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GLENCOE CORRELATION MATHEMATICS: APPLICATIONS AND CONCEPTS COURSES 1, 2, and 3 NEBRASKA Mathematics Standards for Grade 8 PAGE REFERENCES STANDARDS COURSE 1 COURSE 2 COURSE 3 8.1 Numeration/Number Sense 8.1.1 By the end of eighth grade, students will recognize natural numbers, whole numbers, integers, and rational numbers. SE: 294 Prerequisite Skills 586 SE: 106, 230 _44-_49 Key Concept 229 TWE: I 229 _4 SE: 125-129, 130 _18-_23, 147 _25-_30, 149 _9-_11 TWE: A 129 B 62, 125 DI 126 8.1.2 By the end
• various units of volume
• equivalencies among fractions
• appropriate operation
• square foot to square yards
• use for technology
• use technology
• use of technology
• geometric figures
• hands
• numbers
• problems
• area

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1Astronomy & Astrophysics manuscript no. lvemfollowup c ESO 2012
3 January 2012
Implementation and testing of the ﬁrst prompt search for
gravitational wave transients with electromagnetic counterparts
1 1 1 2 3 4 5ac 6 1The LIGO Scientiﬁc Collaboration and Virgo Collaboration: J. Abadie , B. P. Abbott , R. Abbott , T. D. Abbott , M. Abernathy , T. Accadia , F. Acernese , C. Adams , R. Adhikari ,
7,8 1 7,9,8 10 9 11 12 1 9 1 11 1C. Aﬀeldt , P. Ajith , B. Allen , G. S. Allen , E. Amador Ceron , D. Amariutei , R. S. Amin , S. B. Anderson , W. G. Anderson , K. Arai , M. A. Arain , M. C. Araya ,
13 14a 15 8,7 7,8 13 16 17 18 19 15 5ac 3S. M. Aston , P. Astone , D. Atkinson , P. Aufmuth , C. Aulbert , B. E. Aylott , S. Babak , P. Baker , G. Ballardin , S. Ballmer , D. Barker , F. Barone , B. Barr ,
20 21 22 15 23 3 3 24ab 15 7,8 25a 4P. Barriga , L. Barsotti , M. Barsuglia , M. A. Barton , I. Bartos , R. Bassiri , M. Bastarrika , A. Basti , J. Batch , J. Bauchrowitz , Th. S. Bauer , M. Bebronne ,
16 25a 3 4 23 26 15 7,8 1 3 27B. Behnke , M.G. Beker , A. S. Bell , A. Belletoile , I. Belopolski , M. Benacquista , J. M. Berliner , A. Bertolini , J. Betzwieser , N. Beveridge , P. T. Beyersdorf ,
28 1 6 26 24a 29a 1 1 30 20 15 25a 7,8I. A. Bilenko , G. Billingsley , J. Birch , R. Biswas , M. Bitossi , M. A. Bizouard , E. Black , J. K. Blackburn , L. Blackburn , D. Blair , B. Bland , M. Blom , O. Bock ,
21 7,8 31 32b 24ab 33 1 7,8 24a 34 35a 22 24aT. P. Bodiya , C. Bogan , R. Bondarescu , F. Bondu , L. Bonelli , R. Bonnand , R. Bork , M. Born , V. Boschi , S. Bose , L. Bosi , B. Bouhou , S. Braccini ,
24a 9 28 36ab 37 7,8 38 6 32a 7,8 29a 7,8C. Bradaschia , P. R. Brady , V. B. Braginsky , M. Branchesi , J. E. Brau , J. Breyer , T. Briant , D. O. Bridges , A. Brillet , M. Brinkmann , V. Brisson , M. Britzger ,
1 19 39 40bc 25ab 41 9 7,8 4 22 10 42A. F. Brooks , D. A. Brown , A. Brummit , T. Bulik , H. J. Bulten , A. Buonanno , J. Burguet–Castell , O. Burmeister , D. Buskulic , C. Buy , R. L. Byer , L. Cadonati ,
36a 5ab 30 3 30 44 18 45 19 18 46 12 43G. Cagnoli , E. Calloni , J. B. Camp , P. Campsie , J. Cannizzo , K. Cannon , B. Canuel , J. Cao , C. D. Capano , F. Carbognani , S. Caride , S. Caudill , M. Cavaglia` ,
29a 18 24a 1 36b 32a 1 13 47 22 13F. Cavalier , R. Cavalieri , G. Cella , C. Cepeda , E. Cesarini , O. Chaibi , T. Chalermsongsak , E. Chalkley , P. Charlton , E. Chassande Mottin , S. Chelkowski ,
48 49 18 50 51 52 53 20 11 15 10 54 9Y. Chen , A. Chincarini , A. Chiummo , H. Cho , N. Christensen , S. S. Y. Chua , C. T. Y. Chung , S. Chung , G. Ciani , F. Clara , D. E. Clark , J. Clark , J. H. Clayton ,
32a 55ab 38 24ab 18 14ab 14b 14ab 56 15 21 27F. Cleva , E. Coccia , P. F. Cohadon , C. N. Colacino , J. Colas , A. Colla , M. Colombini , A. Conte , R. Conte , D. Cook , T. R. Corbitt , M. Cordier ,
17 1 12 51 32a 19 20 1 9 26 13N. Cornish , A. Corsi , C. A. Costa , M. Coughlin , J. P. Coulon , P. Couvares , D. M. Coward , D. C. Coyne , J. D. E. Creighton , T. D. Creighton , A. M. Cruise ,
3 3 18 13 7,8 28 1 55a 7,8 18 1 26A. Cumming , L. Cunningham , E. Cuoco , R. M. Cutler , K. Dahl , S. L. Danilishin , R. Dannenberg , S. D’Antonio , K. Danzmann , V. Dattilo , B. Daudert , H. Daveloza ,
29a 54 57 18 34 5ab 10 58 7,8 25a 59b 54 1M. Davier , G. Davies , E. J. Daw , R. Day , T. Dayanga , R. De Rosa , D. DeBra , G. Debreczeni , J. Degallaix , W. Del Pozzo , M. del Prete , T. Dent , V. Dergachev ,
12 1 57 60 5a 24ab 7,8 55ac 24a 26 4R. DeRosa , R. DeSalvo , V. Dhillon , S. Dhurandhar , L. Di Fiore , A. Di Lieto , I. Di Palma , M. Di Paolo Emilio , A. Di Virgilio , M. D´ıaz , A. Dietz ,
7,8 21 11 61 59ab 62 1 45 20 21 7,8 3J. DiGuglielmo , F. Donovan , K. L. Dooley , S. Dorsher , M. Drago , R. W. P. Drever , J. C. Driggers , Z. Du , J. C. Dumas , S. Dwyer , T. Eberle , M. Edgar ,
54 12 1 58 1 1 3 21 6 23 55ab 54 20 63M. Edwards , A. Eﬄer , P. Ehrens , G. Endro˝czi , R. Engel , T. Etzel , K. Evans , M. Evans , T. Evans , M. Factourovich , V. Fafone , S. Fairhurst , Y. Fan , B. F. Farr ,
63 63 7,8 11 24ab 24ab 31 18 31 33 15 21 6W. Farr , D. Fazi , H. Fehrmann , D. Feldbaum , I. Ferrante , F. Fidecaro , L. S. Finn , I. Fiori , R. P. Fisher , R. Flaminio , M. Flanigan , S. Foley , E. Forsi ,
5a 1 32a 33 14ab 24a 7,8 64 65 13 37 12 21L. A. Forte , N. Fotopoulos , J. D. Fournier , J. Franc , S. Frasca , F. Frasconi , M. Frede , M. Frei , Z. Frei , A. Freise , R. Frey , T. T. Fricke , J. K. Fridriksson ,
7,8 21 6 13 6 33 35ab 66 15 19 5ab 58D. Friedrich , P. Fritschel , V. V. Frolov , P. J. Fulda , M. Fyﬀe , M. Galimberti , L. Gammaitoni , M. R. Ganija , J. Garcia , J. A. Garofoli , F. Garuﬁ , M. E. Gas´ par´ ,
49 45 18 24a 67 34 12,6 9 6 24a 3 7,8 9´G. Gemme , R. Geng , E. Genin , A. Gennai , L. A. Gergely , S. Ghosh , J. A. Giaime , S. Giampanis , K. D. Giardina , A. Giazotto , C. Gill , E. Goetz , L. M. Goggin ,
12 28 7,8 4 7,8 22 3 20 15 3 39 68G. Gonzal´ ez , M. L. Gorodetsky , S. Goßler , R. Gouaty , C. Graef , M. Granata , A. Grant , S. Gras , C. Gray , N. Gray , R. J. S. Greenhalgh , A. M. Gretarsson ,
32a 26 7,8 16 36ab 6 60 1 46 69 8,7 13 9C. Greverie , R. Grosso , H. Grote , S. Grunewald , G. M. Guidi , C. Guido , R. Gupta , E. K. Gustafson , R. Gustafson , T. Ha , B. Hage , J. M. Hallam , D. Hammer ,
3 15 1,70 6 62 21 54 37 11 3 71 32bG. Hammond , J. Hanks , C. Hanna , J. Hanson , J. Harms , G. M. Harry , I. W. Harry , E. D. Harstad , M. T. Hartman , K. Haughian , K. Hayama , J. F. Hayau ,
