This is the accepted manuscript made available via CHORUS. The article has been published as: Comprehensive all-sky search for periodic gravitational waves in the sixth science run LIGO data B. P. Abbott et al. (LIGO Scientific Collaboration and Virgo Collaboration) Phys. Rev. D 94, 042002 — Published 15 August 2016 DOI: 10.1103/PhysRevD.94.042002 http://dx.doi.org/10.1103/PhysRevD.94.042002 Comprehensive All-sky Search for Periodic Gravitational Waves in the Sixth Science Run LIGO Data 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 M. Chan,38 S. Chao,73 P. Charlton,74 E. Chassande-Mottin,32 B. D. Cheeseboro,75 H. Y. Chen,76 Y. Chen,77 C. Cheng,73 A. Chincarini,48 A. Chiummo,36 H. S. Cho,78 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,79,30 C. G. Collette,80 L. Cominsky,81 M. Constancio Jr.,13 A. Conte,79,30 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,82 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 T. Creighton,87 J. Cripe,2 S. G. Crowder,83 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,84 A. Dasgupta,85 C. F. Da Silva Costa,6 V. Dattilo,36 I. Dave,49 M. Davier,25 G. S. Davies,38 E. J. Daw,86 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,75 S. Dhurandhar,16 M. C. Dı́az,87 L. Di Fiore,5 M. Di Giovanni,88,89 T. Di Girolamo,68,5 A. Di Lieto,20,21 S. Di Pace,79,30 I. Di Palma,31,79,30 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,86 M. C. Edwards,61 A. Effler,7 H.-B. Eggenstein,10 P. Ehrens,1 J. Eichholz,6,1 S. S. Eikenberry,6 W. Engels,77 R. C. Essick,12 T. Etzel,1 M. Evans,12 T. M. Evans,7 R. Everett,90 M. Factourovich,41 V. Fafone,27,15 H. Fair,37 S. Fairhurst,91 X. Fan,71 Q. Fang,52 S. Farinon,48 B. Farr,76 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,79,30 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,96,85 N. Gehrels,69 G. Gemme,48 P. Geng,87 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,85 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,90 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 2 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,76 P. Hopkins,91 J. Hough,38 E. A. Houston,38 E. J. Howell,52 Y. M. Hu,10 S. Huang,73 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,78 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,82 S. Kandhasamy,23 G. Kang,78 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,86 J. S. Key,87 F. Y. Khalili,50 I. Khan,14 S. Khan,91 Z. Khan,85 E. A. Khazanov,109 N. Kijbunchoo,39 Chi-Woong Kim,78 Chunglee Kim,78 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,82 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,85 L. Kuo,73 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,79,30 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,88,89 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 I. Mandel,46 V. Mandic,83 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,79,30 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,75 D. Meacher,90 G. D. Meadors,31,10 J. Meidam,11 A. Melatos,84 G. Mendell,39 R. A. Mercer,18 E. L. Merilh,39 M. Merzougui,54 S. Meshkov,1 C. Messenger,38 C. Messick,90 R. Metzdorff,60 P. M. Meyers,83 F. Mezzani,30,79 H. Miao,46 C. Michel,66 H. Middleton,46 E. E. Mikhailov,123 L. Milano,68,5 A. L. Miller,6,79,30 A. Miller,82 B. B. Miller,82 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,87 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,87 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,79,30 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,87 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,73 C. Pankow,82 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,82 M. Phelps,38 O. J. Piccinni,79,30 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,83 L. R. Price,1 M. Prijatelj,10,36 M. Principe,9 S. Privitera,31 R. Prix,10 G. A. Prodi,88,89 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,87 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,87 P. Rapagnani,79,30 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,79,30 K. Riles,101 M. Rizzo,102N. A. Robertson,1,38 R. Robie,38 F. Robinet,25 A. Rocchi,15 L. Rolland,8 J. G. Rollins,1 V. J. Roma,59 J. D. Romano,87 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,82 J. R. Sanders,37 B. Sassolas,66 B. S. Sathyaprakash,91 P. R. Saulson,37 O. E. S. Sauter,101 3 R. L. Savage,39 A. Sawadsky,19 P. Schale,59 R. Schilling†,10 J. Schmidt,10 P. Schmidt,1,77 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,82 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,85 A. Staley,41 M. Steinke,10 J. Steinlechner,38 S. Steinlechner,38 D. Steinmeyer,10,19 B. C. Stephens,18 R. Stone,87 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,84 S. Sunil,85 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,14,89 V. Tiwari,91 K. V. Tokmakov,106 K. Toland,38 C. Tomlinson,86 M. Tonelli,20,21 Z. Tornasi,38 C. V. Torres‡,87 C. I. Torrie,1 D. Töyrä,46 F. Travasso,34,35 G. Traylor,7 D. Trifirò,23 M. C. Tringali,88,89 L. Trozzo,135,21 M. Tse,12 M. Turconi,54 D. Tuyenbayev,87 D. Ugolini,136 C. S. Unnikrishnan,99 A. L. Urban,18 S. A. Usman,37 H. Vahlbruch,19 G. Vajente,1 G. Valdes,87 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,82 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,82 L. Zhang,1 M. Zhang,123 Y. Zhang,102 C. Zhao,52 M. Zhou,82 Z. Zhou,82 X. J. Zhu,52 M. E. Zucker,1,12 S. E. Zuraw,119 and J. Zweizig1 (LIGO Scientific Collaboration and Virgo Collaboration) †Deceased, May 2015. ‡Deceased, March 2015. 