of 20
Search for gravitational waves from Scorpius X-1 in the second Advanced LIGO
observing run with an improved hidden Markov model
B. P. Abbott,
1
R. Abbott,
1
T. D. Abbott,
2
S. Abraham,
3
F. Acernese,
4, 5
K. Ackley,
6
C. Adams,
7
R. X. Adhikari,
1
V. B. Adya,
8, 9
C. Affeldt,
8, 9
M. Agathos,
10
K. Agatsuma,
11
N. Aggarwal,
12
O. D. Aguiar,
13
L. Aiello,
14, 15
A. Ain,
3
P. Ajith,
16
G. Allen,
17
A. Allocca,
18, 19
M. A. Aloy,
20
P. A. Altin,
21
A. Amato,
22
A. Ananyeva,
1
S. B. Anderson,
1
W. G. Anderson,
23
S. V. Angelova,
24
S. Antier,
25
S. Appert,
1
K. Arai,
1
M. C. Araya,
1
J. S. Areeda,
26
M. Ar`ene,
27
N. Arnaud,
25, 28
S. Ascenzi,
29, 30
G. Ashton,
6
S. M. Aston,
7
P. Astone,
31
F. Aubin,
32
P. Aufmuth,
9
K. AultONeal,
33
C. Austin,
2
V. Avendano,
34
A. Avila-Alvarez,
26
S. Babak,
35, 27
P. Bacon,
27
F. Badaracco,
14, 15
M. K. M. Bader,
36
S. Bae,
37
P. T. Baker,
38
F. Baldaccini,
39, 40
G. Ballardin,
28
S. W. Ballmer,
41
S. Banagiri,
42
J. C. Barayoga,
1
S. E. Barclay,
43
B. C. Barish,
1
D. Barker,
44
K. Barkett,
45
S. Barnum,
12
F. Barone,
4, 5
B. Barr,
43
L. Barsotti,
12
M. Barsuglia,
27
D. Barta,
46
J. Bartlett,
44
I. Bartos,
47
R. Bassiri,
48
A. Basti,
18, 19
M. Bawaj,
49, 40
J. C. Bayley,
43
M. Bazzan,
50, 51
B. B ́ecsy,
52
M. Bejger,
27, 53
I. Belahcene,
25
A. S. Bell,
43
D. Beniwal,
54
B. K. Berger,
48
G. Bergmann,
8, 9
S. Bernuzzi,
55, 56
J. J. Bero,
57
C. P. L. Berry,
58
D. Bersanetti,
59
A. Bertolini,
36
J. Betzwieser,
7
R. Bhandare,
60
J. Bidler,
26
I. A. Bilenko,
61
S. A. Bilgili,
38
G. Billingsley,
1
J. Birch,
7
R. Birney,
24
O. Birnholtz,
57
S. Biscans,
1, 12
S. Biscoveanu,
6
A. Bisht,
9
M. Bitossi,
28, 19
M. A. Bizouard,
25
J. K. Blackburn,
1
C. D. Blair,
7
D. G. Blair,
62
R. M. Blair,
44
S. Bloemen,
63
N. Bode,
8, 9
M. Boer,
64
Y. Boetzel,
65
G. Bogaert,
64
F. Bondu,
66
E. Bonilla,
48
R. Bonnand,
32
P. Booker,
8, 9
B. A. Boom,
36
C. D. Booth,
67
R. Bork,
1
V. Boschi,
28
S. Bose,
68, 3
K. Bossie,
7
V. Bossilkov,
62
J. Bosveld,
62
Y. Bouffanais,
27
A. Bozzi,
28
C. Bradaschia,
19
P. R. Brady,
23
A. Bramley,
7
M. Branchesi,
14, 15
J. E. Brau,
69
T. Briant,
70
J. H. Briggs,
43
F. Brighenti,
71, 72
A. Brillet,
64
M. Brinkmann,
8, 9
V. Brisson,
25,
P. Brockill,
23
A. F. Brooks,
1
D. D. Brown,
54
S. Brunett,
1
A. Buikema,
12
T. Bulik,
73
H. J. Bulten,
74, 36
A. Buonanno,
35, 75
D. Buskulic,
32
C. Buy,
27
R. L. Byer,
48
M. Cabero,
8, 9
L. Cadonati,
76
G. Cagnoli,
22, 77
C. Cahillane,
1
J. Calder ́on Bustillo,
6
T. A. Callister,
1
E. Calloni,
78, 5
J. B. Camp,
79
W. A. Campbell,
6
M. Canepa,
80, 59
K. C. Cannon,
81
H. Cao,
54
J. Cao,
82
E. Capocasa,
27
F. Carbognani,
28
S. Caride,
83
M. F. Carney,
58
G. Carullo,
18
J. Casanueva Diaz,
19
C. Casentini,
29, 30
S. Caudill,
36
M. Cavagli`a,
84
F. Cavalier,
25
R. Cavalieri,
28
G. Cella,
19
P. Cerd ́a-Dur ́an,
20
G. Cerretani,
18, 19
E. Cesarini,
85, 30
O. Chaibi,
64
K. Chakravarti,
3
S. J. Chamberlin,
86
M. Chan,
43
S. Chao,
87
P. Charlton,
88
E. A. Chase,
58
E. Chassande-Mottin,
27
D. Chatterjee,
23
M. Chaturvedi,
60
B. D. Cheeseboro,
38
H. Y. Chen,
89
X. Chen,
62
Y. Chen,
45
H.-P. Cheng,
47
C. K. Cheong,
90
H. Y. Chia,
47
A. Chincarini,
59
A. Chiummo,
28
G. Cho,
91
H. S. Cho,
92
M. Cho,
75
N. Christensen,
64, 93
Q. Chu,
62
S. Chua,
70
K. W. Chung,
90
S. Chung,
62
G. Ciani,
50, 51
A. A. Ciobanu,
54
R. Ciolfi,
94, 95
F. Cipriano,
64
A. Cirone,
80, 59
F. Clara,
44
J. A. Clark,
76
P. Clearwater,
96
F. Cleva,
64
C. Cocchieri,
84
E. Coccia,
14, 15
P.-F. Cohadon,
70
D. Cohen,
25
R. Colgan,
97
M. Colleoni,
98
C. G. Collette,
99
C. Collins,
11
L. R. Cominsky,
100
M. Constancio Jr.,
13
L. Conti,
51
S. J. Cooper,
11
P. Corban,
7
T. R. Corbitt,
2
I. Cordero-Carri ́on,
101
K. R. Corley,
97
N. Cornish,
52
A. Corsi,
83
S. Cortese,
28
C. A. Costa,
13
R. Cotesta,
35
M. W. Coughlin,
1
S. B. Coughlin,
67, 58
J.-P. Coulon,
64
S. T. Countryman,
97
P. Couvares,
1
P. B. Covas,
98
E. E. Cowan,
76
D. M. Coward,
62
M. J. Cowart,
7
D. C. Coyne,
1
R. Coyne,
102
J. D. E. Creighton,
23
T. D. Creighton,
103
J. Cripe,
2
M. Croquette,
70
S. G. Crowder,
104
T. J. Cullen,
2
A. Cumming,
43
L. Cunningham,
43
E. Cuoco,
28
T. Dal Canton,
79
G. D ́alya,
105
S. L. Danilishin,
8, 9
S. D’Antonio,
30
K. Danzmann,
9, 8
A. Dasgupta,
106
C. F. Da Silva Costa,
47
L. E. H. Datrier,
43
V. Dattilo,
28
I. Dave,
60
M. Davier,
25
D. Davis,
41
E. J. Daw,
107
D. DeBra,
48
M. Deenadayalan,
3
J. Degallaix,
22
M. De Laurentis,
78, 5
S. Del ́eglise,
70
W. Del Pozzo,
18, 19
L. M. DeMarchi,
58
N. Demos,
12
T. Dent,
8, 9, 108
R. De Pietri,
109, 56
J. Derby,
26
R. De Rosa,
78, 5
C. De Rossi,
22, 28
R. DeSalvo,
110
O. de Varona,
8, 9
S. Dhurandhar,
3
M. C. D ́ıaz,
103
T. Dietrich,
36
L. Di Fiore,
5
M. Di Giovanni,
111, 95
T. Di Girolamo,
78, 5
A. Di Lieto,
18, 19
B. Ding,
99
S. Di Pace,
112, 31
I. Di Palma,
112, 31
F. Di Renzo,
18, 19
A. Dmitriev,
11
Z. Doctor,
89
F. Donovan,
12
K. L. Dooley,
67, 84
S. Doravari,
