Abbott, B. P. and Jawahar, S. and Lockerbie, N. A. and Tokmakov, K. V.

(2017) Search for continuous gravitational waves from neutron stars in

globular cluster NGC 6544. Physical Review D, 95 (8). ISSN 1550-2368 ,

http://dx.doi.org/10.1103/PhysRevD.95.082005

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Search for continuous gravitational waves from neutron stars in globular cluster

NGC 6544

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 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. Calderon 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. Cavaglia,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 T. Creighton,88

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. Deleglise,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. Dıaz,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 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. Gonzalez,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 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

2

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. Jimenez-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. Kefelian,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. Krolak,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 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. Luck,19,10 A. P. Lundgren,10 R. Lynch,12 Y. Ma,52

B. Machenschalk,10 M. MacInnis,12 D. M. Macleod,2 F. Magana-Sandoval,37 L. Magana 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. Marka,41 Z. Marka,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 P. Patel,1 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. Purrer,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,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 R. Romano,4,5 G. Romanov,123 J. H. Romie,7 D. Rosinska,132,45 S. Rowan,38

A. Rudiger,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

3

J. R. Sanders,37 B. Sassolas,66 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. Schonbeck,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. Szczepanczyk,98 M. Tacca,32 D. Talukder,59 D. B. Tanner,6 M. Tapai,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. Toyra,46 F. Travasso,34,35

G. Traylor,7 D. Trifiro,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. Vasuth,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. Vicere,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. Zadrozny,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 J. Zweizig1

(LIGO Scientific Collaboration and Virgo Collaboration)

and S. Sigurdsson73

∗Deceased, March 2016. †Deceased, May 2015. ‡Deceased, March 2015.1LIGO, California Institute of Technology, Pasadena, CA 91125, USA

2Louisiana State University, Baton Rouge, LA 70803, USA3American University, Washington, D.C. 20016, USA

4Universita di Salerno, Fisciano, I-84084 Salerno, Italy5INFN, Sezione di Napoli, Complesso Universitario di Monte S.Angelo, I-80126 Napoli, Italy

6University of Florida, Gainesville, FL 32611, USA7LIGO Livingston Observatory, Livingston, LA 70754, USA

8Laboratoire d’Annecy-le-Vieux de Physique des Particules (LAPP),Universite 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 fur Gravitationsphysik, D-30167 Hannover, Germany11Nikhef, Science Park, 1098 XG Amsterdam, The Netherlands

12LIGO, Massachusetts Institute of Technology, Cambridge, MA 02139, USA13Instituto Nacional de Pesquisas Espaciais, 12227-010 Sao Jose dos Campos, Sao Paulo, Brazil

14INFN, Gran Sasso Science Institute, I-67100 L’Aquila, Italy15INFN, Sezione di Roma Tor Vergata, I-00133 Roma, Italy

16Inter-University Centre for Astronomy and Astrophysics, Pune 411007, India17International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore 560012, India

18University of Wisconsin-Milwaukee, Milwaukee, WI 53201, USA19Leibniz Universitat Hannover, D-30167 Hannover, Germany

20Universita di Pisa, I-56127 Pisa, Italy21INFN, Sezione di Pisa, I-56127 Pisa, Italy

22Australian National University, Canberra, Australian Capital Territory 0200, Australia23The University of Mississippi, University, MS 38677, USA

4

24California State University Fullerton, Fullerton, CA 92831, USA25LAL, Univ. Paris-Sud, CNRS/IN2P3, Universite Paris-Saclay, Orsay, France

26Chennai Mathematical Institute, Chennai 603103, India27Universita di Roma Tor Vergata, I-00133 Roma, Italy

28University of Southampton, Southampton SO17 1BJ, United Kingdom29Universitat Hamburg, D-22761 Hamburg, Germany

30INFN, Sezione di Roma, I-00185 Roma, Italy31Albert-Einstein-Institut, Max-Planck-Institut fur Gravitationsphysik, D-14476 Potsdam-Golm, Germany

32APC, AstroParticule et Cosmologie, Universite Paris Diderot,CNRS/IN2P3, CEA/Irfu, Observatoire de Paris,

Sorbonne Paris Cite, F-75205 Paris Cedex 13, France33Montana State University, Bozeman, MT 59717, USA

34Universita di Perugia, I-06123 Perugia, Italy35INFN, Sezione di Perugia, I-06123 Perugia, Italy

36European Gravitational Observatory (EGO), I-56021 Cascina, Pisa, Italy37Syracuse University, Syracuse, NY 13244, USA

38SUPA, University of Glasgow, Glasgow G12 8QQ, United Kingdom39LIGO Hanford Observatory, Richland, WA 99352, USA

40Wigner RCP, RMKI, H-1121 Budapest, Konkoly Thege Miklos ut 29-33, Hungary41Columbia University, New York, NY 10027, USA

42Stanford University, Stanford, CA 94305, USA43Universita di Padova, Dipartimento di Fisica e Astronomia, I-35131 Padova, Italy

44INFN, Sezione di Padova, I-35131 Padova, Italy45CAMK-PAN, 00-716 Warsaw, Poland

46University of Birmingham, Birmingham B15 2TT, United Kingdom47Universita degli Studi di Genova, I-16146 Genova, Italy

48INFN, Sezione di Genova, I-16146 Genova, Italy49RRCAT, Indore MP 452013, India

50Faculty of Physics, Lomonosov Moscow State University, Moscow 119991, Russia51SUPA, University of the West of Scotland, Paisley PA1 2BE, United Kingdom52University 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, Universite Cote d’Azur, CNRS, Observatoire Cote d’Azur, CS 34229, Nice cedex 4, France55Institut de Physique de Rennes, CNRS, Universite de Rennes 1, F-35042 Rennes, France

56Washington State University, Pullman, WA 99164, USA57Universita degli Studi di Urbino “Carlo Bo,” I-61029 Urbino, Italy58INFN, Sezione di Firenze, I-50019 Sesto Fiorentino, Firenze, Italy

59University of Oregon, Eugene, OR 97403, USA60Laboratoire Kastler Brossel, UPMC-Sorbonne Universites, CNRS,

ENS-PSL Research University, College de France, F-75005 Paris, France61Carleton College, Northfield, MN 55057, USA

62Astronomical Observatory Warsaw University, 00-478 Warsaw, Poland63VU University Amsterdam, 1081 HV Amsterdam, The Netherlands

64University of Maryland, College Park, MD 20742, USA65Center for Relativistic Astrophysics and School of Physics,

Georgia Institute of Technology, Atlanta, GA 30332, USA66Laboratoire des Materiaux Avances (LMA), CNRS/IN2P3, F-69622 Villeurbanne, France

67Universite Claude Bernard Lyon 1, F-69622 Villeurbanne, France68Universita di Napoli “Federico II,” Complesso Universitario di Monte S.Angelo, I-80126 Napoli, Italy

69NASA/Goddard Space Flight Center, Greenbelt, MD 20771, USA70RESCEU, University of Tokyo, Tokyo, 113-0033, Japan.

