Page 1

arXiv:0909.3583v4 [astro-ph.HE] 26 Feb 2010

Searches for gravitational waves from known pulsars with S5

LIGO data

B. P. Abbott28, R. Abbott28, F. Acernese18ac, R. Adhikari28, P. Ajith2, B. Allen2,75,

G. Allen51, M. Alshourbagy20ab, R. S. Amin33, S. B. Anderson28, W. G. Anderson75,

F. Antonucci21a, S. Aoudia42a, M. A. Arain63, M. Araya28, H. Armandula28, P. Armor75,

K. G. Arun25, Y. Aso28, S. Aston62, P. Astone21a, P. Aufmuth27, C. Aulbert2, S. Babak1,

P. Baker36, G. Ballardin11, S. Ballmer28, C. Barker29, D. Barker29, F. Barone18ac, B. Barr64,

P. Barriga74, L. Barsotti31, M. Barsuglia4, M. A. Barton28, I. Bartos10, R. Bassiri64,

M. Bastarrika64, Th. S. Bauer40a, B. Behnke1, M. Beker40, M. Benacquista58,

J. Betzwieser28, P. T. Beyersdorf47, S. Bigotta20ab, I. A. Bilenko37, G. Billingsley28,

S. Birindelli42a, R. Biswas75, M. A. Bizouard25, E. Black28, J. K. Blackburn28,

L. Blackburn31, D. Blair74, B. Bland29, C. Boccara14, T. P. Bodiya31, L. Bogue30,

F. Bondu42b, L. Bonelli20ab, R. Bork28, V. Boschi28, S. Bose76, L. Bosi19a, S. Braccini20a,

C. Bradaschia20a, P. R. Brady75, V. B. Braginsky37, J. E. Brau69, D. O. Bridges30,

A. Brillet42a, M. Brinkmann2, V. Brisson25, C. Van Den Broeck8, A. F. Brooks28,

D. A. Brown52, A. Brummit46, G. Brunet31, R. Budzy´ nski44b, T. Bulik44cd, A. Bullington51,

H. J. Bulten40ab, A. Buonanno65, O. Burmeister2, D. Buskulic26, R. L. Byer51,

L. Cadonati66, G. Cagnoli16a, E. Calloni18ab, J. B. Camp38, E. Campagna16ac,

J. Cannizzo38, K. C. Cannon28, B. Canuel11, J. Cao31, F. Carbognani11, L. Cardenas28,

S. Caride67, G. Castaldi71, S. Caudill33, M. Cavagli` a55, F. Cavalier25, R. Cavalieri11,

G. Cella20a, C. Cepeda28, E. Cesarini16c, T. Chalermsongsak28, E. Chalkley64,

P. Charlton77, E. Chassande-Mottin4, S. Chatterji28, S. Chelkowski62, Y. Chen1,7,

A. Chincarini17, N. Christensen9, C. T. Y. Chung54, D. Clark51, J. Clark8, J. H. Clayton75,

F. Cleva42a, E. Coccia22ab, T. Cokelaer8, C. N. Colacino13,20, J. Colas11, A. Colla21ab,

M. Colombini21b, R. Conte18c, D. Cook29, T. R. C. Corbitt31, C. Corda20ab, N. Cornish36,

A. Corsi21ab, J.-P. Coulon42a, D. Coward74, D. C. Coyne28, J. D. E. Creighton75,

T. D. Creighton58, A. M. Cruise62, R. M. Culter62, A. Cumming64, L. Cunningham64,

E. Cuoco11, S. L. Danilishin37, S. D’Antonio22a, K. Danzmann2,27, A. Dari19ab, V. Dattilo11,

B. Daudert28, M. Davier25, G. Davies8, E. J. Daw56, R. Day11, R. De Rosa18ab, D. DeBra51,

J. Degallaix2, M. del Prete20ac, V. Dergachev67, S. Desai53, R. DeSalvo28, S. Dhurandhar24,

L. Di Fiore18a, A. Di Lieto20ab, M. Di Paolo Emilio22ad, A. Di Virgilio20a, M. D´ ıaz58,

A. Dietz8,26, F. Donovan31, K. L. Dooley63, E. E. Doomes50, M. Drago43cd,

R. W. P. Drever6, J. Dueck2, I. Duke31, J.-C. Dumas74, J. G. Dwyer10, C. Echols28,

M. Edgar64, A. Effler29, P. Ehrens28, E. Espinoza28, T. Etzel28, M. Evans31, T. Evans30, V.

Fafone22ab, S. Fairhurst8, Y. Faltas63, Y. Fan74, D. Fazi28, H. Fehrmann2, I. Ferrante20ab, F.

