Constraining the p-Mode-g-Mode Tidal Instability with GW170817

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published as:

Constraining the p-Mode–g-Mode Tidal Instability with

GW170817

B. P. Abbott et al. (LIGO Scientific Collaboration and Virgo Collaboration)

Phys. Rev. Lett. 122, 061104 — Published 13 February 2019

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B. P. Abbott,1 _{R. Abbott,}1 _{T. D. Abbott,}2 _{F. Acernese,}3, 4 _{K. Ackley,}5 _{C. Adams,}6 _{T. Adams,}7 _{P. Addesso,}8

R. X. Adhikari,1 _{V. B. Adya,}9, 10 _{C. A↵eldt,}9, 10 _{B. Agarwal,}11 _{M. Agathos,}12_{K. Agatsuma,}13 _{N. Aggarwal,}14

O. D. Aguiar,15_{L. Aiello,}16, 17 _{A. Ain,}18_{P. Ajith,}19 _{B. Allen,}9, 20, 10 _{G. Allen,}11 _{A. Allocca,}21, 22 _{M. A. Aloy,}23

P. A. Altin,24 _{A. Amato,}25 _{A. Ananyeva,}1 _{S. B. Anderson,}1 _{W. G. Anderson,}20 _{S. V. Angelova,}26 _{S. Antier,}27

S. Appert,1_{K. Arai,}1 _{M. C. Araya,}1 _{J. S. Areeda,}28 _{M. Ar`ene,}29 _{N. Arnaud,}27, 30 _{K. G. Arun,}31 _{S. Ascenzi,}32, 33

G. Ashton,5 _{M. Ast,}34 _{S. M. Aston,}6 _{P. Astone,}35 _{D. V. Atallah,}36 _{F. Aubin,}7 _{P. Aufmuth,}10 _{C. Aulbert,}9

K. AultONeal,37 _{C. Austin,}2_{A. Avila-Alvarez,}28 _{S. Babak,}38, 29 _{P. Bacon,}29_{F. Badaracco,}16, 17 _{M. K. M. Bader,}13

S. Bae,39 _{P. T. Baker,}40 _{F. Baldaccini,}41, 42 _{G. Ballardin,}30 _{S. W. Ballmer,}43_{S. Banagiri,}44 _{J. C. Barayoga,}1

S. E. Barclay,45 _{B. C. Barish,}1 _{D. Barker,}46 _{K. Barkett,}47 _{S. Barnum,}14 _{F. Barone,}3, 4 _{B. Barr,}45 _{L. Barsotti,}14

M. Barsuglia,29 _{D. Barta,}48 _{J. Bartlett,}46 _{I. Bartos,}49 _{R. Bassiri,}50 _{A. Basti,}21, 22 _{J. C. Batch,}46 _{M. Bawaj,}51, 42

J. C. Bayley,45 M. Bazzan,52, 53 B. B´ecsy,54 C. Beer,9 M. Bejger,55 I. Belahcene,27 A. S. Bell,45 D. Beniwal,56 M. Bensch,9, 10 _{B. K. Berger,}1_{G. Bergmann,}9, 10 _{S. Bernuzzi,}57, 58 _{J. J. Bero,}59_{C. P. L. Berry,}60 _{D. Bersanetti,}61

A. Bertolini,13 _{J. Betzwieser,}6 _{R. Bhandare,}62 _{I. A. Bilenko,}63 _{S. A. Bilgili,}40 _{G. Billingsley,}1_{C. R. Billman,}49

J. Birch,6 R. Birney,26 O. Birnholtz,59 S. Biscans,1, 14 S. Biscoveanu,5 A. Bisht,9, 10 M. Bitossi,30, 22 M. A. Bizouard,27 _{J. K. Blackburn,}1 _{J. Blackman,}47 _{C. D. Blair,}6 _{D. G. Blair,}64 _{R. M. Blair,}46_{S. Bloemen,}65

O. Bock,9 _{N. Bode,}9, 10 _{M. Boer,}66 _{Y. Boetzel,}67 _{G. Bogaert,}66_{A. Bohe,}38_{F. Bondu,}68_{E. Bonilla,}50 _{R. Bonnand,}7

P. Booker,9, 10 _{B. A. Boom,}13_{C. D. Booth,}36_{R. Bork,}1 _{V. Boschi,}30 _{S. Bose,}69, 18 _{K. Bossie,}6 _{V. Bossilkov,}64

J. Bosveld,64 _{Y. Bou↵anais,}29 _{A. Bozzi,}30 _{C. Bradaschia,}22 _{P. R. Brady,}20 _{A. Bramley,}6 _{M. Branchesi,}16, 17

J. E. Brau,70 _{T. Briant,}71 _{F. Brighenti,}72, 73 _{A. Brillet,}66 _{M. Brinkmann,}9, 10 _{V. Brisson,}27,⇤ _{P. Brockill,}20

A. F. Brooks,1 _{D. D. Brown,}56 _{S. Brunett,}1 _{C. C. Buchanan,}2 _{A. Buikema,}14 _{T. Bulik,}74 _{H. J. Bulten,}75, 13

A. Buonanno,38, 76_{D. Buskulic,}7_{C. Buy,}29_{R. L. Byer,}50 _{M. Cabero,}9_{L. Cadonati,}77 _{G. Cagnoli,}25, 78 _{C. Cahillane,}1

J. Calder´on Bustillo,77 _{T. A. Callister,}1 _{E. Calloni,}79, 4 _{J. B. Camp,}80 _{M. Canepa,}81, 61 _{P. Canizares,}65

K. C. Cannon,82_{H. Cao,}56_{J. Cao,}83 _{C. D. Capano,}9 _{E. Capocasa,}29_{F. Carbognani,}30 _{S. Caride,}84_{M. F. Carney,}85

J. Casanueva Diaz,22_{C. Casentini,}32, 33 _{S. Caudill,}13, 20 _{M. Cavagli`a,}86 _{F. Cavalier,}27 _{R. Cavalieri,}30_{G. Cella,}22

C. B. Cepeda,1_{P. Cerd´a-Dur´an,}23 _{G. Cerretani,}21, 22 _{E. Cesarini,}87, 33 _{O. Chaibi,}66 _{S. J. Chamberlin,}88_{M. Chan,}45

S. Chao,89 _{P. Charlton,}90 _{E. Chase,}91 _{E. Chassande-Mottin,}29 _{D. Chatterjee,}20 _{Katerina Chatziioannou,}92

B. D. Cheeseboro,40 _{H. Y. Chen,}93 _{X. Chen,}64 _{Y. Chen,}47 _{H.-P. Cheng,}49 _{H. Y. Chia,}49 _{A. Chincarini,}61

A. Chiummo,30 _{T. Chmiel,}85_{H. S. Cho,}94_{M. Cho,}76 _{J. H. Chow,}24_{N. Christensen,}95, 66_{Q. Chu,}64 _{A. J. K. Chua,}47

S. Chua,71 _{K. W. Chung,}96 _{S. Chung,}64 _{G. Ciani,}52, 53, 49 _{A. A. Ciobanu,}56 _{R. Ciolfi,}97, 98 _{F. Cipriano,}66

C. E. Cirelli,50 _{A. Cirone,}81, 61 _{F. Clara,}46 _{J. A. Clark,}77 _{P. Clearwater,}99 _{F. Cleva,}66 _{C. Cocchieri,}86

E. Coccia,16, 17 _{P.-F. Cohadon,}71 _{D. Cohen,}27 _{A. Colla,}100, 35 _{C. G. Collette,}101 _{C. Collins,}60 _{L. R. Cominsky,}102

M. Constancio Jr.,15 _{L. Conti,}53_{S. J. Cooper,}60 _{P. Corban,}6 _{T. R. Corbitt,}2 _{I. Cordero-Carri´on,}103_{K. R. Corley,}104

N. Cornish,105 _{A. Corsi,}84 _{S. Cortese,}30_{C. A. Costa,}15 _{R. Cotesta,}38 _{M. W. Coughlin,}1 _{S. B. Coughlin,}36, 91

J.-P. Coulon,66 _{S. T. Countryman,}104 _{P. Couvares,}1 _{P. B. Covas,}106_{E. E. Cowan,}77_{D. M. Coward,}64 _{M. J. Cowart,}6

D. C. Coyne,1 _{R. Coyne,}107 _{J. D. E. Creighton,}20 _{T. D. Creighton,}108 _{J. Cripe,}2 _{S. G. Crowder,}109_{T. J. Cullen,}2

A. Cumming,45 L. Cunningham,45 E. Cuoco,30T. Dal Canton,80 G. D´alya,54 S. L. Danilishin,10, 9 S. D’Antonio,33 K. Danzmann,9, 10 _{A. Dasgupta,}110 _{C. F. Da Silva Costa,}49 _{V. Dattilo,}30 _{I. Dave,}62 _{M. Davier,}27 _{D. Davis,}43

E. J. Daw,111 _{B. Day,}77 _{D. DeBra,}50 _{M. Deenadayalan,}18 _{J. Degallaix,}25 _{M. De Laurentis,}79, 4 _{S. Del´eglise,}71

W. Del Pozzo,21, 22 N. Demos,14 T. Denker,9, 10 T. Dent,9 R. De Pietri,57, 58 J. Derby,28 V. Dergachev,9 R. De Rosa,79, 4 _{C. De Rossi,}25, 30 _{R. DeSalvo,}112_{O. de Varona,}9, 10 _{S. Dhurandhar,}18_{M. C. D´ıaz,}108 _{L. Di Fiore,}4

M. Di Giovanni,113, 98 _{T. Di Girolamo,}79, 4 _{A. Di Lieto,}21, 22 _{B. Ding,}101 _{S. Di Pace,}100, 35 _{I. Di Palma,}100, 35

F. Di Renzo,21, 22 _{A. Dmitriev,}60 _{Z. Doctor,}93 _{V. Dolique,}25 _{F. Donovan,}14 _{K. L. Dooley,}36, 86 _{S. Doravari,}9, 10

