Upper limits on the rates of binary neutron star and neutron-star–black-hole mergers from Advanced LIGO’s first observing run

Upper limits on the rates of binary neutron star and neutron-star–black-hole mergers from Advanced LIGO’s first observing run

B. P. Abbott,1 R. Abbott,1 T. D. Abbott,2 M. R. Abernathy,3 F. Acernese,4 5 K. Ackley,6 C. Adams,7 T. Adams,8 P. Addesso,9 R. X. Adhikari,1 V. B. Adya,10 C. Affeldt,10 M. Agathos,11 K. Agatsuma,11 N. Aggarwal,12 O. D. Aguiar,13 L. Aiello,14 15 A. Ain,16 P. Ajith,17 B. Allen,10 18 19 A. Allocca,20 21 P. A. Altin,22 S. B. Anderson,1 W. G. Anderson,18 K. Arai,1 M. C. Araya,1 C. C. Arceneaux,23 J. S. Areeda,24 N. Arnaud,25 K. G. Arun,26 S. Ascenzi,27 15 G. Ashton,28 M. Ast,29 S. M. Aston,7 P. Astone,30 P. Aufmuth,19 C. Aulbert,10 S. Babak,31 P. Bacon,32 M. K. M. Bader,11 P. T. Baker,33 F. Baldaccini,34 35 G. Ballardin,36 S. W. Ballmer,37 J. C. Barayoga,1 S. E. Barclay,38 B. C. Barish,1 D. Barker,39 F. Barone,4 5 B. Barr,38 L. Barsotti,12 M. Barsuglia,32 D. Barta,40 J. Bartlett,39 I. Bartos,41 R. Bassiri,42 A. Basti,20 21 J. C. Batch,39 C. Baune,10 V. Bavigadda,36 M. Bazzan,43 44 M. Bejger,45 A. S. Bell,38 B. K. Berger,1 G. Bergmann,10 C. P. L. Berry,46 D. Bersanetti,47 48 A. Bertolini,11 J. Betzwieser,7 S. Bhagwat,37 R. Bhandare,49 I. A. Bilenko,50 G. Billingsley,1 J. Birch,7 R. Birney,51 S. Biscans,12 A. Bisht,10 19 M. Bitossi,36 C. Biwer,37 M. A. Bizouard,25 J. K. Blackburn,1 C. D. Blair,52 D. G. Blair,52 R. M. Blair,39 S. Bloemen,53 O. Bock,10 M. Boer,54 G. Bogaert,54 C. Bogan,10 A. Bohe,31 C. Bond,46 F. Bondu,55 R. Bonnand,8 B. A. Boom,11 R. Bork,1 V. Boschi,20 21 S. Bose,56 16 Y. Bouffanais,32 A. Bozzi,36 C. Bradaschia,21 P. R. Brady,18 V. B. Braginsky,50 M. Branchesi,57 58 J. E. Brau,59 T. Briant,60 A. Brillet,54 M. Brinkmann,10 V. Brisson,25 P. Brockill,18 J. E. Broida,61 A. F. Brooks,1 D. A. Brown,37 D. D. Brown,46 N. M. Brown,12 S. Brunett,1 C. C. Buchanan,2 A. Buikema,12 T. Bulik,62 H. J. Bulten,63 11 A. Buonanno,31 64 D. Buskulic,8 C. Buy,32 R. L. Byer,42 M. Cabero,10 L. Cadonati,65 G. Cagnoli,66 67 C. Cahillane,1 J. Calderón Bustillo,65 T. Callister,1 E. Calloni,68 5 J. B. Camp,69 K. C. Cannon,70 J. Cao,71 C. D. Capano,10 E. Capocasa,32 F. Carbognani,36 S. Caride,72 J. Casanueva Diaz,25 C. Casentini,27 15 S. Caudill,18 M. Cavaglià,23 F. Cavalier,25 R. Cavalieri,36 G. Cella,21 C. B. Cepeda,1 L. Cerboni Baiardi,57 58 G. Cerretani,20 21 E. Cesarini,27 15 S. J. Chamberlin,73 M. Chan,38 S. Chao,74 P. Charlton,75 E. Chassande-Mottin,32 B. D. Cheeseboro,76 H. Y. Chen,77 Y. Chen,78 C. Cheng,74 A. Chincarini,48 A. Chiummo,36 H. S. Cho,79 M. Cho,64 J. H. Chow,22 N. Christensen,61 Q. Chu,52 S. Chua,60 S. Chung,52 G. Ciani,6 F. Clara,39 J. A. Clark,65 F. Cleva,54 E. Coccia,27 14 P.-F. Cohadon,60 A. Colla,80 30 C. G. Collette,81 L. Cominsky,82 M. Constancio Jr.,13 A. Conte,80 30 L. Conti,44 D. Cook,39 T. R. Corbitt,2 N. Cornish,33 A. Corsi,72 S. Cortese,36 C. A. Costa,13 M. W. Coughlin,61 S. B. Coughlin,83 J.-P. Coulon,54 S. T. Countryman,41 P. Couvares,1 E. E. Cowan,65 D. M. Coward,52 M. J. Cowart,7 D. C. Coyne,1 R. Coyne,72 K. Craig,38 J. D. E. Creighton,18 J. Cripe,2 S. G. Crowder,84 A. Cumming,38 L. Cunningham,38 E. Cuoco,36 T. Dal Canton,10 S. L. Danilishin,38 S. D’Antonio,15 K. Danzmann,19 10 N. S. Darman,85 A. Dasgupta,86 C. F. Da Silva Costa,6 V. Dattilo,36 I. Dave,49 M. Davier,25 G. S. Davies,38 E. J. Daw,87 R. Day,36 S. De,37 D. DeBra,42 G. Debreczeni,40 J. Degallaix,66 M. De Laurentis,68 5 S. Deléglise,60 W. Del Pozzo,46 T. Denker,10 T. Dent,10 V. Dergachev,1 R. De Rosa,68 5 R. T. DeRosa,7 R. DeSalvo,9 R. C. Devine,76 S. Dhurandhar,16 M. C. Díaz,88 L. Di Fiore,5 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 Virgilio,21 V. Dolique,66 F. Donovan,12 K. L. Dooley,23 S. Doravari,10 R. Douglas,38 T. P. Downes,18 M. Drago,10 R. W. P. Drever,1 J. C. Driggers,39 M. Ducrot,8 S. E. Dwyer,39 T. B. Edo,87 M. C. Edwards,61 A. Effler,7 H.-B. Eggenstein,10 P. Ehrens,1 J. Eichholz,6 1 S. S. Eikenberry,6 W. Engels,78 R. C. Essick,12 T. Etzel,1 M. Evans,12 T. M. Evans,7 R. Everett,73 M. Factourovich,41 V. Fafone,27 15 H. Fair,37 S. Fairhurst,91 X. Fan,71 Q. Fang,52 S. Farinon,48 B. Farr,77 W. M. Farr,46 M. Favata,92 M. Fays,91 H. Fehrmann,10 M. M. Fejer,42 E. Fenyvesi,93 I. Ferrante,20 21 E. C. Ferreira,13 F. Ferrini,36 F. Fidecaro,20 21 I. Fiori,36 D. Fiorucci,32 R. P. Fisher,37 R. Flaminio,66 94 M. Fletcher,38 J.-D. Fournier,54 S. Frasca,80 30 F. Frasconi,21 Z. Frei,93 A. Freise,46 R. Frey,59 V. Frey,25 P. Fritschel,12 V. V. Frolov,7 P. Fulda,6 M. Fyffe,7 H. A. G. Gabbard,23 J. R. Gair,95 L. Gammaitoni,34 S. G. Gaonkar,16 F. Garufi,68 5 G. Gaur,96 86 N. Gehrels,69 G. Gemme,48 P. Geng,88 E. Genin,36 A. Gennai,21 J. George,49 L. Gergely,97 V. Germain,8 Abhirup Ghosh,17 Archisman Ghosh,17 S. Ghosh,53 11 J. A. Giaime,2 7 K. D. Giardina,7 A. Giazotto,21 K. Gill,98 A. Glaefke,38 E. Goetz,39 R. Goetz,6 L. Gondan,93 G. González,2 J. M. Gonzalez Castro,20 21 A. Gopakumar,99 N. A. Gordon,38 M. L. Gorodetsky,50 S. E. Gossan,1 M. Gosselin,36 R. Gouaty,8 A. Grado,100 5 C. Graef,38 P. B. Graff,64 M. Granata,66 A. Grant,38 S. Gras,12 C. Gray,39 G. Greco,57 58 A. C. Green,46 P. Groot,53 H. Grote,10 S. Grunewald,31 G. M. Guidi,57 58 X. Guo,71 A. Gupta,16 M. K. Gupta,86 K. E. Gushwa,1 E. K. Gustafson,1 R. Gustafson,101 J. J. Hacker,24 B. R. Hall,56 E. D. Hall,1 G. Hammond,38 M. Haney,99 M. M. Hanke,10 J. Hanks,39 C. Hanna,73 M. D. Hannam,91 J. Hanson,7 T. Hardwick,2 J. Harms,57 58 G. M. Harry,3 I. W. Harry,31 M. J. Hart,38 M. T. Hartman,6 C.-J. Haster,46 K. Haughian,38 A. Heidmann,60 M. C. Heintze,7 H. Heitmann,54 P. Hello,25 G. Hemming,36 M. Hendry,38 I. S. Heng,38 J. Hennig,38 J. Henry,102 A. W. Heptonstall,1 M. Heurs,10 19 S. Hild,38 D. Hoak,36 D. Hofman,66 K. Holt,7 D. E. Holz,77 P. Hopkins,91 J. Hough,38 E. A. Houston,38 E. J. Howell,52 Y. M. Hu,10 S. Huang,74 E. A. Huerta,103 D. Huet,25 B. Hughey,98 S. Husa,104 S. H. Huttner,38 T. Huynh-Dinh,7 N. Indik,10 D. R. Ingram,39 R. Inta,72 H. N. Isa,38 J.-M. Isac,60 M. Isi,1 T. Isogai,12 B. R. Iyer,17 K. Izumi,39 T. Jacqmin,60 H. Jang,79 K. Jani,65 P. Jaranowski,105 S. Jawahar,106 L. Jian,52 F. Jiménez-Forteza,104 W. W. Johnson,2 D. I. Jones,28 R. Jones,38 R. J. G. Jonker,11 L. Ju,52 Haris K,107 C. V. Kalaghatgi,91 V. Kalogera,83 S. Kandhasamy,23 G. Kang,79 J. B. Kanner,1 S. J. Kapadia,10 S. Karki,59 K. S. Karvinen,10 M. Kasprzack,36 2 E. Katsavounidis,12 W. Katzman,7 S. Kaufer,19 T. Kaur,52 K. Kawabe,39 F. Kéfélian,54 M. S. Kehl,108 D. Keitel,104 D. B. Kelley,37 W. Kells,1 R. Kennedy,87 J. S. Key,88 F. Y. Khalili,50 I. Khan,14 S. Khan,91 Z. Khan,86 E. A. Khazanov,109 N. Kijbunchoo,39 Chi-Woong Kim,79 Chunglee Kim,79 J. Kim,110 K. Kim,111 N. Kim,42 W. Kim,112 Y.-M. Kim,110 S. J. Kimbrell,65 E. J. King,112 P. J. King,39 J. S. Kissel,39 B. Klein,83 L. Kleybolte,29 S. Klimenko,6 S. M. Koehlenbeck,10 S. Koley,11 V. Kondrashov,1 A. Kontos,12 M. Korobko,29 W. Z. Korth,1 I. Kowalska,62 D. B. Kozak,1 V. Kringel,10 B. Krishnan,10 A. Królak,113 114 C. Krueger,19 G. Kuehn,10 P. Kumar,108 R. Kumar,86 L. Kuo,74 A. Kutynia,113 B. D. Lackey,37 M. Landry,39 J. Lange,102 B. Lantz,42 P. D. Lasky,115 M. Laxen,7 A. Lazzarini,1 C. Lazzaro,44 P. Leaci,80 30 S. Leavey,38 E. O. Lebigot,32 71 C. H. Lee,110 H. K. Lee,111 H. M. Lee,116 K. Lee,38 A. Lenon,37 M. Leonardi,89 90 J. R. Leong,10 N. Leroy,25 N. Letendre,8 Y. Levin,115 J. B. Lewis,1 T. G. F. Li,117 A. Libson,12 T. B. Littenberg,118 N. A. Lockerbie,106 A. L. Lombardi,119 L. T. London,91 J. E. Lord,37 M. Lorenzini,14 15 V. Loriette,120 M. Lormand,7 G. Losurdo,58 J. D. Lough,10 19 H. Lück,19 10 A. P. Lundgren,10 R. Lynch,12 Y. Ma,52 B. Machenschalk,10 M. MacInnis,12 D. M. Macleod,2 F. Magaña-Sandoval,37 L. Magaña Zertuche,37 R. M. Magee,56 E. Majorana,30 I. Maksimovic,120 V. Malvezzi,27 15 N. Man,54 V. Mandic,84 V. Mangano,38 G. L. Mansell,22 M. Manske,18 M. Mantovani,36 F. Marchesoni,121 35 F. Marion,8 S. Márka,41 Z. Márka,41 A. S. Markosyan,42 E. Maros,1 F. Martelli,57 58 L. Martellini,54 I. W. Martin,38 D. V. Martynov,12 J. N. Marx,1 K. Mason,12 A. Masserot,8 T. J. Massinger,37 M. Masso-Reid,38 S. Mastrogiovanni,80 30 F. Matichard,12 L. Matone,41 N. Mavalvala,12 N. Mazumder,56 R. McCarthy,39 D. E. McClelland,22 S. McCormick,7 S. C. McGuire,122 G. McIntyre,1 J. McIver,1 D. J. McManus,22 T. McRae,22 S. T. McWilliams,76 D. Meacher,73 G. D. Meadors,31 10 J. Meidam,11 A. Melatos,85 G. Mendell,39 R. A. Mercer,18 E. L. Merilh,39 M. Merzougui,54 S. Meshkov,1 C. Messenger,38 C. Messick,73 