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Directly comparing GW150914 with numerical solutions of Einstein’s equations for binary black hole coalescence

B. P. Abbott¹, R. Abbott¹, T. D. Abbott², M. R. Abernathy³, F. Acernese^4,5, K. Ackley⁶, C. Adams⁷, T. Adams⁸, P. Addesso⁹ et al. (LIGO Scientific Collaboration and Virgo Collaboration)

P. Addesso⁹, R. X. Adhikari¹, V. B. Adya¹⁰, C. Affeldt¹⁰, M. Agathos¹¹, K. Agatsuma¹¹, N. Aggarwal¹², O. D. Aguiar¹³, L. Aiello^14,15, A. Ain¹⁶, P. Ajith¹⁷, B. Allen^10,18,19, A. Allocca^20,21, P. A. Altin²², S. B. Anderson¹, W. G. Anderson¹⁸, K. Arai¹, M. C. Araya¹, C. C. Arceneaux²³, J. S. Areeda²⁴, N. Arnaud²⁵, K. G. Arun²⁶, S. Ascenzi^27,15, G. Ashton²⁸, M. Ast²⁹, S. M. Aston⁷, P. Astone³⁰, P. Aufmuth¹⁹, C. Aulbert¹⁰, S. Babak³¹, P. Bacon³², M. K. M. Bader¹¹, P. T. Baker³³, F. Baldaccini^34,35, G. Ballardin³⁶, S. W. Ballmer³⁷, J. C. Barayoga¹, S. E. Barclay³⁸, B. C. Barish¹, D. Barker³⁹, F. Barone^4,5, B. Barr³⁸, L. Barsotti¹², M. Barsuglia³², D. Barta⁴⁰, J. Bartlett³⁹, I. Bartos⁴¹, R. Bassiri⁴², A. Basti^20,21, J. C. Batch³⁹, C. Baune¹⁰, V. Bavigadda³⁶, M. Bazzan^43,44, M. Bejger⁴⁵, A. S. Bell³⁸, B. K. Berger¹, G. Bergmann¹⁰, C. P. L. Berry⁴⁶, D. Bersanetti^47,48, A. Bertolini¹¹, J. Betzwieser⁷, S. Bhagwat³⁷, R. Bhandare⁴⁹, I. A. Bilenko⁵⁰, G. Billingsley¹, J. Birch⁷, I. A. Birney⁵¹, S. Biscans¹², A. Bisht^10,19, M. Bitossi³⁶, C. Biwer³⁷, M. A. Bizouard²⁵, J. K. Blackburn¹, C. D. Blair⁵², D. G. Blair⁵², R. M. Blair³⁹, S. Bloemen⁵³, O. Bock¹⁰, M. Boer⁵⁴, G. Bogaert⁵⁴, C. Bogan¹⁰, A. Bohe³¹, C. Bond⁴⁶, F. Bondu⁵⁵, R. Bonnand⁸, B. A. Boom¹¹, R. Bork¹, V. Boschi^20,21, S. Bose^56,16, Y. Bouffanais³², A. Bozzi³⁶, C. Bradaschia²¹, P. R. Brady¹⁸, V. B. Braginsky^50,†, M. Branchesi^57,58, J. E. Brau⁵⁹, T. Briant⁶⁰, A. Brillet⁵⁴, M. Brinkmann¹⁰, V. Brisson²⁵, P. Brockill¹⁸, J. E. Broida⁶¹, A. F. Brooks¹, D. A. Brown³⁷, D. D. Brown⁴⁶, N. M. Brown¹², S. Brunett¹, C. C. Buchanan², A. Buikema¹², T. Bulik⁶², H. J. Bulten^63,11, A. Buonanno^31,64, D. Buskulic⁸, C. Buy³², R. L. Byer⁴², M. Cabero¹⁰, L. Cadonati⁶⁵, G. Cagnoli^66,67, C. Cahillane¹, J. Calderón Bustillo⁶⁵, T. Callister¹, E. Calloni^68,5, J. B. Camp⁶⁹, K. C. Cannon⁷⁰, J. Cao⁷¹, C. D. Capano¹⁰, E. Capocasa³², F. Carbognani³⁶, S. Caride⁷², J. Casanueva Diaz²⁵, C. Casentini^27,15, S. Caudill¹⁸, M. Cavaglià²³, F. Cavalier²⁵, R. Cavalieri³⁶, G. Cella²¹, C. B. Cepeda¹, L. Cerboni Baiardi^57,58, G. Cerretani^20,21, E. Cesarini^27,15, S. J. Chamberlin⁷³, M. Chan³⁸, S. Chao⁷⁴, P. Charlton⁷⁵, E. Chassande-Mottin³², B. D. Cheeseboro⁷⁶, H. Y. Chen⁷⁷, Y. Chen⁷⁸, C. Cheng⁷⁴, A. Chincarini⁴⁸, A. Chiummo³⁶, H. S. Cho⁷⁹, M. Cho⁶⁴, J. H. Chow²², N. Christensen⁶¹, Q. Chu⁵², S. Chua⁶⁰, S. Chung⁵², G. Ciani⁶, F. Clara³⁹, J. A. Clark⁶⁵, F. Cleva⁵⁴, E. Coccia^27,14, P.-F. Cohadon⁶⁰, A. Colla^80,30, C. G. Collette⁸¹, L. Cominsky⁸², M. Constancio, Jr.¹³, A. Conte^80,30, L. Conti⁴⁴, D. Cook³⁹, T. R. Corbitt², N. Cornish³³, A. Corsi⁷², S. Cortese³⁶, C. A. Costa¹³, M. W. Coughlin⁶¹, S. B. Coughlin⁸³, J.