I. Dorrington,36_{M. Dovale ´}_Alvarez,60_{T. P. Downes,}20 _{M. Drago,}9, 16, 17_{C. Dreissigacker,}9, 10 _{J. C. Driggers,}46

Z. Du,83 _{P. Dupej,}45 _{S. E. Dwyer,}46_{P. J. Easter,}5 _{T. B. Edo,}111_{M. C. Edwards,}95_{A. E✏er,}6 _{H.-B. Eggenstein,}9, 10

P. Ehrens,1 _{J. Eichholz,}1_{S. S. Eikenberry,}49 _{M. Eisenmann,}7 _{R. A. Eisenstein,}14 _{R. C. Essick,}93 _{H. Estelles,}106

D. Estevez,7 _{Z. B. Etienne,}40 _{T. Etzel,}1 _{M. Evans,}14 _{T. M. Evans,}6 _{V. Fafone,}32, 33, 16 _{H. Fair,}43 _{S. Fairhurst,}36

X. Fan,83 _{S. Farinon,}61 _{B. Farr,}70 _{W. M. Farr,}60 _{E. J. Fauchon-Jones,}36_{M. Favata,}114 _{M. Fays,}36 _{C. Fee,}85

H. Fehrmann,9 _{J. Feicht,}1 _{M. M. Fejer,}50 _{F. Feng,}29 _{A. Fernandez-Galiana,}14 _{I. Ferrante,}21, 22 _{E. C. Ferreira,}15

F. Ferrini,30 _{F. Fidecaro,}21, 22 _{I. Fiori,}30 _{D. Fiorucci,}29 _{M. Fishbach,}93 _{R. P. Fisher,}43 _{J. M. Fishner,}14

M. Fitz-Axen,44 _{R. Flaminio,}7, 115 _{M. Fletcher,}45_{H. Fong,}116_{J. A. Font,}23, 117_{P. W. F. Forsyth,}24 _{S. S. Forsyth,}77

J.-D. Fournier,66 _{S. Frasca,}100, 35 _{F. Frasconi,}22 _{Z. Frei,}54 _{A. Freise,}60 _{R. Frey,}70 _{V. Frey,}27 _{P. Fritschel,}14

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L. Gammaitoni,41 _{M. R. Ganija,}56 _{S. G. Gaonkar,}18_{A. Garcia,}28 _{C. Garc´ıa-Quir´os,}106_{F. Garufi,}79, 4 _{B. Gateley,}46

S. Gaudio,37 G. Gaur,119 V. Gayathri,120 G. Gemme,61 E. Genin,30 A. Gennai,22 D. George,11 J. George,62 L. Gergely,121_{V. Germain,}7 _{S. Ghonge,}77_{Abhirup Ghosh,}19_{Archisman Ghosh,}13 _{S. Ghosh,}20 _{B. Giacomazzo,}113, 98

J. A. Giaime,2, 6 _{K. D. Giardina,}6 _{A. Giazotto,}22,† _{K. Gill,}37 _{G. Giordano,}3, 4 _{L. Glover,}112 _{E. Goetz,}46 _{R. Goetz,}49

B. Goncharov,5 _{G. Gonz´}_alez,2 _{J. M. Gonzalez Castro,}21, 22 _{A. Gopakumar,}122_{M. L. Gorodetsky,}63 _{S. E. Gossan,}1

M. Gosselin,30 _{R. Gouaty,}7 _{A. Grado,}123, 4 _{C. Graef,}45 _{M. Granata,}25 _{A. Grant,}45 _{S. Gras,}14 _{C. Gray,}46

G. Greco,72, 73 _{A. C. Green,}60 _{R. Green,}36 _{E. M. Gretarsson,}37 _{P. Groot,}65 _{H. Grote,}36 _{S. Grunewald,}38

P. Gruning,27 _{G. M. Guidi,}72, 73 _{H. K. Gulati,}110 _{X. Guo,}83 _{A. Gupta,}88 _{M. K. Gupta,}110 _{K. E. Gushwa,}1

E. K. Gustafson,1 _{R. Gustafson,}124_{O. Halim,}17, 16 _{B. R. Hall,}69_{E. D. Hall,}14 _{E. Z. Hamilton,}36 _{H. F. Hamilton,}125

G. Hammond,45 _{M. Haney,}67 _{M. M. Hanke,}9, 10 _{J. Hanks,}46 _{C. Hanna,}88 _{M. D. Hannam,}36 _{O. A. Hannuksela,}96

J. Hanson,6 _{T. Hardwick,}2 _{J. Harms,}16, 17 _{G. M. Harry,}126 _{I. W. Harry,}38 _{M. J. Hart,}45 _{C.-J. Haster,}116

K. Haughian,45 _{J. Healy,}59 _{A. Heidmann,}71 _{M. C. Heintze,}6 _{H. Heitmann,}66 _{P. Hello,}27 _{G. Hemming,}30

M. Hendry,45 _{I. S. Heng,}45 _{J. Hennig,}45 _{A. W. Heptonstall,}1 _{F. J. Hernandez,}5 _{M. Heurs,}9, 10 _{S. Hild,}45

T. Hinderer,65 _{D. Hoak,}30_{S. Hochheim,}9, 10 _{D. Hofman,}25_{N. A. Holland,}24 _{K. Holt,}6 _{D. E. Holz,}93 _{P. Hopkins,}36

C. Horst,20 _{J. Hough,}45 _{E. A. Houston,}45 _{E. J. Howell,}64 _{A. Hreibi,}66_{E. A. Huerta,}11 _{D. Huet,}27_{B. Hughey,}37

M. Hulko,1 _{S. Husa,}106 _{S. H. Huttner,}45 _{T. Huynh-Dinh,}6 _{A. Iess,}32, 33 _{N. Indik,}9 _{C. Ingram,}56 _{R. Inta,}84

G. Intini,100, 35 _{H. N. Isa,}45_{J.-M. Isac,}71_{M. Isi,}1_{B. R. Iyer,}19_{K. Izumi,}46_{T. Jacqmin,}71_{K. Jani,}77_{P. Jaranowski,}127

D. S. Johnson,11 _{W. W. Johnson,}2 _{D. I. Jones,}128 _{R. Jones,}45 _{R. J. G. Jonker,}13 _{L. Ju,}64 _{J. Junker,}9, 10

C. V. Kalaghatgi,36 _{V. Kalogera,}91 _{B. Kamai,}1 _{S. Kandhasamy,}6 _{G. Kang,}39 _{J. B. Kanner,}1 _{S. J. Kapadia,}20

S. Karki,70 _{K. S. Karvinen,}9, 10 _{M. Kasprzack,}2 _{M. Katolik,}11 _{S. Katsanevas,}30_{E. Katsavounidis,}14_{W. Katzman,}6

S. Kaufer,9, 10 _{K. Kawabe,}46 _{N. V. Keerthana,}18 _{F. K´ef´elian,}66 _{D. Keitel,}45 _{A. J. Kemball,}11 _{R. Kennedy,}111

J. S. Key,129 _{F. Y. Khalili,}63_{B. Khamesra,}77 _{H. Khan,}28 _{I. Khan,}16, 33 _{S. Khan,}9_{Z. Khan,}110 _{E. A. Khazanov,}130

N. Kijbunchoo,24_{Chunglee Kim,}131_{J. C. Kim,}132_{K. Kim,}96 _{W. Kim,}56 _{W. S. Kim,}133 _{Y.-M. Kim,}134 _{E. J. King,}56

P. J. King,46 _{M. Kinley-Hanlon,}126_{R. Kirchho↵,}9, 10 _{J. S. Kissel,}46 _{L. Kleybolte,}34 _{S. Klimenko,}49 _{T. D. Knowles,}40

P. Koch,9, 10 _{S. M. Koehlenbeck,}9, 10 _{S. Koley,}13 _{V. Kondrashov,}1 _{A. Kontos,}14 _{M. Korobko,}34 _{W. Z. Korth,}1

I. Kowalska,74 _{D. B. Kozak,}1 _{C. Kr¨amer,}9 _{V. Kringel,}9, 10 _{B. Krishnan,}9 _{A. Kr´olak,}135, 136 _{G. Kuehn,}9, 10

P. Kumar,137 R. Kumar,110 S. Kumar,19 L. Kuo,89 A. Kutynia,135 S. Kwang,20 B. D. Lackey,38 K. H. Lai,96 M. Landry,46 _{R. N. Lang,}138_{J. Lange,}59 _{B. Lantz,}50_{R. K. Lanza,}14 _{A. Lartaux-Vollard,}27_{P. D. Lasky,}5 _{M. Laxen,}6

A. Lazzarini,1 _{C. Lazzaro,}53_{P. Leaci,}100, 35 _{S. Leavey,}9, 10 _{C. H. Lee,}94 _{H. K. Lee,}139 _{H. M. Lee,}131_{H. W. Lee,}132

K. Lee,45 _{J. Lehmann,}9, 10 _{A. Lenon,}40 _{M. Leonardi,}9, 10, 115 _{N. Leroy,}27 _{N. Letendre,}7 _{Y. Levin,}5 _{J. Li,}83

T. G. F. Li,96 _{X. Li,}47 _{S. D. Linker,}112 _{T. B. Littenberg,}140 _{J. Liu,}64 _{X. Liu,}20 _{R. K. L. Lo,}96 _{N. A. Lockerbie,}26

L. T. London,36 _{A. Longo,}141, 142 _{M. Lorenzini,}16, 17 _{V. Loriette,}143 _{M. Lormand,}6 _{G. Losurdo,}22 _{J. D. Lough,}9, 10

G. Lovelace,28 _{H. L¨}_uck,9, 10 _{D. Lumaca,}32, 33 _{A. P. Lundgren,}9 _{R. Lynch,}14_{Y. Ma,}47 _{R. Macas,}36 _{S. Macfoy,}26

B. Machenschalk,9 _{M. MacInnis,}14 _{D. M. Macleod,}36 _{I. Maga˜}_{na Hernandez,}20 _{F. Maga˜}_na-Sandoval,43

L. Maga˜na Zertuche,86 _{R. M. Magee,}88 _{E. Majorana,}35 _{I. Maksimovic,}143 _{N. Man,}66 _{V. Mandic,}44_{V. Mangano,}45

