# IceCube search for neutrinos coincident with gravitational wave events from
LIGO/Virgo run O3

R. Abbasi Department of Physics, Loyola University Chicago, Chicago, IL 60660,
USA  M. Ackermann DESY, D-15738 Zeuthen, Germany  J. Adams  Dept. of Physics
and Astronomy, University of Canterbury, Private Bag 4800, Christchurch, New
Zealand  N. Aggarwal  Dept. of Physics, University of Alberta, Edmonton,
Alberta, Canada T6G 2E1  J. A. Aguilar Université Libre de Bruxelles, Science
Faculty CP230, B-1050 Brussels, Belgium  M. Ahlers Niels Bohr Institute,
University of Copenhagen, DK-2100 Copenhagen, Denmark  M. Ahrens  Oskar Klein
Centre and Dept. of Physics, Stockholm University, SE-10691 Stockholm, Sweden
J.M. Alameddine Dept. of Physics, TU Dortmund University, D-44221 Dortmund,
Germany  A. A. Alves Jr  Karlsruhe Institute of Technology, Institute for
Astroparticle Physics, D-76021 Karlsruhe, Germany  N. M. Amin  Bartol Research
Institute and Dept. of Physics and Astronomy, University of Delaware, Newark,
DE 19716, USA  K. Andeen  Department of Physics, Marquette University,
Milwaukee, WI, 53201, USA  T. Anderson  Dept. of Astronomy and Astrophysics,
Pennsylvania State University, University Park, PA 16802, USA  Dept. of
Physics, Pennsylvania State University, University Park, PA 16802, USA  G.
Anton Erlangen Centre for Astroparticle Physics, Friedrich-Alexander-
Universität Erlangen-Nürnberg, D-91058 Erlangen, Germany  C. Argüelles
Department of Physics and Laboratory for Particle Physics and Cosmology,
Harvard University, Cambridge, MA 02138, USA  Y. Asali  Dept. of Astronomy,
Yale University, New Haven, CT 06520, USA  Dept. of Physics, Columbia
University, New York, NY 10027, USA  Y. Ashida  Dept. of Physics and Wisconsin
IceCube Particle Astrophysics Center, University of Wisconsin–Madison,
Madison, WI 53706, USA  S. Athanasiadou  DESY, D-15738 Zeuthen, Germany  S.
Axani  Dept. of Physics, Massachusetts Institute of Technology, Cambridge, MA
02139, USA  X. Bai  Physics Department, South Dakota School of Mines and
Technology, Rapid City, SD 57701, USA  A. Balagopal V. Dept. of Physics and
Wisconsin IceCube Particle Astrophysics Center, University of
Wisconsin–Madison, Madison, WI 53706, USA  M. Baricevic  Dept. of Physics and
Wisconsin IceCube Particle Astrophysics Center, University of
Wisconsin–Madison, Madison, WI 53706, USA  I. Bartos  Dept. of Physics,
University of Florida, Gainesville, FL 32611-8440, USA  S. W. Barwick Dept. of
Physics and Astronomy, University of California, Irvine, CA 92697, USA  V.
Basu Dept. of Physics and Wisconsin IceCube Particle Astrophysics Center,
University of Wisconsin–Madison, Madison, WI 53706, USA  R. Bay  Dept. of
Physics, University of California, Berkeley, CA 94720, USA  J. J. Beatty Dept.
of Astronomy, Ohio State University, Columbus, OH 43210, USA  Dept. of Physics
and Center for Cosmology and Astro-Particle Physics, Ohio State University,
Columbus, OH 43210, USA  K.-H. Becker  Dept. of Physics, University of
Wuppertal, D-42119 Wuppertal, Germany  J. Becker Tjus Fakultät für Physik &
Astronomie, Ruhr-Universität Bochum, D-44780 Bochum, Germany  J. Beise Dept.
of Physics and Astronomy, Uppsala University, Box 516, S-75120 Uppsala, Sweden
C. Bellenghi  Physik-department, Technische Universität München, D-85748
Garching, Germany  S. Benda  Dept. of Physics and Wisconsin IceCube Particle
Astrophysics Center, University of Wisconsin–Madison, Madison, WI 53706, USA
S. BenZvi Dept. of Physics and Astronomy, University of Rochester, Rochester,
NY 14627, USA  D. Berley  Dept. of Physics, University of Maryland, College
Park, MD 20742, USA  E. Bernardini also at Università di Padova, I-35131
Padova, Italy  DESY, D-15738 Zeuthen, Germany  D. Z. Besson  Dept. of Physics
and Astronomy, University of Kansas, Lawrence, KS 66045, USA  G. Binder  Dept.