39 1 38 11 32 29a 3 3 1 10 7,8 3 42T. Hayler , J. Heefner , A. Heidmann , M. C. Heintze , H. Heitmann , P. Hello , M. A. Hendry , I. S. Heng , A. W. Heptonstall , V. Herrera , M. Hewitson , S. Hild , D. Hoak ,
1 6 21 48 20 66 3 20 9 72 3 6 15K. A. Hodge , K. Holt , J. Homan , T. Hong , S. Hooper , D. J. Hosken , J. Hough , E. J. Howell , B. Hughey , S. Husa , S. H. Huttner , T. Huynh Dinh , D. R. Ingram ,
52 51 1 71 1 73 40d 12 74 54 3 20 1 63R. Inta , T. Isogai , A. Ivanov , K. Izumi , M. Jacobson , H. Jang , P. Jaranowski , W. W. Johnson , D. I. Jones , G. Jones , R. Jones , L. Ju , P. Kalmus , V. Kalogera ,
54 61 73 41 21 6 7,8 15 71 7,8 1 1I. Kamaretsos , S. Kandhasamy , G. Kang , J. B. Kanner , E. Katsavounidis , W. Katzman , H. Kaufer , K. Kawabe , S. Kawamura , F. Kawazoe , W. Kells , D. G. Keppel ,
67 7,8 28 75 73 76 20 7,8 77 10 50 1 31Z. Keresztes , A. Khalaidovski , F. Y. Khalili , E. A. Khazanov , B. Kim , C. Kim , D. Kim , H. Kim , K. Kim , N. Kim , Y. M. Kim , P. J. King , M. Kinsey ,
6 21 11 13 1 31 9 1 40b 1 7,8 63D. L. Kinzel , J. S. Kissel , S. Klimenko , K. Kokeyama , V. Kondrashov , R. Kopparapu , S. Koranda , W. Z. Korth , I. Kowalska , D. Kozak , V. Kringel , S. Krishnamurthy ,
16 40ae 7,8 3 8,7 20 52 15 31 10 7,8 3 1B. Krishnan , A. Kro´lak , G. Kuehn , R. Kumar , P. Kwee , M. Laas Bourez , P. K. Lam , M. Landry , M. Lang , B. Lantz , N. Lastzka , C. Lawrie , A. Lazzarini ,
16 50 78 10 7,8 37 29a 4 45 25a 59ab 1 79P. Leaci , C. H. Lee , H. M. Lee , N. Leindecker , J. R. Leong , I. Leonor , N. Leroy , N. Letendre , J. Li , T. G. F. Li , N. Liguori , P. E. Lindquist , N. A. Lockerbie ,
13 36a 29b 6 36a 48 15 7,8 31 3 7,8 21D. Lodhia , M. Lorenzini , V. Loriette , M. Lormand , G. Losurdo , J. Luan , M. Lubinski , H. Lu¨ck , A. P. Lundgren , E. Macdonald , B. Machenschalk , M. MacInnis ,
54 1 1 14a 29b 32a 21 61 24ac 10 35aD. M. Macleod , M. Mageswaran , K. Mailand , E. Majorana , I. Maksimovic , N. Man , I. Mandel , V. Mandic , M. Mantovani , A. Marandi , F. Marchesoni ,
4 23 23 10 1 18 36ab 3 11 1 21 4 21F. Marion , S. Mark´ a , Z. Mark´ a , A. Markosyan , E. Maros , J. Marque , F. Martelli , I. W. Martin , R. M. Martin , J. N. Marx , K. Mason , A. Masserot , F. Matichard ,
23 64 21 7,8 15 52 21 80 1 42 54L. Matone , R. A. Matzner , N. Mavalvala , G. Mazzolo , R. McCarthy , D. E. McClelland , P. McDaniel , S. C. McGuire , G. McIntyre , J. McIver , D. J. A. McKechan ,
46 7,8 8,7 53 81 15 31 9 1 54 6 20G. D. Meadors , M. Mehmet , T. Meier , A. Melatos , A. C. Melissinos , G. Mendell , D. Menendez , R. A. Mercer , S. Meshkov , C. Messenger , M. S. Meyer , H. Miao ,
33 5ab 52 55a 28 11 21 71 9 16 18 26C. Michel , L. Milano , J. Miller , Y. Minenkov , V. P. Mitrofanov , G. Mitselmakher , R. Mittleman , O. Miyakawa , B. Moe , P. Moesta , M. Mohan , S. D. Mohanty ,
42 15 15 33 55ab 71 5ab 7,8 4 52 11 11S. R. P. Mohapatra , D. Moraru , G. Moreno , N. Morgado , A. Morgia , T. Mori , S. Mosca , K. Mossavi , B. Mours , C. M. Mow–Lowry , C. L. Mueller , G. Mueller ,
26 52 7,8 66 23 3 11 1 14ab 3 11 3S. Mukherjee , A. Mullavey , H. Mu¨ller Ebhardt , J. Munch , D. Murphy , P. G. Murray , A. Mytidis , T. Nash , L. Naticchioni , R. Nawrodt , V. Necula , J. Nelson ,
3 71 18 6 54 41 39 21 1 69 69 9 6G. Newton , A. Nishizawa , F. Nocera , D. Nolting , L. Nuttall , E. Ochsner , J. O’Dell , E. Oelker , G. H. Ogin , J. J. Oh , S. H. Oh , R. G. Oldenburg , B. O’Reilly ,
9 1 48 66 11 6 31 13 55ac 55ac 14a 41R. O’Shaughnessy , C. Osthelder , C. D. Ott , D. J. Ottaway , R. S. Ottens , H. Overmier , B. J. Owen , A. Page , G. Pagliaroli , L. Palladino , C. Palomba , Y. Pan ,
11 24a,18 16,9 5ab 18 24ab 24a 1 1 82 19 83 16C. Pankow , F. Paoletti , M. A. Papa , M. Parisi , A. Pasqualetti , R. Passaquieti , D. Passuello , P. Patel , M. Pedraza , P. Peiris , L. Pekowsky , S. Penn , C. Peralta ,
19 5ab 1 7,8 36ab 40d 33 84 3 7,8 3 24abA. Perreca , G. Persichetti , M. Phelps , M. Pickenpack , F. Piergiovanni , M. Pietka , L. Pinard , I. M. Pinto , M. Pitkin , H. J. Pletsch , M. V. Plissi , R. Poggiani ,
7,8 56 49 54 1 7,8 84 1 7,8 59ab 28 7,8 35aJ. Po¨ld , F. Postiglione , M. Prato , V. Predoi , L. R. Price , M. Prijatelj , M. Principe , S. Privitera , R. Prix , G. A. Prodi , L. Prokhorov , O. Puncken , M. Punturo ,
14a 26 15 25ab 58 15 65 26 6 43 14ab 52,92P. Puppo , V. Quetschke , F. J. Raab , D. S. Rabeling , I. Racz´ , H. Radkins , P. Raﬀai , M. Rakhmanov , C. R. Ramet , B. Rankins , P. Rapagnani , S. Rapoport ,
63 55ab 23 15 85 32a 3 11 14ab 6 46 1,3 29aV. Raymond , V. Re , K. Redwine , C. M. Reed , T. Reed , T. Regimbau , S. Reid , D. H. Reitze , F. Ricci , R. Riesen , K. Riles , N. A. Robertson , F. Robinet ,
54 16 55a 6 63 15 4 23 26 5ac 6 40c fC. Robinson , E. L. Robinson , A. Rocchi , S. Roddy , C. Rodriguez , M. Rodruck , L. Rolland , J. Rollins , J. D. Romano , R. Romano , J. H. Romie , D. Rosin´ska ,
7,8 3 7,8 18 15 7,8 11 15 7,8 7,8 53 72C. Ro¨ver , S. Rowan , A. Ru¨diger , P. Ruggi , K. Ryan , H. Ryll , P. Sainathan , M. Sakosky , F. Salemi , A. Samblowski , L. Sammut , L. Sancho de la Jordana ,
15 21 1 1 3 86 33 54 71 19 15V. Sandberg , S. Sankar , V. Sannibale , L. Santamar´ıa , I. Santiago Prieto , G. Santostasi , B. Sassolas , B. S. Sathyaprakash , S. Sato , P. R. Saulson , R. L. Savage ,
7,8 87 7,8 37 7,8 16,54 15 3 52 1 1 6R. Schilling , S. Schlamminger , R. Schnabel , R. M. S. Schoﬁeld , B. Schulz , B. F. Schutz , P. Schwinberg , J. Scott , S. M. Scott , A. C. Searle , F. Seifert , D. Sellers ,
1 18 75 52 7,8 21 41 21 6 9 15 1A. S. Sengupta , D. Sentenac , A. Sergeev , D. A. Shaddock , M. Shaltev , B. Shapiro , P. Shawhan , D. H. Shoemaker , A. Sibley , X. Siemens , D. Sigg , A. Singer ,
1 72 9 52 12 2 1 21 13 48 3 21 3L. Singer , A. M. Sintes , G. Skelton , B. J. J. Slagmolen , J. Slutsky , J. R. Smith , M. R. Smith , N. D. Smith , R. J. E. Smith , K. Somiya , B. Sorazu , J. Soto , F. C. Speirits ,
55ab 52 21 15 7,8 7,8 34 1 26 3 28 26L. Sperandio , M. Stefszky , A. J. Stein , E. Steinert , J. Steinlechner , S. Steinlechner , S. Steplewski , A. Stochino , R. Stone , K. A. Strain , S. Strigin , A. S. Stroeer ,
36ab 6 88 12 20 54 18 18 59c 34 11 7,8R. Sturani , A. L. Stuver , T. Z. Summerscales , M. Sung , S. Susmithan , P. J. Sutton , B. Swinkels , M. Tacca , L. Taﬀarello , D. Talukder , D. B. Tanner , S. P. Tarabrin ,