71Tsinghua University, Beijing 100084, China72Texas Tech University, Lubbock, TX 79409, USA

73The Pennsylvania State University, University Park, PA 16802, USA74National Tsing Hua University, Hsinchu City, 30013 Taiwan, Republic of China

75Charles Sturt University, Wagga Wagga, New South Wales 2678, Australia76West Virginia University, Morgantown, WV 26506, USA

77University of Chicago, Chicago, IL 60637, USA78Caltech CaRT, Pasadena, CA 91125, USA

79Korea Institute of Science and Technology Information, Daejeon 305-806, Korea80Universita di Roma “La Sapienza,” I-00185 Roma, Italy

81University of Brussels, Brussels 1050, Belgium82Sonoma State University, Rohnert Park, CA 94928, USA

5

83Center for Interdisciplinary Exploration & Research in Astrophysics (CIERA),Northwestern University, Evanston, IL 60208, USA

84University of Minnesota, Minneapolis, MN 55455, USA85The University of Melbourne, Parkville, Victoria 3010, Australia86Institute for Plasma Research, Bhat, Gandhinagar 382428, India87The University of Sheffield, Sheffield S10 2TN, United Kingdom

88The University of Texas Rio Grande Valley, Brownsville, TX 78520, USA89Universita di Trento, Dipartimento di Fisica, I-38123 Povo, Trento, Italy

90INFN, Trento Institute for Fundamental Physics and Applications, I-38123 Povo, Trento, Italy91Cardiff University, Cardiff CF24 3AA, United Kingdom92Montclair State University, Montclair, NJ 07043, USA

93MTA Eotvos University, “Lendulet” Astrophysics Research Group, Budapest 1117, Hungary94National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan

95School of Mathematics, University of Edinburgh, Edinburgh EH9 3FD, United Kingdom96Indian Institute of Technology, Gandhinagar Ahmedabad Gujarat 382424, India

97University of Szeged, Dom ter 9, Szeged 6720, Hungary98Embry-Riddle Aeronautical University, Prescott, AZ 86301, USA99Tata Institute of Fundamental Research, Mumbai 400005, India

100INAF, Osservatorio Astronomico di Capodimonte, I-80131, Napoli, Italy101University of Michigan, Ann Arbor, MI 48109, USA

102Rochester Institute of Technology, Rochester, NY 14623, USA103NCSA, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA104Universitat de les Illes Balears, IAC3—IEEC, E-07122 Palma de Mallorca, Spain

105University of Bia lystok, 15-424 Bia lystok, Poland106SUPA, University of Strathclyde, Glasgow G1 1XQ, United Kingdom

107IISER-TVM, CET Campus, Trivandrum Kerala 695016, India108Canadian Institute for Theoretical Astrophysics,

University of Toronto, Toronto, Ontario M5S 3H8, Canada109Institute of Applied Physics, Nizhny Novgorod, 603950, Russia

110Pusan National University, Busan 609-735, Korea111Hanyang University, Seoul 133-791, Korea

112University of Adelaide, Adelaide, South Australia 5005, Australia113NCBJ, 05-400 Swierk-Otwock, Poland

114IM-PAN, 00-956 Warsaw, Poland115Monash University, Victoria 3800, Australia

116Seoul National University, Seoul 151-742, Korea117The Chinese University of Hong Kong, Shatin, NT, Hong Kong SAR, China

118University of Alabama in Huntsville, Huntsville, AL 35899, USA119University of Massachusetts-Amherst, Amherst, MA 01003, USA

120ESPCI, CNRS, F-75005 Paris, France121Universita di Camerino, Dipartimento di Fisica, I-62032 Camerino, Italy

122Southern University and A&M College, Baton Rouge, LA 70813, USA123College of William and Mary, Williamsburg, VA 23187, USA

124Instituto de Fısica Teorica, University Estadual Paulista/ICTP SouthAmerican Institute for Fundamental Research, Sao Paulo SP 01140-070, Brazil

125University of Cambridge, Cambridge CB2 1TN, United Kingdom126IISER-Kolkata, Mohanpur, West Bengal 741252, India

127Rutherford Appleton Laboratory, HSIC, Chilton, Didcot, Oxon OX11 0QX, United Kingdom128Whitman College, 345 Boyer Avenue, Walla Walla, WA 99362 USA129National Institute for Mathematical Sciences, Daejeon 305-390, Korea

130Universite de Lyon, F-69361 Lyon, France131Hobart and William Smith Colleges, Geneva, NY 14456, USA

132Janusz Gil Institute of Astronomy, University of Zielona Gora, 65-265 Zielona Gora, Poland133King’s College London, University of London, London WC2R 2LS, United Kingdom

134Andrews University, Berrien Springs, MI 49104, USA135Universita di Siena, I-53100 Siena, Italy

136Trinity University, San Antonio, TX 78212, USA137University of Washington, Seattle, WA 98195, USA

138Kenyon College, Gambier, OH 43022, USA139Abilene Christian University, Abilene, TX 79699, USA

We describe a directed search for continuous gravitational waves in data from the sixth initialLIGO science run. The target was the nearby globular cluster NGC 6544 at a distance of ≈ 2.7 kpc.The search covered a broad band of frequencies along with first and second frequency derivatives

6

for a fixed sky position. The search coherently integrated data from the two LIGO interferometersover a time span of 9.2 days using the matched-filtering F-statistic. We found no gravitational-wave signals and set 95% confidence upper limits as stringent as 6.0× 10−25 on intrinsic strain and8.5 × 10−6 on fiducial ellipticity. These values beat the indirect limits from energy conservation forstars with characteristic spindown ages older than 300 years and are within the range of theoreticalpredictions for possible neutron-star ellipticities. An important feature of this search was use of abarycentric resampling algorithm which substantially reduced computational cost; this method willbe used extensively in searches of Advanced LIGO and Virgo detector data.