G. L. Mansell,24 _{M. Manske,}20, 24 _{M. Mantovani,}30 _{F. Marchesoni,}51, 42 _{F. Marion,}7 _{S. M´arka,}104_{Z. M´arka,}104

C. Markakis,11 _{A. S. Markosyan,}50 _{A. Markowitz,}1_{E. Maros,}1 _{A. Marquina,}103 _{F. Martelli,}72, 73 _{L. Martellini,}66

I. W. Martin,45 _{R. M. Martin,}114 _{D. V. Martynov,}14 _{K. Mason,}14_{E. Massera,}111_{A. Masserot,}7 _{T. J. Massinger,}1

M. Masso-Reid,45 _{S. Mastrogiovanni,}100, 35 _{A. Matas,}44 _{F. Matichard,}1, 14 _{L. Matone,}104 _{N. Mavalvala,}14

N. Mazumder,69 _{J. J. McCann,}64 _{R. McCarthy,}46 _{D. E. McClelland,}24 _{S. McCormick,}6 _{L. McCuller,}14

S. C. McGuire,144 _{J. McIver,}1 _{D. J. McManus,}24 _{T. McRae,}24_{S. T. McWilliams,}40 _{D. Meacher,}88 _{G. D. Meadors,}5

M. Mehmet,9, 10 _{J. Meidam,}13 _{E. Mejuto-Villa,}8 _{A. Melatos,}99 _{G. Mendell,}46 _{D. Mendoza-Gandara,}9, 10

R. A. Mercer,20 _{L. Mereni,}25 _{E. L. Merilh,}46 _{M. Merzougui,}66 _{S. Meshkov,}1 _{C. Messenger,}45 _{C. Messick,}88

R. Metzdor↵,71 _{P. M. Meyers,}44_{H. Miao,}60 _{C. Michel,}25 _{H. Middleton,}99 _{E. E. Mikhailov,}145 _{L. Milano,}79, 4

A. L. Miller,49 _{A. Miller,}100, 35 _{B. B. Miller,}91 _{J. Miller,}14 _{M. Millhouse,}105_{J. Mills,}36 _{M. C. Milovich-Go↵,}112

O. Minazzoli,66, 146 _{Y. Minenkov,}33 _{J. Ming,}9, 10 _{C. Mishra,}147 _{S. Mitra,}18_{V. P. Mitrofanov,}63 _{G. Mitselmakher,}49

R. Mittleman,14_{D. Mo↵a,}85_{K. Mogushi,}86_{M. Mohan,}30_{S. R. P. Mohapatra,}14 _{M. Montani,}72, 73 _{C. J. Moore,}12

D. Moraru,46 _{G. Moreno,}46 _{S. Morisaki,}82 _{B. Mours,}7 _{C. M. Mow-Lowry,}60 _{G. Mueller,}49 _{A. W. Muir,}36

Arunava Mukherjee,9, 10 _{D. Mukherjee,}20 _{S. Mukherjee,}108 _{N. Mukund,}18 _{A. Mullavey,}6 _{J. Munch,}56 _{E. A. Mu˜}_niz,43

M. Muratore,37 _{P. G. Murray,}45 _{A. Nagar,}87, 148, 149 _{K. Napier,}77 _{I. Nardecchia,}32, 33 _{L. Naticchioni,}100, 35

R. K. Nayak,150 _{J. Neilson,}112 _{G. Nelemans,}65, 13 _{T. J. N. Nelson,}6 _{M. Nery,}9, 10 _{A. Neunzert,}124 _{L. Nevin,}1

J. M. Newport,126K. Y. Ng,14 S. Ng,56P. Nguyen,70T. T. Nguyen,24 D. Nichols,65A. B. Nielsen,9 S. Nissanke,65, 13 A. Nitz,9 _{F. Nocera,}30 _{D. Nolting,}6_{C. North,}36_{L. K. Nuttall,}36 _{M. Obergaulinger,}23 _{J. Oberling,}46_{B. D. O’Brien,}49

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G. D. O’Dea,112 _{G. H. Ogin,}151 _{J. J. Oh,}133 _{S. H. Oh,}133 _{F. Ohme,}9 _{H. Ohta,}82 _{M. A. Okada,}15 _{M. Oliver,}106

P. Oppermann,9, 10 Richard J. Oram,6 B. O’Reilly,6 R. Ormiston,44 L. F. Ortega,49 R. O’Shaughnessy,59 S. Ossokine,38 _{D. J. Ottaway,}56 _{H. Overmier,}6 _{B. J. Owen,}84 _{A. E. Pace,}88 _{G. Pagano,}21, 22 _{J. Page,}140

M. A. Page,64_{A. Pai,}120_{S. A. Pai,}62_{J. R. Palamos,}70 _{O. Palashov,}130 _{C. Palomba,}35_{A. Pal-Singh,}34_{Howard Pan,}89

Huang-Wei Pan,89 _{B. Pang,}47 _{P. T. H. Pang,}96 _{C. Pankow,}91 _{F. Pannarale,}36 _{B. C. Pant,}62 _{F. Paoletti,}22

A. Paoli,30 _{M. A. Papa,}9, 20, 10 _{A. Parida,}18 _{W. Parker,}6 _{D. Pascucci,}45 _{A. Pasqualetti,}30 _{R. Passaquieti,}21, 22

D. Passuello,22_{M. Patil,}136_{B. Patricelli,}152, 22 _{B. L. Pearlstone,}45 _{C. Pedersen,}36 _{M. Pedraza,}1 _{R. Pedurand,}25, 153

L. Pekowsky,43 _{A. Pele,}6 _{S. Penn,}154_{C. J. Perez,}46_{A. Perreca,}113, 98 _{L. M. Perri,}91 _{H. P. Pfei↵er,}116, 38 _{M. Phelps,}45

K. S. Phukon,18 _{O. J. Piccinni,}100, 35 _{M. Pichot,}66_{F. Piergiovanni,}72, 73 _{V. Pierro,}8_{G. Pillant,}30_{L. Pinard,}25

I. M. Pinto,8 _{M. Pirello,}46 _{M. Pitkin,}45 _{R. Poggiani,}21, 22 _{P. Popolizio,}30 _{E. K. Porter,}29 _{L. Possenti,}155, 73

A. Post,9 _{J. Powell,}156 _{J. Prasad,}18_{J. W. W. Pratt,}37 _{G. Pratten,}106_{V. Predoi,}36_{T. Prestegard,}20_{M. Principe,}8

S. Privitera,38 _{G. A. Prodi,}113, 98 _{L. G. Prokhorov,}63 _{O. Puncken,}9, 10 _{M. Punturo,}42 _{P. Puppo,}35 _{M. P¨}_urrer,38

H. Qi,20 _{V. Quetschke,}108 _{E. A. Quintero,}1 _{R. Quitzow-James,}70 _{D. S. Rabeling,}24 _{H. Radkins,}46 _{P. Ra↵ai,}54

S. Raja,62_{C. Rajan,}62_{B. Rajbhandari,}84 _{M. Rakhmanov,}108_{K. E. Ramirez,}108 _{A. Ramos-Buades,}106_{Javed Rana,}18

P. Rapagnani,100, 35 _{V. Raymond,}36 _{M. Razzano,}21, 22 _{J. Read,}28 _{T. Regimbau,}66, 7 _{L. Rei,}61 _{S. Reid,}26

D. H. Reitze,1, 49 _{W. Ren,}11 _{F. Ricci,}100, 35 _{P. M. Ricker,}11 _{K. Riles,}124 _{M. Rizzo,}59_{N. A. Robertson,}1, 45 _{R. Robie,}45

F. Robinet,27 _{T. Robson,}105_{A. Rocchi,}33 _{L. Rolland,}7 _{J. G. Rollins,}1 _{V. J. Roma,}70 _{R. Romano,}3, 4 _{C. L. Romel,}46

J. H. Romie,6 _{D. Rosi´}_nska,157, 55 _{M. P. Ross,}158 _{S. Rowan,}45_{A. R¨}_udiger,9, 10 _{P. Ruggi,}30 _{G. Rutins,}159_{K. Ryan,}46

S. Sachdev,1 _{T. Sadecki,}46 _{M. Sakellariadou,}160 _{L. Salconi,}30 _{M. Saleem,}120 _{F. Salemi,}9 _{A. Samajdar,}150, 13

L. Sammut,5_{L. M. Sampson,}91 _{E. J. Sanchez,}1 _{L. E. Sanchez,}1_{N. Sanchis-Gual,}23 _{V. Sandberg,}46 _{J. R. Sanders,}43

N. Sarin,5 _{B. Sassolas,}25 _{P. R. Saulson,}43 _{O. Sauter,}124_{R. L. Savage,}46 _{A. Sawadsky,}34 _{P. Schale,}70 _{M. Scheel,}47

J. Scheuer,91 _{P. Schmidt,}65_{R. Schnabel,}34 _{R. M. S. Schofield,}70 _{A. Sch¨}_onbeck,34 _{E. Schreiber,}9, 10 _{D. Schuette,}9, 10

B. W. Schulte,9, 10 _{B. F. Schutz,}36, 9 _{S. G. Schwalbe,}37 _{J. Scott,}45 _{S. M. Scott,}24 _{E. Seidel,}11 _{D. Sellers,}6

A. S. Sengupta,161 _{D. Sentenac,}30 _{V. Sequino,}32, 33, 16 _{A. Sergeev,}130 _{Y. Setyawati,}9 _{D. A. Shaddock,}24

T. J. Sha↵er,46_{A. A. Shah,}140_{M. S. Shahriar,}91 _{M. B. Shaner,}112_{L. Shao,}38_{B. Shapiro,}50_{P. Shawhan,}76 _{H. Shen,}11

