Volume 529, Issue 1-2 1600209
Original Paper
Open Access

The basic physics of the binary black hole merger GW150914

LIGO Scientific and VIRGO Collaborations

Corresponding Author

LIGO Scientific and VIRGO Collaborations

[email protected]

Full author list appears at the end.

Corresponding author E-mail: [email protected]Search for more papers by this author
B. P. Abbott

B. P. Abbott

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

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R. Abbott

R. Abbott

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

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T. D. Abbott

T. D. Abbott

Louisiana State University, Baton Rouge, LA 70803 USA

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M. R. Abernathy

M. R. Abernathy

American University, Washington, D.C., 20016 USA

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F. Acernese

F. Acernese

Università di Salerno, Fisciano, I-84084 Salerno, Italy

INFN, Sezione di Napoli, Complesso Universitario di Monte S.Angelo, I-80126 Napoli Italy

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K. Ackley

K. Ackley

University of Florida, Gainesville, FL, 32611 USA

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C. Adams

C. Adams

LIGO Livingston Observatory, Livingston, LA 70754 USA

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T. Adams

T. Adams

Laboratoire d'Annecy-le-Vieux de Physique des Particules (LAPP), Université Savoie Mont Blanc, CNRS/IN2P3, F-74941 Annecy-le-Vieux France

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P. Addesso

P. Addesso

University of Sannio at Benevento, I-82100 Benevento, Italy and INFN, Sezione di Napoli, I-80100 Napoli, Italy

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R. X. Adhikari

R. X. Adhikari

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

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V. B. Adya

V. B. Adya

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-30167 Hannover, Germany

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C. Affeldt

C. Affeldt

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-30167 Hannover, Germany

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M. Agathos

M. Agathos

Nikhef, Science Park, 1098 XG, Amsterdam, The Netherlands

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K. Agatsuma

K. Agatsuma

Nikhef, Science Park, 1098 XG, Amsterdam, The Netherlands

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N. Aggarwal

N. Aggarwal

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

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O. D. Aguiar

O. D. Aguiar

Instituto Nacional de Pesquisas Espaciais, 12227-010 São José dos Campos, São Paulo, Brazil

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L. Aiello

L. Aiello

INFN, Gran Sasso Science Institute, I-67100 L'Aquila Italy

INFN, Sezione di Roma Tor Vergata, I-00133 Roma Italy

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A. Ain

A. Ain

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

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P. Ajith

P. Ajith

International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore 560012 India

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B. Allen

B. Allen

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-30167 Hannover, Germany

University of Wisconsin-Milwaukee, Milwaukee, WI 53201 USA

Leibniz Universität Hannover, D-30167 Hannover Germany

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A. Allocca

A. Allocca

Università di Pisa, I-56127 Pisa Italy

INFN, Sezione di Pisa, I-56127 Pisa Italy

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P. A. Altin

P. A. Altin

Australian National University, Canberra, Australian Capital Territory 0200, Australia

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S. B. Anderson

S. B. Anderson

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

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W. G. Anderson

W. G. Anderson

University of Wisconsin-Milwaukee, Milwaukee, WI 53201 USA

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K. Arai

K. Arai

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

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M. C. Araya

M. C. Araya

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

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C. C. Arceneaux

C. C. Arceneaux

The University of Mississippi, University, MS 38677 USA

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J. S. Areeda

J. S. Areeda

California State University Fullerton, Fullerton, CA 92831 USA

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N. Arnaud

N. Arnaud

LAL, Univ. Paris-Sud, CNRS/IN2P3, Université Paris-Saclay, Orsay, France

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K. G. Arun

K. G. Arun

Chennai Mathematical Institute, Chennai 603103 India

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S. Ascenzi

S. Ascenzi

Università di Roma Tor Vergata, I-00133 Roma Italy

INFN, Sezione di Roma Tor Vergata, I-00133 Roma Italy

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G. Ashton

G. Ashton

University of Southampton, Southampton SO17 1BJ United Kingdom

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M. Ast

M. Ast

Universität Hamburg, D-22761 Hamburg Germany

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S. M. Aston

S. M. Aston

LIGO Livingston Observatory, Livingston, LA 70754 USA

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P. Astone

P. Astone

INFN, Sezione di Roma, I-00185 Roma Italy

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P. Aufmuth

P. Aufmuth

Leibniz Universität Hannover, D-30167 Hannover Germany

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C. Aulbert

C. Aulbert

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-30167 Hannover, Germany

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S. Babak

S. Babak

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-14476 Potsdam-Golm Germany

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P. Bacon

P. Bacon

APC, AstroParticule et Cosmologie, Université Paris Diderot, CNRS/IN2P3, CEA/Irfu, Observatoire de Paris, Sorbonne Paris Cité, F-75205 Paris Cedex 13, France

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M. K. M. Bader

M. K. M. Bader

Nikhef, Science Park, 1098 XG, Amsterdam, The Netherlands

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F. Baldaccini

F. Baldaccini

Università di Perugia, I-06123 Perugia Italy

INFN, Sezione di Perugia, I-06123 Perugia Italy

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G. Ballardin

G. Ballardin

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

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S. W. Ballmer

S. W. Ballmer

Syracuse University, Syracuse, NY 13244 USA

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J. C. Barayoga

J. C. Barayoga

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

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S. E. Barclay

S. E. Barclay

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

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B. C. Barish

B. C. Barish

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

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D. Barker

D. Barker

LIGO Hanford Observatory, Richland, WA 99352 USA

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F. Barone

F. Barone

Università di Salerno, Fisciano, I-84084 Salerno, Italy

INFN, Sezione di Napoli, Complesso Universitario di Monte S.Angelo, I-80126 Napoli Italy

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B. Barr

B. Barr

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

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L. Barsotti

L. Barsotti

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

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M. Barsuglia

M. Barsuglia

APC, AstroParticule et Cosmologie, Université Paris Diderot, CNRS/IN2P3, CEA/Irfu, Observatoire de Paris, Sorbonne Paris Cité, F-75205 Paris Cedex 13, France

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D. Barta

D. Barta

Wigner RCP, RMKI, H-1121 Budapest, Konkoly Thege Miklós út 29-33, Hungary

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J. Bartlett

J. Bartlett

LIGO Hanford Observatory, Richland, WA 99352 USA

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I. Bartos

I. Bartos

Columbia University, New York, NY 10027 USA

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R. Bassiri

R. Bassiri

Stanford University, Stanford, CA 94305 USA

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A. Basti

A. Basti

Università di Pisa, I-56127 Pisa Italy

INFN, Sezione di Pisa, I-56127 Pisa Italy

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J. C. Batch

J. C. Batch

LIGO Hanford Observatory, Richland, WA 99352 USA

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C. Baune

C. Baune

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-30167 Hannover, Germany

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V. Bavigadda

V. Bavigadda

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

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M. Bazzan

M. Bazzan

Università di Padova, Dipartimento di Fisica e Astronomia, I-35131 Padova Italy

INFN, Sezione di Padova, I-35131 Padova Italy

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M. Bejger

M. Bejger

CAMK-PAN, 00-716 Warsaw Poland

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A. S. Bell

A. S. Bell

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

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G. Bergmann

G. Bergmann

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-30167 Hannover, Germany

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C. P. L. Berry

C. P. L. Berry

University of Birmingham, Birmingham B15 2TT United Kingdom

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D. Bersanetti

D. Bersanetti

Università degli Studi di Genova, I-16146 Genova Italy

INFN, Sezione di Genova, I-16146 Genova Italy

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A. Bertolini

A. Bertolini

Nikhef, Science Park, 1098 XG, Amsterdam, The Netherlands

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J. Betzwieser

J. Betzwieser

LIGO Livingston Observatory, Livingston, LA 70754 USA

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S. Bhagwat

S. Bhagwat

Syracuse University, Syracuse, NY 13244 USA

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R. Bhandare

R. Bhandare

RRCAT, Indore, MP 452013 India

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I. A. Bilenko

I. A. Bilenko

Faculty of Physics, Lomonosov Moscow State University, Moscow 119991 Russia

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G. Billingsley

G. Billingsley

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

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J. Birch

J. Birch

LIGO Livingston Observatory, Livingston, LA 70754 USA

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I.A. Birney

I.A. Birney

SUPA, University of the West of Scotland, Paisley PA1 2BE United Kingdom

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O. Birnholtz

O. Birnholtz

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-30167 Hannover, Germany

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S. Biscans

S. Biscans

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

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A. Bisht

A. Bisht

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-30167 Hannover, Germany

Leibniz Universität Hannover, D-30167 Hannover Germany

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M. Bitossi

M. Bitossi

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

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C. Biwer

C. Biwer

Syracuse University, Syracuse, NY 13244 USA

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M. A. Bizouard

M. A. Bizouard

LAL, Univ. Paris-Sud, CNRS/IN2P3, Université Paris-Saclay, Orsay, France

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J. K. Blackburn

J. K. Blackburn

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

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C. D. Blair

C. D. Blair

University of Western Australia, Crawley, Western Australia 6009 Australia

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D. G. Blair

D. G. Blair

University of Western Australia, Crawley, Western Australia 6009 Australia

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R. M. Blair

R. M. Blair

LIGO Hanford Observatory, Richland, WA 99352 USA

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S. Bloemen

S. Bloemen

Department of Astrophysics/IMAPP, Radboud University Nijmegen, P.O. Box 9010, 6500 GL, Nijmegen, The Netherlands

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O. Bock

O. Bock

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-30167 Hannover, Germany

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M. Boer

M. Boer

Artemis, Université Côte d'Azur, CNRS, Observatoire Côte d'Azur, CS 34229 Nice cedex 4, France

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G. Bogaert

G. Bogaert

Artemis, Université Côte d'Azur, CNRS, Observatoire Côte d'Azur, CS 34229 Nice cedex 4, France

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C. Bogan

C. Bogan

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-30167 Hannover, Germany

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A. Bohe

A. Bohe

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-14476 Potsdam-Golm Germany

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C. Bond

C. Bond

University of Birmingham, Birmingham B15 2TT United Kingdom

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F. Bondu

F. Bondu

Institut de Physique de Rennes, CNRS, Université de Rennes 1, F-35042 Rennes France

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R. Bonnand

R. Bonnand

Laboratoire d'Annecy-le-Vieux de Physique des Particules (LAPP), Université Savoie Mont Blanc, CNRS/IN2P3, F-74941 Annecy-le-Vieux France

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B. A. Boom

B. A. Boom

Nikhef, Science Park, 1098 XG, Amsterdam, The Netherlands

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R. Bork

R. Bork

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

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V. Boschi

V. Boschi

Università di Pisa, I-56127 Pisa Italy

INFN, Sezione di Pisa, I-56127 Pisa Italy

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S. Bose

S. Bose

Washington State University, Pullman, WA 99164 USA

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

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Y. Bouffanais

Y. Bouffanais

APC, AstroParticule et Cosmologie, Université Paris Diderot, CNRS/IN2P3, CEA/Irfu, Observatoire de Paris, Sorbonne Paris Cité, F-75205 Paris Cedex 13, France

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A. Bozzi

A. Bozzi

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

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C. Bradaschia

C. Bradaschia

INFN, Sezione di Pisa, I-56127 Pisa Italy

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V. B. Braginsky

V. B. Braginsky

Faculty of Physics, Lomonosov Moscow State University, Moscow 119991 Russia

Deceased, March 2016.

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M. Branchesi

M. Branchesi

Università degli Studi di Urbino “Carlo Bo”, I-61029 Urbino Italy

INFN, Sezione di Firenze, I-50019 Sesto Fiorentino Firenze, Italy

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J. E. Brau

J. E. Brau

University of Oregon, Eugene, OR 97403 USA

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T. Briant

T. Briant

Laboratoire Kastler Brossel, UPMC-Sorbonne Universités, CNRS, ENS-PSL Research University, Collège de France, F-75005 Paris France

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A. Brillet

A. Brillet

Artemis, Université Côte d'Azur, CNRS, Observatoire Côte d'Azur, CS 34229 Nice cedex 4, France

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M. Brinkmann

M. Brinkmann

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-30167 Hannover, Germany

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V. Brisson

V. Brisson

LAL, Univ. Paris-Sud, CNRS/IN2P3, Université Paris-Saclay, Orsay, France

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P. Brockill

P. Brockill

University of Wisconsin-Milwaukee, Milwaukee, WI 53201 USA

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J. E. Broida

J. E. Broida

Carleton College, Northfield, MN 55057 USA

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A. F. Brooks

A. F. Brooks

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

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D. A. Brown

D. A. Brown

Syracuse University, Syracuse, NY 13244 USA

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D. D. Brown

D. D. Brown

University of Birmingham, Birmingham B15 2TT United Kingdom

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N. M. Brown

N. M. Brown

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

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S. Brunett

S. Brunett

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

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C. C. Buchanan

C. C. Buchanan

Louisiana State University, Baton Rouge, LA 70803 USA

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A. Buikema

A. Buikema

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

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T. Bulik

T. Bulik

Astronomical Observatory Warsaw University, 00-478 Warsaw Poland

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H. J. Bulten

H. J. Bulten

VU University Amsterdam, 1081 HV Amsterdam, The Netherlands

Nikhef, Science Park, 1098 XG, Amsterdam, The Netherlands

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A. Buonanno

A. Buonanno

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-14476 Potsdam-Golm Germany

University of Maryland, College Park, MD 20742 USA

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D. Buskulic

D. Buskulic

Laboratoire d'Annecy-le-Vieux de Physique des Particules (LAPP), Université Savoie Mont Blanc, CNRS/IN2P3, F-74941 Annecy-le-Vieux France

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C. Buy

C. Buy

APC, AstroParticule et Cosmologie, Université Paris Diderot, CNRS/IN2P3, CEA/Irfu, Observatoire de Paris, Sorbonne Paris Cité, F-75205 Paris Cedex 13, France

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R. L. Byer

R. L. Byer

Stanford University, Stanford, CA 94305 USA

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M. Cabero

M. Cabero

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-30167 Hannover, Germany

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L. Cadonati

L. Cadonati

Center for Relativistic Astrophysics and School of Physics, Georgia Institute of Technology, Atlanta, GA 30332 USA

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G. Cagnoli

G. Cagnoli

Laboratoire des Matériaux Avancés (LMA), CNRS/IN2P3, F-69622 Villeurbanne France

Université Claude Bernard Lyon 1, F-69622 Villeurbanne France

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C. Cahillane

C. Cahillane

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

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J. Calderón Bustillo

J. Calderón Bustillo

Center for Relativistic Astrophysics and School of Physics, Georgia Institute of Technology, Atlanta, GA 30332 USA

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T. Callister

T. Callister

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

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E. Calloni

E. Calloni

Università di Napoli “Federico II”, Complesso Universitario di Monte S.Angelo, I-80126 Napoli Italy

INFN, Sezione di Napoli, Complesso Universitario di Monte S.Angelo, I-80126 Napoli Italy

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J. B. Camp

J. B. Camp

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

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K. C. Cannon

K. C. Cannon

RESCEU, University of Tokyo, Tokyo, 113-0033 Japan

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J. Cao

J. Cao

Tsinghua University, Beijing 100084 China

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C. D. Capano

C. D. Capano

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-30167 Hannover, Germany

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E. Capocasa

E. Capocasa

APC, AstroParticule et Cosmologie, Université Paris Diderot, CNRS/IN2P3, CEA/Irfu, Observatoire de Paris, Sorbonne Paris Cité, F-75205 Paris Cedex 13, France

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F. Carbognani

F. Carbognani

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

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S. Caride

S. Caride

Texas Tech University, Lubbock, TX 79409 USA

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J. Casanueva Diaz

J. Casanueva Diaz

LAL, Univ. Paris-Sud, CNRS/IN2P3, Université Paris-Saclay, Orsay, France

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C. Casentini

C. Casentini

Università di Roma Tor Vergata, I-00133 Roma Italy

INFN, Sezione di Roma Tor Vergata, I-00133 Roma Italy

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S. Caudill

S. Caudill

University of Wisconsin-Milwaukee, Milwaukee, WI 53201 USA

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M. Cavaglià

M. Cavaglià

The University of Mississippi, University, MS 38677 USA

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F. Cavalier

F. Cavalier

LAL, Univ. Paris-Sud, CNRS/IN2P3, Université Paris-Saclay, Orsay, France

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R. Cavalieri

R. Cavalieri

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

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G. Cella

G. Cella

INFN, Sezione di Pisa, I-56127 Pisa Italy

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C. B. Cepeda

C. B. Cepeda

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

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L. Cerboni Baiardi

L. Cerboni Baiardi

Università degli Studi di Urbino “Carlo Bo”, I-61029 Urbino Italy

INFN, Sezione di Firenze, I-50019 Sesto Fiorentino Firenze, Italy

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G. Cerretani

G. Cerretani

Università di Pisa, I-56127 Pisa Italy

INFN, Sezione di Pisa, I-56127 Pisa Italy

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E. Cesarini

E. Cesarini

Università di Roma Tor Vergata, I-00133 Roma Italy

INFN, Sezione di Roma Tor Vergata, I-00133 Roma Italy

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S. J. Chamberlin

S. J. Chamberlin

The Pennsylvania State University, University Park, PA 16802 USA

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M. Chan

M. Chan

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

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S. Chao

S. Chao

National Tsing Hua University, Hsinchu City 30013 Taiwan, Republic of China

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P. Charlton

P. Charlton

Charles Sturt University, Wagga Wagga, New South Wales 2678 Australia

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E. Chassande-Mottin

E. Chassande-Mottin

APC, AstroParticule et Cosmologie, Université Paris Diderot, CNRS/IN2P3, CEA/Irfu, Observatoire de Paris, Sorbonne Paris Cité, F-75205 Paris Cedex 13, France