1LIGO, California Institute of Technology, Pasadena, CA 91125, USA 2Louisiana State University, Baton Rouge, LA 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, FL 32611, USA 7LIGO Livingston Observatory, Livingston, LA 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 Gravitationsphysik, D-30167 Hannover, Germany 11Nikhef, Science Park, 1098 XG Amsterdam, The Netherlands 12LIGO, Massachusetts Institute of Technology, Cambridge, MA 02139, USA 13Instituto Nacional de Pesquisas Espaciais, 12227-010 São José dos Campos, São 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, WI 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, MS 38677, USA 24California State University Fullerton, Fullerton, CA 92831, USA 25LAL, Univ. Paris-Sud, CNRS/IN2P3, Université Paris-Saclay, Orsay, France 4 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 Gravitationsphysik, 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, MT 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, NY 13244, USA 38SUPA, University of Glasgow, Glasgow G12 8QQ, United Kingdom 39LIGO Hanford Observatory, Richland, WA 99352, USA 40Wigner RCP, RMKI, H-1121 Budapest, Konkoly Thege Miklós út 29-33, Hungary 41Columbia University, New York, NY 10027, USA 42Stanford University, Stanford, CA 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 MP 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, WA 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, OR 97403, USA 60Laboratoire Kastler Brossel, UPMC-Sorbonne Universités, CNRS, ENS-PSL Research University, Collège de France, F-75005 Paris, France 61Carleton College, Northfield, MN 55057, USA 62Astronomical Observatory Warsaw University, 00-478 Warsaw, Poland 63VU University Amsterdam, 1081 HV Amsterdam, The Netherlands 64University of Maryland, College Park, MD 20742, USA 65Center for Relativistic Astrophysics and School of Physics, Georgia Institute of Technology, Atlanta, GA 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, MD 20771, USA 70RESCEU, University of Tokyo, Tokyo, 113-0033, Japan. 71Tsinghua University, Beijing 100084, China 72Texas Tech University, Lubbock, TX 79409, USA 73National Tsing Hua University, Hsinchu City, 30013 Taiwan, Republic of China 74Charles Sturt University, Wagga Wagga, New South Wales 2678, Australia 75West Virginia University, Morgantown, WV 26506, USA 76University of Chicago, Chicago, IL 60637, USA 77Caltech CaRT, Pasadena, CA 91125, USA 78Korea Institute of Science and Technology Information, Daejeon 305-806, Korea 79Università di Roma “La Sapienza,” I-00185 Roma, Italy 80University of Brussels, Brussels 1050, Belgium 81Sonoma State University, Rohnert Park, CA 94928, USA 82Center for Interdisciplinary Exploration & Research in Astrophysics (CIERA), Northwestern University, Evanston, IL 60208, USA 83University of Minnesota, Minneapolis, MN 55455, USA 5 84The University of Melbourne, Parkville, Victoria 3010, Australia 85Institute for Plasma Research, Bhat, Gandhinagar 382428, India 86The University of Sheffield, Sheffield S10 2TN, United Kingdom 87The University of Texas Rio Grande Valley, Brownsville, TX 78520, USA 88Università di Trento, Dipartimento di Fisica, I-38123 Povo, Trento, Italy 89INFN, Trento Institute for Fundamental Physics and Applications, I-38123 Povo, Trento, Italy 90The Pennsylvania State University, University Park, PA 16802, USA 91Cardiff University, Cardiff CF24 3AA, United Kingdom 92Montclair State University, Montclair, NJ 07043, USA 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, MI 48109, USA 102Rochester Institute of Technology, Rochester, NY 14623, USA 103NCSA, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA 104Universitat de les Illes Balears, IAC3—IEEC, E-07122 Palma de Mallorca, Spain 105University of Bia lystok, 15-424 Bia lystok, Poland 106SUPA, University of Strathclyde, Glasgow G1 1XQ, United Kingdom 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, AL 35899, USA 119University of Massachusetts-Amherst, Amherst, MA 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, LA 70813, USA 123College of William and Mary, Williamsburg, VA 23187, USA 124Instituto de F́ısica Teórica, University Estadual Paulista/ICTP South American Institute for Fundamental Research, São Paulo SP 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, WA 99362 USA 129National Institute for Mathematical Sciences, Daejeon 305-390, Korea 130Université de Lyon, F-69361 Lyon, France 131Hobart and William Smith Colleges, Geneva, NY 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, MI 49104, USA 135Università di Siena, I-53100 Siena, Italy 136Trinity University, San Antonio, TX 78212, USA 137University of Washington, Seattle, WA 98195, USA 138Kenyon College, Gambier, OH 43022, USA 139Abilene Christian University, Abilene, TX 79699, USA We report on a comprehensive all-sky search for periodic gravitational waves in the frequency band 100-1500 Hz and with a frequency time derivative in the range of [−1.18,+1.00] × 10−8 Hz/s. Such a signal could be produced by a nearby spinning and slightly non-axisymmetric isolated neutron star in our galaxy. This search uses the data from the Initial LIGO sixth science run and