7,8 1 15 6 48 61 8,7 31 79 24ab 24ab 24acJ. R. Taylor , R. Taylor , P. Thomas , K. A. Thorne , K. S. Thorne , E. Thrane , A. Thu¨ring , C. Titsler , K. V. Tokmakov , A. Toncelli , M. Tonelli , O. Torre ,
6 1,3 4 35ab 6 72 10 89 10 8,7 24ab 48C. Torres , C. I. Torrie , E. Tourneﬁer , F. Travasso , G. Traylor , M. Trias , K. Tseng , D. Ugolini , K. Urbanek , H. Vahlbruch , G. Vajente , M. Vallisneri ,
25ab 25a 25a 3 1 58 21 29a 13 59c 54J. F. J. van den Brand , C. Van Den Broeck , S. van der Putten , A. A. van Veggel , S. Vass , M. Vasuth , R. Vaulin , M. Vavoulidis , A. Vecchio , G. Vedovato , J. Veitch ,
66 7,8 4 36ab 36ab 1 32a 68 25a 35a 15 28 52P. J. Veitch , C. Veltkamp , D. Verkindt , F. Vetrano , A. Vicere´ , A. E. Villar , J. Y. Vinet , S. Vitale , S. Vitale , H. Vocca , C. Vorvick , S. P. Vyatchanin , A. Wade ,
21 1 45 45 45 7,8 22 29a 19 7,8 1 21 48,20 6S. J. Waldman , L. Wallace , Y. Wan , X. Wang , Z. Wang , A. Wanner , R. L. Ward , M. Was , P. Wei , M. Weinert , A. J. Weinstein , R. Weiss , L. Wen , S. Wen ,
7,8 19 7,8 7,8 82 1,20 57 11 15 1 31 11P. Wessels , M. West , T. Westphal , K. Wette , J. T. Whelan , S. E. Whitcomb , D. White , B. F. Whiting , C. Wilkinson , P. A. Willems , H. R. Williams , L. Williams ,
7,8 7,8 7,8 21 9 7,8 3 6 15 63 6 1B. Willke , L. Winkelmann , W. Winkler , C. C. Wipf , A. G. Wiseman , H. Wittel , G. Woan , R. Wooley , J. Worden , J. Yablon , I. Yakushin , H. Yamamoto ,
7,8 48 1 90 9 4 40e,91 68 59c 45 1 45 20K. Yamamoto , H. Yang , D. Yeaton Massey , S. Yoshida , P. Yu , M. Yvert , A. Zadrozn´ y , M. Zanolin , J. P. Zendri , F. Zhang , L. Zhang , W. Zhang , Z. Zhang ,
20 85 21 1C. Zhao , N. Zotov , M. E. Zucker , J. Zweizig ,
46 93 74 30 94 62,95 31 91 96 97 98 98C. Akerlof , M. Boer , R. Fender , N. Gehrels , A. Klotz , E. O. Ofek , M. Smith , M. Sokolowski , B. W. Stappers , I. Steele , J. Swinbank , R. A. M. J. Wijers , and
46W. Zheng
(Aﬃliations can be found after the references)
Preprint online version: 3 January 2012
Aims. A transient astrophysical event observed in both gravitational wave (GW) and electromagnetic (EM) channels would yield rich scientiﬁcABSTRACT
Aims. A transient astrophysical event observed in both gravitational wave (GW) and electromagnetic (EM) channels would yield
rich scientiﬁc rewards. A ﬁrst program initiating EM follow-ups to possible transient GW events has been developed and exercised
by the LIGO and Virgo community in association with several partners. In this paper, we describe and evaluate the methods used to
promptly identify and localize GW event candidates and to request images of targeted sky locations.
Methods. During two observing periods (Dec 17 2009 to Jan 8 2010 and Sep 2 to Oct 20 2010), a low-latency analysis pipeline was
used to identify GW event candidates and to reconstruct maps of possible sky locations. A catalog of nearby galaxies and Milky Way
globular clusters was used to select the most promising sky positions to be imaged, and this directional information was delivered to
EM observatories with time lags of about thirty minutes. A Monte Carlo simulation has been used to evaluate the low-latency GW
pipeline’s ability to reconstruct source positions correctly.
Results. For signals near the detection threshold, our low-latency algorithms often localized simulated GW burst signals to tens
of square degrees, while neutron star/neutron star inspirals and neutron star/black hole inspirals were localized to a few hundred
square degrees. Localization precision improves for moderately stronger signals. The correct sky location of signals well above
threshold and originating from nearby galaxies may be observed with∼50% or better probability with a few pointings of wide-ﬁeld
telescopes.
Key words. gravitational waves - methods: observationalLSC+Virgo+others: First prompt search for GW transients with EM counterparts 3
1. Introduction consisting of two neutron stars (NS-NS) or a neutron star and
a stellar-mass black hole (NS-BH), the inspiral stage produces
The Laser Interferometer Gravitational-Wave Observatory the most readily detectable GW signal. The energy ﬂux reach-
(LIGO) (Abbott et al. 2009a) and Virgo (Accadia et al. ing Earth depends on the inclination angle of the binary orbit
2011) have taken signiﬁcant steps toward gravitational wave relative to the line of sight. The initial LIGO-Virgo network is
(GW) astronomy over the past decade. The LIGO Scientiﬁc sensitive to optimally oriented NS-NS mergers from as far away
Collaboration operates two LIGO observatories in the U.S. along as 30 Mpc, and mergers between a NS and a 10 M black hole⊙
with the GEO 600 detector (Lu¨ck et al. 2010) in Germany. out to 70 Mpc (Abadie et al. 2010c). Models of the stellar com-
Together with Virgo, located in Italy, they form a detector net- pact object population in the local universe estimate the rate of
work capable of detecting GW signals arriving from all direc- NS-NS mergers detectable with initial detectors to be between
tions. Their most recent joint data taking run was between July −42× 10 and 0.2 per year. With advanced detectors, these range
2009 and October 2010. GEO 600 and Virgo are currently oper- limits are expected to increase to 440 and 930 Mpc, respectively.
ating during summer 2011, while the LIGO interferometers have
The energetics of these systems suggest that an EM counter-
been decommissioned for the upgrade to the next-generation 53part is likely. The ﬁnal plunge radiates of order 10 ergs of grav-
Advanced LIGO detectors (Harry et al. 2010), expected to be
itational binding energy as gravitational waves. If even a small
operational around 2015. Virgo will also be upgraded to become fraction of this energy escapes as photons in the observing band,
Advanced Virgo (Acernese et al. 2008). Additionally, the new the resulting counterpart could be observable to large distances.
LCGT detector (Kuroda & The LCGT Collaboration 2010) is The EM transients that are likely to follow a NS-BH or NS-NS
planned in Japan. These “advanced era” detectors are expected merger are described below.
to detect compact binary coalescences, possibly at a rate of Short-hard gamma-ray bursts (SGRBs), which typically have
dozens per year, after reaching design sensitivity (Abadie et al. durations of 2 seconds or less, may be powered by NS-NS
2010c). or NS-BH mergers (Nakar 2007; Me´sza´ros 2006; Piran 2004).