R. Metzdorff,60 P. M. Meyers,84 F. Mezzani,30 80 H. Miao,46 C. Michel,66 H. Middleton,46 E. E. Mikhailov,123 L. Milano,68 5 A. L. Miller,6 80 30 A. Miller,83 B. B. Miller,83 J. Miller,12 M. Millhouse,33 Y. Minenkov,15 J. Ming,31 S. Mirshekari,124 C. Mishra,17 S. Mitra,16 V. P. Mitrofanov,50 G. Mitselmakher,6 R. Mittleman,12 A. Moggi,21 M. Mohan,36 S. R. P. Mohapatra,12 M. Montani,57 58 B. C. Moore,92 C. J. Moore,125 D. Moraru,39 G. Moreno,39 S. R. Morriss,88 K. Mossavi,10 B. Mours,8 C. M. Mow-Lowry,46 G. Mueller,6 A. W. Muir,91 Arunava Mukherjee,17 D. Mukherjee,18 S. Mukherjee,88 N. Mukund,16 A. Mullavey,7 J. Munch,112 D. J. Murphy,41 P. G. Murray,38 A. Mytidis,6 I. Nardecchia,27 15 L. Naticchioni,80 30 R. K. Nayak,126 K. Nedkova,119 G. Nelemans,53 11 T. J. N. Nelson,7 M. Neri,47 48 A. Neunzert,101 G. Newton,38 T. T. Nguyen,22 A. B. Nielsen,10 S. Nissanke,53 11 A. Nitz,10 F. Nocera,36 D. Nolting,7 M. E. N. Normandin,88 L. K. Nuttall,37 J. Oberling,39 E. Ochsner,18 J. O’Dell,127 E. Oelker,12 G. H. Ogin,128 J. J. Oh,129 S. H. Oh,129 F. Ohme,91 M. Oliver,104 P. Oppermann,10 Richard J. Oram,7 B. O’Reilly,7 R. O’Shaughnessy,102 D. J. Ottaway,112 H. Overmier,7 B. J. Owen,72 A. Pai,107 S. A. Pai,49 J. R. Palamos,59 O. Palashov,109 C. Palomba,30 A. Pal-Singh,29 H. Pan,74 C. Pankow,83 F. Pannarale,91 B. C. Pant,49 F. Paoletti,36 21 A. Paoli,36 M. A. Papa,31 18 10 H. R. Paris,42 W. Parker,7 D. Pascucci,38 A. Pasqualetti,36 R. Passaquieti,20 21 D. Passuello,21 B. Patricelli,20 21 Z. Patrick,42 B. L. Pearlstone,38 M. Pedraza,1 R. Pedurand,66 130 L. Pekowsky,37 A. Pele,7 S. Penn,131 A. Perreca,1 L. M. Perri,83 M. Phelps,38 O. J. Piccinni,80 30 M. Pichot,54 F. Piergiovanni,57 58 V. Pierro,9 G. Pillant,36 L. Pinard,66 I. M. Pinto,9 M. Pitkin,38 M. Poe,18 R. Poggiani,20 21 P. Popolizio,36 A. Post,10 J. Powell,38 J. Prasad,16 V. Predoi,91 T. Prestegard,84 L. R. Price,1 M. Prijatelj,10 36 M. Principe,9 S. Privitera,31 R. Prix,10 G. A. Prodi,89 90 L. Prokhorov,50 O. Puncken,10 M. Punturo,35 P. Puppo,30 M. Pürrer,31 H. Qi,18 J. Qin,52 S. Qiu,115 V. Quetschke,88 E. A. Quintero,1 R. Quitzow-James,59 F. J. Raab,39 D. S. Rabeling,22 H. Radkins,39 P. Raffai,93 S. Raja,49 C. Rajan,49 M. Rakhmanov,88 P. Rapagnani,80 30 V. Raymond,31 M. Razzano,20 21 V. Re,27 J. Read,24 C. M. Reed,39 T. Regimbau,54 L. Rei,48 S. Reid,51 D. H. Reitze,1 6 H. Rew,123 S. D. Reyes,37 F. Ricci,80 30 K. Riles,101 M. Rizzo,102 N. A. Robertson,1 38 R. Robie,38 F. Robinet,25 A. Rocchi,15 L. Rolland,8 J. G. Rollins,1 V. J. Roma,59 R. Romano,4 5 G. Romanov,123 J. H. Romie,7 D. Rosińska,132 45 S. Rowan,38 A. Rüdiger,10 P. Ruggi,36 K. Ryan,39 S. Sachdev,1 T. Sadecki,39 L. Sadeghian,18 M. Sakellariadou,133 L. Salconi,36 M. Saleem,107 F. Salemi,10 A. Samajdar,126 L. Sammut,115 E. J. Sanchez,1 V. Sandberg,39 B. Sandeen,83 J. R. Sanders,37 B. Sassolas,66 B. S. Sathyaprakash,91 P. R. Saulson,37 O. E. S. Sauter,101 R. L. Savage,39 A. Sawadsky,19 P. Schale,59 R. Schilling,10 J. Schmidt,10 P. Schmidt,1 78 R. Schnabel,29 R. M. S. Schofield,59 A. Schönbeck,29 E. Schreiber,10 D. Schuette,10 19 B. F. Schutz,91 31 J. Scott,38 S. M. Scott,22 D. Sellers,7 A. S. Sengupta,96 D. Sentenac,36 V. Sequino,27 15 A. Sergeev,109 Y. Setyawati,53 11 D. A. Shaddock,22 T. Shaffer,39 M. S. Shahriar,83 M. Shaltev,10 B. Shapiro,42 P. Shawhan,64 A. Sheperd,18 D. H. Shoemaker,12 D. M. Shoemaker,65 K. Siellez,65 X. Siemens,18 M. Sieniawska,45 D. Sigg,39 A. D. Silva,13 A. Singer,1 L. P. Singer,69 A. Singh,31 10 19 R. Singh,2 A. Singhal,14 A. M. Sintes,104 B. J. J. Slagmolen,22 J. R. Smith,24 N. D. Smith,1 R. J. E. Smith,1 E. J. Son,129 B. Sorazu,38 F. Sorrentino,48 T. Souradeep,16 A. K. Srivastava,86 A. Staley,41 M. Steinke,10 J. Steinlechner,38 S. Steinlechner,38 D. Steinmeyer,10 19 B. C. Stephens,18 R. Stone,88 K. A. Strain,38 N. Straniero,66 G. Stratta,57 58 N. A. Strauss,61 S. Strigin,50 R. Sturani,124 A. L. Stuver,7 T. Z. Summerscales,134 L. Sun,85 S. Sunil,86 P. J. Sutton,91 B. L. Swinkels,36 M. J. Szczepańczyk,98 M. Tacca,32 D. Talukder,59 D. B. Tanner,6 M. Tápai,97 S. P. Tarabrin,10 A. Taracchini,31 R. Taylor,1 T. Theeg,10 M. P. Thirugnanasambandam,1 E. G. Thomas,46 M. Thomas,7 P. Thomas,39 K. A. Thorne,7 E. Thrane,115 S. Tiwari,14 90 V. Tiwari,91 K. V. Tokmakov,106 K. Toland,38 C. Tomlinson,87 M. Tonelli,20 21 Z. Tornasi,38 C. V. Torres,88 C. I. Torrie,1 D. Töyrä,46 F. Travasso,34 35 G. Traylor,7 D. Trifirò,23 M. C. Tringali,89 90 L. Trozzo,135 21 M. Tse,12 M. Turconi,54 D. Tuyenbayev,88 D. Ugolini,136 C. S. Unnikrishnan,99 A. L. Urban,18 S. A. Usman,37 H. Vahlbruch,19 G. Vajente,1 G. Valdes,88 N. van Bakel,11 M. van Beuzekom,11 J. F. J. van den Brand,63 11 C. Van Den Broeck,11 D. C. Vander-Hyde,37 L. van der Schaaf,11 J. V. van Heijningen,11 A. A. van Veggel,38 M. Vardaro,43 44 S. Vass,1 M. Vasúth,40 R. Vaulin,12 A. Vecchio,46 G. Vedovato,44 J. Veitch,46 P. J. Veitch,112 K. Venkateswara,137 D. Verkindt,8 F. Vetrano,57 58 A. Viceré,57 58 S. Vinciguerra,46 D. J. Vine,51 J.-Y. Vinet,54 S. Vitale,12 T. Vo,37 H. Vocca,34 35 C. Vorvick,39 D. V. Voss,6 W. D. Vousden,46 S. P. Vyatchanin,50 A. R. Wade,22 L. E. Wade,138 M. Wade,138 M. Walker,2 L. Wallace,1 S. Walsh,31 10 G. Wang,14 58 H. Wang,46 M. Wang,46 X. Wang,71 Y. Wang,52 R. L. Ward,22 J. Warner,39 M. Was,8 B. Weaver,39 L.-W. Wei,54 M. Weinert,10 A. J. Weinstein,1 R. Weiss,12 L. Wen,52 P. Weßels,10 T. Westphal,10 K. Wette,10 J. T. Whelan,102 B. F. Whiting,6 R. D. Williams,1 A. R. Williamson,91 J. L. Willis,139 B. Willke,19 10 M. H. Wimmer,10 19 W. Winkler,10 C. C. Wipf,1 H. Wittel,10 19 G. Woan,38 J. Woehler,10 J. Worden,39 J. L. Wright,38 D. S. Wu,10 G. Wu,7 J. Yablon,83 W. Yam,12 H. Yamamoto,1 C. C. Yancey,64 H. Yu,12 M. Yvert,8 A. Zadrożny,113 L. Zangrando,44 M. Zanolin,98 J.-P. Zendri,44 M. Zevin,83 L. Zhang,1 M. Zhang,123 Y. Zhang,102 C. Zhao,52 M. Zhou,83 Z. Zhou,83 X. J. Zhu,52 M. E. Zucker,1 12 S. E. Zuraw,119 and J. Zweizig1 Deceased, March 2016. Deceased, May 2015. Deceased, March 2015.
(LIGO Scientific Collaboration and Virgo Collaboration)
1affiliation: LIGO, California Institute of Technology, Pasadena, CA 91125, USA
2affiliation: Louisiana State University, Baton Rouge, LA 70803, USA
3affiliation: American University, Washington, D.C. 20016, USA
4affiliation: Università di Salerno, Fisciano, I-84084 Salerno, Italy
5affiliation: INFN, Sezione di Napoli, Complesso Universitario di Monte S.Angelo, I-80126 Napoli, Italy
6affiliation: University of Florida, Gainesville, FL 32611, USA
7affiliation: LIGO Livingston Observatory, Livingston, LA 70754, USA
8affiliation: Laboratoire d’Annecy-le-Vieux de Physique des Particules (LAPP), Université Savoie Mont Blanc, CNRS/IN2P3, F-74941 Annecy-le-Vieux, France
9affiliation: University of Sannio at Benevento, I-82100 Benevento, Italy and INFN, Sezione di Napoli, I-80100 Napoli, Italy
10affiliation: Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-30167 Hannover, Germany
11affiliation: Nikhef, Science Park, 1098 XG Amsterdam, The Netherlands
12affiliation: LIGO, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
13affiliation: Instituto Nacional de Pesquisas Espaciais, 12227-010 São José dos Campos, São Paulo, Brazil
14affiliation: INFN, Gran Sasso Science Institute, I-67100 L’Aquila, Italy
15affiliation: INFN, Sezione di Roma Tor Vergata, I-00133 Roma, Italy
16affiliation: Inter-University Centre for Astronomy and Astrophysics, Pune 411007, India
17affiliation: International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore 560012, India
18affiliation: University of Wisconsin-Milwaukee, Milwaukee, WI 53201, USA
19affiliation: Leibniz Universität Hannover, D-30167 Hannover, Germany
20affiliation: Università di Pisa, I-56127 Pisa, Italy
21affiliation: INFN, Sezione di Pisa, I-56127 Pisa, Italy
22affiliation: Australian National University, Canberra, Australian Capital Territory 0200, Australia
23affiliation: The University of Mississippi, University, MS 38677, USA
24affiliation: California State University Fullerton, Fullerton, CA 92831, USA
25affiliation: LAL, Univ. Paris-Sud, CNRS/IN2P3, Université Paris-Saclay, Orsay, France
26affiliation: Chennai Mathematical Institute, Chennai 603103, India
27affiliation: Università di Roma Tor Vergata, I-00133 Roma, Italy
28affiliation: University of Southampton, Southampton SO17 1BJ, United Kingdom
29affiliation: Universität Hamburg, D-22761 Hamburg, Germany
30affiliation: INFN, Sezione di Roma, I-00185 Roma, Italy
31affiliation: Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-14476 Potsdam-Golm, Germany