D. H. Shoemaker,14_{D. M. Shoemaker,}77 _{K. Siellez,}77 _{X. Siemens,}20 _{M. Sieniawska,}55 _{D. Sigg,}46 _{A. D. Silva,}15

L. P. Singer,80A. Singh,9, 10 A. Singhal,16, 35 A. M. Sintes,106 B. J. J. Slagmolen,24 T. J. Slaven-Blair,64B. Smith,6 J. R. Smith,28 _{R. J. E. Smith,}5 _{S. Somala,}162 _{E. J. Son,}133 _{B. Sorazu,}45 _{F. Sorrentino,}61 _{T. Souradeep,}18

A. P. Spencer,45 _{A. K. Srivastava,}110 _{K. Staats,}37 _{M. Steinke,}9, 10 _{J. Steinlechner,}34, 45 _{S. Steinlechner,}34

D. Steinmeyer,9, 10 _{B. Steltner,}9, 10 _{S. P. Stevenson,}156 _{D. Stocks,}50 _{R. Stone,}108 _{D. J. Stops,}60_{K. A. Strain,}45

G. Stratta,72, 73 _{S. E. Strigin,}63 _{A. Strunk,}46 _{R. Sturani,}163 _{A. L. Stuver,}164 _{T. Z. Summerscales,}165 _{L. Sun,}99

S. Sunil,110 _{J. Suresh,}18 _{P. J. Sutton,}36 _{B. L. Swinkels,}13 _{M. J. Szczepa´}_nczyk,37 _{M. Tacca,}13 _{S. C. Tait,}45

C. Talbot,5 _{D. Talukder,}70 _{D. B. Tanner,}49 _{M. T´apai,}121 _{A. Taracchini,}38 _{J. D. Tasson,}95 _{J. A. Taylor,}140

R. Taylor,1 _{S. V. Tewari,}154 _{T. Theeg,}9, 10 _{F. Thies,}9, 10 _{E. G. Thomas,}60 _{M. Thomas,}6_{P. Thomas,}46_{K. A. Thorne,}6

E. Thrane,5 _{S. Tiwari,}16, 98 _{V. Tiwari,}36 _{K. V. Tokmakov,}26 _{K. Toland,}45 _{M. Tonelli,}21, 22 _{Z. Tornasi,}45

A. Torres-Forné,23 _{C. I. Torrie,}1 _{D. Töyrä,}60 _{F. Travasso,}30, 42 _{G. Traylor,}6 _{J. Trinastic,}49 _{M. C. Tringali,}113, 98

L. Trozzo,166, 22 _{K. W. Tsang,}13 _{M. Tse,}14 _{R. Tso,}47 _{D. Tsuna,}82 _{L. Tsukada,}82 _{D. Tuyenbayev,}108 _{K. Ueno,}20

D. Ugolini,167 _{A. L. Urban,}1 _{S. A. Usman,}36 _{H. Vahlbruch,}9, 10 _{G. Vajente,}1 _{G. Valdes,}2 _{N. van Bakel,}13

M. van Beuzekom,13 _{J. F. J. van den Brand,}75, 13 _{C. Van Den Broeck,}13, 168 _{D. C. Vander-Hyde,}43

L. van der Schaaf,13 _{J. V. van Heijningen,}13 _{A. A. van Veggel,}45 _{M. Vardaro,}52, 53 _{V. Varma,}47 _{S. Vass,}1

M. Vas´uth,48 _{A. Vecchio,}60 _{G. Vedovato,}53 _{J. Veitch,}45 _{P. J. Veitch,}56 _{K. Venkateswara,}158 _{G. Venugopalan,}1

D. Verkindt,7 _{F. Vetrano,}72, 73 _{A. Vicer´e,}72, 73 _{A. D. Viets,}20 _{S. Vinciguerra,}60 _{D. J. Vine,}159 _{J.-Y. Vinet,}66

S. Vitale,14_{T. Vo,}43 _{H. Vocca,}41, 42 _{C. Vorvick,}46 _{S. P. Vyatchanin,}63_{A. R. Wade,}1 _{L. E. Wade,}85_{M. Wade,}85

R. Walet,13 _{M. Walker,}28 _{L. Wallace,}1 _{S. Walsh,}20, 9 _{G. Wang,}16, 22 _{H. Wang,}60_{J. Z. Wang,}124 _{W. H. Wang,}108

Y. F. Wang,96 _{R. L. Ward,}24 _{J. Warner,}46 _{M. Was,}7_{J. Watchi,}101_{B. Weaver,}46 _{L.-W. Wei,}9, 10 _{M. Weinert,}9, 10

A. J. Weinstein,1 _{R. Weiss,}14 _{F. Wellmann,}9, 10 _{L. Wen,}64 _{E. K. Wessel,}11 _{P. Weßels,}9, 10 _{J. Westerweck,}9

K. Wette,24 _{J. T. Whelan,}59 _{B. F. Whiting,}49 _{C. Whittle,}14 _{D. Wilken,}9, 10 _{D. Williams,}45 _{R. D. Williams,}1

A. R. Williamson,59, 65 _{J. L. Willis,}1, 125 _{B. Willke,}9, 10 _{M. H. Wimmer,}9, 10 _{W. Winkler,}9, 10 _{C. C. Wipf,}1

H. Wittel,9, 10 _{G. Woan,}45 _{J. Woehler,}9, 10 _{J. K. Wo↵ord,}59 _{W. K. Wong,}96 _{J. Worden,}46 _{J. L. Wright,}45

D. S. Wu,9, 10 _{D. M. Wysocki,}59 _{S. Xiao,}1 _{W. Yam,}14 _{H. Yamamoto,}1 _{C. C. Yancey,}76 _{L. Yang,}169_{M. J. Yap,}24

M. Yazback,49 _{Hang Yu,}14 _{Haocun Yu,}14 _{M. Yvert,}7 _{A. Zadro˙zny,}135 _{M. Zanolin,}37 _{T. Zelenova,}30

J.-P. Zendri,53 M. Zevin,91 J. Zhang,64 L. Zhang,1 M. Zhang,145 T. Zhang,45 Y.-H. Zhang,9, 10 C. Zhao,64 M. Zhou,91 _{Z. Zhou,}91 _{S. J. Zhu,}9, 10 _{X. J. Zhu,}5 _{A. B. Zimmerman,}92, 170 _{M. E. Zucker,}1, 14 _{and J. Zweizig}1

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(The LIGO Scientific Collaboration and the Virgo Collaboration)

N. N. Weinberg171

1_{LIGO, California Institute of Technology, Pasadena, CA 91125, USA} 2_{Louisiana State University, Baton Rouge, LA 70803, USA}

3_Universit`_{a di Salerno, Fisciano, I-84084 Salerno, Italy}

4_{INFN, Sezione di Napoli, Complesso Universitario di Monte S.Angelo, I-80126 Napoli, Italy} 5_{OzGrav, School of Physics & Astronomy, Monash University, Clayton 3800, Victoria, Australia}

6_{LIGO Livingston Observatory, Livingston, LA 70754, USA}

7_{Laboratoire d’Annecy de Physique des Particules (LAPP), Univ. Grenoble Alpes,}

Universit´e Savoie Mont Blanc, CNRS/IN2P3, F-74941 Annecy, France

8_{University of Sannio at Benevento, I-82100 Benevento,}

Italy and INFN, Sezione di Napoli, I-80100 Napoli, Italy

9_{Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-30167 Hannover, Germany} 10_{Leibniz Universit¨}_{at Hannover, D-30167 Hannover, Germany}

11_{NCSA, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA} 12_{University of Cambridge, Cambridge CB2 1TN, United Kingdom} 13_{Nikhef, Science Park 105, 1098 XG Amsterdam, The Netherlands} 14_{LIGO, Massachusetts Institute of Technology, Cambridge, MA 02139, USA}

15_{Instituto Nacional de Pesquisas Espaciais, 12227-010 S˜}_{ao Jos´e dos Campos, S˜}_{ao Paulo, Brazil} 16_{Gran Sasso Science Institute (GSSI), I-67100 L’Aquila, Italy}

17_{INFN, Laboratori Nazionali del Gran Sasso, I-67100 Assergi, Italy} 18_{Inter-University Centre for Astronomy and Astrophysics, Pune 411007, India}

19_{International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India} 20_{University of Wisconsin-Milwaukee, Milwaukee, WI 53201, USA}

21_Universit`_{a di Pisa, I-56127 Pisa, Italy} 22_{INFN, Sezione di Pisa, I-56127 Pisa, Italy}

23_{Departamento de Astronom´ıa y Astrof´ısica, Universitat de Val`encia, E-46100 Burjassot, Val`encia, Spain} 24_{OzGrav, Australian National University, Canberra, Australian Capital Territory 0200, Australia}

25_{Laboratoire des Mat´eriaux Avanc´es (LMA), CNRS/IN2P3, F-69622 Villeurbanne, France} 26_{SUPA, University of Strathclyde, Glasgow G1 1XQ, United Kingdom}

27_{LAL, Univ. Paris-Sud, CNRS/IN2P3, Universit´e Paris-Saclay, F-91898 Orsay, France} 28_{California State University Fullerton, Fullerton, CA 92831, USA}

29_{APC, AstroParticule et Cosmologie, Universit´e Paris Diderot,}

CNRS/IN2P3, CEA/Irfu, Observatoire de Paris, Sorbonne Paris Cit´e, F-75205 Paris Cedex 13, France

30_{European Gravitational Observatory (EGO), I-56021 Cascina, Pisa, Italy} 31_{Chennai Mathematical Institute, Chennai 603103, India}

32_Universit`_{a di Roma Tor Vergata, I-00133 Roma, Italy} 33_{INFN, Sezione di Roma Tor Vergata, I-00133 Roma, Italy}

34_Universit¨_{at Hamburg, D-22761 Hamburg, Germany} 35_{INFN, Sezione di Roma, I-00185 Roma, Italy} 36_{Cardi↵ University, Cardi↵ CF24 3AA, United Kingdom} 37_{Embry-Riddle Aeronautical University, Prescott, AZ 86301, USA}