8, 9
I. Dorrington,
67
T. P. Downes,
23
M. Drago,
14, 15
J. C. Driggers,
44
Z. Du,
82
J.-G. Ducoin,
25
P. Dupej,
43
S. E. Dwyer,
44
P. J. Easter,
6
T. B. Edo,
107
M. C. Edwards,
93
A. Effler,
7
P. Ehrens,
1
J. Eichholz,
1
S. S. Eikenberry,
47
M. Eisenmann,
32
R. A. Eisenstein,
12
R. C. Essick,
89
H. Estelles,
98
D. Estevez,
32
Z. B. Etienne,
38
T. Etzel,
1
M. Evans,
12
T. M. Evans,
7
V. Fafone,
29, 30, 14
H. Fair,
41
S. Fairhurst,
67
X. Fan,
82
S. Farinon,
59
B. Farr,
69
W. M. Farr,
11
E. J. Fauchon-Jones,
67
M. Favata,
34
M. Fays,
107
M. Fazio,
113
C. Fee,
114
J. Feicht,
1
M. M. Fejer,
48
F. Feng,
27
A. Fernandez-Galiana,
12
I. Ferrante,
18, 19
E. C. Ferreira,
13
T. A. Ferreira,
13
F. Ferrini,
28
F. Fidecaro,
18, 19
I. Fiori,
28
D. Fiorucci,
27
M. Fishbach,
89
R. P. Fisher,
41, 115
J. M. Fishner,
12
M. Fitz-Axen,
42
R. Flaminio,
32, 116
M. Fletcher,
43
E. Flynn,
26
H. Fong,
117
J. A. Font,
20, 118
P. W. F. Forsyth,
21
J.-D. Fournier,
64
S. Frasca,
112, 31
F. Frasconi,
19
Z. Frei,
105
A. Freise,
11
R. Frey,
69
V. Frey,
25
P. Fritschel,
12
V. V. Frolov,
7
P. Fulda,
47
M. Fyffe,
7
H. A. Gabbard,
43
arXiv:1906.12040v1 [gr-qc] 28 Jun 2019
2
B. U. Gadre,
3
S. M. Gaebel,
11
J. R. Gair,
119
L. Gammaitoni,
39
M. R. Ganija,
54
S. G. Gaonkar,
3
A. Garcia,
26
C. Garc ́ıa-Quir ́os,
98
F. Garufi,
78, 5
B. Gateley,
44
S. Gaudio,
33
G. Gaur,
120
V. Gayathri,
121
G. Gemme,
59
E. Genin,
28
A. Gennai,
19
D. George,
17
J. George,
60
L. Gergely,
122
V. Germain,
32
S. Ghonge,
76
Abhirup Ghosh,
16
Archisman Ghosh,
36
S. Ghosh,
23
B. Giacomazzo,
111, 95
J. A. Giaime,
2, 7
K. D. Giardina,
7
A. Giazotto,
19,
K. Gill,
33
G. Giordano,
4, 5
L. Glover,
110
P. Godwin,
86
E. Goetz,
44
R. Goetz,
47
B. Goncharov,
6
G. Gonz ́alez,
2
J. M. Gonzalez Castro,
18, 19
A. Gopakumar,
123
M. L. Gorodetsky,
61
S. E. Gossan,
1
M. Gosselin,
28
R. Gouaty,
32
A. Grado,
124, 5
C. Graef,
43
M. Granata,
22
A. Grant,
43
S. Gras,
12
P. Grassia,
1
C. Gray,
44
R. Gray,
43
G. Greco,
71, 72
A. C. Green,
11, 47
R. Green,
67
E. M. Gretarsson,
33
P. Groot,
63
H. Grote,
67
S. Grunewald,
35
P. Gruning,
25
G. M. Guidi,
71, 72
H. K. Gulati,
106
Y. Guo,
36
A. Gupta,
86
M. K. Gupta,
106
E. K. Gustafson,
1
R. Gustafson,
125
L. Haegel,
98
O. Halim,
15, 14
B. R. Hall,
68
E. D. Hall,
12
E. Z. Hamilton,
67
G. Hammond,
43
M. Haney,
65
M. M. Hanke,
8, 9
J. Hanks,
44
C. Hanna,
86
M. D. Hannam,
67
O. A. Hannuksela,
90
J. Hanson,
7
T. Hardwick,
2
K. Haris,
16
J. Harms,
14, 15
G. M. Harry,
126
I. W. Harry,
35
C.-J. Haster,
117
K. Haughian,
43
F. J. Hayes,
43
J. Healy,
57
A. Heidmann,
70
M. C. Heintze,
7
H. Heitmann,
64
P. Hello,
25
G. Hemming,
28
M. Hendry,
43
I. S. Heng,
43
J. Hennig,
8, 9
A. W. Heptonstall,
1
Francisco Hernandez Vivanco,
6
M. Heurs,
8, 9
S. Hild,
43
T. Hinderer,
127, 36, 128
D. Hoak,
28
S. Hochheim,
8, 9
D. Hofman,
22
A. M. Holgado,
17
N. A. Holland,
21
K. Holt,
7
D. E. Holz,
89
P. Hopkins,
67
C. Horst,
23
J. Hough,
43
E. J. Howell,
62
C. G. Hoy,
67
A. Hreibi,
64
E. A. Huerta,
17
D. Huet,
25
B. Hughey,
33
M. Hulko,
1
S. Husa,
98
S. H. Huttner,
43
T. Huynh-Dinh,
7
B. Idzkowski,
73
A. Iess,
29, 30
C. Ingram,
54
R. Inta,
83
G. Intini,
112, 31
B. Irwin,
114
H. N. Isa,
43
J.-M. Isac,
70
M. Isi,
1
B. R. Iyer,
16
K. Izumi,
44
T. Jacqmin,
70
S. J. Jadhav,
129
K. Jani,
76
N. N. Janthalur,
129
P. Jaranowski,
130
A. C. Jenkins,
131
J. Jiang,
47
D. S. Johnson,
17
A. W. Jones,
11
D. I. Jones,
132
R. Jones,
43
R. J. G. Jonker,
36
L. Ju,
62
J. Junker,
8, 9
C. V. Kalaghatgi,
67
V. Kalogera,
58
B. Kamai,
1
S. Kandhasamy,
84
G. Kang,
37
J. B. Kanner,
1
S. J. Kapadia,
23
S. Karki,
69
K. S. Karvinen,
8, 9
R. Kashyap,
16
M. Kasprzack,
1
S. Katsanevas,
28
E. Katsavounidis,
12
W. Katzman,
7
S. Kaufer,
9
K. Kawabe,
44
N. V. Keerthana,
3
F. K ́ef ́elian,
64
D. Keitel,
43
R. Kennedy,
107
J. S. Key,
133
F. Y. Khalili,
61
H. Khan,
26
I. Khan,
14, 30
S. Khan,
8, 9
Z. Khan,
106
E. A. Khazanov,
134
M. Khursheed,
60
N. Kijbunchoo,
21
Chunglee Kim,
135
J. C. Kim,
136
K. Kim,
90
W. Kim,
54
W. S. Kim,
137
Y.-M. Kim,
138
C. Kimball,
58
E. J. King,
54
P. J. King,
44
M. Kinley-Hanlon,
126
R. Kirchhoff,
8, 9
J. S. Kissel,
44
L. Kleybolte,
139
J. H. Klika,
23
S. Klimenko,
47
T. D. Knowles,
38
P. Koch,
8, 9
S. M. Koehlenbeck,
8, 9
G. Koekoek,
36, 140
S. Koley,
36
V. Kondrashov,
1
A. Kontos,
12
N. Koper,
8, 9
M. Korobko,
139
W. Z. Korth,
1
I. Kowalska,
73
D. B. Kozak,
1
V. Kringel,
8, 9
N. Krishnendu,
141
A. Kr ́olak,
142, 143
G. Kuehn,
8, 9
A. Kumar,
129
P. Kumar,
144
R. Kumar,
106
S. Kumar,
16
L. Kuo,
87
A. Kutynia,
142
S. Kwang,
23
B. D. Lackey,
35
K. H. Lai,
90
T. L. Lam,
90
M. Landry,
44
B. B. Lane,
12
R. N. Lang,
145
J. Lange,
57
B. Lantz,
48
R. K. Lanza,
12
A. Lartaux-Vollard,
25
P. D. Lasky,
6
M. Laxen,
7
A. Lazzarini,
1
C. Lazzaro,
51
P. Leaci,
112, 31
S. Leavey,
8, 9
Y. K. Lecoeuche,
44
C. H. Lee,
92
H. K. Lee,
146
H. M. Lee,
147
H. W. Lee,
136
J. Lee,
91
K. Lee,
43
J. Lehmann,
8, 9
A. Lenon,
