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Upper limit map of a background of gravitational waves

B. Abbott¹⁴, R. Abbott¹⁴, R. Adhikari¹⁴, J. Agresti¹⁴, P. Ajith², B. Allen^2,51, R. Amin¹⁸, S. B. Anderson¹⁴, W. G. Anderson⁵¹ et al. (LIGO Scientific Collaboration)

W. G. Anderson⁵¹, M. Arain³⁹, M. Araya¹⁴, H. Armandula¹⁴, M. Ashley⁴, S. Aston³⁸, P. Aufmuth³⁶, C. Aulbert¹, S. Babak¹, S. Ballmer¹⁴, H. Bantilan⁸, B. C. Barish¹⁴, C. Barker¹⁵, D. Barker¹⁵, B. Barr⁴⁰, P. Barriga⁵⁰, M. A. Barton⁴⁰, K. Bayer¹⁷, K. Belczynski²⁴, J. Betzwieser¹⁷, P. T. Beyersdorf²⁷, B. Bhawal¹⁴, I. A. Bilenko²¹, G. Billingsley¹⁴, R. Biswas⁵¹, E. Black¹⁴, K. Blackburn¹⁴, L. Blackburn¹⁷, D. Blair⁵⁰, B. Bland¹⁵, J. Bogenstahl⁴⁰, L. Bogue¹⁶, R. Bork¹⁴, V. Boschi¹⁴, S. Bose⁵², P. R. Brady⁵¹, V. B. Braginsky²¹, J. E. Brau⁴³, M. Brinkmann², A. Brooks³⁷, D. A. Brown^14,6, A. Bullington³⁰, A. Bunkowski², A. Buonanno⁴¹, O. Burmeister², D. Busby¹⁴, R. L. Byer³⁰, L. Cadonati¹⁷, G. Cagnoli⁴⁰, J. B. Camp²², J. Cannizzo²², K. Cannon⁵¹, C. A. Cantley⁴⁰, J. Cao¹⁷, L. Cardenas¹⁴, M. M. Casey⁴⁰, G. Castaldi⁴⁶, C. Cepeda¹⁴, E. Chalkey⁴⁰, P. Charlton⁹, S. Chatterji¹⁴, S. Chelkowski², Y. Chen¹, F. Chiadini⁴⁵, D. Chin⁴², E. Chin⁵⁰, J. Chow⁴, N. Christensen⁸, J. Clark⁴⁰, P. Cochrane², T. Cokelaer⁷, C. N. Colacino³⁸, R. Coldwell³⁹, R. Conte⁴⁵, D. Cook¹⁵, T. Corbitt¹⁷, D. Coward⁵⁰, D. Coyne¹⁴, J. D. E. Creighton⁵¹, T. D. Creighton¹⁴, R. P. Croce⁴⁶, D. R. M. Crooks⁴⁰, A. M. Cruise³⁸, A. Cumming⁴⁰, J. Dalrymple³¹, E. D’Ambrosio¹⁴, K. Danzmann^36,2, G. Davies⁷, D. DeBra³⁰, J. Degallaix⁵⁰, M. Degree³⁰, T. Demma⁴⁶, V. Dergachev⁴², S. Desai³², R. DeSalvo¹⁴, S. Dhurandhar¹³, M. Díaz³³, J. Dickson⁴, A. Di Credico³¹, G. Diederichs³⁶, A. Dietz⁷, E. E. Doomes²⁹, R. W. P. Drever⁵, J.-C. Dumas⁵⁰, R. J. Dupuis¹⁴, J. G. Dwyer¹⁰, P. Ehrens¹⁴, E. Espinoza¹⁴, T. Etzel¹⁴, M. Evans¹⁴, T. Evans¹⁶, S. Fairhurst^7,14, Y. Fan⁵⁰, D. Fazi¹⁴, M. M. Fejer³⁰, L. S. Finn³², V. Fiumara⁴⁵, N. Fotopoulos⁵¹, A. Franzen³⁶, K. Y. Franzen³⁹, A. Freise³⁸, R. Frey⁴³, T. Fricke⁴⁴, P. Fritschel¹⁷, V. V. Frolov¹⁶, M. Fyffe¹⁶, V. Galdi⁴⁶, J. Garofoli¹⁵, I. Gholami¹, J. A. Giaime^16,18, S. Giampanis⁴⁴, K. D. Giardina¹⁶, K. Goda¹⁷, E. Goetz⁴², L. M. Goggin¹⁴, G. González¹⁸, S. Gossler⁴, A. Grant⁴⁰, S. Gras⁵⁰, C. Gray¹⁵, M. Gray⁴, J. Greenhalgh²⁶, A. M. Gretarsson¹¹, R. Grosso³³, H. Grote², S. Grunewald¹, M. Guenther¹⁵, R. Gustafson⁴², B. Hage³⁶, D. Hammer⁵¹, C. Hanna¹⁸, J. Hanson¹⁶, J. Harms², G. Harry¹⁷, E. Harstad⁴³, T. Hayler²⁶, J. Heefner¹⁴, I. S. Heng⁴⁰, A. Heptonstall⁴⁰, M. Heurs², M. Hewitson², S. Hild³⁶, E. Hirose³¹, D. Hoak¹⁶, D. Hosken³⁷, J. Hough⁴⁰, E. Howell⁵⁰, D. Hoyland³⁸, S. H. Huttner⁴⁰, D. Ingram¹⁵, E. Innerhofer¹⁷, M. Ito⁴³, Y. Itoh⁵¹, A. Ivanov¹⁴, D. Jackrel³⁰, B. Johnson¹⁵, W. W. Johnson¹⁸, D. I. Jones⁴⁷, G. Jones⁷, R. Jones⁴⁰, L. Ju⁵⁰, P. Kalmus¹⁰, V. Kalogera²⁴, D. Kasprzyk³⁸, E. Katsavounidis¹⁷, K. Kawabe¹⁵, S. Kawamura²³, F. Kawazoe²³, W. Kells¹⁴, D. G. Keppel¹⁴, F. Ya. Khalili²¹, C. Kim²⁴, P. King¹⁴, J. S. Kissel¹⁸, S. Klimenko³⁹, K. Kokeyama²³, V. Kondrashov¹⁴, R. K. Kopparapu¹⁸, D. Kozak¹⁴, B. Krishnan¹, P. Kwee³⁶, P. K. Lam⁴, M. Landry¹⁵, B. Lantz³⁰, A. Lazzarini¹⁴, B. Lee⁵⁰, M. Lei¹⁴, J. Leiner⁵², V. Leonhardt²³, I. Leonor⁴³, K. Libbrecht¹⁴, P. Lindquist¹⁴, N. A. Lockerbie⁴⁸, M. Longo⁴⁵, M. Lormand¹⁶, M. Lubinski¹⁵, H. Lück^2,36, B. Machenschalk¹, M. MacInnis¹⁷, M. Mageswaran¹⁴, K. Mailand¹⁴, M. Malec³⁶, V. Mandic¹⁴, S. Marano⁴⁵, S. Márka¹⁰, J. Markowitz¹⁷, E. Maros¹⁴, I. Martin⁴⁰, J. N. Marx¹⁴, K. Mason¹⁷, L. Matone¹⁰, V. Matta⁴⁵, N. Mavalvala¹⁷, R. McCarthy¹⁵, D. E. McClelland⁴, S. C. McGuire²⁹, M. McHugh²⁰, K. McKenzie⁴, J. W. C. McNabb³², S. McWilliams²², T. Meier³⁶, A. Melissinos⁴⁴, G. Mendell¹⁵, R. A. Mercer³⁹, S. Meshkov¹⁴, E. Messaritaki¹⁴, C. J. Messenger⁴⁰, D. Meyers¹⁴, E. Mikhailov¹⁷, S. Mitra¹³, V. P. Mitrofanov²¹, G. Mitselmakher³⁹, R. Mittleman¹⁷, O. Miyakawa¹⁴, S. Mohanty³³, G. Moreno¹⁵, K. Mossavi², C. MowLowry⁴, A. Moylan⁴, D. Mudge³⁷, G. Mueller³⁹, S. Mukherjee³³, H. Müller-Ebhardt², J. Munch³⁷, P. Murray⁴⁰, E. Myers¹⁵, J. Myers¹⁵, G. Newton⁴⁰, A. Nishizawa²³, K. Numata²², B. O’Reilly¹⁶, R. O’Shaughnessy²⁴, D. J. Ottaway¹⁷, H. Overmier¹⁶, B. J. Owen³², Y. Pan⁴¹, M. A. Papa^1,51, V. Parameshwaraiah¹⁵, P. Patel¹⁴, M. Pedraza¹⁴, S. Penn¹², V. Pierro⁴⁶, I. M. Pinto⁴⁶, M. Pitkin⁴⁰, H. Pletsch², M. V. Plissi⁴⁰, F. Postiglione⁴⁵, R. Prix¹, V. Quetschke³⁹, F. Raab¹⁵, D. Rabeling⁴, H. Radkins¹⁵, R. Rahkola⁴³, N. Rainer², M. Rakhmanov³², K. Rawlins¹⁷, S. Ray-Majumder⁵¹, V. Re³⁸, H. Rehbein², S. Reid⁴⁰, D. H. Reitze³⁹, L. Ribichini², R. Riesen¹⁶, K. Riles⁴², B. Rivera¹⁵, N. A. Robertson^14,40, C. Robinson⁷, E. L. Robinson³⁸, S. Roddy¹⁶, A. Rodriguez¹⁸, A. M. Rogan⁵², J. Rollins¹⁰, J. D. Romano⁷, J. Romie¹⁶, R. Route³⁰, S. Rowan⁴⁰, A. Rüdiger², L. Ruet¹⁷, P. Russell¹⁴, K. Ryan¹⁵, S. Sakata²³, M. Samidi¹⁴, L. Sancho de la Jordana³⁵, V. Sandberg¹⁵, V. Sannibale¹⁴, S. Saraf²⁵, P. Sarin¹⁷, B. S. Sathyaprakash⁷, S. Sato²³, P. R. Saulson³¹, R. Savage¹⁵, P. Savov⁶, S. Schediwy⁵⁰, R. Schilling², R. Schnabel², R. Schofield⁴³, B. F. Schutz^1,7, P. Schwinberg¹⁵, S. M. Scott⁴, A. C. Searle⁴, B. Sears¹⁴, F. Seifert², D. Sellers¹⁶, A. S. Sengupta⁷, P. Shawhan⁴¹, D. H. Shoemaker¹⁷, A. Sibley¹⁶, J. A. Sidles⁴⁹, X. Siemens^6,14, D. Sigg¹⁵, S. Sinha³⁰, A. M. Sintes^1,35, B. J. J. Slagmolen⁴, J. Slutsky¹⁸, J. R. Smith², M. R. Smith¹⁴, K. Somiya^2,1, K. A. Strain⁴⁰, D. M. Strom⁴³, A. Stuver³², T. Z. Summerscales³, K.-X. Sun³⁰, M. Sung¹⁸, P. J. Sutton¹⁴, H. Takahashi¹, D. B. Tanner³⁹, M. Tarallo¹⁴, R. Taylor¹⁴, R. Taylor⁴⁰, J. Thacker¹⁶, K. A. Thorne³², K. S. Thorne⁶, A. Thüring³⁶, K. V. Tokmakov⁴⁰, C. Torres³³, C. Torrie⁴⁰, G. Traylor¹⁶, M. Trias³⁵, W. Tyler¹⁴, D. Ugolini³⁴, C. Ungarelli³⁸, K. Urbanek³⁰, H. Vahlbruch³⁶, M. Vallisneri⁶, C. Van Den Broeck⁷, M. Varvella¹⁴, S. Vass¹⁴, A. Vecchio³⁸, J. Veitch⁴⁰, P. Veitch³⁷, A. Villar¹⁴, C. Vorvick¹⁵, S. P. Vyachanin²¹, S. J. Waldman¹⁴, L. Wallace¹⁴, H. Ward⁴⁰, R. Ward¹⁴, K. Watts¹⁶, D. Webber¹⁴, A. Weidner², M. Weinert², A. Weinstein¹⁴, R. Weiss¹⁷, S. Wen¹⁸, K. Wette⁴, J. T. Whelan¹, D. M. Whitbeck³², S. E. Whitcomb¹⁴, B. F. Whiting³⁹, C. Wilkinson¹⁵, P. A. Willems¹⁴, L. Williams³⁹, B. Willke^2,36, I. Wilmut²⁶, W. Winkler², C. C. Wipf¹⁷, S. Wise³⁹, A. G. Wiseman⁵¹, G. Woan⁴⁰, D. Woods⁵¹, R. Wooley¹⁶, J. Worden¹⁵, W. Wu³⁹, I. Yakushin¹⁶, H. Yamamoto¹⁴, Z. Yan⁵⁰, S. Yoshida²⁸, N. Yunes³², M. Zanolin¹⁷, J. Zhang⁴², L. Zhang¹⁴, C. Zhao⁵⁰, N. Zotov¹⁹, M. Zucker¹⁷, H. zur Mühlen³⁶, and J. Zweizig¹⁴ (LIGO Scientific Collaboration)