38_{Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-14476 Potsdam-Golm, Germany} 39_{Korea Institute of Science and Technology Information, Daejeon 34141, Korea}

40_{West Virginia University, Morgantown, WV 26506, USA} 41_Universit`_{a di Perugia, I-06123 Perugia, Italy} 42_{INFN, Sezione di Perugia, I-06123 Perugia, Italy}

43_{Syracuse University, Syracuse, NY 13244, USA} 44_{University of Minnesota, Minneapolis, MN 55455, USA} 45_{SUPA, University of Glasgow, Glasgow G12 8QQ, United Kingdom}

46_{LIGO Hanford Observatory, Richland, WA 99352, USA} 47_{Caltech CaRT, Pasadena, CA 91125, USA}

48_{Wigner RCP, RMKI, H-1121 Budapest, Konkoly Thege Mikl´}_{os ´}_{ut 29-33, Hungary} 49_{University of Florida, Gainesville, FL 32611, USA}

50_{Stanford University, Stanford, CA 94305, USA}

51_Universit`_{a di Camerino, Dipartimento di Fisica, I-62032 Camerino, Italy} 52_Universit`_{a di Padova, Dipartimento di Fisica e Astronomia, I-35131 Padova, Italy}

53_{INFN, Sezione di Padova, I-35131 Padova, Italy}

54_{MTA-ELTE Astrophysics Research Group, Institute of Physics, E¨}_otv¨_{os University, Budapest 1117, Hungary} 55_{Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, 00-716, Warsaw, Poland}

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57_{Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Universit`}_{a di Parma, I-43124 Parma, Italy} 58_{INFN, Sezione di Milano Bicocca, Gruppo Collegato di Parma, I-43124 Parma, Italy}

59_{Rochester Institute of Technology, Rochester, NY 14623, USA} 60_{University of Birmingham, Birmingham B15 2TT, United Kingdom}

61_{INFN, Sezione di Genova, I-16146 Genova, Italy} 62_{RRCAT, Indore, Madhya Pradesh 452013, India}

63_{Faculty of Physics, Lomonosov Moscow State University, Moscow 119991, Russia} 64_{OzGrav, University of Western Australia, Crawley, Western Australia 6009, Australia}

65_{Department of Astrophysics/IMAPP, Radboud University Nijmegen,}

P.O. Box 9010, 6500 GL Nijmegen, The Netherlands

66_{Artemis, Universit´e Cˆ}_{ote d’Azur, Observatoire Cˆ}_{ote d’Azur,}

CNRS, CS 34229, F-06304 Nice Cedex 4, France

67_{Physik-Institut, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland} 68_{Univ Rennes, CNRS, Institut FOTON - UMR6082, F-3500 Rennes, France}

69_{Washington State University, Pullman, WA 99164, USA} 70_{University of Oregon, Eugene, OR 97403, USA} 71_{Laboratoire Kastler Brossel, Sorbonne Universit´e, CNRS,}

ENS-Universit´e PSL, Coll`ege de France, F-75005 Paris, France

72_Universit`_{a degli Studi di Urbino ’Carlo Bo,’ I-61029 Urbino, Italy} 73_{INFN, Sezione di Firenze, I-50019 Sesto Fiorentino, Firenze, Italy} 74_{Astronomical Observatory Warsaw University, 00-478 Warsaw, Poland}

75_{VU University Amsterdam, 1081 HV Amsterdam, The Netherlands} 76_{University of Maryland, College Park, MD 20742, USA}

77_{School of Physics, Georgia Institute of Technology, Atlanta, GA 30332, USA} 78_{Universit´e Claude Bernard Lyon 1, F-69622 Villeurbanne, France}

79_Universit`_{a di Napoli ’Federico II,’ Complesso Universitario di Monte S.Angelo, I-80126 Napoli, Italy} 80_{NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA}

81_{Dipartimento di Fisica, Universit`}_{a degli Studi di Genova, I-16146 Genova, Italy} 82_{RESCEU, University of Tokyo, Tokyo, 113-0033, Japan.}

83_{Tsinghua University, Beijing 100084, China} 84_{Texas Tech University, Lubbock, TX 79409, USA}

85_{Kenyon College, Gambier, OH 43022, USA} 86_{The University of Mississippi, University, MS 38677, USA} 87_{Museo Storico della Fisica e Centro Studi e Ricerche “Enrico Fermi”,}

I-00184 Roma, Italyrico Fermi, I-00184 Roma, Italy

88_{The Pennsylvania State University, University Park, PA 16802, USA} 89_{National Tsing Hua University, Hsinchu City, 30013 Taiwan, Republic of China}

90_{Charles Sturt University, Wagga Wagga, New South Wales 2678, Australia} 91_{Center for Interdisciplinary Exploration & Research in Astrophysics (CIERA),}

Northwestern University, Evanston, IL 60208, USA

92_{Canadian Institute for Theoretical Astrophysics,}

60 St. George Street, Toronto, Ontario, M5S 3H8, Canada

93_{University of Chicago, Chicago, IL 60637, USA} 94_{Pusan National University, Busan 46241, Korea} 95_{Carleton College, Northfield, MN 55057, USA}

96_{The Chinese University of Hong Kong, Shatin, NT, Hong Kong} 97_{INAF, Osservatorio Astronomico di Padova, I-35122 Padova, Italy}

98_{INFN, Trento Institute for Fundamental Physics and Applications, I-38123 Povo, Trento, Italy} 99_{OzGrav, University of Melbourne, Parkville, Victoria 3010, Australia}

100_Universit`_{a di Roma ’La Sapienza,’ I-00185 Roma, Italy} 101_{Universit´e Libre de Bruxelles, Brussels 1050, Belgium} 102_{Sonoma State University, Rohnert Park, CA 94928, USA}

103_{Departamento de Matem´}_{aticas, Universitat de Val`encia, E-46100 Burjassot, Val`encia, Spain} 104_{Columbia University, New York, NY 10027, USA}

105_{Montana State University, Bozeman, MT 59717, USA}

106_{Universitat de les Illes Balears, IAC3—IEEC, E-07122 Palma de Mallorca, Spain} 107_{University of Rhode Island}

108_{The University of Texas Rio Grande Valley, Brownsville, TX 78520, USA} 109_{Bellevue College, Bellevue, WA 98007, USA}

110_{Institute for Plasma Research, Bhat, Gandhinagar 382428, India} 111_{The University of Sheffield, Sheffield S10 2TN, United Kingdom}

112_{California State University, Los Angeles, 5151 State University Dr, Los Angeles, CA 90032, USA} 113_Universit`_{a di Trento, Dipartimento di Fisica, I-38123 Povo, Trento, Italy}

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115_{National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan} 116_{Canadian Institute for Theoretical Astrophysics,}

University of Toronto, Toronto, Ontario M5S 3H8, Canada

117_{Observatori Astron`}_{omic, Universitat de Val`encia, E-46980 Paterna, Val`encia, Spain} 118_{School of Mathematics, University of Edinburgh, Edinburgh EH9 3FD, United Kingdom}

119_{University and Institute of Advanced Research,}

Koba Institutional Area, Gandhinagar Gujarat 382007, India

120_{Indian Institute of Technology Bombay}

121_{University of Szeged, D´}_{om t´er 9, Szeged 6720, Hungary} 122_{Tata Institute of Fundamental Research, Mumbai 400005, India} 123_{INAF, Osservatorio Astronomico di Capodimonte, I-80131, Napoli, Italy}

124_{University of Michigan, Ann Arbor, MI 48109, USA} 125_{Abilene Christian University, Abilene, TX 79699, USA}

126_{American University, Washington, D.C. 20016, USA} 127_{University of Bia lystok, 15-424 Bia lystok, Poland}

128_{University of Southampton, Southampton SO17 1BJ, United Kingdom} 129_{University of Washington Bothell, 18115 Campus Way NE, Bothell, WA 98011, USA}

130_{Institute of Applied Physics, Nizhny Novgorod, 603950, Russia} 131_{Korea Astronomy and Space Science Institute, Daejeon 34055, Korea}

132_{Inje University Gimhae, South Gyeongsang 50834, Korea} 133_{National Institute for Mathematical Sciences, Daejeon 34047, Korea}

134_{Ulsan National Institute of Science and Technology} 135_{NCBJ, 05-400 ´}_{Swierk-Otwock, Poland}

136_{Institute of Mathematics, Polish Academy of Sciences, 00656 Warsaw, Poland} 137_{Cornell Universtiy}

138_{Hillsdale College, Hillsdale, MI 49242, USA} 139_{Hanyang University, Seoul 04763, Korea}

140_{NASA Marshall Space Flight Center, Huntsville, AL 35811, USA} 141_{Dipartimento di Fisica, Universit`}_{a degli Studi Roma Tre, I-00154 Roma, Italy}

142_{INFN, Sezione di Roma Tre, I-00154 Roma, Italy} 143_{ESPCI, CNRS, F-75005 Paris, France}

144_{Southern University and A&M College, Baton Rouge, LA 70813, USA} 145_{College of William and Mary, Williamsburg, VA 23187, USA} 146_{Centre Scientifique de Monaco, 8 quai Antoine Ier, MC-98000, Monaco}

147_{Indian Institute of Technology Madras, Chennai 600036, India} 148_{INFN Sezione di Torino, Via P. Giuria 1, I-10125 Torino, Italy} 149_{Institut des Hautes Etudes Scientifiques, F-91440 Bures-sur-Yvette, France}

150_{IISER-Kolkata, Mohanpur, West Bengal 741252, India} 151_{Whitman College, 345 Boyer Avenue, Walla Walla, WA 99362 USA} 152_{Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56126 Pisa, Italy}

153_{Universit´e de Lyon, F-69361 Lyon, France}

154_{Hobart and William Smith Colleges, Geneva, NY 14456, USA} 155_Universit`_{a degli Studi di Firenze, I-50121 Firenze, Italy}

156_{OzGrav, Swinburne University of Technology, Hawthorn VIC 3122, Australia} 157_{Janusz Gil Institute of Astronomy, University of Zielona G´}_{ora, 65-265 Zielona G´}_{ora, Poland}