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H. Y. Chen

H. Y. Chen

University of Chicago, Chicago, IL 60637 USA

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Y. Chen

Y. Chen

Caltech CaRT, Pasadena, CA 91125 USA

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C. Cheng

C. Cheng

National Tsing Hua University, Hsinchu City 30013 Taiwan, Republic of China

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A. Chincarini

A. Chincarini

INFN, Sezione di Genova, I-16146 Genova Italy

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A. Chiummo

A. Chiummo

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

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H. S. Cho

H. S. Cho

Korea Institute of Science and Technology Information, Daejeon 305-806 Korea

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M. Cho

M. Cho

University of Maryland, College Park, MD 20742 USA

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J. H. Chow

J. H. Chow

Australian National University, Canberra, Australian Capital Territory 0200, Australia

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N. Christensen

N. Christensen

Carleton College, Northfield, MN 55057 USA

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Q. Chu

Q. Chu

University of Western Australia, Crawley, Western Australia 6009 Australia

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S. Chua

S. Chua

Laboratoire Kastler Brossel, UPMC-Sorbonne Universités, CNRS, ENS-PSL Research University, Collège de France, F-75005 Paris France

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S. Chung

S. Chung

University of Western Australia, Crawley, Western Australia 6009 Australia

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G. Ciani

G. Ciani

University of Florida, Gainesville, FL, 32611 USA

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F. Clara

F. Clara

LIGO Hanford Observatory, Richland, WA 99352 USA

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J. A. Clark

J. A. Clark

Center for Relativistic Astrophysics and School of Physics, Georgia Institute of Technology, Atlanta, GA 30332 USA

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F. Cleva

F. Cleva

Artemis, Université Côte d'Azur, CNRS, Observatoire Côte d'Azur, CS 34229 Nice cedex 4, France

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E. Coccia

E. Coccia

Università di Roma Tor Vergata, I-00133 Roma Italy

INFN, Gran Sasso Science Institute, I-67100 L'Aquila Italy

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P.-F. Cohadon

P.-F. Cohadon

Laboratoire Kastler Brossel, UPMC-Sorbonne Universités, CNRS, ENS-PSL Research University, Collège de France, F-75005 Paris France

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A. Colla

A. Colla

Università di Roma “La Sapienza”, I-00185 Roma Italy

INFN, Sezione di Roma, I-00185 Roma Italy

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C. G. Collette

C. G. Collette

University of Brussels, Brussels 1050 Belgium

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L. Cominsky

L. Cominsky

Sonoma State University, Rohnert Park, CA 94928 USA

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M. Constancio Jr.

M. Constancio Jr.

Instituto Nacional de Pesquisas Espaciais, 12227-010 São José dos Campos, São Paulo, Brazil

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A. Conte

A. Conte

Università di Roma “La Sapienza”, I-00185 Roma Italy

INFN, Sezione di Roma, I-00185 Roma Italy

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L. Conti

L. Conti

INFN, Sezione di Padova, I-35131 Padova Italy

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D. Cook

D. Cook

LIGO Hanford Observatory, Richland, WA 99352 USA

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T. R. Corbitt

T. R. Corbitt

Louisiana State University, Baton Rouge, LA 70803 USA

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A. Corsi

A. Corsi

Texas Tech University, Lubbock, TX 79409 USA

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S. Cortese

S. Cortese

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

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C. A. Costa

C. A. Costa

Instituto Nacional de Pesquisas Espaciais, 12227-010 São José dos Campos, São Paulo, Brazil

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M. W. Coughlin

M. W. Coughlin

Carleton College, Northfield, MN 55057 USA

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S. B. Coughlin

S. B. Coughlin

Center for Interdisciplinary Exploration & Research in Astrophysics (CIERA), Northwestern University, Evanston, IL 60208 USA

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J.-P. Coulon

J.-P. Coulon

Artemis, Université Côte d'Azur, CNRS, Observatoire Côte d'Azur, CS 34229 Nice cedex 4, France

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S. T. Countryman

S. T. Countryman

Columbia University, New York, NY 10027 USA

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P. Couvares

P. Couvares

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

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E. E. Cowan

E. E. Cowan

Center for Relativistic Astrophysics and School of Physics, Georgia Institute of Technology, Atlanta, GA 30332 USA

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D. M. Coward

D. M. Coward

University of Western Australia, Crawley, Western Australia 6009 Australia

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M. J. Cowart

M. J. Cowart

LIGO Livingston Observatory, Livingston, LA 70754 USA

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D. C. Coyne

D. C. Coyne

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

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R. Coyne

R. Coyne

Texas Tech University, Lubbock, TX 79409 USA

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K. Craig

K. Craig

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

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J. D. E. Creighton

J. D. E. Creighton

University of Wisconsin-Milwaukee, Milwaukee, WI 53201 USA

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J. Cripe

J. Cripe

Louisiana State University, Baton Rouge, LA 70803 USA

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S. G. Crowder

S. G. Crowder

University of Minnesota, Minneapolis, MN 55455 USA

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A. Cumming

A. Cumming

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

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L. Cunningham

L. Cunningham

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

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E. Cuoco

E. Cuoco

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

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T. Dal Canton

T. Dal Canton

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-30167 Hannover, Germany

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S. L. Danilishin

S. L. Danilishin

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

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S. D'Antonio

S. D'Antonio

INFN, Sezione di Roma Tor Vergata, I-00133 Roma Italy

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K. Danzmann

K. Danzmann

Leibniz Universität Hannover, D-30167 Hannover Germany

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-30167 Hannover, Germany

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N. S. Darman

N. S. Darman

The University of Melbourne, Parkville, Victoria 3010 Australia

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A. Dasgupta

A. Dasgupta

Institute for Plasma Research, Bhat, Gandhinagar 382428 India

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C. F. Da Silva Costa

C. F. Da Silva Costa

University of Florida, Gainesville, FL, 32611 USA

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V. Dattilo

V. Dattilo

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

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I. Dave

I. Dave

RRCAT, Indore, MP 452013 India

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M. Davier

M. Davier

LAL, Univ. Paris-Sud, CNRS/IN2P3, Université Paris-Saclay, Orsay, France

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G. S. Davies

G. S. Davies

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

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E. J. Daw

E. J. Daw

The University of Sheffield, Sheffield S10 2TN United Kingdom

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R. Day

R. Day

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

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S. De

S. De

Syracuse University, Syracuse, NY 13244 USA

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D. DeBra

D. DeBra

Stanford University, Stanford, CA 94305 USA

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G. Debreczeni

G. Debreczeni

Wigner RCP, RMKI, H-1121 Budapest, Konkoly Thege Miklós út 29-33, Hungary

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J. Degallaix

J. Degallaix

Laboratoire des Matériaux Avancés (LMA), CNRS/IN2P3, F-69622 Villeurbanne France

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M. De Laurentis

M. De Laurentis

Università di Napoli “Federico II”, Complesso Universitario di Monte S.Angelo, I-80126 Napoli Italy

INFN, Sezione di Napoli, Complesso Universitario di Monte S.Angelo, I-80126 Napoli Italy

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S. Deléglise

S. Deléglise

Laboratoire Kastler Brossel, UPMC-Sorbonne Universités, CNRS, ENS-PSL Research University, Collège de France, F-75005 Paris France

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W. Del Pozzo

W. Del Pozzo

University of Birmingham, Birmingham B15 2TT United Kingdom

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T. Denker

T. Denker

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-30167 Hannover, Germany

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T. Dent

T. Dent

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-30167 Hannover, Germany

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V. Dergachev

V. Dergachev

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

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R. De Rosa

R. De Rosa

Università di Napoli “Federico II”, Complesso Universitario di Monte S.Angelo, I-80126 Napoli Italy

INFN, Sezione di Napoli, Complesso Universitario di Monte S.Angelo, I-80126 Napoli Italy

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R. T. DeRosa

R. T. DeRosa

LIGO Livingston Observatory, Livingston, LA 70754 USA

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R. DeSalvo

R. DeSalvo

University of Sannio at Benevento, I-82100 Benevento, Italy and INFN, Sezione di Napoli, I-80100 Napoli, Italy

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R. C. Devine

R. C. Devine

West Virginia University, Morgantown, WV 26506 USA

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S. Dhurandhar

S. Dhurandhar

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

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M. C. Díaz

M. C. Díaz

The University of Texas Rio Grande Valley, Brownsville, TX 78520 USA

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L. Di Fiore

L. Di Fiore

INFN, Sezione di Napoli, Complesso Universitario di Monte S.Angelo, I-80126 Napoli Italy

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M. Di Giovanni

M. Di Giovanni

Università di Trento, Dipartimento di Fisica, I-38123 Povo Trento, Italy

INFN, Trento Institute for Fundamental Physics and Applications, I-38123 Povo Trento, Italy

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T. Di Girolamo

T. Di Girolamo

Università di Napoli “Federico II”, Complesso Universitario di Monte S.Angelo, I-80126 Napoli Italy

INFN, Sezione di Napoli, Complesso Universitario di Monte S.Angelo, I-80126 Napoli Italy

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A. Di Lieto

A. Di Lieto

Università di Pisa, I-56127 Pisa Italy

INFN, Sezione di Pisa, I-56127 Pisa Italy

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S. Di Pace

S. Di Pace

Università di Roma “La Sapienza”, I-00185 Roma Italy

INFN, Sezione di Roma, I-00185 Roma Italy

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I. Di Palma

I. Di Palma

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-14476 Potsdam-Golm Germany

Università di Roma “La Sapienza”, I-00185 Roma Italy

INFN, Sezione di Roma, I-00185 Roma Italy

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A. Di Virgilio

A. Di Virgilio

INFN, Sezione di Pisa, I-56127 Pisa Italy

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V. Dolique

V. Dolique

Laboratoire des Matériaux Avancés (LMA), CNRS/IN2P3, F-69622 Villeurbanne France

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F. Donovan

F. Donovan

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

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K. L. Dooley

K. L. Dooley

The University of Mississippi, University, MS 38677 USA

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S. Doravari

S. Doravari

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-30167 Hannover, Germany

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R. Douglas

R. Douglas

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

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T. P. Downes

T. P. Downes

University of Wisconsin-Milwaukee, Milwaukee, WI 53201 USA

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M. Drago

M. Drago

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-30167 Hannover, Germany

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R. W. P. Drever

R. W. P. Drever

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

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J. C. Driggers

J. C. Driggers

LIGO Hanford Observatory, Richland, WA 99352 USA

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M. Ducrot

M. Ducrot

Laboratoire d'Annecy-le-Vieux de Physique des Particules (LAPP), Université Savoie Mont Blanc, CNRS/IN2P3, F-74941 Annecy-le-Vieux France

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S. E. Dwyer

S. E. Dwyer

LIGO Hanford Observatory, Richland, WA 99352 USA

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T. B. Edo

T. B. Edo

The University of Sheffield, Sheffield S10 2TN United Kingdom

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M. C. Edwards

M. C. Edwards

Carleton College, Northfield, MN 55057 USA

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A. Effler

A. Effler

LIGO Livingston Observatory, Livingston, LA 70754 USA

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H.-B. Eggenstein

H.-B. Eggenstein

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-30167 Hannover, Germany

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P. Ehrens

P. Ehrens

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

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J. Eichholz

J. Eichholz

University of Florida, Gainesville, FL, 32611 USA

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

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S. S. Eikenberry

S. S. Eikenberry

University of Florida, Gainesville, FL, 32611 USA

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W. Engels

W. Engels

Caltech CaRT, Pasadena, CA 91125 USA

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R. C. Essick

R. C. Essick

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

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T. Etzel

T. Etzel

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

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M. Evans

M. Evans

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

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T. M. Evans

T. M. Evans

LIGO Livingston Observatory, Livingston, LA 70754 USA

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R. Everett

R. Everett

The Pennsylvania State University, University Park, PA 16802 USA

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M. Factourovich

M. Factourovich

Columbia University, New York, NY 10027 USA

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V. Fafone

V. Fafone

Università di Roma Tor Vergata, I-00133 Roma Italy

INFN, Sezione di Roma Tor Vergata, I-00133 Roma Italy

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H. Fair

H. Fair

Syracuse University, Syracuse, NY 13244 USA

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S. Fairhurst

S. Fairhurst

Cardiff University, Cardiff CF24 3AA, United Kingdom

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X. Fan

X. Fan

Tsinghua University, Beijing 100084 China

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Q. Fang

Q. Fang

University of Western Australia, Crawley, Western Australia 6009 Australia

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S. Farinon

S. Farinon

INFN, Sezione di Genova, I-16146 Genova Italy

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B. Farr

B. Farr

University of Chicago, Chicago, IL 60637 USA

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W. M. Farr

W. M. Farr

University of Birmingham, Birmingham B15 2TT United Kingdom

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M. Favata

M. Favata

Montclair State University, Montclair, NJ 07043 USA

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M. Fays

M. Fays

Cardiff University, Cardiff CF24 3AA, United Kingdom

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H. Fehrmann

H. Fehrmann

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-30167 Hannover, Germany

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M. M. Fejer

M. M. Fejer

Stanford University, Stanford, CA 94305 USA

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E. Fenyvesi

E. Fenyvesi

MTA Eötvös University, “Lendulet” Astrophysics Research Group, Budapest 1117 Hungary

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I. Ferrante

I. Ferrante

Università di Pisa, I-56127 Pisa Italy

INFN, Sezione di Pisa, I-56127 Pisa Italy

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E. C. Ferreira

E. C. Ferreira

Instituto Nacional de Pesquisas Espaciais, 12227-010 São José dos Campos, São Paulo, Brazil

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F. Ferrini

F. Ferrini

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

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F. Fidecaro

F. Fidecaro

Università di Pisa, I-56127 Pisa Italy

INFN, Sezione di Pisa, I-56127 Pisa Italy

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I. Fiori

I. Fiori

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

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D. Fiorucci

D. Fiorucci

APC, AstroParticule et Cosmologie, Université Paris Diderot, CNRS/IN2P3, CEA/Irfu, Observatoire de Paris, Sorbonne Paris Cité, F-75205 Paris Cedex 13, France

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R. P. Fisher

R. P. Fisher

Syracuse University, Syracuse, NY 13244 USA

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R. Flaminio

R. Flaminio

Laboratoire des Matériaux Avancés (LMA), CNRS/IN2P3, F-69622 Villeurbanne France

National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588 Japan

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M. Fletcher

M. Fletcher

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

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J.-D. Fournier

J.-D. Fournier

Artemis, Université Côte d'Azur, CNRS, Observatoire Côte d'Azur, CS 34229 Nice cedex 4, France

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S. Frasca

S. Frasca

Università di Roma “La Sapienza”, I-00185 Roma Italy

INFN, Sezione di Roma, I-00185 Roma Italy

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F. Frasconi

F. Frasconi

INFN, Sezione di Pisa, I-56127 Pisa Italy

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Z. Frei

Z. Frei

MTA Eötvös University, “Lendulet” Astrophysics Research Group, Budapest 1117 Hungary

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A. Freise

A. Freise

University of Birmingham, Birmingham B15 2TT United Kingdom

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R. Frey

R. Frey

University of Oregon, Eugene, OR 97403 USA

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V. Frey

V. Frey

LAL, Univ. Paris-Sud, CNRS/IN2P3, Université Paris-Saclay, Orsay, France

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P. Fritschel

P. Fritschel

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

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V. V. Frolov

V. V. Frolov

LIGO Livingston Observatory, Livingston, LA 70754 USA

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P. Fulda

P. Fulda

University of Florida, Gainesville, FL, 32611 USA

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M. Fyffe

M. Fyffe

LIGO Livingston Observatory, Livingston, LA 70754 USA

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H. A. G. Gabbard

H. A. G. Gabbard

The University of Mississippi, University, MS 38677 USA

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J. R. Gair

J. R. Gair

School of Mathematics, University of Edinburgh, Edinburgh EH9 3FD United Kingdom

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L. Gammaitoni

L. Gammaitoni

Università di Perugia, I-06123 Perugia Italy

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S. G. Gaonkar

S. G. Gaonkar

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

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F. Garufi

F. Garufi

Università di Napoli “Federico II”, Complesso Universitario di Monte S.Angelo, I-80126 Napoli Italy

INFN, Sezione di Napoli, Complesso Universitario di Monte S.Angelo, I-80126 Napoli Italy

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G. Gaur

G. Gaur

Indian Institute of Technology, Gandhinagar Ahmedabad, Gujarat 382424 India

Institute for Plasma Research, Bhat, Gandhinagar 382428 India

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N. Gehrels

N. Gehrels

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

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G. Gemme

G. Gemme

INFN, Sezione di Genova, I-16146 Genova Italy

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P. Geng

P. Geng

The University of Texas Rio Grande Valley, Brownsville, TX 78520 USA

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E. Genin

E. Genin

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

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A. Gennai

A. Gennai

INFN, Sezione di Pisa, I-56127 Pisa Italy

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J. George

J. George

RRCAT, Indore, MP 452013 India

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L. Gergely

L. Gergely

University of Szeged, Dóm tér 9, Szeged 6720 Hungary

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V. Germain

V. Germain

Laboratoire d'Annecy-le-Vieux de Physique des Particules (LAPP), Université Savoie Mont Blanc, CNRS/IN2P3, F-74941 Annecy-le-Vieux France