-P. Coulon⁵⁴, S. T. Countryman⁴¹, P. Couvares¹, E. E. Cowan⁶⁵, D. M. Coward⁵², M. J. Cowart⁷, D. C. Coyne¹, R. Coyne⁷², K. Craig³⁸, J. D. E. Creighton¹⁸, J. Cripe², S. G. Crowder⁸⁴, A. Cumming³⁸, L. Cunningham³⁸, E. Cuoco³⁶, T. Dal Canton¹⁰, S. L. Danilishin³⁸, S. D’Antonio¹⁵, K. Danzmann^19,10, N. S. Darman⁸⁵, A. Dasgupta⁸⁶, C. F. Da Silva Costa⁶, V. Dattilo³⁶, I. Dave⁴⁹, M. Davier²⁵, G. S. Davies³⁸, E. J. Daw⁸⁷, R. Day³⁶, S. De³⁷, D. DeBra⁴², G. Debreczeni⁴⁰, J. Degallaix⁶⁶, M. De Laurentis^68,5, S. Deléglise⁶⁰, W. Del Pozzo⁴⁶, T. Denker¹⁰, T. Dent¹⁰, V. Dergachev¹, R. De Rosa^68,5, R. T. DeRosa⁷, R. DeSalvo⁹, R. C. Devine⁷⁶, S. Dhurandhar¹⁶, M. C. Díaz⁸⁸, L. Di Fiore⁵, M. Di Giovanni^89,90, T. Di Girolamo^68,5, A. Di Lieto^20,21, S. Di Pace^80,30, I. Di Palma^31,80,30, A. Di Virgilio²¹, V. Dolique⁶⁶, F. Donovan¹², K. L. Dooley²³, S. Doravari¹⁰, R. Douglas³⁸, T. P. Downes¹⁸, M. Drago¹⁰, R. W. P. Drever¹, J. C. Driggers³⁹, M. Ducrot⁸, S. E. Dwyer³⁹, T. B. Edo⁸⁷, M. C. Edwards⁶¹, A. Effler⁷, H.-B. Eggenstein¹⁰, P. Ehrens¹, J. Eichholz^6,1, S. S. Eikenberry⁶, W. Engels⁷⁸, R. C. Essick¹², T. Etzel¹, M. Evans¹², T. M. Evans⁷, R. Everett⁷³, M. Factourovich⁴¹, V. Fafone^27,15, H. Fair³⁷, X. Fan⁷¹, Q. Fang⁵², S. Farinon⁴⁸, B. Farr⁷⁷, W. M. Farr⁴⁶, M. Favata⁹¹, M. Fays⁹², H. Fehrmann¹⁰, M. M. Fejer⁴², E. Fenyvesi⁹³, I. Ferrante^20,21, E. C. Ferreira¹³, F. Ferrini³⁶, F. Fidecaro^20,21, I. Fiori³⁶, D. Fiorucci³², R. P. Fisher³⁷, R. Flaminio^66,94, M. Fletcher³⁸, J.-D. Fournier⁵⁴, S. Frasca^80,30, F. Frasconi²¹, Z. Frei⁹³, A. Freise⁴⁶, R. Frey⁵⁹, V. Frey²⁵, P. Fritschel¹², V. V. Frolov⁷, P. Fulda⁶, M. Fyffe⁷, H. A. G. Gabbard²³, J. R. Gair⁹⁵, L. Gammaitoni³⁴, S. G. Gaonkar¹⁶, F. Garufi^68,5, G. Gaur^96,86, N. Gehrels⁶⁹, G. Gemme⁴⁸, P. Geng⁸⁸, E. Genin³⁶, A. Gennai²¹, J. George⁴⁹, L. Gergely⁹⁷, V. Germain⁸, Abhirup Ghosh¹⁷, Archisman Ghosh¹⁷, S. Ghosh^53,11, J. A. Giaime^2,7, K. D. Giardina⁷, A. Giazotto²¹, K. Gill⁹⁸, A. Glaefke³⁸, E. Goetz³⁹, R. Goetz⁶, L. Gondan⁹³, G. González², J. M. Gonzalez Castro^20,21, A. Gopakumar⁹⁹, N. A. Gordon³⁸, M. L. Gorodetsky⁵⁰, S. E. Gossan¹, M. Gosselin³⁶, R. Gouaty⁸, A. Grado^100,5, C. Graef³⁸, P. B. Graff⁶⁴, M. Granata⁶⁶, A. Grant³⁸, S. Gras¹², C. Gray³⁹, G. Greco^57,58, A. C. Green⁴⁶, P. Groot⁵³, H. Grote¹⁰, S. Grunewald³¹, G. M. Guidi^57,58, X. Guo⁷¹, A. Gupta¹⁶, M. K. Gupta⁸⁶, K. E. Gushwa¹, E. K. Gustafson¹, R. Gustafson¹⁰¹, J. J. Hacker²⁴, B. R. Hall⁵⁶, E. D. Hall¹, G. Hammond³⁸, M. Haney⁹⁹, M. M. Hanke¹⁰, J. Hanks³⁹, C. Hanna⁷³, J. Hanson⁷, T. Hardwick², J. Harms^57,58, G. M. Harry³, I. W. Harry³¹, M. J. Hart³⁸, M. T. Hartman⁶, C.-J. Haster⁴⁶, K. Haughian³⁸, A. Heidmann⁶⁰, M. C. Heintze⁷, H. Heitmann⁵⁴, P. Hello²⁵, G. Hemming³⁶, M. Hendry³⁸, I. S. Heng³⁸, J. Hennig³⁸, J. Henry¹⁰², A. W. Heptonstall¹, M. Heurs^10,19, S. Hild³⁸, D. Hoak³⁶, D. Hofman⁶⁶, K. Holt⁷, D. E. Holz⁷⁷, P. Hopkins⁹², J. Hough³⁸, E. A. Houston³⁸, E. J. Howell⁵², Y. M. Hu¹⁰, S. Huang⁷⁴, E. A. Huerta¹⁰³, D. Huet²⁵, B. Hughey⁹⁸, S. H. Huttner³⁸, T. Huynh-Dinh⁷, N. Indik¹⁰, D. R. Ingram³⁹, R. Inta⁷², H. N. Isa³⁸, J.-M. Isac⁶⁰, M. Isi¹, T. Isogai¹², B. R. Iyer¹⁷, K. Izumi³⁹, T. Jacqmin⁶⁰, H. Jang⁷⁹, K. Jani⁶⁵, P. Jaranowski¹⁰⁴, S. Jawahar¹⁰⁵, L. Jian⁵², F. Jiménez-Forteza¹⁰⁶, W. W. Johnson², D. I. Jones²⁸, R. Jones³⁸, R. J. G. Jonker¹¹, L. Ju⁵², Haris K.¹⁰⁷, C. V. Kalaghatgi⁹², V. Kalogera⁸³, S. Kandhasamy²³, G. Kang⁷⁹, J. B. Kanner¹, S. J. Kapadia¹⁰, S. Karki⁵⁹, K. S. Karvinen¹⁰, M. Kasprzack^36,2, E. Katsavounidis¹², W. Katzman⁷, S. Kaufer¹⁹, T. Kaur⁵², K. Kawabe³⁹, F. Kéfélian⁵⁴, M. S. Kehl¹⁰⁸, D. Keitel¹⁰⁶, D. B. Kelley³⁷, W. Kells¹, R. Kennedy⁸⁷, J. S. Key⁸⁸, F. Y. Khalili⁵⁰, I. Khan¹⁴, Z. Khan⁸⁶, E. A. Khazanov¹⁰⁹, N. Kijbunchoo³⁹, Chi-Woong Kim⁷⁹, Chunglee Kim⁷⁹, J. Kim¹¹⁰, K. Kim¹¹¹, N. Kim⁴², W. Kim¹¹², Y.