38
N. Leroy,
25
N. Letendre,
32
Y. Levin,
6, 97
J. Li,
82
K. J. L. Li,
90
T. G. F. Li,
90
X. Li,
45
F. Lin,
6
F. Linde,
36
S. D. Linker,
110
T. B. Littenberg,
148
J. Liu,
62
X. Liu,
23
R. K. L. Lo,
90, 1
N. A. Lockerbie,
24
L. T. London,
67
A. Longo,
149, 150
M. Lorenzini,
14, 15
V. Loriette,
151
M. Lormand,
7
G. Losurdo,
19
J. D. Lough,
8, 9
C. O. Lousto,
57
G. Lovelace,
26
M. E. Lower,
152
H. L ̈uck,
9, 8
D. Lumaca,
29, 30
A. P. Lundgren,
153
R. Lynch,
12
Y. Ma,
45
R. Macas,
67
S. Macfoy,
24
M. MacInnis,
12
D. M. Macleod,
67
A. Macquet,
64
F. Maga ̃na-Sandoval,
41
L. Maga ̃na Zertuche,
84
R. M. Magee,
86
E. Majorana,
31
I. Maksimovic,
151
A. Malik,
60
N. Man,
64
V. Mandic,
42
V. Mangano,
43
G. L. Mansell,
44, 12
M. Manske,
23, 21
M. Mantovani,
28
F. Marchesoni,
49, 40
F. Marion,
32
S. M ́arka,
97
Z. M ́arka,
97
C. Markakis,
10, 17
A. S. Markosyan,
48
A. Markowitz,
1
E. Maros,
1
A. Marquina,
101
S. Marsat,
35
F. Martelli,
71, 72
I. W. Martin,
43
R. M. Martin,
34
D. V. Martynov,
11
K. Mason,
12
E. Massera,
107
A. Masserot,
32
T. J. Massinger,
1
M. Masso-Reid,
43
S. Mastrogiovanni,
112, 31
A. Matas,
42, 35
F. Matichard,
1, 12
L. Matone,
97
N. Mavalvala,
12
N. Mazumder,
68
J. J. McCann,
62
R. McCarthy,
44
D. E. McClelland,
21
S. McCormick,
7
L. McCuller,
12
S. C. McGuire,
154
J. McIver,
1
D. J. McManus,
21
T. McRae,
21
S. T. McWilliams,
38
D. Meacher,
86
G. D. Meadors,
6
M. Mehmet,
8, 9
A. K. Mehta,
16
J. Meidam,
36
A. Melatos,
96
G. Mendell,
44
R. A. Mercer,
23
L. Mereni,
22
E. L. Merilh,
44
M. Merzougui,
64
S. Meshkov,
1
C. Messenger,
43
C. Messick,
86
R. Metzdorff,
70
P. M. Meyers,
96
H. Miao,
11
C. Michel,
22
H. Middleton,
96
E. E. Mikhailov,
155
L. Milano,
78, 5
A. L. Miller,
47
A. Miller,
112, 31
M. Millhouse,
52
J. C. Mills,
67
M. C. Milovich-Goff,
110
O. Minazzoli,
64, 156
Y. Minenkov,
30
A. Mishkin,
47
C. Mishra,
157
T. Mistry,
107
S. Mitra,
3
V. P. Mitrofanov,
61
G. Mitselmakher,
47
R. Mittleman,
12
G. Mo,
93
D. Moffa,
114
K. Mogushi,
84
S. R. P. Mohapatra,
12
M. Montani,
71, 72
C. J. Moore,
10
D. Moraru,
44
G. Moreno,
44
S. Morisaki,
81
B. Mours,
32
C. M. Mow-Lowry,
11
Arunava Mukherjee,
8, 9
D. Mukherjee,
23
S. Mukherjee,
103
N. Mukund,
3
A. Mullavey,
7
J. Munch,
54
E. A. Mu ̃niz,
41
M. Muratore,
33
P. G. Murray,
43
A. Nagar,
85, 158, 159
I. Nardecchia,
29, 30
L. Naticchioni,
112, 31
R. K. Nayak,
160
J. Neilson,
110
3
G. Nelemans,
63, 36
T. J. N. Nelson,
7
M. Nery,
8, 9
A. Neunzert,
125
K. Y. Ng,
12
S. Ng,
54
P. Nguyen,
69
D. Nichols,
127, 36
S. Nissanke,
127, 36
F. Nocera,
28
C. North,
67
L. K. Nuttall,
153
M. Obergaulinger,
20
J. Oberling,
44
B. D. O’Brien,
47
G. D. O’Dea,
110
G. H. Ogin,
161
J. J. Oh,
137
S. H. Oh,
137
F. Ohme,
8, 9
H. Ohta,
81
M. A. Okada,
13
M. Oliver,
98
P. Oppermann,
8, 9
Richard J. Oram,
7
B. O’Reilly,
7
R. G. Ormiston,
42
L. F. Ortega,
47
R. O’Shaughnessy,
57
S. Ossokine,
35
D. J. Ottaway,
54
H. Overmier,
7
B. J. Owen,
83
A. E. Pace,
86
G. Pagano,
18, 19
M. A. Page,
62
A. Pai,
121
S. A. Pai,
60
J. R. Palamos,
69
O. Palashov,
134
C. Palomba,
31
A. Pal-Singh,
139
Huang-Wei Pan,
87
B. Pang,
45
P. T. H. Pang,
90
C. Pankow,
58
F. Pannarale,
112, 31
B. C. Pant,
60
F. Paoletti,
19
A. Paoli,
28
A. Parida,
3
W. Parker,
7, 154
D. Pascucci,
43
A. Pasqualetti,
28
R. Passaquieti,
18, 19
D. Passuello,
19
M. Patil,
143
B. Patricelli,
18, 19
B. L. Pearlstone,
43
C. Pedersen,
67
M. Pedraza,
1
R. Pedurand,
22, 162
A. Pele,
7
S. Penn,
163
C. J. Perez,
44
A. Perreca,
111, 95
H. P. Pfeiffer,
35, 117
M. Phelps,
8, 9
K. S. Phukon,
3
O. J. Piccinni,
112, 31
M. Pichot,
64
F. Piergiovanni,
71, 72
G. Pillant,
28
L. Pinard,
22
M. Pirello,
44
M. Pitkin,
43
R. Poggiani,
18, 19
D. Y. T. Pong,
90
S. Ponrathnam,
3
P. Popolizio,
28
E. K. Porter,
27
J. Powell,
152
A. K. Prajapati,
106
J. Prasad,
3
K. Prasai,
48
R. Prasanna,
129
G. Pratten,
98
T. Prestegard,
23
S. Privitera,
35
G. A. Prodi,
111, 95
L. G. Prokhorov,
61
O. Puncken,
8, 9
M. Punturo,
40
P. Puppo,
31
M. P ̈urrer,
35
H. Qi,
23
V. Quetschke,
103
P. J. Quinonez,
33
E. A. Quintero,
1
R. Quitzow-James,
69
F. J. Raab,
44
H. Radkins,
44
N. Radulescu,
64
P. Raffai,
105
S. Raja,
60
C. Rajan,
60
B. Rajbhandari,
83
M. Rakhmanov,
103
K. E. Ramirez,
103
A. Ramos-Buades,
98
Javed Rana,
3
K. Rao,
58
P. Rapagnani,
112, 31
V. Raymond,
67
M. Razzano,
18, 19
J. Read,
26
T. Regimbau,
32
L. Rei,
59
S. Reid,
24
D. H. Reitze,
1, 47
W. Ren,
17
F. Ricci,
112, 31
C. J. Richardson,
33
J. W. Richardson,
1
P. M. Ricker,
17
K. Riles,
125
M. Rizzo,
58
N. A. Robertson,
1, 43
R. Robie,
43
F. Robinet,
25
A. Rocchi,
30
L. Rolland,
32
J. G. Rollins,
1
V. J. Roma,
69
M. Romanelli,
66
R. Romano,
4, 5
C. L. Romel,
44
J. H. Romie,
7
K. Rose,
114
D. Rosi ́nska,
164, 53
S. G. Rosofsky,
17
M. P. Ross,
165
S. Rowan,
43
A. R ̈udiger,
8, 9,
P. Ruggi,
28
G. Rutins,
166
K. Ryan,
44
S. Sachdev,
1
T. Sadecki,
44
M. Sakellariadou,
131
L. Salconi,
28
M. Saleem,
141
A. Samajdar,
36
L. Sammut,
6
E. J. Sanchez,