I. INTRODUCTION

The LIGO Scientific Collaboration (LSC) and VirgoCollaboration have undertaken numerous searches forcontinuous gravitational waves (GW). None has yet de-tected a signal, but many have placed interesting upperlimits on possible sources. These searches have generallybeen drawn from one of three types.

Targeted searches are aimed at a single known pulsar,with a known precise timing solution. The first search forcontinuous waves, using data from the first initial LIGOscience run (S1), was of this type [1], and subsequentsearches have probed the Crab and Vela pulsars, amongothers [2–7]. A number of these most recent searcheshave been able to set direct upper limits on GW emissioncomparable to or stricter than the indirect “spin-downlimits” (derived from energy conservation, as well as thedistance from Earth of the target, its gravitational-wavefrequency, and the frequency’s first derivative, the “spin-down”) for a few of the pulsars searched.

All-sky searches, as their name suggests, survey theentire sky for neutron stars not seen as pulsars. Theseare very computationally costly, searching over wide fre-quency bands and covering large ranges of spin-down pa-rameters [8–17]. The latest of these have incorporatednew techniques to cover possible binary parameters aswell [18]. Recent all-sky searches have set direct upperlimits close to indirect upper limits derived from galacticneutron-star population simulations [19].

Directed searches sit between these two extremes. Asin the all-sky case, their targets are neutron stars not seenas pulsars, so that the frequency and other parametersare unknown. They focus, however, on a known sky loca-tion (and therefore a known detector-frame Doppler mod-ulation). This directionality allows for searching over awide range of frequencies and frequency derivatives whileremaining much cheaper computationally than an all-skysearch without sacrificing sensitivity. This approach wasfirst used in a search for the accreting neutron star in thelow-mass X-ray binary Sco X-1 [9, 20, 21].

The search for the central compact object (CCO) in thesupernova remnant (SNR) Cassiopeia A (Cas A)[22] wasthe first directed search for a young neutron star withoutelectromagnetically detected pulsation, motivated by theidea that young neutron stars might be promising emit-ters of continuous GW. The Cas A search [22] set upperlimits on GW strain which beat an indirect limit derivedfrom energy conservation and the age of the remnant [23]over a wide frequency band. Other directed searches have

since followed in its footsteps, using different data anal-ysis methods, for supernova 1987A and unseen neutronstars near the galactic center [21, 24]. Most method-ologically similar to this search and the S5 Cas A searchwas a recent search for nine supernova remnants [25],which also used fully coherent integration over observa-tion times on the order of 10 days.

In this article, we describe a search of data from thesixth initial LIGO science run (S6) for potential youngisolated neutron stars with no observed electromagneticpulsations in the nearby (d ≈ 2.7 kpc) globular clus-ter NGC 6544. Globular clusters are unlikely to containyoung neutron stars, but in these dense environmentsolder neutron stars may be subject to debris accretion(see Sec. II C) or other events which could render themdetectable as gravitational wave sources. This particularglobular cluster was chosen so that a computationally-feasible coherent search similar to [22] could beat theage-based indirect limits on GW emission.

The search did not find a GW signal, and hence themain result is a set of upper limits on strain amplitude,fiducial ellipticity, and r-mode amplitude α, similar tothose presented in [22]. An important new feature ofthe search described here was use of a barycentric re-sampling algorithm which substantially reduced compu-tational cost, allowing a search over a larger parameterspace using a longer coherence time (see Sec. II D). Thisbarycentric resampling method will be used extensivelyin searches of Advanced LIGO and Virgo detector data.

This article is structured as follows: In Sec. II wepresent the method, implementation, and results of thesearch. The upper limits set in the absence of a signalare presented in Sec. III, and the results are discussed inSec. IV.

II. SEARCHES

A. Data selection

The sixth initial LIGO science run (S6) extended fromJuly 7 2009 21:00:00 UTC (GPS 931035615) to October21 2010 00:00:00 UTC (GPS 971654415) and includedtwo initial LIGO detectors with 4-km arm lengths, H1 atLIGO Hanford Observatory (LHO) near Hanford, Wash-ington and L1 at LIGO Livingston Observatory (LLO)near Livingston, Louisiana.

After optimization at fixed computing cost determinedan optimum coherence time of 9.2 days (see Sec. IID),

7

S6 sampling timesLabel GPS Start GPS End Dates (UTC)

Week 1 931053000 931657800 Jul 8-15, 2009Week 2 936053000 936657800 Sep 3-10, 2009Week 3 941053000 941657800 Oct 31-Nov 7, 2009Week 4 946053000 946657800 Dec 28, 2009-Jan 4, 2010Week 5 951053000 951657800 Feb 24-Mar 3, 2010Week 6 956053000 956657800 Apr 23-30, 2010Week 7 961053000 961657800 Jun 20-27, 2010Week 8 966053000 966657800 Aug 17-24, 2010Week 9 971053000 971657800 Oct 14-21, 2010

TABLE I. The weeks sampled to find the most sensitive S6data. Times are given both in GPS and UTC calendar dates.

two different methods were used to determine whichdata would be searched, producing two different 9.2-daystretches. Both were searched, allowing for the compari-son of search results between them.

The first method was to look for the most sensitive av-erage data from S6. This was done by taking nine week-long data samples from each detector spaced roughly 55days apart, giving nine evenly spaced weeks throughoutthe duration of S6. The data samples used are shownin Table I. We chose four representative frequencies(100 Hz, 200 Hz, 400 Hz, 600 Hz) and generated joint-detector strain noise power spectral densities (PSDs) in1-Hz bands about these frequencies, using 0.01-Hz bin-ning. The sensitivity hsens was then taken to be

hjsens =

1√

(1/100) ·∑100

i=0(Sih(fi))−1

j

(1)

where Sih(f) represents the PSD value of the ith bin, at

frequency fi, and the index j runs from 1 through 4 andrepresents the four representative frequencies (note thatthis is not an actual estimate of detectable strain). Atall four frequencies, detector sensitivity improved as therun progressed. Using this figure of merit, it was foundthat the final nine days of S6 yielded the most sensitivedata stretch for all four frequencies: October 11-20, 2010(GPS 970840605 – 971621841).

