key: cord-0482336-55mc1170
authors: Collaboration, The LIGO Scientific; Collaboration, the Virgo; Abbott, the KAGRA Collaboration R.; Abe, H.; Acernese, F.; Ackley, K.; Adhikari, N.; Adhikari, R. X.; Adkins, V. K.; Adya, V. B.; Affeldt, C.; Agarwal, D.; Agathos, M.; Agatsuma, K.; Aggarwal, N.; Aguiar, O. D.; Aiello, L.; Ain, A.; Ajith, P.; Akutsu, T.; Albanesi, S.; Alfaidi, R. A.; Allocca, A.; Altin, P. A.; Amato, A.; Anand, C.; Anand, S.; Ananyeva, A.; Anderson, S. B.; Anderson, W. G.; Ando, M.; Andrade, T.; Andres, N.; Andr'es-Carcasona, M.; Andri'c, T.; Angelova, S. V.; Ansoldi, S.; Antelis, J. M.; Antier, S.; Apostolatos, T.; Appavuravther, E. Z.; Appert, S.; Apple, S. K.; Arai, K.; Araya, A.; Araya, M. C.; Areeda, J. S.; Arene, M.; Aritomi, N.; Arnaud, N.; Arogeti, M.; Aronson, S. M.; Asada, H.; Asali, Y.; Ashton, G.; Aso, Y.; Assiduo, M.; Melo, S. Assis de Souza; Aston, S. M.; Astone, P.; Aubin, F.; AultONeal, K.; Austin, C.; Babak, S.; Badaracco, F.; Bader, M. K. M.; Badger, C.; Bae, S.; Bae, Y.; Baer, A. M.; Bagnasco, S.; Bai, Y.; Baird, J.; Bajpai, R.; Baka, T.; Ball, M.; Ballardin, G.; Ballmer, S. W.; Balsamo, A.; Baltus, G.; Banagiri, S.; Banerjee, B.; Bankar, D.; Barayoga, J. C.; Barbieri, C.; Barish, B. C.; Barker, D.; Barneo, P.; Barone, F.; Barr, B.; Barsotti, L.; Barsuglia, M.; Barta, D.; Bartlett, J.; Barton, M. A.; Bartos, I.; Basak, S.; Bassiri, R.; Basti, A.; Bawaj, M.; Bayley, J. C.; Bazzan, M.; Becher, B. R.; B'ecsy, B.; Bedakihale, V. M.; Beirnaert, F.; Bejger, M.; Belahcene, I.; Benedetto, V.; Beniwal, D.; Benjamin, M. G.; Bennett, T. F.; Bentley, J. D.; BenYaala, M.; Bera, S.; Berbel, M.; Bergamin, F.; Berger, B. K.; Bernuzzi, S.; Bersanetti, D.; Bertolini, A.; Betzwieser, J.; Beveridge, D.; Bhandare, R.; Bhandari, A. V.; Bhardwaj, U.; Bhatt, R.; Bhattacharjee, D.; Bhaumik, S.; Bianchi, A.; Bilenko, I. A.; Billingsley, G.; Bini, S.; Birney, R.; Birnholtz, O.; Biscans, S.; Bischi, M.; Biscoveanu, S.; Bisht, A.; Biswas, B.; Bitossi, M.; Bizouard, M.-A.; Blackburn, J. K.; Blair, C. D.; Blair, D. G.; Blair, R. M.; Bobba, F.; Bode, N.; Boer, M.; Bogaert, G.; Boldrini, M.; Bolingbroke, G. N.; Bonavena, L. D.; Bondu, F.; Bonilla, E.; Bonnand, R.; Booker, P.; Boom, B. A.; Bork, R.; Boschi, V.; Bose, N.; Bose, S.; Bossilkov, V.; Boudart, V.; Bouffanais, Y.; Bozzi, A.; Bradaschia, C.; Brady, P. R.; Bramley, A.; Branch, A.; Branchesi, M.; Brau, J. E.; Breschi, M.; Briant, T.; Briggs, J. H.; Brillet, A.; Brinkmann, M.; Brockill, P.; Brooks, A. F.; Brooks, J.; Brown, D. D.; Brunett, S.; Bruno, G.; Bruntz, R.; Bryant, J.; Bucci, F.; Bulik, T.; Bulten, H. J.; Buonanno, A.; Burtnyk, K.; Buscicchio, R.; Buskulic, D.; Buy, C.; Byer, R. L.; Davies, G. S. Cabourn; Cabras, G.; Cabrita, R.; Cadonati, L.; Caesar, M.; Cagnoli, G.; Cahillane, C.; Bustillo, J. Calder'on; Callaghan, J. D.; Callister, T. A.; Calloni, E.; Cameron, J.; Camp, J. B.; Canepa, M.; Canevarolo, S.; Cannavacciuolo, M.; Cannon, K. C.; Cao, H.; Cao, Z.; Capocasa, E.; Capote, E.; Carapella, G.; Carbognani, F.; Carlassara, M.; Carlin, J. B.; Carney, M. F.; Carpinelli, M.; Carrillo, G.; Carullo, G.; Carver, T. L.; Diaz, J. Casanueva; Casentini, C.; Castaldi, G.; Caudill, S.; Cavaglia, M.; Cavalier, F.; Cavalieri, R.; Cella, G.; Cerd'a-Dur'an, P.; Cesarini, E.; Chaibi, W.; Subrahmanya, S. Chalathadka; Champion, E.; Chan, C.-H.; Chan, C.; Chan, C. L.; Chan, K.; Chan, M.; Chandra, K.; Chang, I. P.; Chanial, P.; Chao, S.; Chapman-Bird, C.; Charlton, P.; Chase, E. A.; Chassande-Mottin, E.; Chatterjee, C.; Chatterjee, Debarati; Chatterjee, Deep; Chaturvedi, M.; Chaty, S.; Chen, C.; Chen, D.; Chen, H. Y.; Chen, J.; Chen, K.; Chen, X.; Chen, Y.-B.; Chen, Y.-R.; Chen, Z.; Cheng, H.; Cheong, C. K.; Cheung, H. Y.; Chia, H. Y.; Chiadini, F.; Chiang, C-Y.; Chiarini, G.; Chierici, R.; Chincarini, A.; Chiofalo, M. L.; Chiummo, A.; Choudhary, R. K.; Choudhary, S.; Christensen, N.; Chu, Q.; Chu, Y-K.; Chua, S. S. Y.; Chung, K. W.; Ciani, G.; Ciecielag, P.; Cie'slar, M.; Cifaldi, M.; Ciobanu, A. A.; Ciolfi, R.; Cipriano, F.; Clara, F.; Clark, J. A.; Clearwater, P.; Clesse, S.; Cleva, F.; Coccia, E.; Codazzo, E.; Cohadon, P.-F.; Cohen, D. E.; Colleoni, M.; Collette, C. G.; Colombo, A.; Colpi, M.; Compton, C. M.; Constancio, M.; Conti, L.; Cooper, S. J.; Corban, P.; Corbitt, T. R.; Cordero-Carri'on, I.; Corezzi, S.; Corley, K. R.; Cornish, N. J.; Corre, D.; Corsi, A.; Cortese, S.; Costa, C. A.; Cotesta, R.; Cottingham, R.; Coughlin, M. W.; Coulon, J.-P.; Countryman, S. T.; Cousins, B.; Couvares, P.; Coward, D. M.; Cowart, M. J.; Coyne, D. C.; Coyne, R.; Creighton, J. D. E.; Creighton, T. D.; Criswell, A. W.; Croquette, M.; Crowder, S. G.; Cudell, J. R.; Cullen, T. J.; Cumming, A.; Cummings, R.; Cunningham, L.; Cuoco, E.; Curylo, M.; Dabadie, P.; Canton, T. Dal; Dall'Osso, S.; D'alya, G.; Dana, A.; D'Angelo, B.; Danilishin, S.; D'Antonio, S.; Danzmann, K.; Darsow-Fromm, C.; Dasgupta, A.; Datrier, L. E. H.; Datta, Sayak; Datta, Sayantani; Dattilo, V.; Dave, I.; Davier, M.; Davis, D.; Davis, M. C.; Daw, E. J.; Dean, R.; DeBra, D.; Deenadayalan, M.; Degallaix, J.; Laurentis, M. De; Del'eglise, S.; Favero, V. Del; Lillo, F. De; Lillo, N. De; Dell'Aquila, D.; Pozzo, W. Del; DeMarchi, L. M.; Matteis, F. De; D'Emilio, V.; Demos, N.; Dent, T.; Depasse, A.; Pietri, R. De; Rosa, R. De; Rossi, C. De; DeSalvo, R.; Simone, R. De; Dhurandhar, S.; D'iaz, M. C.; Didio, N. A.; Dietrich, T.; Fiore, L. Di; Fronzo, C. Di; Giorgio, C. Di; Giovanni, F. Di; Giovanni, M. Di; Girolamo, T. Di; Lieto, A. Di; Michele, A. Di; Ding, B.; Pace, S. Di; Palma, I. Di; Renzo, F. Di; Divakarla, A. K.; Dmitriev, A.; Doctor, Z.; Donahue, L.; D'Onofrio, L.; Donovan, F.; Dooley, K. L.; Doravari, S.; Drago, M.; Driggers, J. C.; Drori, Y.; Ducoin, J.-G.; Dupej, P.; Dupletsa, U.; Durante, O.; D'Urso, D.; Duverne, P.-A.; Dwyer, S. E.; Eassa, C.; Easter, P. J.; Ebersold, M.; Eckhardt, T.; Eddolls, G.; Edelman, B.; Edo, T. B.; Edy, O.; Effler, A.; Eguchi, S.; Eichholz, J.; Eikenberry, S. S.; Eisenmann, M.; Eisenstein, R. A.; Ejlli, A.; Engelby, E.; Enomoto, Y.; Errico, L.; Essick, R. C.; Estell'es, H.; Estevez, D.; Etienne, Z.; Etzel, T.; Evans, M.; Evans, T. M.; Evstafyeva, T.; Ewing, B. E.; Fabrizi, F.; Faedi, F.; Fafone, V.; Fair, H.; Fairhurst, S.; Fan, P. C.; Farah, A. M.; Farinon, S.; Farr, B.; Farr, W. M.; Fauchon-Jones, E. J.; Favaro, G.; Favata, M.; Fays, M.; Fazio, M.; Feicht, J.; Fejer, M. M.; Fenyvesi, E.; Ferguson, D. L.; Fernandez-Galiana, A.; Ferrante, I.; Ferreira, T. A.; Fidecaro, F.; Figura, P.; Fiori, A.; Fiori, I.; Fishbach, M.; Fisher, R. P.; Fittipaldi, R.; Fiumara, V.; Flaminio, R.; Floden, E.; Fong, H. K.; Font, J. A.; Fornal, B.; Forsyth, P. W. F.; Franke, A.; Frasca, S.; Frasconi, F.; Freed, J. P.; Frei, Z.; Freise, A.; Freitas, O.; Frey, R.; Fritschel, P.; Frolov, V. V.; Fronz'e, G. G.; Fujii, Y.; Fujikawa, Y.; Fujimoto, Y.; Fulda, P.; Fyffe, M.; Gabbard, H. A.; Gabella, W. E.; Gadre, B. U.; Gair, J. R.; Gais, J.; Galaudage, S.; Gamba, R.; Ganapathy, D.; Ganguly, A.; Gao, D.; Gaonkar, S. G.; Garaventa, B.; N'unez, C. Garc'ia; Garc'ia-Quir'os, C.; Garufi, F.; Gateley, B.; Gayathri, V.; Ge, G.-G.; Gemme, G.; Gennai, A.; George, J.; Gerberding, O.; Gergely, L.; Gewecke, P.; Ghonge, S.; Ghosh, Abhirup; Ghosh, Archisman; Ghosh, Shaon; Ghosh, Shrobana; Ghosh, Tathagata; Giacomazzo, B.; Giacoppo, L.; Giaime, J. A.; Giardina, K. D.; Gibson, D. R.; Gier, C.; Giesler, M.; Giri, P.; Gissi, F.; Gkaitatzis, S.; Glanzer, J.; Gleckl, A. E.; Godwin, P.; Goetz, E.; Goetz, R.; Gohlke, N.; Golomb, J.; Goncharov, B.; Gonz'alez, G.; Gosselin, M.; Gouaty, R.; Gould, D. W.; Goyal, S.; Grace, B.; Grado, A.; Graham, V.; Granata, M.; Granata, V.; Grant, A.; Gras, S.; Grassia, P.; Gray, C.; Gray, R.; Greco, G.; Green, A. C.; Green, R.; Gretarsson, A. M.; Gretarsson, E. M.; Griffith, D.; Griffiths, W. L.; Griggs, H. L.; Grignani, G.; Grimaldi, A.; Grimes, E.; Grimm, S. J.; Grote, H.; Grunewald, S.; Gruning, P.; Gruson, A. S.; Guerra, D.; Guidi, G. M.; Guimaraes, A. R.; Guix'e, G.; Gulati, H. K.; Gunny, A. M.; Guo, H.