1
L. E. Sanchez,
1
N. Sanchis-Gual,
20
V. Sandberg,
44
J. R. Sanders,
41
K. A. Santiago,
34
N. Sarin,
6
B. Sassolas,
22
P. R. Saulson,
41
O. Sauter,
125
R. L. Savage,
44
P. Schale,
69
M. Scheel,
45
J. Scheuer,
58
P. Schmidt,
63
R. Schnabel,
139
R. M. S. Schofield,
69
A. Sch ̈onbeck,
139
E. Schreiber,
8, 9
B. W. Schulte,
8, 9
B. F. Schutz,
67
S. G. Schwalbe,
33
J. Scott,
43
S. M. Scott,
21
E. Seidel,
17
D. Sellers,
7
A. S. Sengupta,
167
N. Sennett,
35
D. Sentenac,
28
V. Sequino,
29, 30, 14
A. Sergeev,
134
Y. Setyawati,
8, 9
D. A. Shaddock,
21
T. Shaffer,
44
M. S. Shahriar,
58
M. B. Shaner,
110
L. Shao,
35
P. Sharma,
60
P. Shawhan,
75
H. Shen,
17
R. Shink,
168
D. H. Shoemaker,
12
D. M. Shoemaker,
76
S. ShyamSundar,
60
K. Siellez,
76
M. Sieniawska,
53
D. Sigg,
44
A. D. Silva,
13
L. P. Singer,
79
N. Singh,
73
A. Singhal,
14, 31
A. M. Sintes,
98
S. Sitmukhambetov,
103
V. Skliris,
67
B. J. J. Slagmolen,
21
T. J. Slaven-Blair,
62
J. R. Smith,
26
R. J. E. Smith,
6
S. Somala,
169
E. J. Son,
137
B. Sorazu,
43
F. Sorrentino,
59
T. Souradeep,
3
E. Sowell,
83
A. P. Spencer,
43
A. K. Srivastava,
106
V. Srivastava,
41
K. Staats,
58
C. Stachie,
64
M. Standke,
8, 9
D. A. Steer,
27
M. Steinke,
8, 9
J. Steinlechner,
139, 43
S. Steinlechner,
139
D. Steinmeyer,
8, 9
S. P. Stevenson,
152
D. Stocks,
48
R. Stone,
103
D. J. Stops,
11
K. A. Strain,
43
G. Stratta,
71, 72
S. E. Strigin,
61
A. Strunk,
44
R. Sturani,
170
A. L. Stuver,
171
V. Sudhir,
12
T. Z. Summerscales,
172
L. Sun,
1
S. Sunil,
106
J. Suresh,
3
P. J. Sutton,
67
B. L. Swinkels,
36
M. J. Szczepa ́nczyk,
33
M. Tacca,
36
S. C. Tait,
43
C. Talbot,
6
D. Talukder,
69
D. B. Tanner,
47
M. T ́apai,
122
A. Taracchini,
35
J. D. Tasson,
93
R. Taylor,
1
F. Thies,
8, 9
M. Thomas,
7
P. Thomas,
44
S. R. Thondapu,
60
K. A. Thorne,
7
E. Thrane,
6
Shubhanshu Tiwari,
111, 95
Srishti Tiwari,
123
V. Tiwari,
67
K. Toland,
43
M. Tonelli,
18, 19
Z. Tornasi,
43
A. Torres-Forn ́e,
173
C. I. Torrie,
1
D. T ̈oyr ̈a,
11
F. Travasso,
28, 40
G. Traylor,
7
M. C. Tringali,
73
A. Trovato,
27
L. Trozzo,
174, 19
R. Trudeau,
1
K. W. Tsang,
36
M. Tse,
12
R. Tso,
45
L. Tsukada,
81
D. Tsuna,
81
D. Tuyenbayev,
103
K. Ueno,
81
D. Ugolini,
175
C. S. Unnikrishnan,
123
A. L. Urban,
2
S. A. Usman,
67
H. Vahlbruch,
9
G. Vajente,
1
G. Valdes,
2
N. van Bakel,
36
M. van Beuzekom,
36
J. F. J. van den Brand,
74, 36
C. Van Den Broeck,
36, 176
D. C. Vander-Hyde,
41
J. V. van Heijningen,
62
L. van der Schaaf,
36
A. A. van Veggel,
43
M. Vardaro,
50, 51
V. Varma,
45
S. Vass,
1
M. Vas ́uth,
46
A. Vecchio,
11
G. Vedovato,
51
J. Veitch,
43
P. J. Veitch,
54
K. Venkateswara,
165
G. Venugopalan,
1
D. Verkindt,
32
F. Vetrano,
71, 72
A. Vicer ́e,
71, 72
A. D. Viets,
23
D. J. Vine,
166
J.-Y. Vinet,
64
S. Vitale,
12
T. Vo,
41
H. Vocca,
39, 40
C. Vorvick,
44
S. P. Vyatchanin,
61
A. R. Wade,
1
L. E. Wade,
114
M. Wade,
114
R. Walet,
36
M. Walker,
26
L. Wallace,
1
S. Walsh,
23
G. Wang,
14, 19
H. Wang,
11
J. Z. Wang,
125
W. H. Wang,
103
Y. F. Wang,
90
R. L. Ward,
21
Z. A. Warden,
33
J. Warner,
44
M. Was,
32
J. Watchi,
99
B. Weaver,
44
L.-W. Wei,
8, 9
M. Weinert,
8, 9
A. J. Weinstein,
1
R. Weiss,
12
F. Wellmann,
8, 9
L. Wen,
62
E. K. Wessel,
17
P. Weßels,
8, 9
J. W. Westhouse,
33
K. Wette,
21
J. T. Whelan,
57
B. F. Whiting,
47
C. Whittle,
12
D. M. Wilken,
8, 9
D. Williams,
43
A. R. Williamson,
127, 36
J. L. Willis,
1
B. Willke,
8, 9
M. H. Wimmer,
8, 9
W. Winkler,
8, 9
C. C. Wipf,
1
H. Wittel,
8, 9
G. Woan,
43
J. Woehler,
8, 9
J. K. Wofford,
57
J. Worden,
44
J. L. Wright,
43
D. S. Wu,
8, 9
D. M. Wysocki,
57
L. Xiao,
1
H. Yamamoto,
1
C. C. Yancey,
75
L. Yang,
113
M. J. Yap,
21
M. Yazback,
47
D. W. Yeeles,
67
Hang Yu,
12
Haocun Yu,
12
4
S. H. R. Yuen,
90
M. Yvert,
32
A. K. Zadro ̇zny,
103, 142
M. Zanolin,
33
T. Zelenova,
28
J.-P. Zendri,
51
M. Zevin,
58
J. Zhang,
62
L. Zhang,
1
T. Zhang,
43
C. Zhao,
62
M. Zhou,
58
Z. Zhou,
58
X. J. Zhu,
6
M. E. Zucker,
1, 12
and J. Zweizig
1
(The LIGO Scientific Collaboration and the Virgo Collaboration)
L. M. Dunn,
96
S. Suvorova,
96
R. J. Evans,
96
and W. Moran
96
1
LIGO, California Institute of Technology, Pasadena, CA 91125, USA
2
Louisiana State University, Baton Rouge, LA 70803, USA
3
Inter-University Centre for Astronomy and Astrophysics, Pune 411007, India
4
Universit`a di Salerno, Fisciano, I-84084 Salerno, Italy
5
INFN, Sezione di Napoli, Complesso Universitario di Monte S.Angelo, I-80126 Napoli, Italy
6
OzGrav, School of Physics & Astronomy, Monash University, Clayton 3800, Victoria, Australia
7
LIGO Livingston Observatory, Livingston, LA 70754, USA
8
Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-30167 Hannover, Germany
9
Leibniz Universit ̈at Hannover, D-30167 Hannover, Germany
10
University of Cambridge, Cambridge CB2 1TN, United Kingdom
11
University of Birmingham, Birmingham B15 2TT, United Kingdom
12
LIGO, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
13