158_{University of Washington, Seattle, WA 98195, USA}

159_{SUPA, University of the West of Scotland, Paisley PA1 2BE, United Kingdom} 160_{King’s College London, University of London, London WC2R 2LS, United Kingdom}

161_{Indian Institute of Technology, Gandhinagar Ahmedabad Gujarat 382424, India} 162_{Indian Institute of Technology Hyderabad, Sangareddy, Khandi, Telangana 502285, India}

163_{International Institute of Physics, Universidade Federal do Rio Grande do Norte, Natal RN 59078-970, Brazil} 164_{Villanova University, 800 Lancaster Ave, Villanova, PA 19085, USA}

165_{Andrews University, Berrien Springs, MI 49104, USA} 166_Universit`_{a di Siena, I-53100 Siena, Italy} 167_{Trinity University, San Antonio, TX 78212, USA} 168_{Van Swinderen Institute for Particle Physics and Gravity,}

University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands

169_{Colorado State University, Fort Collins, CO 80523, USA} 170_{University of Texas at Austin, Austin, TX 78712, USA}

171_{Department of Physics, and Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology,}

Cambridge, MA 02139, USA

We analyze the impact of a proposed tidal instability coupling p-modes and g-modes within neutron stars on GW170817. This non-resonant instability transfers energy from the orbit of the

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binary to internal modes of the stars, accelerating the gravitational-wave driven inspiral. We model the impact of this instability on the phasing of the gravitational wave signal using three parameters per star: an overall amplitude, a saturation frequency, and a spectral index. Incorporating these additional parameters, we compute the Bayes Factor (ln B_!pgpg) comparing our p-g model to a standard one. We find that the observed signal is consistent with waveform models that neglect p-g e↵ects, with ln B_!pgpg = 0.03+0.70

0.58(maximum a posteriori and 90% credible region). By injecting simulated

signals that do not include p-g e↵ects and recovering them with the p-g model, we show that there is a ' 50% probability of obtaining similar ln Bpg

!pg even when p-g e↵ects are absent. We find

that the p-g amplitude for 1.4 M neutron stars is constrained to less than a few tenths of the theoretical maximum, with maxima a posteriori near one tenth this maximum and p-g saturation frequency_{⇠ 70 Hz. This suggests that there are less than a few hundred excited modes, assuming} they all saturate by wave breaking. For comparison, theoretical upper bounds suggest. 103 modes saturate by wave breaking. Thus, the measured constraints only rule out extreme values of the p-g parameters. They also imply that the instability dissipates. 1051_{ergs over the entire inspiral,}

i.e., less than a few percent of the energy radiated as gravitational waves.

I. INTRODUCTION

Detailed analysis of the gravitational-wave (GW) sig-nal received from the first binary neutron star (NS) co-alescence event (GW170817 [1]) constrains the tidal de-formability of NSs and thus the equation of state (EOS) above nuclear saturation density [2–4]. Studies of NS tidal deformation typically focus on the linear, quasi-static tidal bulge induced in each NS by its companion. Such deformations modify the system’s binding energy and GW luminosity and thereby alter its orbital dynam-ics. The degree of deformation is often expressed in terms of the tidal deformability ⇤i / (Ri/mi)5of each

compo-nent [5], or a particular mass-weighted average thereof (˜⇤) [2]. The strong dependence on compactness R/m means that a sti↵er EOS, which has larger R for the same m, imprints a larger tidal signals than a softer EOS. Cur-rent analyses of GW data from the LIGO [6] and Virgo [7] detectors favor a soft EOS [3,8]. Specifically, [2] finds ˜

⇤. 730 at the 90% credible level for all waveform models considered, allowing for the components to spin rapidly. The pressure at twice nuclear saturation density is also constrained to P = 3.5+2.71.7⇥ 1034 dyn/cm2(median and

90% credible region) [3] assuming small component spins. In addition to GW phasing, the EOS-dependence of ˜⇤ should correlate with post-merger signals [9], possible tidal disruptions, and kilonova observations [10]. Ob-served light-curves for the kilonova suggest a lower bound of ˜⇤& 200 [11,12].

Although some dynamical tidal e↵ects are incorpo-rated in these analyses (see, e.g., [2, 13]), the impact of several types of dynamical tidal e↵ects are neglected be-cause they are assumed to be small or have large theoret-ical uncertainties. These e↵ects arise because tidal fields, in addition to raising a quasi-static bulge, excite stellar normal modes. Three such excitation mechanisms are (i) resonant linear excitation, (ii) resonant nonlinear exci-tation, and (iii) non-resonant nonlinear excitation (see,

⇤_{Deceased, February 2018.} †_{Deceased, November 2017.}

e.g., [14]). The first occurs when the GW frequency (the oscillation frequency of the tidal field) sweeps through a mode’s natural frequency (see, e.g., [15–22]). However, since the GW frequency increases rapidly during the late inspiral, the time spent near resonance is too short to excite modes to large amplitudes. As a result, for modes with natural frequencies within the sensitive bands of ground-based GW detectors, the change in orbital phas-ing is expected to be small ( . 10 2 _{rad) unless the}

stars are rapidly rotating [17–19]. The impact of reso-nant nonlinear mode excitation (i.e., the parametric sub-harmonic instability) is likewise limited by the swiftness of the inspiral [23].

The proposed p-g tidal instability is a non-resonant, nonlinear instability in which the tidal bulge excites a low-frequency buoyancy-supported g-mode and a high-frequency pressure-supported p-mode [23–26]. It occurs in the inner core of the NS, where the stratification is weak and the shear due to the tidal bulge is especially sus-ceptible to instability. Unlike resonantly excited modes, an unstable p-g pair continuously drains energy from the orbit once excited, even after the orbital frequency changes significantly. There are many potentially unsta-ble p-g pairs, each becoming unstaunsta-ble at a di↵erent fre-quency and growing at a di↵erent rate. Although there is considerable uncertainty about the number of unstable pairs, their exact growth rates, and how they saturate, estimates suggest that the impact could be measurable with current detectors [27].

In this letter, we investigate the possible impact of the p-g instability on GW170817 using the phenomenologi-cal model developed in [27]. The model describes the energy dissipated by the instability within each NS, in-dexed by i, in terms of three parameters: (i) an overall amplitude Ai, which is related to the number of modes

participating in the instability, their growth rates, and their saturation energies, (ii) a frequency fi

correspond-ing to when the instability saturates, and (iii) a spectral index ni describing how the saturation energy evolves

with frequency. In Section II, we describe our models in detail. In SectionIII, we compare the statistical evi-dence for models that include the p-g instability relative to those that do not. In Section IV, we investigate the

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constraints on the p-g parameters from GW170817, and in SectionVwe conclude.

II. PHENOMENOLOGICAL MODEL Following [27], we extend a post-Newtonian (PN) waveform by including a parametrized model of the p-g instability. For the initial PN model, we use the TaylorF2frequency-domain approximant (see, e.g., [28]) terminated at the inner-most stable circular orbit, which includes the e↵ects of linear tides (˜⇤) and spins aligned with the orbital angular momentum (the impact of mis-aligned spins on p-g e↵ects is not known). Waveform

systematics between di↵erent existing approximants may be important for small p-g e↵ects. However, by compar-ing the waveform mismatches between several other mod-els (TaylorF2, SEOBNRT, PhenomDNRT, and PhenomPNRT, see [2]), we find these systematic become important for p-g e↵ects roughly an order of magnitude smaller than the upper limits set by our analysis (see Section IV). We expect TaylorF2 to be reasonably accurate and de-fer a complete analysis of waveform systematics to future work.

Assuming the p-g e↵ects are a perturbation to TaylorF2, we find that they modify the phase in the frequency-domain by (f ) = 2C1 3B2₍₃ _n 1)(4 n1) " ⇥1 ✓ f fref ◆n1 3 + (1 ⇥1) ✓ f1 fref ◆n1 3✓ (4 n1) (3 n1) ✓ f f1 ◆◆# + (1$ 2), (1)

where fi is the saturation frequency, fref ⌘ 100 Hz is a

reference frequency with no intrinsic significance, Ci =

[2mi/(m1 + m2)]2/3Ai, B = (32/5)(GM⇡fref/c3)5/3,

M = (m1m2)3/5/(m1+ m2)1/5, and ⇥i = ⇥(f fi)

where ⇥ is the Heaviside function. This approximant is slightly di↵erent than that of [27] because they in-correctly applied the saddle-point approximation to ob-tain the frequency-domain waveform from time-domain phasing [29]. This correction renders the p-g instability slightly more difficult to measure than predicted in [27], although the observed behavior is qualitatively similar. Specifically, we find that in order to achieve the same | |, Ai needs to be larger than [27] found by a factor

of⇠ (4 ni), although the precise factor also depends on

the other p-g parameters.

The expression contains three types of terms: a constant term, a linear term_{/ (1} ⇥i)f , and a

power-law term_{/ ⇥}ifni 3. The constant term corresponds to

an overall phase o↵set and is degenerate with the orbital phase at coalescence. The linear term corresponds to a change in the time of coalescence; because the p-g insta-bility transfers energy from the orbit to stellar normal modes, the binary inspirals faster than it would if the e↵ect was absent. The power-law term accounts for the competition between the rate of p-g energy dissipation and the rate of inspiral, both of which increase as f in-creases. As argued in [27], we expect ni < 3, which

implies that the phase shift accumulates primarily at fre-quencies just above the “turn-on” (saturation) frequency f & fi.

When ni< 3, p-g e↵ects are most important at lower

frequencies whereas linear tides (˜⇤) and spins ( i =

cSi/Gm2i, where Si is the spin-angular momentum of

each component) have their largest impact at higher fre-quencies (see, e.g., [30]). The priors placed on the latter quantities can, however, a↵ect our inference of p-g

pa-rameters.

In order to account for a possible dependence on the component masses (mi), we parametrize our model using

a Taylor expansion in the p-g parameters around mi =

1.4M and sample from the posterior using the first two coefficients. Our model computes Ai as

Ai(mi) = A0+

dA dm _1.4M

!