covers a larger parameter space with respect to any past search. A Loosely Coherent detection pipeline was 6 applied to follow up weak outliers in both Gaussian (95% recovery rate) and non-Gaussian (75% recovery rate) bands. No gravitational wave signals were observed, and upper limits were placed on their strength. Our smallest upper limit on worst-case (linearly polarized) strain amplitude h0 is 9.7×10−25 near 169 Hz, while at the high end of our frequency range we achieve a worst-case upper limit of 5.5 × 10−24. Both cases refer to all sky locations and entire range of frequency derivative values. I. INTRODUCTION In this paper we report the results of a compre- hensive all-sky search for continuous, nearly monochro- matic gravitational waves in data from LIGO’s sixth science (S6) run. The search covered frequencies from 100 Hz through 1500 Hz and frequency derivatives from −1.18× 10−8 Hz/s through 1.00× 10−8 Hz/s. A number of searches for periodic gravitational waves have been carried out previously in LIGO data [1–10], including coherent searches for gravitational radiation from known radio and X-ray pulsars. An Einstein@Home search running on the BOINC infrastructure [11] has per- formed blind all-sky searches on S4 and S5 data [12–14]. The results in this paper were produced with the Pow- erFlux search program. It was first described in [1] together with two other semi-coherent search pipelines (Hough, Stackslide). The sensitivities of all three meth- ods were compared, with PowerFlux showing better re- sults in frequency bands lacking severe spectral artifacts. A subsequent article [3] based on the data from the S5 run featured improved upper limits and a systematic out- lier follow-up search based on the Loosely Coherent algo- rithm [15]. The analysis of the data set from the sixth science run described in this paper has several distinguishing features from previously published results: • A number of upgrades to the detector were made in order to field-test the technology for Advanced LIGO interferometers. This resulted in a factor of about two improvement in intrinsic noise level at high frequencies compared to previously published results [3]. • The higher sensitivity allowed us to use less data while still improving upper limits in high frequency bands by 25% over previously published results. This smaller dataset allowed covering larger param- eter space, and comprehensive exploration of high frequency data. • This search improved on previous analyses by par- titioning the data in ≈ 1 month chunks and look- ing for signals in any contiguous sequence of these chunks. This enables detections of signals that con- form to ideal signal model over only part of the data. Such signals could arise because of a glitch, or because of influence of a long-period companion object. • The upgrades to the detector, while improving sen- sitivity on average, introduced a large number of detector artifacts, with 20% of frequency range con- taminated by non-Gaussian noise. We addressed this issue by developing a new Universal statistic [16] that provides correct upper limits regardless of the noise distribution of the underlying data, while still showing close to optimal performance for Gaus- sian data. We have observed no evidence of gravitational radia- tion and have established the most sensitive upper limits to date in the frequency band 100-1500 Hz. Our smallest 95% confidence level upper limit on worst-case (linearly polarized) strain amplitude h0 is 9.7×10−25 near 169 Hz, while at the high end of our frequency range we achieve a worst-case upper limit of 5.5×10−24. Both cases refer to all sky locations and entire range of frequency derivative values. II. LIGO INTERFEROMETERS AND S6 SCIENCE RUN The LIGO gravitational wave network consists of two observatories, one in Hanford, Washington and the other in Livingston, Louisiana, separated by a 3000 km base- line. During the S6 run each site housed one suspended interferometer with 4 km long arms. While the sixth science run spanned a ≈ 15 months pe- riod of data acquisition, this analysis used only data from GPS 951534120 (2010 Mar 02 03:01:45 UTC) through GPS 971619922 (2010 Oct 20 14:25:07 UTC), for which strain sensitivity was best. Since interferometers spo- radically fall out of operation (“lose lock”) due to en- vironmental or instrumental disturbances or for sched- uled maintenance periods, the dataset was not contigu- ous. The Hanford interferometer H1 had a duty factor of 53%, while the Livingston interferometer L1 had a duty factor of 51%. The strain sensitivity was not uniform, exhibiting a ∼ 50% daily variation from anthropogenic activity as well as gradual improvement toward the end of the run [17, 18]. Non-stationarity of noise was especially severe at fre- quencies below 100 Hz, and since the average detector sensitivity for such frequencies was not significantly bet- ter than that observed in the longer S5 run [3], this search was restricted to frequencies above 100 Hz. A detailed description of the instruments and data can be found in [19]. 