Instituto Nacional de Pesquisas Espaciais, 12227-010 S ̃ao Jos ́e dos Campos, S ̃ao Paulo, Brazil
14
Gran Sasso Science Institute (GSSI), I-67100 L’Aquila, Italy
15
INFN, Laboratori Nazionali del Gran Sasso, I-67100 Assergi, Italy
16
International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India
17
NCSA, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
18
Universit`a di Pisa, I-56127 Pisa, Italy
19
INFN, Sezione di Pisa, I-56127 Pisa, Italy
20
Departamento de Astronom ́ıa y Astrof ́ısica, Universitat de Val`encia, E-46100 Burjassot, Val`encia, Spain
21
OzGrav, Australian National University, Canberra, Australian Capital Territory 0200, Australia
22
Laboratoire des Mat ́eriaux Avanc ́es (LMA), CNRS/IN2P3, F-69622 Villeurbanne, France
23
University of Wisconsin-Milwaukee, Milwaukee, WI 53201, USA
24
SUPA, University of Strathclyde, Glasgow G1 1XQ, United Kingdom
25
LAL, Univ. Paris-Sud, CNRS/IN2P3, Universit ́e Paris-Saclay, F-91898 Orsay, France
26
California State University Fullerton, Fullerton, CA 92831, USA
27
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
28
European Gravitational Observatory (EGO), I-56021 Cascina, Pisa, Italy
29
Universit`a di Roma Tor Vergata, I-00133 Roma, Italy
30
INFN, Sezione di Roma Tor Vergata, I-00133 Roma, Italy
31
INFN, Sezione di Roma, I-00185 Roma, Italy
32
Laboratoire d’Annecy de Physique des Particules (LAPP), Univ. Grenoble Alpes,
Universit ́e Savoie Mont Blanc, CNRS/IN2P3, F-74941 Annecy, France
33
Embry-Riddle Aeronautical University, Prescott, AZ 86301, USA
34
Montclair State University, Montclair, NJ 07043, USA
35
Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-14476 Potsdam-Golm, Germany
36
Nikhef, Science Park 105, 1098 XG Amsterdam, The Netherlands
37
Korea Institute of Science and Technology Information, Daejeon 34141, South Korea
38
West Virginia University, Morgantown, WV 26506, USA
39
Universit`a di Perugia, I-06123 Perugia, Italy
40
INFN, Sezione di Perugia, I-06123 Perugia, Italy
41
Syracuse University, Syracuse, NY 13244, USA
42
University of Minnesota, Minneapolis, MN 55455, USA
43
SUPA, University of Glasgow, Glasgow G12 8QQ, United Kingdom
44
LIGO Hanford Observatory, Richland, WA 99352, USA
45
Caltech CaRT, Pasadena, CA 91125, USA
46
Wigner RCP, RMKI, H-1121 Budapest, Konkoly Thege Mikl ́os ́ut 29-33, Hungary
47
University of Florida, Gainesville, FL 32611, USA
48
Stanford University, Stanford, CA 94305, USA
49
Universit`a di Camerino, Dipartimento di Fisica, I-62032 Camerino, Italy
50
Universit`a di Padova, Dipartimento di Fisica e Astronomia, I-35131 Padova, Italy
51
INFN, Sezione di Padova, I-35131 Padova, Italy
52
Montana State University, Bozeman, MT 59717, USA
53
Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, 00-716, Warsaw, Poland
54
OzGrav, University of Adelaide, Adelaide, South Australia 5005, Australia
5
55
Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universit ̈at Jena, D-07743 Jena, Germany
56
INFN, Sezione di Milano Bicocca, Gruppo Collegato di Parma, I-43124 Parma, Italy
57
Rochester Institute of Technology, Rochester, NY 14623, USA
58
Center for Interdisciplinary Exploration & Research in Astrophysics (CIERA),
Northwestern University, Evanston, IL 60208, USA
59
INFN, Sezione di Genova, I-16146 Genova, Italy
60
RRCAT, Indore, Madhya Pradesh 452013, India
61
Faculty of Physics, Lomonosov Moscow State University, Moscow 119991, Russia
62
OzGrav, University of Western Australia, Crawley, Western Australia 6009, Australia
63
Department of Astrophysics/IMAPP, Radboud University Nijmegen,
P.O. Box 9010, 6500 GL Nijmegen, The Netherlands
64
Artemis, Universit ́e Cˆote d’Azur, Observatoire Cˆote d’Azur,
CNRS, CS 34229, F-06304 Nice Cedex 4, France
65
Physik-Institut, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland
66
Univ Rennes, CNRS, Institut FOTON - UMR6082, F-3500 Rennes, France
67
Cardiff University, Cardiff CF24 3AA, United Kingdom
68
Washington State University, Pullman, WA 99164, USA
69
University of Oregon, Eugene, OR 97403, USA
70
Laboratoire Kastler Brossel, Sorbonne Universit ́e, CNRS,
ENS-Universit ́e PSL, Coll`ege de France, F-75005 Paris, France
71
Universit`a degli Studi di Urbino ’Carlo Bo,’ I-61029 Urbino, Italy
72
INFN, Sezione di Firenze, I-50019 Sesto Fiorentino, Firenze, Italy
73
Astronomical Observatory Warsaw University, 00-478 Warsaw, Poland
74
VU University Amsterdam, 1081 HV Amsterdam, The Netherlands
75
University of Maryland, College Park, MD 20742, USA
76
School of Physics, Georgia Institute of Technology, Atlanta, GA 30332, USA
77
Universit ́e Claude Bernard Lyon 1, F-69622 Villeurbanne, France
78
Universit`a di Napoli ’Federico II,’ Complesso Universitario di Monte S.Angelo, I-80126 Napoli, Italy
79
NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA
80
Dipartimento di Fisica, Universit`a degli Studi di Genova, I-16146 Genova, Italy
81
RESCEU, University of Tokyo, Tokyo, 113-0033, Japan.