-M. Kim¹¹⁰, S. J. Kimbrell⁶⁵, E. J. King¹¹², P. J. King³⁹, J. S. Kissel³⁹, B. Klein⁸³, L. Kleybolte²⁹, S. Klimenko⁶, S. M. Koehlenbeck¹⁰, S. Koley¹¹, V. Kondrashov¹, A. Kontos¹², M. Korobko²⁹, W. Z. Korth¹, I. Kowalska⁶², D. B. Kozak¹, V. Kringel¹⁰, A. Królak^113,114, C. Krueger¹⁹, G. Kuehn¹⁰, P. Kumar¹⁰⁸, R. Kumar⁸⁶, L. Kuo⁷⁴, A. Kutynia¹¹³, B. D. Lackey³⁷, M. Landry³⁹, J. Lange¹⁰², B. Lantz⁴², P. D. Lasky¹¹⁵, M. Laxen⁷, A. Lazzarini¹, C. Lazzaro⁴⁴, P. Leaci^80,30, S. Leavey³⁸, E. O. Lebigot^32,71, C. H. Lee¹¹⁰, H. K. Lee¹¹¹, H. M. Lee¹¹⁶, K. Lee³⁸, A. Lenon³⁷, M. Leonardi^89,90, J. R. Leong¹⁰, N. Leroy²⁵, N. Letendre⁸, Y. Levin¹¹⁵, J. B. Lewis¹, T. G. F. Li¹¹⁷, A. Libson¹², T. B. Littenberg¹¹⁸, N. A. Lockerbie¹⁰⁵, A. L. Lombardi¹¹⁹, J. E. Lord³⁷, M. Lorenzini^14,15, V. Loriette¹²⁰, M. Lormand⁷, G. Losurdo⁵⁸, J. D. Lough^10,19, H. Lück^19,10, A. P. Lundgren¹⁰, R. Lynch¹², Y. Ma⁵², B. Machenschalk¹⁰, M. MacInnis¹², D. M. Macleod², F. Magaña-Sandoval³⁷, L. Magaña Zertuche³⁷, R. M. Magee⁵⁶, E. Majorana³⁰, I. Maksimovic¹²⁰, V. Malvezzi^27,15, N. Man⁵⁴, V. Mandic⁸⁴, V. Mangano³⁸, G. L. Mansell²², M. Manske¹⁸, M. Mantovani³⁶, F. Marchesoni^121,35, F. Marion⁸, S. Márka⁴¹, Z. Márka⁴¹, A. S. Markosyan⁴², E. Maros¹, F. Martelli^57,58, L. Martellini⁵⁴, I. W. Martin³⁸, D. V. Martynov¹², J. N. Marx¹, K. Mason¹², A. Masserot⁸, T. J. Massinger³⁷, M. Masso-Reid³⁸, S. Mastrogiovanni^80,30, F. Matichard¹², L. Matone⁴¹, N. Mavalvala¹², N. Mazumder⁵⁶, R. McCarthy³⁹, D. E. McClelland²², S. McCormick⁷, S. C. McGuire¹²², G. McIntyre¹, J. McIver¹, D. J. McManus²², T. McRae²², S. T. McWilliams⁷⁶, D. Meacher⁷³, G. D. Meadors^31,10, J. Meidam¹¹, A. Melatos⁸⁵, G. Mendell³⁹, R. A. Mercer¹⁸, E. L. Merilh³⁹, M. Merzougui⁵⁴, S. Meshkov¹, C. Messenger³⁸, C. Messick⁷³, R. Metzdorff⁶⁰, P. M. Meyers⁸⁴, F. Mezzani^30,80, H. Miao⁴⁶, C. Michel⁶⁶, H. Middleton⁴⁶, E. E. Mikhailov¹²³, L. Milano^68,5, A. L. Miller^6,80,30, A. Miller⁸³, B. B. Miller⁸³, J. Miller¹², M. Millhouse³³, Y. Minenkov¹⁵, J. Ming³¹, S. Mirshekari¹²⁴, C. Mishra¹⁷, S. Mitra¹⁶, V. P. Mitrofanov⁵⁰, G. Mitselmakher⁶, R. Mittleman¹², A. Moggi²¹, M. Mohan³⁶, S. R. P. Mohapatra¹², M. Montani^57,58, B. C. Moore⁹¹, C. J. Moore¹²⁵, D. Moraru³⁹, G. Moreno³⁹, S. R. Morriss⁸⁸, K. Mossavi¹⁰, B. Mours⁸, C. M. Mow-Lowry⁴⁶, G. Mueller⁶, A. W. Muir⁹², Arunava Mukherjee¹⁷, D. Mukherjee¹⁸, S. Mukherjee⁸⁸, N. Mukund¹⁶, A. Mullavey⁷, J. Munch¹¹², D. J. Murphy⁴¹, P. G. Murray³⁸, A. Mytidis⁶, I. Nardecchia^27,15, L. Naticchioni^80,30, R. K. Nayak¹²⁶, K. Nedkova¹¹⁹, G. Nelemans^53,11, T. J. N. Nelson⁷, M. Neri^47,48, A. Neunzert¹⁰¹, G. Newton³⁸, T. T. Nguyen²², A. B. Nielsen¹⁰, S. Nissanke^53,11, A. Nitz¹⁰, F. Nocera³⁶, D. Nolting⁷, M. E. N. Normandin⁸⁸, L. K. Nuttall³⁷, J. Oberling³⁹, E. Ochsner¹⁸, J. O’Dell¹²⁷, E. Oelker¹², G. H. Ogin¹²⁸, J. J. Oh¹²⁹, S. H. Oh¹²⁹, F. Ohme⁹², M. Oliver¹⁰⁶, P. Oppermann¹⁰, Richard