An alternate data selection scheme [22, 25], whichtakes detector duty cycle into account is to maximizethe figure of merit

∑

k,f

1

Sh(f)(2)

where Sh(f) represents the strain noise power spectraldensity at frequency f in the kth Short Fourier Transform(SFT), and the sum is taken across all frequencies f inthe search band and all SFTs in a given 9.2-day (seeSec. II D below) observation time. The SFT format isscience-mode detector data split into 1800s segments,band-pass filtered from 40–2035 Hz, Tukey windowed in

the time domain, and Fourier transformed. This methodfavored a different data stretch: July 24–August 2, 2010(GPS 964007133 – 964803598). This second data stretchhad slightly worse average sensitivity than the first, buta higher detector livetime: our first (October) data setcontained 374 SFTs (202 from Hanford and 172 from Liv-ingston) with average sensitivity h200Hz

sens = 1.92 × 10−23;the second (July-August) data set contained 642 SFTs(368 from Hanford and 274 from Livingston) with aver-age sensitivity h200Hz

sens = 1.95 × 10−23.

B. Analysis method

The analysis was based on matched filtering, the op-timal method for detecting signals of known functionalform. To obtain that form we assumed that the poten-tial target neutron star did not glitch (suffer an abruptfrequency jump) or have significant timing noise (addi-tional, possibly stochastic, time dependence of the fre-quency) [26] during the observation. We also neglectedthird and higher derivatives of the GW frequency, basedon the time span and range of f and f (the first twoderivatives) covered. The precise expression for the in-terferometer strain response h(t) to an incoming contin-uous GW also includes amplitude and phase modulationby the changing of the beam patterns as the interferom-eter rotates with the earth. It depends on the source’ssky location and orientation angles, as well as on the pa-rameters of the interferometer. The full expression canbe found in [27].

The detection statistic used was the multi-interferometer F-statistic [28], based on the single-interferometer F-statistic [27]. This combines theresults of matched filters for the signal in a way that iscomputationally fast and nearly optimal [29]. AssumingGaussian noise, 2F is drawn from a χ2 distribution withfour degrees of freedom.

We used the implementation of the F-statistic inthe LALSuite package [30]. In particular most ofthe computing power of the search was spent in theComputeFStatistic v2 program. Unlike the versionused in preceding methodologically similar searches [22,25], this one implements an option to use a barycentricresampling algorithm which significantly speeds up theanalysis.

The method of efficiently computing the F-statisticby barycentering and Fast-Fourier-transforming the datawas first proposed in [27]. Various implementations ofthis method have been developed and used in previoussearches, such as [31–33]. Here we are using a new LAL-Suite [30] implementation of this method, which evolvedout of [33], and which will be described in more detail in afuture publication. It converts the input data into a het-erodyned, downsampled timeseries weighted by antenna-pattern coefficients, and then resamples this timeseriesat the solar system barycenter using an interpolationtechnique. The resampled time series is then Fourier-

8

transformed to return to the frequency domain, and fromthere the F-statistic is calculated. For this search, bothsingle-detector and multi-detector F-statistics were cal-culated (see Vetoes section below).

Timing tests run on a modern processor (ca. 2011)showed that the resampling code was more than 24 timesfaster in terms of seconds per template per SFT. Thisimprovement, by more than an order of magnitude, wasused to perform a deeper search over a wider parame-ter space than previously possible for the computationalcost incurred (see target selection and search parametersbelow).

C. Target selection

Unlike previous directed searches, this one targets aglobular cluster. Since stars in globular clusters are veryold, it is unlikely that a young neutron star will be foundin such an environment. However, some neutron starsare known to be accompanied by debris disks [34] andeven planets [35–37]. In the densely populated core ofa globular cluster, close encounters may stimulate bom-bardment episodes as debris orbits are destabilized, akinto cometary bombardments in our solar system when theOort cloud is perturbed [38]. A neutron star which hasrecently accreted debris could have it funneled by themagnetic field into mountains which relax on timescalesof 105–108 years [39] and emit gravitational waves forthat duration. Other mechanisms are likely to last a fewyears at most [40]. Hence an old neutron star could bea good gravitational wave source with a low spin-downage.

The first step in picking a globular cluster is a figure ofmerit based on that for directed searches for supernovaremnants [23], an indirect upper limit on gravitationalwave strain based on energy conservation and the age ofthe object. Here the inverse of the object age is replacedby the interaction rate of the globular cluster, whichscales like density(3/2) times core radius2 [38, 41], reflect-ing the mean time since last bombardment. It is hard toknow when the most recent bombardment episode was,and thus the constant factor out in front, but globularclusters can be ranked with respect to each other by amaximum-strain type figure of merit

h0 ∝ ρ3/4c rc/d, (3)

where ρc is the globular cluster core density, rc is thecore radius, d is the distance to the cluster, and thus rc/dis the angular radius of the core. We ranked the Harriscatalog of globular clusters [42, 43] by this figure of meritand looked at the top few choices, which were mainlynearby core-collapsed clusters. The closest is NGC 6397at ≈ 2.2 kpc, but it is at high declination. This lessensthe Doppler modulation of any gravitational wave signal,making it harder to distinguish from stationary spectralline artifacts, which tend to contaminate searches at high

declination near the ecliptic pole. Hence we chose thenext closest, NGC 6544, which is at a declination of lessthan 30 degrees and only slightly further away at ≈ 2.7kpc.

We restrict the search described below to sources forwhich the bombardment history corresponds to a charac-teristic spindown age older than 300 years. The figure of300 years is mainly a practical consideration: the cost ofa search rises steeply for lower spin-down ages, and 300years proved tractable for the Cas A search [22].