82
Tsinghua University, Beijing 100084, China
83
Texas Tech University, Lubbock, TX 79409, USA
84
The University of Mississippi, University, MS 38677, USA
85
Museo Storico della Fisica e Centro Studi e Ricerche “Enrico Fermi”,
I-00184 Roma, Italyrico Fermi, I-00184 Roma, Italy
86
The Pennsylvania State University, University Park, PA 16802, USA
87
National Tsing Hua University, Hsinchu City, 30013 Taiwan, Republic of China
88
Charles Sturt University, Wagga Wagga, New South Wales 2678, Australia
89
University of Chicago, Chicago, IL 60637, USA
90
The Chinese University of Hong Kong, Shatin, NT, Hong Kong
91
Seoul National University, Seoul 08826, South Korea
92
Pusan National University, Busan 46241, South Korea
93
Carleton College, Northfield, MN 55057, USA
94
INAF, Osservatorio Astronomico di Padova, I-35122 Padova, Italy
95
INFN, Trento Institute for Fundamental Physics and Applications, I-38123 Povo, Trento, Italy
96
OzGrav, University of Melbourne, Parkville, Victoria 3010, Australia
97
Columbia University, New York, NY 10027, USA
98
Universitat de les Illes Balears, IAC3—IEEC, E-07122 Palma de Mallorca, Spain
99
Universit ́e Libre de Bruxelles, Brussels 1050, Belgium
100
Sonoma State University, Rohnert Park, CA 94928, USA
101
Departamento de Matem ́aticas, Universitat de Val`encia, E-46100 Burjassot, Val`encia, Spain
102
University of Rhode Island, Kingston, RI 02881, USA
103
The University of Texas Rio Grande Valley, Brownsville, TX 78520, USA
104
Bellevue College, Bellevue, WA 98007, USA
105
MTA-ELTE Astrophysics Research Group, Institute of Physics, E ̈otv ̈os University, Budapest 1117, Hungary
106
Institute for Plasma Research, Bhat, Gandhinagar 382428, India
107
The University of Sheffield, Sheffield S10 2TN, United Kingdom
108
IGFAE, Campus Sur, Universidade de Santiago de Compostela, 15782 Spain
109
Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Universit`a di Parma, I-43124 Parma, Italy
110
California State University, Los Angeles, 5151 State University Dr, Los Angeles, CA 90032, USA
111
Universit`a di Trento, Dipartimento di Fisica, I-38123 Povo, Trento, Italy
112
Universit`a di Roma ’La Sapienza,’ I-00185 Roma, Italy
113
Colorado State University, Fort Collins, CO 80523, USA
6
114
Kenyon College, Gambier, OH 43022, USA
115
Christopher Newport University, Newport News, VA 23606, USA
116
National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan
117
Canadian Institute for Theoretical Astrophysics,
University of Toronto, Toronto, Ontario M5S 3H8, Canada
118
Observatori Astron`omic, Universitat de Val`encia, E-46980 Paterna, Val`encia, Spain
119
School of Mathematics, University of Edinburgh, Edinburgh EH9 3FD, United Kingdom
120
Institute Of Advanced Research, Gandhinagar 382426, India
121
Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India
122
University of Szeged, D ́om t ́er 9, Szeged 6720, Hungary
123
Tata Institute of Fundamental Research, Mumbai 400005, India
124
INAF, Osservatorio Astronomico di Capodimonte, I-80131, Napoli, Italy
125
University of Michigan, Ann Arbor, MI 48109, USA
126
American University, Washington, D.C. 20016, USA
127
GRAPPA, Anton Pannekoek Institute for Astronomy and Institute of High-Energy Physics,
University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
128
Delta Institute for Theoretical Physics, Science Park 904, 1090 GL Amsterdam, The Netherlands
129
Directorate of Construction, Services & Estate Management, Mumbai 400094 India
130
University of Bia lystok, 15-424 Bia lystok, Poland
131
King’s College London, University of London, London WC2R 2LS, United Kingdom
132
University of Southampton, Southampton SO17 1BJ, United Kingdom
133
University of Washington Bothell, Bothell, WA 98011, USA
134
Institute of Applied Physics, Nizhny Novgorod, 603950, Russia
135
Ewha Womans University, Seoul 03760, South Korea
136
Inje University Gimhae, South Gyeongsang 50834, South Korea
137
National Institute for Mathematical Sciences, Daejeon 34047, South Korea
138
Ulsan National Institute of Science and Technology, Ulsan 44919, South Korea
139
Universit ̈at Hamburg, D-22761 Hamburg, Germany
140
Maastricht University, P.O. Box 616, 6200 MD Maastricht, The Netherlands
141
Chennai Mathematical Institute, Chennai 603103, India
142
NCBJ, 05-400
́
Swierk-Otwock, Poland
143
Institute of Mathematics, Polish Academy of Sciences, 00656 Warsaw, Poland
144
Cornell University, Ithaca, NY 14850, USA
145
Hillsdale College, Hillsdale, MI 49242, USA
146
Hanyang University, Seoul 04763, South Korea
147
Korea Astronomy and Space Science Institute, Daejeon 34055, South Korea
148
NASA Marshall Space Flight Center, Huntsville, AL 35811, USA
149
Dipartimento di Matematica e Fisica, Universit`a degli Studi Roma Tre, I-00146 Roma, Italy
150
INFN, Sezione di Roma Tre, I-00146 Roma, Italy
151
ESPCI, CNRS, F-75005 Paris, France
152
OzGrav, Swinburne University of Technology, Hawthorn VIC 3122, Australia
153
University of Portsmouth, Portsmouth, PO1 3FX, United Kingdom
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College of William and Mary, Williamsburg, VA 23187, USA
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Centre Scientifique de Monaco, 8 quai Antoine Ier, MC-98000, Monaco
157
Indian Institute of Technology Madras, Chennai 600036, India
158
INFN Sezione di Torino, Via P. Giuria 1, I-10125 Torino, Italy
159
Institut des Hautes Etudes Scientifiques, F-91440 Bures-sur-Yvette, France
160
IISER-Kolkata, Mohanpur, West Bengal 741252, India
161
Whitman College, 345 Boyer Avenue, Walla Walla, WA 99362 USA
162
Universit ́e de Lyon, F-69361 Lyon, France
163
Hobart and William Smith Colleges, Geneva, NY 14456, USA
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Janusz Gil Institute of Astronomy, University of Zielona G ́ora, 65-265 Zielona G ́ora, Poland
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SUPA, University of the West of Scotland, Paisley PA1 2BE, United Kingdom
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Indian Institute of Technology, Gandhinagar Ahmedabad Gujarat 382424, India
168
Universit ́e de Montr ́eal/Polytechnique, Montreal, Quebec H3T 1J4, Canada
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Indian Institute of Technology Hyderabad, Sangareddy, Khandi, Telangana 502285, India
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International Institute of Physics, Universidade Federal do Rio Grande do Norte, Natal RN 59078-970, Brazil
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172
Andrews University, Berrien Springs, MI 49104, USA
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Max Planck Institute for Gravitationalphysik (Albert Einstein Institute), D-14476 Potsdam-Golm, Germany
174
Universit`a di Siena, I-53100 Siena, Italy
175
Trinity University, San Antonio, TX 78212, USA
7
176
Van Swinderen Institute for Particle Physics and Gravity,
University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands
We present results from a semicoherent search for continuous gravitational waves from the low-
mass X-ray binary Scorpius X-1, using a hidden Markov model (HMM) to track spin wandering. This
search improves on previous HMM-based searches of LIGO data by using an improved frequency do-
main matched filter, the
J
-statistic, and by analysing data from Advanced LIGO’s second observing
run. In the frequency range searched, from 60 to 650 Hz, we find no evidence of gravitational radi-
ation. At 194
.
6 Hz, the most sensitive search frequency, we report an upper limit on gravitational
wave strain (at 95% confidence) of
h
95%
0
= 3
.
47
×
10
25
when marginalising over source inclination
angle. This is the most sensitive search for Scorpius X-1, to date, that is specifically designed to be
robust in the presence of spin wandering.
I. INTRODUCTION
Rotating neutron stars with non-axisymmetric de-
formations are predicted to emit persistent, periodic
gravitational radiation.
They are a key target for
continuous-wave searches performed with gravitational
wave (GW) detectors such as the second-generation Ad-
vanced Laser Interferometer Gravitational-wave Obser-
vatory (Advanced LIGO) [1–5] and Virgo [4]. The time-
varying quadrupole moment necessary for GW emission
may result from thermal [6, 7], or magnetic [8–10] gradi-
ents,
r
-modes [11–13], or nonaxisymmetric circulation of
the superfluid interior [14–17]. These mechanisms pro-
duce signals at certain multiples of the spin frequency
f
?
[1]. Of particular interest are accreting low-mass X-ray
binaries (LMXB), such as Scorpius X-1 (Sco X-1), where
a neutron star is spun up by accretion from its stellar
companion. Electromagnetic observations of LMXBs to
date imply
f
?
.
620 Hz [18], well short of the theoretical
centrifugal break-up limit
f
?
.
1
.
5 kHz [19]. Regard-
less of the exact GW mechanism, the latter observation
suggests an equilibrium between the spin-up accretion
torque, and GW spin-down torque [20–22]. Torque bal-
ance also implies a relation between X-ray luminosity and
the GW strain, making Sco X-1, the brightest LMXB X-
ray source, the most promising known target.
Initial LIGO, a first-generation detector, started tak-
ing science data in 2002. It reached its design sensitivity
in Science Run 5 (S5), starting 2005 [23], and exceeded it
in Science Run 6 (S6) [24]. Following detector upgrades,
the second-generation Advanced LIGO interferometer [2]
began taking science data during Observing Run 1 (O1),
which ran from September 2015 to January 2016. The
strain noise in O1 is three to four times lower than S6 be-
tween 100 Hz and 300 Hz [25]. During this period, LIGO
observed three binary black hole mergers, GW150914
[26], GW151012 and GW151226 [27]. Observing Run 2
(O2) began on November 2016, and ran until 26 August
2017. From 1 August 2017, the two LIGO detectors were
joined by Virgo, resulting in a three-detector network.
Deceased, February 2018.
Deceased, November 2017.
Deceased, July 2018.
As well as further binary black hole mergers [28], LIGO
and Virgo made the first gravitational wave observation
of a binary neutron-star merger during O2 [29].