¹Albert-Einstein-Institut, Max-Planck-Institutfür Gravitationsphysik, D-14476 Golm, Germany
²Albert-Einstein-Institut, Max-Planck-Institutfür Gravitationsphysik, D-30167 Hannover, Germany
³Andrews University, Berrien Springs,Michigan 49104 USA
⁴Australian National University,Canberra, 0200, Australia
⁵California Institute of Technology,Pasadena, California 91125, USA
⁶Caltech-CaRT, Pasadena, California91125, USA
⁷Cardiff University, Cardiff, CF23YB, United Kingdom
⁸Carleton College, Northfield, Minnesota55057, USA
⁹Charles Sturt University, WaggaWagga, NSW 2678, Australia
¹⁰Columbia University, New York,New York 10027, USA
¹¹Embry-Riddle Aeronautical University,Prescott, Arizona 86301 USA
¹²Hobart and William Smith Colleges,Geneva, New York 14456, USA
¹³Inter-University Centre for Astronomy and Astrophysics,Pune - 411007, India
¹⁴LIGO–California Institute of Technology,Pasadena, California 91125, USA
¹⁵LIGO Hanford Observatory, Richland,Washington 99352, USA
¹⁶LIGO Livingston Observatory, Livingston,Louisiana 70754, USA
¹⁷LIGO–Massachusetts Institute of Technology,Cambridge, Massachusetts 02139, USA
¹⁸Louisiana State University, BatonRouge, Louisiana 70803, USA
¹⁹Louisiana Tech University, Ruston,Louisiana 71272, USA
²⁰Loyola University, New Orleans,Louisiana 70118, USA
²¹Moscow State University, Moscow,119992, Russia
²²NASA/Goddard Space Flight Center,Greenbelt, Maryland 20771, USA
²³National Astronomical Observatory of Japan,Tokyo 181-8588, Japan
²⁴Northwestern University, Evanston,Illinois 60208, USA
²⁵Rochester Institute of Technology,Rochester, New York 14623, USA
²⁶Rutherford Appleton Laboratory,Chilton, Didcot, Oxon OX11 0QX United Kingdom
²⁷San Jose State University, SanJose, California 95192, USA
²⁸Southeastern Louisiana University,Hammond, Louisiana 70402, USA
²⁹Southern University and A&MCollege, Baton Rouge, Louisiana 70813, USA
³⁰Stanford University, Stanford,California 94305, USA
³¹Syracuse University, Syracuse,New York 13244, USA
³²The Pennsylvania State University,University Park, Pennsylvania 16802, USA
³³The University of Texas at Brownsville and TexasSouthmost College, Brownsville, Texas 78520, USA
³⁴Trinity University, San Antonio,Texas 78212, USA
³⁵Universitat de les Illes Balears,E-07122 Palma de Mallorca, Spain
³⁶Universität Hannover, D-30167Hannover, Germany
³⁷University of Adelaide, Adelaide,SA 5005, Australia
³⁸University of Birmingham, Birmingham,B15 2TT, United Kingdom
³⁹University of Florida, Gainesville,Florida 32611, USA
⁴⁰University of Glasgow, Glasgow,G12 8QQ, United Kingdom
⁴¹University of Maryland, CollegePark, Maryland 20742 USA
⁴²University of Michigan, Ann Arbor,Michigan 48109, USA
⁴³University of Oregon, Eugene,Oregon 97403, USA
⁴⁴University of Rochester, Rochester,New York 14627, USA
⁴⁵University of Salerno, 84084 Fisciano(Salerno), Italy
⁴⁶University of Sannio at Benevento,I-82100 Benevento, Italy
⁴⁷University of Southampton, Southampton,SO17 1BJ, United Kingdom
⁴⁸University of Strathclyde, Glasgow,G1 1XQ, United Kingdom
⁴⁹University of Washington, Seattle,Washington, 98195, USA
⁵⁰University of Western Australia,Crawley, WA 6009, Australia
⁵¹University of Wisconsin-Milwaukee,Milwaukee, Wisconsin 53201, USA
⁵²Washington State University, Pullman,Washington 99164, USA