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Abhirup Ghosh

Abhirup Ghosh

International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore 560012 India

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Archisman Ghosh

Archisman Ghosh

International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore 560012 India

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S. Ghosh

S. Ghosh

Department of Astrophysics/IMAPP, Radboud University Nijmegen, P.O. Box 9010, 6500 GL, Nijmegen, The Netherlands

Nikhef, Science Park, 1098 XG, Amsterdam, The Netherlands

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J. A. Giaime

J. A. Giaime

Louisiana State University, Baton Rouge, LA 70803 USA

LIGO Livingston Observatory, Livingston, LA 70754 USA

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K. D. Giardina

K. D. Giardina

LIGO Livingston Observatory, Livingston, LA 70754 USA

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A. Giazotto

A. Giazotto

INFN, Sezione di Pisa, I-56127 Pisa Italy

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K. Gill

K. Gill

Embry-Riddle Aeronautical University, Prescott, AZ 86301 USA

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A. Glaefke

A. Glaefke

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

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E. Goetz

E. Goetz

LIGO Hanford Observatory, Richland, WA 99352 USA

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R. Goetz

R. Goetz

University of Florida, Gainesville, FL, 32611 USA

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L. Gondan

L. Gondan

MTA Eötvös University, “Lendulet” Astrophysics Research Group, Budapest 1117 Hungary

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G. González

G. González

Louisiana State University, Baton Rouge, LA 70803 USA

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J. M. Gonzalez Castro

J. M. Gonzalez Castro

Università di Pisa, I-56127 Pisa Italy

INFN, Sezione di Pisa, I-56127 Pisa Italy

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A. Gopakumar

A. Gopakumar

Tata Institute of Fundamental Research, Mumbai 400005 India

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N. A. Gordon

N. A. Gordon

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

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M. L. Gorodetsky

M. L. Gorodetsky

Faculty of Physics, Lomonosov Moscow State University, Moscow 119991 Russia

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S. E. Gossan

S. E. Gossan

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

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M. Gosselin

M. Gosselin

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

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R. Gouaty

R. Gouaty

Laboratoire d'Annecy-le-Vieux de Physique des Particules (LAPP), Université Savoie Mont Blanc, CNRS/IN2P3, F-74941 Annecy-le-Vieux France

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A. Grado

A. Grado

INAF, Osservatorio Astronomico di Capodimonte, I-80131 Napoli Italy

INFN, Sezione di Napoli, Complesso Universitario di Monte S.Angelo, I-80126 Napoli Italy

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C. Graef

C. Graef

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

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P. B. Graff

P. B. Graff

University of Maryland, College Park, MD 20742 USA

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M. Granata

M. Granata

Laboratoire des Matériaux Avancés (LMA), CNRS/IN2P3, F-69622 Villeurbanne France

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A. Grant

A. Grant

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

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S. Gras

S. Gras

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

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C. Gray

C. Gray

LIGO Hanford Observatory, Richland, WA 99352 USA

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G. Greco

G. Greco

Università degli Studi di Urbino “Carlo Bo”, I-61029 Urbino Italy

INFN, Sezione di Firenze, I-50019 Sesto Fiorentino Firenze, Italy

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A. C. Green

A. C. Green

University of Birmingham, Birmingham B15 2TT United Kingdom

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P. Groot

P. Groot

Department of Astrophysics/IMAPP, Radboud University Nijmegen, P.O. Box 9010, 6500 GL, Nijmegen, The Netherlands

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H. Grote

H. Grote

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-30167 Hannover, Germany

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S. Grunewald

S. Grunewald

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-14476 Potsdam-Golm Germany

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G. M. Guidi

G. M. Guidi

Università degli Studi di Urbino “Carlo Bo”, I-61029 Urbino Italy

INFN, Sezione di Firenze, I-50019 Sesto Fiorentino Firenze, Italy

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X. Guo

X. Guo

Tsinghua University, Beijing 100084 China

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A. Gupta

A. Gupta

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

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M. K. Gupta

M. K. Gupta

Institute for Plasma Research, Bhat, Gandhinagar 382428 India

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K. E. Gushwa

K. E. Gushwa

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

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E. K. Gustafson

E. K. Gustafson

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

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R. Gustafson

R. Gustafson

University of Michigan, Ann Arbor, MI 48109 USA

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J. J. Hacker

J. J. Hacker

California State University Fullerton, Fullerton, CA 92831 USA

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B. R. Hall

B. R. Hall

Washington State University, Pullman, WA 99164 USA

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E. D. Hall

E. D. Hall

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

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G. Hammond

G. Hammond

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

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M. Haney

M. Haney

Tata Institute of Fundamental Research, Mumbai 400005 India

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M. M. Hanke

M. M. Hanke

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-30167 Hannover, Germany

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J. Hanks

J. Hanks

LIGO Hanford Observatory, Richland, WA 99352 USA

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C. Hanna

C. Hanna

The Pennsylvania State University, University Park, PA 16802 USA

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M. D. Hannam

M. D. Hannam

Cardiff University, Cardiff CF24 3AA, United Kingdom

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J. Hanson

J. Hanson

LIGO Livingston Observatory, Livingston, LA 70754 USA

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T. Hardwick

T. Hardwick

Louisiana State University, Baton Rouge, LA 70803 USA

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J. Harms

J. Harms

Università degli Studi di Urbino “Carlo Bo”, I-61029 Urbino Italy

INFN, Sezione di Firenze, I-50019 Sesto Fiorentino Firenze, Italy

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G. M. Harry

G. M. Harry

American University, Washington, D.C., 20016 USA

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I. W. Harry

I. W. Harry

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-14476 Potsdam-Golm Germany

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M. J. Hart

M. J. Hart

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

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M. T. Hartman

M. T. Hartman

University of Florida, Gainesville, FL, 32611 USA

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C.-J. Haster

C.-J. Haster

University of Birmingham, Birmingham B15 2TT United Kingdom

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K. Haughian

K. Haughian

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

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A. Heidmann

A. Heidmann

Laboratoire Kastler Brossel, UPMC-Sorbonne Universités, CNRS, ENS-PSL Research University, Collège de France, F-75005 Paris France

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M. C. Heintze

M. C. Heintze

LIGO Livingston Observatory, Livingston, LA 70754 USA

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H. Heitmann

H. Heitmann

Artemis, Université Côte d'Azur, CNRS, Observatoire Côte d'Azur, CS 34229 Nice cedex 4, France

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P. Hello

P. Hello

LAL, Univ. Paris-Sud, CNRS/IN2P3, Université Paris-Saclay, Orsay, France

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G. Hemming

G. Hemming

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

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M. Hendry

M. Hendry

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

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I. S. Heng

I. S. Heng

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

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J. Hennig

J. Hennig

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

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J. Henry

J. Henry

Rochester Institute of Technology, Rochester, NY 14623 USA

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A. W. Heptonstall

A. W. Heptonstall

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

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M. Heurs

M. Heurs

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-30167 Hannover, Germany

Leibniz Universität Hannover, D-30167 Hannover Germany

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S. Hild

S. Hild

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

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D. Hoak

D. Hoak

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

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D. Hofman

D. Hofman

Laboratoire des Matériaux Avancés (LMA), CNRS/IN2P3, F-69622 Villeurbanne France

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K. Holt

K. Holt

LIGO Livingston Observatory, Livingston, LA 70754 USA

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D. E. Holz

D. E. Holz

University of Chicago, Chicago, IL 60637 USA

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P. Hopkins

P. Hopkins

Cardiff University, Cardiff CF24 3AA, United Kingdom

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J. Hough

J. Hough

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

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E. A. Houston

E. A. Houston

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

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E. J. Howell

E. J. Howell

University of Western Australia, Crawley, Western Australia 6009 Australia

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Y. M. Hu

Y. M. Hu

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-30167 Hannover, Germany

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S. Huang

S. Huang

National Tsing Hua University, Hsinchu City 30013 Taiwan, Republic of China

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E. A. Huerta

E. A. Huerta

NCSA, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801 USA

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D. Huet

D. Huet

LAL, Univ. Paris-Sud, CNRS/IN2P3, Université Paris-Saclay, Orsay, France

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B. Hughey

B. Hughey

Embry-Riddle Aeronautical University, Prescott, AZ 86301 USA

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S. Husa

S. Husa

Universitat de les Illes Balears, IAC3—IEEC, E-07122 Palma de Mallorca Spain

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S. H. Huttner

S. H. Huttner

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

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T. Huynh-Dinh

T. Huynh-Dinh

LIGO Livingston Observatory, Livingston, LA 70754 USA

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N. Indik

N. Indik

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-30167 Hannover, Germany

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D. R. Ingram

D. R. Ingram

LIGO Hanford Observatory, Richland, WA 99352 USA

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R. Inta

R. Inta

Texas Tech University, Lubbock, TX 79409 USA

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H. N. Isa

H. N. Isa

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

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J.-M. Isac

J.-M. Isac

Laboratoire Kastler Brossel, UPMC-Sorbonne Universités, CNRS, ENS-PSL Research University, Collège de France, F-75005 Paris France

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M. Isi

M. Isi

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

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T. Isogai

T. Isogai

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

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B. R. Iyer

B. R. Iyer

International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore 560012 India

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K. Izumi

K. Izumi

LIGO Hanford Observatory, Richland, WA 99352 USA

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T. Jacqmin

T. Jacqmin

Laboratoire Kastler Brossel, UPMC-Sorbonne Universités, CNRS, ENS-PSL Research University, Collège de France, F-75005 Paris France

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H. Jang

H. Jang

Korea Institute of Science and Technology Information, Daejeon 305-806 Korea

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K. Jani

K. Jani

Center for Relativistic Astrophysics and School of Physics, Georgia Institute of Technology, Atlanta, GA 30332 USA

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P. Jaranowski

P. Jaranowski

University of Białystok, 15-424 Białystok, Poland

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S. Jawahar

S. Jawahar

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

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L. Jian

L. Jian

University of Western Australia, Crawley, Western Australia 6009 Australia

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F. Jiménez-Forteza

F. Jiménez-Forteza

Universitat de les Illes Balears, IAC3—IEEC, E-07122 Palma de Mallorca Spain

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W. W. Johnson

W. W. Johnson

Louisiana State University, Baton Rouge, LA 70803 USA

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D. I. Jones

D. I. Jones

University of Southampton, Southampton SO17 1BJ United Kingdom

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R. Jones

R. Jones

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

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R. J. G. Jonker

R. J. G. Jonker

Nikhef, Science Park, 1098 XG, Amsterdam, The Netherlands

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L. Ju

L. Ju

University of Western Australia, Crawley, Western Australia 6009 Australia

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Haris K

Haris K

IISER-TVM, CET Campus, Trivandrum, Kerala 695016 India

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C. V. Kalaghatgi

C. V. Kalaghatgi

Cardiff University, Cardiff CF24 3AA, United Kingdom

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V. Kalogera

V. Kalogera

Center for Interdisciplinary Exploration & Research in Astrophysics (CIERA), Northwestern University, Evanston, IL 60208 USA

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S. Kandhasamy

S. Kandhasamy

The University of Mississippi, University, MS 38677 USA

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G. Kang

G. Kang

Korea Institute of Science and Technology Information, Daejeon 305-806 Korea

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J. B. Kanner

J. B. Kanner

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

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S. J. Kapadia

S. J. Kapadia

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-30167 Hannover, Germany

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S. Karki

S. Karki

University of Oregon, Eugene, OR 97403 USA

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K. S. Karvinen

K. S. Karvinen

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-30167 Hannover, Germany

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M. Kasprzack

M. Kasprzack

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

Louisiana State University, Baton Rouge, LA 70803 USA

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E. Katsavounidis

E. Katsavounidis

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

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W. Katzman

W. Katzman

LIGO Livingston Observatory, Livingston, LA 70754 USA

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S. Kaufer

S. Kaufer

Leibniz Universität Hannover, D-30167 Hannover Germany

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T. Kaur

T. Kaur

University of Western Australia, Crawley, Western Australia 6009 Australia

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K. Kawabe

K. Kawabe

LIGO Hanford Observatory, Richland, WA 99352 USA

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F. Kéfélian

F. Kéfélian

Artemis, Université Côte d'Azur, CNRS, Observatoire Côte d'Azur, CS 34229 Nice cedex 4, France

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M. S. Kehl

M. S. Kehl

Canadian Institute for Theoretical Astrophysics, University of Toronto, Toronto, Ontario M5S 3H8 Canada

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D. Keitel

D. Keitel

Universitat de les Illes Balears, IAC3—IEEC, E-07122 Palma de Mallorca Spain

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D. B. Kelley

D. B. Kelley

Syracuse University, Syracuse, NY 13244 USA

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W. Kells

W. Kells

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

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R. Kennedy

R. Kennedy

The University of Sheffield, Sheffield S10 2TN United Kingdom

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J. S. Key

J. S. Key

The University of Texas Rio Grande Valley, Brownsville, TX 78520 USA

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F. Y. Khalili

F. Y. Khalili

Faculty of Physics, Lomonosov Moscow State University, Moscow 119991 Russia

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I. Khan

I. Khan

INFN, Gran Sasso Science Institute, I-67100 L'Aquila Italy

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S. Khan

S. Khan

Cardiff University, Cardiff CF24 3AA, United Kingdom

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Z. Khan

Z. Khan

Institute for Plasma Research, Bhat, Gandhinagar 382428 India

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E. A. Khazanov

E. A. Khazanov

Institute of Applied Physics, Nizhny Novgorod, 603950 Russia

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N. Kijbunchoo

N. Kijbunchoo

LIGO Hanford Observatory, Richland, WA 99352 USA

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Chi-Woong Kim

Chi-Woong Kim

Korea Institute of Science and Technology Information, Daejeon 305-806 Korea

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Chunglee Kim

Chunglee Kim

Korea Institute of Science and Technology Information, Daejeon 305-806 Korea

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J. Kim

J. Kim

Pusan National University, Busan 609-735 Korea

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K. Kim

K. Kim

Hanyang University, Seoul 133-791 Korea

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N. Kim

N. Kim

Stanford University, Stanford, CA 94305 USA

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W. Kim

W. Kim

University of Adelaide, Adelaide, South Australia 5005 Australia

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Y.-M. Kim

Y.-M. Kim

Pusan National University, Busan 609-735 Korea

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S. J. Kimbrell

S. J. Kimbrell

Center for Relativistic Astrophysics and School of Physics, Georgia Institute of Technology, Atlanta, GA 30332 USA

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E. J. King

E. J. King

University of Adelaide, Adelaide, South Australia 5005 Australia

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P. J. King

P. J. King

LIGO Hanford Observatory, Richland, WA 99352 USA

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J. S. Kissel

J. S. Kissel

LIGO Hanford Observatory, Richland, WA 99352 USA

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B. Klein

B. Klein

Center for Interdisciplinary Exploration & Research in Astrophysics (CIERA), Northwestern University, Evanston, IL 60208 USA

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L. Kleybolte

L. Kleybolte

Universität Hamburg, D-22761 Hamburg Germany

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S. Klimenko

S. Klimenko

University of Florida, Gainesville, FL, 32611 USA

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S. M. Koehlenbeck

S. M. Koehlenbeck

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-30167 Hannover, Germany

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S. Koley

S. Koley

Nikhef, Science Park, 1098 XG, Amsterdam, The Netherlands

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V. Kondrashov

V. Kondrashov

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

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A. Kontos

A. Kontos

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

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M. Korobko

M. Korobko

Universität Hamburg, D-22761 Hamburg Germany

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W. Z. Korth

W. Z. Korth

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

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I. Kowalska

I. Kowalska

Astronomical Observatory Warsaw University, 00-478 Warsaw Poland

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D. B. Kozak

D. B. Kozak

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

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V. Kringel

V. Kringel

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-30167 Hannover, Germany

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B. Krishnan

B. Krishnan

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-30167 Hannover, Germany

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A. Królak

A. Królak

NCBJ, 05-400 Świerk-Otwock Poland

IM-PAN, 00-956 Warsaw Poland

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C. Krueger

C. Krueger

Leibniz Universität Hannover, D-30167 Hannover Germany

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G. Kuehn

G. Kuehn

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-30167 Hannover, Germany

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P. Kumar

P. Kumar

Canadian Institute for Theoretical Astrophysics, University of Toronto, Toronto, Ontario M5S 3H8 Canada

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R. Kumar

R. Kumar

Institute for Plasma Research, Bhat, Gandhinagar 382428 India

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L. Kuo

L. Kuo

National Tsing Hua University, Hsinchu City 30013 Taiwan, Republic of China

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A. Kutynia

A. Kutynia

NCBJ, 05-400 Świerk-Otwock Poland

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B. D. Lackey

B. D. Lackey

Syracuse University, Syracuse, NY 13244 USA

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M. Landry

M. Landry

LIGO Hanford Observatory, Richland, WA 99352 USA

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J. Lange

J. Lange

Rochester Institute of Technology, Rochester, NY 14623 USA

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B. Lantz

B. Lantz

Stanford University, Stanford, CA 94305 USA

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P. D. Lasky

P. D. Lasky

Monash University, Victoria 3800 Australia

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M. Laxen

M. Laxen

LIGO Livingston Observatory, Livingston, LA 70754 USA

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A. Lazzarini

A. Lazzarini

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

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C. Lazzaro

C. Lazzaro

INFN, Sezione di Padova, I-35131 Padova Italy

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P. Leaci

P. Leaci

Università di Roma “La Sapienza”, I-00185 Roma Italy

INFN, Sezione di Roma, I-00185 Roma Italy

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S. Leavey

S. Leavey

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

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E. O. Lebigot

E. O. Lebigot

APC, AstroParticule et Cosmologie, Université Paris Diderot, CNRS/IN2P3, CEA/Irfu, Observatoire de Paris, Sorbonne Paris Cité, F-75205 Paris Cedex 13, France