32affiliation: APC, AstroParticule et Cosmologie, Université Paris Diderot, CNRS/IN2P3, CEA/Irfu, Observatoire de Paris, Sorbonne Paris Cité, F-75205 Paris Cedex 13, France
33affiliation: Montana State University, Bozeman, MT 59717, USA
34affiliation: Università di Perugia, I-06123 Perugia, Italy
35affiliation: INFN, Sezione di Perugia, I-06123 Perugia, Italy
36affiliation: European Gravitational Observatory (EGO), I-56021 Cascina, Pisa, Italy
37affiliation: Syracuse University, Syracuse, NY 13244, USA
38affiliation: SUPA, University of Glasgow, Glasgow G12 8QQ, United Kingdom
39affiliation: LIGO Hanford Observatory, Richland, WA 99352, USA
40affiliation: Wigner RCP, RMKI, H-1121 Budapest, Konkoly Thege Miklós út 29-33, Hungary
41affiliation: Columbia University, New York, NY 10027, USA
42affiliation: Stanford University, Stanford, CA 94305, USA
43affiliation: Università di Padova, Dipartimento di Fisica e Astronomia, I-35131 Padova, Italy
44affiliation: INFN, Sezione di Padova, I-35131 Padova, Italy
45affiliation: CAMK-PAN, 00-716 Warsaw, Poland
46affiliation: University of Birmingham, Birmingham B15 2TT, United Kingdom
47affiliation: Università degli Studi di Genova, I-16146 Genova, Italy
48affiliation: INFN, Sezione di Genova, I-16146 Genova, Italy
49affiliation: RRCAT, Indore MP 452013, India
50affiliation: Faculty of Physics, Lomonosov Moscow State University, Moscow 119991, Russia
51affiliation: SUPA, University of the West of Scotland, Paisley PA1 2BE, United Kingdom
52affiliation: University of Western Australia, Crawley, Western Australia 6009, Australia
53affiliation: Department of Astrophysics/IMAPP, Radboud University Nijmegen, P.O. Box 9010, 6500 GL Nijmegen, The Netherlands
54affiliation: Artemis, Université Côte d’Azur, CNRS, Observatoire Côte d’Azur, CS 34229, Nice cedex 4, France
55affiliation: Institut de Physique de Rennes, CNRS, Université de Rennes 1, F-35042 Rennes, France
56affiliation: Washington State University, Pullman, WA 99164, USA
57affiliation: Università degli Studi di Urbino “Carlo Bo,” I-61029 Urbino, Italy
58affiliation: INFN, Sezione di Firenze, I-50019 Sesto Fiorentino, Firenze, Italy
59affiliation: University of Oregon, Eugene, OR 97403, USA
60affiliation: Laboratoire Kastler Brossel, UPMC-Sorbonne Universités, CNRS, ENS-PSL Research University, Collège de France, F-75005 Paris, France
61affiliation: Carleton College, Northfield, MN 55057, USA
62affiliation: Astronomical Observatory Warsaw University, 00-478 Warsaw, Poland
63affiliation: VU University Amsterdam, 1081 HV Amsterdam, The Netherlands
64affiliation: University of Maryland, College Park, MD 20742, USA
65affiliation: Center for Relativistic Astrophysics and School of Physics, Georgia Institute of Technology, Atlanta, GA 30332, USA
66affiliation: Laboratoire des Matériaux Avancés (LMA), CNRS/IN2P3, F-69622 Villeurbanne, France
67affiliation: Université Claude Bernard Lyon 1, F-69622 Villeurbanne, France
68affiliation: Università di Napoli “Federico II,” Complesso Universitario di Monte S.Angelo, I-80126 Napoli, Italy
69affiliation: NASA/Goddard Space Flight Center, Greenbelt, MD 20771, USA
70affiliation: RESCEU, University of Tokyo, Tokyo, 113-0033, Japan.
71affiliation: Tsinghua University, Beijing 100084, China
72affiliation: Texas Tech University, Lubbock, TX 79409, USA
73affiliation: The Pennsylvania State University, University Park, PA 16802, USA
74affiliation: National Tsing Hua University, Hsinchu City, 30013 Taiwan, Republic of China
75affiliation: Charles Sturt University, Wagga Wagga, New South Wales 2678, Australia
76affiliation: West Virginia University, Morgantown, WV 26506, USA
77affiliation: University of Chicago, Chicago, IL 60637, USA
78affiliation: Caltech CaRT, Pasadena, CA 91125, USA
79affiliation: Korea Institute of Science and Technology Information, Daejeon 305-806, Korea
80affiliation: Università di Roma “La Sapienza,” I-00185 Roma, Italy
81affiliation: University of Brussels, Brussels 1050, Belgium
82affiliation: Sonoma State University, Rohnert Park, CA 94928, USA
83affiliation: Center for Interdisciplinary Exploration & Research in Astrophysics (CIERA), Northwestern University, Evanston, IL 60208, USA
84affiliation: University of Minnesota, Minneapolis, MN 55455, USA
85affiliation: The University of Melbourne, Parkville, Victoria 3010, Australia
86affiliation: Institute for Plasma Research, Bhat, Gandhinagar 382428, India
87affiliation: The University of Sheffield, Sheffield S10 2TN, United Kingdom
88affiliation: The University of Texas Rio Grande Valley, Brownsville, TX 78520, USA
89affiliation: Università di Trento, Dipartimento di Fisica, I-38123 Povo, Trento, Italy
90affiliation: INFN, Trento Institute for Fundamental Physics and Applications, I-38123 Povo, Trento, Italy
91affiliation: Cardiff University, Cardiff CF24 3AA, United Kingdom
92affiliation: Montclair State University, Montclair, NJ 07043, USA
93affiliation: MTA Eötvös University, “Lendulet” Astrophysics Research Group, Budapest 1117, Hungary
94affiliation: National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan
95affiliation: School of Mathematics, University of Edinburgh, Edinburgh EH9 3FD, United Kingdom
96affiliation: Indian Institute of Technology, Gandhinagar Ahmedabad Gujarat 382424, India
97affiliation: University of Szeged, Dóm tér 9, Szeged 6720, Hungary
98affiliation: Embry-Riddle Aeronautical University, Prescott, AZ 86301, USA
99affiliation: Tata Institute of Fundamental Research, Mumbai 400005, India
100affiliation: INAF, Osservatorio Astronomico di Capodimonte, I-80131, Napoli, Italy
101affiliation: University of Michigan, Ann Arbor, MI 48109, USA
102affiliation: Rochester Institute of Technology, Rochester, NY 14623, USA
103affiliation: NCSA, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
104affiliation: Universitat de les Illes Balears, IAC3—IEEC, E-07122 Palma de Mallorca, Spain
105affiliation: University of Białystok, 15-424 Białystok, Poland
106affiliation: SUPA, University of Strathclyde, Glasgow G1 1XQ, United Kingdom
107affiliation: IISER-TVM, CET Campus, Trivandrum Kerala 695016, India
108affiliation: Canadian Institute for Theoretical Astrophysics, University of Toronto, Toronto, Ontario M5S 3H8, Canada
109affiliation: Institute of Applied Physics, Nizhny Novgorod, 603950, Russia
110affiliation: Pusan National University, Busan 609-735, Korea
111affiliation: Hanyang University, Seoul 133-791, Korea
112affiliation: University of Adelaide, Adelaide, South Australia 5005, Australia
113affiliation: NCBJ, 05-400 Świerk-Otwock, Poland
114affiliation: IM-PAN, 00-956 Warsaw, Poland
115affiliation: Monash University, Victoria 3800, Australia
116affiliation: Seoul National University, Seoul 151-742, Korea
117affiliation: The Chinese University of Hong Kong, Shatin, NT, Hong Kong
118affiliation: University of Alabama in Huntsville, Huntsville, AL 35899, USA
119affiliation: University of Massachusetts-Amherst, Amherst, MA 01003, USA
120affiliation: ESPCI, CNRS, F-75005 Paris, France
121affiliation: Università di Camerino, Dipartimento di Fisica, I-62032 Camerino, Italy
122affiliation: Southern University and A&M College, Baton Rouge, LA 70813, USA
123affiliation: College of William and Mary, Williamsburg, VA 23187, USA
124affiliation: Instituto de Física Teórica, University Estadual Paulista/ICTP South American Institute for Fundamental Research, São Paulo SP 01140-070, Brazil
125affiliation: University of Cambridge, Cambridge CB2 1TN, United Kingdom
126affiliation: IISER-Kolkata, Mohanpur, West Bengal 741252, India
127affiliation: Rutherford Appleton Laboratory, HSIC, Chilton, Didcot, Oxon OX11 0QX, United Kingdom
128affiliation: Whitman College, 345 Boyer Avenue, Walla Walla, WA 99362 USA
129affiliation: National Institute for Mathematical Sciences, Daejeon 305-390, Korea
130affiliation: Université de Lyon, F-69361 Lyon, France
131affiliation: Hobart and William Smith Colleges, Geneva, NY 14456, USA
132affiliation: Janusz Gil Institute of Astronomy, University of Zielona Góra, 65-265 Zielona Góra, Poland
133affiliation: King’s College London, University of London, London WC2R 2LS, United Kingdom
134affiliation: Andrews University, Berrien Springs, MI 49104, USA
135affiliation: Università di Siena, I-53100 Siena, Italy
136affiliation: Trinity University, San Antonio, TX 78212, USA
137affiliation: University of Washington, Seattle, WA 98195, USA
138affiliation: Kenyon College, Gambier, OH 43022, USA
139affiliation: Abilene Christian University, Abilene, TX 79699, USA
August 17, 2019
Abstract