J. Oram⁷, B. O’Reilly⁷, R. O’Shaughnessy¹⁰², D. J. Ottaway¹¹², H. Overmier⁷, B. J. Owen⁷², A. Pai¹⁰⁷, S. A. Pai⁴⁹, J. R. Palamos⁵⁹, O. Palashov¹⁰⁹, C. Palomba³⁰, A. Pal-Singh²⁹, H. Pan⁷⁴, C. Pankow⁸³, B. C. Pant⁴⁹, F. Paoletti^36,21, A. Paoli³⁶, M. A. Papa^31,18,10, H. R. Paris⁴², W. Parker⁷, D. Pascucci³⁸, A. Pasqualetti³⁶, R. Passaquieti^20,21, D. Passuello²¹, B. Patricelli^20,21, Z. Patrick⁴², B. L. Pearlstone³⁸, M. Pedraza¹, R. Pedurand^66,130, L. Pekowsky³⁷, A. Pele⁷, S. Penn¹³¹, A. Perreca¹, L. M. Perri⁸³, M. Phelps³⁸, O. J. Piccinni^80,30, M. Pichot⁵⁴, F. Piergiovanni^57,58, V. Pierro⁹, G. Pillant³⁶, L. Pinard⁶⁶, I. M. Pinto⁹, M. Pitkin³⁸, M. Poe¹⁸, R. Poggiani^20,21, P. Popolizio³⁶, A. Post¹⁰, J. Powell³⁸, J. Prasad¹⁶, V. Predoi⁹², T. Prestegard⁸⁴, L. R. Price¹, M. Prijatelj^10,36, M. Principe⁹, S. Privitera³¹, G. A. Prodi^89,90, L. Prokhorov⁵⁰, O. Puncken¹⁰, M. Punturo³⁵, P. Puppo³⁰, M. Pürrer³¹, H. Qi¹⁸, J. Qin⁵², S. Qiu¹¹⁵, V. Quetschke⁸⁸, E. A. Quintero¹, R. Quitzow-James⁵⁹, F. J. Raab³⁹, D. S. Rabeling²², H. Radkins³⁹, P. Raffai⁹³, S. Raja⁴⁹, C. Rajan⁴⁹, M. Rakhmanov⁸⁸, P. Rapagnani^80,30, V. Raymond³¹, M. Razzano^20,21, V. Re²⁷, J. Read²⁴, C. M. Reed³⁹, T. Regimbau⁵⁴, L. Rei⁴⁸, S. Reid⁵¹, D. H. Reitze^1,6, H. Rew¹²³, S. D. Reyes³⁷, F. Ricci^80,30, K. Riles¹⁰¹, M. Rizzo¹⁰², N. A. Robertson^1,38, R. Robie³⁸, F. Robinet²⁵, A. Rocchi¹⁵, L. Rolland⁸, J. G. Rollins¹, V. J. Roma⁵⁹, J. D. Romano⁸⁸, R. Romano^4,5, G. Romanov¹²³, J. H. Romie⁷, D. Rosińska^132,45, S. Rowan³⁸, A. Rüdiger¹⁰, P. Ruggi³⁶, K. Ryan³⁹, S. Sachdev¹, T. Sadecki³⁹, L. Sadeghian¹⁸, M. Sakellariadou¹³³, L. Salconi³⁶, M. Saleem¹⁰⁷, F. Salemi¹⁰, A. Samajdar¹²⁶, L. Sammut¹¹⁵, E. J. Sanchez¹, V. Sandberg³⁹, B. Sandeen⁸³, J. R. Sanders³⁷, B. Sassolas⁶⁶, P. R. Saulson³⁷, O. E. S. Sauter¹⁰¹, R. L. Savage³⁹, A. Sawadsky¹⁹, P. Schale⁵⁹, R. Schilling^10,†, J. Schmidt¹⁰, P. Schmidt^1,78, R. Schnabel²⁹, R. M. S. Schofield⁵⁹, A. Schönbeck²⁹, E. Schreiber¹⁰, D. Schuette^10,19, B. F. Schutz^92,31, J. Scott³⁸, S. M. Scott²², D. Sellers⁷, A. S. Sengupta⁹⁶, D. Sentenac³⁶, V. Sequino^27,15, A. Sergeev¹⁰⁹, Y. Setyawati^53,11, D. A. Shaddock²², T. Shaffer³⁹, M. S. Shahriar⁸³, M. Shaltev¹⁰, B. Shapiro⁴², P. Shawhan⁶⁴, A. Sheperd¹⁸, D. H. Shoemaker¹², K. Siellez⁶⁵, X. Siemens¹⁸, M. Sieniawska⁴⁵, D. Sigg³⁹, A. D. Silva¹³, A. Singer¹, L. P. Singer⁶⁹, A. Singh^31,10,19, R. Singh², A. Singhal¹⁴, A. M. Sintes¹⁰⁶, B. J. J. Slagmolen²², J. R. Smith²⁴, N. D. Smith¹, R. J. E. Smith¹, E. J. Son¹²⁹, B. Sorazu³⁸, F. Sorrentino⁴⁸, T. Souradeep¹⁶, A. K. Srivastava⁸⁶, A. Staley⁴¹, M. Steinke¹⁰, J. Steinlechner³⁸, S. Steinlechner³⁸, D. Steinmeyer^10,19, B. C. Stephens¹⁸, R. Stone⁸⁸, K. A. Strain³⁸, N. Straniero⁶⁶, G. Stratta^57,58, N. A. Strauss⁶¹, S. Strigin⁵⁰, R. Sturani¹²⁴, A. L. Stuver⁷, T. Z. Summerscales¹³⁴, L. Sun⁸⁵, S. Sunil⁸⁶, P. J. Sutton⁹², B. L. Swinkels³⁶, M. J. Szczepańczyk⁹⁸, M. Tacca³², D. Talukder⁵⁹, D. B. Tanner⁶, M. Tápai⁹⁷, S. P. Tarabrin¹⁰, A. Taracchini³¹, R. Taylor¹, T. Theeg¹⁰, M. P. Thirugnanasambandam¹, E. G. Thomas⁴⁶, M. Thomas⁷, P. Thomas³⁹, K. A. Thorne⁷, K. S. Thorne⁷⁸, E. Thrane¹¹⁵, S. Tiwari^14,90, V. Tiwari⁹², K. V. Tokmakov¹⁰⁵, K. Toland³⁸, C. Tomlinson⁸⁷, M. Tonelli^20,21, Z. Tornasi³⁸, C. V. Torres^88,†, C. I. Torrie¹, D. Töyrä⁴⁶, F. Travasso^34,35, G. Traylor⁷, D. Trifirò²³, M. C. Tringali^89,90, L. Trozzo^135,21, M. Tse¹², M. Turconi⁵⁴, D. Tuyenbayev⁸⁸, D. Ugolini¹³⁶, C. S. Unnikrishnan⁹⁹, A. L. Urban¹⁸, S. A. Usman³⁷, H. Vahlbruch¹⁹, G. Vajente¹, G. Valdes⁸⁸, N. van Bakel¹¹, M. van Beuzekom¹¹, J. F. J. van den Brand^63,11, C. 