7 Frequency (Hz) h0 50 300 500 700 900 1100 1300 1500 1e − 25 1e − 24 1e − 23 ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ●● ● ●● ● ●● ● ● ●● ● ● ● ● ● ● ● ●● ● ●●● ● ●● ● ● ● ● ●● ● ● ●● ● ● ● ● ● ●● ● ● ● ● ●●● ● ● ●●● ● ● ●● ● ● ●●● ● ● ● ● ●● ● ● ● ● ● ● ● ● ●● ●● ● ● ●● ● ●● ● ●● ● ●● ● ● ●●● ●●● ● ●● ● ●●● ●● ● ● ● ●● ● ●● ●● ●● ●● ● ●● ● ●● ● ●●●● ● ● ● ● ● ● ●●● ● ● ● ● ●● ● ●●● ● ●● ● ●●●●●●●●●● ● ● ● ● ● ●● ● ● ● ● ●●●●●● ● ● ● ● ●● ●●●●●● ● ●●●●● ● ● ● ● ● ●● ● ● ● ● ● ●● ● ● ● ● ●● ● ● ●● ●● ●● ●●● ● ●● ● ●● ● ● ●● ● ●● ● ●● ● ●●● ● ●● ● ●● ● ●●● ● ●● ● ● ● ● ●● ● ● ●● ● ●●● ●● ● ●● ● ● ● ● ● ● ●●● ●● ● ● ●● ● ● ● ●●● ● ● ●● ●●● ●● ● ● ●● ● ●● ● ●●●● ●● ● ●●● ●●●● ●●● ●● ● ●●●● ●●● ● ●● ●●● ● ● ●● ●● ● ●●●● ● ● ● ●● ● ●●●● ●● ● ●● ● ●●● ● ● ●● ●●●●●●●●●● ● ● ● ● ● ●● ● ● ● ●●●●●●● ● ●● ● ● ● ● ●●●● ● ● ●●●●● − − ● worst case (linear) best case (circular) 60 Hz harmonics FIG. 1. S6 upper limits. The upper (yellow) curve shows worst-case (linearly polarized) 95% CL upper limits in analyzed 0.25 Hz bands (see Table I for list of excluded bands). The lower (grey) curve shows upper limits assuming a circularly polarized source. The values of solid points and circles mark frequencies within 1.25 Hz of 60 Hz power line harmonics for circularly (solid points) and linearly (open circles) polarized sources. The data for this plot can be found in [20]. (color online) III. THE SEARCH FOR CONTINUOUS GRAVITATIONAL RADIATION A. Overview In this paper we assume a classical model of a spin- ning neutron star with a rotating quadrupole moment that produces circularly polarized gravitational radiation along the rotation axis and linearly polarized radiation in the directions perpendicular to the rotation axis. The linear polarization is the worst case as such signals con- tribute the smallest amount of power to the detector. The strain signal template is assumed to be h(t) = h0 ( F+(t, α0, δ0, ψ) 1+cos2(ι) 2 cos(Φ(t))+ + F×(t, α0, δ0, ψ) cos(ι) sin(Φ(t)) ) , (1) where F+ and F× characterize the detector responses to signals with “+” and “×” quadrupolar polarizations [1– 3], the sky location is described by right ascension α0 and declination δ0, the inclination of the source rotation axis to the line of sight is denoted ι, and the phase evolution of the signal is given by the formula Φ(t) = 2π ( fsource · (t− t0) + f (1) · (t− t0)2/2 ) + φ , (2) with fsource being the source frequency and f (1) denoting the first frequency derivative (which, when negative, is termed the spindown). We use t to denote the time in the Solar System barycenter frame. The initial phase φ is computed relative to reference time t0. When expressed as a function of local time of ground-based detectors the equation 2 acquires sky-position-dependent Doppler shift terms. We use ψ to denote the polarization angle of the 8 projected source rotation axis in the sky plane. The search has two main components. First, the main PowerFlux algorithm [1–3, 21–23] was run to establish upper limits and produce lists of outliers with signal- to-noise ratio (SNR) greater than 5. Next, the Loosely Coherent detection pipeline [3, 15, 24] was used to reject or confirm collected outliers. Both algorithms calculate power for a bank of signal model templates and compute upper limits and signal- to-noise ratios for each template based on comparison to templates with nearby frequencies and the same sky loca- tion and spindown. The input time series is broken into 50% overlapping 1800 s long segments which are Hann windowed and Fourier transformed. The resulting short Fourier transforms (SFTs) are arranged into an input matrix with time and frequency dimensions. The power calculation can be expressed as a bilinear form of the input matrix {at,f}: P [f ] = ∑ t1,t2 at1,f+δf(t1)a ∗ t2,f+δf(t2) Kt1,t2,f (3) Here δf(t) denotes the detector frame frequency drift due to the effects from both Doppler shifts and the first fre- quency derivative. The sum is taken over all times t cor- responding to the midpoint of the short Fourier transform time interval. The kernel Kt1,t2,f includes the contribu- tion of time dependent SFT weights, antenna response, signal polarization parameters and relative phase terms [15, 24]. The main semi-coherent PowerFlux algorithm uses a kernel with main diagonal terms only and is very fast. The Loosely Coherent algorithms increase coherence time while still allowing for controlled deviation in phase [15]. This is done by more complicated kernels that increase effective coherence length. The effective coherence length is captured in a param- eter δ, which describes the amount of phase drift that the kernel allows between SFTs, with δ = 0 correspond- ing to a fully coherent case, and δ = 2π corresponding to incoherent power sums. Depending on the terms used, the data from different interferometers can be combined incoherently (such as in stages 0 and 1, see Table II) or coherently (as used in stages 2, 3 and 4). The coherent combination is more computationally expensive but provides much better pa- rameter estimation. The upper limits (Figure 1) are reported in terms of the worst-case value of h0 (which applies to linear polar- izations with ι = π/2) and for the most sensitive circular polarization (ι = 0 or π). As described in the previous paper [3], the pipeline does retain some sensitivity, how- ever, to non-general-relativity GW polarization models, including a longitudinal component, and to slow ampli- tude evolution. The 95% confidence level upper limits (see Figure 1) produced in the first stage