Fidecaro20ab, L. S. Finn53, I. Fiori11, R. Flaminio32, K. Flasch75, S. Foley31, C. Forrest70,

N. Fotopoulos75, J.-D. Fournier42a, J. Franc32, A. Franzen27, S. Frasca21ab, F. Frasconi20a,

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M. Frede2, M. Frei57, Z. Frei13, A. Freise62, R. Frey69, T. Fricke30, P. Fritschel31,

V. V. Frolov30, M. Fyffe30, V. Galdi71, L. Gammaitoni19ab, J. A. Garofoli52, F. Garufi18ab,

G. Gemme17, E. Genin11, A. Gennai20a, I. Gholami1, J. A. Giaime33,30, S. Giampanis2,

K. D. Giardina30, A. Giazotto20a, K. Goda31, E. Goetz67, L. M. Goggin75, G. Gonz´ alez33,

M. L. Gorodetsky37, S. Goßler2,40, R. Gouaty33, M. Granata4, V. Granata26, A. Grant64,

S. Gras74, C. Gray29, M. Gray5, R. J. S. Greenhalgh46, A. M. Gretarsson12, C. Greverie42a,

F. Grimaldi31, R. Grosso58, H. Grote2, S. Grunewald1, M. Guenther29, G. Guidi16ac,

E. K. Gustafson28, R. Gustafson67, B. Hage27, J. M. Hallam62, D. Hammer75,

G. D. Hammond64, C. Hanna28, J. Hanson30, J. Harms68, G. M. Harry31, I. W. Harry8,

E. D. Harstad69, K. Haughian64, K. Hayama58, J. Heefner28, H. Heitmann42, P. Hello25,

I. S. Heng64, A. Heptonstall28, M. Hewitson2, S. Hild62, E. Hirose52, D. Hoak30,

K. A. Hodge28, K. Holt30, D. J. Hosken61, J. Hough64, D. Hoyland74, D. Huet11,

B. Hughey31, S. H. Huttner64, D. R. Ingram29, T. Isogai9, M. Ito69, A. Ivanov28,

P. Jaranowski44e, B. Johnson29, W. W. Johnson33, D. I. Jones72, G. Jones8, R. Jones64,

L. Sancho de la Jordana60, L. Ju74, P. Kalmus28, V. Kalogera41, S. Kandhasamy68,

J. Kanner65, D. Kasprzyk62, E. Katsavounidis31, K. Kawabe29, S. Kawamura39,

F. Kawazoe2, W. Kells28, D. G. Keppel28, A. Khalaidovski2, F. Y. Khalili37, R. Khan10,

E. Khazanov23, P. King28, J. S. Kissel33, S. Klimenko63, K. Kokeyama39, V. Kondrashov28,

R. Kopparapu53, S. Koranda75, I. Kowalska44c, D. Kozak28, B. Krishnan1, A. Kr´ olak44af,

R. Kumar64, P. Kwee27, P. La Penna11, P. K. Lam5, M. Landry29, B. Lantz51,

A. Lazzarini28, H. Lei58, M. Lei28, N. Leindecker51, I. Leonor69, N. Leroy25, N. Letendre26,

C. Li7, H. Lin63, P. E. Lindquist28, T. B. Littenberg36, N. A. Lockerbie73, D. Lodhia62,

M. Longo71, M. Lorenzini16a, V. Loriette14, M. Lormand30, G. Losurdo16a, P. Lu51,

M. Lubinski29, A. Lucianetti63, H. L¨ uck2,27, B. Machenschalk1, M. MacInnis31, J.-M.

Mackowski32, M. Mageswaran28, K. Mailand28, E. Majorana21a, N. Man42a, I. Mandel41,

V. Mandic68, M. Mantovani20c, F. Marchesoni19a, F. Marion26, S. M´ arka10, Z. M´ arka10,

A. Markosyan51, J. Markowitz31, E. Maros28, J. Marque11, F. Martelli16ac, I. W. Martin64,

R. M. Martin63, J. N. Marx28, K. Mason31, A. Masserot26, F. Matichard33, L. Matone10,

R. A. Matzner57, N. Mavalvala31, R. McCarthy29, D. E. McClelland5, S. C. McGuire50,

M. McHugh35, G. McIntyre28, D. J. A. McKechan8, K. McKenzie5, M. Mehmet2,

A. Melatos54, A. C. Melissinos70, G. Mendell29, D. F. Men´ endez53, F. Menzinger11,

R. A. Mercer75, S. Meshkov28, C. Messenger2, M. S. Meyer30, C. Michel32, L. Milano18ab,

J. Miller64, J. Minelli53, Y. Minenkov22a, Y. Mino7, V. P. Mitrofanov37, G. Mitselmakher63,

R. Mittleman31, O. Miyakawa28, B. Moe75, M. Mohan11, S. D. Mohanty58,

S. R. P. Mohapatra66, J. Moreau14, G. Moreno29, N. Morgado32, A. Morgia22ab,

T. Morioka39, K. Mors2, S. Mosca18ab, V. Moscatelli21a, K. Mossavi2, B. Mours26,

C. MowLowry5, G. Mueller63, D. Muhammad30, H. zur M¨ uhlen27, S. Mukherjee58,

H. Mukhopadhyay24, A. Mullavey5, H. M¨ uller-Ebhardt2, J. Munch61, P. G. Murray64,

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E. Myers29, J. Myers29, T. Nash28, J. Nelson64, I. Neri19ab, G. Newton64, A. Nishizawa39,