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Yamamoto¹, C. C. Yancey⁶⁴, H. Yu¹², M. Yvert⁸, A. Zadrożny¹¹³, L. Zangrando⁴⁴, M. Zanolin⁹⁸, J.-P. Zendri⁴⁴, M. Zevin⁸³, L. Zhang¹, M. Zhang¹²³, Y. Zhang¹⁰², C. Zhao⁵², M. Zhou⁸³, Z. Zhou⁸³, X. J. Zhu⁵², M. E. Zucker^1,12, S. E. Zuraw¹¹⁹, J. Zweizig¹, M. Boyle¹⁴⁰, M. Campanelli¹⁰², T. Chu¹⁰⁸, M. Clark⁶⁵, E. Fauchon-Jones⁹², H. Fong¹⁰⁸, J. Healy¹⁰², D. Hemberger⁷⁸, I. Hinder³¹, S. Husa¹⁰⁶, C. Kalaghati⁹², S. Khan⁹², L. E. Kidder¹⁴⁰, M. Kinsey⁶⁵, P. Laguna⁶⁵, L. T. London⁹², C. O. Lousto¹⁰², G. Lovelace²⁴, S. Ossokine³¹, F. Pannarale⁹², H. P. Pfeiffer^108,31, M. Scheel⁷⁸, D. M. Shoemaker⁶⁵, B. Szilagyi⁷⁸, S. Teukolsky¹⁴⁰, A. Vano Vinuales⁹², and Y. Zlochower¹⁰² (LIGO Scientific Collaboration and Virgo Collaboration)

¹LIGO, California Institute of Technology, Pasadena, California 91125, USA
²Louisiana State University, Baton Rouge, Los Angeles 70803, USA
³American University, Washington, D.C. 20016, USA
⁴Università di Salerno, Fisciano, I-84084 Salerno, Italy
⁵INFN, Sezione di Napoli, Complesso Universitario di Monte S.Angelo, I-80126 Napoli, Italy
⁶University of Florida, Gainesville, Florida 32611, USA
⁷LIGO Livingston Observatory, Livingston, Los Angeles 70754, USA
⁸Laboratoire d’Annecy-le-Vieux de Physique des Particules (LAPP), Université Savoie Mont Blanc, CNRS/IN2P3, F-74941 Annecy-le-Vieux, France
⁹University of Sannio at Benevento, I-82100 Benevento, Italy and INFN, Sezione di Napoli, I-80100 Napoli, Italy
¹⁰Albert-Einstein-Institut, Max-Planck-Institut für Gravi\-ta\-tions\-physik, D-30167 Hannover, Germany
¹¹Nikhef, Science Park, 1098 XG Amsterdam, The Netherlands
¹²LIGO, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
¹³Instituto Nacional de Pesquisas Espaciais, 12227-010 Sao José dos Campos, Sao Paulo, Brazil
¹⁴INFN, Gran Sasso Science Institute, I-67100 L’Aquila, Italy
¹⁵INFN, Sezione di Roma Tor Vergata, I-00133 Roma, Italy
¹⁶Inter-University Centre for Astronomy and Astrophysics, Pune 411007, India
¹⁷International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore 560012, India
¹⁸University of Wisconsin-Milwaukee, Milwaukee, Wisconsin 53201, USA
¹⁹Leibniz Universität Hannover, D-30167 Hannover, Germany
²⁰Università di Pisa, I-56127 Pisa, Italy
²¹INFN, Sezione di Pisa, I-56127 Pisa, Italy
²²Australian National University, Canberra, Australian Capital Territory 0200, Australia
²³The University of Mississippi, University, Mississippi 38677, USA
²⁴California State University Fullerton, Fullerton, California 92831, USA
²⁵LAL, Univ. Paris-Sud, CNRS/IN2P3, Université Paris-Saclay, Orsay 91405, France
²⁶Chennai Mathematical Institute, Chennai 603103, India
²⁷Università di Roma Tor Vergata, I-00133 Roma, Italy
²⁸University of Southampton, Southampton SO17 1BJ, United Kingdom
²⁹Universität Hamburg, D-22761 Hamburg, Germany
³⁰INFN, Sezione di Roma, I-00185 Roma, Italy
³¹Albert-Einstein-Institut, Max-Planck-Institut für Gravitations\-physik, D-14476 Potsdam-Golm, Germany
³²APC, AstroParticule et Cosmologie, Université Paris Diderot, CNRS/IN2P3, CEA/Irfu, Observatoire de Paris, Sorbonne Paris Cité, F-75205 Paris Cedex 13, France
³³Montana State University, Bozeman, Montana 59717, USA
³⁴Università di Perugia, I-06123 Perugia, Italy
³⁵INFN, Sezione di Perugia, I-06123 Perugia, Italy
³⁶European Gravitational Observatory (EGO), I-56021 Cascina, Pisa, Italy