Tsinghua University, Beijing 100084 China

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C. H. Lee

C. H. Lee

Pusan National University, Busan 609-735 Korea

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H. K. Lee

H. K. Lee

Hanyang University, Seoul 133-791 Korea

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H. M. Lee

H. M. Lee

Seoul National University, Seoul 151-742 Korea

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K. Lee

K. Lee

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

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A. Lenon

A. Lenon

Syracuse University, Syracuse, NY 13244 USA

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M. Leonardi

M. Leonardi

Università di Trento, Dipartimento di Fisica, I-38123 Povo Trento, Italy

INFN, Trento Institute for Fundamental Physics and Applications, I-38123 Povo Trento, Italy

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J. R. Leong

J. R. Leong

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-30167 Hannover, Germany

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N. Leroy

N. Leroy

LAL, Univ. Paris-Sud, CNRS/IN2P3, Université Paris-Saclay, Orsay, France

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N. Letendre

N. Letendre

Laboratoire d'Annecy-le-Vieux de Physique des Particules (LAPP), Université Savoie Mont Blanc, CNRS/IN2P3, F-74941 Annecy-le-Vieux France

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Y. Levin

Y. Levin

Monash University, Victoria 3800 Australia

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J. B. Lewis

J. B. Lewis

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

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T. G. F. Li

T. G. F. Li

The Chinese University of Hong Kong, Shatin, NT, Hong Kong SAR, China

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A. Libson

A. Libson

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

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T. B. Littenberg

T. B. Littenberg

University of Alabama in Huntsville, Huntsville, AL 35899 USA

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N. A. Lockerbie

N. A. Lockerbie

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

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A. L. Lombardi

A. L. Lombardi

University of Massachusetts-Amherst, Amherst, MA 01003 USA

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L. T. London

L. T. London

Cardiff University, Cardiff CF24 3AA, United Kingdom

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J. E. Lord

J. E. Lord

Syracuse University, Syracuse, NY 13244 USA

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M. Lorenzini

M. Lorenzini

INFN, Gran Sasso Science Institute, I-67100 L'Aquila Italy

INFN, Sezione di Roma Tor Vergata, I-00133 Roma Italy

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V. Loriette

V. Loriette

ESPCI, CNRS, F-75005 Paris France

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M. Lormand

M. Lormand

LIGO Livingston Observatory, Livingston, LA 70754 USA

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G. Losurdo

G. Losurdo

INFN, Sezione di Firenze, I-50019 Sesto Fiorentino Firenze, Italy

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J. D. Lough

J. D. Lough

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-30167 Hannover, Germany

Leibniz Universität Hannover, D-30167 Hannover Germany

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H. Lück

H. Lück

Leibniz Universität Hannover, D-30167 Hannover Germany

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-30167 Hannover, Germany

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A. P. Lundgren

A. P. Lundgren

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-30167 Hannover, Germany

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R. Lynch

R. Lynch

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

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Y. Ma

Y. Ma

University of Western Australia, Crawley, Western Australia 6009 Australia

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B. Machenschalk

B. Machenschalk

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-30167 Hannover, Germany

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M. MacInnis

M. MacInnis

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

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D. M. Macleod

D. M. Macleod

Louisiana State University, Baton Rouge, LA 70803 USA

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F. Magaña-Sandoval

F. Magaña-Sandoval

Syracuse University, Syracuse, NY 13244 USA

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L. Magaña Zertuche

L. Magaña Zertuche

Syracuse University, Syracuse, NY 13244 USA

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R. M. Magee

R. M. Magee

Washington State University, Pullman, WA 99164 USA

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E. Majorana

E. Majorana

INFN, Sezione di Roma, I-00185 Roma Italy

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I. Maksimovic

I. Maksimovic

ESPCI, CNRS, F-75005 Paris France

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V. Malvezzi

V. Malvezzi

Università di Roma Tor Vergata, I-00133 Roma Italy

INFN, Sezione di Roma Tor Vergata, I-00133 Roma Italy

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N. Man

N. Man

Artemis, Université Côte d'Azur, CNRS, Observatoire Côte d'Azur, CS 34229 Nice cedex 4, France

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V. Mandic

V. Mandic

University of Minnesota, Minneapolis, MN 55455 USA

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V. Mangano

V. Mangano

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

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G. L. Mansell

G. L. Mansell

Australian National University, Canberra, Australian Capital Territory 0200, Australia

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M. Manske

M. Manske

University of Wisconsin-Milwaukee, Milwaukee, WI 53201 USA

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M. Mantovani

M. Mantovani

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

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F. Marchesoni

F. Marchesoni

Università di Camerino, Dipartimento di Fisica, I-62032 Camerino Italy

INFN, Sezione di Perugia, I-06123 Perugia Italy

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F. Marion

F. Marion

Laboratoire d'Annecy-le-Vieux de Physique des Particules (LAPP), Université Savoie Mont Blanc, CNRS/IN2P3, F-74941 Annecy-le-Vieux France

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S. Márka

S. Márka

Columbia University, New York, NY 10027 USA

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Z. Márka

Z. Márka

Columbia University, New York, NY 10027 USA

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A. S. Markosyan

A. S. Markosyan

Stanford University, Stanford, CA 94305 USA

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E. Maros

E. Maros

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

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F. Martelli

F. Martelli

Università degli Studi di Urbino “Carlo Bo”, I-61029 Urbino Italy

INFN, Sezione di Firenze, I-50019 Sesto Fiorentino Firenze, Italy

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L. Martellini

L. Martellini

Artemis, Université Côte d'Azur, CNRS, Observatoire Côte d'Azur, CS 34229 Nice cedex 4, France

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I. W. Martin

I. W. Martin

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

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D. V. Martynov

D. V. Martynov

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

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J. N. Marx

J. N. Marx

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

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K. Mason

K. Mason

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

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A. Masserot

A. Masserot

Laboratoire d'Annecy-le-Vieux de Physique des Particules (LAPP), Université Savoie Mont Blanc, CNRS/IN2P3, F-74941 Annecy-le-Vieux France

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T. J. Massinger

T. J. Massinger

Syracuse University, Syracuse, NY 13244 USA

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M. Masso-Reid

M. Masso-Reid

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

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S. Mastrogiovanni

S. Mastrogiovanni

Università di Roma “La Sapienza”, I-00185 Roma Italy

INFN, Sezione di Roma, I-00185 Roma Italy

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F. Matichard

F. Matichard

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

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L. Matone

L. Matone

Columbia University, New York, NY 10027 USA

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N. Mavalvala

N. Mavalvala

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

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N. Mazumder

N. Mazumder

Washington State University, Pullman, WA 99164 USA

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R. McCarthy

R. McCarthy

LIGO Hanford Observatory, Richland, WA 99352 USA

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D. E. McClelland

D. E. McClelland

Australian National University, Canberra, Australian Capital Territory 0200, Australia

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S. McCormick

S. McCormick

LIGO Livingston Observatory, Livingston, LA 70754 USA

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S. C. McGuire

S. C. McGuire

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

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G. McIntyre

G. McIntyre

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

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J. McIver

J. McIver

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

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D. J. McManus

D. J. McManus

Australian National University, Canberra, Australian Capital Territory 0200, Australia

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T. McRae

T. McRae

Australian National University, Canberra, Australian Capital Territory 0200, Australia

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D. Meacher

D. Meacher

The Pennsylvania State University, University Park, PA 16802 USA

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G. D. Meadors

G. D. Meadors

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-14476 Potsdam-Golm Germany

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-30167 Hannover, Germany

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J. Meidam

J. Meidam

Nikhef, Science Park, 1098 XG, Amsterdam, The Netherlands

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A. Melatos

A. Melatos

The University of Melbourne, Parkville, Victoria 3010 Australia

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G. Mendell

G. Mendell

LIGO Hanford Observatory, Richland, WA 99352 USA

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R. A. Mercer

R. A. Mercer

University of Wisconsin-Milwaukee, Milwaukee, WI 53201 USA

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E. L. Merilh

E. L. Merilh

LIGO Hanford Observatory, Richland, WA 99352 USA

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M. Merzougui

M. Merzougui

Artemis, Université Côte d'Azur, CNRS, Observatoire Côte d'Azur, CS 34229 Nice cedex 4, France

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S. Meshkov

S. Meshkov

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

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C. Messenger

C. Messenger

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

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C. Messick

C. Messick

The Pennsylvania State University, University Park, PA 16802 USA

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R. Metzdorff

R. Metzdorff

Laboratoire Kastler Brossel, UPMC-Sorbonne Universités, CNRS, ENS-PSL Research University, Collège de France, F-75005 Paris France

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P. M. Meyers

P. M. Meyers

University of Minnesota, Minneapolis, MN 55455 USA

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F. Mezzani

F. Mezzani

INFN, Sezione di Roma, I-00185 Roma Italy

Università di Roma “La Sapienza”, I-00185 Roma Italy

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H. Miao

H. Miao

University of Birmingham, Birmingham B15 2TT United Kingdom

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C. Michel

C. Michel

Laboratoire des Matériaux Avancés (LMA), CNRS/IN2P3, F-69622 Villeurbanne France

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H. Middleton

H. Middleton

University of Birmingham, Birmingham B15 2TT United Kingdom

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E. E. Mikhailov

E. E. Mikhailov

College of William and Mary, Williamsburg, VA 23187 USA

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L. Milano

L. Milano

Università di Napoli “Federico II”, Complesso Universitario di Monte S.Angelo, I-80126 Napoli Italy

INFN, Sezione di Napoli, Complesso Universitario di Monte S.Angelo, I-80126 Napoli Italy

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A. L. Miller

A. L. Miller

University of Florida, Gainesville, FL, 32611 USA

Università di Roma “La Sapienza”, I-00185 Roma Italy

INFN, Sezione di Roma, I-00185 Roma Italy

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A. Miller

A. Miller

Center for Interdisciplinary Exploration & Research in Astrophysics (CIERA), Northwestern University, Evanston, IL 60208 USA

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B. B. Miller

B. B. Miller

Center for Interdisciplinary Exploration & Research in Astrophysics (CIERA), Northwestern University, Evanston, IL 60208 USA

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J. Miller

J. Miller

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

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M. Millhouse

M. Millhouse

Montana State University, Bozeman, MT 59717 USA

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Y. Minenkov

Y. Minenkov

INFN, Sezione di Roma Tor Vergata, I-00133 Roma Italy

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J. Ming

J. Ming

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-14476 Potsdam-Golm Germany

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S. Mirshekari

S. Mirshekari

Instituto de Fí sica Teórica, University Estadual Paulista/ICTP South American Institute for Fundamental Research, São Paulo, SP 01140-070 Brazil

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C. Mishra

C. Mishra

International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore 560012 India

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S. Mitra

S. Mitra

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

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V. P. Mitrofanov

V. P. Mitrofanov

Faculty of Physics, Lomonosov Moscow State University, Moscow 119991 Russia

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G. Mitselmakher

G. Mitselmakher

University of Florida, Gainesville, FL, 32611 USA

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R. Mittleman

R. Mittleman

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

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A. Moggi

A. Moggi

INFN, Sezione di Pisa, I-56127 Pisa Italy

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M. Mohan

M. Mohan

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

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S. R. P. Mohapatra

S. R. P. Mohapatra

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

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M. Montani

M. Montani

Università degli Studi di Urbino “Carlo Bo”, I-61029 Urbino Italy

INFN, Sezione di Firenze, I-50019 Sesto Fiorentino Firenze, Italy

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B. C. Moore

B. C. Moore

Montclair State University, Montclair, NJ 07043 USA

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C. J. Moore

C. J. Moore

University of Cambridge, Cambridge, CB2 1TN, United Kingdom

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D. Moraru

D. Moraru

LIGO Hanford Observatory, Richland, WA 99352 USA

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G. Moreno

G. Moreno

LIGO Hanford Observatory, Richland, WA 99352 USA

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S. R. Morriss

S. R. Morriss

The University of Texas Rio Grande Valley, Brownsville, TX 78520 USA

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K. Mossavi

K. Mossavi

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-30167 Hannover, Germany

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B. Mours

B. Mours

Laboratoire d'Annecy-le-Vieux de Physique des Particules (LAPP), Université Savoie Mont Blanc, CNRS/IN2P3, F-74941 Annecy-le-Vieux France

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C. M. Mow-Lowry

C. M. Mow-Lowry

University of Birmingham, Birmingham B15 2TT United Kingdom

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G. Mueller

G. Mueller

University of Florida, Gainesville, FL, 32611 USA

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A. W. Muir

A. W. Muir

Cardiff University, Cardiff CF24 3AA, United Kingdom

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Arunava Mukherjee

Arunava Mukherjee

International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore 560012 India

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D. Mukherjee

D. Mukherjee

University of Wisconsin-Milwaukee, Milwaukee, WI 53201 USA

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S. Mukherjee

S. Mukherjee

The University of Texas Rio Grande Valley, Brownsville, TX 78520 USA

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N. Mukund

N. Mukund

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

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A. Mullavey

A. Mullavey

LIGO Livingston Observatory, Livingston, LA 70754 USA

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J. Munch

J. Munch

University of Adelaide, Adelaide, South Australia 5005 Australia

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D. J. Murphy

D. J. Murphy

Columbia University, New York, NY 10027 USA

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P. G. Murray

P. G. Murray

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

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A. Mytidis

A. Mytidis

University of Florida, Gainesville, FL, 32611 USA

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I. Nardecchia

I. Nardecchia

Università di Roma Tor Vergata, I-00133 Roma Italy

INFN, Sezione di Roma Tor Vergata, I-00133 Roma Italy

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L. Naticchioni

L. Naticchioni

Università di Roma “La Sapienza”, I-00185 Roma Italy

INFN, Sezione di Roma, I-00185 Roma Italy

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R. K. Nayak

R. K. Nayak

IISER-Kolkata, Mohanpur, West Bengal 741252 India

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K. Nedkova

K. Nedkova

University of Massachusetts-Amherst, Amherst, MA 01003 USA

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G. Nelemans

G. Nelemans

Department of Astrophysics/IMAPP, Radboud University Nijmegen, P.O. Box 9010, 6500 GL, Nijmegen, The Netherlands

Nikhef, Science Park, 1098 XG, Amsterdam, The Netherlands

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T. J. N. Nelson

T. J. N. Nelson

LIGO Livingston Observatory, Livingston, LA 70754 USA

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M. Neri

M. Neri

Università degli Studi di Genova, I-16146 Genova Italy

INFN, Sezione di Genova, I-16146 Genova Italy

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A. Neunzert

A. Neunzert

University of Michigan, Ann Arbor, MI 48109 USA

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G. Newton

G. Newton

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

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T. T. Nguyen

T. T. Nguyen

Australian National University, Canberra, Australian Capital Territory 0200, Australia

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A. B. Nielsen

A. B. Nielsen

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-30167 Hannover, Germany

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S. Nissanke

S. Nissanke

Department of Astrophysics/IMAPP, Radboud University Nijmegen, P.O. Box 9010, 6500 GL, Nijmegen, The Netherlands

Nikhef, Science Park, 1098 XG, Amsterdam, The Netherlands

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A. Nitz

A. Nitz

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-30167 Hannover, Germany

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F. Nocera

F. Nocera

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

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D. Nolting

D. Nolting

LIGO Livingston Observatory, Livingston, LA 70754 USA

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M. E. N. Normandin

M. E. N. Normandin

The University of Texas Rio Grande Valley, Brownsville, TX 78520 USA

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L. K. Nuttall

L. K. Nuttall

Syracuse University, Syracuse, NY 13244 USA

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J. Oberling

J. Oberling

LIGO Hanford Observatory, Richland, WA 99352 USA

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E. Ochsner

E. Ochsner

University of Wisconsin-Milwaukee, Milwaukee, WI 53201 USA

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J. O'Dell

J. O'Dell

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

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E. Oelker

E. Oelker

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

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G. H. Ogin

G. H. Ogin

Whitman College, 345 Boyer Avenue, Walla Walla, WA 99362 USA

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J. J. Oh

J. J. Oh

National Institute for Mathematical Sciences, Daejeon 305-390 Korea

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S. H. Oh

S. H. Oh

National Institute for Mathematical Sciences, Daejeon 305-390 Korea

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F. Ohme

F. Ohme

Cardiff University, Cardiff CF24 3AA, United Kingdom

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M. Oliver

M. Oliver

Universitat de les Illes Balears, IAC3—IEEC, E-07122 Palma de Mallorca Spain

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P. Oppermann

P. Oppermann

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-30167 Hannover, Germany

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Richard J. Oram

Richard J. Oram

LIGO Livingston Observatory, Livingston, LA 70754 USA

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B. O'Reilly

B. O'Reilly

LIGO Livingston Observatory, Livingston, LA 70754 USA

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R. O'Shaughnessy

R. O'Shaughnessy

Rochester Institute of Technology, Rochester, NY 14623 USA

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D. J. Ottaway

D. J. Ottaway

University of Adelaide, Adelaide, South Australia 5005 Australia

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H. Overmier

H. Overmier

LIGO Livingston Observatory, Livingston, LA 70754 USA

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B. J. Owen

B. J. Owen

Texas Tech University, Lubbock, TX 79409 USA

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A. Pai

A. Pai

IISER-TVM, CET Campus, Trivandrum, Kerala 695016 India

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S. A. Pai

S. A. Pai

RRCAT, Indore, MP 452013 India

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J. R. Palamos

J. R. Palamos

University of Oregon, Eugene, OR 97403 USA

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O. Palashov

O. Palashov

Institute of Applied Physics, Nizhny Novgorod, 603950 Russia

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C. Palomba

C. Palomba

INFN, Sezione di Roma, I-00185 Roma Italy

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A. Pal-Singh

A. Pal-Singh

Universität Hamburg, D-22761 Hamburg Germany

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H. Pan

H. Pan

National Tsing Hua University, Hsinchu City 30013 Taiwan, Republic of China

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C. Pankow

C. Pankow

Center for Interdisciplinary Exploration & Research in Astrophysics (CIERA), Northwestern University, Evanston, IL 60208 USA