Detectable, transient GW signals in the LIGO/Virgo fre- Afterglows of SGRBs have been observed in wavelengths from
quency band require bulk motion of mass on short time scales. radio to X-ray, and out to Gpc distances (Nakar 2007; Gehrels
Emission in other channels is also possible in many such rapidly et al. 2009). Optical afterglows have been observed from a few
changing massive systems. This leads to the prospect that some tens of seconds to a few days after the GRB trigger (see, for
transient GW sources may have corresponding electromagnetic −αexample, Klotz et al. (2009a)), and fade with a power law t ,
(EM) counterparts which could be discovered with a low latency whereα is between 1 and 1.5. At 1 day after the trigger time, the
response to GW triggers (Sylvestre 2003; Kanner et al. 2008; apparent optical magnitude would be between 12 and 20 for a
Stubbs 2008; Kulkarni & Kasliwal 2009; Bloom et al. 2009). source at 50 Mpc (Kann et al. 2011), comparable to the distance
Finding these EM counterparts would yield rich scientiﬁc to which LIGO and Virgo could detect the merger.
rewards (see Sect. 2), but is technically challenging due to im- Even if a compact binary coalescence is not observable in
perfect localization of the gravitational wave signal and uncer- gamma-rays, there is reason to expect it will produce an observ-
tainty regarding the relative timing of the GW and EM emis- able optical counterpart. Li & Paczyn´ski (1998) suggested that,
sions. This paper details our recent eﬀort to construct a prompt during a NS-NS or NS-BH merger, some of the neutron star’s
search for joint GW/EM sources between the LIGO/Virgo de- mass is tidally ejected. In their model, the ejected neutron-rich
tector network and partner EM observatories (see Sect. 3). The matter produces heavy elements through r-process nucleosyn-
search was demonstrated during two periods of live LIGO/Virgo thesis, which subsequently decay and heat the ejecta, powering
running: the “winter” observing period in December 2009 and an optical afterglow known as a kilonova. The predicted optical
January 2010 and the “autumn” observing period in September emission is roughly isotropic, and so is observable regardless of
and October 2010. We focus here on the design and performance the orientation of the original binary system. This emission is
of software developed for rapid EM follow-ups of GW candi- expected to peak after about one day, around magnitude 18 for a
date events, as well as the procedures used to identify signiﬁcant source at 50 Mpc (Metzger et al. 2010), and then fade over the
GW triggers and to communicate the most likely sky locations course of a few days following the merger.
to partner EM observatories. The analysis of the observational
data is in progress, and will be the subject of future publications.
2.1.2. Stellar Core Collapse
Beyond the compact object mergers described above, some other
2. Motivation
astrophysical processes are plausible sources of observable GW
emission. GW transients with unknown waveforms may be dis-2.1. Sources
covered by searching the LIGO and Virgo data for short periods
A variety of EM emission mechanisms, both observed and the- of excess power (bursts). The EM counterparts to some likely
oretical, may occur in association with observable GW sources. sources of GW burst signals are described below.
Characteristics of a few scenarios helped inform the design and Core-collapse supernovae are likely to produce some amount
execution of this search. Here, some likely models are presented, of gravitational radiation, though large uncertainties still exist
along with characteristics of the associated EM emission. in the expected waveforms and energetics. Most models predict
GW spectra that would be observable by initial LIGO and Virgo
from distances within some fraction of the Milky Way, but not2.1.1. Compact Binary Coalescence
from the Mpc distances needed to observe GWs from another
Compact binary systems consisting of neutron stars and/or black galaxy (Ott 2009). Neutrino detectors such as SuperKamiokande
holes are thought to be the most common sources of GW emis- and IceCube should also detect a large number of neutrinos from
a Galactic supernova (Beacom & Vogel 1999; Halzen & Raﬀeltsion detectable with ground-based interferometers. Radiation of
energy and angular momentum causes the orbit to decay (inspi- 2009; Leonor et al. 2010). Galactic supernovae normally would
ral) until the objects merge (Cutler et al. 1993). For a system be very bright in the optical band, but could be less than obviousLSC+Virgo+others: First prompt search for GW transients with EM counterparts 4
if obscured by dust or behind the Galactic center. Optical emis- 1993; Vallisneri 2000; Flanagan & Hinderer 2008; Andersson
sion would ﬁrst appear hours after the GW and neutrino signal et al. 2011; Pannarale et al. 2011; Hinderer et al. 2010).
and would peak days to weeks later, fading over the course of Observing EM counterparts of NS-NS and NS-BH merger
weeks or months. events will give strong evidence as to which class of source, if
either, is the source of SGRBs (Bloom et al. 2009). In addition,Long-soft gamma-ray bursts (LGRBs) are believed to be as-
if some neutron star mergers are the sources of SGRBs, a collec-sociated with the core collapse of massive stars (Woosley 1993;
tion of joint EM/GW observations would allow an estimate ofMacFadyen & Woosley 1999; Piran 2004; Woosley & Bloom
the SGRB jet opening angle by comparing the number of merger2006; Metzger et al. 2011). A large variety of possible GW emit-
events with and without observable prompt EM emission, andting mechanisms within these systems have been proposed, with
some information would be obtainable even from a single loudsome models predicting GW spectra that would be observable
event (Kobayashi & Me´sza´ros 2003b; Seto 2007).from distances of a few Mpc with initial LIGO and Virgo (Fryer
An ensemble of these observations could provide a novelet al. 2002; Kobayashi & Me´sza´ros 2003a; Corsi & Me´sza´ros
measurement of cosmological parameters. Analysis of the well-2009; Piro & Pfahl 2007; Korobkin et al. 2011; Kiuchi et al.
modeled GW signal will provide a measurement of the lumi-2011). The afterglows of LGRBs, like the afterglows of SGRBs,
nosity distance to the source, while the redshift distance is mea-typically show power law fading with α = 1 − 1.5. However,
surable from the EM data. Taken together, they provide a di-the peak isotropic equivalent luminosity of LGRB afterglows is
rect measurement of the local Hubble constant (Schutz 1986;typically a factor of 10 brighter than SGRB afterglows (Nakar
Markovic 1993; Dalal et al. 2006; Nissanke et al. 2010).2007; Kann et al. 2010).
Finally, all of the above assume that general relativity is theAn oﬀ-axis or sub-energetic LGRB may also be observed as
correct theory of gravity on macroscopic scales. Joint EM/GWan orphan afterglow or dirty ﬁreball (Granot et al. 2002; Rhoads
observations can also be used to test certain predictions of gen-2003). These transients brighten over the course of several days
eral relativity, such as the propagation speed and polarizations ofor even weeks, depending on the observing band and viewing an-
GWs (Will 2005; Yunes et al. 2010; Kahya 2011).gle. Identifying orphan afterglows in large area surveys, such as
In the case that the transient GW source is not a binaryRykoﬀ et al. (2005), has proven diﬃcult, but a GW trigger may
merger event, the combination of GW and EM information willhelp distinguish orphan afterglows from other EM variability.
again prove very valuable. In this scenario, the gravitational
waveform will not be known a priori. Any distance estimate
2.1.3. Other Possible Sources would be derived from the EM data, which would then set the
overall scale for the energy released as GWs.
Cosmic string cusps are another possible joint source of GW As in the merger case, the linking of a GW signal with a
(Siemens et al. 2006; Damour & Vilenkin 2000) and EM known EM phenomenon will provide insight into the underlying
(Vachaspati 2008) radiation. If present, their distinct GW sig- physical process. For example, the details of the central engine
nature will distinguish them from other sources. On the other that drives LGRBs are unknown. The GW signal could give cru-
hand, even unmodeled GW emissions can be detected using GW cial clues to the motion of matter in the source, and potentially
burst search algorithms, and such events may in some cases pro- distinguish between competing models. A similar insight into
duce EM radiation either through internal dynamics or through the source mechanism could be achieved for an observation of
interaction with the surrounding medium. Thus, our joint search GW emission associated with a supernova. Rapid identiﬁcation
methods should allow for a wide range of possible sources. may also allow observation of a supernova in its earliest mo-
ments, an opportunity that currently depends on luck (Soderberg
et al. 2008).2.2. Investigations enabled by joint GW/EM observations
A variety of astrophysical information could potentially be ex-
2.3. Extend GW Detector Reach
tracted from a joint GW/EM signal. In understanding the pro-
genitor physics, the EM and GW signals are essentially com- Finding an EM counterpart associated with a LIGO/Virgo trig-
plementary. The GW time series directly traces the bulk motion ger would increase conﬁdence that a truly astrophysical event
of mass in the source, whereas EM emissions arising from out- had been observed in the GW data. Using EM transients to help
ﬂows or their interaction with the interstellar medium give only distinguish low amplitude GW signals from noise events allows
indirect information requiring inference and modeling. On the a lowering of the detection threshold, as was done in searches
other hand, observing an EM counterpart to a GW signal reduces such as Abbott et al. (2010). Kochanek & Piran (1993) estimated
the uncertainty in the source position from degrees to arcsec- that the detectable amplitude could be reduced by as much as a
onds. This precise directional information can lead to identiﬁca- factor of 1.5, increasing the eﬀective detector horizon distance
tion of a host galaxy, and a measurement of redshift. Some spe- (the maximum distance at which an optimally oriented and lo-
ciﬁc questions that may be addressed with a collection of joint cated system could be detected) by the same factor and thus in-
GW/EM signals are discussed below. creasing the detection rate by a factor of 3. In practice, the actual
If the GW source is identiﬁed as a NS-NS or NS-BH merger, improvement in GW sensitivity achieved by pairing EM and GW
additional investigations are enabled with an EM counterpart. observations depends on many factors unique to each search, in-
The observation of the EM signal will improve the estimation of cluding details of the source model and data set, and so is diﬃ-
astrophysical source parameters. For example, when attempting cult to predict in advance.