are based on the overall noise level and largest outlier in strain found for every template in each 0.25 Hz band in the first stage of the pipeline. The 0.25 Hz bands are analyzed by separate instances of PowerFlux [3]. A followup search for detection is car- ried out for high-SNR outliers found in the first stage. Certain frequency ranges (Table I) were excluded from the analysis because of gross contamination by detector artifacts. B. Universal statistics The detector sensitivity upgrades introduced many ar- tifacts, so that in 20% of the sensitive frequency range the noise follows non-Gaussian distributions which, in addi- tion, are unknown. As the particular non-Gaussian dis- tribution can vary widely depending on particular detec- tor artifacts, the ideal estimate based on full knowledge of the distribution is not usually available. In the previ- ous analysis [1–3], the frequency bands where the noise distribution was non-Gaussian were not used to put up- per limits. However, in the present case this approach would have resulted in excluding most of the frequency bands below 400 Hz and many above 400 Hz; even though the average strain sensitivity in many of these frequency bands is better than in the past. log10(Injection strain) lo g 1 0(U pp er li m it) −24 −23 −22 −21 −20 −19 −18 −24.5 −24.0 −23.5 −23.0 ● ●● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●●● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ●● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ●● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ●● ● ● ●● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ●● ● ● ● ●● ● ● ● ● ●● ● ● ● ●● ●● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ●●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ●● ● ● ●●● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● 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Upper limit validation. Each point represents a sep- arate injection in the 400-1500 Hz frequency range. Each es- tablished upper limit (vertical axis) is compared against the injected strain value (horizontal axis, red line) (color online). To make use of the entire spectrum, we used in this work the Universal statistic algorithm [16] for establish- ing upper limits. The algorithm is derived from the Markov inequality and shares its independence from the underlying noise distribution. It produces upper limits less than 5% above optimal in case of Gaussian noise. In non-Gaussian bands it can report values larger than what 9 Category Description First harmonic of violin modes 343.25-343.75 Hz, 347-347.25 Hz Second harmonic of violin modes 686.25-687.5 Hz Third harmonic of violin modes 1031.00-1031.25 Hz TABLE I. Frequency regions excluded from upper limit analysis. “Violin modes” are resonant vibrations of the wires which suspend the many mirrors of the interferometer. would be obtained if the distribution were known, but the upper limits are always at least 95% valid. Figure 2 shows results of an injection run performed as described in [3]. Correctly established upper limits are above the red line. C. Detection pipeline The detection pipeline used in [3] was extended with additional stages (see Table II) to winnow the larger num- ber of initial outliers, expected because of non-Gaussian artifacts and larger initial search space. This detection pipeline was also used in the search of the Orion spur [4]. The initial stage (marked 0) scans the entire sky with semi-coherent algorithm that computes weighted sums of powers of 1800 s Hann-windowed SFTs. These power sums are then analyzed to identify high-SNR outliers. A separate algorithm uses universal statistics [16] to estab- lish upper limits. The entire dataset was partitioned into 7 segments of equal length and power sums were produced indepen- dently for any contiguous combinations of these stretches. As in [4] the outlier identification was performed indepen- dently in each stretch. High-SNR outliers were subject to a coincidence test. For each outlier with SNR > 7 in the combined H1 and L1 data, we required there to be outliers in the indi- vidual detector data that had SNR > 5, matching the parameters of the combined-detector outlier within a dis- tance of 0.03 rad · 400 Hz/f on the sky, 2 mHz in fre- quency, and 3 × 10−10 Hz/s in spindown. However, the combined-detector SNR could not be lower than either single-detector SNR. The identified outliers using combined data are then passed to followup stage using Loosely Coherent algo- rithm [15] with progressively tighter phase coherence pa- rameters δ, and improved determination of frequency, spindown and sky location. As the initial stage 0 only sums powers it does not use relative phase between interferometers, which results in some degeneracy between sky position, frequency and spindown. The first Loosely Coherent followup stage also combines interferometer powers incoherently, but demands greater temporal coherence (smaller δ) within each interferometer, which should boost SNR of viable outiers by at least 20%. Subsequent stages use data co- herently providing tighter bounds on outlier location. The testing of the pipeline was done above 400 Hz and included both Gaussian and non-Gaussian bands. We focused on high frequency performance because prelimi- nary S6 data indicated the sensitivity