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F. Pannarale

F. Pannarale

Cardiff University, Cardiff CF24 3AA, United Kingdom

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B. C. Pant

B. C. Pant

RRCAT, Indore, MP 452013 India

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F. Paoletti

F. Paoletti

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

INFN, Sezione di Pisa, I-56127 Pisa Italy

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A. Paoli

A. Paoli

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

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M. A. Papa

M. A. Papa

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-14476 Potsdam-Golm Germany

University of Wisconsin-Milwaukee, Milwaukee, WI 53201 USA

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-30167 Hannover, Germany

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H. R. Paris

H. R. Paris

Stanford University, Stanford, CA 94305 USA

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W. Parker

W. Parker

LIGO Livingston Observatory, Livingston, LA 70754 USA

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D. Pascucci

D. Pascucci

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

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A. Pasqualetti

A. Pasqualetti

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

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R. Passaquieti

R. Passaquieti

Università di Pisa, I-56127 Pisa Italy

INFN, Sezione di Pisa, I-56127 Pisa Italy

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D. Passuello

D. Passuello

INFN, Sezione di Pisa, I-56127 Pisa Italy

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B. Patricelli

B. Patricelli

Università di Pisa, I-56127 Pisa Italy

INFN, Sezione di Pisa, I-56127 Pisa Italy

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Z. Patrick

Z. Patrick

Stanford University, Stanford, CA 94305 USA

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B. L. Pearlstone

B. L. Pearlstone

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

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M. Pedraza

M. Pedraza

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

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R. Pedurand

R. Pedurand

Laboratoire des Matériaux Avancés (LMA), CNRS/IN2P3, F-69622 Villeurbanne France

Université de Lyon, F-69361 Lyon France

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L. Pekowsky

L. Pekowsky

Syracuse University, Syracuse, NY 13244 USA

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A. Pele

A. Pele

LIGO Livingston Observatory, Livingston, LA 70754 USA

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S. Penn

S. Penn

Hobart and William Smith Colleges, Geneva, NY 14456 USA

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A. Perreca

A. Perreca

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

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L. M. Perri

L. M. Perri

Center for Interdisciplinary Exploration & Research in Astrophysics (CIERA), Northwestern University, Evanston, IL 60208 USA

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M. Phelps

M. Phelps

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

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O. J. Piccinni

O. J. Piccinni

Università di Roma “La Sapienza”, I-00185 Roma Italy

INFN, Sezione di Roma, I-00185 Roma Italy

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M. Pichot

M. Pichot

Artemis, Université Côte d'Azur, CNRS, Observatoire Côte d'Azur, CS 34229 Nice cedex 4, France

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F. Piergiovanni

F. Piergiovanni

Università degli Studi di Urbino “Carlo Bo”, I-61029 Urbino Italy

INFN, Sezione di Firenze, I-50019 Sesto Fiorentino Firenze, Italy

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V. Pierro

V. Pierro

University of Sannio at Benevento, I-82100 Benevento, Italy and INFN, Sezione di Napoli, I-80100 Napoli, Italy

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G. Pillant

G. Pillant

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

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L. Pinard

L. Pinard

Laboratoire des Matériaux Avancés (LMA), CNRS/IN2P3, F-69622 Villeurbanne France

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I. M. Pinto

I. M. Pinto

University of Sannio at Benevento, I-82100 Benevento, Italy and INFN, Sezione di Napoli, I-80100 Napoli, Italy

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M. Pitkin

M. Pitkin

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

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M. Poe

M. Poe

University of Wisconsin-Milwaukee, Milwaukee, WI 53201 USA

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R. Poggiani

R. Poggiani

Università di Pisa, I-56127 Pisa Italy

INFN, Sezione di Pisa, I-56127 Pisa Italy

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P. Popolizio

P. Popolizio

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

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A. Post

A. Post

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-30167 Hannover, Germany

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J. Powell

J. Powell

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

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J. Prasad

J. Prasad

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

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J. Pratt

J. Pratt

Embry-Riddle Aeronautical University, Prescott, AZ 86301 USA

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V. Predoi

V. Predoi

Cardiff University, Cardiff CF24 3AA, United Kingdom

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T. Prestegard

T. Prestegard

University of Minnesota, Minneapolis, MN 55455 USA

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L. R. Price

L. R. Price

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

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M. Prijatelj

M. Prijatelj

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-30167 Hannover, Germany

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

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M. Principe

M. Principe

University of Sannio at Benevento, I-82100 Benevento, Italy and INFN, Sezione di Napoli, I-80100 Napoli, Italy

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S. Privitera

S. Privitera

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-14476 Potsdam-Golm Germany

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R. Prix

R. Prix

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-30167 Hannover, Germany

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G. A. Prodi

G. A. Prodi

Università di Trento, Dipartimento di Fisica, I-38123 Povo Trento, Italy

INFN, Trento Institute for Fundamental Physics and Applications, I-38123 Povo Trento, Italy

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L. Prokhorov

L. Prokhorov

Faculty of Physics, Lomonosov Moscow State University, Moscow 119991 Russia

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O. Puncken

O. Puncken

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-30167 Hannover, Germany

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M. Punturo

M. Punturo

INFN, Sezione di Perugia, I-06123 Perugia Italy

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P. Puppo

P. Puppo

INFN, Sezione di Roma, I-00185 Roma Italy

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M. Pürrer

M. Pürrer

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-14476 Potsdam-Golm Germany

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H. Qi

H. Qi

University of Wisconsin-Milwaukee, Milwaukee, WI 53201 USA

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J. Qin

J. Qin

University of Western Australia, Crawley, Western Australia 6009 Australia

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S. Qiu

S. Qiu

Monash University, Victoria 3800 Australia

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V. Quetschke

V. Quetschke

The University of Texas Rio Grande Valley, Brownsville, TX 78520 USA

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E. A. Quintero

E. A. Quintero

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

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R. Quitzow-James

R. Quitzow-James

University of Oregon, Eugene, OR 97403 USA

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F. J. Raab

F. J. Raab

LIGO Hanford Observatory, Richland, WA 99352 USA

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D. S. Rabeling

D. S. Rabeling

Australian National University, Canberra, Australian Capital Territory 0200, Australia

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H. Radkins

H. Radkins

LIGO Hanford Observatory, Richland, WA 99352 USA

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P. Raffai

P. Raffai

MTA Eötvös University, “Lendulet” Astrophysics Research Group, Budapest 1117 Hungary

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S. Raja

S. Raja

RRCAT, Indore, MP 452013 India

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C. Rajan

C. Rajan

RRCAT, Indore, MP 452013 India

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M. Rakhmanov

M. Rakhmanov

The University of Texas Rio Grande Valley, Brownsville, TX 78520 USA

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P. Rapagnani

P. Rapagnani

Università di Roma “La Sapienza”, I-00185 Roma Italy

INFN, Sezione di Roma, I-00185 Roma Italy

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V. Raymond

V. Raymond

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-14476 Potsdam-Golm Germany

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M. Razzano

M. Razzano

Università di Pisa, I-56127 Pisa Italy

INFN, Sezione di Pisa, I-56127 Pisa Italy

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V. Re

V. Re

Università di Roma Tor Vergata, I-00133 Roma Italy

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J. Read

J. Read

California State University Fullerton, Fullerton, CA 92831 USA

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C. M. Reed

C. M. Reed

LIGO Hanford Observatory, Richland, WA 99352 USA

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T. Regimbau

T. Regimbau

Artemis, Université Côte d'Azur, CNRS, Observatoire Côte d'Azur, CS 34229 Nice cedex 4, France

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L. Rei

L. Rei

INFN, Sezione di Genova, I-16146 Genova Italy

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S. Reid

S. Reid

SUPA, University of the West of Scotland, Paisley PA1 2BE United Kingdom

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H. Rew

H. Rew

College of William and Mary, Williamsburg, VA 23187 USA

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S. D. Reyes

S. D. Reyes

Syracuse University, Syracuse, NY 13244 USA

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F. Ricci

F. Ricci

Università di Roma “La Sapienza”, I-00185 Roma Italy

INFN, Sezione di Roma, I-00185 Roma Italy

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K. Riles

K. Riles

University of Michigan, Ann Arbor, MI 48109 USA

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M. Rizzo

M. Rizzo

Rochester Institute of Technology, Rochester, NY 14623 USA

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N. A. Robertson

N. A. Robertson

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

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

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R. Robie

R. Robie

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

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F. Robinet

F. Robinet

LAL, Univ. Paris-Sud, CNRS/IN2P3, Université Paris-Saclay, Orsay, France

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A. Rocchi

A. Rocchi

INFN, Sezione di Roma Tor Vergata, I-00133 Roma Italy

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L. Rolland

L. Rolland

Laboratoire d'Annecy-le-Vieux de Physique des Particules (LAPP), Université Savoie Mont Blanc, CNRS/IN2P3, F-74941 Annecy-le-Vieux France

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J. G. Rollins

J. G. Rollins

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

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V. J. Roma

V. J. Roma

University of Oregon, Eugene, OR 97403 USA

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J. D. Romano

J. D. Romano

The University of Texas Rio Grande Valley, Brownsville, TX 78520 USA

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R. Romano

R. Romano

Università di Salerno, Fisciano, I-84084 Salerno, Italy

INFN, Sezione di Napoli, Complesso Universitario di Monte S.Angelo, I-80126 Napoli Italy

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G. Romanov

G. Romanov

College of William and Mary, Williamsburg, VA 23187 USA

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J. H. Romie

J. H. Romie

LIGO Livingston Observatory, Livingston, LA 70754 USA

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D. Rosińska

D. Rosińska

Janusz Gil Institute of Astronomy, University of Zielona Góra, 65-265 Zielona Góra, Poland

CAMK-PAN, 00-716 Warsaw Poland

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S. Rowan

S. Rowan

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

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A. Rüdiger

A. Rüdiger

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-30167 Hannover, Germany

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P. Ruggi

P. Ruggi

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

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K. Ryan

K. Ryan

LIGO Hanford Observatory, Richland, WA 99352 USA

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S. Sachdev

S. Sachdev

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

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T. Sadecki

T. Sadecki

LIGO Hanford Observatory, Richland, WA 99352 USA

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L. Sadeghian

L. Sadeghian

University of Wisconsin-Milwaukee, Milwaukee, WI 53201 USA

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M. Sakellariadou

M. Sakellariadou

King's College London, University of London, London WC2R 2LS United Kingdom

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L. Salconi

L. Salconi

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

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M. Saleem

M. Saleem

IISER-TVM, CET Campus, Trivandrum, Kerala 695016 India

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F. Salemi

F. Salemi

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-30167 Hannover, Germany

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A. Samajdar

A. Samajdar

IISER-Kolkata, Mohanpur, West Bengal 741252 India

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L. Sammut

L. Sammut

Monash University, Victoria 3800 Australia

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E. J. Sanchez

E. J. Sanchez

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

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V. Sandberg

V. Sandberg

LIGO Hanford Observatory, Richland, WA 99352 USA

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B. Sandeen

B. Sandeen

Center for Interdisciplinary Exploration & Research in Astrophysics (CIERA), Northwestern University, Evanston, IL 60208 USA

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J. R. Sanders

J. R. Sanders

Syracuse University, Syracuse, NY 13244 USA

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B. Sassolas

B. Sassolas

Laboratoire des Matériaux Avancés (LMA), CNRS/IN2P3, F-69622 Villeurbanne France

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P. R. Saulson

P. R. Saulson

Syracuse University, Syracuse, NY 13244 USA

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O. E. S. Sauter

O. E. S. Sauter

University of Michigan, Ann Arbor, MI 48109 USA

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R. L. Savage

R. L. Savage

LIGO Hanford Observatory, Richland, WA 99352 USA

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A. Sawadsky

A. Sawadsky

Leibniz Universität Hannover, D-30167 Hannover Germany

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P. Schale

P. Schale

University of Oregon, Eugene, OR 97403 USA

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R. Schilling

R. Schilling

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-30167 Hannover, Germany

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J. Schmidt

J. Schmidt

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-30167 Hannover, Germany

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P. Schmidt

P. Schmidt

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

Caltech CaRT, Pasadena, CA 91125 USA

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R. Schnabel

R. Schnabel

Universität Hamburg, D-22761 Hamburg Germany

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R. M. S. Schofield

R. M. S. Schofield

University of Oregon, Eugene, OR 97403 USA

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A. Schönbeck

A. Schönbeck

Universität Hamburg, D-22761 Hamburg Germany

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E. Schreiber

E. Schreiber

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-30167 Hannover, Germany

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D. Schuette

D. Schuette

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-30167 Hannover, Germany

Leibniz Universität Hannover, D-30167 Hannover Germany

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B. F. Schutz

B. F. Schutz

Cardiff University, Cardiff CF24 3AA, United Kingdom

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-14476 Potsdam-Golm Germany

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J. Scott

J. Scott

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

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S. M. Scott

S. M. Scott

Australian National University, Canberra, Australian Capital Territory 0200, Australia

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D. Sellers

D. Sellers

LIGO Livingston Observatory, Livingston, LA 70754 USA

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A. S. Sengupta

A. S. Sengupta

Indian Institute of Technology, Gandhinagar Ahmedabad, Gujarat 382424 India

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D. Sentenac

D. Sentenac

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

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V. Sequino

V. Sequino

Università di Roma Tor Vergata, I-00133 Roma Italy

INFN, Sezione di Roma Tor Vergata, I-00133 Roma Italy

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A. Sergeev

A. Sergeev

Institute of Applied Physics, Nizhny Novgorod, 603950 Russia

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Y. Setyawati

Y. Setyawati

Department of Astrophysics/IMAPP, Radboud University Nijmegen, P.O. Box 9010, 6500 GL, Nijmegen, The Netherlands

Nikhef, Science Park, 1098 XG, Amsterdam, The Netherlands

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D. A. Shaddock

D. A. Shaddock

Australian National University, Canberra, Australian Capital Territory 0200, Australia

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T. Shaffer

T. Shaffer

LIGO Hanford Observatory, Richland, WA 99352 USA

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M. S. Shahriar

M. S. Shahriar

Center for Interdisciplinary Exploration & Research in Astrophysics (CIERA), Northwestern University, Evanston, IL 60208 USA

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M. Shaltev

M. Shaltev

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-30167 Hannover, Germany

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B. Shapiro

B. Shapiro

Stanford University, Stanford, CA 94305 USA

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P. Shawhan

P. Shawhan

University of Maryland, College Park, MD 20742 USA

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A. Sheperd

A. Sheperd

University of Wisconsin-Milwaukee, Milwaukee, WI 53201 USA

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D. H. Shoemaker

D. H. Shoemaker

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

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D. M. Shoemaker

D. M. Shoemaker

Center for Relativistic Astrophysics and School of Physics, Georgia Institute of Technology, Atlanta, GA 30332 USA

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K. Siellez

K. Siellez

Center for Relativistic Astrophysics and School of Physics, Georgia Institute of Technology, Atlanta, GA 30332 USA

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X. Siemens

X. Siemens

University of Wisconsin-Milwaukee, Milwaukee, WI 53201 USA

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M. Sieniawska

M. Sieniawska

CAMK-PAN, 00-716 Warsaw Poland

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D. Sigg

D. Sigg

LIGO Hanford Observatory, Richland, WA 99352 USA

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A. D. Silva

A. D. Silva

Instituto Nacional de Pesquisas Espaciais, 12227-010 São José dos Campos, São Paulo, Brazil

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A. Singer

A. Singer

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

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L. P. Singer

L. P. Singer

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

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A. Singh

A. Singh

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-14476 Potsdam-Golm Germany

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-30167 Hannover, Germany

Leibniz Universität Hannover, D-30167 Hannover Germany

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R. Singh

R. Singh

Louisiana State University, Baton Rouge, LA 70803 USA

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A. Singhal

A. Singhal

INFN, Gran Sasso Science Institute, I-67100 L'Aquila Italy

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A. M. Sintes

A. M. Sintes

Universitat de les Illes Balears, IAC3—IEEC, E-07122 Palma de Mallorca Spain

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B. J. J. Slagmolen

B. J. J. Slagmolen

Australian National University, Canberra, Australian Capital Territory 0200, Australia