-K.; Guo, Y.; Gupta, Anchal; Gupta, Anuradha; Gupta, I. M.; Gupta, P.; Gupta, S. K.; Gustafson, R.; Guzman, F.; Ha, S.; Hadiputrawan, I. P. W.; Haegel, L.; Haino, S.; Halim, O.; Hall, E. D.; Hamilton, E. Z.; Hammond, G.; Han, W.-B.; Haney, M.; Hanks, J.; Hanna, C.; Hannam, M. D.; Hannuksela, O.; Hansen, H.; Hansen, T. J.; Hanson, J.; Harder, T.; Haris, K.; Harms, J.; Harry, G. M.; Harry, I. W.; Hartwig, D.; Hasegawa, K.; Haskell, B.; Haster, C.-J.; Hathaway, J. S.; Hattori, K.; Haughian, K.; Hayakawa, H.; Hayama, K.; Hayes, F. J.; Healy, J.; Heidmann, A.; Heidt, A.; Heintze, M. C.; Heinze, J.; Heinzel, J.; Heitmann, H.; Hellman, F.; Hello, P.; Helmling-Cornell, A. F.; Hemming, G.; Hendry, M.; Heng, I. S.; Hennes, E.; Hennig, J.; Hennig, M. H.; Henshaw, C.; Hernandez, A. G.; Vivanco, F. Hernandez; Heurs, M.; Hewitt, A. L.; Higginbotham, S.; Hild, S.; Hill, P.; Himemoto, Y.; Hines, A. S.; Hirata, N.; Hirose, C.; Ho, T-C.; Hochheim, S.; Hofman, D.; Hohmann, J. N.; Holcomb, D. G.; Holland, N. A.; Hollows, I. J.; Holmes, Z. J.; Holt, K.; Holz, D. E.; Hong, Q.; Hough, J.; Hourihane, S.; Howell, E. J.; Hoy, C. G.; Hoyland, D.; Hreibi, A.; Hsieh, B-H.; Hsieh, H-F.; Hsiung, C.; Hsu, Y.; Huang, H-Y.; Huang, P.; Huang, Y-C.; Huang, Y.-J.; Huang, Yiting; Huang, Yiwen; Hubner, M. T.; Huddart, A. D.; Hughey, B.; Hui, D. C. Y.; Hui, V.; Husa, S.; Huttner, S. H.; Huxford, R.; Huynh-Dinh, T.; Ide, S.; Idzkowski, B.; Iess, A.; Inayoshi, K.; Inoue, Y.; Iosif, P.; Isi, M.; Isleif, K.; Ito, K.; Itoh, Y.; Iyer, B. R.; JaberianHamedan, V.; Jacqmin, T.; Jacquet, P.-E.; Jadhav, S. J.; Jadhav, S. P.; Jain, T.; James, A. L.; Jan, A. Z.; Jani, K.; Janquart, J.; Janssens, K.; Janthalur, N. N.; Jaranowski, P.; Jariwala, D.; Jaume, R.; Jenkins, A. C.; Jenner, K.; Jeon, C.; Jia, W.; Jiang, J.; Jin, H.-B.; Johns, G. R.; Johnston, R.; Jones, A. W.; Jones, D. I.; Jones, P.; Jones, R.; Joshi, P.; Ju, L.; Jue, A.; Jung, P.; Jung, K.; Junker, J.; Juste, V.; Kaihotsu, K.; Kajita, T.; Kakizaki, M.; Kalaghatgi, C. V.; Kalogera, V.; Kamai, B.; Kamiizumi, M.; Kanda, N.; Kandhasamy, S.; Kang, G.; Kanner, J. B.; Kao, Y.; Kapadia, S. J.; Kapasi, D. P.; Karathanasis, C.; Karki, S.; Kashyap, R.; Kasprzack, M.; Kastaun, W.; Kato, T.; Katsanevas, S.; Katsavounidis, E.; Katzman, W.; Kaur, T.; Kawabe, K.; Kawaguchi, K.; K'ef'elian, F.; Keitel, D.; Key, J. S.; Khadka, S.; Khalili, F. Y.; Khan, S.; Khanam, T.; Khazanov, E. A.; Khetan, N.; Khursheed, M.; Kijbunchoo, N.; Kim, A.; Kim, C.; Kim, J. C.; Kim, J.; Kim, K.; Kim, W. S.; Kim, Y.-M.; Kimball, C.; Kimura, N.; Kinley-Hanlon, M.; Kirchhoff, R.; Kissel, J. S.; Klimenko, S.; Klinger, T.; Knee, A. M.; Knowles, T. D.; Knust, N.; Knyazev, E.; Kobayashi, Y.; Koch, P.; Koekoek, G.; Kohri, K.; Kokeyama, K.; Koley, S.; Kolitsidou, P.; Kolstein, M.; Komori, K.; Kondrashov, V.; Kong, A. K. H.; Kontos, A.; Koper, N.; Korobko, M.; Kovalam, M.; Koyama, N.; Kozak, D. B.; Kozakai, C.; Kringel, V.; Krishnendu, N. V.; Kr'olak, A.; Kuehn, G.; Kuei, F.; Kuijer, P.; Kulkarni, S.; Kumar, A.; Kumar, Prayush; Kumar, Rahul; Kumar, Rakesh; Kume, J.; Kuns, K.; Kuromiya, Y.; Kuroyanagi, S.; Kwak, K.; Lacaille, G.; Lagabbe, P.; Laghi, D.; Lalande, E.; Lalleman, M.; Lam, T. L.; Lamberts, A.; Landry, M.; Lane, B. B.; Lang, R. N.; Lange, J.; Lantz, B.; Rosa, I. La; Lartaux-Vollard, A.; Lasky, P. D.; Laxen, M.; Lazzarini, A.; Lazzaro, C.; Leaci, P.; Leavey, S.; LeBohec, S.; Lecoeuche, Y. K.; Lee, E.; Lee, H. M.; Lee, H. W.; Lee, K.; Lee, R.; Legred, I. N.; Lehmann, J.; Lemaitre, A.; Lenti, M.; Leonardi, M.; Leonova, E.; Leroy, N.; Letendre, N.; Levesque, C.; Levin, Y.; Leviton, J. N.; Leyde, K.; Li, A. K. Y.; Li, B.; Li, J.; Li, K. L.; Li, P.; Li, T. G. F.; Li, X.; Lin, C-Y.; Lin, E. T.; Lin, F-K.; Lin, F-L.; Lin, H. L.; Lin, L. C.-C.; Linde, F.; Linker, S. D.; Linley, J. N.; Littenberg, T. B.; Liu, G. C.; Liu, J.; Liu, K.; Liu, X.; Llamas, F.; Lo, R. K. L.; Lo, T.; London, L. T.; Longo, A.; Lopez, D.; Portilla, M. Lopez; Lorenzini, M.; Loriette, V.; Lormand, M.; Losurdo, G.; Lott, T. P.; Lough, J. D.; Lousto, C. O.; Lovelace, G.; Lucaccioni, J. F.; Luck, H.; Lumaca, D.; Lundgren, A. P.; Luo, L.-W.; Lynam, J. E.; Ma'arif, M.; Macas, R.; Machtinger, J. B.; MacInnis, M.; Macleod, D. M.; MacMillan, I. A. O.; Macquet, A.; Hernandez, I. Magana; Magazzu, C.; Magee, R. M.; Maggiore, R.; Magnozzi, M.; Mahesh, S.; Majorana, E.; Maksimovic, I.; Maliakal, S.; Malik, A.; Man, N.; Mandic, V.; Mangano, V.; Mansell, G. L.; Manske, M.; Mantovani, M.; Mapelli, M.; Marchesoni, F.; Pina, D. Mar'in; Marion, F.; Mark, Z.; M'arka, S.; M'arka, Z.; Markakis, C.; Markosyan, A. S.; Markowitz, A.; Maros, E.; Marquina, A.; Marsat, S.; Martelli, F.; Martin, I. W.; Martin, R. M.; Martinez, M.; Martinez, V. A.; Martinez, V.; Martinovic, K.; Martynov, D. V.; Marx, E. J.; Masalehdan, H.; Mason, K.; Massera, E.; Masserot, A.; Masso-Reid, M.; Mastrogiovanni, S.; Matas, A.; Mateu-Lucena, M.; Matichard, F.; Matiushechkina, M.; Mavalvala, N.; McCann, J. J.; McCarthy, R.; McClelland, D. E.; McClincy, P. K.; McCormick, S.; McCuller, L.; McGhee, G. I.; McGuire, S. C.; McIsaac, C.; McIver, J.; McRae, T.; McWilliams, S. T.; Meacher, D.; Mehmet, M.; Mehta, A. K.; Meijer, Q.; Melatos, A.; Melchor, D. A.; Mendell, G.; Menendez-Vazquez, A.; Menoni, C. S.; Mercer, R. A.; Mereni, L.; Merfeld, K.; Merilh, E. L.; Merritt, J. D.; Merzougui, M.; Meshkov, S.; Messenger, C.; Messick, C.; Meyers, P. M.; Meylahn, F.; Mhaske, A.; Miani, A.; Miao, H.; Michaloliakos, I.; Michel, C.; Michimura, Y.; Middleton, H.; Mihaylov, D. P.; Milano, L.; Miller, A. L.; Miller, A.; Miller, B.; Millhouse, M.; Mills, J. C.; Milotti, E.; Minenkov, Y.; Mio, N.; Mir, Ll. M.; Miravet-Ten'es, M.; Mishkin, A.; Mishra, C.; Mishra, T.; Mistry, T.; Mitra, S.; Mitrofanov, V. P.; Mitselmakher, G.; Mittleman, R.; Miyakawa, O.; Miyo, K.; Miyoki, S.; Mo, Geoffrey; Modafferi, L. M.; Moguel, E.; Mogushi, K.; Mohapatra, S. R. P.; Mohite, S. R.; Molina, I.; Molina-Ruiz, M.; Mondin, M.; Montani, M.; Moore, C. J.; Moragues, J.; Moraru, D.; Morawski, F.; More, A.; Moreno, C.; Moreno, G.; Mori, Y.; Morisaki, S.; Morisue, N.; Moriwaki, Y.; Mours, B.; Mow-Lowry, C. M.; Mozzon, S.; Muciaccia, F.; Mukherjee, Arunava; Mukherjee, D.; Mukherjee, Soma; Mukherjee, Subroto; Mukherjee, Suvodip; Mukund, N.; Mullavey, A.; Munch, J.; Muniz, E. A.; Murray, P. G.; Musenich, R.; Muusse, S.; Nadji, S. L.; Nagano, K.; Nagar, A.; Nakamura, K.; Nakano, H.; Nakano, M.; Nakayama, Y.; Napolano, V.; Nardecchia, I.; Narikawa, T.; Narola, H.; Naticchioni, L.; Nayak, B.; Nayak, R. K.; Neil, B. F.; Neilson, J.; Nelson, A.; Nelson, T. J. N.; Nery, M.; Neubauer, P.; Neunzert, A.; Ng, K. Y.; Ng, S. W. S.; Nguyen, C.; Nguyen, P.; Nguyen, T.; Quynh, L. Nguyen; Ni, J.; Ni, W.-T.; Nichols, S. A.; Nishimoto, T.; Nishizawa, A.; Nissanke, S.; Nitoglia, E.; Nocera, F.; Norman, M.; North, C.; Nozaki, S.; Nurbek, G.; Nuttall, L. K.; Obayashi, Y.; Oberling, J.; O'Brien, B. D.; O'Dell, J.; Oelker, E.; Ogaki, W.; Oganesyan, G.; Oh, J. J.; Oh, K.; Oh, S. H.; Ohashi, M.; Ohashi, T.; Ohkawa, M.; Ohme, F.; Ohta, H.; Okada, M. A.; Okutani, Y.; Olivetto, C.; Oohara, K.; Oram, R.; O'Reilly, B.; Ormiston, R. G.; Ormsby, N. D.; O'Shaughnessy, R.; O'Shea, E.; Oshino, S.; Ossokine, S.; Osthelder, C.; Otabe, S.; Ottaway, D. J.; Overmier, H.; Pace, A. E.; Pagano, G.; Pagano, R.; Page, M. 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title: Search for gravitational waves from Scorpius X-1 with a hidden Markov model in O3 LIGO data
date: 2022-01-25
journal: nan
DOI: nan
sha: 69db5aec494bd50f01a29b9dea26cbadd2f800bf
doc_id: 482336
cord_uid: 55mc1170