parameter estimation with a bank of templates and a single data In the case of a coincidence between a GW signal and a dis-
stream, the source’s distance, inclination angle, and angular po- covered EM transient, the joint signiﬁcance may be calculated
sition are largely degenerate. A precise source position from an by assuming that the backgrounds of the EM and GW search are
EM counterpart would help break this degeneracy (Dalal et al. independent. The False Alarm Rate (FAR) of a GW/EM coin-
2006; Nissanke et al. 2010). High precision parameter estima- cidence is the FAR of the GW signal, as described in Sect. 4.2,
tion may even constrain the NS equation of state (Cutler et al. times α, the expected fraction of observations associated with aLSC+Virgo+others: First prompt search for GW transients with EM counterparts 5
false or unrelated EM transient. The false alarm fraction α may GW counterparts can dramatically reduce the needed sky cov-
be estimated using ﬁelds from surveys not associated with GW erage by focusing observations on galaxies within the distance
triggers. The measured value of α will depend heavily on the limits of the GW detectors (Kanner et al. 2008; Nuttall & Sutton
telescope being used, the cuts selected in image analysis, galac- 2010). Limiting the search area to known galaxies may also
tic latitude of the source and other factors. For example, surveys improve the feasibility of identifying the true counterpart from
with the Palomar Transient Factory require a sophisticated clas- among other objects with time-varying EM emissions (Kulkarni
siﬁcation mechanism for rejecting contaminants. Each set of im- & Kasliwal 2009). Even within the Milky Way, a search may
5age subtractions covering 100 - 200 square degrees yields∼ 10 emphasize known targets by seeking counterparts within globu-
candidates. Of these, 30 - 150 sources are selected after impos- lar clusters, where binary systems of compact objects may form
ing cuts optimized for the detection of fast evolving transients eﬃciently (O’Leary et al. 2007).
(Bloom et al. 2011). Using classiﬁcation software designed for An emphasis on extragalactic and globular-cluster sources
PTF data (Oarical) (Bloom et al. 2011), the selected sources un- has the potential drawback that any counterparts in the plane of
dergo an automatic classiﬁcation as type “transient” or “variable the Milky Way may be missed. Also, neutron star mergers that
star” based on time-domain and context properties. Promising occur at large distances from their host galaxies may not be ob-
candidates are selected for additional, spectroscopic observation. served, though the population with large kicks should be small
Of the sources that are classiﬁed as transients, and then followed (Berger 2010; Kelley et al. 2010).
up spectroscopically,∼ 82% are supernovae (Bloom et al. 2011). Our selection of ﬁelds to observe was weighted towards ar-
To use EM transience to improve conﬁdence in a GW signal, the eas containing known galaxies within 50 Mpc. The utilized cata-
time-domain sky in the wavelength of interest must be well un- log of nearby galaxies and globular clusters, and the process for
derstood. Transients that are found in directional and time coin- selecting ﬁelds to observe, is described in Sect. 5.
cidence with GW triggers would increase conﬁdence in the GW
signal only if the chance of a similar, incidental coincidence is
3. GW and EM Instrumentsunderstood to be low (Kulkarni & Kasliwal 2009).
3.1. Gravitational Wave Detector Network
2.4. Implications for Search Design The LIGO and Virgo detectors are based on Michelson-type
interferometers, with Fabry-Perot cavities in each arm and aCharacteristics of the target sources helped determine when and
power recycling mirror between the laser and beamsplitter towhere to seek the EM counterparts to GW event candidates. For
dramatically increase the power in the arms relative to a simplereasons discussed in this section, the search strategy presented
Michelson design. The GEO 600 detector uses a folded interfer-in this paper emphasizes capturing images as soon as possible
ometer without Fabry-Perot arm cavities but with an additionalafter the GW trigger, along with follow-up images over subse-
recycling mirror at the output to resonantly enhance the GW sig-quent nights. The rates of stellar core-collapse and compact ob-
nal. As a gravitational wave passes through each interferometer,ject mergers within our own galaxy are much less than one per
it induces a “strain” (a minuscule change in length on the orderyear, and so ﬁeld selection was strongly weighted towards re-
21of 1 part in 10 or less) on each arm of the interferometer duegions containing nearby galaxies.
to the quadrupolar perturbation of the spacetime metric. The in-The observations and theoretical models of EM transients
terferometers are designed to measure the diﬀerential strain ondiscussed above provided guidance when choosing the observ-
the two arms through interference of the laser light when the twoing cadence. GRB optical afterglows have been observed during
beams are recombined at the beam splitter, with the relative op-the prompt emission phase (Klotz et al. 2009b) and up to many
tical phase modulated by the passing gravitational wave (Abbotthours after the trigger. For this search, the ﬁrst attempt to image
et al. 2009a).the source position was made as soon as possible after validat-
In 2009–2010 there were two operating LIGO interfer-ing a GW trigger. In both the kilonova (Li & Paczyn´ski 1998)
ometers, each with 4-km arms: H1, located near Hanford,and supernova (Ott 2009) models, some time lag exists between
1Washington, and L1, located in Livingston Parish, Louisiana.the release of GW and EM emission, primarily due to the time
Virgo (V1) has arms of length 3 km and is located near Cascina,it takes the outﬂowing material to become optically thin. This
Italy. GEO 600 data was not used in the online search describedtime lag may be from several hours for a kilonova, up to days
in this paper, but was available for oﬄine reanalysis of promis-for a core-collapse supernova. Furthermore, Coward et al. (2011)
ing event candidates. The large physical separation between theshow that for GRBs that are oﬀ-axis, the optical afterglow may
instruments means that the eﬀects of local environmental back-not be visible until days after the burst. For these reasons, re-
ground can be mitigated by requiring a coincident signal in mul-peated observations over several nights are desirable. Also, the
tiple interferometers. Each interferometer is most sensitive tolight curves obtained by observing the same ﬁelds over multiple
GW signals traveling parallel or anti-parallel to zenith, but thenights are critical clues for discovering and classifying transient
antenna pattern varies gradually over the sky, so that the detec-sources.
tors are essentially all-sky monitors.Knowing where to look for the counterpart to a GW trig-
The EM follow-up program described in this paper was exer-ger is challenging. Directional estimates of low signal to noise
cised during the 2009–2010 science runs. While single-detectorratio (SNR) binary inspiral sources with the 2009–10 GW detec-
triggers had been generated with low latency in earlier sciencetor network have uncertainties of several tens of square degrees
runs for diagnostic and prototyping purposes, 2009–2010 was(Fairhurst 2009). This suggests using telescopes with a ﬁeld of
the ﬁrst time that a systematic search for GW transients usingview (FOV) of at least a few square degrees if possible. Even
with such a “wide ﬁeld” instrument, there is a striking mismatch 1 Earlier science runs included a second interferometer at Hanford,
between the large area needing to be searched, and the size of a called H2, with 2-km arms. H2 will reappear as part of Advanced LIGO,
single FOV. either as a second 4-km interferometer at Hanford or else at a site in
The problem may be partially mitigated by making use of Western Australia. The latter option would greatly improve the source
the known mass distribution in the nearby universe. A search for localization capabilities of the network (Fairhurst 2011; Schutz 2011).LSC+Virgo+others: First prompt search for GW transients with EM counterparts 6
the full LIGO-Virgo network was performed with low latency,
and the ﬁrst time that alerts were sent to external observatories.
3.2. Optical and Other Electromagnetic Observatories
In an eﬀort to explore various approaches, the telescope network
used in 2009–10 was intentionally heterogeneous. However,
most of instruments had large ﬁelds of view to accommodate
the imprecise GW position estimate. The approximate location
of each EM observatory is shown in Fig. 1, and Tables 1 and 2
show some of the properties of each observatory.