We report here the non-detection of gravitational waves from the merger of binary neutron star systems and neutron-star–black-hole systems during the first observing run of Advanced LIGO. In particular we searched for gravitational wave signals from binary neutron star systems with component masses and component dimensionless spins . We also searched for neutron-star–black-hole systems with the same neutron star parameters, black hole mass and no restriction on the black hole spin magnitude. We assess the sensitivity of the two LIGO detectors to these systems, and find that they could have detected the merger of binary neutron star systems with component mass distributions of at a volume-weighted average distance of 70 , and for neutron-star–black-hole systems with neutron star masses of and black hole masses of at least , a volume-weighted average distance of at least 110 . From this we constrain with 90% confidence the merger rate to be less than 12,600 Gpc yr for binary-neutron star systems and less than 3,600 Gpc yr for neutron-star–black-hole systems. We discuss the astrophysical implications of these results, which we find to be in tension with only the most optimistic predictions. However, we find that if no detection of neutron-star binary mergers is made in the next two Advanced LIGO and Advanced Virgo observing runs we would place significant constraints on the merger rates. Finally, assuming a rate of Gpcyr short gamma ray bursts beamed towards the Earth and assuming that all short gamma-ray bursts have binary-neutron-star (neutron-star–black-hole) progenitors we can use our 90% confidence rate upper limits to constrain the beaming angle of the gamma-ray burst to be greater than  ().