Results are presented for a semi-coherent search for continuous gravitational waves from the low-mass X-ray binary Scorpius X-1, using a hidden Markov model (HMM) to allow for spin wandering. This search improves on previous HMM-based searches of Laser Interferometer Gravitational-wave Observatory (LIGO) data by including the orbital period in the search template grid, and by analyzing data from the latest (third) observing run (O3). In the frequency range searched, from 60 to 500 Hz, we find no evidence of gravitational radiation. This is the most sensitive search for Scorpius X-1 using a HMM to date. For the most sensitive sub-band, starting at $256.06$Hz, we report an upper limit on gravitational wave strain (at $95 %$ confidence) of $h_{0}^{95%}=6.16times10^{-26}$, assuming the orbital inclination angle takes its electromagnetically restricted value $iota=44^{circ}$. The upper limits on gravitational wave strain reported here are on average a factor of $sim 3$ lower than in the O2 HMM search. This is the first Scorpius X-1 HMM search with upper limits that reach below the indirect torque-balance limit for certain sub-bands, assuming $iota=44^{circ}$.

Results are presented for a semi-coherent search for continuous gravitational waves from the lowmass X-ray binary Scorpius X-1, using a hidden Markov model (HMM) to allow for spin wandering. This search improves on previous HMM-based searches of Laser Interferometer Gravitational-wave Observatory (LIGO) data by including the orbital period in the search template grid, and by analyzing data from the latest (third) observing run (O3). In the frequency range searched, from 60 to 500 Hz, we find no evidence of gravitational radiation. This is the most sensitive search for Scorpius X-1 using a HMM to date. For the most sensitive sub-band, starting at 256.06Hz, we report an upper limit on gravitational wave strain (at 95% confidence) of h 95% 0 = 6.16 × 10 −26 , assuming the orbital inclination angle takes its electromagnetically restricted value ι = 44 • . The upper limits on gravitational wave strain reported here are on average a factor of ∼ 3 lower than in the O2 HMM search. This is the first Scorpius X-1 HMM search with upper limits that reach below the indirect torque-balance limit for certain sub-bands, assuming ι = 44 • .