Fig. 1. A map showing the approximate positions of telescopes
3.2.1. Optical Instruments that participated in the project. The Swift satellite observatory is
noted at an arbitrary location. The image is adapted from a blank
The Palomar Transient Factory (PTF) (Law et al. 2009; Rau
´world map placed in the public domain by P. Dlouhy.
et al. 2009) operates a 7.3 square degree FOV camera mounted
on the 1.2 m Oschin Telescope at Palomar Observatory. A typ-
ical 60 s exposure detects objects with a limiting magnitude
R = 20.5. For the autumn observing period, the PTF team de- R band for a typical 180 s exposure. For each accepted trigger
voted ten ﬁelds over several nights at a target rate of 1 trigger for in the autumn run, Zadko repeatedly observed the ﬁve galaxies
every three weeks. considered most likely to host the source over several nights. The
Pi of the Sky (Malek et al. 2009) observed using a camera target trigger rate for Zadko was one trigger per week.
with a 400 square degree FOV and exposures to limiting mag- The Liverpool telescope (Steele et al. 2004) is a 2 m
nitude 11–12. It was located in Koczargi Stare, near Warsaw. robotic telescope situated at the Observatorio del Roque de Los
The camera was a prototype for a planned system that will si- Muchachos on La Palma. For this project the RATCam instru-
multaneously image two steradians of sky. The target rate was ment, with a 21 square arcminute ﬁeld of view, was used. This
approximately 1 per week in the autumn run, followed up with instrumentation allows a ﬁve minute exposure to reach magni-
′hundreds of 10 s exposures over several nights. tude r = 21. This project was awarded 8 hours of target-of-
opportunity time, which was split into 8 observations of 1 hourThe QUEST camera (Baltay et al. 2007), currently mounted
each, with a target rate of 1 trigger per week.on the 1 m ESO Schmidt Telescope at La Silla Observatory,
views 9.4 square degrees of sky in each exposure. The telescope
is capable of viewing to a limiting magnitude of R ∼ 20. The
QUEST team devoted twelve 60 s exposures over several nights
for each trigger in both the winter and autumn periods, with a LOFAR (Fender et al. 2006; de Vos et al. 2009; Stappers et al.
target rate of 1 trigger per week. 2011) is a dipole array radio telescope based in the Netherlands
but with stations across Europe. The array is sensitive to fre-ROTSE III (Akerlof et al. 2003) is a collection of four robotic
quencies in the range of 30 to 80 MHz and 110 to 240 MHz, andtelescopes spread around the world, each with a 0.45 m aperture
and 3.4 square degree FOV. No ﬁlters are used, so the spectral can observe multiple simultaneous beams, each with a FWHM
oresponse is that of the CCDs, spanning roughly 400 to 900 nm. varying with frequency up to a maximum of around 23 . During
The equivalent R band limiting magnitude is about 17 in a 20 s the autumn run, LOFAR accepted triggers at a target rate of 1
exposure. The ROTSE team arranged for a series of thirty images per week and followed up each with a four-hour observation in
for the ﬁrst night, and several images on following nights, for its higher frequency band, providing a ∼25 square degree ﬁeld
each autumn run trigger, with a target rate of 1 trigger per week. of view.
Although not used in the prompt search during the scienceSkyMapper (Keller et al. 2007) is a survey telescope located
run, the Expanded Very Large Array (Perley et al. 2011) wasat Siding Spring observatory in Australia. The mosaic camera
used to follow up a few triggers after the run with latencies of 3covers 5.7 square degrees of sky in each ﬁeld, and is mounted
and 5 weeks.on a 1.35 m telescope with a collecting area equivalent to an
The Swift satellite (Gehrels et al. 2004) carries three instru-unobscured 1.01 m aperture. It is designed to reach a limiting
ments, each in diﬀerent bands. Swift granted several target ofmagnitude g ∼ 21 (>7 sigma) in a 110 s exposure. SkyMapper
opportunity observations with two of these, the X-ray Telescopeaccepted triggers in the autumn run with a target rate of 1 per
(XRT) and UV/Optical Telescope (UVOT), for the winter andweek, with several ﬁelds collected for each trigger.
autumn observing periods. The XRT is an imaging instrumentTAROT (Klotz et al. 2009a) operates two robotic 25 cm tele-
−13with a 0.15 square degree FOV, sensitive to ﬂuxes around 10scopes, one at La Silla in Chile and one in Calern, France. Like
2ergs/cm /s in the 0.5-10 keV band. A few ﬁelds were imaged forthe ROTSE III system, each TAROT instrument has a 3.4 square
each trigger that Swift accepted.degree FOV. A 180 second image with TAROT in ideal condi-
tions has a limiting R magnitude of 17.5. During the winter run,
TAROT observed a single ﬁeld during one night for each trig-
4. Trigger Selection
ger. In the autumn run, the ﬁeld selected for each trigger was
observed over several nights. TAROT accepted triggers with a The online analysis process which produced GW candidate trig-
target rate of 1 per week. gers to be sent to telescopes is outlined in Fig. 2. After data and
Zadko Telescope (Coward et al. 2010) is a 1 m telescope lo- information on data quality were copied from the interferome-
cated in Western Australia. The current CCD imager observes ter sites to computing centers, three diﬀerent data analysis algo-
ﬁelds of 0.15 square degrees down to magnitude ∼ 20 in the rithms identiﬁed triggers and determined probability skymaps.LSC+Virgo+others: First prompt search for GW transients with EM counterparts 7
a detection statistic above a nominal threshold, and occurring in
times where all three detectors were operating normally, were
recorded in the Gravitational-wave Candidate Event Database
(GraCEDb).
The trigger generators also produced likelihood maps over
the sky (skymaps), indicating the location from which the signal
was most likely to have originated. A brief introduction to each
trigger generator is presented in Sects. 4.1.1 – 4.1.3.
4.1.1. Coherent WaveBurst
Fig. 2. A simpliﬁed ﬂowchart of the online analysis with approx- Coherent WaveBurst has been used in previous searches for GW
imate time requirements for each stage. Data and information bursts, such as Abbott et al. (2009b) and Abadie et al. (2010b).
on data quality were generated at the Hanford, Livingston, and The algorithm performs a time-frequency analysis of data in
Virgo interferometers (H1, L1, and V1) and copied to central- the wavelet domain. It coherently combines data from all de-
ized computer centers. The online event trigger generators pro-
tectors to reconstruct the two GW polarization waveforms h (t)+duced coincident triggers which were written into the GraCEDb
and h (t) and the source coordinates on the sky. A statistic is×archive. The LUMIN and GEM algorithms selected statistically
constructed from the coherent terms of the maximum likeli-
signiﬁcant triggers from the archive and chose pointing loca-
hood ratio functional (Flanagan & Hughes 1998; Klimenko et al.
tions. Signiﬁcant triggers generated alerts, and were validated
2005) for each possible sky location, and is used to rank each
manually. If no obvious problem was found, the trigger’s esti-
location in a grid that covers the sky (skymap). A detailed de-
mated coordinates were sent to telescopes for potential follow-
scription of the likelihood analysis, the sky localization statistic
up.
and the performance of the cWB algorithm is published else-
where (Klimenko et al. 2011).
The search was run in two conﬁgurations which diﬀer in
their assumptions about the GW signal. The “unconstrained”The process of downselecting this large collection of triggers to
search places minimal assumptions on the GW waveform, whilethe few event candidates that received EM follow-up is described
the “linear” search assumes the signal is dominated by a singlein this section.
GW polarization state (Klimenko et al. 2011). While the uncon-After event candidates were placed in a central archive, addi-
strained search is more general, and is the conﬁguration that wastional software used the locations of nearby galaxies and Milky
used in previous burst analyses, the linear search has been shown
Way globular clusters to select likely source positions (Sect. 5).
to better estimate source positions for some classes of signals.
Triggers were manually vetted, then the selected targets were
For the online analysis, the two searches were run in parallel.
passed to partner observatories which imaged the sky in an at-
tempt to ﬁnd an associated EM transient. Studies demonstrating
the performance of this pipeline on simulated GWs are presented 4.1.2. Omega Pipeline
in Sect. 7.