F. Nocera11, K. Numata38, E. Ochsner65, J. O’Dell46, G. H. Ogin28, B. O’Reilly30,

R. O’Shaughnessy53, D. J. Ottaway61, R. S. Ottens63, H. Overmier30, B. J. Owen53,

G. Pagliaroli22ad, C. Palomba21a, Y. Pan65, C. Pankow63, F. Paoletti20a,11, M. A. Papa1,75,

V. Parameshwaraiah29, S. Pardi18ab, A. Pasqualetti11, R. Passaquieti20ab, D. Passuello20a,

P. Patel28, M. Pedraza28, S. Penn15, A. Perreca62, G. Persichetti18ab, M. Pichot42a,

F. Piergiovanni16ac, V. Pierro71, M. Pietka44e, L. Pinard32, I. M. Pinto71, M. Pitkin64,

H. J. Pletsch2, M. V. Plissi64, R. Poggiani20ab, F. Postiglione18c, M. Prato17, M. Principe71,

R. Prix2, G. A. Prodi43ab, L. Prokhorov37, O. Puncken2, M. Punturo19a, P. Puppo21a,

V. Quetschke63, F. J. Raab29, O. Rabaste4, D. S. Rabeling40ab, H. Radkins29, P. Raffai13,

Z. Raics10, N. Rainer2, M. Rakhmanov58, P. Rapagnani21ab, V. Raymond41, V. Re43ab,

C. M. Reed29, T. Reed34, T. Regimbau42a, H. Rehbein2, S. Reid64, D. H. Reitze63,

F. Ricci21ab, R. Riesen30, K. Riles67, B. Rivera29, P. Roberts3, N. A. Robertson28,64,

F. Robinet25, C. Robinson8, E. L. Robinson1, A. Rocchi22a, S. Roddy30, L. Rolland26,

J. Rollins10, J. D. Romano58, R. Romano18ac, J. H. Romie30, D. Rosi´ nska44gd, C. R¨ over2,

S. Rowan64, A. R¨ udiger2, P. Ruggi11, P. Russell28, K. Ryan29, S. Sakata39, F. Salemi43ab,

V. Sandberg29, V. Sannibale28, L. Santamar´ ıa1, S. Saraf48, P. Sarin31, B. Sassolas32,

B. S. Sathyaprakash8, S. Sato39, M. Satterthwaite5, P. R. Saulson52, R. Savage29, P. Savov7,

M. Scanlan34, R. Schilling2, R. Schnabel2, R. Schofield69, B. Schulz2, B. F. Schutz1,8,

P. Schwinberg29, J. Scott64, S. M. Scott5, A. C. Searle28, B. Sears28, F. Seifert2,

D. Sellers30, A. S. Sengupta28, D. Sentenac11, A. Sergeev23, B. Shapiro31, P. Shawhan65,

D. H. Shoemaker31, A. Sibley30, X. Siemens75, D. Sigg29, S. Sinha51, A. M. Sintes60,

B. J. J. Slagmolen5, J. Slutsky33, M. V. van der Sluys41, J. R. Smith52, M. R. Smith28,

N. D. Smith31, K. Somiya7, B. Sorazu64, A. Stein31, L. C. Stein31, S. Steplewski76,

A. Stochino28, R. Stone58, K. A. Strain64, S. Strigin37, A. Stroeer38, R. Sturani16ac,

A. L. Stuver30, T. Z. Summerscales3, K. -X. Sun51, M. Sung33, P. J. Sutton8, B. Swinkels11,

G. P. Szokoly13, D. Talukder76, L. Tang58, D. B. Tanner63, S. P. Tarabrin37, J. R. Taylor2,

R. Taylor28, R. Terenzi22ac, J. Thacker30, K. A. Thorne30, K. S. Thorne7, A. Th¨ uring27,

K. V. Tokmakov64, A. Toncelli20ab, M. Tonelli20ab, C. Torres30, C. Torrie28, E. Tournefier26,

F. Travasso19ab, G. Traylor30, M. Trias60, J. Trummer26, D. Ugolini59, J. Ulmen51,

K. Urbanek51, H. Vahlbruch27, G. Vajente20ab, M. Vallisneri7, J. F. J. van den Brand40ab, S.

van der Putten40a, S. Vass28, R. Vaulin75, M. Vavoulidis25, A. Vecchio62, G. Vedovato43c,

A. A. van Veggel64, J. Veitch62, P. Veitch61, C. Veltkamp2, D. Verkindt26, F. Vetrano16ac,

A. Vicer´ e16ac, A. Villar28, J.-Y. Vinet42a, H. Vocca19a, C. Vorvick29, S. P. Vyachanin37,

S. J. Waldman31, L. Wallace28, R. L. Ward28, M. Was25, A. Weidner2, M. Weinert2,

A. J. Weinstein28, R. Weiss31, L. Wen7,74, S. Wen33, K. Wette5, J. T. Whelan1,45,

S. E. Whitcomb28, B. F. Whiting63, C. Wilkinson29, P. A. Willems28, H. R. Williams53,

L. Williams63, B. Willke2,27, I. Wilmut46, L. Winkelmann2, W. Winkler2, C. C. Wipf31,

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A. G. Wiseman75, G. Woan64, R. Wooley30, J. Worden29, W. Wu63, I. Yakushin30,

H. Yamamoto28, Z. Yan74, S. Yoshida49, M. Yvert26, M. Zanolin12, J. Zhang67, L. Zhang28,

C. Zhao74, N. Zotov34, M. E. Zucker31, J. Zweizig28

The LIGO Scientific Collaboration & The Virgo Collaboration

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1Albert-Einstein-Institut, Max-Planck-Institut f¨ ur Gravitationsphysik, D-14476 Golm, Germany

2Albert-Einstein-Institut, Max-Planck-Institut f¨ ur Gravitationsphysik, D-30167 Hannover, Germany

3Andrews University, Berrien Springs, MI 49104 USA

4AstroParticule et Cosmologie (APC), CNRS: UMR7164-IN2P3-Observatoire de Paris-Universit´ e Denis