Rotating neutron stars are promising candidates for continuous-wave searches with terrestrial gravitational wave (GW) detectors such as the second-generation Advanced Laser Interferometer Gravitational-wave Observatory (LIGO) [1] [2] [3] [4] [5] , Advanced Virgo [4] , and the Kamioka Gravitational Wave Detector (KAGRA) [6] . Continuous GWs from neutron stars are emitted by an oscillating quadrupole moment, which can be produced in various ways, including elastic strain [7, 8] , magnetic gradients [9] [10] [11] , r-modes [12] [13] [14] , or nonaxisymmetric circulation of the superfluid interior [15] [16] [17] [18] . These mechanisms emit GWs at specific multiples of the spin frequency f [1] . Low-mass X-ray binaries (LMXBs) have been targeted by previous LIGO searches, [19] [20] [21] [22] [23] [24] because they may emit GWs relatively strongly while existing in a state of rotational equilibrium, in which the accretion torque balances the GW torque [25] [26] [27] . Under torque balance conditions, the characteristic GW strain h 0 is proportional to the square root of the X-ray flux, implying that the brightest LMXB, Scorpius X-1 (Sco X-1), is also a strong GW emitter [1, 27] .

Continuous-wave searches directed at Sco X-1 have been performed with data from the first (O1) and second (O2) observing runs of LIGO [19-21, 23, 28-31] . No signal has been detected to date, but astrophysically interesting upper limits have been obtained. For O1 a hidden Markov model (HMM) pipeline [29] obtained an upper limit at 95% confidence level of h 95% 0 = 8.3 × 10 −25 in the 100-200 Hz frequency range, while a cross-correlation (CrossCorr) pipeline [28, 32] achieved h 95% 0 = 2.3×10 −25 in the same frequency range. For O2, the HMM pipeline [21] obtained h 95% 0 = 3.47 × 10 −25 , in the 100-200Hz frequency range, while CrossCorr [23] improved on the O1 results by a factor of ≈ 1.8. All of these upper limits on h 95% 0 are marginalized over the neutron star spin incli- * Deceased, August 2020. † Deceased, April 2021. nation ι, assuming an isotropic prior. If instead one assumes an electromagnetically informed prior, ι = 44 • ±6 • [33] , the O2 upper limits obtained by CrossCorr reduce to ∼ 10 −26 [23] . Now, the third observation run (O3), which is longer and more sensitive than O1 and O2, offers an opportunity to repeat the O1 and O2 searches with improved sensitivity. The improved search is the subject of this paper.