³⁷Syracuse University, Syracuse, New York 13244, USA
³⁸SUPA, University of Glasgow, Glasgow G12 8QQ, United Kingdom
³⁹LIGO Hanford Observatory, Richland, Washington 99352, USA
⁴⁰Wigner RCP, RMKI, H-1121 Budapest, Konkoly Thege Miklós út 29-33, Hungary
⁴¹Columbia University, New York, New York 10027, USA
⁴²Stanford University, Stanford, California 94305, USA
⁴³Università di Padova, Dipartimento di Fisica e Astronomia, I-35131 Padova, Italy
⁴⁴INFN, Sezione di Padova, I-35131 Padova, Italy
⁴⁵CAMK-PAN, 00-716 Warsaw, Poland
⁴⁶University of Birmingham, Birmingham B15 2TT, United Kingdom
⁴⁷Università degli Studi di Genova, I-16146 Genova, Italy
⁴⁸INFN, Sezione di Genova, I-16146 Genova, Italy
⁴⁹RRCAT, Indore Madhya Pradesh 452013, India
⁵⁰Faculty of Physics, Lomonosov Moscow State University, Moscow 119991, Russia
⁵¹SUPA, University of the West of Scotland, Paisley PA1 2BE, United Kingdom
⁵²University of Western Australia, Crawley, Western Australia 6009, Australia
⁵³Department of Astrophysics/IMAPP, Radboud University Nijmegen, P.O. Box 9010, 6500 GL Nijmegen, The Netherlands
⁵⁴Artemis, Université Côte d’Azur, CNRS, Observatoire Côte d’Azur, CS 34229, Nice cedex 4, France
⁵⁵Institut de Physique de Rennes, CNRS, Université de Rennes 1, F-35042 Rennes, France
⁵⁶Washington State University, Pullman, Washington 99164, USA
⁵⁷Università degli Studi di Urbino “Carlo Bo,” I-61029 Urbino, Italy
⁵⁸INFN, Sezione di Firenze, I-50019 Sesto Fiorentino, Firenze, Italy
⁵⁹University of Oregon, Eugene, Oregon 97403, USA
⁶⁰Laboratoire Kastler Brossel, UPMC-Sorbonne Universités, CNRS, ENS-PSL Research University, Collège de France, F-75005 Paris, France
⁶¹Carleton College, Northfield, Minnesota 55057, USA
⁶²Astronomical Observatory Warsaw University, 00-478 Warsaw, Poland
⁶³VU University Amsterdam, 1081 HV Amsterdam, The Netherlands
⁶⁴University of Maryland, College Park, Maryland 20742, USA
⁶⁵Center for Relativistic Astrophysics and School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
⁶⁶Laboratoire des Matériaux Avancés (LMA), CNRS/IN2P3, F-69622 Villeurbanne, France
⁶⁷Université Claude Bernard Lyon 1, F-69622 Villeurbanne, France
⁶⁸Università di Napoli “Federico II,” Complesso Universitario di Monte S.Angelo, I-80126 Napoli, Italy
⁶⁹NASA/Goddard Space Flight Center, Greenbelt, Maryland 20771, USA
⁷⁰RESCEU, University of Tokyo, Tokyo 113-0033, Japan
⁷¹Tsinghua University, Beijing 100084, China
⁷²Texas Tech University, Lubbock, Texas 79409, USA
⁷³The Pennsylvania State University, University Park, Pennsylvania 16802, USA
⁷⁴National Tsing Hua University, Hsinchu City, 30013 Taiwan, Republic of China
⁷⁵Charles Sturt University, Wagga Wagga, New South Wales 2678, Australia
⁷⁶West Virginia University, Morgantown, West Virginia 26506, USA
⁷⁷University of Chicago, Chicago, Illinois 60637, USA
⁷⁸Caltech CaRT, Pasadena, California 91125, USA
⁷⁹Korea Institute of Science and Technology Information, Daejeon 305-806, Korea
⁸⁰Università di Roma “La Sapienza,” I-00185 Roma, Italy
⁸¹University of Brussels, Brussels 1050, Belgium
⁸²Sonoma State University, Rohnert Park, California 94928, USA
⁸³Center for Interdisciplinary Exploration & Research in Astrophysics (CIERA), Northwestern University, Evanston, Illinois 60208, USA
⁸⁴University of Minnesota, Minneapolis, Minnesota 55455, USA
⁸⁵The University of Melbourne, Parkville, Victoria 3010, Australia