at low frequencies was unlikely to improve over S5 results due to detector artifacts. h0 relative to upper limit % fo un d 0 20 40 60 80 100 0 1 2 3 4 ●●●●●●●●●●●● ● ● ● ● ● ● ● ● ● ● ● ● ●●● ● ●● ●● ● ● ● ● ● ● ● ● Stage_0 Stage_1 Stage_2 Stage_3 Stage_4● FIG. 3. Injection recovery in frequency bands above 400 Hz. The injected strain divided by the upper limit in this band (before injection) is shown on the horizontal axis. The per- centage of surviving injections is shown on the vertical axis, with horizontal line drawn at 95% level. Stage 0 is the output of the coincidence test after the initial semi-coherent search. (color online). The followup code was tested to recover 95% of injec- tions 50% above the upper limit level assuming uniform distribution of injection frequency. (Figure 3). Recovery of signals injected into frequency bands which exhibits non-Gaussian noise was 75% (Figure 4). Our recovery criterion demanded that an outlier close to the true injec- tion location (within 2 mHz in frequency f , 3×10−10 Hz/s in spindown and 12 rad·Hz/f in sky location) be found and successfully pass through all stages of the detection pipeline. As each stage of the pipeline only passes out- liers with an increase in SNR, this resulted in an outlier that strongly stood out above the background, with good estimates of the parameters of the underlying signal. It should be noted that the injection recovery curve 10 Stage Instrument sum Phase coherence Spindown step Sky refinement Frequency refinement SNR increase rad Hz/s % 0 Initial/upper limit semi-coherent NA 2 × 10−10 1 1/2 NA 1 incoherent π/2 1.0 × 10−10 1/4 1/8 20 2 coherent π/2 5.0 × 10−11 1/4 1/8 0 3 coherent π/4 2.5 × 10−11 1/8 1/16 12 4 coherent π/8 5.0 × 10−12 1/16 1/32 12 TABLE II. Analysis pipeline parameters. Starting with stage 1, all stages used the Loosely Coherent algorithm for demodulation. The sky and frequency refinement parameters are relative to values used in the semicoherent PowerFlux search. h0 relative to upper limit % fo un d 0 20 40 60 80 0.0 0.5 1.0 1.5 2.0 2.5 ●●●●●●●● ● ● ● ● ● ● ● ● ● ● ● ● Stage_0 Stage_1 Stage_2 Stage_3 Stage_4● FIG. 4. Injection recovery in non-Gaussian bands above 400 Hz. The injected strain divided by the upper limit in this band (before injection) is shown on the horizontal axis. The percentage of surviving injections is shown on the vertical axis, with horizontal line drawn at 75% level. (color online) in Figure 3 passes slightly below the 95% level for h0 equal to the upper limit. However, the upper limits are based on power levels measured by stage 0, independent of any follow-up criteria. That is, we can say with 95% confidence that a signal above the upper limit level is inconsistent with the observed power, even though such a (hypothetical) signal might not pass all of our follow- up criteria to be “detected”. The main reason that these injections fail to be detected is the different sensitivities of the H1 and L1 detectors. When one interferometer is less sensitive sensitive we can still set a good upper limit, but the initial coincidence criteria requires that an outlier be marginally seen in both interferometers. In the previous analysis [3] the interferometers had similar sensitivity and the curve passed through the intersection of the green lines (horizontal axis value of 1, vertical axis value of 95%). D. Gaussian false alarm event rate The computation of the false alarm rate for the out- liers passing all stages of the pipeline is complicated by the fact that most outliers are caused by instrumental artifacts for which we do not know the underlying prob- ability distribution. In principle, one could repeat the analysis many times using non-physical frequency shifts (which would exclude picking up a real signal by acci- dent) in order to obtain estimates of false alarm rate, but this approach is very computationally expensive. Even assuming a perfect Gaussian background, it is difficult to analytically model the pipeline in every detail to ob- tain an accurate estimate of the false alarm rate, given the gaps in interferometer operations and non-stationary noise. Instead, following [4], we compute a figure of merit that overestimates the actual Gaussian false alarm event rate. We simplify the problem by assuming that the en- tire analysis was carried out with the resolution of the very last stage of follow-up and we are merely triggering on the SNR value of the last stage. This is extremely conservative as we ignore the consistency requirements that allow the outlier to proceed from one stage of the pipeline to the next; the actual false alarm rate could be lower. The SNR of each outlier is computed relative to the Loosely Coherent power sum for 501 frequency bins spaced at 1/1800 Hz intervals (including the outlier) but with all the other signal parameters held constant. The spacing assures that correllations between neighboring sub-bins do not affect the statistics of the power sum. To simplify computation we assume that we are deal- ing with a simple χ2 distribution with the number of degrees of freedom given by the timebase divided by the coherence length and multiplied by a conservative duty factor reflecting interferometer uptime and the worst-case weights from linearly-polarized signals. Thus to find the number N of