Searching for LMXBs presents two challenges. First, f (and hence the GW frequency) wanders stochastically in objects where it is measured electromagnetically, due to fluctuations in the hydromagnetic accretion torque [34] [35] [36] [37] . Second, in some LMXBs including Sco X-1, which do not exhibit X-ray pulsations, f is not measured electromagnetically [1, 37] . Hence a GW search must cover a wide band (width ∼ 1kHz) looking for an unknown, wandering, quasimonochromatic tone [38, 39] . HMM tracking is a tried and tested method for searches of the above sort, with a long history of practical use in telecommunications [40] and remote sensing [41] . HMM tracking has been used in numerous searches for GWs, e.g. for Sco X-1 in O1 [29] and O2 [21] , young supernova remnants in O3 [42] , accreting millisecond X-ray pulsars in O2 [22] and O3 [24] , all sky searches [43] , and longduration transients [44] .

The J -statistic [45] , a frequency domain matched filter, is used in tandem with the HMM described in references [21, 29, 45, 46] . The outline of the rest of the paper is as follows. Section II explains briefly the HMM formulation used and the J -statistic. In Section III the search pipeline and parameter space are described. In Sections IV and V, we present the search results and upper limits, respectively. We conclude in Section VI.

In Section II A we review the HMM formalism used to track the wandering GW emission frequency from one time step to the next, according to a user-selected set of transition probabilities. For each time-step we calculate the likelihood of a signal being present given the data, via a maximum likelihood matched filter called the Jstatistic, which is reviewed in Section II B.

A HMM is a probabilistic finite state automaton characterized by a hidden state variable, q(t), which takes the discrete values {q 1 , ... , q N Q }, and an observable state variable, o(t), which takes the discrete values {o 1 , ... , o N O }. The automaton jumps between states at discrete time epochs {t 1 , ... , t N T }. The probability of being in hidden state q(t n+1 ) at time t n+1 depends only upon the state at the previous time step t n . This is known as a Markov process.

To complete the model two matrices are defined. First, the transition probability matrix, A q(tn+1)q(tn) , which relates the probability of a state q(t n ) to jump to q(t n+1 ), takes the form

where δ ij is the Kronecker delta. Eq. (1) defines the signal model as a piece-wise constant function that jumps by −1, 0, or 1 frequency bin ∆q at each discrete transition time. See Section III A for the details on the search frequency bin size. The other matrix is the emission probability matrix L o(tn)q(tn) that relates the likelihood of observing o(t n ) if the hidden state variable is q(t n ). L o(tn)q(tn) is constructed from the matched-filter J -statistic, which we review in Section II B. In our GW application, f (t) maps onto q(t), noting that f (t) is hidden because it cannot be measured electromagnetically for Sco X-1. The data, specifically the Fourier transform of the time series output by the detector, map onto o(t). The total observation time T obs is divided into N T segments of duration T drift rounded down to the nearest integer, i.e. N T = T obs /T drift . T drift is chosen to prevent f (t) from wandering by more than one frequency bin per time step. The rate of spin wandering is unknown a priori in Sco X-1, as f (t) cannot be measured electromagnetically. The observed X-ray flux variability can be used to estimate the stochastic variation in f (t) [38, 47] , and from this we make an informed choice of T drift , as in previous searches.

The probability that the hidden state follows some path Q = {q(t 1 ), ... , q t N T } given some observed data O = {o(t 0 ), ... , o(t N T )} is then given by the product of the transition and emission probabilities for each step, viz

where we define the prior probability of being in some initial state q(t 0 ) at time t 0 as Π (t0) . In this paper we assign equal probability to all initial states, with Π q(t0) = 1/N Q . We seek the path Q * that maximizes P (Q|O) in Eq. (2) . But it is computationally inefficient to consider all the N N T +1 Q possible paths. A robust and computationally efficient way to find Q * is the Viterbi algorithm [48] . This recursive algorithm exploits the principle of optimality to find Q * given O. A comprehensive description of the algorithm can be found in Appendix A of Ref. [29] .

In this paper we use as detection statistic the loglikelihood of the most likely path L = ln P (Q * |O).

The emission probability L o(tn)q(tn) relates the observed data, o(t n ), collected in the interval t n ≤ t ≤ t n + T drift to the hidden states q(t n ). In this paper, we express L o(tn)q(tn) in terms of the J -statistic [21, 45] . The J -statistic is a maximum likelihood, frequency domain, matched-filter which tracks the orbital phase of the neutron star in its binary system. It is an extension of the traditional F-statistic [49] , which is a matched filter for a biaxial rotor [50] . The Doppler shift due to the binary motion disperses the F-statistic power into orbital sidebands of the GW carrier frequency. Although the F-statistic can be used to produce matched filters to account for the Doppler shift due to the binary motion, the J -statistic is used for computational efficiency. Section III in Ref. [45] presents the detailed derivation of the J -statistic.

In general, to account for the dispersed power, the Jstatistic is constructed from matched filters of the suggestive form

with

where ⊗ denotes convolution, J s (x) is the Bessel function of the first kind of order s, with m = ceil (2πf 0 a 0 ). Eq. (4) assumes the GW signal is produced by a biaxial rotor in a circular Keplerian orbit, and requires three binary orbital parameters: the projected semi-major axis a 0 , the orbital phase at a reference time φ a , and P is the binary orbital period.

In this section we discuss the practical details of the search. Sections III A and III B define the parameter domain and grid respectively. Section III C sets out the workflow. Section III D justifies the selection of the false alarm probability in terms of the number of search templates. Section III E specifies the primary and secondary data products ingested by the search.

The J -statistic depends on the direction of the source, described by the right ascension α, and declination δ. It also depends on the three binary orbital elements: P , a 0 , and φ a . The time of passage through the ascending node, T asc , is linked to φ a via φ a = 2πT asc /P (mod2π). Henceforth we use T asc instead of φ a . Some of these parameters have been measured electromagnetically for Sco X-1. Their values and uncertainties are summarized in Table I .

The last electromagnetic measurements [51] for 

where P 0 = 68 023.86048s is the central value of the orbital period in Table I , and N orb =

is the number of full orbits between the reference time T 0 and T O3,0 . The original uncertainties for T asc,ref and P are also propagated using Eq. (5). This is illustrated in Fig The propagated priors on T asc and P change throughout the search duration as their correlation grows with time. The lower panel of Figure 1 shows the change from the start of O3 marked as solid color lines, to its end, T O3end = 1269361423 GPS time, shown as dotted lines. The search has been designed to cover the whole 3σ region of the propagated T asc -P space, from start to end of O3.

For a 0 , we cover the range 1.45 ≤ a 0 /(1 s) ≤ 3.25, following the electromagnetic measurements presented in [51] . We can write this range equivalently asā 0 ± 3σ a0 , withā 0 = 2.35s and σ a0 = 0.3s.

The coherence time is set to T drift = 10 d. The latter choice is justified astrophysically: it is the characteristic time-scale of the random walk in f inferred from accretion-driven fluctuations in the X-ray flux of Sco X-1 [19, 38, 47] . It also matches the value used in previous published searches for Sco X-1, enabling direct comparison with historical results [19, 21, 28, 29] . The resolution in frequency space ∆f drift , i.e the size of the frequency bins, is set by the coherence time as ∆f drift = 1/(2T drift ) = 5.787037 × 10 −7 Hz.

The range of frequencies to be searched, 60 Hz to 500 Hz, covers the region where LIGO is most sensitive. This frequency range is divided into sub-bands. This eases the manipulation of the data and allows one to approximate f 0 in Eq. (4) by the mid-point frequencyf in each subband, accelerating the process of creating each matched filter via Eq. (4) [45] . The sub-bands are designed to contain a number of frequency bins N f that is a power of two, in order to accelerate the fast Fourier transform involved in calculating the convolution in Eq. (4) . For this search we use N f = 2 20 , setting the sub-band width to ∆f sub = N f ∆f drift = 0.6068148 Hz. As such the total number of sub-bands to consider in our search is N sub = (500 − 60)Hz/∆f sub = 725. As the J -statistic is less sensitive farther away fromf , we create sub-bands with an overlap of ∆f sub /4. This way the area with less sensitivity in a sub-band is covered with greater sensitivity in the neighbouring sub-band. All of the parameters discussed in this section are summarized in Table I .