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Phys. Rev. D 76, 082003 – Published 29 October, 2007Erratum Phys. Rev. D 77, 069903 (2008)

DOI: https://doi.org/10.1103/PhysRevD.76.082003

Abstract

We searched for an anisotropic background of gravitational waves using data from the LIGO S4 science run and a method that is optimized for point sources. This is appropriate if, for example, the gravitational wave background is dominated by a small number of distinct astrophysical sources. No signal was seen. Upper limit maps were produced assuming two different power laws for the source strain power spectrum. For an $f^{- 3}$ power law and using the 50 Hz to 1.8 kHz band the upper limits on the source strain power spectrum vary between $1.2 \times 10^{- 48} {Hz}^{- 1}$ $(100 Hz / f)^{3}$ and $1.2 \times 10^{- 47} {Hz}^{- 1}$ $(100 Hz / f)^{3}$ , depending on the position in the sky. Similarly, in the case of constant strain power spectrum, the upper limits vary between $8.5 \times 10^{- 49} {Hz}^{- 1}$ and $6.1 \times 10^{- 48} {Hz}^{- 1}$ . As a side product a limit on an isotropic background of gravitational waves was also obtained. All limits are at the 90% confidence level. Finally, as an application, we focused on the direction of Sco-X1, the brightest low-mass x-ray binary. We compare the upper limit on strain amplitude obtained by this method to expectations based on the x-ray flux from Sco-X1.