. Inorder to ascertain the systematic error from environmen-tal correlated noise, we construct a correlated noise bud-get. We employ a number of conservative assumptions inorder to estimate the worst-case-scenario contamination.The first step is to measure the frequency-dependentcoupling of the detector to ambient magnetic fields usingexternal coils as an actuator [54, 55]. It is not practi-cal to induce fields that act on the entire detector si-multaneously, so we measure the coupling at each testmass. Next, we use magnetometers to measure the mag-netic coherence between the two sites. Using the methoddescribed in [54, 55], we combine the magnetic cross-power spectra and the coupling functions to estimate theworst-case correlated noise from Schumann resonancesΩ noise ( f ). Our conservative noise budget for O1 corre- −14 −12 −10 −8 −6 −4 −2 Frequency (Hz) Ω G W O1 PI CurveCorrelated Noise Budget
FIG. 6. We show the O1 power-law integrated curve (PIcurve) along with the correlated noise budget as describedin the text. The noise budget falling below the O1 PI curveindicates that correlated noise does not affect the O1 analysis. sponds to the solid black curve in Figure 6. This curve isobtained by fitting a power law to the magnetic noisebudget. We compare the noise budget to the power-law integrated energy density spectrum (dashed blackcurve) [59], which represent the statistical uncertaintyof the stochastic search. During O1, the correlated noiseis sufficiently low as to be ignored, contributing much lessthan one sigma. (If the correlated noise estimate was sig-nificant, the noise budget would be comparable to or inexcess of the dashed curve in the region of ∼∼