In this subsection we describe the procedure to calculate and place the orbital templates needed to cover the search parameter domain per sub-band.

As explained in Section III A, the forward propagation of the reference T asc,ref increases its uncertainty as a function of N orb . To be conservative, we choose to propagate TABLE I. Search parameters and their range. The column headed "EM data" records the availability of electromagnetic measurements in the references in the last column. All parameter ranges include the central value together with ± 1σ uncertainties; values without uncertainties are treated as constants. In the text generally the central values are denoted with the subscript 0, e.g. P0. The time of ascension Tasc stands for the value in [51] propagated up to the start of O3, as described in Section III A. As written here Tasc and P , plus their uncertainties, define a rectangular parameter domain. We only search over the grid points that have support from the propagated priors, defined by all the ellipses in the lower panel of Figure 1 ; See Section III B for details. 

where one has N orb,end = T O3end −T0

, and σ T asc,ref = 50s and σ P = 0.0432s are the uncertainties for T asc,ref and P respectively, the result σ Tasc = 200s is included in Table I . Although the uncertainties are propagated to the end of O3, the central value for the time of ascension is only propagated to the start of O3, T asc0 = 1 238 149 477.03488 s, as shown in Section III A.

We cover the parameter space by using a rectangular grid defined by the limits (ā 0 ± 3σ a0 , T asc ± 3σ Tasc 0 , P 0 ± 3σ P ). We set the spacing of the grid points by selecting an acceptable maximum mismatch µ max , following [53] . This mismatch represents the fractional loss in signalto-noise ratio between the search with the true parameters and the nearest grid point. For the search we use µ max = 0.1. The number of grid points needed to cover the (a 0 , T asc , P ) space, for a given µ max , are calculated using Eq. (71) of Ref. [53] , namely

For O3 the number of contiguous semi-coherent segments is N T = 36. To be conservative when applying Eqs.(7)-(9), we use the highest frequency in each subband for f , the highest a 0 =ā 0 + 3σ a0 and the lowest P = P 0 − 3σ P . Table II the points defined by Eqs.(7)-(9) that lie within the start (color lines) and end (dotted lines) ellipses in the bottom panel of Figure 1 .

The workflow for the search is illustrated in Figure 2 , as a flow chart.

At the outset, the time series from the detector is converted into short Fourier transforms (SFTs) lasting T SFT = 1800 s. The corresponding data, for each frequency sub-band, are divided into N T blocks of duration T drift = 10 d. All of the SFTs in a single block are used to calculate an F-statistic atom [54] with the fixed parameters α and δ in Table I . The process is repeated for all the blocks, generating N T atoms. The F-statistic atoms do not depend on the orbital parameters so they are stored in a look-up table. The steps in this paragraph conclude in the blue parallelogram denoted "N T F-statistic atoms" in Figure 2 .

In every sub-band, each F-statistic atom is fed into the J -statistic in Eq. (4) for a triad of orbital parameters (a 0 , T asc , P ). The Viterbi algorithm (see [48] or Section II.B of Ref. [45] ) finds the optimal frequency path connecting the J -statistic blocks and its associated log likelihood. In Figure 2 , the latter steps extend from the orange rectangle "Calculate the J -statistic" up to the blue parallelogram marked "log likelihood and optimal path for (a 0 , T asc , P ) i ".

For a sub-band centered on the frequencyf , the search scans over all binary templates (a 0 , T asc , P ) i with 1 ≤ i ≤ N a0 (f )N Tasc (f )N P (f ), calculated using Eqs.(7)-(9). This step is illustrated as the green oval denoted "Used all templates?" in Figure 2 . For each (a 0 , T asc , P ) i an optimal path and its associated log likelihood are recorded.

Following the loop over all binary templates, the optimal path with highest log likelihood, denoted max(L), is selected in the blue parallelogram marked "max(L) and assoc. optimal path" in Figure 2 . If max(L) is higher than the detection threshold (see Section III D), then the sub-band is recorded as a candidate and passed through a hierarchy of vetoes (see Section IV B), via the "yes" output of the upper green oval.

Sub-bands with max(L) below the detection threshold are used to calculate GW strain upper limits via the "no" output of the upper green oval. Vetoed sub-bands are not used to calculate GW upper-limits.

A sub-band is registered as a candidate, when max(L) exceeds a threshold, L th , corresponding to a user-selected false alarm probability. As the distribution of max(L) in pure noise is unknown we rely on Monte-Carlo simulations to determine L th in each sub-band of the search. To estimate the distribution of max(L) in pure noise, we generate synthetic Gaussian data using the lalapp Makefakedata v5 program in the LIGO Scientific Collaboration Algorithm Library (LALSuite) [55] . The synthetic data are generated for a sub-band centered on the frequencyf , with α and δ copied from Table I . Then the search workflow described in Section III C is applied. To avoid needless computation, we limit the grid to N a0 = 322, N Tasc = 35, and N P = 5 in every sub-band, independent off .

In general L th depends on the number of generated log likelihoods per sub-band, i.e. N tot = N f N a0 N Tasc N P . We describe the false alarm probability, α Ntot , of a subband with N tot log likelihoods in terms of the probability of a false alarm in a single terminating frequency bin per orbital template, α, as

Historically HMM Sco X-1 searches [21, 29] use α Ntot = 0.01, a choice we adopt here. A false-alarm probability of 1% per sub-band applied to a total of 725 sub-bands implies we should expect ∼ 7 false alarms from the search. Searches with electromagnetically constrained f such as Ref. [22] and Ref. [24] allow for α Ntot = 0.3, given the reduced search space. Appendix A in Ref. [24] presents the detailed procedure to set thresholds using Monte-Carlo simulations.

FIG. 2. Flowchart of the search pipeline for a sub-band. The light red octagons are the start and end points, the orange rectangles are processes, the blue parallelograms are input or output data, and the green ovals stand for decision points. The full search repeats the steps in the flowchart for 725 subbands from 60Hz to 500Hz.

The search uses all the O3 dataset, starting April 1, 2019, 15:00 UTC and finishing March 27, 2020, 17:00 UTC. The dataset is divided in two. The first part (O3a) spans 1 April 2019 to 1 Oct 2019 followed by a month long commissioning break. The second part (O3b) was intended to span 1 November 2019 to 30 April 2020 but was suspended in March 2020 due to the COVID-19 coronavirus pandemic. SFTs are generated from the "C01 calibrated self-gated" dataset, specifically designed to remove loud glitches from the strain data, following the procedure in Ref. [56] .

Due to the month-long commissioning break between O3a and O3b, two out of N T segments have no SFTs.

The two segments are dated October 8, 2019, 15:00 UTC and October 15, 2019, 15:00 UTC, respectively. We replace them by segments with uniform log-likelihood across all frequency bins, to allow the HMM to connect data from O3a with data from O3b while accommodating spin wandering. Every time atoms are created, such as in Sections III D, IV B 2 and IV B, the relevant missing atoms are replaced with uniform log-likelihood atoms.