1 Introduction

Between September 12, 2015 and January 19, 2016  the two advanced Laser Interferometer Gravitational Wave Observatory (LIGO) detectors conducted their first observing period (O1). During O1, two high-mass binary black-hole (BBH) events were identified with high confidence (): GW150914 (Abbott et al., 2016a) and GW151226 (Abbott et al., 2016b). A third signal, LVT151012, was also identified with  confidence (Abbott et al., 2016c, d) In all three cases the component masses are confidently constrained to be above the upper mass limit of neutron-stars set by theoretical considerations (Rhoades and Ruffini, 1974; Abbott et al., 2016e). The details of these observations, investigations about the properties of the observed BBH mergers, and the astrophysical implications are explored in (Abbott et al., 2016e, f, g, h, c, i).

The search methods that successfully observed these BBH mergers also target other types of compact binary coalescences, specifically the inspiral and merger of binary neutron-star (BNS) systems and neutron-star–black-hole (NSBH) systems. Such systems were considered among the most promising candidates for an observation in O1. For example, a simple calculation prior to the start of O1 predicted 0.0005 - 4 detections of BNS signals during O1 (Aasi et al., 2016).

In this paper we report on the search for BNS and NSBH mergers in O1. We have searched for BNS systems with component masses , component dimensionless spins and spin orientations aligned or anti-aligned with the orbital angular momentum. We have searched for NSBH systems with neutron star mass , black-hole (BH) mass neutron star dimensionless spin magnitude , BH dimensionless spin magnitude and both spins aligned or anti-aligned with the orbital angular momentum. No observation of either BNS or NSBH mergers was made in O1. We explore the astrophysical implications of this result, placing upper limits on the rates of such merger events in the local Universe that are roughly an order of magnitude smaller than those obtained with data from Initial LIGO and Initial Virgo (Abbott et al., 2009; Acernese et al., 2008; Abadie et al., 2012a). We compare these updated rate limits to current predictions of BNS and NSBH merger rates and explore how the non-detection of BNS and NSBH systems in O1 can be used to explore possible constraints of the opening angle of the radiation cone of short gamma-ray bursts, assuming that short GRB progenitors are BNS or NSBH mergers.

The layout of this paper is as follows. In §  2 we describe the motivation for our search parameter space. In §  3 we briefly describe the search methodology, then describe the results of the search in §  4. We then discuss the constraints that can be placed on the rates of BNS and NSBH mergers in §  5 and the astrophysical implications of the rates in §  6. Finally, we conclude in §  7.

2 Source considerations

There are currently thousands of known NSs, most detected as pulsars (Hobbs et al., ; Manchester et al., 2005). Of these, are found in binary systems and allow estimates of the NS mass (Ott et al., ; Lattimer, 2012; Ozel and Freire, 2016). Published mass estimates range from (Falanga et al., 2015) to (Freire et al., 2008) although there is some uncertainty in some of these measurements. Considering only precise mass measurements from these observations one can set a lower bound on the maximum possible neutron star mass of  (Antoniadis et al., 2013) and theoretical considerations set an upper bound on the maximum possible neutron star mass of (Rhoades and Ruffini, 1974; Kalogera and Baym, 1996). The standard formation scenario of core-collapse supernovae restricts the birth masses of neutron stars to be above (Ozel et al., 2012; Lattimer, 2012; Kiziltan et al., 2013).

Eight candidate BNS systems allow mass measurements for individual components, giving a much narrower mass distribution (Lorimer, 2008). Masses are reported between and  (Ott et al., ; Ozel and Freire, 2016), and are consistent with an underlying mass distribution of  (Kiziltan et al., 2010). These observational measurements assume masses are greater than .

The fastest spinning pulsar observed so far rotates with a frequency of 716 Hz (Hessels et al., 2006). This corresponds to a dimensionless spin of roughly 0.4, where is the object’s mass and is the angular momentum.111Assuming a mass of and a moment of inertia of  g cm; the exact moment of inertia is dependent on the unknown NS equation-of-state (Lattimer, 2012). Such rapid rotation rates likely require the NS to have been spun up through mass-transfer from its companion. The fastest spinning pulsar in a confirmed BNS system has a spin frequency of 44 Hz (Kramer and Wex, 2009), implying that dimensionless spins for NS in BNS systems are  (Brown et al., 2012). However, recycled NS can have larger spins, and the potential BNS pulsar J1807-2500B (Lynch et al., 2012) has a spin of 4.19 ms, giving a dimensionless spin of up to .222Calculated with a pulsar mass of and a high moment of inertia,  g cm.

Given these considerations, we search for BNS systems with both masses and component dimensionless spins . We have found that BNS systems with spins are generally still recovered well even though they are not explicitly covered by our search space. Increasing the search space to include BNS systems with spins was found to not improve overall search sensitivity (Nitz, 2015).

NSBH systems are thought to be efficiently formed in one of two ways: either through the stellar evolution of field binaries or through dynamical capture of a NS by a BH (Grindlay et al., 2006; Sadowski et al., 2008; Lee et al., 2010; Benacquista and Downing, 2013). Though no NSBH systems are known to exist, one likely progenitor has been observed, Cyg X-3 (Belczynski et al., 2013).

Measurements of galactic stellar mass BHs in X-ray binaries yield BH masses  (Farr et al., 2011; Ozel et al., 2010; Merloni, 2008; Wiktorowicz et al., 2013). Extragalactic high-mass X-ray binaries, such as IC10 X-1 and NGC300 X-1 suggest BH masses of . Advanced LIGO has observed two definitive BBH systems and constrained the masses of the 4 component BHs to and , respectively, and the masses of the two resulting BHs to and . In addition if one assumes that the candidate BBH merger LVT151012 was of astrophysical origin than its component BHs had masses constrained to and with a resulting BH mass of . There is an apparent gap of BHs in the mass range , which has been ascribed to the supernova explosion mechanism (Belczynski et al., 2012; Fryer et al., 2012). However, BHs formed from stellar evolution may exist with masses down to , especially if they are formed from matter accreted onto neutron stars (O’Shaughnessy et al., 2005). Population synthesis models typically allow for stellar-mass BH up to  (Fryer et al., 2012; Belczynski et al., 2010; Dominik et al., 2012); stellar BHs with mass above are also conceivable however (Belczynski et al., 2014; de Mink and Belczynski, 2015).

X-ray observations of accreting BHs indicate a broad distribution of BH spin (Miller et al., 2009; Shafee et al., 2006; McClintock et al., 2006; Liu et al., 2008; Gou et al., 2009; Davis et al., 2006; Li et al., 2005; Miller and Miller, 2014). Some BHs observed in X-ray binaries have very large dimensionless spins (e.g Cygnus X-1 at (Fabian et al., 2012; Gou et al., 2011)), while others could have much lower spins ((McClintock et al., 2011). Measured BH spins in high-mass X-ray binary systems tend to have large values (), and these systems are more likely to be progenitors of NSBH binaries (McClintock et al., 2014). Isolated BH spins are only constrained by the relativistic Kerr bound  Misner et al. (1973). LIGO’s observations of merging binary BH systems yield weak constraints on component spins (Abbott et al., 2016e, b, c). The microquasar XTE J1550-564 (Steiner and McClintock, 2012) and population synthesis models (Fragos et al., 2010) indicate small spin-orbit misalignment in field binaries. Dynamically formed NSBH systems, in contrast, are expected to have no correlation between the spins and the orbit.

We search for NSBH systems with NS mass , NS dimensionless spins , BH mass and BH spin magnitude . Current search techniques are restricted to waveform models where the spins are (anti-)aligned with the orbit (Messick et al., 2016; Usman et al., 2015), although methods to extend this to generic spins are being explored (Harry et al., 2016). Nevertheless, aligned-spin searches have been shown to have good sensitivity to systems with generic spin orientations in O1 (Dal Canton et al., 2015; Harry et al., 2016). An additional search for BBH systems with total mass greater than 100 is also being performed, the results of which will be reported in a future publication.

3 Search Description

To observe compact binary coalescences in data taken from Advanced LIGO we use matched-filtering against models of compact binary merger gravitational wave (GW) signals (Wainstein and Zubakov, 1962). Matched-filtering has long been the primary tool for modeled GW searches (Abbott et al., 2004; Abadie et al., 2012a). As the emitted GW signal varies significantly over the range of masses and spins in the BNS and NSBH parameter space, the matched-filtering process must be repeated over a large set of filter waveforms, or “template bank” (Owen and Sathyaprakash, 1999). The ranges of masses considered in the searches are shown in Figure 1. The matched-filter process is conducted independently for each of the two LIGO observatories before searching for any potential GW signals observed at both observatories with the same masses and spins and within the expected light travel time delay. A summary statistic is then assigned to each coincident event based on the estimated rate of false alarms produced by the search background that would be more significant than the event.