D. Search parameter space

An iterative method was used to generate the param-eter space to be searched. Starting with an (assumed)spin-down age no younger than 300 years, a braking in-dex n = 5 (see below), and the known distance to theglobular cluster, we calculated the age-based indirect up-per limit. This is an optimistic limit on the gravitationalwave strain h0 which assumes that all energy lost as thetarget neutron star spins down is radiated away as grav-itational waves[23]:

h0 ≤ 1

d

√

5GI

2c3τ(n − 1). (4)

Here d is the distance to the target, τ the assumed ageof the target object, and I a fiducial moment of inertiafor a neutron star (1038kg · m2). G and c are the grav-itational constant and the speed of light, respectively.This age-based limit was then superimposed on a curveof expected upper limits in the absence of signal for theLIGO detectors, obtained from the noise power spectraldensity (PSD) harmonically averaged over all of S6 andboth interferometers. A running median with a 16-Hzwindow was further applied to smooth the curve. Thecurve is given by:

h95%0 = Θ

√

Sh

Tdata(5)

where Sh is the harmonically averaged noise, Tdata is thecoherence time (the total data livetime searched coher-ently), initially estimated at two weeks, and Θ is a sen-sitivity factor that includes a trials factor, or number oftemplates searched, and uncertainty in the source orien-tation [23]. For a directed search like ours, Θ is approx-imately 35 [23, 44]. The intersection of this coherence-time adjusted upper limit curve and our indirect limit(Eq. (4)) gives an initial frequency band over which theindirect limit can be beaten. The braking index is relatedto the frequency parameters by the definition:

n =ff

f2. (6)

9

Assuming a braking index n between 2 and 7 covers mostaccepted neutron star models (n = 5, the neutron starradiating all energy as gravitational waves via the massquadrupole, is used to obtain the indirect limit). We al-low the braking indices in these expressions to range from2 to 7 independently, to reflect the fact that in generalmultiple processes are operating and f is not a simplepower law. This constraint on the braking indices thenproduces limits on the frequency derivatives given by [23]

f

τ≤ −f ≤ f

6τ(7)

for the spindown at each frequency and

2f2

f≤ f ≤ 7f2

f(8)

for the second spindown at each (f, f). The step sizes forfrequency and its derivatives are given by the equations[33, 45, 46]

df =2√

3m

π

1

Tdata, (9)

df =12√

5m

π

1

T 2data

, (10)

and

df =20√

7m

π

1

T 3data

. (11)

where m is the mismatch parameter, the maximum loss of2F due to discretization of the frequency and derivatives[47, 48]. This search used a mismatch parameter m = 0.2at all stages.

From these relations the total number of templates(points in frequency parameter space) to be searched canbe calculated, and with knowledge of the per-templatetime taken by the code (obtained from timing tests), thetotal computing time can be obtained. Limiting the tar-get computing time, in our case to 1000 core-months,then allows us to solve for the coherence time Tdata, whichwe then feed back into Eq. (5) to begin the process anewuntil it iteratively converges on a parameter space andaccompanying coherence time. The iterative algorithmthus balances the computational gains from resamplingbetween the use of a longer coherence time (giving bet-ter sensitivity) and the expansion of the parameter spaceover which the indirect limit can be beaten (caused bythe improved sensitivity). The result for the globularcluster NGC 6544 is a search over the frequency range92.5 Hz to 675 Hz, with a coherence time of 9.2 days.

Band Job min. and max. Notefrequency (Hz)

370.1 370.1 370.2 L1 Output Mode Cleaner (OMC) Jitter Line393.1 393.1 393.2 H1 Calibration Line396.7 396.7 396.8 L1 Calibration Line400.2 400.2 400.3 H1 OMC Quad Photodiode (QPD) Line403.8 403.8 403.9 L1 OMC QPD Line417.1 417.1 417.2 H1 OMC QPD Line580.0 580.0 580.1 L1 2Hz Harmonic

TABLE II. Search sub-bands that, due to the identified dis-turbances, produced an excessive number of candidates andwere aborted. The 580.0 Hz sub-band had to be stopped onlyfor the July-August run; the other six bands were vetoed inboth searches.

The peculiar velocities of globular clusters are negli-gible, as they represent an essentially constant Dopplershift of order 1 × 10−3; so is velocity dispersion, whichis an order of magnitude smaller. Since we search downto 300-year timescales, the acceleration of the cluster isalso not an issue [49].

E. Implementation

All searches were run on the LIGO-Caltech Comput-ing Cluster at the California Insitute of Technology inPasadena, CA, under the control of the Condor queu-ing system for parallel processing. The search pro-cess was split into 5825 individual Condor jobs, each ofwhich searched over a 0.1-Hz subband and correspondingswathes of (f , f). The number of templates searched byeach job thus varied as a function of frequency.

Each search job produced three distinct outputs. First,a record was made of all candidates with 2F above 45.0,a choice of recording different from the the fifth initialLIGO science run (S5) search which recorded the loud-est 0.01% of events. This was needed because of thecontamination of the S6 noise by detector artifacts, aswell as limits on the disk space available and the in-put/output capability of the cluster filesystem. Second,a histogram of 2F values for all templates searched wasproduced to verify that the data matched the expectedchi-square distribution (described in Subsec. II B above).Last, each job produced a record of the loudest (highest-2F-valued) candidate in its 0.1-Hz band, regardless ofthreshold. This data was used in the setting and valida-tion of upper limits (see Section III below).

F. Vetoes

A high value of 2F is not enough to claim a detec-tion, since instrumental artifacts lead to non-Gaussianand/or non-stationary noise in many narrow frequencybands. A variety of veto techniques were used to trimdown the initial list of candidates and arrive at a finallist of outliers.

10

Six 0.1 Hz sub-bands (see Table (II)) had to be man-ually aborted in both searches, with a seventh abortedin the July-August search, as even with the thresholdin place, they produced an excessive number of candi-dates. Each of these subbands was compared to recordsof known noise artifacts and disturbances in the detec-tor, and in each case a known instrumental line was con-firmed. These sub-bands were later rerun with the recordof candidates disabled in order to produce histograms andloudest-outlier files for upper limit validation.

To protect against spurious noise lines, a second vetobased on the F-statistic consistency veto introduced in[15] was used. This uses the fact that an astrophysicalsignal should have a higher joint value of 2F (combiningdata from the two interferometers) than in either inter-ferometer alone. Recorded candidates that violate thisinequality were vetoed. This is a simpler version of themore recent line veto [50].