O3 ANALYSIS

The results of the search are plotted in Figure 3 . On the horizontal axis we show the terminating frequency bin of the optimal path, i.e q * (t N T ) per sub-band, that satisfies max(L) > L th , defining preliminary signal candidates. On the vertical axes we graph the orbital parameters a 0 (left panel), T asc (middle panel), and P (right panel). Figure 3 contains 35 candidates with max(L) > L th . To eliminate false alarms we use the hierarchy of vetoes employed in Ref. [21] . The vetoes discard candidates that (i) lie near an instrumental noise line (known line veto) or (ii) appear in one interferometer (IFO) but not the other (single IFO veto). In previous searches other vetoes, e.g. candidates that appear in half of the observation time (T obs /2 veto), have been used in addition to (i) and (ii) [21, 22, 24, 29, 42] . Additional vetoes are unnecessary in this paper; all but one of the candidates are vetoed by (i) and (ii), and the survivor is eliminated by other means, as discussed below. The outcomes of the vetoes in the 35 sub-bands containing outliers are recorded in Table III .

The sole candidate that passes vetoes (i) and (ii), contained in the sub-band starting at 60.05 Hz, is suspiciously close to the known 60 Hz noise line due to the United States of America power grid [57] . Additionally, several other candidates appear near harmonics of 60.05 Hz, for instance 119.52 Hz and 179.60 Hz. When we search the sub-band using the C01 calibrated self-gated 60 Hz subtracted dataset, which uses the algorithm described in Ref. [58] to subtract the 60 Hz noise line, the candidate disappears.

B. Vetoes

Narrowband noise features in the IFO are caused by a plethora of reasons, such as the suspension system or the electricity grid [59, 60] . As noise lines artificially increase the output of the F-statistic, sub-bands that contain them tend to be flagged as candidates. In response, we veto any candidate whose optimal frequency path f (t i ) satisfies

for any epoch t i in the search. Here f line is the frequency of the noise line. We refer to the vetted known lines list in Ref. [61] . This test vetoes 30 out of the 35 candidates. We note that the number of remaining candidates, after eliminating those caused by noise lines, is consistent with our original number of expected candidates.

A plausible astrophysical signal that has escaped detection in prior searches would likely be weak enough to need data from both IFOs to be detectable, or strong enough to be seen in both, given their comparable sensitivities in most frequency bands. In contrast, instrumental artifacts are unlikely to appear simultaneously in both IFOs. Let max(L) a and max(L) b > max(L) a denote the log likelihoods in each IFO, and let max(L) ∪ denote the log likelihood of the original candidate. There are four possible outcomes:

1. If one finds max(L) a < L th and max(L) b > max(L) ∪ , and the optimal path, f b (t i ), associated with max(L) b , satisfies

for any epoch t i in the search, where f ∪ (t i ) is the optimal path associated with max(L) ∪ then the candidate is consistent with an instrumental artifact in detector b. It is vetoed.

2. If one finds max(L) a < L th and max(L) b > max(L) ∪ but the candidate does not satisfy Eq. (12), then it is saved for further postprocessing. Such a candidate could be a faint astrophysical signal which needs both IFOs to be detected.

3. If one finds max(L) a > L th and max(L) b > L th , then the candidate could be a strong astrophysical signal. It could also imply a common noise source in both detectors. The candidate is flagged for postprocessing. Candidates marked with purple squares are eliminated by the single IFO veto, while red circles mark the ones eliminated by the known lines veto. The candidate with no marking survives both the single IFO and known lines vetoes, but is eliminated by its absence when using noise-subtracted data (See Section IV A).

Sub-bands without candidates are used to place upper limits on the gravitational wave strain detectable at a 95% confidence level, h 95% 0 . We use the approach in the historical HMM Sco X-1 searches [21, 29] to set frequentist upper limits. This is done to facilitate comparison with previous upper limits.

To capture the variation of the wave strain as a function of the inclination angle ι, we define the effective strain [47] 

We note that Eq. (13) allows us to re-scale h 95% 0 for the circularly polarized case, |cos ι| = 1, to any other inclination angle ι. For example if we assume the electromagnetically measured inclination of Sco X-1 orbit as ι = 44 • then Eq. (13) yields h eff,95%

To set frequentist upper limits in a sub-band with central frequencyf , we start by generating 100 copies of the O3 data for this sub-band. A Sco X-1-like signal, i.e using the astrophysical parameters in Table I , is injected into each copy of the sub-band. The parameters {ψ, a 0 , T asc , P } inj used to create the injected signal are drawn from uniform distributions within the range given by their respective 3σ error bars. We make sure the in-jected T asc,inj and P inj values lie inside the propagated priors shown in Figure 1 , second panel. The injected frequency f inj is uniformly selected from the intervalf ± δf with δf = 0.05Hz. The intervalf ± δf is chosen for simplicity. The initial value of h 0 is chosen such that there is at least one frequency path with max(L) > L th . We progressively reduce h 0 , holding {ψ, a 0 , T asc , P } inj constant, until the signal is no longer detectable. We record the last detectable amplitude as h 0 min i . The procedure is repeated for all copies of the sub-band, choosing a new set of injection parameters {ψ, a 0 , T asc , P } inj per copy. Finally {h 0 min 1 , ..., h 0 min 100 } are sorted in ascending order and the 95th becomes h 95% 0 . The injections have |cos ι| = 1, so we use Eq. (13) to convert h 95% 0 to other polarizations.

The limits on h 95% 0 are plotted in Figure 4 . We present three cases, as in Ref. [21] : circular polarization ι = 0 (blue dots in Figure 4 ), ι = 44 • (following the electromagnetic measurements in Ref. [51] ; denoted by green dots in Figure 4) , and unknown polarization (orange dots in Figure 4 ). In the latter context, unknown polarization means we marginalize over all possible polarizations assuming a uniform distribution in cos ι from −1 to 1.

The upper limits from the O3 search are on average ∼ 3 times lower than those from the O2 HMM search TABLE III. Candidates for the O3 search. The first column corresponds to the minimum frequency in the sub-band that contains the candidate. The second column is the log likelihood of the candidate. The other columns record the outcome of the two vetoes used in Section IV B 1 and IV B 2. A candidate that passes or fails a veto is marked with a or X respectively. H and L are the Hanford-only and Livingston-only max(L) values. The remaining candidate, contained in the 60.05 Hz sub-band, is eliminated when using the "C01 calibrated self-gated 60 Hz subtracted" dataset. [21] . For the sub-band starting at 256.06Hz we obtain the lowest h 95% 0 , given by 4.56 × 10 −26 , 6.16 × 10 −26 , and 9.41 × 10 −26 for circular, electromagnetically restricted (ι = 44 • ) and unknown polarizations, respectively. Compared to the most sensitive sub-bands in previous HMM Sco X-1 searches the lowest h 95% 0 is a factor of ∼ 13 lower than in O1 data [29] and ∼ 3 lower than in O2 data [21] . Figure 5 , which is included for illustrative purposes, shows the GW upper limits marginalized over possible polarizations, for four different searches: CrossCorr O1 [29] (black line), CrossCorr O2 [23] (brown line), Radiometer O3 [62] (light pink line), and our results (green line). Each search is conditional on a different signal model, so the upper limits are not directly comparable.