BNS and NSBH mergers are prime candidates not only for observation with GW facilities, but also for coincident observation with electromagnetic (EM) observatories (Eichler et al., 1989; Hansen and Lyutikov, 2001; Narayan et al., 1992; Li and Paczynski, 1998; Nakar, 2007; Metzger and Berger, 2012; Nakar and Piran, 2011; Berger, 2014; Zhang, 2014; Fong et al., 2015). We have a long history of working with the Fermi, Swift and IPN GRB teams to perform sub-threshold searches of GW data in a narrow window around the time of observed GRBs (Abbott et al., 2005, 2008; Abadie et al., 2012b, c). Such a search is currently being performed on O1 data and will be reported in a forthcoming publication. In O1 we also aimed to rapidly alert EM partners if a GW observation was made (Abbott et al., 2016j). Therefore it was critical for us to run “online” searches to identify potential BNS or NSBH mergers within a timescale of minutes after the data is taken, to give EM partners the best chance to perform a coincident observation.

Nevertheless, analyses running with minute latency do not have access to full data-characterization studies, which can take weeks to perform, or to data with the most complete knowledge about calibration and associated uncertainties. Additionally, in rare instances, online analyses may fail to analyse stretches of data due to computational failure. Therefore it is also important to have an “offline” search, which performs the most sensitive search possible for BNS and NSBH sources. We give here a brief description of both the offline and online searches, referring to other works to give more details when relevant.

Figure 1: The range of template mass parameters considered for the three different template banks used in the search. The offline analyses and online GstLAL after December 23, 2015, used the largest bank up to total masses of . The online mbta bank covered primary masses below and chirp masses3 below . The early online GstLAL bank up to December 23, 2015, covered primary masses up to and secondary masses up to . The spin ranges are not shown here but are discussed in the text.

3.1 Offline Search

The offline compact binary coalescence (CBC) search of the O1 data set consists of two independently-implemented matched-filter analyses: GstLAL (Messick et al., 2016) and PyCBC (Usman et al., 2015). For detailed descriptions of these analyses and associated methods we refer the reader to (Babak et al., 2013; Dal Canton et al., 2014; Usman et al., 2015) for PyCBC and (Cannon et al., 2012, 2013; Privitera et al., 2014; Messick et al., 2016) for GstLAL. We also refer the reader to (Abbott et al., 2016c, d) for a detailed description of the offline search of the O1 dataset, here we give only a brief overview.

In contrast to the online search, the offline search uses data produced with smaller calibration errors (Abbott et al., 2016k), uses complete information about the instrumental data quality (Abbott et al., 2016l) and ensures that all available data is analysed. The offline search in O1 forms a single search targeting BNS, NSBH, and BBH systems. The waveform filters cover systems with individual component masses ranging from 1 to 99 , total mass constrained to less than 100 (see Figure 1), and component dimensionless spins up to 0.05 for components with mass less than 2 and 0.99 otherwise (Abbott et al., 2016c; Capano et al., 2016). Waveform filters with total mass less than 4 (chirp mass less than 333The “chirp mass” is the combination of the two component masses that LIGO is most sensitive to, given by , where denotes the two component masses) for PyCBC (GstLAL) are modeled with the inspiral-only, post-Newtonian, frequency-domain approximant “TaylorF2” (Arun et al., 2009; Bohé et al., 2013; Blanchet, 2014; Bohé et al., 2015; Mishra et al., 2016). At larger masses it becomes important to also include the merger and ringdown components of the waveform. There a reduced-order model of the effective-one-body waveform calibrated against numerical relativity is used (Taracchini et al., 2014; Pürrer, 2016).

3.2 Online Search

The online CBC search of the O1 data also consisted of two analyses; an online version of GstLAL(Messick et al., 2016) and mbta(Adams et al., 2015). For detailed descriptions of the mbta analysis we refer the reader to (Beauville et al., 2008; Abadie et al., 2012d; Adams et al., 2015). The bank of waveform filters used by GstLAL up to December 23, 2015—and by mbta for the duration of O1—targeted systems that contained at least one NS. Such systems are most likely to have an EM counterpart, which would be powered by the material from a disrupted NS. These sets of waveform filters were constructed using methods described in (Brown et al., 2012; Harry et al., 2014; Pannarale and Ohme, 2014). GstLAL chose to cover systems with component masses of and mbta covered with a limit on chirp mass (see Figure 1). In GstLAL component spins were limited to for and otherwise, for mbta  for and otherwise. GstLAL also chose to limit the template bank to include only systems for which it is possible for a NS to have disrupted during the late inspiral using constraints described in (Pannarale and Ohme, 2014). For the mbta search the waveform filters were modelled using the “TaylorT4” time-domain, post-Newtonian inspiral approximant (Buonanno et al., 2009). For GstLAL the TaylorF2 frequency-domain, post-Newtonian waveform approximant was used (Arun et al., 2009; Bohé et al., 2013; Blanchet, 2014; Bohé et al., 2015; Mishra et al., 2016). All waveform models used in this paper are publicly available in the lalsimulation repository (Mercer et al., ).444The internal lalsimulation names for the waveforms used as filters described in this work are “TaylorF2” for the frequency-domain post-Newtonian approximant, “SpinTaylorT4” for the time-domain approximant used by mbta and “SEOBNRv2_ROM_DoubleSpin” for the aligned-spin effective one body waveform. In addition, for calculation of rate estimates describe in Section 5, the “SpinTaylorT4” model is used to simulate BNS signals and “SEOBNRv3” is used to simulate NSBH signals.

After December 23, 2015, and triggered by the discovery of GW150914, the GstLAL analysis was extended to cover the same search space—using the same set of waveform filters—as the offline search (Capano et al., 2016; Abbott et al., 2016c).

3.3 Dataset

Advanced LIGO’s first observing run occurred between September 12, 2015 and January 19, 2016 and consists of data from the two LIGO observatories in Hanford, WA and Livingston, LA. The LIGO detectors were running stably with roughly 40% coincident operation, and had been commissioned to roughly a third of the design sensitivity by the time of the start of O1 (Martynov et al., 2016). During this observing run the final offline dataset consisted of 76.7 days of analyzable data from the Hanford observatory, and 65.8 days of data from the Livingston observatory. We analyze only times during which both observatories took analyzable data, which is 49.0 days. Characterization studies of the analysable data found 0.5 days of coincident data during which time there was some identified instrumental problem—known to introduce excess noise—in at least one of the interferometers (Abbott et al., 2016l). These times are removed before assessing the significance of events in the remaining analysis time. Some additional time is not analysed because of restrictions on the minimal length of data segments and because of data lost at the start and end of those segments (Abbott et al., 2016d, c). These requirements are slightly different between the two offline analyses and PyCBC analysed 46.1 days of data while GstLAL analysed 48.3 days of data.

The data available to the online analyses are not exactly the same as that available to the offline analyses. Some data were not available online due to (for example) software failures, and can later be made available for offline analysis. In contrast, some data identified as analysable for the online codes may later be identified as invalid as the result of updated data-characterization studies or because of problems in the calibration of the data. During O1 a total of 52.2 days of coincident data was made available for online analysis. Of this coincident online data mbta analysed 50.5 days (96.6 %) and GstLAL analysed 49.4 days (94.6 %). A total of 52.0 days (99.5 %) of data was analysed by at least one of the online analyses.

4 Search Results

Figure 2: Latency of the online searches during O1. The latency is measured as the time between the event arriving at Earth and time at which the event is uploaded to GraCEDb.

The offline search, targeting BBH as well as BNS and NSBH mergers, identified two signals with confidence in the O1 dataset (Abbott et al., 2016a, b). A third signal was also identified with  confidence (Abbott et al., 2016c, d). Subsequent parameter inference on all three of these events has determined that, to very high confidence, they were not produced by a BNS or NSBH merger (Abbott et al., 2016e, c). No other events are significant with respect to the noise background in the offline search (Abbott et al., 2016c), and we therefore state that no BNS or NSBH mergers were observed.

The online search identified a total of 8 unique GW candidate events with a false-alarm rate (FAR) less than . Events with a FAR less than this are sent to electromagnetic partners if they pass event validation. Six of the events were rejected during the event validation as they were associated with known non-Gaussian behavior in one of the observatories. Of the remaining events, one was the BBH merger GW151226 reported in (Abbott et al., 2016b). The second event identified by GstLAL was only narrowly below the FAR threshold, with a FAR of . This event was also detected by mbta with a higher FAR of . This is consistent with noise in the online searches and the candidate event was later identified to have a false alarm rate of in the offline GstLAL analysis. Nevertheless, the event passed all event validation and was released for EM follow-up observations, which showed no significant counterpart. The results of the EM follow-up program are discussed in more detail in (Abbott et al., 2016j).

All events identified by the GstLAL or mbta online analyses with a false alarm rate of less than are uploaded to an internal database known as the gravitational-wave candidate event database (GraCEDb(Moe et al., ). In total 486 events were uploaded from mbta and 868 from GstLAL. We can measure the latency of the online pipelines from the time between the inferred arrival time of each event at the Earth and the time at which the event is uploaded to GraCEDb. This latency is illustrated in Fig. 2, where it can be seen that both online pipelines acheived median latencies on the order of one minute. We note that GstLAL uploaded twice as many events as mbta because of a difference in how the FAR was defined. The FAR reported by mbta was defined relative to the rate of coincident data such that an event with a FAR of is expected to occur once in a year of coincident data. The FAR reported by GstLAL was defined relative to wall-clock time such that an event with a FAR of is expected to occur once in a calendar year. In the following section we use the mbta definition of FAR when computing rate upper limits.