In the Omega Pipeline search (Abadie et al. 2010b), triggers
are ﬁrst identiﬁed by performing a matched ﬁlter search with
4.1. Trigger Generation a bank of basis waveforms which are approximately (co)sine-
Gaussians. The search assumes that a GW signal can be decom-Sending GW triggers to observatories with less than an hour la-
posed into a small number of these basis waveforms, and so istency represents a major shift from past LIGO/Virgo data anal-
most sensitive to signals with a small time-frequency volume.yses, which were reported outside the collaboration at soonest
Coincidence criteria are then applied, requiring a trigger withseveral months after the data collection. Reconstructing source
consistent frequency in another interferometer within a physi-positions requires combining the data streams from the LIGO-
cally consistent time window. A coherent Bayesian position re-Virgo network using either fully coherent analysis or a coinci-
construction code (Searle et al. 2008, 2009) is then applied todence analysis of single-detector trigger times. A key step in la-
remaining candidates. The code performs Bayesian marginaliza-tency reduction was the rapid data replication process, in which
tion over all parameters (time of arrival, amplitude and polariza-data from all three GW observatory sites were copied to several
tion) other than direction. This results in a skymap providing thecomputing centers within a minute of collection.
probability that a signal arrived at any time, with any amplitudeFor the EM follow-up program, three independent GW de-
and polarization, as a function of direction. Further marginaliza-tection algorithms (trigger generators), ran promptly as data
tion is performed over this entire probability skymap to arrive atbecame available, generating candidate triggers with latencies
a single number, the estimated probability that a signal arrivedbetween ﬁve and eight minutes. Omega Pipeline and coherent
from any direction. TheΩ statistic is constructed from this num-WaveBurst (cWB), which are both described in Abadie et al.
ber and other trigger properties.(2010b), searched for transients (bursts) with only loose as-
sumptions regarding waveform morphology. The Multi-Band
Template Analysis (MBTA) (Marion 2004), searched for sig- 4.1.3. MBTA
nals from coalescing compact binaries. Triggers were ranked by
their “detection statistic”, a ﬁgure of merit for each analysis, The Multi-Band Template Analysis (MBTA) is a low-latency
known as Ω, η, and ρ , respectively. The statistics η for implementation of the matched ﬁlter search that is typically usedcombined
to search for compact binary inspirals (Marion 2004; BuskuliccWB and ρ for MBTA are related to the amplitude SNRcombined
of the signal across all interferometers whileΩ is related to the 2010). In contrast to burst searches which do not assume any
Bayesian likelihood of a GW signal being present. Triggers with particular waveform morphology, MBTA speciﬁcally targets theLSC+Virgo+others: First prompt search for GW transients with EM counterparts 8
waveforms expected from NS-NS, NS-BH and BH-BH inspi- include times of large seismic disturbance, non-standard inter-
rals. In this way it provides complementary coverage to the burst ferometer conﬁgurations, and temporary saturations of various
searches described above. photodiodes in the interferometer sensing and control system.
To mark such times, monitor programs analyze auxiliary data toThe search uses templates computed from a second order
produce lists of abnormal time segments with low latency. Whenpost-Newtonian approximation for the phase evolution of the
a trigger was identiﬁed, it was automatically checked againstsignal, with component masses in the range 1–34 M and a total⊙
these lists; triggers which occurred in stretches of unacceptablemass of < 35 M . However, triggers generated from templates⊙
data were automatically rejected. During this search, all threewith both component masses larger than the plausible limit of the
GW detectors were simultaneously collecting science qualityNS mass—conservatively taken to be 3.5 M for this check—⊙
data for roughly 45% of the time.were not considered for EM follow-up, since the optical emis-
sion is thought to be associated with the merger of two neutron
stars or with the disruption of a neutron star by a stellar-mass
4.4. Manual Event Validationblack hole.
Triggers from each interferometer are clustered and used to
In addition to automated checks on data quality, signiﬁcant trig-search for coincidence among the individual detectors. To gen-
gers were manually vetted. Trigger alerts were broadcast to col-erate a candidate event for follow-up, triggers with consistent
laboration members via e-mail, text message, a website, and inphysical parameters must be present in all three LIGO/Virgo in-
the interferometer control rooms as audio alarms. For each alert,terferometers. For each triple coincident trigger, the sky location
a low-latency pipeline expert conferred with personnel at each ofwas estimated using the time delay between detector sites and
the three observatory sites to validate the event. Pipeline expertsthe amplitude of the signal measured in each detector (Fairhurst
and scientists monitoring data on-site provided 24/7 coverage in2009). Before the observing period, a set of simulated gravita-
8 hour shifts. Assigned personnel conﬁrmed the automated datational wave signals was used to measure the distribution of er-
quality results, checked plots for obvious abnormalities, and ver-rors in recovering the time delays and signal amplitudes. The
iﬁed that there were no known disturbances at any of the threesky localization algorithm then uses these distributions to assign
observatory sites.probabilities to each pixel on the sky.
The intention of manual event validation was to veto spuri-
ous events caused by known non-GW mechanisms that have not4.2. Estimating False Alarm Rates
been caught by low-latency data quality cuts, not to remove ev-
The primary quantity used to decide whether an event should be ery non-GW trigger. In fact, at current sensitivities, most or all
considered a candidate for follow-ups was its FAR, the average of the triggers are unlikely to represent true astrophysical events.
rate at which noise ﬂuctuations create events with an equal or The trade-oﬀ for this additional check on the quality of the trig-
greater value of the detection statistic. For the winter run, a FAR gers was added latency (usually 10 to 20 minutes) between trig-
of less than 1 event per day of livetime was required to send an ger identiﬁcation and reporting to the EM observatories. It is
imaging request to the ground-based telescopes, with a higher possible that as the search matures in the Advanced LIGO/Virgo
threshold for Swift. For the autumn run, the FAR threshold was era the validation process can be fully automated.
0.25 events per day of livetime for most telescopes, with stricter
requirements for sending triggers to Palomar Transient Factory
and Swift. Livetime is here deﬁned as time all three interferom-
eters were simultaneously collecting usable science data.
As in previous all-sky burst searches, e.g. Abbott et al. 5. Choosing Fields to Observe
(2009b) and Abadie et al. (2010b), the FAR for the two burst
pipelines was evaluated using the time-shift method. In this The uncertainty associated with GW position estimates, ex-
method, artiﬁcial time shifts, between one second and a few hun- pected to be several tens of square degrees (Fairhurst 2009), is
dred seconds, are applied to the strain series of one or more in- large compared to the FOV of most astronomical instruments.
terferometers, and the shifted data streams are analyzed with the Moreover, the likely sky regions calculated from interferometer
regular coherent search algorithm. The shifted data provide an data may be irregularly shaped, or even contain several disjoint
estimate of the background noise trigger rate without any true regions. It is impractical to image these entire regions given a
coincident gravitational wave signals. During the online anal- limited amount of observing time for a given instrument. There
ysis, at least 100 time shifts were continuously evaluated with is thus a need to carefully prioritize ﬁelds, or tiles, of an instru-
latencies between 10 minutes and several hours. The FAR of ment to optimize the likelihood of imaging the true gravitational
each event candidate was evaluated with the most recent avail- wave source.
able time shifts.
The LUMIN software package was created to gather GW
The MBTA pipeline evaluated the FAR analytically based on triggers from the three trigger generators, and use the skymaps
single interferometer trigger rates, rather than using time shifts. and locations of known galaxies to select ﬁelds for each opti-
This is computationally simpler than the burst method. It is valid cal or radio instrument to observe. In addition, LUMIN includes
since MBTA is a coincident rather than a coherent analysis, and tools that were used to facilitate trigger validation (Sect. 4.4) and
allows the FAR to be evaluated with data from the minutes im- communication with robotic telescopes. Fields for observation
mediately preceding the trigger time (Marion 2004). with the Swift XRT and UVOT were selected with slightly dif-
ferent criteria by a separate software package, the Gravitational
to Electro-Magnetic Processor (GEM). During the testing pro-4.3. Online Data Quality
cess, GEM also applied the tiling criteria for optical telescopes
A number of common occurrences may make a stretch of inter- to simulated skymaps, and so provided an important consistency
ferometer data unsuitable for sensitive GW searches. Examples check between LUMIN and GEM.LSC+Virgo+others: First prompt search for GW transients with EM counterparts 9
5.1. Galaxy Catalog Unlike the burst algorithms, MBTA assumes the GW source
is a merging binary, and estimates some of the source’s physical
The Gravitational Wave Galaxy Catalog (GWGC) (White et al. parameters for each trigger. This allows the galaxy catalog to be
2011) was created to help this and future searches quickly iden- applied in a slightly diﬀerent way. Each interferometer measures
tify nearby galaxies. a quantity known as eﬀective distance
The catalog contains up-to-date information compiled from
the literature on sky position, distance, blue magnitude, ma-
  ! −1/22jor and minor diameters, position angle and galaxy type for 2 1+ cos ι  2 2 2  D = DF + F cos ι , (2)53,225 galaxies ranging out to 100 Mpc, as well as 150 Milky eﬀ  + × 2
Way globular clusters. White et al. (2011) compared the catalog
with an expected blue light distribution derived from SDSS data
and concluded that the GWGC is nearly complete out to ∼40 where D is the actual distance to the source, ι is the inclination
Mpc. The catalog improves on the issue of multiple entries for angle between the direction to the observer and the angular mo-
the same galaxy suﬀered by previous catalogs by creating the mentum vector of the binary, and F and F are the antenna re-+ ×
GWGC from a subset of 4 large catalogs, each of which lists sponse functions of the particular interferometer. The important
a unique Principal Galaxy Catalogue (PGC) number for every feature of the eﬀective distance is that it is always greater than or
galaxy (Paturel et al. 1989). The catalogs used were: an updated equal to the true distance to the source. For each MBTA trigger
version of the Tully Nearby Galaxies Catalog (Tully 1987), the the galaxy catalog is then only considered out to the smallest ef-
Catalog of Neighboring Galaxies (Karachentsev et al. 2004), the fective distance measured for that trigger, with a maximum pos-
V8k catalog (Tully et al. 2009), and HyperLEDA (Paturel et al. sible eﬀective distance of 50 Mpc. After the catalog is downse-
2003). Also included is a list of 150 known Milky Way globular lected in this way, each pixel is weighted by the fraction of the
clusters (Harris 1996). These are all available freely online, but a catalog’s total mass contained in that pixel, i.e.
local, homogeneous list is essential for rapid follow-up purposes.