Diderot-Paris VII - CEA : DSM/IRFU

5Australian National University, Canberra, 0200, Australia

6California Institute of Technology, Pasadena, CA 91125, USA

7Caltech-CaRT, Pasadena, CA 91125, USA

8Cardiff University, Cardiff, CF24 3AA, United Kingdom

9Carleton College, Northfield, MN 55057, USA

77Charles Sturt University, Wagga Wagga, NSW 2678, Australia

10Columbia University, New York, NY 10027, USA

11European Gravitational Observatory (EGO), I-56021 Cascina (Pi), Italy

12Embry-Riddle Aeronautical University, Prescott, AZ 86301 USA

13E¨ otv¨ os University, ELTE 1053 Budapest, Hungary

14ESPCI, CNRS, F-75005 Paris, France

15Hobart and William Smith Colleges, Geneva, NY 14456, USA

16INFN, Sezione di Firenze, I-50019 Sesto Fiorentinoa; Universit` a degli Studi di Firenze, I-50121b, Firenze;

Universit` a degli Studi di Urbino ’Carlo Bo’, I-61029 Urbinoc, Italy

17INFN, Sezione di Genova; I-16146 Genova, Italy

18INFN, sezione di Napolia; Universit` a di Napoli ’Federico II’bComplesso Universitario di Monte S.Angelo,

I-80126 Napoli; Universit` a di Salerno, Fisciano, I-84084 Salernoc, Italy

19INFN, Sezione di Perugiaa; Universit` a di Perugiab, I-6123 Perugia,Italy

20INFN, Sezione di Pisaa; Universit` a di Pisab; I-56127 Pisa; Universit` a di Siena, I-53100 Sienac, Italy

21INFN, Sezione di Romaa; Universit` a ’La Sapienza’b, I-00185 Roma, Italy

22INFN, Sezione di Roma Tor Vergataa; Universit` a di Roma Tor Vergatab, Istituto di Fisica dello Spazio

Interplanetario (IFSI) INAFc, I-00133 Roma; Universit` a dell’Aquila, I-67100 L’Aquilad, Italy

23Institute of Applied Physics, Nizhny Novgorod, 603950, Russia

24Inter-University Centre for Astronomy and Astrophysics, Pune - 411007, India

25LAL, Universit´ e Paris-Sud, IN2P3/CNRS, F-91898 Orsay, France

26Laboratoire d’Annecy-le-Vieux de Physique des Particules (LAPP), IN2P3/CNRS, Universit´ e de Savoie,

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F-74941 Annecy-le-Vieux, France

27Leibniz Universit¨ at Hannover, D-30167 Hannover, Germany

28LIGO - California Institute of Technology, Pasadena, CA 91125, USA

29LIGO - Hanford Observatory, Richland, WA 99352, USA

30LIGO - Livingston Observatory, Livingston, LA 70754, USA

31LIGO - Massachusetts Institute of Technology, Cambridge, MA 02139, USA

32Laboratoire des Mat´ eriaux Avanc´ es (LMA), IN2P3/CNRS, F-69622 Villeurbanne, Lyon, France

33Louisiana State University, Baton Rouge, LA 70803, USA

34Louisiana Tech University, Ruston, LA 71272, USA

35Loyola University, New Orleans, LA 70118, USA

36Montana State University, Bozeman, MT 59717, USA

37Moscow State University, Moscow, 119992, Russia

38NASA/Goddard Space Flight Center, Greenbelt, MD 20771, USA

39National Astronomical Observatory of Japan, Tokyo 181-8588, Japan

40Nikhef, National Institute for Subatomic Physics, P.O. Box 41882, 1009 DB Amsterdam, The

Netherlandsa; VU University Amsterdam, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlandsb

41Northwestern University, Evanston, IL 60208, USA

42Departement Artemis, Observatoire de la Cˆ ote d’Azur, CNRS, F-06304 Nicea; Institut de Physique de

Rennes, CNRS, Universit´ e de Rennes 1, 35042 Rennesb; France

43INFN, Gruppo Collegato di Trentoaand Universit` a di Trentob, I-38050 Povo, Trento, Italy; INFN,

Sezione di Padovacand Universit` a di Padovad, I-35131 Padova, Italy

44IM-PAN 00-956 Warsawa; Warsaw Univ. 00-681b; Astro. Obs. Warsaw Univ. 00-478c; CAMK-PAM

00-716 Warsawd; Bialystok Univ. 15-424e; IPJ 05-400 Swierk-Otwockf; Inst. of Astronomy 65-265 Zielona

Gorag, Poland

45Rochester Institute of Technology, Rochester, NY 14623, USA

46Rutherford Appleton Laboratory, HSIC, Chilton, Didcot, Oxon OX11 0QX United Kingdom

47San Jose State University, San Jose, CA 95192, USA

48Sonoma State University, Rohnert Park, CA 94928, USA

49Southeastern Louisiana University, Hammond, LA 70402, USA

50Southern University and A&M College, Baton Rouge, LA 70813, USA

51Stanford University, Stanford, CA 94305, USA

52Syracuse University, Syracuse, NY 13244, USA

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S. B´ egin86,89, A. Corongiu82, N. D’Amico82,81, P. C. C. Freire78,90, J. W. T. Hessels85,79,