5 Rates

5.1 Calculating upper limits

Given no evidence for BNS or NSBH coalescences during O1, we seek to place an upper limit on the astrophysical rate of such events. The expected number of observed events in a given analysis can be related to the astrophysical rate of coalescences for a given source by {linenomath*}

(1)

Here, is the space-time volume that the detectors are sensitive to—averaged over space, observation time, and the parameters of the source population of interest. The likelihood for finding zero observations in the data follows the Poisson distribution for zero events . Bayes’ theorem then gives the posterior for {linenomath*}

(2)

where is the prior on .

Searches of Initial LIGO and Initial Virgo data used a uniform prior on  (Abadie et al., 2012a) but included prior information from previous searches. For the O1 BBH search, however, a Jeffreys prior of for the Poisson likelihood was used (Farr et al., 2015; Abbott et al., 2016f, c). A Jeffreys prior has the convenient property that the resulting posterior is invariant under a change in parametrization. However, for consistency with past BNS and NSBH results we will primarily use a uniform prior, and note that a Jeffreys prior generally predicts a rate upper limit that is % smaller. We do not include additional prior information because the sensitive from all previous runs is an order of magnitude smaller than that of O1. We estimate by adding a large number of simulated waveforms sampled from an astrophysical population into the data. These simulated signals are recovered with an estimate of the FAR using the offline analyses. Monte-Carlo integration methods are then utilized to estimate the sensitive volume to which the detectors can recover gravitational-wave signals below a chosen FAR threshold, which in this paper we will choose to be . This threshold is low enough that only signals that are likely to be true events are counted as found, and we note that varying this threshold in the range 0.0001–1 yr only changes the calculated by about .

Calibration uncertainties lead to a difference between the amplitude of simulated waveforms and the amplitude of real waveforms with the same luminosity distance . During O1, the uncertainty in the strain amplitude was 6%, resulting in an 18% uncertainty in the measured . Results presented here also assume that injected waveforms are accurate representations of astrophysical sources. We use a time-domain, aligned-spin, post-Newtonian point-particle approximant to model BNS injections (Buonanno et al., 2009), and a time-domain, effective-one-body waveform calibrated against numerical relativity to model NSBH injections (Pan et al., 2014; Taracchini et al., 2014). Waveform differences between these models and the offline search templates are therefore including in the calculated . The injected NSBH waveform model is not calibrated at high mass ratios (), so there is some additional modeling uncertainty for large-mass NSBH systems. The true sensitive volume will also be smaller if the effect of tides in BNS or NSBH mergers is extreme. However, for most scenarios the effects of waveform modeling will be smaller than the effects of calibration errors and the choice of prior discussed above.

The posterior on (Eq. 2) can be reexpressed as a joint posterior on the astrophysical rate and the sensitive volume {linenomath*}

(3)

The new prior can be expanded as . For , we will either use a uniform prior on or a prior proportional to the Jeffreys prior . As with Refs. (Abbott et al., 2016f, m, c), we use a log-normal prior on {linenomath*}

(4)

where is the calculated value of and represents the fractional uncertainty in . Below, we will use an uncertainty of due mainly to calibration errors.

Finally, a posterior for the rate is obtained by marginalizing over {linenomath*}

(5)

The upper limit on the rate with confidence is then given by the solution to {linenomath*}

(6)

For reference, we note that in the limit of zero uncertainty in , the uniform prior for gives a rate upper limit of {linenomath*}

(7)

corresponding to for a 90% confidence upper limit (Biswas et al., 2009). For a Jeffreys prior on , this upper limit is {linenomath*}

(8)

corresponding to for a 90% confidence upper limit.

5.2 BNS rate limits

Figure 3: Posterior density on the rate of BNS mergers calculated using the PyCBC analysis. Blue curves represent a uniform prior on the Poisson parameter , while green curves represent a Jeffreys prior on . The solid (low spin population) and dotted (high spin population) posteriors almost overlap. The vertical dashed and solid lines represent the 50% and 90% confidence upper limits respectively for each choice of prior on . For each pair of vertical lines, the left line is the upper limit for the low spin population and the right line is the upper limit for the high spin population. Also shown are the realistic and high end of the expected BNS merger rates identified in Ref. (Abadie et al., 2010).
Figure 4: 90% confidence upper limit on the BNS merger rate as a function of the two component masses using the PyCBC analysis. Here the upper limit for each bin is obtained assuming a BNS population with masses distributed uniformly within the limits of each bin, considering isotropic spin direction and dimensionless spin magnitudes uniformly distributed in .

Motivated by considerations in Section 2, we begin by considering a population of BNS sources with a narrow range of component masses sampled from the normal distribution and truncated to remove samples outside the range . We consider both a “low spin” BNS population, where spins are distributed with uniform dimensionless spin magnitude and isotropic direction, and a “high spin” BNS population with a uniform dimensionless spin magnitude and isotropic direction. Our population uses an isotropic distribution of sky location and source orientation and chooses distances assuming a uniform distribution in volume. These simulations are modeled using a post-Newtonian waveform model, expanded using the “TaylorT4” formalism (Buonanno et al., 2009). From this population we compute the space-time volume that Advanced LIGO was sensitive to during the O1 observing run. Results are shown for the measured in Table 1 using a detection threshold of . Because the template bank for the searches use only aligned-spin BNS templates with component spins up to 0.05, the PyCBC (GstLAL) pipelines are 4% (6%) more sensitive to the low-spin population than to the high-spin population. The difference in between the two analyses is no larger than 5%, which is consistent with the difference in time analyzed in the two analyses. In addition, the calculated has a Monte Carlo integration uncertainty of due to the finite number of injection samples.

Injection Range of spin (Gpc yr) Range (Mpc) (Gpc yr)
set magnitudes PyCBC GstLAL PyCBC GstLAL PyCBC GstLAL
Isotropic low spin [0, 0.05] 73.2 73.4 12,100 11,500
Isotropic high spin [0, 0.4] 72.1 72.0 12,600 12,200
Table 1: Sensitive space-time volume and 90% confidence upper limit for BNS systems. Component masses are sampled from a normal distribution ) with samples outside the range removed. Values are shown for both the pycbc and gstlal pipelines. is calculated using a FAR threshold of 0.01 yr. The rate upper limit is calculated using a uniform prior on and an 18% uncertainty in from calibration errors.

Using the measured , the rate posterior and upper limit can be calculated from Eqs. 5 and 6 respectively. The posterior and upper limits are shown in Figure 3 and depend sensitively on the choice of uniform versus Jeffreys prior for . However, they depend only weakly on the spin distribution of the BNS population and on the width of the uncertainty in . For the conservative uniform prior on and an uncertainty in due to calibration errors of 18%, we find the 90% confidence upper limit on the rate of BNS mergers to be 12,100 Gpc yr for low spin and 12,600 Gpc yr for high spin using the values of calculated with PyCBC; results for GstLAL are also shown in Table 1. These numbers can be compared to the upper limit computed from analysis of Initial LIGO and Initial Virgo data (Abadie et al., 2012a). There, the upper limit for non-spinning BNS mergers is given as 130,000 . The O1 upper limit is more than an order of magnitude lower than this previous upper limit.

To allow for uncertainties in the mass distribution of BNS systems we also derive 90% confidence upper limits as a function of the NS component masses. To do this we construct a population of software injections with component masses sampled uniformly in the range , and an isotropic distribution of component spins with magnitudes uniformly distributed in . We then bin the BNS injections by mass, and calculate and the associated 90% confidence rate upper limit for each bin. The 90% rate upper limit for the conservative uniform prior on as a function of component masses is shown in Figure 4 for PyCBC. The fractional difference between the PyCBC and GstLAL results range from 1% to 16%.

5.3 NSBH rate limits

NS mass BH mass Spin (Gpc yr) Range (Mpc) (Gpc yr)
() () distribution PyCBC GstLAL PyCBC GstLAL PyCBC GstLAL
1.4 5 Isotropic 110 112 3,600 3,270
1.4 5 Aligned 114 117 3,210 2,820
1.4 10 Isotropic 123 122 2,530 2,490
1.4 10 Aligned 137 140 1,850 1,660
1.4 30 Isotropic 127 118 2,300 2,800
1.4 30 Aligned 155 153 1,280 1,270
Table 2: Sensitive space-time volume and 90% confidence upper limit for NSBH systems with isotropic and aligned spin distributions. The NS spin magnitudes are in the range and the BH spin magnitudes are in the range . Values are shown for both the pycbc and gstlal pipelines. is calculated using a FAR threshold of 0.01 yr. The rate upper limit is calculated using a uniform prior on and an 18% uncertainty in from calibration errors.
Figure 5: 50% and 90% upper limits on the NSBH merger rate as a function of the BH mass using the more conservative uniform prior for the counts . Blue curves represent the PyCBC analysis and red curves represent the GstLAL analysis. The NS mass is assumed to be . The spin magnitudes were sampled uniformly in the range [0, 0.04] for NSs and [0, 1] for BHs. For the aligned spin injection set, the spins of both the NS and BH are aligned (or anti-aligned) with the orbital angular momentum. For the isotropic spin injection set, the orientation for the spins of both the NS and BH are sampled isotropically. The isotropic spin distribution results in a larger upper limit. Also shown are the realistic and high end of the expected NSBH merger rates identified in Ref. (Abadie et al., 2010).