(mi 1.4M ) , (2)

and uses A0 and dA/dm instead of A1 and A2. The

model uses similar representations for fiand niin terms

of the parameters f0, df /dm, n0, and dn/dm. We assume

a uniform prior on log10A0 within 10 10 A0 10 5.5,

a uniform prior in f0 within 10 Hz  f0  100 Hz, and

a uniform prior in n0 within 1  n0  3. The priors

on the first-order terms (dA/dm, df /dm, dn/dm) are the same as those in [27]; when m1 ⇠ m2, they imply A1 ⇠

A2, etc.

We investigate GW170817 using data from several dif-ferent frequency bands and with di↵erent spin priors, but unless otherwise noted we focus on results for data above 30 Hz with | i|  0.89. Throughout this letter,

results from GW170817 were obtained using the same data conditioning as [2], including the removal of a short-duration noise artifact from the Livingston data ([31] and discussion in [1]) along with other independently measured noise sources (see, e.g., [32–35]), calibration [36, 37], marginalization over calibration uncertainties, and whitening procedures [38,39].

III. MODEL SELECTION

Using GW data from GW170817, we perform Bayesian model selection. We compare a model that includes

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lin-ear tides, spin components alinged with the orbital an-gular momentum, and PN phasing e↵ects up to 3.5 PN phase terms (_H!pg) to an extension of this model that

also includes p-g e↵ects (_Hpg). Since we have nested

models (H!pg is obtained fromHpg as Ai ! 0)1, we use

the Savage-Dickey Density Ratio (see, e.g., [40–42]) to estimate the Bayes Factor (B_!pgpg = p(D_|Hpg)/p(D|H!pg),

where ✓ refers to all parameters besides the p-g phenomenological parameters, we note that R

df dn p(fi, ni|Ai,Hpg) = 18 Ai, and hxip denotes

the average of x with respect to the measure defined by p. Assuming that p(✓_|Hpg) = p(✓|H!pg), we

deter-mine ln B!pgpg from the ratio, as Ai ! 0, of the marginal

distribution of Aia priori to the distribution a posteriori

ln B_!pgpg = lim

Ai!0

[ln p(Ai|Hpg) ln p(Ai|D, Hpg)] . (4)

This allows us to directly measure ln B_!pgpg by extracting p(A|D, Hpg) from Monte-Carlo analyses with a known

prior p(A|H!pg). We confirmed that this estimate agrees

with estimates from both nested sampling [44] and ther-modynamic integration [45].

Figure 1 shows ln B_!pgpg as a function of flow, the

min-imum GW frequency considered. At a given flow, we

show the distribution of ln B_!pgpg due to the sampling un-certainty from the finite length of our MCMC chains. The solid and dashed curves correspond to the high-spin (_| i|  0.89) and low-spin (| i|  0.05) priors discussed

in [1–3].

For certain combinations of flow and | i|, we find

ln B_!pgpg > 0, suggesting Hpg is more likely than

H!pg. In order to assess how likely such values are,

we calculate ln B_!pgpg for a large number of simulated, high-spin signals with Ai = 0 and distinct

realiza-tions of detector noise from times near GW170817. We find that simulated signals without p-g e↵ects can readily produce ln B_!pgpg at least as large as the ones we measured from GW170817. For exam-ple, for the 30 Hz high-spin data we obtain ln B_!pgpg = 0.03+0.70_0.58(maximum a posteriori and 90% credible region) (bottom panel of Fig. 1), whereas approximately half

1 _{Since we use a uniform-in-log}

10A0prior,Hpg does not formally

include Ai= 0. Nonetheless, our lower limit on Aiis sufficiently

small thatH!pg is e↵ectively nested inHpg.

FIG. 1. Distributions of ln Bpg_!pg due to sampling uncertainty when analyzing GW170817 data with di↵erent values of flow.

The solid red curves assume high-spin priors (_| i|  0.89) and

the dashed blue curves assume low-spin priors (_| i|  0.05).

of our simulated signals yield ln B_!pgpgat least this large, i.e., a False Alarm Probability (FAP)_{⇡ 50%. We focus} on the 30 Hz, high-spin data because it corresponds to the largest bandwidth investigated and the largest signal-to-noise ratio. The high-spin prior is the most inclusive prior considered, and therefore allows the most model freedom when fitting p-g e↵ects.

In our model of the instability, the phase shift accumulates primarily at frequencies just above the

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sat-uration frequency f & fi. Therefore, if it is present, its

impact should become more apparent as we decrease the minimum GW frequency considered from flow fi to

flow. fi. We do see some indication of this behavior in

Fig. 1. However, we note that if our phenomenological model breaks down at f < fidue to poor modeling of the

pre-saturation behavior (e.g., if our step-function turn-on at fiis not a good approximation to the instability’s

in-duced phase shift), we might expect ln B_!pgpg to decrease as we lower flow below fi. If the fidelity of our model

is sufficiently poor, we could be insensitive to p-g e↵ects even at frequencies above flow.

IV. PARAMETER INFERENCE

We now investigate the constraints obtained from GW170817. Figure 2 shows the joint posterior distri-butions for both _Hpg and H!pg. We find that Hpg and

H!pg yield similar posterior distributions for all

non-p-g parameters, including both extrinsic and intrinsic parameters. The constraints on the chirp mass (_M), ef-fective spin e↵ = (m1 1 + m2 2)/(m1+ m2), and ˜⇤

are slightly weaker in _Hpg than H!pg. This is because

Hpg provides extra freedom to the signal’s duration in

the time-domain.

Regarding the p-g parameters, we find a noticeable peak near A0 ⇠ 10 7 with a flat tail to small A0. We

find A0  3.3 ⇥ 10 7 assuming a uniform-in-log10A0

prior and A0  6.8 ⇥ 10 7 assuming a uniform-in-A0

prior, both at 90% confidence.2 _{We also find a peak} at f0 ⇠ 70 Hz. The peaks persist when we analyze the

data from each interferometer separately, with reason-ably consistent locations and shapes (Fig.2). However, we find that the simulated signals with Ai = 0 can

pro-duce similar peaks, suggesting they may be due to noise alone. Similar to [27], we find that niis not strongly

con-strained and the gradient terms in the Taylor expansions are not measurable.

Theoretical arguments suggest an upper bound of A0 . 10 6 [27]. Therefore, our A0 constraint only rules

out the most extreme values of the p-g parameters.

V. DISCUSSION

While GW170817 is consistent with models that ne-glect p-g e↵ects, it is also consistent with a broad range of p-g parameters. The constraints from GW170817 im-ply that there are . 200 excited modes at f = 100 Hz, assuming all modes grow as rapidly as possible and sat-urate at their breaking amplitudes ( = = 1 in Eq. (7)

2 _{The upper limit with a uniform-in-A}

0prior is larger only because

we weight larger values of A0more a priori than with a

uniform-in-log10A0 prior.

of [27]) and that the frequency at which modes become unstable is well approximated by f0. For comparison,

theoretical arguments suggest an upper bound of_{⇠ 10}3

modes saturating by wave breaking [27]. More modes may be excited if they grow more slowly or saturate be-low their wave breaking energy.

We can also use the measured constraints to place up-per limits on the amount of energy dissipated by the p-g instability. As Fig. 3 shows, p-g e↵ects dissipate . 2.7 ⇥ 1051_{ergs throughout the entire inspiral at 90%}

confidence. In comparison, GWs carry away& 1053_ergs.

This implies time-domain phase shifts | | . 7.6 rad (0.6 orbits) at 100 Hz and _| _{| . 32 rad (2.6 orbits)} at 1000 Hz after accounting for the joint uncertainty in component masses, spins, linear tides, and p-g e↵ects.

A g-mode with natural frequency fg is

pre-dicted to become unstable at a frequency fcrit '

45 Hz(fg/10 4 fdyn)1/2, where fdynis the dynamical

fre-quency of the NS and is a slowly varying function typ-ically between 0.1 1 [25, 27]. Since the modes grow quickly, the frequency at which the instability saturates is likely close to the frequency at which the modes become unstable (f0 ' fcrit). If we assume that the observed

peak near f0⇠ 70 Hz is not due to noise alone, then the

maximum a posteriori estimate for f0along with

approx-imate values for the masses (1.4 M ) and radii (11 km) of the components [3] imply fg' 0.5 Hz.

With several more signals comparable to GW170817, it should be possible to improve the amplitude constraint to A0 . 10 7. Obtaining even tighter constraints will

likely require many more detections, especially since most events will have smaller SNR. Future measurements will also benefit from a better understanding of how the in-stability saturates. To date, there have only been de-tailed theoretical studies of the instability’s threshold and growth rate [23–26], not its saturation. As a result, we cannot be certain of the fidelity of our phenomenological model.

While this letter was in review, related work was posted [46] with the conclusion that the H!pg model is

strongly favored over the_Hpgmodel by a factor of at least

104_{. In Ref. [}₄₇_{], some of the authors of this work}

in-vestigate the origin of the discrepancy by analyzing pub-licly available posterior samples from Ref. [46]. Contrary to the claims in Ref. [46], they find that samples from Ref. [46] yield B_!pgpg _{⇠ 1 and therefore conclude that this} posterior data, like what is presented here, does not dis-favor the _Hpg model. Ref. [47] suggests that the error

stems from using too few temperatures when implement-ing thermodynamic integration.

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

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FIG. 2. Posterior distribributions for_H!pg (red) andHpgwith Hanford, Livingston, and Virgo data (thick black, grey shading),

Hanford data only (dark blue), and Livingston data only (light blue) using GW data above 30 Hz,| i|  0.89, and a

uniform-in-log₁₀A0 prior. Left: a subset of parameters shared byH!pgandHpg. Right: a subset of parameters belonging only toHpg. We

only show one-dimensional posteriors for the single instrument data, although the multi-dimensional posteriors are similarly consistent with the full Hpg data. Contours in the two-dimensional distributions represent 10%, 50%, and 90% confidence

regions for the_Hpg andH!pg models, respectively.