G. B. Hobbs80, M. Kramer87, A. G. Lyne87, R. N. Manchester80, F. E. Marshall88,

J. Middleditch83, A. Possenti82, S. M. Ransom84, I. H. Stairs86, and B. Stappers87

53The Pennsylvania State University, University Park, PA 16802, USA

54The University of Melbourne, Parkville VIC 3010, Australia

55The University of Mississippi, University, MS 38677, USA

56The University of Sheffield, Sheffield S10 2TN, United Kingdom

57The University of Texas at Austin, Austin, TX 78712, USA

58The University of Texas at Brownsville and Texas Southmost College, Brownsville, TX 78520, USA

59Trinity University, San Antonio, TX 78212, USA

60Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain

61University of Adelaide, Adelaide, SA 5005, Australia

62University of Birmingham, Birmingham, B15 2TT, United Kingdom

63University of Florida, Gainesville, FL 32611, USA

64University of Glasgow, Glasgow, G12 8QQ, United Kingdom

65University of Maryland, College Park, MD 20742 USA

66University of Massachusetts - Amherst, Amherst, MA 01003, USA

67University of Michigan, Ann Arbor, MI 48109, USA

68University of Minnesota, Minneapolis, MN 55455, USA

69University of Oregon, Eugene, OR 97403, USA

70University of Rochester, Rochester, NY 14627, USA

71University of Sannio at Benevento, I-82100 Benevento, Italy

72University of Southampton, Southampton, SO17 1BJ, United Kingdom

73University of Strathclyde, Glasgow, G1 1XQ, United Kingdom

74University of Western Australia, Crawley, WA 6009, Australia

75University of Wisconsin-Milwaukee, Milwaukee, WI 53201, USA

76Washington State University, Pullman, WA 99164, USA

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ABSTRACT

We present a search for gravitational waves from 116 known millisecond and

young pulsars using data from the fifth science run of the LIGO detectors. For

this search ephemerides overlapping the run period were obtained for all pulsars

using radio and X-ray observations. We demonstrate an updated search method

that allows for small uncertainties in the pulsar phase parameters to be included

in the search. We report no signal detection from any of the targets and therefore

interpret our results as upper limits on the gravitational wave signal strength.

The most interesting limits are those for young pulsars. We present updated

limits on gravitational radiation from the Crab pulsar, where the measured limit

is now a factor of seven below the spin-down limit. This limits the power radiated

via gravitational waves to be less than ∼2% of the available spin-down power. For

the X-ray pulsar J0537−6910 we reach the spin-down limit under the assumption

that any gravitational wave signal from it stays phase locked to the X-ray pulses

over timing glitches, and for pulsars J1913+1011 and J1952+3252 we are only

a factor of a few above the spin-down limit. Of the recycled millisecond pulsars

78Arecibo Observatory, HC 3 Box 53995, Arecibo, Puerto Rico 00612, USA

79Astronomical Institute “Anton Pannekoek”, University of Amsterdam, 1098 SJ Amsterdam, The Nether-

lands

80Australia Telescope National Facility, CSIRO, PO Box 76, Epping NSW 1710, Australia

81Dipartimento di Fisica Universit` a di Cagliari, Cittadella Universitaria, I-09042 Monserrato, Italy

82INAF - Osservatorio Astronomico di Cagliari, Poggio dei Pini, 09012 Capoterra, Italy

83Modeling, Algorithms, and Informatics, CCS-3, MS B265, Computer, Computational, and Statistical

Sciences Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA

84National Radio Astronomy Observatory, Charlottesville, VA 22903, USA

85Netherlands Institute for Radio Astronomy (ASTRON), Postbus 2, 7990AA Dwingeloo, The Netherlands

86Department of Physics and Astronomy, University of British Columbia, 6224 Agricultural Road, Van-

couver, BC V6T 1Z1, Canada

87University of Manchester, Jodrell Bank Centre for Astrophysics Alan-Turing Building, Oxford Road,

Manchester M13 9PL, UK

88NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA

89D´ epartement de physique, de g´ enie physique et d’optique, Universit´ e Laval, Qu´ ebec, QC G1K 7P4,

Canada.

90West Virginia University, Department of Physics, PO Box 6315, Morgantown, WV 26506, USA

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several of the measured upper limits are only about an order of magnitude above

their spin-down limits. For these our best (lowest) upper limit on gravitational

wave amplitude is 2.3×10−26for J1603−7202 and our best (lowest) limit on the

inferred pulsar ellipticity is 7.0×10−8for J2124−3358.

Subject headings: gravitational waves - pulsars: general

1.Introduction

Within our Galaxy some of the best targets for gravitational wave searches in the sen-

sitive frequency band of current interferometric gravitational wave detectors (∼40–2000Hz)

are millisecond and young pulsars. There are currently just over 200 known pulsars with

spin frequencies greater than 20Hz, which therefore are within this band. In this paper we

describe the latest results from the ongoing search for gravitational waves from these known

pulsars using data from the Laser Interferometric Gravitational-Wave Observatory (LIGO).

As this search looks for objects with known positions and spin-evolutions it can use long

time spans of data in a fully coherent way to dig deeply into the detector noise. Here we use

data from the entire two-year run of the three LIGO detectors, entitled Science Run 5 (S5),

during which the detectors reached their design sensitivities (Abbott et al. 2009b). This run

started on 2005 November 4 and ended on 2007 October 1. The detectors (the 4km and 2km

detectors at LIGO Hanford Observatory, H1 and H2, and the 4km detector at the LIGO Liv-

ingston Observatory, L1) had duty factors of 78% for H1, 79% for H2, and 66% for L1. The

GEO600 detector also participated in S5 (Grote & the LIGO Scientific Collaboration 2008),

but at lower sensitivities that meant it was not able to enhance this search. The Virgo detec-

tor also had data overlapping with S5 during Virgo Science Run 1 (VSR1) (Acernese et al.