of Physics, University of California, Berkeley, CA 94720, USA  Lawrence
Berkeley National Laboratory, Berkeley, CA 94720, USA  D. Bindig  Dept. of
Physics, University of Wuppertal, D-42119 Wuppertal, Germany  E. Blaufuss
Dept. of Physics, University of Maryland, College Park, MD 20742, USA  S. Blot
DESY, D-15738 Zeuthen, Germany  F. Bontempo  Karlsruhe Institute of
Technology, Institute for Astroparticle Physics, D-76021 Karlsruhe, Germany
J. Y. Book Department of Physics and Laboratory for Particle Physics and
Cosmology, Harvard University, Cambridge, MA 02138, USA  J. Borowka  III.
Physikalisches Institut, RWTH Aachen University, D-52056 Aachen, Germany  S.
Böser Institute of Physics, University of Mainz, Staudinger Weg 7, D-55099
Mainz, Germany  O. Botner Dept. of Physics and Astronomy, Uppsala University,
Box 516, S-75120 Uppsala, Sweden  J. Böttcher  III. Physikalisches Institut,
RWTH Aachen University, D-52056 Aachen, Germany  E. Bourbeau  Niels Bohr
Institute, University of Copenhagen, DK-2100 Copenhagen, Denmark  F. Bradascio
DESY, D-15738 Zeuthen, Germany  J. Braun  Dept. of Physics and Wisconsin
IceCube Particle Astrophysics Center, University of Wisconsin–Madison,
Madison, WI 53706, USA  B. Brinson  School of Physics and Center for
Relativistic Astrophysics, Georgia Institute of Technology, Atlanta, GA 30332,
USA  S. Bron  Département de physique nucléaire et corpusculaire, Université
de Genève, CH-1211 Genève, Switzerland  J. Brostean-Kaiser  DESY, D-15738
Zeuthen, Germany  R. T. Burley  Department of Physics, University of Adelaide,
Adelaide, 5005, Australia  R. S. Busse  Institut für Kernphysik, Westfälische
Wilhelms-Universität Münster, D-48149 Münster, Germany  M. A. Campana Dept. of
Physics, Drexel University, 3141 Chestnut Street, Philadelphia, PA 19104, USA
E. G. Carnie-Bronca  Department of Physics, University of Adelaide, Adelaide,
5005, Australia  C. Chen School of Physics and Center for Relativistic
Astrophysics, Georgia Institute of Technology, Atlanta, GA 30332, USA  Z. Chen
Dept. of Physics and Astronomy, Stony Brook University, Stony Brook, NY
11794-3800, USA  D. Chirkin Dept. of Physics and Wisconsin IceCube Particle
Astrophysics Center, University of Wisconsin–Madison, Madison, WI 53706, USA
K. Choi  Dept. of Physics, Sungkyunkwan University, Suwon 16419, Korea  B. A.
Clark Dept. of Physics and Astronomy, Michigan State University, East Lansing,
MI 48824, USA  L. Classen  Institut für Kernphysik, Westfälische Wilhelms-
Universität Münster, D-48149 Münster, Germany  A. Coleman Bartol Research
Institute and Dept. of Physics and Astronomy, University of Delaware, Newark,
DE 19716, USA  G. H. Collin  Dept. of Physics, Massachusetts Institute of
Technology, Cambridge, MA 02139, USA  A. Connolly  Dept. of Astronomy, Ohio
State University, Columbus, OH 43210, USA  Dept. of Physics and Center for
Cosmology and Astro-Particle Physics, Ohio State University, Columbus, OH
43210, USA  J. M. Conrad Dept. of Physics, Massachusetts Institute of
Technology, Cambridge, MA 02139, USA  P. Coppin Vrije Universiteit Brussel
(VUB), Dienst ELEM, B-1050 Brussels, Belgium  P. Correa Vrije Universiteit
Brussel (VUB), Dienst ELEM, B-1050 Brussels, Belgium  S. T. Countryman  Dept.
of Physics, Columbia University, New York, NY 10027, USA  D. F. Cowen  Dept.