Torque-balance assumes the spin-down torque due to gravitational wave emission balances the accretion spinup torque. From this assumption theoretical upper limits on gravitational wave strain can be estimated from X-ray observations. Following Eq. (4) in Ref. [23] , the amplitude of the GW signal produced in torque equilibrium, h eq 0 , is

In Eq. (14) , F X is the X-ray flux, M is the fiducial neutron star mass, r m is the lever arm, R is the neutron star radius and f GW is the GW frequency. Eq. (14) assumes the maximum accretion luminosity is completely radiated as X-rays, i.e. X = 1 in Eq. (4) of Ref. [23] . To calculate Eq. (14), we use r m = R = 10 km, plotted as a solid red line in Figure 4 , or r m = R A , where R A is the Alfvén radius, which corresponds approximately to the inner edge of the accretion disk [29, 36] . This is given by

km, (15) where B is the polar magnetic field strength at the stellar surface, G is Newton's gravitational constant, andṀ is the accretion rate set to the Eddington limit 2 × 10 −8 M yr −1 , for a fiducial neutron star with mass M = 1.4M and radius R = 10 km [63, 64] . This limit is plotted in Figure 4 as the dashed red line. The electromagnetic inclination ι = 44 • produces upper limits that dip under the theoretical torque-balance limits (red lines in Figure 4 ) for the first time in the HMM Sco X-1 search history. The CrossCorr search pipeline achieved this milestone in the O2 search; see Figure 1 in Ref. [23] . Again, the reader is reminded that different pipelines assume different signal models, and upper limits conditional on different signal models cannot be compared directly.

In this paper we search the LIGO O3 data for continuous GWs from the LMXB Sco X-1, using a hidden Markov model, combined with the maximum-likelihood J -statistic and a binary template grid that includes the projected semi major axis a 0 , time of ascension T asc and orbital period P . The binary orbital elements are constrained via electromagnetic observations, but the spin frequency is unknown. Monte-Carlo simulations are used to establish a detection threshold, L th , with a false alarm probability α Ntot = 0.01, per sub-band. The search is conducted in the range 60Hz to 500Hz, partitioned into sub-bands of width ∆f sub = 0.606Hz. The sub-bands with an optimal path satisfying max(L) > L th are passed 25 through a hierarchy of vetoes. One candidate survives the vetoes, but this candidate is eliminated when using the "C01 calibrated self-gated 60 Hz subtracted" dataset. The most sensitive sub-band, starting at 256.06Hz, yields h 95% 0 = 4.56×10 −26 , 6.16×10 −26 , and 9.41×10 −26 for circular, electromagnetically restricted (ι = 44 • ) and unknown polarizations, respectively.

The above results improve on the two previous HMM Sco X-1 searches [21, 29] by using data from O3 and including the orbital period P in the searched template grid. For comparison, the most sensitive sub-band in the O2 HMM search, 194.6 Hz, obtained h 95% 0 = 1.42×10 −25 for ι = 0 [21] , while for the same sub-band and polarization the present search obtains h 95% 0 = 5.40 × 10 −26 . On average our upper limits are a factor of ∼ 3 below the O2 HMM results. The present search sets the lowest upper-limits for the HMM searches, beating for first time the torque-balance limit for the electromagnetically restricted ι = 44 • case.

Other LMXBs are not as bright in X-rays as Sco X-1, but they are important targets too. Some LMXBs emit X-ray pulsations, so that f is measured to high precision electromagnetically, an important advantage. However the gravitational wave frequency emitted by such objects may be displaced from f and wander randomly with respect to it. An HMM-based search is well placed to track such wandering. Searches for LMXBs with electromagnetically-constrained rotation frequencies have been performed in O2 [22] and O3 [24] data. Ref. [24] reported strain upper limits in the range 5.1 × 10 −26 ≤ h 95% 0 ≤ 1.1 × 10 −25 for its 20 candidates. Such searches offer considerable promise in future observing runs.

This material is based upon work supported by NSF's LIGO Laboratory which is a major facility fully funded by the National Science Foundation. The authors also gratefully acknowledge the support of the Science and Technology Facilities Council (STFC) of the United Kingdom, the Max-Planck-Society (MPS), and the State of Niedersachsen/Germany for support of the construc-tion of Advanced LIGO and construction and operation of the GEO 600 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 Netherlands Organization for Scientific Research (NWO), for the construction and operation of the Virgo detector and the creation and support of the EGO consortium. The authors also gratefully acknowledge research support from these agencies as well as by the 

18 D. Passuello, 18 M. Patel, 63 M. Pathak, 88 B. Patricelli , 47, 18 A. S. Patron, 7 S. Paul , 66 E. Payne, 5 M. Pedraza, 1 R. Pedurand, 103 M. Pegoraro

72 C. Périgois, 30 C. C. Perkins, 76 A. Perreca , 98, 99 S. Perriès, 140 D. Pesios

57 M. Pichot , 37 M. Piendibene, 78, 18 F. Piergiovanni, 54, 55 L. Pierini

47 M. Pillas, 46 F. Pilo, 18 L. Pinard, 157 C. Pineda-Bosque, 90 I. M. Pinto

6 K. Piotrzkowski, 58 M. Pirello, 72 M. D. Pitkin , 193 A. Placidi , 40, 79 E. Placidi

14 P. Prosposito, 123, 124 L. Prudenzi, 111 A. Puecher, 59, 65 M. Punturo , 40 F. Puosi, 18, 78 P. Puppo

18 Z. Tornasi, 24 A. Torres-Forné , 126 C. I. Torrie, 1 I

59 M. van Beuzekom , 59 M. van Dael

67 H. van Haevermaet , 205 J. V. van Heijningen , 58 M. H. P. M. van Putten, 288 N. van Remortel , 205 M. Vardaro, 212, 59 A. F. Vargas, 120 V. Varma , 111 M. Vasúth , 75 A. Vecchio

Development and Innovation Office Hungary (NKFIH), the National Research Foundation of Korea, the Natural Science and Engineering Research Council Canada, Canadian Foundation for Innovation (CFI), the Brazilian Ministry of Science, Technology, and Innovations, the International Center for Theoretical Physics South American Institute for Fundamental Research (ICTP-SAIFR), the Research Grants Council of Hong Kong, the National Natural Science Foundation of China (NSFC), the Leverhulme Trust, the Research Corporation, the Ministry of Science and Technology (MOST), Taiwan, the United States Department of Energy, and the Kavli Foundation. The authors gratefully acknowledge the support of the NSF, STFC, INFN and CNRS for provision of computational resources. This work was supported by MEXT, JSPS Leading-edge Research Infrastructure Program, JSPS Grant-in-Aid for Specially Promoted Research 26000005, JSPS Grant-in-Aid for

Gravitational waves: Sources, detectors and searches

Advanced LIGO: the next generation of gravitational wave detectors

Advanced Virgo: a secondgeneration interferometric gravitational wave detector

Gravitational waves from neutron stars: promises and challenges

KAGRA: 2.5 generation interferometric gravitational wave detector

Deformations of accreting neutron star crusts and gravitational wave emission

Maximum elastic deformations of relativistic stars

Gravitational waves from neutron stars with large toroidal B fields

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Continuous-wave gravitational radiation from pulsar glitch recovery

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Directed search for gravitational waves from Scorpius X-1 with initial LIGO data

Model-based cross-correlation search for gravitational waves from Scorpius X-1

Search for gravitational waves from Scorpius X-1 in the second Advanced LIGO observing run with an improved hidden Markov model

Search for gravitational waves from five low mass x-ray binaries in the second Advanced LIGO observing run with an improved hidden Markov model

Search for Continuous Gravitational Waves from Scorpius X-1 in LIGO O2 Data

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Gravitational radiation from accreting neutron stars

Gravitational Radiation and Rotation of Accreting Neutron Stars

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An empirical torque noise and spin-up model for accretion-powered X-ray pulsars

Observations of Accreting Pulsars

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Search Methods for Continuous Gravitational-Wave Signals from Unknown Sources in the Advanced-Detector Era

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Generalized application of the Viterbi algorithm to searches for continuous gravitational-wave signals

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High-Resolution Parallax Measurements of Scorpius X-1

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LIGO Algorithm Library -LALSuite, free software (GPL)

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Identification and mitigation of narrow spectral artifacts that degrade searches for persistent gravitational waves in the first two observing runs of Advanced LIGO

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