No search has yet reported a detection of a continu-
ous wave source. To date, four searches for Sco X-1 have
been conducted on Initial LIGO data, and three on Ad-
vanced LIGO data. The first search coherently analysed
the most-sensitive six hour segment from Science Run
2 (S2) using the
F
-statistic [30], a maximum likelihood
detection statistic [31]. The second was a directed, semi-
coherent analysis using the
C
-statistic [32]. The third,
also a directed analysis, used the TwoSpect algorithm
on doubly Fourier transformed S5 data [33–35]. The
fourth applied the radiometer algorithm [36] to conduct
a directed search on S4 [37], S5 [38], and later O1 [39]
data. Three LMXB searches have been performed with
Advanced LIGO data, comprising the radiometer search
[39], an analysis based on a hidden Markov model (HMM)
[40], and a cross-correlation analysis [41–43]. The upper
limits established by these searches are summarized in
Table I.
Astrophysical modeling and X-ray observations sug-
gest that the spin frequency of an LMXB wanders
stochastically in response to fluctuations in the hydro-
magnetic accretion torque [44–47]. As no electromagnetic
measurements of
f
?
are available to guide a gravitational
wave search for Sco X-1, such searches must either ac-
count for spin wandering or limit their observing times
and/or coherence times in accordance with the antici-
pated timescale and amplitude of the spin wandering [48].
For example, the sideband search described in Ref. [32]
is restricted to data segments no longer than ten days.
The hidden Markov model (HMM) tracker, first applied
to the search for Sco X-1 in Ref. [40], is an effective tech-
nique for detecting the most probable underlying spin
frequency,
f
?
(
t
) and thus accounting for spin wandering.
The signal from an binary source is Doppler shifted,
as the neutron star revolves around the barycentre of
the binary, dispersing power into orbital sidebands near
the source frame emission frequency. The separation of
these sidebands and the source-frame frequency depends
on the binary orbital parameters and
f
, but is typically
within 0.05 per cent of the gravitational wave frequency
for a source such as Sco X-1. Four maximum-likelihood
matched filters have been developed to detect these side-
bands: the
C
-statistic, which weights sidebands equally
8
[32], the binary modulated
F
-statistic [49], the Bessel-
weighted
F
-statistic [50], and the
J
-statistic, which ex-
tends the Bessel-weighted
F
-statistic to account for the
phase of the binary orbit [51]. Any of these matched fil-
ters can be combined with the HMM to conduct a search
for signals from a binary source that accounts for spin
wandering.
In this paper, we combine the
J
-statistic described
in Ref. [51] with the HMM described in that paper and
Refs. [50] and [40], and perform a directed search of Ad-
vanced LIGO O2 data for evidence of a gravitational
wave signal from Sco X-1. In the search band 60–650 Hz,
we find no evidence of a gravitational wave signal. The
paper is organized as follows. In Section II, we briefly
review the HMM and the
J
-statistic. In Section III, we
discuss the search strategy and parameter space. In Sec-
tion IV, we report on the results from the search and
veto candidates corresponding to instrumental artifacts.
In Section V, we discuss the search sensitivity and con-
sequent upper limits on the gravitational wave strain.
II. SEARCH ALGORITHM
In this section, we outline the two key components
of the search algorithm: the HMM, used to recover the
most probable spin history
f
0
(
t
), and the
J
-statistic, the
matched filter that accounts for the Doppler shifts in-
troduced by the orbital motions of the Earth and the
LMXB. The HMM formalism is the same as used in
Refs. [40, 50, 51], so we review it only briefly. The
J
-
statistic is described fully in Ref. [51]; again, we review
it briefly.
A. HMM formalism
A Markov model describes a stochastic process in
terms of a state variable
q
(
t
), which transitions be-
tween allowable states
{
q
1
,
···
,q
N
Q
}
at discrete times
{
t
0
,
···
,t
N
T
}
. The transition matrix
A
q
j
q
i
represents the
probability of jumping from state
q
i
at the time
t
=
t
n
to
q
j
at
t
=
t
n
+1
depending only on
q
(
t
n
). A HMM
extends the Markov model to situations where direct ob-
servation of
q
(
t
) is impossible [
q
(
t
) is called the hidden
state]. Instead one measures an observable state
o
(
t
),
selected from
{
o
1
,
···
,o
N
o
}
, which is related to the hid-
den state by the emission matrix
L
o
j
q
i
, which gives the
likelihood that the system is in state
q
i
given the obser-
vation
o
j
. In gravitational wave searches for LMXBs like
Sco X-1, where the spin frequency cannot be measured
electromagnetically, it is natural to map
q
(
t
) to
f
0
(
t
) and
o
(
t
) to the raw interferometer data, some equivalent in-
termediate data product (e.g. short Fourier transforms),
or a detection statistic (e.g.,
F
-statistic,
J
-statistic).
In an LMXB search, we divide the total observa-
tion (duration
T
obs
) into
N
T
equal segments of length
T
drift
=
T
obs
/N
T
.
In each segment, the emission
probability
L
o
j
q
i
is computed from some frequency do-
main estimator
G
(
f
) such as the maximum likelihood
F
- or
J
-statistic (discussed in Section II B). The fre-
quency resolution of the estimator is ∆
f
drift
= 1
/
(2
T
drift
)
(Nyquist). The probability that an observation
O
=
{
o
(
t
0
)
,
···
,o
(
t
N
T
)
}
is associated with a particular hid-
den path
Q
=
{
q
(
t
0
)
,
···
,q
(
t
N
T
)
}
is then given by:
P
(
Q
|
O
) =
L
o
(
t
N
T
)
q
(
t
N
T
)
A
q
(
t
N
T
)
q
(
t
N
T
1
)
···
L
o
(
t
1
)
q
(
t
1
)
×
A
q
(
t
1
)
q
(
t
0
)
Π
q
(
t
0
)
,
(1)
where Π
q
i
is the prior, i.e., the probability the system
starts in state
q
i
at
t
=
t
0
. For this search, we take a
flat prior. The task, then, is to find the optimal hidden
path
Q
?
, that is, the path
Q
?
that maximizes
P
(
Q
|
O
)
given
O
. We find
Q
?
efficiently with the recursive Viterbi
algorithm [54], which is discussed in detail in Appendix A
of Ref. [40].
In this paper, we follow the convention in Ref. [40] of
defining the Viterbi detection score
S
for a path as the
number of standard deviations by which that path’s log
likelihood exceeds the mean log likelihood of all paths.
Mathematically we have
S
=
ln
δ
q
?
(
t
N
T
)
μ
ln
δ
(
t
N
T
)
σ
ln
δ
(
t
N
T
)
,
(2)
where
μ
ln
δ
(
t
N
T
)
=
N
1
Q
N
Q
i
=1
ln
δ
q
i
(
t
N
T
)
,
(3)
σ
2
ln
δ
(
t
N
T
)
=
N
1
Q
N
Q
i
=1
[ln
δ
q
i
(
t
N
T
)
μ
ln
δ
(
t
N
T
)
]
2
,
(4)
δ
q
i
(
t
N
T
) denotes the likelihood of the most likely
path ending in state
q
i
at step
N
T
, and
δ
q
?
(
t
N
T
) =
max
i
δ
q
i
(
t
N
T
) is the likelihood of the optimal path over-
all.
B.
J
-statistic
The frequency domain estimator
G
(
f
) converts the
interferometer data into the likelihood that a signal is
present at frequency
f
. For a continuous-wave search
for an isolated neutron star, the maximum-likelihood
F
-
statistic [30] is a typical choice for
G
(
f
). The
F
-statistic
accounts for the diurnal rotation of the Earth, and its or-
bit around the Solar System barycentre. It is an almost
optimal matched filter for a biaxial rotor [55].
For a neutron star in a binary system, such as an
LMXB, the signal is frequency (Doppler) modulated by
the binary orbital motion as well. Ref. [40] used the
Bessel-weighted
F
-statistic to account for this modula-
tion, without using information about the orbital phase.
9
TABLE I: Summary of indicative upper limits achieved in previous searches for Sco X-1. VSR2 and VSR3 are Virgo
Science Runs 2 and 3, respectively. Where applicable, the upper limits refer to signals of unknown polarization.
Search
Data
Upper limit
Reference
F
-statistic
S2
h
95%
0
.
2
×
10
22
at 464–484 Hz, 604 – 626 Hz [31]
C
-statistic
S5
h
95%
0
.
8
×
10
25
at 150 Hz
[32]
TwoSpect
S6, VSR2, VSR3
h
95%
0
.
2
×
10
23
at 20 – 57.25 Hz
[34]
Radiometer
S4, S5
h
90%
0
.