of Astronomy and Astrophysics, Pennsylvania State University, University Park,
PA 16802, USA  Dept. of Physics, Pennsylvania State University, University
Park, PA 16802, USA  R. Cross Dept. of Physics and Astronomy, University of
Rochester, Rochester, NY 14627, USA  C. Dappen  III. Physikalisches Institut,
RWTH Aachen University, D-52056 Aachen, Germany  P. Dave School of Physics and
Center for Relativistic Astrophysics, Georgia Institute of Technology,
Atlanta, GA 30332, USA  C. De Clercq Vrije Universiteit Brussel (VUB), Dienst
ELEM, B-1050 Brussels, Belgium  J. J. DeLaunay Dept. of Physics and Astronomy,
University of Alabama, Tuscaloosa, AL 35487, USA  D. Delgado López Department
of Physics and Laboratory for Particle Physics and Cosmology, Harvard
University, Cambridge, MA 02138, USA  H. Dembinski Bartol Research Institute
and Dept. of Physics and Astronomy, University of Delaware, Newark, DE 19716,
USA  K. Deoskar  Oskar Klein Centre and Dept. of Physics, Stockholm
University, SE-10691 Stockholm, Sweden  A. Desai Dept. of Physics and
Wisconsin IceCube Particle Astrophysics Center, University of
Wisconsin–Madison, Madison, WI 53706, USA  P. Desiati Dept. of Physics and
Wisconsin IceCube Particle Astrophysics Center, University of
Wisconsin–Madison, Madison, WI 53706, USA  K. D. de Vries Vrije Universiteit
Brussel (VUB), Dienst ELEM, B-1050 Brussels, Belgium  G. de Wasseige Centre
for Cosmology, Particle Physics and Phenomenology - CP3, Université catholique
de Louvain, Louvain-la-Neuve, Belgium  T. DeYoung Dept. of Physics and
Astronomy, Michigan State University, East Lansing, MI 48824, USA  A. Diaz
Dept. of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139,
USA  J. C. Díaz-Vélez Dept. of Physics and Wisconsin IceCube Particle
Astrophysics Center, University of Wisconsin–Madison, Madison, WI 53706, USA
M. Dittmer  Institut für Kernphysik, Westfälische Wilhelms-Universität
Münster, D-48149 Münster, Germany  H. Dujmovic Karlsruhe Institute of
Technology, Institute for Astroparticle Physics, D-76021 Karlsruhe, Germany
M. A. DuVernois Dept. of Physics and Wisconsin IceCube Particle Astrophysics
Center, University of Wisconsin–Madison, Madison, WI 53706, USA  T. Ehrhardt
Institute of Physics, University of Mainz, Staudinger Weg 7, D-55099 Mainz,
Germany  P. Eller Physik-department, Technische Universität München, D-85748
Garching, Germany  R. Engel  Karlsruhe Institute of Technology, Institute for
Astroparticle Physics, D-76021 Karlsruhe, Germany  Karlsruhe Institute of
Technology, Institute of Experimental Particle Physics, D-76021 Karlsruhe,
Germany  H. Erpenbeck  III. Physikalisches Institut, RWTH Aachen University,
D-52056 Aachen, Germany  J. Evans  Dept. of Physics, University of Maryland,
College Park, MD 20742, USA  P. A. Evenson  Bartol Research Institute and
Dept. of Physics and Astronomy, University of Delaware, Newark, DE 19716, USA
K. L. Fan  Dept. of Physics, University of Maryland, College Park, MD 20742,
USA  A. R. Fazely Dept. of Physics, Southern University, Baton Rouge, LA
70813, USA  A. Fedynitch Institute of Physics, Academia Sinica, Taipei, 11529,
Taiwan  N. Feigl  Institut für Physik, Humboldt-Universität zu Berlin, D-12489
Berlin, Germany  S. Fiedlschuster  Erlangen Centre for Astroparticle Physics,
Friedrich-Alexander-Universität Erlangen-Nürnberg, D-91058 Erlangen, Germany
A. T. Fienberg  Dept. of Physics, Pennsylvania State University, University
Park, PA 16802, USA  C. Finley Oskar Klein Centre and Dept. of Physics,
Stockholm University, SE-10691 Stockholm, Sweden  L. Fischer  DESY, D-15738
Zeuthen, Germany  D. Fox Dept. of Astronomy and Astrophysics, Pennsylvania
State University, University Park, PA 16802, USA  A. Franckowiak Fakultät für
Physik & Astronomie, Ruhr-Universität Bochum, D-44780 Bochum, Germany  DESY,
D-15738 Zeuthen, Germany  E. Friedman  Dept. of Physics, University of
Maryland, College Park, MD 20742, USA  A. Fritz  Institute of Physics,
University of Mainz, Staudinger Weg 7, D-55099 Mainz, Germany  P. Fürst  III.