⁸⁶Institute for Plasma Research, Bhat, Gandhinagar 382428, India
⁸⁷The University of Sheffield, Sheffield S10 2TN, United Kingdom
⁸⁸The University of Texas Rio Grande Valley, Brownsville, Texas 78520, USA
⁸⁹Università di Trento, Dipartimento di Fisica, I-38123 Povo, Trento, Italy
⁹⁰INFN, Trento Institute for Fundamental Physics and Applications, I-38123 Povo, Trento, Italy
⁹¹Montclair State University, Montclair, New Jersey 07043, USA
⁹²Cardiff University, Cardiff CF24 3AA, United Kingdom
⁹³MTA Eötvös University, “Lendulet” Astrophysics Research Group, Budapest 1117, Hungary
⁹⁴National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan
⁹⁵School of Mathematics, University of Edinburgh, Edinburgh EH9 3FD, United Kingdom
⁹⁶Indian Institute of Technology, Gandhinagar Ahmedabad Gujarat 382424, India
⁹⁷University of Szeged, Dóm tér 9, Szeged 6720, Hungary
⁹⁸Embry-Riddle Aeronautical University, Prescott, AZ 86301, USA
⁹⁹Tata Institute of Fundamental Research, Mumbai 400005, India
¹⁰⁰INAF, Osservatorio Astronomico di Capodimonte, I-80131, Napoli, Italy
¹⁰¹University of Michigan, Ann Arbor, Michigan 48109, USA
¹⁰²Rochester Institute of Technology, Rochester, New York 14623, USA
¹⁰³NCSA, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
¹⁰⁴University of Biał ystok, 15-424 Biał ystok, Poland
¹⁰⁵SUPA, University of Strathclyde, Glasgow G1 1XQ, United Kingdom
¹⁰⁶Universitat de les Illes Balears, IAC3—IEEC, E-07122 Palma de Mallorca, Spain
¹⁰⁷IISER-TVM, CET Campus, Trivandrum Kerala 695016, India
¹⁰⁸Canadian Institute for Theoretical Astrophysics, University of Toronto, Toronto, Ontario M5S 3H8, Canada
¹⁰⁹Institute of Applied Physics, Nizhny Novgorod 603950, Russia
¹¹⁰Pusan National University, Busan 609-735, Korea
¹¹¹Hanyang University, Seoul 133-791, Korea
¹¹²University of Adelaide, Adelaide, South Australia 5005, Australia
¹¹³NCBJ, 05-400 Świerk-Otwock, Poland
¹¹⁴IM-PAN, 00-956 Warsaw, Poland
¹¹⁵Monash University, Victoria 3800, Australia
¹¹⁶Seoul National University, Seoul 151-742, Korea
¹¹⁷The Chinese University of Hong Kong, Shatin, NT, Hong Kong SAR, China
¹¹⁸University of Alabama in Huntsville, Huntsville, Alabama 35899, USA
¹¹⁹University of Massachusetts-Amherst, Amherst, Massachusetts 01003, USA
¹²⁰ESPCI, CNRS, F-75005 Paris, France
¹²¹Università di Camerino, Dipartimento di Fisica, I-62032 Camerino, Italy
¹²²Southern University and A&M College, Baton Rouge, Los Angeles 70813, USA
¹²³College of William and Mary, Williamsburg, Virginia 23187, USA
¹²⁴Instituto de Física Teórica, University Estadual Paulista/ICTP South American Institute for Fundamental Research, S ao Paulo São Paulo 01140-070, Brazil
¹²⁵University of Cambridge, Cambridge CB2 1TN, United Kingdom
¹²⁶IISER-Kolkata, Mohanpur, West Bengal 741252, India
¹²⁷Rutherford Appleton Laboratory, HSIC, Chilton, Didcot, Oxon OX11 0QX, United Kingdom
¹²⁸Whitman College, 345 Boyer Avenue, Walla Walla, Washington 99362 USA
¹²⁹National Institute for Mathematical Sciences, Daejeon 305-390, Korea
¹³⁰Université de Lyon, F-69361 Lyon, France
¹³¹Hobart and William Smith Colleges, Geneva, New York 14456, USA
¹³²Janusz Gil Institute of Astronomy, University of Zielona Góra, 65-265 Zielona Góra, Poland
¹³³King’s College London, University of London, London WC2R 2LS, United Kingdom