FIG. 3. Upper limits on the cumulative enegy dissipated by the p-g instability as a function of frequency. We note the rel-atively strong constraints at lower frequencies, where p-g ef-fects are more pronounced.

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, the De-partment of Science and Technology, India, the Science & Engineering Research Board (SERB), India, the Min-istry of Human Resource Development, India, the Span-ish Agencia Estatal de Investigación, the Vicepresidència i Conselleria d’Innovació, Recerca i Turisme and the Con-selleria d’Educació i Universitat del Govern de les Illes Balears, the Conselleria d’Educació, Investigació, Cul-tura i Esport de la Generalitat Valenciana, the National Science Centre of Poland, the Swiss National Science Foundation (SNSF), the Russian Foundation for Basic Research, the Russian Science Foundation, the European Commission, the European Regional Development Funds (ERDF), the Royal Society, the Scottish Funding

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Coun-cil, the Scottish Universities Physics Alliance, the Hun-garian Scientific Research Fund (OTKA), the Lyon In-stitute of Origins (LIO), the Paris ˆIle-de-France Region, the National Research, Development and Innovation Of-fice Hungary (NKFI), the National Research Foundation of Korea, Industry Canada and the Province of Ontario through the Ministry of Economic Development and In-novation, the Natural Science and Engineering Research Council Canada, the Canadian Institute for Advanced Research, the Brazilian Ministry of Science,

Technol-ogy, Innovations, and Communications, the International Center for Theoretical Physics South American Insti-tute for Fundamental Research (ICTP-SAIFR), the Re-search Grants Council of Hong Kong, the National Natu-ral Science Foundation of China (NSFC), the Leverhulme Trust, the Research Corporation, the Ministry of Science and Technology (MOST), Taiwan and the Kavli Foun-dation. The authors gratefully acknowledge the support of the NSF, STFC, MPS, INFN, CNRS and the State of Niedersachsen/Germany for provision of computational resources. N. Weinberg was supported in part by NASA grant NNX14AB40G.

[1] B. P. Abbott and etal (LIGO Scientific Collaboration and Virgo Collaboration),Phys. Rev. Lett. 119, 161101 (2017).

[2] The LIGO Scientific Collaboration, the Virgo Collabora-tion, B. P. Abbott, R. Abbott, T. D. Abbott, F. Acer-nese, K. Ackley, C. Adams, T. Adams, P. Addesso, and et al., ArXiv e-prints (2018),arXiv:1805.11579 [gr-qc]. [3] The LIGO Scientific Collaboration, the Virgo

Collabora-tion, B. P. Abbott, R. Abbott, T. D. Abbott, F. Acer-nese, K. Ackley, C. Adams, T. Adams, P. Addesso, and et al., ArXiv e-prints (2018),arXiv:1805.11581 [gr-qc]. [4] S. De, D. Finstad, J. M. Lattimer, D. A. Brown,

E. Berger, and C. M. Biwer, ArXiv e-prints (2018), arXiv:1804.08583 [astro-ph.HE].

[5] E. E. Flanagan and T. Hinderer,Phys. Rev. D 77, 021502 (2008).

[6] The LIGO Scientific Collaboration,Classical and Quan-tum Gravity 32, 074001 (2015).

[7] F. A. et al,Classical and Quantum Gravity 32, 024001 (2015).

[8] B. P. Abbott and et al.,The Astrophysical Journal Let-ters 848, L13 (2017).

[9] The LIGO Scientific Collaboration and The Virgo Col-laboration,The Astrophysical Journal Letters 851, L16 (2017).

[10] The LIGO Scientific Collaboration and The Virgo Col-laboration,The Astrophysical Journal Letters 850, L39 (2017).

[11] D. Radice, A. Perego, F. Zappa, and S. Bernuzzi, The Astrophysical Journal Letters 852, L29 (2018).

[12] M. W. Coughlin, T. Dietrich, Z. Doctor, D. Kasen, S. Coughlin, A. Jerkstrand, G. Leloudas, O. McBrien, B. D. Metzger, R. O’Shaughnessy, and S. J. Smartt, ArXiv e-prints (2018),arXiv:1805.09371 [astro-ph.HE]. [13] T. Hinderer, A. Taracchini, F. Foucart, A. Buonanno,

J. Steinho↵, M. Duez, L. E. Kidder, H. P. Pfei↵er, M. A. Scheel, B. Szilagyi, K. Hotokezaka, K. Kyutoku, M. Shi-bata, and C. W. Carpenter,Phys. Rev. Lett. 116, 181101 (2016).

[14] N. Andersson and W. C. G. Ho,Phys. Rev. D 97, 023016 (2018).

[15] D. Lai,Monthly Notices of the Royal Astronomical Soci-ety 270, 611 (1994).

[16] A. Reisenegger and P. Goldreich,Astrophys. J. 426, 688 (1994).

[17] W. C. G. Ho and D. Lai,Monthly Notices of the Royal

Astronomical Society 308, 153 (1999).

[18] D. Lai and Y. Wu, Phys. Rev. D 74, 024007 (2006), arXiv:astro-ph/0604163.

[19] É. É. Flanagan and É. Racine,Phys. Rev. D 75, 044001 (2007),arXiv:gr-qc/0601029.

[20] H. Yu and N. N. Weinberg,Monthly Notices of the Royal Astronomical Society 464, 2622 (2017).

[21] H. Yu and N. N. Weinberg,Monthly Notices of the Royal Astronomical Society 470, 350 (2017).

[22] W. Xu and D. Lai, Phys. Rev. D 96, 083005 (2017), arXiv:1708.01839 [astro-ph.HE].

[23] N. N. Weinberg, P. Arras, and J. Burkart,The Astro-physical Journal 769, 121 (2013).

[24] T. Venumadhav, A. Zimmerman, and C. M. Hirata,The Astrophysical Journal 781, 23 (2014).

[25] N. N. Weinberg, The Astrophysical Journal 819, 109 (2016).

[26] Y. Zhou and F. Zhang,The Astrophysical Journal 849, 114 (2017).

[27] R. Essick, S. Vitale, and N. N. Weinberg,Phys. Rev. D 94, 103012 (2016).

[28] A. Buonanno, B. R. Iyer, E. Ochsner, Y. Pan, and B. S. Sathyaprakash,Phys. Rev. D 80, 084043 (2009). [29] C. Cutler and E. E. Flanagan,Phys. Rev. D 49, 2658

(1994).

[30] M. Agathos, W. Del Pozzo, T. G. F. Li, C. Van Den Broeck, J. Veitch, and S. Vitale,Phys. Rev. D 89, 082001 (2014).

[31] C. Pankow, K. Chatziioannou, E. A. Chase, T. B. Litten-berg, M. Evans, J. McIver, N. J. Cornish, C.-J. Haster, J. Kanner, V. Raymond, S. Vitale, and A. Zimmerman, ArXiv e-prints (2018),arXiv:1808.03619 [gr-qc]. [32] J. C. Driggers et al., (2018),arXiv:1806.00532 [gr-qc]. [33] J. C. Driggers, M. Evans, K. Pepper, and R. Adhikari,

Review of Scientific Instruments 83, 024501 (2012), https://doi.org/10.1063/1.3675891.

[34] G. D. Meadors, K. Kawabe, and K. Riles,Classical and Quantum Gravity 31, 105014 (2014).

[35] V. Tiwari, M. Drago, V. Frolov, S. Klimenko, G. Mitsel-makher, V. Necula, G. Prodi, V. Re, F. Salemi, G. Ve-dovato, and I. Yakushin,Classical and Quantum Gravity 32, 165014 (2015).

[36] C. Cahillane, J. Betzwieser, D. A. Brown, E. Goetz, E. D. Hall, K. Izumi, S. Kandhasamy, S. Karki, J. S. Kissel, G. Mendell, R. L. Savage, D. Tuyenbayev, A. Urban, A. Viets, M. Wade, and A. J. Weinstein,Phys. Rev. D

(14)

96, 102001 (2017).

[37] A. D. Viets, M. Wade, A. L. Urban, S. Kand-hasamy, J. Betzwieser, D. A. Brown, J. Burguet-Castell, C. Cahillane, E. Goetz, K. Izumi, S. Karki, J. S. Kissel, G. Mendell, R. L. Savage, X. Siemens, D. Tuyenbayev, and A. J. Weinstein,Classical and Quantum Gravity 35, 095015 (2018).

[38] N. J. Cornish and T. B. Littenberg,Classical and Quan-tum Gravity 32, 135012 (2015).

[39] T. B. Littenberg and N. J. Cornish, Phys. Rev. D 91, 084034 (2015).

[40] J. M. Dickey and B. P. Lientz,Ann. Math. Statist. 41, 214 (1970).

[41] I. Verdinelli and L. Wasserman,Journal of the American Statistical Association 90, 614 (1995).

[42] E.-J. Wagenmakers, T. Lodewyckx, H. Kuriyal, and

R. Grasman,Cognitive Psychology 60, 158 (2010). [43] J. Veitch, V. Raymond, B. Farr, W. Farr, P. Gra↵,

S. Vitale, B. Aylott, K. Blackburn, N. Christensen, M. Coughlin, W. Del Pozzo, F. Feroz, J. Gair, C.-J. Haster, V. Kalogera, T. Littenberg, I. Mandel, R. O’Shaughnessy, M. Pitkin, C. Rodriguez, C. R¨over, T. Sidery, R. Smith, M. Van Der Sluys, A. Vecchio, W. Vousden, and L. Wade, Phys. Rev. D 91, 042003 (2015).

[44] J. Skilling,Bayesian Anal. 1, 833 (2006).

[45] N. Lartillot and H. Philippe,Systematic Biology 55, 195 (2006).

[46] S. Reyes and D. A. Brown, ArXiv e-prints (2018), arXiv:1808.07013 [astro-ph.HE].

[47] R. Essick and N. N. Weinberg, ArXiv e-prints (2018), arXiv:1809.00264 [astro-ph.HE].