Finally, to enforce coincidence between detectors, asingle-detector threshold was employed. Since a true as-trophysical signal should be present in both detectors at asignificant level, any candidates passing the initial joint-detector detection criteria (see II G) also had to pass anadditional threshold on the individual-detector values of2F .

The 0.1 Hz band between 200 and 200.1 Hz was ar-bitrarily chosen as a test band. The joint-detector 2Fvalues were taken from the loudest-candidate files andused to semi-analytically compute [51] an estimate ofthe 95% upper limit for that subband using the SFTsemployed by the search. Sets of 1,000 software injectionswere performed with strengths of 100%, 80%, 60%, 40%and 20% of this estimated upper limit. The results wereused to set a threshold of 2F ≥ 20 in each individualdetector, leading to an additional false dismissal rate of1.5% of injections at the 95% confidence upper limit es-timate. Candidates failing to meet this criterion werevetoed.

G. Detection criteria and results

The results of a mock data challenge (MDC) wereused to set a detection criterion for the joint-detector2F value. The mock data challenge consisted of a setof 1577 artificial continuous wave (CW) signals injectedinto a set of real detector data from S6, which were thensearched for using the same resampled F-Statistic usedin the search. A survey of the loudest joint-detector 2Fvalue reported for background subbands known to be freeof injected signals for the band between 200 Hz and 240Hz (used in a pilot MDC run) gave a mean loudest joint-detector 2F ≈ 55. While we cannot be sure there werezero true signals in these subbands, the fact that no trueCW signal has ever been reported in the S6 data im-plies that the odds that real signals were present, in highenough number and strength to significantly alter thatmean, are very low. This threshold was confirmed to

be appropriate for other bands as well, via visual ex-amination of distributions of the detection statistic in alarge sampling of 0.1 Hz bins throughout the full searchband and via examination of the loudest detection statis-tic from each 0.1 Hz subband for all 0.1 Hz subbands.Given this background level, the detection criterion waschosen to be joint-detector 2F ≥ 60 to maintain highefficiency and low false-alarm rate (the false-alarm ratewas 3.17% in these pilot subbands).

With these detection criteria, a search was carried outin S6 data. The lists of all templates with joint-detector2F greater than 45.0 were filtered for the individual de-tector threshold and the consistency veto, both singlyand in tandem. If the loudest template failed eithercheck, the list was used to move to the next-loudest tem-plate until the loudest template passing all thresholdsand vetoes was identified. This created three sets ofresults (threshold-only, veto-only, and threshold+veto)which could all be queried independently.

The joint 2F values for the loudest single template(passing all thresholds and vetoes) in each 0.1 Hz sub-band were collated into lists spanning 10Hz (100 joint2F values per list). These lists were then parsed, andany joint 2F values greater than the joint 2F thresh-old of 60 were identified. Each such entry’s correspond-ing template was then added to a list of outliers. Thismethod produced a list of 168 outliers for the entirety ofthe search band in the October data, and a list of 155outliers for the entirety of the search band in the July-August data.

These outliers were then tested using time shifts andextended looks. In a time shift, the frequency param-eters of the outliers from each data stretch (Octoberand July-August) were evolved forwards or backwardsin time, as appropriate, and sought in the opposite datastretch, under the assumption that a true astrophysicalsignal should be present in both data sets for the im-plicitly long-lived CW signals searched for here. A setof 1000 software injections (simulated signals with ran-domly generated parameters) underwent the same treat-ment to provide a baseline 2F threshold for signal detec-tion, and outliers surpassing the threshold were consid-ered present.

In an extended look, each outlier was sought in an ex-panded 20-day coherence time encompassing the originalnine-day coherence time; the same assumption of signalcontinuity would predict, roughly, a doubling of the 2Fvalue for a doubling of coherence time. These cases aswell were tested with software injections to determine athreshold.

In both time shifts and extended looks, the searcheswere conducted over a parameter space envelope obtainedby starting at the outlier frequency parameters (f, f , f)±2 bins, and evolving those ranges backwards or forwardsin time using the extremum values of the next derivative(e.g., f evolved at maximum f , f evolved at maximum

f) to achieve a conservatively wide envelope.Outliers detected in time shifts and extended looks

11

with joint 2F greater than the threshold established bythe software injections were labeled candidates. The timeshift and extended look tests were not cumulative; anoutlier needed only to survive any one test, not all ofthem, to persist as a candidate. The software injectionthreshold for both types of test was placed at a value forjoint 2F yielding 80% injection recovery; because eachoutlier would receive further consideration if it passedeither test, the false dismissal probability for the firstfollow-up stage was ≈ 4%. The combined 323 outliersproduced only seven candidates, listed in Table III.

These seven candidates were subject to manual fol-lowup. They were compared to strain histograms of run-averaged (i.e., over all of S6) spectra from each detec-tor, to identify instrumental noise lines which could beresponsible. In five of the seven cases, the strain his-tograms gave clear evidence of an instrumental noise lineresponsible for the candidate, and in these cases recordsof prior detector characterization studies were consultedto provide explanations for the noise artifacts. In thosecases the artifact is listed in Table III as well. Two of theartifacts arose from hardware injections located at otherpoints in the sky, used to test interferometer response[25].

The final remaining two candidates, which were notassociated with known instrumental lines, were given an-other subsequent round of followup: a time shift andextended look performed in data from June 2010, thefarthest removed (in the time domain) available data ofcomparable sensitivity. The large time separation createsa large difference in the Doppler corrections needed to re-construct an astrophysical source, making these correc-tions unlikely to reinforce instrumental or environmentalartifacts. Both outliers failed to pass the 2F thresholdsestablished by software injections in any of their Junetests.

The loudest 2F value expected in the absence of signaldepends on the number of templates searched [51];1 forour search, the largest expected 2F value lies in the range72 ≤ 2F ≤ 80 with 90% confidence. The 2F valuesassociated with the two remaining candidates, outliers 79and 131, were joint-detector 2F = 61.3 and joint-detector2F = 61.9, respectively. The final two candidates’ failureto pass the June tests and their marginal 2F values ledus to dismiss them as noise fluctuations.