2008). However this was also generally at a lower sensitivity than the LIGO detectors and

had an observation time of only about 4 months, meaning that no significant sensitivity

improvements could be made by including this data. Due to its multi-stage seismic isola-

tion system Virgo does have better sensitivity than the LIGO detectors below about 40Hz,

opening the possibility of searching for more young pulsars, including the Vela pulsar. These

lower frequency searches will be explored more in the future.

This search assumes that the pulsars are triaxial stars emitting gravitational waves at

precisely twice their observed spin frequencies, i.e. the emission mechanism is an ℓ = m = 2

quadrupole, and that gravitational waves are phase-locked with the electromagnetic signal.

We use the so-called spin-down limit on strain tensor amplitude hsd

for each pulsar in our analysis. This can be calculated, by assuming that the observed spin-

down rate of a pulsar is entirely due to energy loss through gravitational radiation from an

0as a sensitivity target

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– 10 –

ℓ = m = 2 quadrupole, as

hsd

0= 8.06×10−19I38r−1

kpc(|˙ ν|/ν)1/2, (1)

where I38 is the pulsar’s principal moment of inertia (Izz) in units of 1038kgm2, rkpc is

the pulsar distance in kpc, ν is the spin-frequency in Hz, and ˙ ν is the spin-down rate in

Hzs−1. Due to uncertainties in Izz and r, hsd

Part of this is due to the uncertainty in Izzwhich, though predicted to lie roughly in the

range 1–3×1038kgm2, has not been measured for any neutron star; and the best (though

still uncertain) prospect is star A of the double pulsar system J0737-3039 with 20 years’

more observation (Kramer & Wex 2009). Distance estimates based on dispersion measure

can also be wrong by a factor 2–3, as confirmed by recent parallax observations of the

double pulsar (Deller et al. 2009). For pulsars with measured braking indices, n = ν¨ ν/˙ ν2,

the assumption that spin-down is dominated by gravitational wave emission is known to be

false (the braking index for quadrupolar gravitational wave emission should be 5, but all

measured n’s are less than 3) and a stricter indirect limit on gravitational wave emission can

be set. A phenomenological investigation of some young pulsars (Palomba 2000) indicates

that this limit is lower than hsd

Abbott et al. (2007) and Abbott et al. (2008) for more discussion of the uncertainties in

indirect limits. Recycled millisecond pulsars have intrinsically small spin-downs, so for the

majority of pulsars in our search these spin-down limits will be well below our current

sensitivities, making detection unlikely. However, our search also covers four young pulsars

with large spin-down luminosities, and for these we can potentially beat or reach their spin-

down limits using current data.

0 is typically uncertain by about a factor 2.

0 by a factor 2.5 or more, depending on the pulsar. See

The LIGO band covers the fastest (highest-ν) known pulsars, and the quadrupole for-

mula for strain tensor amplitude

h0= 4.2 × 10−26ν2

100I38ε−6r−1

kpc

(2)

indicates that these pulsars are the best gravitational wave emitters for a given equatorial

ellipticity ε = (Ixx− Iyy)/Izz(here ν100= ν/(100 Hz) and ε−6= ε/10−6). The pulsars with

high spin-downs are almost all less than ∼ 104years old. Usually this is interpreted as greater

electromagnetic activity (including particle winds) in younger objects, but it could also mean

that they are more active in gravitational wave emission. This is plausible on theoretical

grounds too. Strong internal magnetic fields may cause significant ellipticities (Cutler 2002)

which would then decay as the field decays or otherwise changes (Goldreich & Reisenegger

1992). The initial crust may be asymmetric if it forms on a time scale on which the neutron

star is still perturbed by its violent formation and aftermath, including a possible lengthy

perturbation due to the fluid r-modes (Lindblom et al. 2000; Wu et al. 2001), and asymme-

tries may slowly relax due to mechanisms such as viscoelastic creep. Also the fluid r-modes

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may remain unstable to gravitational wave emission for up to a few thousand years after

the neutron star’s birth, depending on its composition, viscosity, and initial spin frequency

(Owen et al. 1998; Bondarescu et al. 2009). Such r-modes are expected to have a gravita-

tional wave frequency about 4/3 the spin frequency. However, we do not report on r-mode

searches in this paper.

1.1. Previous analyses

The first search for gravitational waves from a known pulsar using LIGO and GEO600

data came from the first science run (S1) in 2002 September. This targeted just one pulsar

in the approximately one weeks worth of data – the then fastest known pulsar J1939+2134

(Abbott et al. 2004). Data from LIGO’s second science run (S2), which spanned from 2003

February to 2003 April, was used to search for 28 isolated pulsars (i.e. those not in binary

systems) (Abbott et al. 2005). The last search for gravitational waves from multiple known

pulsars using LIGO data combined data from the third and fourth science runs and had 78

targets, including isolated pulsars and those in binary systems (Abbott et al. 2007). The

best (lowest), 95% degree-of-belief, upper limit on gravitational wave amplitude obtained

from the search was h95%

0

= 2.6×10−25for J1603−7202, and the best (smallest) limit on

ellipticity was just under 10−6for J2124−3358. The data run used in this paper is almost

an order of magnitude longer, and has a best strain noise amplitude around a factor of two

smaller, than that used in the best previous search.