2
×
10
24
at 150 Hz
[38, 52]
TwoSpect
S6
h
95%
0
.
1
.
8
×
10
24
at 165 Hz
[53]
Radiometer
O1
h
90%
0
.
6
.
7
×
10
25
at 130 – 175 Hz
[39]
Viterbi 1.0
O1
h
95%
0
.
8
.
3
×
10
25
at 106 Hz
[40]
Cross correlation O1
h
95%
0
.
2
.
3
×
10
25
at 175 Hz
[43]
Ref. [51] introduced the
J
-statistic, which is a matched
filter that extends the
F
-statistic to include orbital phase
in the signal model. The orbital Doppler effect dis-
tributes the
F
-statistic power into approximately 2
m
+ 1
orbital sidebands separated by
P
1
, with
m
=
d
2
πf
?
a
0
e
,
where
d·e
denotes rounding up to the nearest integer,
P
is
the orbital period and
a
0
= (
a
sin
i
)
/c
is the light travel
time across the projected semi-major axis (where
a
is
semi-major axis and
i
is the inclination angle of the bi-
nary). For a zero-eccentricity Keplerian orbit, the Jacobi-
Anger identity may be used to expand the signal
h
(
t
) in
terms of Bessel functions, suggesting a matched filter of
the form [50, 51]
G
(
f
) =
F
(
f
)
B
(
f
)
,
(5)
with
B
(
f
) =
m
s
=
m
J
s
(2
πf
0
a
0
)
e
isφ
a
δ
(
f
s/P
)
,
(6)
where
J
s
(
z
) is the Bessel function of the first kind of
order
s
,
φ
a
is the orbital phase at a reference time, and
δ
is the Dirac delta function.
The Bessel-weighted
F
-statistic requires a search over
a
0
but does not depend on
φ
a
. By contrast, the more-
sensitive
J
-statistic involves searching over
φ
a
too. In
this paper we apply the
J
-statistic to search for Sco X-1.
Details of the search and priors derived from electromag-
netic measurements are discussed in Section III.
III. LIGO O2 SEARCH
A. Sco X-1 parameters
The matched filter described in Section II B depends
on three binary orbital parameters: the period
P
, the
projected semi-major axis
a
0
and the phase
φ
a
. The
F
-
statistic also depends on the sky location
α
(right ascen-
sion) and
δ
(declination). These parameters have been
measured electromagnetically for Sco X-1 and are pre-
sented in Table II.
For
α
,
δ
and
P
, the uncertainties in the electromag-
netic measurements are small enough that they have
no appreciable effect on the sensitivity of the search
[49, 56, 57], and a single, central value can be assumed.
However, the uncertainties in
a
0
and
φ
a
cannot be ne-
glected. The time spent searching orbital parameters
scales as the number of (
a
0
,
φ
a
) pairs. Careful selection
of the ranges of
a
0
and
φ
a
is essential to keep computa-
tional costs low.
The previous analysis, described in Ref. [40], used the
Bessel-weighted
F
-statistic in place of the
J
-statistic,
and searched over a uniformly-gridded range of
a
0
, where
the grid resolution did not depend on frequency. How-
ever, the
J
-statistic is more sensitive to mismatch in the
binary orbital parameters, so a finer grid is required. We
must also choose an appropriate grid for
φ
a
. (The Bessel-
weighted
F
-statistic is independent of
φ
a
.)
As the
J
-statistic has a similar overall response to pa-
rameter mismatches as the binary
F
-statistic, we follow
the formalism in Ref. [49] to select an appropriate param-
eter space gridding. We choose a grid which limits the
maximum loss in signal-to-noise ratio (mismatch)
μ
max
to
μ
max
= 0
.
1. Equation (71) in Ref. [49] gives a general
equation for the number of grid points needed for each
search parameter. For the particular search considered
in this paper, the number of choices for
a
0
and
φ
a
are
N
a
0
=
π
2
2
μ
max
f
0
a
0
,
(7)
N
φ
a
=
1
2
μ
max
f
0
a
0
(
2
π
P
)
φ
a
,
(8)
where ∆
a
0
and ∆
φ
a
are the widths of the search ranges
for
a
0
and
φ
a
respectively. The number of orbital pa-
rameters to be searched depends on the search frequency.
Accordingly for each search sub-band, we adopt a differ-
ent grid resolution, with the grid refined at higher fre-
quencies. In the sub-band beginning at 60 Hz, we have
N
a
0
= 768 and
N
φ
a
= 78; in the sub-band beginning at
650 Hz, we have
N
a
0
= 8 227 and
N
φ
a
= 824. In prin-
ciple we could achieve further computational savings by
10
noting that
N
φ
a
also depends on
a
0
, but for safety we
use the largest
a
0
.
The search range for
a
0
is 1
.
45
a
0
/
(1 s)
3
.
25, which
matches the most recent electromagnetic measurement
[58] and widens the error bars on the widely-cited and
previous best published measurement,
a
0
= 1
.
44
±
0
.
18 s.
[59].
The orbital phase
φ
a
can be related to the elecromag-
netically measured time of ascension,
T
asc
, given in Ta-
ble II, by
φ
a
= 2
πT
asc
/P
(mod 2
π
)
.
(9)
The one-sigma uncertainty in the published value for
T
asc
is
±
50 s [58, 60], for a time of ascension at GPS time
974 416 624 s (in November 2010). As O2 took place sig-
nificantly after this time, to make a conservative esti-
mate on appropriate error bars for
T
asc
, we advance
T
asc
by adding 3 135 orbital periods to the time of ascension
taken from Ref. [58]. As there is uncertainty associated
with the measured orbital period, this widens the one-
sigma uncertainty of
T
asc
to
±
144 s, which we round up
to
±
150 s. To cover a significant portion of the measured
T
asc
range while keeping the search computationally fea-
sible, we search a two-sigma range around the central
T
asc
, namely, 1 164 543 014
T
asc
/
(1 s)
1 164 543 614
(expressed for presentation purposes as the time of the
last ascension before the start of O2).
As there is no electromagnetic measurement of
f
?
for
Sco X-1, we search the band 60
f
?
/
(1 Hz)
650, where
LIGO is most sensitive, again adopting a uniform prior
(see Section II A for a discussion of the HMM prior). The
same band is analysed in Ref. [40]. For computational
convenience, we split the band into blocks of approxi-
mately 0.61 Hz (discussed further in Section III B).
The final electromagnetically measured parameter is
the polarization angle,
ψ
. Because the
F
-statistic com-
ponents of the
J
-statistic are maximized over the polar-
ization angle, the
J
-statistic is insensitive to
ψ
.
A summary of the search ranges flowing from the elec-
tromagnetically measured parameters of Sco X-1 is pre-
sented in Table II.
B. Workflow
The workflow for the search is displayed as a flowchart
in Figure 1.
The data from the detector are provided as short
Fourier transforms (SFTs), each covering
T
SFT
= 1800 s.
We divide the search into sub-bands, both to facilitate
managing the volume of data, and to ensure that replac-
ing the search frequency
f
with the mid-point of the sub-
band,
̄
f
, is a good approximation in Equation (6). A sub-
band width of ∆
f
band
= 2
20
f
drift
= 0
.
6068148 Hz fulfils
both these objectives and yields a number of frequency
bins that is a power of two, which considerably speeds up
the fast Fourier transform to compute the convolution in
(6).
No
Yes
No
Yes
While
more
a
0
,
φ
a
to search
Start
Compute
F
-statistic
atoms for each block
N blocks of SFTs,
search target
α
,
δ
T
N
T
blocks of
F
-statistic atoms
Compute the
J
-statistic
P, all a
0
,
φ
a
N
T
blocks of
J
-statistic values
Run Viterbi HMM
Viterbi scores,
optimal path
Best Viterbi
score > threshold?
Compute upper
limits
Does any veto
test apply?
Upper limits
Veto
Detection
Find best path and
score from all a
0
,
φ
a
Viterbi score,
path, a
0
,
φ
a
FIG. 1: Flowchart of the
J
-statistic search pipeline for
each sub-band. Note that the
F
-statistic atoms are
computed once per block and per sub-band, then the
J
-statistic is recalculated for each (
a
0
a
) pair. The
grey ovals are the start and end of the algorithm, the
green rectangles are procedures, the blue solid (red
dashed) parallelograms are intermediate (input) data,
the yellow diamonds are decision points, and the grey
dashed line represents a loop repeated once for each
choice of parameter.