For ease of understanding, Table IV illustrates the suc-cessive stages of followup, and the number of remainingcandidates after each step.

Thus no credible gravitational wave signals were de-tected by our search. In the absence of a detection, wecan set upper limits on the possible strength of gravita-tional waves in our data.

1 The NT templates used in our searches are not completely inde-pendent, but can be represented by N statistically independenttemplates where N ≈ 0.88NT . See section 8.7 of [51].

III. UPPER LIMITS

A. Methods

The method of setting upper limits was a variation onthat used in [22]and [25]. This upper limit determinationis based only of the F-statistic and does not include ad-ditional criteria involved in candidate followup. We splitthe frequency band into 0.1-Hz subbands, and for each ofthese used a semi-analytic Monte Carlo method to esti-mate a 95% upper limit, defined as the strain h0 at whichour detection criterion would successfully detect 95% ofsignals. Due to the high computational cost of individu-ally verifying all 5800 such subbands, these 0.1-Hz upperlimit bands were consolidated into 1-Hz subbands. Foreach such 1-Hz band, we performed 1,000 software injec-tions, split into eight groups of 125 signals. The strainh0 of each group was ±5%,±10%,±15%, and ± 20% ofthe semi-analytic upper limit estimates (ULEs), respec-tively. A software injection was considered validated ifit returned a value of 2F greater than or equal to theloudest outlier in its 0.1-Hz subband, thus maintainingthe original granularity. For each 1-Hz band, these 1,000injections thus produced eight points on a detection ef-ficiency curve. We then used a least-squares method toproduce a sigmoid fit to the data points, and from thiscurve determined a true 95% upper limit, defined as thevalue of h0 at which the fitting curve intersected 95% ef-ficiency. Figure 1 shows such a plot for a sample band.In cases where the 95% point was extrapolated (as op-posed to interpolated) from the eight points, and in caseswhere the uncertainty on the 95% point was greater than5%, a new set of eight points were generated using the95% point as the initial h0 estimate and a 95% point wasdetermined from the combined sets (e.g., a curve was fitto 16 points after one rerun, 24 points after two reruns,etc.).

A small number of 0.1-Hz bands had outliers so largethat the semi-analytic method failed to converge to anestimate for h0. Instrumental artifacts at these frequen-cies were identified using S6 run-averaged spectra andthe respective 1-Hz bands were then rerun with the dis-turbed 0.1-Hz subband excluded. The excluded bandsare detailed in Table V.

B. Results

Figure 2 shows the 95% confidence upper limits (ULs)over the full band for the July-August data set, whichwas the more sensitive of the two because of its muchgreater livetime (642 SFTs vs. 374 SFTs for the Octoberdata set). The blue curve represents the expected sensi-tivity of the search for this data set, computed from thepower spectral density at each frequency; there is goodagreement with the ULs. The black line represents theage-based limit derived when first considering the param-eter space. Its intersection with the ULs at either end of

12

July-August DataOutlier Search f (Hz) Followup f (Hz) Search 2FJ Followup 2FJ Artifact, if any

27 192.4907 192.4956 612.969 300.712 Hardware Injection74 392.2232 392.2315 189.903 173.787 Clock noise77 394.0231 394.0307 228.268 197.300 Digital line

October data27 192.4195 192.4313 875.575 484.254 Hardware Injection79 403.6424 403.8612 114.626 61.331 —–85 417.0394 417.1384 60.309 176.200 H1 Output Mode

Cleaner Line131 575.9658 576.5057 61.943 53.805 —–

TABLE III. The seven candidates that passed the first round of outlier followup. The columns give, respectively: the outlier’sidentifying number; the frequency of the outlier in the search; the frequency of the outlier in the followup data set in which itappeared; the 2F value of the outlier in the search; the 2F value of the outlier in the followup data set in which it appeared; theexplanation, if any, provided by comparison with run-averaged strain histograms in conjunction with detector characterizationrecords. For outliers due to random noise and for many instrumental artifacts, we expect the follow-up 2F to be smaller thanthe originally obtained 2F , in contrast to true signals for which 2F should increase with observation time.

Followup stage Remaining candidates (nomenclature)Initial search 323 (outliers)

Time shifts + extended looks 7 (candidates)Manual followup: strain histograms 2 (candidates)

June data tests + loudest expected 2F 0 (candidates)

TABLE IV. An illustration of the followup process, trackingthe number of remaining candidates (and the nomenclatureused for them in this paper) after each successive stage offollowup.

the plot is a confirmation that we correctly estimated thefrequency band to search over.

Figure 3 is a similar plot converting the upper limitson h0 to upper limits on fiducial ellipticity ǫ, using theformula [52]

ǫ =c4

4π2G

d

Izzf2h0. (12)

The black curve represents the age-based limit on fiducialellipticity, using the same assumptions (braking indexn = 5, age τ = 300 years) used in the parameter spacecalculations.

The amplitude α of r-mode oscillations in a neutronstar is related to the gravitational wave strain amplitudeh0 by [53]

α = 0.028

(

h0

10−24

) (

r

1 kpc

) (

100 Hz

f

)3

. (13)

Figure 4 uses this formula to convert the upper limitson h0 to upper limits on the r-mode amplitude α. Theblack curve represents the age-based limit on α, under

FIG. 1. A demonstration of the upper limit validation tech-nique for a sample band (101 Hz; October data). The x-axisis hnom, h0 divided by the ULE for this upper-limit band;the eight points represent detection efficiencies for eight setsof 125 software injections. These eight points are then fit toa sigmoid curve (in black); the 95% upper limit can then beread off from the point where the curve crosses 95% detectionefficiency.

the same age assumptions used for h0 and ellipticity, butwith n = 7, which characterizes r-mode emission. In allthree plots, the age-based limit is beaten everywhere theupper limits lie below the black curve.

IV. DISCUSSION

This search has placed the first explicit upper lim-its on continuous gravitational wave strength from thenearby globular cluster NGC 6544 for spin-down ages asyoung as 300 years, and is the first directed CW search

13

FIG. 2. Upper limits at 95% confidence (red circles) compared to the upper limit estimate curve of the detector (blue curve)and the initial age-based limit on h0 (black line). The upper limit estimate curve is based on Eq. (5) over the 9.2 days ofcoherence time, corrected for detector livetime and sky location and summed over detectors in inverse quadrature.