We have also previously searched the first nine months of S5 data for a signal from the

Crab pulsar (Abbott et al. 2008). That analysis used two methods to search for a signal:

one in which the signal was assumed to be precisely phase-locked with the electromagnetic

signal, and another which searched a small range of frequencies and frequency derivatives

around the electromagnetic parameters. The time span of data analysed was dictated by

a timing glitch in the pulsar on 2006 August 23, which was used as the end point of the

analysis. In that search the spin-down limit for the Crab pulsar was beaten for the first

time (indeed it was the first time a spin-down limit had been reached for any pulsar), with

a best limit of h95%

0

= 2.7×10−25, or slightly below one-fifth of the spin-down limit. This

allowed the total power radiated in gravitational waves to be constrained to less than 4%

of the spin-down power. We have since discovered an error in the signal template used for

the search (Abbott et al. 2009a). We have re-analysed the data and find a new upper limit

based on the early S5 data alone at the higher value shown in Table 3, along with the smaller

upper limit based on the full S5 data.

For this analysis we have approximately 525 days of H1 data, 532 days of H2 data and

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437 days of L1 data. This is using all data flagged as science mode during the run (i.e. taken

when the detector is locked in its operating condition on the dark fringe of the interference

pattern, and relatively stable), except data one minute prior to loss of lock, during which

time it is often seen to become more noisy.

1.2.Electromagnetic observations

The radio pulsar parameters used for our searches are based on ongoing radio pulsar

monitoring programs, using data from the Jodrell Bank Observatory (JBO), the NRAO

100m Green Bank Telescope (GBT) and the Parkes radio telescope of the Australia Telescope

National Facility. We used radio data coincident with the S5 run as these would reliably

represent the pulsars’ actual phase evolution during our searches. We obtained data for 44

pulsars from JBO (including the Crab pulsar ephemeris, Lyne et al. (1993, 2009)), 39 pulsars

within the Terzan 5 and M28 globular clusters from GBT, and 47 from Parkes, including

pulsars timed as part of the Parkes Pulsar Timing Array (Manchester 2008). For 15 of these

pulsars there were observations from more than one site, making a total of 115 radio pulsars

in the analysis (see Table 1 for list of the pulsars, including the observatory and time span of

the observations). For the pulsars observed at JBO and Parkes we have obtained parameters

fit to data overlapping with the entire S5 run. For the majority of pulsars observed at GBT

the parameters have been fit to data overlapping approximately the first quarter of S5.

Pulsars generally exhibit timing noise on long time scales. Over tens of years this can

cause correlations in the pulse time of arrivals which can give systematic errors in the pa-

rameter fits produced, by the standard pulsar timing package TEMPO91, of order 2–10 times

the regular errors that TEMPO assigns to each parameter (Verbiest et al. 2008), depending

on the amplitude of the noise. For our pulsars, with relatively short observation periods

of around two years, the long-term timing noise variations should be largely folded in to

the parameter fitting, leaving approximately white uncorrelated residuals. Also millisecond

pulsars, in general, have intrinsically low levels of timing noise, showing comparatively white

residuals. This should mean that the errors produced by TEMPO are approximately the

true 1σ errors on the fitted values.

The regular pulse timing observations of the Crab pulsar (Lyne et al. 1993, 2009) in-

dicate that the 2006 August 23 glitch was the only glitch during the S5 run. One other

radio pulsar, J1952+3252, was observed to glitch during the run (see §5.1.3.) Independent

ephemerides are available before and after each glitch.

91http://www.atnf.csiro.au/research/pulsar/tempo/

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We include one pulsar in our analysis that is not observed as a radio pulsar. This is

PSRJ0537−6910 in the Large Magellanic Cloud, for which only X-ray timings currently exist.

Data for this source come from dedicated time on the Rossi X-ray Timing Explorer (RXTE)

(Middleditch et al. 2006), giving ephemerides covering the whole of S5. These ephemerides

comprise seven inter-glitch segments, each of which produces phase-stable timing solutions.

The segments are separated by times when the pulsar was observed to glitch. Due to the

complexity of the pulsar behaviour near glitches, which is not reflected in the simple model

used to predict pulse times of arrival, sometimes up to ∼ 30 days around them are not

covered by the ephemerides.

2. Gravitational wave search method

The details of the search method are discussed in Dupuis & Woan (2005) and Abbott et al.

(2007), but we will briefly review them here. Data from the gravitational wave detectors are

heterodyned using twice the known electromagnetic phase evolution of each pulsar, which

removes this rapidly varying component of the signal, leaving only the daily varying ampli-

tude modulation caused by each detector’s antenna response. Once heterodyned the (now

complex) data are low-pass filtered at 0.25Hz, and then heavily down-sampled, by averaging,

from the original sample rate of 16384Hz to 1/60Hz. Using these down-sampled data (Bk,

where k represents the kthsample) we perform parameter estimation over the signal model

yk(a) given the unknown signal parameters a. This is done by calculating the posterior

probability distribution (Abbott et al. 2007)

p(a|{Bk}) ∝

M

?

j

?

n

?

k

(ℜ{Bk} − ℜ{yk(a)})2+ (ℑ{Bk} − ℑ{yk(a)})2

?−mj

× p(a),(3)

where the first term on the right hand side is the likelihood (marginalised over the data

variance, giving a Student’s-t-like distribution), p(a) is the prior distribution for a, M is

the number of data segments into which the Bks have been cut (we assume stationarity of

the data during each segment), mjis the number of data points in the jth segment (with a

maximum value of 30, i.e. we only assume stationarity for periods less than, or equal to, 30

minutes in length), and n =?j

Kolmogorov-Smirnov tests performed to assess these in previous analyses).

j=1mj. The assumption of Gaussianity and stationarity of

the segments holds well for this analysis (see §4.5 of Dupuis (2004) for examples of χ2and

We have previously (Abbott et al. 2004, 2005, 2007) performed parameter estimation

over the four unknown gravitational wave signal parameters of amplitude h0, initial phase φ0,

cosine of the orientation angle cosι, and polarisation angle ψ, giving a = {h0,φ0,cosι,ψ}.