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J. R. Smith

J. R. Smith

California State University Fullerton, Fullerton, CA 92831 USA

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N. D. Smith

N. D. Smith

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

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R. J. E. Smith

R. J. E. Smith

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

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E. J. Son

E. J. Son

National Institute for Mathematical Sciences, Daejeon 305-390 Korea

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B. Sorazu

B. Sorazu

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

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F. Sorrentino

F. Sorrentino

INFN, Sezione di Genova, I-16146 Genova Italy

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T. Souradeep

T. Souradeep

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

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A. K. Srivastava

A. K. Srivastava

Institute for Plasma Research, Bhat, Gandhinagar 382428 India

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A. Staley

A. Staley

Columbia University, New York, NY 10027 USA

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M. Steinke

M. Steinke

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-30167 Hannover, Germany

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J. Steinlechner

J. Steinlechner

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

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S. Steinlechner

S. Steinlechner

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

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D. Steinmeyer

D. Steinmeyer

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-30167 Hannover, Germany

Leibniz Universität Hannover, D-30167 Hannover Germany

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B. C. Stephens

B. C. Stephens

University of Wisconsin-Milwaukee, Milwaukee, WI 53201 USA

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R. Stone

R. Stone

The University of Texas Rio Grande Valley, Brownsville, TX 78520 USA

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K. A. Strain

K. A. Strain

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

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N. Straniero

N. Straniero

Laboratoire des Matériaux Avancés (LMA), CNRS/IN2P3, F-69622 Villeurbanne France

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G. Stratta

G. Stratta

Università degli Studi di Urbino “Carlo Bo”, I-61029 Urbino Italy

INFN, Sezione di Firenze, I-50019 Sesto Fiorentino Firenze, Italy

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N. A. Strauss

N. A. Strauss

Carleton College, Northfield, MN 55057 USA

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S. Strigin

S. Strigin

Faculty of Physics, Lomonosov Moscow State University, Moscow 119991 Russia

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R. Sturani

R. Sturani

Instituto de Fí sica Teórica, University Estadual Paulista/ICTP South American Institute for Fundamental Research, São Paulo, SP 01140-070 Brazil

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A. L. Stuver

A. L. Stuver

LIGO Livingston Observatory, Livingston, LA 70754 USA

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T. Z. Summerscales

T. Z. Summerscales

Andrews University, Berrien Springs, MI 49104 USA

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L. Sun

L. Sun

The University of Melbourne, Parkville, Victoria 3010 Australia

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S. Sunil

S. Sunil

Institute for Plasma Research, Bhat, Gandhinagar 382428 India

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P. J. Sutton

P. J. Sutton

Cardiff University, Cardiff CF24 3AA, United Kingdom

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B. L. Swinkels

B. L. Swinkels

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

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M. J. Szczepańczyk

M. J. Szczepańczyk

Embry-Riddle Aeronautical University, Prescott, AZ 86301 USA

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M. Tacca

M. Tacca

APC, AstroParticule et Cosmologie, Université Paris Diderot, CNRS/IN2P3, CEA/Irfu, Observatoire de Paris, Sorbonne Paris Cité, F-75205 Paris Cedex 13, France

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D. Talukder

D. Talukder

University of Oregon, Eugene, OR 97403 USA

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D. B. Tanner

D. B. Tanner

University of Florida, Gainesville, FL, 32611 USA

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M. Tápai

M. Tápai

University of Szeged, Dóm tér 9, Szeged 6720 Hungary

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S. P. Tarabrin

S. P. Tarabrin

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-30167 Hannover, Germany

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A. Taracchini

A. Taracchini

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-14476 Potsdam-Golm Germany

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R. Taylor

R. Taylor

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

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T. Theeg

T. Theeg

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-30167 Hannover, Germany

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M. P. Thirugnanasambandam

M. P. Thirugnanasambandam

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

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E. G. Thomas

E. G. Thomas

University of Birmingham, Birmingham B15 2TT United Kingdom

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M. Thomas

M. Thomas

LIGO Livingston Observatory, Livingston, LA 70754 USA

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P. Thomas

P. Thomas

LIGO Hanford Observatory, Richland, WA 99352 USA

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K. A. Thorne

K. A. Thorne

LIGO Livingston Observatory, Livingston, LA 70754 USA

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K. S. Thorne

K. S. Thorne

Caltech CaRT, Pasadena, CA 91125 USA

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E. Thrane

E. Thrane

Monash University, Victoria 3800 Australia

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S. Tiwari

S. Tiwari

INFN, Gran Sasso Science Institute, I-67100 L'Aquila Italy

INFN, Trento Institute for Fundamental Physics and Applications, I-38123 Povo Trento, Italy

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V. Tiwari

V. Tiwari

Cardiff University, Cardiff CF24 3AA, United Kingdom

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K. V. Tokmakov

K. V. Tokmakov

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

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K. Toland

K. Toland

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

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C. Tomlinson

C. Tomlinson

The University of Sheffield, Sheffield S10 2TN United Kingdom

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M. Tonelli

M. Tonelli

Università di Pisa, I-56127 Pisa Italy

INFN, Sezione di Pisa, I-56127 Pisa Italy

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Z. Tornasi

Z. Tornasi

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

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C. V. Torres

C. V. Torres

The University of Texas Rio Grande Valley, Brownsville, TX 78520 USA

Deceased, March 2015.

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C. I. Torrie

C. I. Torrie

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

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D. Töyrä

D. Töyrä

University of Birmingham, Birmingham B15 2TT United Kingdom

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F. Travasso

F. Travasso

Università di Perugia, I-06123 Perugia Italy

INFN, Sezione di Perugia, I-06123 Perugia Italy

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G. Traylor

G. Traylor

LIGO Livingston Observatory, Livingston, LA 70754 USA

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D. Trifirò

D. Trifirò

The University of Mississippi, University, MS 38677 USA

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M. C. Tringali

M. C. Tringali

Università di Trento, Dipartimento di Fisica, I-38123 Povo Trento, Italy

INFN, Trento Institute for Fundamental Physics and Applications, I-38123 Povo Trento, Italy

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L. Trozzo

L. Trozzo

Università di Siena, I-53100 Siena Italy

INFN, Sezione di Pisa, I-56127 Pisa Italy

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M. Tse

M. Tse

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

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M. Turconi

M. Turconi

Artemis, Université Côte d'Azur, CNRS, Observatoire Côte d'Azur, CS 34229 Nice cedex 4, France

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D. Tuyenbayev

D. Tuyenbayev

The University of Texas Rio Grande Valley, Brownsville, TX 78520 USA

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D. Ugolini

D. Ugolini

Trinity University, San Antonio, TX 78212 USA

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C. S. Unnikrishnan

C. S. Unnikrishnan

Tata Institute of Fundamental Research, Mumbai 400005 India

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A. L. Urban

A. L. Urban

University of Wisconsin-Milwaukee, Milwaukee, WI 53201 USA

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S. A. Usman

S. A. Usman

Syracuse University, Syracuse, NY 13244 USA

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H. Vahlbruch

H. Vahlbruch

Leibniz Universität Hannover, D-30167 Hannover Germany

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G. Vajente

G. Vajente

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

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G. Valdes

G. Valdes

The University of Texas Rio Grande Valley, Brownsville, TX 78520 USA

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N. van Bakel

N. van Bakel

Nikhef, Science Park, 1098 XG, Amsterdam, The Netherlands

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M. van Beuzekom

M. van Beuzekom

Nikhef, Science Park, 1098 XG, Amsterdam, The Netherlands

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J. F. J. van den Brand

J. F. J. van den Brand

VU University Amsterdam, 1081 HV Amsterdam, The Netherlands

Nikhef, Science Park, 1098 XG, Amsterdam, The Netherlands

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C. Van Den Broeck

C. Van Den Broeck

Nikhef, Science Park, 1098 XG, Amsterdam, The Netherlands

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D. C. Vander-Hyde

D. C. Vander-Hyde

Syracuse University, Syracuse, NY 13244 USA

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L. van der Schaaf

L. van der Schaaf

Nikhef, Science Park, 1098 XG, Amsterdam, The Netherlands

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J. V. van Heijningen

J. V. van Heijningen

Nikhef, Science Park, 1098 XG, Amsterdam, The Netherlands

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A. A. van Veggel

A. A. van Veggel

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

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M. Vardaro

M. Vardaro

Università di Padova, Dipartimento di Fisica e Astronomia, I-35131 Padova Italy

INFN, Sezione di Padova, I-35131 Padova Italy

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S. Vass

S. Vass

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

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M. Vasúth

M. Vasúth

Wigner RCP, RMKI, H-1121 Budapest, Konkoly Thege Miklós út 29-33, Hungary

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

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University of Birmingham, Birmingham B15 2TT United Kingdom

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INFN, Sezione di Padova, I-35131 Padova Italy

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University of Birmingham, Birmingham B15 2TT United Kingdom

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Università degli Studi di Urbino “Carlo Bo”, I-61029 Urbino Italy

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Università degli Studi di Urbino “Carlo Bo”, I-61029 Urbino Italy

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University of Birmingham, Birmingham B15 2TT United Kingdom

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SUPA, University of the West of Scotland, Paisley PA1 2BE United Kingdom

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

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Syracuse University, Syracuse, NY 13244 USA

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Università di Perugia, I-06123 Perugia Italy

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LIGO Hanford Observatory, Richland, WA 99352 USA

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University of Florida, Gainesville, FL, 32611 USA

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University of Birmingham, Birmingham B15 2TT United Kingdom

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Faculty of Physics, Lomonosov Moscow State University, Moscow 119991 Russia

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Australian National University, Canberra, Australian Capital Territory 0200, Australia

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Kenyon College, Gambier, OH 43022 USA

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Kenyon College, Gambier, OH 43022 USA

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Louisiana State University, Baton Rouge, LA 70803 USA

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Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-14476 Potsdam-Golm Germany

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INFN, Gran Sasso Science Institute, I-67100 L'Aquila Italy

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University of Birmingham, Birmingham B15 2TT United Kingdom

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Tsinghua University, Beijing 100084 China

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University of Western Australia, Crawley, Western Australia 6009 Australia

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Australian National University, Canberra, Australian Capital Territory 0200, Australia

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LIGO Hanford Observatory, Richland, WA 99352 USA

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LIGO Hanford Observatory, Richland, WA 99352 USA

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Artemis, Université Côte d'Azur, CNRS, Observatoire Côte d'Azur, CS 34229 Nice cedex 4, France

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Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-30167 Hannover, Germany

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Rochester Institute of Technology, Rochester, NY 14623 USA

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University of Florida, Gainesville, FL, 32611 USA

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Cardiff University, Cardiff CF24 3AA, United Kingdom

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Abilene Christian University, Abilene, TX 79699 USA

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Leibniz Universität Hannover, D-30167 Hannover Germany

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

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LIGO Livingston Observatory, Livingston, LA 70754 USA

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Center for Interdisciplinary Exploration & Research in Astrophysics (CIERA), Northwestern University, Evanston, IL 60208 USA

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First published: 04 October 2016
Citations: 85

Full author list appears at the end.

Abstract

The first direct gravitational-wave detection was made by the Advanced Laser Interferometer Gravitational Wave Observatory on September 14, 2015. The GW150914 signal was strong enough to be apparent, without using any waveform model, in the filtered detector strain data. Here, features of the signal visible in the data are analyzed using concepts from Newtonian physics and general relativity, accessible to anyone with a general physics background. The simple analysis presented here is consistent with the fully general-relativistic analyses published elsewhere, in showing that the signal was produced by the inspiral and subsequent merger of two black holes. The black holes were each of approximately urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0001, still orbited each other as close as ∼350 km apart and subsequently merged to form a single black hole. Similar reasoning, directly from the data, is used to roughly estimate how far these black holes were from the Earth, and the energy that they radiated in gravitational waves.

1 Introduction

Advanced LIGO made the first observation of a gravitational wave (GW) signal, GW150914 1, on September 14th, 2015, a successful confirmation of a prediction by Einstein's theory of general relativity (GR). The signal was clearly seen by the two LIGO detectors located in Hanford, WA and Livingston, LA. Extracting the full information about the source of the signal requires detailed analytical and computational methods (see 2-6 and references therein for details). However, much can be learned about the source by direct inspection of the detector data and some basic physics 7, accessible to a general physics audience, as well as students and teachers. This simple analysis indicates that the source is two black holes (BHs) orbiting around one another and then merging to form another black hole.

A black hole is a region of space-time where the gravitational field is so intense that neither matter nor radiation can escape. There is a natural “gravitational radius” associated with a mass m, called the Schwarzschild radius, given by
urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0002(1)
where urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0003 is the mass of the Sun, urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0004 is Newton's gravitational constant, and urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0005 is the speed of light. According to the hoop conjecture, if a non-spinning mass is compressed to within that radius, then it must form a black hole  8. Once the black hole is formed, any object that comes within this radius can no longer escape out of it.

Here, the result that GW150914 was emitted by the inspiral and merger of two black holes follows from (1) the strain data visible at the instrument output, (2) dimensional and scaling arguments, (3) primarily Newtonian orbital dynamics and (4) the Einstein quadrupole formula for the luminosity of a gravitational wave source. These calculations are straightforward enough that they can be readily verified with pencil and paper in a short time. Our presentation is by design approximate, emphasizing simple arguments.

Specifically, while the orbital motion of two bodies is approximated by Newtonian dynamics and Kepler's laws to high precision at sufficiently large separations and sufficiently low velocities, we will invoke Newtonian dynamics to describe the motion even toward the end point of orbital motion (We revisit this assumption in Sec. 4.4). The theory of general relativity is a fully nonlinear theory, which could make any Newtonian analysis wholly unreliable; however, solutions of Einstein's equations using numerical relativity (NR) 11-13 have shown that a binary system's departures from Newtonian dynamics can be described well using a quantifiable analytic perturbation until quite late in its evolution - late enough for our argument (as shown in Sec. 4.4).

The approach presented here, using basic physics, is intended as a pedagogical introduction to the physics of gravitational wave signals, and as a tool to build intuition using rough, but straightforward, checks. Our presentation here is by design elementary, but gives results consistent with more advanced treatments. The fully rigorous arguments, as well as precise numbers describing the system, have already been published elsewhere 2-6.

The paper is organized as follows: our presentation begins with the data output by the detectors. Section 2 describes the properties of the signal read off the strain data, and how they determine the quantities relevant for analyzing the system as a binary inspiral. We then discuss in Sec. 3, using the simplest assumptions, how the binary constituents must be heavy and small, consistent only with being black holes. In Sec. 4 we examine and justify the assumptions made, and constrain both masses to be well above the heaviest known neutron stars. Section 5 uses the peak gravitational wave luminosity to estimate the distance to the source, and calculates the total luminosity of the system. The appendices provide a calculation of gravitational radiation strain and radiated power (App. A), and discuss astrophysical compact objects of high mass (App. B) as well as what one might learn from the waveform after the peak (App. C).

2 Analyzing the observed data

Our starting point is shown in Fig. 1: the instrumentally observed strain data urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0006, after applying a band-pass filter to the LIGO sensitive frequency band (35–350 Hz), and a band-reject filter around known instrumental noise frequencies 14. The time-frequency behavior of the signal is depicted in Fig.  2. An approximate version of the time-frequency evolution can also be obtained directly from the strain data in Fig.  1 by measuring the time differences urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0007 between successive zero-crossings and estimating urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0008, without assuming a waveform model. We plot the urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0009 power of these estimated frequencies in Fig.  3, and explain its physical relevance below.

Details are in the caption following the image
The instrumental strain data in the Livingston detector (blue) and Hanford detector (red), as shown in Figure 1 of 1. Both have been bandpass- and notch-filtered. The Hanford strain has been shifted back in time by 6.9 ms and inverted. Times shown are relative to 09:50:45 Coordinated Universal Time (UTC) on September 14, 2015.
Details are in the caption following the image
A representation of the strain-data as a time-frequency plot (taken from 1), where the increase in signal frequency (“chirp”) can be traced over time.
Details are in the caption following the image
A linear fit (green) of urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0010. While this interpolation used the combined strain data from H1 and L1 (in fact, the sum of L1 with time shifted and sign-flipped H1, as explained). A similar fit can be done using either H1 or L1 strain independently. The fit shown has residual sum of squares urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0011; we have also found urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0012 and urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0013. The slope of this fitted line gives an estimate of the chirp mass of urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0014 using Eq. 8. The blue and red lines indicate urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0015 of 30urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0016and 40urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0017, respectively. The error-bars have been estimated by repeating the procedure for waves of the same amplitudes and frequencies added to the LIGO strain data just before GW150914. A similar error estimate has been found using the differences between H1 and L1 zero-crossings.

The signal is dominated by several cycles of a wave pattern whose amplitude is initially increasing, starting from around the time mark 0.30 s. In this region the gravitational wave period is decreasing, thus the frequency is increasing. After a time around 0.42 s, the amplitude drops rapidly, and the frequency appears to stabilize. The last clearly visible cycles (in both detectors, after accounting for a 6.9 ms time-of-flight-delay 1) indicate that the final instantaneous frequency is above 200 Hz. The entire visible part of the signal lasts for around 0.15s.

In general relativity, gravitational waves are produced by accelerating masses 15. Since the waveform clearly shows at least eight oscillations, we know that a mass or masses are oscillating. The increase in gravitational wave frequency and amplitude also indicate that during this time the oscillation frequency of the source system is increasing. This initial behavior cannot be due to a perturbed system returning back to stable equilibrium, since oscillations around equilibrium are generically characterized by roughly constant frequencies and decaying amplitudes. For example, in the case of a fluid ball, the oscillations would be damped by viscous forces. Here, the data demonstrate very different behavior.

During the period when the gravitational wave frequency and amplitude are increasing, orbital motion of two bodies is the only plausible explanation: there, the only “damping forces” are provided by gravitational wave emission, which brings the orbiting bodies closer (an “inspiral”), increasing the orbital frequency and amplifying the gravitational wave energy output from the system.