FIG. 3. Upper limits at 95% confidence (red circles) comparedto the initial age-based limit on fiducial ellipticity ǫ (blackline).

for any globular cluster. The most stringent upper lim-its on strain (hUL

0 ) obtained were hUL0 = 6.7 × 10−25

for the 173-174 Hz band in the October data set, andhUL

0 = 6.0 × 10−25 for the 170-171 Hz band in the July-August data.

The best upper limit is comparable to the best upperlimit of 7×10−25 at 150 Hz obtained by the Cas A search[22]; the recent search over nine supernova remnants,done without resampling, [25] set upper limits as low as3.7 × 10−25 for the supernova remnant G93.3+6.9, but

FIG. 4. Upper limits at 95% confidence (red circles) comparedto the initial age-based limit on r-mode amplitude α (blackline).

used a coherence time of over 23 days (and a frequencyband of only 264 Hz). The same analysis set a compa-rable 95% upper limit of 6.4 × 10−25 for the supernovaremnant G1.9+0.3, as expected given its similar declina-tion and the search’s similar coherence time (9.2 days forNGC 6544 vs. 9.1 days for G1.9+0.3). Note, however,that the G1.9+0.3 search was limited to a 146 Hz searchband, compared to 583 Hz for NGC 6544. The searchreported here was carried out at substantially less com-putational cost because of barycentric resampling, and

14

Affected 1-Hz Band Vetoed 0.1-Hz subband Artifact180 180.0-180.1 Power mains har-

monic192 192.4-192.5 Hardware injection217 217.5-217.6 Known instrumental

artifact234 234.0-234.1 Digital line (L1)290 290.0-290.1 Digital line (L1)370 370.1-370.2 L1 Output Mode

Cleaner Line393 393.1-393.2 Calibration line (H1)396 396.7-396.8 Calibration Line (L1)400 400.2-400.3 H1 Output Mode

Cleaner Line403 403.8-403.9 L1 Output Mode

Cleaner Line417 417.1-417.2 H1 Output Mode

Cleaner Line580 580.0-580.1 Digital line (L1)

TABLE V. The twelve 0.1-Hz bands with outliers too largefor the semi-analytic method to converge to an estimate forh0. These 0.1-Hz subbands were excluded from upper limitanalysis; the quoted upper limits (Figure 2) represent the re-mainder of their respective 1-Hz bands. The first column liststhe affected 1-Hz band; the second column lists the respectivevetoed 0.1-Hz subband; the third column lists the instrumen-tal artifact identified using S6 run-averaged spectra.

could thus search over a much larger parameter space.The best upper limit on fiducial ellipticity, established

using the July-August data set, was ǫ = 8.5 × 10−6, forthe 1-Hz band starting at 670 Hz. This is comparable tothe best upper limit (4 × 10−5) obtained by the Cas Asearch [51]; the supernova remnant search [25] set a com-parable upper limit on fiducial ellipticity at 7.6 × 10−5

for the supernova remnant G1.9+0.3.These ellipticities are within the range of maximum

theoretical ellipticities predicted for stars with some ex-otic phases in the core [54, 55], and the lowest of them isachievable for purely nucleonic stars with a sufficientlystiff equation of state and low mass [55]. Hence thesearch could have detected some exotic stars if they weresupporting close to their maximum possible ellipticity;however, the lack of a detection cannot be used to in-fer constraints on the composition of any star, since thedeformation could be much less than its maximum sup-portable value.

The first observing run of the Advanced LIGO detec-tors began in September 2015 [56] and the sensitivityof the detectors is already three times or more betterthan that used in this search, with an order of magni-tude improvement over S6 expected eventually [57]. Thebarycentric resampling algorithm first implemented inthis search is being used extensively in CW searches in

the advanced detector era; it has been integrated intothe search codes for both coherent searches (like the su-pernova remnant search) [58] and semi-coherent searches(Einstein@Home).

V. ACKNOWLEDGMENTS

The authors gratefully acknowledge the support of theUnited States National Science Foundation (NSF) forthe construction and operation of the LIGO Laboratoryand 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 ofNiedersachsen/Germany for support of the constructionof Advanced LIGO and construction and operation ofthe GEO600 detector. Additional support for AdvancedLIGO was provided by the Australian Research Council.The authors gratefully acknowledge the Italian IstitutoNazionale di Fisica Nucleare (INFN), the French CentreNational de la Recherche Scientifique (CNRS) and theFoundation for Fundamental Research on Matter sup-ported by the Netherlands Organisation for Scientific Re-search, for the construction and operation of the Virgodetector and the creation and support of the EGO consor-tium. The authors also gratefully acknowledge researchsupport from these agencies as well as by the Council ofScientific and Industrial Research of India, Departmentof Science and Technology, India, Science & Engineer-ing Research Board (SERB), India, Ministry of HumanResource Development, India, the Spanish Ministerio deEconomıa y Competitividad, the Conselleria d’Economiai Competitivitat and Conselleria d’Educacio, Cultura iUniversitats of the Govern de les Illes Balears, the Na-tional Science Centre of Poland, the European Commis-sion, the Royal Society, the Scottish Funding Council,the Scottish Universities Physics Alliance, the Hungar-ian Scientific Research Fund (OTKA), the Lyon Insti-tute of Origins (LIO), the National Research Foundationof Korea, Industry Canada and the Province of Ontariothrough the Ministry of Economic Development and In-novation, the Natural Science and Engineering ResearchCouncil Canada, Canadian Institute for Advanced Re-search, the Brazilian Ministry of Science, Technology,and Innovation, Fundacao de Amparo a Pesquisa do Es-tado de Sao Paulo (FAPESP), Russian Foundation forBasic Research, the Leverhulme Trust, the Research Cor-poration, Ministry of Science and Technology (MOST),Taiwan and the Kavli Foundation. The authors grate-fully acknowledge the support of the NSF, STFC, MPS,INFN, CNRS and the State of Niedersachsen/Germanyfor provision of computational resources.

This document has been assigned LIGO Laboratorydocument number LIGO-P1500225.

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