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Priors on each parameter are set to be uniform over their allowed ranges, with the upper end

of the range for h0set empirically from the noise level of the data. We choose a uniform prior

on h0for consistency with our previous analyses (Dupuis & Woan 2005; Abbott et al. 2004,

2005, 2007) and to facilitate straightforward comparison of sensitivity. Extensive trials with

software injections have shown this to be a very reasonable choice, returning a conservative

(i.e. high) upper limit consistent with the data and any possible signal.

Using a uniformly spaced grid on this four-dimensional parameter space the posterior is

calculated at each point. To obtain a posterior for each individual parameter we marginalise

over the three others. Using the marginalised posterior on h0 we can set an upper limit

by calculating the value that, integrating up from zero, bounds the required cumulative

probability (which we have taken as 95%). We also combine the data from multiple detectors

to give a joint posterior. To do this we simply take the product of the likelihoods for each

detector and multiply this joint likelihood by the prior. This is possible due to the phase

coherence between detectors. Again we can marginalise to produce posteriors for individual

parameters.

Below, in §2.1, we discuss exploring and expanding this parameter space to more di-

mensions using a Markov chain Monte Carlo (MCMC) technique.

2.1. MCMC parameter search

When high resolutions are needed it can be computationally time consuming to calculate

the posterior over an entire grid as described above, and redundant areas of parameter space

with very little probability are explored for a disproportionately large amount of time. A

more efficient way to carry out such a search is with a Markov chain Monte Carlo (MCMC)

technique, in which the parameter space is explored more efficiently and without spending

much time in the areas with very low probability densities.

An MCMC integration explores the parameter space by stepping from one position

in parameter space to another, comparing the posterior probability of the two points and

using a simple algorithm to determine whether the step should be accepted. If accepted

it moves to that new position and repeats; if it is rejected it stays at the current position

and repeats. Each iteration of the chain, whether it stays in the same position or not, is

recorded and the amount of time the chain spends in a particular part of parameter space is

directly proportional to the posterior probability density there. The new points are drawn

randomly from a specific proposal distribution, often given by a multivariate Gaussian with

a mean set as the current position, and a predefined covariance. For an efficient MCMC the

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proposal distribution should reflect the underlying posterior it is sampling, but any proposal

(that does not explicitly exclude the posterior), given enough time, will sample the posterior

and deliver an accurate result. We use the Metropolis-Hastings (MH) algorithm to set the

acceptance/rejection ratio. Given a current position aiMH accepts the new position ai+1

with probability

?

where p(a|d) is the posterior value at a given data d, and q(a|b) is the proposal distribution

defining how we choose position a given a current position b. In our case we have symmet-

ric proposal distributions, so q(ai+1|a)/q(ai|ai+1) = 1 and therefore only the ratio of the

posteriors is needed.

α(ai+1|ai) = min1,p(ai+1|d)

p(ai|d)

q(ai|ai+1)

q(ai+1|ai)

?

, (4)

A well-tuned MCMC will efficiently explore the parameter space and generate chains

that, in histogram form, give the marginalised posterior distribution for each parameter.

Defining a good set of proposal distributions for the parameters in a has been done experi-

mentally assuming that they are uncorrelated and therefore have independent distributions.

(There are in fact correlations between the h0and cosι parameters and the φ0and ψ pa-

rameters, but in our studies these do not significantly alter the efficiency from assuming

independent proposals.) The posterior distributions of these parameters will also generally

not be Gaussian, especially in low SNR cases (which is the regime in which we expect to

be), but a Gaussian proposal is easiest to implement and again does not appear to sig-

nificantly affect the chain efficiency. We find that, for the angular parameters, Gaussian

proposal distributions with standard deviations of an eighth the allowed parameter range

(i.e. σφ0= π/4rad, σcosι= 1/4 and σψ= π/16rad) provide a good exploration of the pa-

rameter space (as determined from the ratio of accepted to rejected jumps in the chain) for

low SNR signals. We have performed many simulations comparing the output of the MCMC

and grid-based searches, both on simulated noise and simulated signals, and both codes give

results consistent to within a few percent. In these tests we find that the computational

speed of the MCMC code is about three times faster than the grid-based code, although this

can vary by tuning the codes.

An MCMC integration may take time to converge on the bulk of the probability distri-

bution to be sampled, especially if the chains start a long way in parameter space from the

majority of the posterior probability. Chains are therefore allowed a burn-in phase, during

which the positions in the chain are not recorded. For low SNR signals, where the signal

amplitude is close to zero and the posteriors are reasonably broad, this burn-in time can be

short. To aid the convergence we use simulated annealing in which a temperature parame-

ter is used to flatten the posterior during burn-in to help the chain explore the space more

quickly. We do however use techniques to assess whether our chains have converged (see

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