degrees of freedom we will use the formula N ≈ timebase · δ · duty factor 1800 s · 2π (4) with the duty factor taken to be 0.125 and δ giving 11 the phase coherence parameter of the Loosely Coherent search. The duty factor was chosen to allow for only 50% interferometer uptime and only one quarter of the data receiving high weights from our procedure, which weights the contribution of data inversely as the square of the estimated noise [21, 22]. Thus we define the outlier figure of merit describing Gaussian false alarm (GFA) event rate as GFA = K · Pχ2 ( N + SNR · √ 2N ;N ) (5) where N defines the number of degrees of freedom as given by equation 4, Pχ2(x;N) gives the probability for a χ2 distribution with N degrees of freedom to exceed x, and K = 1.3×1014 is the estimated number of templates. We point out that the GFA is overly conservative when applied to frequency bands with Gaussian noise, but is only loosely applicable to bands with detector artifacts, which can affect both the estimate of the number of de- grees of freedom of the underlying distribution and the assumption of uncorrelated underlying noise. IV. RESULTS 0 500 1000 1500 − 1e − 08 0e + 00 5e − 09 1e − 08 Frequency, Hz S pi nd ow n, H z/ s PowerFlux S6 PowerFlux S5 Einstein@Home S5 FIG. 5. Parameter space covered in the analysis. Ein- stein@Home searches use longer coherence times than Pow- erFlux, with better sensitivity to narrow band signals. The results for area marked “PowerFlux S6” are reported in this paper. (color online) The PowerFlux algorithm and Loosely Coherent method compute power estimates for gravitational waves in a given frequency band for a fixed set of templates. The template parameters usually include frequency, first frequency derivative and sky location. Since the search target is a rare monochromatic sig- nal, it would contribute excess power to one of the fre- quency bins after demodulation. The upper limit on the maximum excess relative to the nearby power values can then be established. For this analysis we use a univer- sal statistic [16] that places conservative 95% confidence level upper limits for an arbitrary statistical distribution of noise power. The universal statistic has been designed to provide close to optimal values in the common case of Gaussian distribution. The PowerFlux algorithm and Loosely Coherent method have been described in detail in [1, 2, 15, 21– 23]. Most natural sources are expected to have negative first frequency derivative, as the energy lost in gravita- tional or electromagnetic waves would make the source spin more slowly. The frequency derivative can be pos- itive when the source is affected by a strong slowly- variable Doppler shift, such as due to a long-period orbit. The large gap in data taking due to installation of Ad- vanced LIGO interferometers provided an opportunity to cover an extended parameter space (Figure 5). With re- spect to previous searches, we have chosen to explore comprehensively both negative and positive frequency derivatives to avoid missing any unexpected sources in our data. The upper limits obtained in the search are shown in figure 1. The numerical data for this plot can be obtained separately [20]. The upper (yellow) curve shows the up- per limits for a worst-case (linear) polarizations when the smallest amount of gravitational energy is projected to- wards Earth. The lower curve shows upper limits for an optimally oriented source. Because of the day-night variability of the interferometer sensitivity due to anthro- pogenic noise, the linearly polarized sources are more sus- ceptible to detector artifacts, as the detector response to such sources varies with the same period. The neigh- borhood of 60 Hz harmonics is shown as circles for worst case upper limits and dots for circular polarization up- per limits. Thanks to the use of universal statistic they do represent valid values even if contaminated by human activity. Each point in figure 1 represents a maximum over the sky: only a small excluded portion of the sky near eclip- tic poles that is highly susceptible to detector artifacts, due to stationary frequency evolution produced by the combination of frequency derivative and Doppler shifts. The exclusion procedure is described in [3] and applied to 0.033% of the sky over the entire run. A few frequency bands shown in Table I were so con- taminated that every SFT was vetoed by data condi- tioning code and the analysis terminated before reaching universal statistic stage. While the universal statistic could have established upper limits with veto turned off, we opted to simply exclude these bands, as the contam- ination would raise upper limits to be above physically interesting values. If one assumes that the source spindown is solely due 12 to emission of gravitational waves, then it is possible to recast upper limits on source amplitude as a limit on source ellipticity. Figure 6 shows the reach of our search under different assumptions on source distance. Super- imposed are lines corresponding to sources of different ellipticities. Frequency (Hz) F re qu en cy d er iv at iv e (H z/ s) 100 300 500 700 1100 1e − 13 1e − 11 1e − 09 1e − 07 ε=1e−5 ε= 1e − 6 ε= 1e − 7 ε= 1e − 8 10 pc 100 pc 1 kpc ε=8e−7 at 1500 Hz 10 kpc FIG. 6. Range of the PowerFlux search for neutron stars