Gravitational radiation has many aspects analogous to electromagnetic (EM) radiation from accelerating charges. A significant difference is that there is no analog to EM dipole radiation, whose amplitude is proportional to the second time derivative of the electric dipole moment. This is because the gravitational analog is the mass dipole moment (urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0018 at leading order in the velocity) whose first time derivative is the total linear momentum, which is conserved for a closed system, and whose second derivative therefore vanishes. Hence, at leading order, gravitational radiation is quadrupolar. Because the quadrupole moment (defined in App. A) is symmetric under rotations by π about the orbital axis, the radiation has a frequency twice that of the orbital frequency (for a detailed calculation for a 2-body system, see App. A and pp. 356-357 of 16).

The eight gravitational wave cycles of increasing frequency therefore require at least four orbital revolutions, at separations large enough (compared to the size of the bodies) that the bodies do not collide. The rising frequency signal eventually terminates, suggesting the end of inspiraling orbital motion. As the amplitude decreases and the frequency stabilizes the system returns to a stable equilibrium configuration. We shall show that the only reasonable explanation for the observed frequency evolution is that the system consisted of two black holes that orbited each other and subsequently merged.

Determining the frequency at maximum strain amplitude urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0019: The single most important quantity for the reasoning in this paper is the gravitational wave frequency at which the waveform has maximum amplitude. Using the zero-crossings around the peak of Fig.  1 and/or the brightest point of Fig.  2, we take the conservative (low) value
urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0020(2)
where here and elsewhere the notation indicates that the quantity before the vertical line is evaluated at the time indicated after the line. We thus interpret the observational data as indicating that the bodies were orbiting each other (roughly Keplerian dynamics) up to at least an orbital angular frequency
urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0021(3)
Determining the mass scale: Einstein found 17 that the gravitational wave strain h at a (luminosity) distance urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0022 from a system whose traceless mass quadrupole moment is urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0023 (defined in App. A) is
urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0024(4)
and that the rate at which energy is carried away by these gravitational waves is given by the quadrupole formula 17
urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0025(5)
the integral is over a sphere at radius urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0026 (contributing a factor urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0027), and the quantity on the right-hand side must be averaged over (say) one orbit.

In our case, Eq. 5 gives the rate of loss of orbital energy to gravitational waves, when the velocities of the orbiting objects are not too close to the speed of light, and the strain is not too large 15; we will apply it until the frequency urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0028, see Sec. 4.4. This wave description is applicable in the “wave zone” 19, where the gravitational field is weak and the expansion of the universe is ignored (see Sec. 4.6).

For the binary system we denote the two masses by m1 and m2, the total mass by urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0029, and the reduced mass by urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0030. We define the mass ratio urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0031 and without loss of generality assume that urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0032 so that urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0033. To describe the gravitational wave emission from a binary system, a useful mass quantity is the chirp mass, urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0034, related to the component masses by
urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0035(6)
Using Newton's laws of motion, Newton's universal law of gravitation, and Einstein's quadrupole formula for the gravitational wave luminosity of a system, a simple formula is derived in App. A (following 20, 21) relating the frequency and frequency derivative of emitted gravitational waves to the chirp mass,
urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0036(7)
where urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0037 is the rate-of-change of the frequency (see Eq. A5 and Eq.  3 of 22). This equation is expected to hold as long as the Newtonian approximation is valid (see Sec. 4.4).

Thus, a value for the chirp mass can be determined directly from the observational data, using the frequency and frequency derivative of the gravitational waves at any moment in time. For example, values for the frequency can be estimated from the time-frequency plot of the observed gravitational wave strain data (Fig.  2), and for the frequency derivative by drawing tangents to the same curve (see figure on journal cover). The time interval during which the inspiral signal is in the sensitive band of the detector (and hence is visible) corresponds to gravitational wave frequencies in the range urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0038 Hz. Over this time, the frequency (period) varies by a factor of 5 (urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0039), and the frequency derivative varies by more than two orders-of-magnitude. The implied chirp mass value, however, remains constant to within 35%. The exact value of urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0040 is not critical to the arguments that we present here, so for simplicity we take urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0041.

Note that the characteristic mass scale of the radiating system is obtained by direct inspection of the time-frequency behavior of the observational data.

The fact that the chirp mass remains approximately constant for urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0042Hz is strong support for the orbital interpretation. The fact that the amplitude of the gravitational wave strain increases with frequency also supports this interpretation, and suggests that the assumptions that go into the calculation which leads to these formulae are applicable: the velocities in the binary system are not too close to the speed of light, and the orbital motion has an adiabatically changing radius and a period described instantaneously by Kepler's laws. The data also indicate that these assumptions certainly break down at a gravitational wave frequency above urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0043, as the amplitude stops growing.

Alternatively, Eq. 7 can be integrated to obtain
urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0044(8)
which does not involve urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0045 explicitly, and can therefore be used to calculate urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0046 directly from the time periods between zero-crossings in the strain data. The constant of integration urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0047 is the time of coalescense. We have performed such an analysis, presented in Fig.  3, to find similar results. We henceforth adopt a conservative lower estimate of urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0048 for the chirp mass. We remark that this mass is derived from quantities measured in the detector frame, thus it and the quantities we derive from it are given in the detector frame. Discussion of redshift from the source frame appears in Sec. 4.6.

3 Evidence for compactness in the simplest case

For simplicity, suppose that the two bodies have equal masses, urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0049. The value of the chirp mass then implies that urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0050, so that the total mass would be urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0051. We also assume for now that the objects are not spinning, and that their orbits remain Keplerian and essentially circular until the point of peak amplitude.

Around the time of peak amplitude the bodies therefore had an orbital separation R given by
urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0052(9)
Compared to normal length scales for stars, this is a tiny value. This constrains the objects to be exceedingly small, or else they would have collided and merged long before reaching such close proximity. Main-sequence stars have radii measured in hundreds of thousands or millions of kilometers, and white dwarf (WD) stars have radii which are typically ten thousand kilometers. Scaling Eq. 9 shows that such stars' inspiral evolution would have terminated with a collision at an orbital frequency of a few mHz (far below 1 Hz).

The most compact stars known are neutron stars, which have radii of about ten kilometers. Two neutron stars could have orbited at this separation without colliding or merging together – but the maximum mass that a neutron star can have before collapsing into a black hole is about 3 urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0053 (see App. B).

In our case, the bodies of mass urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0054 each have a Schwarzschild radius of 103 km. This is illustrated in Fig.  4. The orbital separation of these objects, 350 km, is only about twice the sum of their Schwarzschild radii.

Details are in the caption following the image
A demonstration of the scale of the orbit at minimal separation (black, 350 km) vs. the scale of the compact radii: Schwarzschild (red, diameter 200 km) and extremal Kerr (blue, diameter 100 km). Note the masses here are equal; as Sec. 4.2 explains, the system is even more compact for unequal masses. While identification of a rigid reference frame for measuring distances between points is not unique in relativity, this complication only really arises with strong gravitational fields, while in the Keplerian regime (of low compactness and low gravitational potentials) the system's center-of-mass rest-frame can be used. Therefore if the system is claimed to be non-compact, the Keplerian argument should hold, and constrain the distances to be compact. Thus the possibility of non-compactness is inconsistent with the data; see also Sec. 4.4.

In order to quantify the closeness of the two objects relative to their natural gravitational radius, we introduce the compactness ratio urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0055. This is defined as the Newtonian orbital separation between the centers of the objects divided by the sum of their smallest possible respective radii (as compact objects). For the non-spinning, circular orbit, equal-mass case just discussed urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0056.

For comparison with other known Keplerian systems, the orbit of Mercury, the innermost planet in our solar system, has urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0057, the binary orbit for the stellar black hole in Cyg X-1 has urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0058, and the binary system of highest known orbital frequency, the WD system HM Cancri (RX J0806), has urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0059 24. Observations of orbits around our galactic center indicate the presence of a supermassive black hole, named Sgr A* 25, 26, with the star S2 orbiting it as close as urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0060. For a system of two neutron stars just touching, urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0061 would be between ∼2 and ∼5.

The fact that the Newtonian/Keplerian evolution of the orbit inferred from the signal of GW150914 breaks down when the separation is about the order of the black hole radii (compactness ratio urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0062 of order 1) is further evidence that the objects are highly compact.

4 Revisiting the assumptions

In Sec. 3 we used the data to show that the coalescing objects are black holes under the assumptions of a circular orbit, equal masses, and no spin. It is not possible, working at the level of approximation that we are using here, to directly constrain these parameters of the system (although more advanced techniques are able to constrain them, see 2). However, it is possible to examine how these assumptions affect our conclusions and in this section we show that relaxing them does not significantly change the outcome. We also use the Keplerian approximation to discuss these three modifications (Sec. 4.14.3), then revisit the Keplerian assumption itself, and discuss the consequences of foregoing it (Sec. 4.44.5). In Sec. 4.6 we discuss the distance to the source, and its potential effects.

4.1 Orbital eccentricity

For non-circular orbits with eccentricity urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0063, the R of Kepler's third law (Eq. 9) no longer refers to the orbital separation but rather to the semi-major axis. The instantaneous orbital separation rsep is bounded from above by R, and from below by the point of closest approach (periapsis), urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0064. We thus see that the compactness bound imposed by eccentric orbits is even tighter (the compactness ratio urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0065 is smaller).

There is also a correction to the luminosity which depends on the eccentricity. However, this correction is significant only for highly eccentric orbits. For these, the signal should display a modulation 27: the velocity would be greater near periapsis than near apoapsis, so the signal would alternate between high-amplitude and low-amplitude peaks. Such modulation is not seen in the data, whose amplitude grows monotonically.

This is not surprising, as the angular momentum that gravitational waves carry away causes the orbits to circularize much faster than they shrink 20, 21. This correction can thus be neglected.

4.2 The case of unequal masses

It is easy to see that the compactness ratio urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0066 also gets smaller with increasing mass-ratio, as that implies a higher total mass for the observed value of the Newtonian order chirp mass. To see this explicitly, we express the component masses and total mass in terms of the chirp mass urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0067 and the mass ratio q, as urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0068, urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0069, and
urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0070(10)
The compactness ratio urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0071 is the ratio of the orbital separation R to the sum of the Schwarzschild radii of the two component masses, urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0072, giving
urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0073(11)
This quantity is plotted in Fig.  5, which clearly shows that for mass ratios urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0074 the compactness ratio decreases: the separation between the objects becomes smaller when measured in units of the sum of their Schwarzschild radii. Thus, for a given chirp mass and orbital frequency, a system composed of unequal masses is more compact than one composed of equal masses.
Details are in the caption following the image
This figure shows the compactness ratio constraints imposed on the binary system by urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0075 and urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0076. It plots the compactness ratio (the ratio of the separation between the two objects to the sum of their Schwarzschild radii) as a function of mass ratio and eccentricity from urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0077 to the very high (arbitrary) value of urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0078. The bottom-left corner (urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0079) corresponds to the case given in Sec. 3. At fixed mass ratio, the system becomes more compact with growing eccentricity until urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0080, as explained in Sec. 4.1. The bottom edge (urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0081) illustrates the argument given in Sec. 4.2 and Eq. 11: the system becomes more compact as the mass ratio increases. We note that (for urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0082) beyond mass ratio of urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0083 (urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0084) the system would become more compact than the sum of the component Schwarzschild radii.

One can also place an upper limit on the mass ratio q, thus a lower bound on the smaller mass m2, based purely on the data. This bound arises from minimal compactness: we see from the compactness ratio plot in Fig.  5 that beyond the mass ratio of urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0085 the system becomes so compact that it will be within the Schwarzschild radii of the combined mass of the two bodies. This gives us a limit for the mass of the smaller object urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0086. As this is 3–4 times more massive than the neutron star limit, both bodies are expected to be black holes .

4.3 The effect of objects' spins

The third assumption we relax concerns the spins of the objects. For a mass m with spin angular momentum S we define the dimensionless spin parameter
urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0087(12)
The spins of m1 and m2 modify their gravitational radii as described in this subsection, as well as the orbital dynamics, as described in the next subsection.
The smallest radius a non-spinning object (urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0088) could have without being a black hole is its Schwarzschild radius. Allowing the objects to have angular momentum (spin) pushes the limit down by a factor of two, to the radius of an extremal Kerr black hole (for which urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0089), urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0090. As this is linear in the mass, and summing radii linearly, we obtain a lower limit on the Newtonian separation of two adjacent non-black hole bodies of total mass M is
urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0091(13)
The compactness ratio can also be defined in relation to rEK rather than rSchwarz, which is at most a factor of two larger than for non-spinning objects.
We may thus constrain the orbital compactness ratio (now accounting for eccentricity, unequal masses, and spin) by
urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0092(14)
where in the last step we used urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0093 and urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0094 Hz. This constrains the constituents to be under 3.4 (1.7) times their extremal Kerr (Schwarzschild) radii, making them highly compact. The compact arrangement is illustrated in Fig. 4.
We can also derive an upper limit on the value of the mass ratio q, from the constraint that the compactness ratio must be larger than unity. This is because, for a fixed value of the chirp mass urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0095 and a fixed value of urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0096, the compactness ratio urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0097 decreases as the mass ratio q increases. Thus, the constraint urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0098, puts a limit on the maximal possible q and thus on the maximum total mass Mmax,
urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0099(15)
which for GW150914 implies urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0100 (and urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0101). This again forces the smaller mass to be at least urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0102 – well above the neutron star mass limit (App. B).

The conclusion is the same as in the equal-mass or non-spinning case: both objects must be black holes.

4.4 Newtonian dynamics and compactness

We now examine the applicability of Newtonian dynamics. The dynamics will depart from the Newtonian approximation when the relative velocity v approaches the speed of light or when the gravitational energy becomes large compared to the rest mass energy. For a binary system bound by gravity and with orbital velocity v, these two limits coincide and may be quantified by the post-Newtonian (PN) parameter 28 urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0103. Corrections to Newtonian dynamics may be expanded in powers of x, and are enumerated by their PN order. The 0PN approximation is precisely correct at urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0104, where dynamics are Newtonian and gravitational wave emission is described exactly by the quadrupole formula (Eq. 5).

The expression for the dimensionless PN parameter includes the Schwarzschild radius, so x can be immediately recast in terms of the compactness ratio, urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0105. As Newtonian dynamics holds when x is small, the Newtonian approximation is valid down to compactness urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0106 of order of a few. Arguing by contradiction, if one assumes that the orbit is non-compact, then our analysis of the data using Newtonian mechanics is justified as an approximation of general relativity and leads to the conclusion that the orbit is compact.

If either of the bodies is rapidly spinning, their rotational velocity may also approach the speed of light, modifying the Newtonian dynamics, effectively adding spin-orbit and spin-spin interactions. However, these are also suppressed with a power of the PN parameter (1.5PN and 2PN, respectively 28-30), and thus are significant only for compact orbits.

The same reasoning may also be applied to the use of the quadrupole formula 15 and/or to using the coordinate R for the comparison of the Keplerian separation to the corresponding compact object radii (see Fig.  4 and its caption), as both of these are not entirely general and might be inaccurate. The separations are also subject to some arbitrariness due to gauge freedom. However here too, the errors in using these coordinates are non-negligible only in the orbits very close to a black hole, so again this argument does not refute our conclusions.

4.5 Is the chirp mass well measured? – constraints on the individual masses

As we are analyzing the final cycles before merger, having accepted that the bodies were compact, one might still ask whether Eq. 7 correctly describes the chirp mass in the non-Newtonian regime 31. In fact for the last orbits, it does not: In Newtonian dynamics stable circular orbits may exist all the way down to merger, and energy lost to gravitational waves drives the inspiral between them. However in general relativity, close to the merger of compact objects (at least when one of the objects is much larger than the other) there are no such orbits past the innermost stable circular orbit (ISCO), whose typical location is given below. Allowed interior trajectories must be non-circular and “plunge” inwards (see pp. 911 of 18). The changes in orbital separation and frequency in the final revolutions are thus not driven by the gravitational wave emission given by Eq. 7. This is why we used urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0107 at the peak, rather than the final frequency urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0108.

We shall now constrain the individual masses based on urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0109, for which we do not need the Newtonian approximation at the late stage. No neutron stars have been observed above urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0110; we shall rely on an even more conservative neutron star mass upper bound at urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0111, a value chosen because given urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0112 from the early visible cycles, in order for the smaller mass m2 to be below this threshold, m1 must be at least urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0113, which implies urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0114. Is such a high q possible with the data that we have? Such a high mass ratio suggests a treatment of the system as an extremal mass ratio inspiral (EMRI), where the smaller mass approximately follows a geodesic orbit around the larger mass (urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0115). The frequencies of test-particle orbits (hence waveforms) around an object scale with the inverse of its mass, and also involve its dimensionless spin χ. The orbital frequency ωorb as measured at infinity of a circular, equatorial orbit at radius r (in Boyer-Lindquist coordinates) is given by 32
urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0116(16)
For example, around a Schwarzschild black hole (urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0117) the quadrupole gravitational wave frequency at the innermost stable circular orbit (which is at urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0118) is hence equal to urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0119 kHz, while for an extremal Kerr black hole (urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0120) the orbital frequency at ISCO (urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0121) is urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0122, and the quadrupole gravitational frequency is urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0123 kHz. For a gravitational wave from the final plunge, the highest expected frequency is approximately the frequency from the light ring (LR), as nothing physical is expected to orbit faster than light, and as waves originating within the light ring encounter an effective potential barrier at the light ring going out 33-37 . The light ring is at
urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0124(17)
This radius is urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0125 for a Schwarzschild black hole, while for a spinning Kerr black hole, as the spin χ increases the light ring radius decreases. For an extremal Kerr black hole it coincides with the innermost stable circular orbit at urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0126. The maximal gravitational wave frequency for a plunge into m1 is then 67 Hz.