Given the absence of known NSBH systems and uncertainty in the BH mass, we evaluate the rate upper limit for a range of BH masses. We use three masses that span the likely range of BH masses: , , and . For the NS mass, we use the canonical value of . We assume a distribution of BH spin magnitudes uniform in and NS spin magnitudes uniform in . For these three mass pairs, we compute upper limits for an isotropic spin distribution on both bodies, and for a case where both spins are aligned or anti-aligned with the orbital angular momentum (with equal probability of aligned vs anti-aligned). Our NSBH population uses an isotropic distribution of sky location and source orientation and chooses distances assuming a uniform distribution in volume. Waveforms are modeled using the spin-precessing, effective-one-body model calibrated against numerical relativity waveforms described in Ref. (Taracchini et al., 2014; Babak et al., 2016).

The measured for a FAR threshold of is given in Table 2 for PyCBC and GstLAL. The uncertainty in the Monte Carlo integration of is 1.5%–2%. The corresponding 90% confidence upper limits are also given using the conservative uniform prior on and an 18% uncertainty in . Analysis-specific differences in the limits range from 1% to 20%, comparable or less than other uncertainties such as calibration. These results can be compared to the upper limits found for initial LIGO and Virgo for a population of NSBH binaries with isotropic spin of 36,000 at 90% confidence (Abadie et al., 2012a). As with the BNS case, this is an improvement in the upper limit of over an order of magnitude.

We also plot the 50% and 90% confidence upper limits from PyCBC and GstLAL as a function of mass in Figure 5 for the uniform prior. The search is less sensitive to isotropic spins than to (anti-)aligned spins due to two factors. First, the volume-averaged signal power is larger for a population of (anti-)aligned spin systems than for isotropic-spin systems. Second, the search uses a template bank of (anti-)aligned spin systems, and thus loses sensitivity when searching for systems with significantly misaligned spins. As a result, the rate upper limits are less constraining for the isotropic spin distribution than for the (anti-)aligned spin case.

6 Astrophysical Interpretation

Figure 6: A comparison of the O1 90% upper limit on the BNS merger rate to other rates discussed in the text (Abadie et al., 2010; Kim et al., 2015; Fong et al., 2015; Siellez et al., 2014; Coward et al., 2012; Petrillo et al., 2013; Jin et al., 2015; Vangioni et al., 2016; de Mink and Belczynski, 2015; Dominik et al., 2015). The region excluded by the low-spin BNS rate limit is shaded in blue. Continued non-detection in O2 (slash) and O3 (dot) with higher sensitivities and longer operation time would imply stronger upper limits. The O2 and O3 BNS ranges are assumed to be 1-1.9 and 1.9-2.7 times larger than O1. The operation times are assumed to be 6 and 9 months (Aasi et al., 2016) with a duty cycle equal to that of O1 ( 40%).
Figure 7: A comparison of the O1 90% upper limit on the NSBH merger rate to other rates discussed in the text (Abadie et al., 2010; Fong et al., 2015; Coward et al., 2012; Petrillo et al., 2013; Jin et al., 2015; Vangioni et al., 2016; de Mink and Belczynski, 2015; Dominik et al., 2015). The dark blue region assumes a NSBH population with masses 5–1.4 and the light blue region assumes a NSBH population with masses 10–1.4 . Both assume an isotropic spin distribution. Continued non-detection in O2 (slash) and O3 (dot) with higher sensitivities and longer operation time would imply stronger upper limits (shown for 10–1.4 NSBH systems). The O2 and O3 ranges are assumed to be 1-1.9 and 1.9-2.7 times larger than O1. The operation times are assumed to be 6 and 9 months (Aasi et al., 2016) with a duty cycle equal to that of O1 ( 40%).
Figure 8: Lower limit on the beaming angle of short GRBs, as a function of the mass of the primary BH or NS, . We take the appropriate 90% rate upper limit from this paper, assume all short GRBs are produced by each case in turn, and assume all have the same beaming angle . The limit is calculated using an observed short GRB rate of Gpc yr and the ranges shown on the plot reflect the uncertainty in this observed rate. For BNS, comes from a Gaussian distribution centered on , and for NSBH it is fixed to .

We can compare our upper limits with rate predictions for compact object mergers involving NSs, shown for BNS in Figure 6 and for NSBH in Figure 7. A wide range of predictions derived from population synthesis and from binary pulsar observations were reviewed in 2010 to produce rate estimates for canonical NSs and BHs (Abadie et al., 2010). We additionally include some more recent estimates from population synthesis for both NSBH and BNS (Dominik et al., 2015; Belczynski et al., 2016; de Mink and Belczynski, 2015) and binary pulsar observations for BNS (Kim et al., 2015).

We also compare our upper limits for NSBH and BNS systems to beaming-corrected estimates of short GRB rates in the local universe. Short GRBs are considered likely to be produced by the merger of compact binaries that include NSs, i.e. BNS or NSBH systems (Berger, 2014). The rate of short GRBs can predict the rate of progenitor mergers (Coward et al., 2012; Petrillo et al., 2013; Siellez et al., 2014; Fong et al., 2015). For NSBH, systems with small BH masses are considered more likely to be able to produce short GRBs (e.g.  (Duez, 2010; Giacomazzo et al., 2013; Pannarale et al., 2015)), so we compare to our NSBH rate constraint. The observation of a kilonova is also considered to be an indicator of a binary merger (Metzger and Berger, 2012), and an estimated kilonova rate gives an additional lower bound on compact binary mergers (Jin et al., 2015).

Finally, some recent work has used the idea that mergers involving NSs are the primary astrophysical source of r-process elements (Lattimer and Schramm, 1974; Qian and Wasserburg, 2007) to constrain the rate of such mergers from nucleosynthesis (Bauswein et al., 2014; Vangioni et al., 2016), and we include rates from (Vangioni et al., 2016) for comparison.

While limits from O1 are not yet in tension with astrophysical models, scaling our results to current expectations for advanced LIGO’s next two observing runs, O2 and O3 (Aasi et al., 2016), suggests that significant constraints or observations of BNS or NSBH mergers are possible in the next two years.

Assuming that short GRBs are produced by BNS or NSBH, but without using beaming angle estimates, we can constrain the beaming angle of the jet of gamma rays emitted from these GRBs by comparing the rates of BNS/NSBH mergers and the rates of short GRBs (Chen and Holz, 2013). For simplicity, we assume here that all short GRBs are associated with BNS or NSBH mergers; the true fraction will depend on the emission mechanism. The short GRB rate , the merger rate , and the beaming angle are then related by {linenomath*}

(9)

We take Gpc yr (Coward et al., 2012; Nakar et al., 2006). Figure 8 shows the resulting GRB beaming lower limits for the 90% BNS and NSBH rate upper limits. With our assumption that all short GRBs are produced by a single progenitor class, the constraint is tighter for NSBH with larger BH mass. Observed GRB beaming angles are in the range of  (Fox et al., 2005; Fong et al., 2015; Grupe et al., 2006; Soderberg et al., 2006; Sakamoto et al., 2013; Margutti et al., 2012; Nicuesa Guelbenzu et al., 2011). Compared to the lower limit derived from our non-detection, these GRB beaming observations start to confine the fraction of GRBs that can be produced by higher-mass NSBH as progenitor systems. Future constraints could also come from GRB and BNS or NSBH joint detections (Dietz, 2011; Regimbau et al., 2015; Clark et al., 2015).

7 Conclusion

We report the non-detection of BNS and NSBH mergers in advanced LIGO’s first observing run. Given the sensitive volume of Advanced LIGO to such systems we are able to place 90% confidence upper limits on the rates of BNS and NSBH mergers, improving upon limits obtained from Initial LIGO and Initial Virgo by roughly an order of magnitude. Specifically we constrain the merger rate of BNS systems with component masses of to be less than 12,600 Gpc yr. We also constrain the rate of NSBH systems with NS masses of and BH masses of at least to be less than 3,210 Gpc yr if one considers a population where the component spins are (anti-)aligned with the orbit, and less than 3,600 Gpc yr if one considers an isotropic distribution of component spin directions.

We compare these upper limits with existing astrophysical rate models and find that the current upper limits are in conflict with only the most optimistic models of the merger rate. However, we expect that during the next two observing runs, O2 and O3, we will either make observations of BNS and NSBH mergers or start placing significant constraints on current astrophysical rates. Finally, we have explored the implications of this non-detection on the beaming angle of short GRBs. We find that, if one assumes that all GRBs are produced by BNS mergers, then the opening angle of gamma-ray radiation must be larger than ; or larger than  if one assumes all GRBs are produced by NSBH mergers.

acknowledgments

The authors gratefully acknowledge 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 support 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 operation of the Virgo detector and the creation and support of the EGO consortium. The authors also gratefully acknowledge 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 Economía y Competitividad, the Conselleria d’Economia i Competitivitat and Conselleria d’Educació, 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 Alliance, the Hungarian Scientific Research Fund (OTKA), the Lyon Institute of Origins (LIO), the National Research 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 Institute for Advanced Research, the Brazilian Ministry of Science, Technology, and Innovation, Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP), Russian Foundation for Basic Research, the Leverhulme Trust, the Research Corporation, Ministry of Science and Technology (MOST), Taiwan and the Kavli Foundation. The authors gratefully acknowledge the support of the NSF, STFC, MPS, INFN, CNRS and the State of Niedersachsen/Germany for provision of computational resources.

References

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