spinning down solely due to gravitational radiation. This is a superposition of two contour plots. The grey and red solid lines are contours of the maximum distance at which a neu- tron star could be detected as a function of gravitational-wave frequency f and its derivative ḟ . The dashed lines are con- tours of the corresponding ellipticity ε(f, ḟ). The fine dotted line marks the maximum spindown searched. Together these quantities tell us the maximum range of the search in terms of various populations (see text for details) (color online). The detection pipeline produced 16 outliers (Table III). Each outlier is identified by a numerical index. We report SNR, decimal logarithm of Gaussian false alarm rate, as well as frequency, spindown and sky location. The “Segment” column describes the persistence of the outlier through the data, and specified which contigu- ous subset of the 7 equal partitions of the timespan con- tributed most significantly to the outlier: see [4] for de- tails. A continuous signal will normally have [0,6] in this column (similar contribution from all 7 segments), or on rare occasions [0,5] or [1,6]. Any other range is indicative of a non-continuous signal or artifact. During the S6 run several simulated pulsar signals were injected into the data by applying a small force to the interferometer mirrors. Several outliers were due to such hardware injections (Table IV). The full list of injections including those too weak to be found by an all-sky search can be found in [25]. The hardware injection ip3 was exceptionally strong with a clear signature even in non- Gaussian band. The recovery of the injections gives us confidence that no potential signal were missed. Manual followup has shown non-injection outliers to be caused by pronounced detector artifacts. V. CONCLUSIONS We have performed the most sensitive all-sky search to date for continuous gravitational waves in the range 100-1500 Hz. We explored both positive and negative spindowns and placed upper limits on expected and un- expected sources. At the highest frequencies we are sen- sitive to neutron stars with an equatorial ellipticity as small as 8 × 10−7 and as far away as 1 kpc for favor- able spin orientations. The use of a universal statistic allowed us to place upper limits on both Gaussian and non-Gaussian frequency bands. The maximum elliptic- ity a neutron star can theoretically support is at least 1× 10−5 according to [26, 27]. Our results exclude such maximally deformed pulsars above 200 Hz pulsar rotation frequency (400 Hz gravitational frequency) within 1 kpc. A detection pipeline based on a Loosely Coherent al- gorithm was applied to outliers from our search. This pipeline was demonstrated to be able to detect simulated signals at the upper limit level for both Gaussian and non-Gaussian bands. Several outliers passed all stages of the coincidence pipeline; their parameters are shown in table III. However, manual examination revealed no true pulsar signals. VI. 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 Tech- nology Facilities Council (STFC) of the United King- dom, 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 sup- ported by the Netherlands Organisation for Scientific Re- search, for the construction and operation of the Virgo detector and the creation and support of the EGO consor- tium. 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 & Engineer- ing Research Board (SERB), India, Ministry of Human Resource Development, India, the Spanish Ministerio de Economı́a y Competitividad, the Conselleria d’Economia i Competitivitat and Conselleria d’Educació, Cultura i 13 Idx SNR log10(GFA) Segment Frequency Spindown RAJ2000 DECJ2000 Description Hz nHz/s degrees degrees 1 3331 −9360 [0, 6] 192.49269 −8.650 351.371 −33.342 Hardware injection ip8 21 1329 −3114 [1, 5] 108.85717 −0.000 178.417 −33.400 Hardware injection ip3, Non Gaussian, disturbed H1 spectrum 42 957 −2622 [0, 6] 575.16354 0.005 215.261 3.370 Hardware injection ip2 69 112 −196 [0, 3] 397.51894 −0.115 271.698 67.257 Non Gaussian, Line in H1, disturbed spectrum in L1 72 93 −78 [4, 4] 1397.76097 −11.220 296.704 −16.069 Induced by loud hardware injection ip4, Non Gaussian, highly disturbed H1+L1 spectra 76 82 −162 [0, 5] 1145.20043 0.400 90.936 −67.610 Highly disturbed H1 spectrum, stationary line area 79 64 −98 [1, 4] 566.08359 −4.850 91.028 86.915 Line in H1 at 566.085 Hz 81 54 −68 [2, 4] 704.03500 4.110 117.932 50.411 Disturbed H1 and L1 spectrum 82 48 −86 [0, 6] 1220.74448 −1.120 223.413 −20.502 Hardware injection ip7, sloping H1 and L1 spectra 83 48 −73 [0, 4] 140.41014 −0.010 270.298 66.821 Highly disturbed H1 spectrum, stationary line area 94 36 −44 [0, 3] 192.65413 9.270 145.440 10.439 Induced by loud hardware injection ip8 95 35 −28 [2, 3] 250.01082 2.750 247.459 −76.842 Lines in H1 and L1, Non Gaussian 101 19 −13 [2, 6] 1145.30312 8.515 196.471 33.778 Highly disturbed H1 spectrum 102 18 −12 [0, 4] 1397.91328 1.070 42.627 32.827 Induced by loud hardware injection ip4, Non Gaussian, highly disturbed H1+L1 spectra 103 17 −4 [3, 4] 1143.41710 −2.455 107.611 −56.347 Highly disturbed H1 spectrum 107 14 −0 [2, 3] 451.47993 −10.880 49.317 33.890 Line in H1 at 451.5 Hz TABLE III. Outliers that passed detection pipeline. Only the highest-SNR outlier is shown for each 0