X
fracP= M L, (3)i5.2. Weighting and Tiling Algorithm
i
To make use of the galaxy catalog, and choose tiles for each GW
trigger, similar algorithms have been implemented in the GEM with the sum over all galaxies associated with the pixel, andP fracand LUMIN software packages. M = 1 for a sum over the downselected catalog.k k
The position information from the trigger generators (see These procedures require a pixel’s coordinates to be consis-
Sect. 4.1) is encoded in skymaps that assign a likelihood to each tent with a known galaxy’s location to be targeted by telescopes.
◦ ◦0.4 × 0.4 pixel in a grid covering the sky. In practice, only However, in the case that the skymap does not intersect with
the 1000 most likely pixels are retained, limiting the sky area to any galaxies in the catalog, the likelihood from the GW skymap
roughly 160 square degrees. The search volume is further lim- alone is used as each pixel’s likelihood (P= L). In practice, this
ited by keeping only objects in the catalog with an estimated dis- is a very rare occurrence and only happens in the case of a very
tance of less than 50 Mpc, as the current sensitivity of the GW well-localized skymap.
detectors makes it unlikely that binaries containing a neutron star
The actual pointing coordinates requested for each telescope
would be detectable beyond this distance. Approximately 8% of
are selected to maximize the total contained P summed over pix-
the pixels in an average skymap contain a local galaxy or globu-
els within the FOV. If multiple pointings are allowed with the
lar cluster listed in the GWGC catalog.
same instrument, additional tiles with the next highest ranking
For burst triggers, the tiling algorithms treat the luminosity are then selected. The tile selection process is illustrated in Fig.
of each galaxy or globular cluster as a prior for its likelihood to
3.
host a GW emitting event. The blue light luminosity is used as a
proxy for star formation, indicating the presence of massive stars
that may be GW burst progenitors themselves and may evolve 5.3. Galaxy Targeting for Small-Field Instruments
into compact binaries that eventually merge. In addition, weak
sources of GWs are assumed to be more numerous than strong The logic used for selecting pointings for the Swift satellite was
sources, so that a closer galaxy should contain more detectable similar to that of ground-based telescopes, except that, because
sources than a more distant galaxy of the same mass (Nuttall & the narrower Swift FOV required greater precision, care was
Sutton 2010). This leads to assigning the following likelihood to taken to ensure the target galaxies were within the selected ﬁeld.
each pixel: The coordinates supplied to Swift for follow-up were those of
X M L the matched galaxy itself in cases where there was only a singlei
P∝ (1) ◦ ◦galaxy in a pixel, but the center of the 0.4 ×0.4 pixel in casesDii where the central coordinates of an extended source were outside
the pixel or there were multiple galaxies in the pixel. Since fewerwhere L is the likelihood based only on the GW data, and M
follow-ups were allowed using Swift than with other scopes, aand D are the blue light luminosity (a rough proxy for mass) and
minimum requirement was placed on the statistic P containeddistance of the associated galaxy or globular cluster. The sum is
within the pixels selected for X-ray observation.over all the objects associated with a particular pixel (which will
be 0 or 1 galaxy for the majority of pixels). Extended nearby Zadko and Liverpool Telescope also have relatively narrow
sources which have a major axis larger than the pixel size have ﬁelds. For these telescopes, no attempt was made to capture mul-
their mass divided evenly over each pixel falling within the el- tiple galaxies in a single ﬁeld. Instead, the weighting scheme in
lipse of the disk deﬁned by their major and minor axes. Once Eqn. 1 was applied to each galaxy rather than each pixel, and the
this calculation is performed for each pixel, the entire skymap is center coordinates of the top ranked galaxies were passed to the
renormalized to a total likelihood equal to unity. observatories.LSC+Virgo+others: First prompt search for GW transients with EM counterparts 10
30 30
20 20
10 10
0 0
−10−10
−20−20
−30−30
−40−40
−50 −50
−60 −60
−70 −70
125 120 115 110 105 100 95 90 85 125 120 115 110 105 100 95 90 85
RA (Degrees) RA (Degrees)
Fig. 3. The weighting and tiling process for a simulated signal reconstructed by cWB. The skymap is shown in the left panel with
the highest likelihood regions in red, and lower ranked pixels in blue, along with galaxy locations marked as black circles. The right
panel shows the location and approximate size of the three chosen QUEST tiles, along with the locations of pixels that are retained
after weighting by the galaxy catalog. The injection location is caught by the southernmost tile, and is marked with an asterisk.
6. Observing Strategy human intervention. In a few cases this allowed response times
of less than a minute after an alert was sent, though response
6.1. Communication times of a few hours were more typical due to wait time for tar-
After an event candidate passed manual inspection, a script was
launched to pass the GPS time and selected ﬁeld center loca-
tions to the QUEST, ROTSE III, SkyMapper, TAROT, Zadko,
During the winter run, QUEST responded to three triggers,
Liverpool Telescope, and LOFAR observatories. During the au-
making 2 exposures of each ﬁeld on the night of the request.
tumn run, a total of ﬁve such alerts were sent. During the (ear-
TAROT responded to one winter run trigger, taking six imageslier) winter run, 8 event candidates were passed to the TAROT
on the night of the request. Swift also responded to one triggerand QUEST observatories. The number of ﬁeld locations passed
in the winter run, taking one exposure of each ﬁeld following theto each telescope for each GW event candidate are listed as the
request, and then a second set of exposures on a later date to be“Tiles per Trigger” in Table 2. During the autumn run, in cases
used as reference images.where the ﬁelds selected for a particular instrument were un-
observable due to daylight or latitude, no alert was sent to the
observatory. In most cases, alerts were sent via a direct socket
For most observatories in the summer run, the observing planconnection from a LIGO computing center at Caltech with IP
called for capturing a ﬁrst image of the selected ﬁelds as rapidlymask protection. Alerts to ROTSE III, SkyMapper, TAROT, and
as possible, with follow-up observations every night or everyZadko used the format of GCN notices. Alerts to LOFAR and
other night out to ﬁve days after the trigger time. For the op-the Liverpool Telescope used the VOEvent format (Williams &
tical observatories, any night’s observation included 2 or moreSeaman 2006). For QUEST, the GPS time and ﬁeld positions
exposures for each ﬁeld, to help eliminate asteroids, CCD ar-were posted as ASCII tables to a password protected web site
tifacts, and other contaminants from the data set. In addition,which was regularly polled by the QUEST scheduler.
some ﬁelds were imaged at later times, up to a month after the
The Palomar Transient Factory received ﬁeld locations and
trigger time, to provide reference images, or possibly to capture
GPS times using the VOEvent format via a socket connection,
a light curve with a late brightening time. TAROT, Zadko, PTF,
but with a more restrictive FAR threshold than the other optical
QUEST, and Pi of the Sky all followed this recipe. ROTSE exe-
telescopes, and so triggers were only sent to PTF if the on-call
cuted a more aggressive observing plan, collecting a set of 30 im-
team executed a separate script. Alerts to Swift also required ex-
ages in rapid succession on the ﬁrst night, and then sets of eight
tra action by the on-call team, who entered ﬁeld coordinates in
images on each of 15 nights following the trigger with intervals
an online form. The Pi of the Sky prototype telescope was en-
of two days on average. As in the winter run, Swift made one
gaged through automated e-mails and manual checks of a pass-
exposure of each ﬁeld following the trigger, and then collected
word protected web page.
a reference image after a lag of several weeks. The Liverpool
Telescope devoted roughly one hour of observation upon receiv-
ing a trigger, and then collected reference images a few weeks6.2. Telescope Response
after the trigger time. The LOFAR response was not automated.
The wide variety of telescopes involved in the search led to a A telescope operator made a single, four hour observation one
to four days after delivery of a trigger. SkyMapper also requireddiversity of observing strategies, with each partnering group ap-
plying a diﬀerent cadence. By design, most of the telescopes in manual intervention to respond to a trigger, and so responded on
the network were robotic, and could respond to alerts without a best eﬀort basis.
Dec (Degrees)
Dec (Degrees)