¹³⁴Andrews University, Berrien Springs, Michigan 49104, USA
¹³⁵Università di Siena, I-53100 Siena, Italy
¹³⁶Trinity University, San Antonio, Texas 78212, USA
¹³⁷University of Washington, Seattle, Washington 98195, USA
¹³⁸Kenyon College, Gambier, Ohio 43022, USA
¹³⁹Abilene Christian University, Abilene, Texas 79699, USA
¹⁴⁰Cornell Center for Astrophysics and Planetary Science, Cornell University, Ithaca, New York 14853, USA

^*Full author list given at the end of the article.
^†Deceased.

PDF

Phys. Rev. D 94, 064035 – Published 14 September, 2016

DOI: https://doi.org/10.1103/PhysRevD.94.064035

Abstract

We compare GW150914 directly to simulations of coalescing binary black holes in full general relativity, including several performed specifically to reproduce this event. Our calculations go beyond existing semianalytic models, because for all simulations—including sources with two independent, precessing spins—we perform comparisons which account for all the spin-weighted quadrupolar modes, and separately which account for all the quadrupolar and octopolar modes. Consistent with the posterior distributions reported by Abbott et al. [Phys. Rev. Lett. 116, 241102 (2016)] (at the 90% credible level), we find the data are compatible with a wide range of nonprecessing and precessing simulations. Follow-up simulations performed using previously estimated binary parameters most resemble the data, even when all quadrupolar and octopolar modes are included. Comparisons including only the quadrupolar modes constrain the total redshifted mass $M_{z} \in [64 M_{⊙} - 82 M_{⊙}]$ , mass ratio $1 / q = m_{2} / m_{1} \in [0.6, 1]$ , and effective aligned spin $χ_{eff} \in [- 0.3, 0.2]$ , where $χ_{eff} = (S_{1} / m_{1} + S_{2} / m_{2}) \cdot \hat{L} / M$ . Including both quadrupolar and octopolar modes, we find the mass ratio is even more tightly constrained. Even accounting for precession, simulations with extreme mass ratios and effective spins are highly inconsistent with the data, at any mass. Several nonprecessing and precessing simulations with similar mass ratio and $χ_{eff}$ are consistent with the data. Though correlated, the components’ spins (both in magnitude and directions) are not significantly constrained by the data: the data is consistent with simulations with component spin magnitudes $a_{1, 2}$ up to at least 0.8, with random orientations. Further detailed follow-up calculations are needed to determine if the data contain a weak imprint from transverse (precessing) spins. For nonprecessing binaries, interpolating between simulations, we reconstruct a posterior distribution consistent with previous results. The final black hole’s redshifted mass is consistent with $M_{f, z}$ in the range $64.0 M_{⊙} - 73.5 M_{⊙}$ and the final black hole’s dimensionless spin parameter is consistent with $a_{f} = 0.62 - 0.73$ . As our approach invokes no intermediate approximations to general relativity and can strongly reject binaries whose radiation is inconsistent with the data, our analysis provides a valuable complement to Abbott et al. [Phys. Rev. Lett. 116, 241102 (2016)].

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Directly comparing GW150914 with numerical solutions of Einstein’s equations for binary black hole coalescence

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