Because we see gravitational wave emission from orbital motion at frequencies much higher than this maximal value, with or without spin, such a system is ruled out. Hence even the lighter of the masses must be at least urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0127, beyond the maximum observed mass of neutron stars.

4.6 Possible redshift of the masses – a constraint from the luminosity

Gravitational waves are stretched by the expansion of the Universe as they travel across it. This increases the wavelength and decreases the frequency of the waves observed on Earth compared to their values when emitted. The same effect accounts for the redshifting of photons from distant objects. The impact of this on the gravitational wave phasing corresponds to a scaling of the masses as measured on Earth; dimensional analysis of Eq. 7 shows that the source frame masses are smaller by urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0128 relative to the detector frame, where z is the redshift. Direct inspection of the detector data yields mass values from the red-shifted waves. How do these differ from their values at the source? In the next section, we estimate the distance to the source and hence the redshift, by relating the amplitude and luminosity of the gravitational wave from the merger to the observed strain and flux at the detector. The redshift is found to be urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0129, so the detector- and source-frame masses differ by less than of order 10%.

5 Luminosity and distance

Basic physics arguments also provide estimates of the peak gravitational wave luminosity of the system, its distance from us, and the total energy radiated in gravitational waves.

The gravitational wave amplitude h falls off with increasing luminosity distance urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0130 as urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0131. As shown in Fig.  1, the measured strain peaks at urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0132. Had our detector been ten times closer to the source, the measured strain would have peaked at a value ten times larger. This could be continued, but the scaling relationship would break before h reached unity, because near the Schwarzschild radius of the combined system urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0133 the non-linear nature of gravity would become apparent. In this way we obtain a crude order-of-magnitude upper bound
urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0134(18)
on the distance to the source.
We can obtain a more accurate distance estimate based on the luminosity, because the gravitational wave luminosity from an equal-mass binary inspiral has a peak value which is independent of the mass. This can be seen from naive dimensional analysis of the quadrupole formula, which gives a luminosity urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0135, with urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0136 and urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0137, and urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0138 for the final tight orbit. Together this gives the Planck luminosity,
urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0139(19)
However, a closer look (Eq. A4) shows the prefactor should be urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0140, which gives urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0141 for an equal-mass system, and is close to that for urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0142. Also, analysis of a small object falling into a Schwarzschild black hole suggests urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0143 and urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0144. Taken together with the correct exponents, L acquires a factor urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0145. While the numerical value may change by a factor of a few with the specific spins, we can treat its order of magnitude as universal for similar-mass binaries.
Using Eq. 5 we relate the luminosity of gravitational waves to their strain h at luminosity distance urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0146,
urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0147(20)
Thus we have
urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0148(21)
and we estimate the distance from the change of the measured strain in time over the cycle at peak amplitude, as
urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0149(22)
which for GW150914 gives urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0150. This distance corresponds to a redshift of urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0151, and so does not substantially affect any of the conclusions. For a different distance-luminosity calculation based only on the strain data (reaching a similar estimate), see 42.
Using the orbital energy Eorb (as defined in App. A) we may also estimate the total energy radiated as gravitational waves during the system's evolution from a very large initial separation (where urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0152) down to a separation r. For GW150914, using urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0153 and urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0154 (Eq. 9),
urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0155(23)
This quantity should be considered an estimate for a lower bound on the total emitted energy (as some energy is emitted in the merger and ringdown); compare with the exact calculations in 1-3.

We note that the amount of energy emitted in this event is remarkable. During its ten-billion-year lifetime, our sun is expected to convert less than 1% of its mass into light and radiation. Not only did GW150914 release ∼300 times as much energy in gravitational waves (almost entirely over the fraction of a second shown in Fig.  1), but for the cycle at peak luminosity, its power Lpeak in the form of gravitational waves was about 22 orders of magnitude greater than the power output from our sun.

6 Conclusions

A lot of insight can be obtained by applying these basic physics arguments to the observed strain data of GW150914. These show the system that produced the gravitational wave was a pair of inspiraling black holes that approached very closely before merging. The system is seen to settle down, most likely to a single black hole. Simple arguments can also give us information about the system's distance and basic properties (for a related phenomenological approach see 43).

With these basic arguments we have only drawn limited conclusions about the mass ratio q, because the frequency evolution described by Eq. 7 does not depend on q. The mass ratio q does appear in the PN corrections 22, 44, thus its value can be further constrained from the data 2, 3.

These arguments will not work for every signal, for instance if the masses are too low to safely rule out a neutron star constituent as done in Sec. 4.5, but should be useful for systems similar to GW150914. There has already been another gravitational wave detection, GW151226 6, 45, whose amplitude is smaller and therefore cannot be seen in the strain data without application of more advanced techniques.

Such techniques, combining analytic and numerical methods, can give us even more information, and we encourage the reader to explore how such analyses and models have been used for estimating the parameters of the system 2, 3, for testing and constraining the validity of general relativity in the highly relativistic, dynamic regime 4 and for astrophysical studies based on this event 5.

We hope that this paper will serve as an invitation to the field, at the beginning of the era of gravitational wave observations.

Acknowledgements

The authors gratefully acknowledge the support of the United States National Science Foundation (NSF) for the construction and operation of the LIGO Laboratory and Advanced LIGO as well as the Science and Technology Facilities Council (STFC) of the United Kingdom, the Max-Planck-Society (MPS), and the State of Niedersachsen/Germany for support of the construction of Advanced LIGO and construction and operation of the GEO600 detector. Additional support for Advanced LIGO was provided by the Australian Research Council. The authors gratefully acknowledge the Italian Istituto Nazionale di Fisica Nucleare (INFN), the French Centre National de la Recherche Scientifique (CNRS) and the Foundation for Fundamental Research on Matter supported by the Netherlands Organisation for Scientific Research, for the construction and operation of the Virgo detector and the creation and support of the EGO consortium. The authors also gratefully acknowledge research support from these agencies as well as by the Council of Scientific and Industrial Research of India, Department of Science and Technology, India, Science & Engineering Research Board (SERB), India, Ministry of Human Resource Development, India, the Spanish Ministerio de Economía y Competitividad, the Conselleria d'Economia i Competitivitat and Conselleria d'Educació, Cultura i Universitats of the Govern de les Illes Balears, the National Science Centre of Poland, the European Commission, the Royal Society, the Scottish Funding Council, the Scottish Universities Physics Alliance, the Hungarian Scientific Research Fund (OTKA), the Lyon Institute of Origins (LIO), the National Research Foundation of Korea, Industry Canada and the Province of Ontario through the Ministry of Economic Development and Innovation, the Natural Science and Engineering Research Council Canada, Canadian Institute for Advanced Research, the Brazilian Ministry of Science, Technology, and Innovation, Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP), Russian Foundation for Basic Research, the Leverhulme Trust, the Research Corporation, Ministry of Science and Technology (MOST), Taiwan and the Kavli Foundation. The authors gratefully acknowledge the support of the NSF, STFC, MPS, INFN, CNRS and the State of Niedersachsen/Germany for provision of computational resources.

  1. 1 In the terminology of GR corrections to Newtonian dynamics, (3) & (4) constitute the “0th post-Newtonian” approximation (0PN) (see Sec. 4.4). A similar approximation was used for the first analysis of binary pulsar PSR 1913+16 9, 10.
  2. 2 The advanced LIGO detectors use laser interferometry to measure the strain caused by passing gravitational waves. For details of how the detectors work, see 1 and its references.
  3. 3 To resolve the crossing at urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0210 s, when the signal amplitude is lower and the true waveform's sign transitions are difficult to pinpoint, we averaged the positions of the five adjacent zero-crossings (over ∼6 ms).
  4. 4 The possibility of a different inspiraling system, whose evolution is not governed by gravitational waves, is explored in App. A.1 and shown to be inconsistent with this data.
  5. 5 See App. A for a worked-out calculation, and pp. 974-977 of 18 for a derivation of these results, obtained by linearizing the Einstein Equation, the central equation of general relativity.
  6. 6 Radio, optical and X-ray telescopes have probed the accretion disk extending much further inside 23.
  7. 7 Eccentricity increases the luminosity 20, 21 by a factor urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0211, thus reducing the chirp mass (inferred using Eq. 7) to urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0212. Taking into account the ratio between the separation at periapsis and the semi-major axis, one obtains urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0213. Hence for the compactness ratio to increase, the eccentricity must be urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0214, and for a factor of 2, urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0215 (see Fig.  5)
  8. 8 Hypothesized frequency up-conversions due to nonlinear GR effects have also been shown by NR to be absent 11-13.
  9. 9 The “Planck luminosity” urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0216 has been proposed as the upper limit on the luminosity of any physical system 38-40. Gibbons 41 has suggested that urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0217 be called the “Dyson luminosity” in honor of the physicist Freeman Dyson and because it is a classical quantity that does not contain the Planck constant ℏ.
  10. Appendix A: Calculation of gravitational radiation from a binary system

    Here we outline the calculation of the energy a binary system emits in gravitational waves and the emitted energy's effect on the system.

    First we calculate the quadrupole moment urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0156 of the system's mass distribution. We use a Cartesian coordinate system urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0157 whose origin is the center-of-mass, with r the radial distance from the origin. urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0158 is the Kronecker-delta and urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0159 denotes the mass density. Then
    urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0160(A1)
    urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0161(A2)
    where the second equality holds for a system of two bodies urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0162 in the urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0163-plane. In the simple case of a circular orbit at separation urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0164 and frequency urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0165, a little trigonometry gives for each object (see Fig.  A1)
    urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0166(A3)
    where urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0167, urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0168, urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0169 and urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0170. Combining we find urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0171, and the gravitational wave luminosity from Eq. 5 is
    urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0172(A4)
    This energy loss drains the orbital energy urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0173, thus urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0174. We assume that the energy radiated away over each orbit is small compared to Eorb, in order to describe each orbit as approximately Keplerian.
    Details are in the caption following the image
    A two-body system, m1 and m2 orbiting in the urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0175-plane around their C.O.M.
    Now using Kepler's third law urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0176 and its derivative urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0177 we can substitute for all the r's and obtain
    urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0178(A5)
    having defined the chirp mass urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0179.

    We can see that Eq. A5 describes the evolution of the system as an inspiral: the orbital frequency goes up (“chirps”), while by Kepler's Law the orbital separation shrinks.

    A.1 Gravitational radiation from a different rotating system

    A rising gravitational wave amplitude can accompany a rise in frequency in other rotating systems, evolving under different mechanisms. An increase in frequency means the system rotates faster and faster, so unless it gains angular momentum, the system's characteristic length urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0180 should be decreasing. For a system not driven by the loss of energy and angular momentum to gravitational waves, rapidly losing angular momentum is also difficult, thus the system should conserve its angular momentum urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0181, and so urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0182.

    The quadrupole formula (Eq. 4) then indicates the gravitational wave strain amplitude should follow the second time derivative of the quadrupole moment, urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0183.

    Thus we see that for a system not driven by emission of gravitational waves, as the characteristic system size r shrinks, both its gravitational wave frequency and amplitude grow, but remain proportional to each other. This is inconsistent with the data of GW150914 (Figs. 1, 2), which show the amplitude only grows by a factor of about 2 while the frequency urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0184 grows by at least a factor of 5.

    Appendix B: Possibilities for massive, compact objects

    We are considering astrophysical objects with mass scale urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0185, which are constrained to fit into a radius R such that the compactness ratio obeys urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0186. This produces a scale for their Newtonian density,
    urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0187(B1)
    where equality is attained for a uniform object. This is a factor of 106 more dense than white dwarfs, so we can rule out objects supported by electron degeneracy pressure, as well as any main-sequence star, which would be less dense. While this density is a factor of ∼102 less dense than neutron stars, these bodies exceed the maximum neutron star mass by an order of magnitude, as the neutron star limit is urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0188 (3.2 urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0189 in 46, 47, 2.9 urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0190 in 48). A more careful analysis of the frequency change, including tidal distortions, would have undoubtedly required the bodies to be even more compact in order to reach the final orbital frequency. This would push these massive bodies even closer to neutron-star density, thus constraining the equation of state into an even narrower corner. Thus, although theoretically a compactness ratio as low as urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0191 is permitted for uniform objects 49, we can conclude that the data do show that if any of these objects were material bodies, they would need to occupy an extreme, narrow and heretofore unexplored and unobserved niche in the stellar continuum. The likeliest objects with such mass and compactness are black holes.

    Appendix C: Post inspiral phase: what we can conclude about the ringdown and the final object?

    We have argued, using basic physics and scaling arguments, that the directly observable properties of the signal waveform for gravitational wave frequencies urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0192 Hz shows that the source had been two black holes, which approached so closely that they subsequently merged. We now discuss the properties of the signal waveform at higher frequencies, and argue that this also lends support to this interpretation.

    The data in Figures 1 and 2 show that after the peak gravitational wave amplitude is reached, the signal makes one to two additional cycles, continuing to rise in frequency until reaching about 250 Hz, while dropping sharply in amplitude. The frequency seems to level off just as the signal amplitude becomes hard to distinguish clearly.

    Is this consistent with a merger remnant black hole? Immediately after being formed in a merger, a black hole horizon is very distorted. It proceeds to “lose its hair” and settle down to a final state of a Kerr black hole, uniquely defined 50 by its mass M and spin parameter χ. Late in this ringdown stage, the remaining perturbations should linearize, and the emitted gravitational wave should thus have characteristic quasi-normal-modes (QNMs). The set of QNMs is enumerated by various discrete indices, and their frequencies and damping times are determined by M and χ. Each such set would have a leading (least-damped) mode – and so finding a ringdown of several cycles with a fixed frequency would be strong evidence that a single final remnant was formed. We do clearly see the gravitational wave stabilizing in frequency (at around 250 Hz) about two cycles after the peak, and dying out in amplitude. Does the end of the observed waveform contain evidence of an exponentially-damped sinusoid of fixed frequency? Were such a mode found, analyzing its frequency and damping time, in conjunction with a model for black hole perturbations, could give an independent estimate of the mass and spin 51.

    C.1 Mode analysis

    The ringing of a Kerr black hole can be thought of as related to a distortion of space-time traveling on a light ring orbit outside the black hole horizon (See 52 and references therein, and Eqs. (16, 17)); the expected frequency for a quadrupolar mode (urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0193 will thus be given as a dimensionless complex number
    urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0194(C1)
    where the real part of ωGW is the angular frequency and the imaginary part is the (inverse) decay time. The ringdown amplitude and damping times are then found from
    urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0195(C2)
    to be urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0196 and urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0197.
    The exact values of x and y can be found as when analyzing the normal modes of a resonant cavity: one uses separation of variables to solve the field equations, and then enforces the boundary conditions to obtain a discrete set of complex eigenfrequencies 52. However, limiting values on x, urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0198, are derived immediately from Eqs. (16, 17), with a factor of 2 between orbital and gravitational wave frequencies. The final gravitational wave frequency is thus determined by the mass (up to the order-of-unity factor x, which embodies the spin). We have in fact already used this to show how our high attained frequency constrains the total mass and the compactness of the objects (objects of larger radius would have distortion bulges orbiting much farther than the light ring, mandating much lower frequencies). For the parameter y determining the damping time, numerical tabulations of the QNMs 52 show that
    urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0199(C3)
    for a broad range of mode numbers and spins, as long as the spin is not close to extremal. This shows that the ringdown is expected to have a damping time roughly equal to the period of oscillation. This is exactly what is seen in the waveform, and is the reason the signal amplitude drops so low by the time the remnant rings at the final frequency.

    While it is beyond the scope of this paper to calculate the exact QNMs for black holes of different spins, or to find the final spin of a general black hole merger, it is worth mentioning that for a wide range of spins for similar-mass binaries, the final spin is expected to be about urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0200, for which Eq. (16, 17) estimate that urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0201.

    The exact value can be found using Table II in 52, where the leading harmonic (urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0202) for a black hole with a spin urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0203 has urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0204, giving a ringdown frequency
    urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0205(C4)
    and a damping time
    urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0206(C5)
    In other words, the signal in the data is fully consistent 42 with the final object being a Kerr black hole with a dimensionless spin parameter urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0207 and a mass urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0208 Such a final mass is consistent with the merger of two black holes of urn:x-wiley:00033804:media:andp201600209:andp201600209-math-0209 each, after accounting for the energy emitted as gravitational waves (Eq. 23). This interpretation of the late part of the signal is also consistent with numerical simulations 53. Full numerical simulations from the peak and onward, where the signal amplitude is considerably higher, also show consistency with the formation of a Kerr black hole remnant 2, 4.

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