Physikalisches Institut, RWTH Aachen University, D-52056 Aachen, Germany  T.
K. Gaisser Bartol Research Institute and Dept. of Physics and Astronomy,
University of Delaware, Newark, DE 19716, USA  J. Gallagher  Dept. of
Astronomy, University of Wisconsin–Madison, Madison, WI 53706, USA  E. Ganster
III. Physikalisches Institut, RWTH Aachen University, D-52056 Aachen, Germany
A. Garcia Department of Physics and Laboratory for Particle Physics and
Cosmology, Harvard University, Cambridge, MA 02138, USA  S. Garrappa DESY,
D-15738 Zeuthen, Germany  L. Gerhardt  Lawrence Berkeley National Laboratory,
Berkeley, CA 94720, USA  A. Ghadimi Dept. of Physics and Astronomy, University
of Alabama, Tuscaloosa, AL 35487, USA  C. Glaser  Dept. of Physics and
Astronomy, Uppsala University, Box 516, S-75120 Uppsala, Sweden  T. Glauch
Physik-department, Technische Universität München, D-85748 Garching, Germany
T. Glüsenkamp Erlangen Centre for Astroparticle Physics, Friedrich-Alexander-
Universität Erlangen-Nürnberg, D-91058 Erlangen, Germany  N. Goehlke
Karlsruhe Institute of Technology, Institute of Experimental Particle Physics,
D-76021 Karlsruhe, Germany  J. G. Gonzalez  Bartol Research Institute and
Dept. of Physics and Astronomy, University of Delaware, Newark, DE 19716, USA
S. Goswami  Dept. of Physics and Astronomy, University of Alabama, Tuscaloosa,
AL 35487, USA  D. Grant  Dept. of Physics and Astronomy, Michigan State
University, East Lansing, MI 48824, USA  T. Grégoire  Dept. of Physics,
Pennsylvania State University, University Park, PA 16802, USA  S. Griswold
Dept. of Physics and Astronomy, University of Rochester, Rochester, NY 14627,
USA  C. Günther  III. Physikalisches Institut, RWTH Aachen University, D-52056
Aachen, Germany  P. Gutjahr Dept. of Physics, TU Dortmund University, D-44221
Dortmund, Germany  C. Haack  Physik-department, Technische Universität
München, D-85748 Garching, Germany  A. Hallgren Dept. of Physics and
Astronomy, Uppsala University, Box 516, S-75120 Uppsala, Sweden  R. Halliday
Dept. of Physics and Astronomy, Michigan State University, East Lansing, MI
48824, USA  L. Halve III. Physikalisches Institut, RWTH Aachen University,
D-52056 Aachen, Germany  F. Halzen Dept. of Physics and Wisconsin IceCube
Particle Astrophysics Center, University of Wisconsin–Madison, Madison, WI
53706, USA  H. Hamdaoui  Dept. of Physics and Astronomy, Stony Brook
University, Stony Brook, NY 11794-3800, USA  M. Ha Minh  Physik-department,
Technische Universität München, D-85748 Garching, Germany  K. Hanson  Dept. of
Physics and Wisconsin IceCube Particle Astrophysics Center, University of
Wisconsin–Madison, Madison, WI 53706, USA  J. Hardin  Dept. of Physics,
Massachusetts Institute of Technology, Cambridge, MA 02139, USA  Dept. of
Physics and Wisconsin IceCube Particle Astrophysics Center, University of
Wisconsin–Madison, Madison, WI 53706, USA  A. A. Harnisch  Dept. of Physics
and Astronomy, Michigan State University, East Lansing, MI 48824, USA  P.
Hatch  Dept. of Physics, Engineering Physics, and Astronomy, Queen’s
University, Kingston, ON K7L 3N6, Canada  A. Haungs Karlsruhe Institute of
Technology, Institute for Astroparticle Physics, D-76021 Karlsruhe, Germany
K. Helbing Dept. of Physics, University of Wuppertal, D-42119 Wuppertal,
Germany  J. Hellrung  III. Physikalisches Institut, RWTH Aachen University,
D-52056 Aachen, Germany  F. Henningsen Physik-department, Technische
Universität München, D-85748 Garching, Germany  L. Heuermann  III.
Physikalisches Institut, RWTH Aachen University, D-52056 Aachen, Germany  S.
Hickford  Dept. of Physics, University of Wuppertal, D-42119 Wuppertal,
Germany  C. Hill Dept. of Physics and The International Center for Hadron
Astrophysics, Chiba University, Chiba 263-8522, Japan  G. C. Hill  Department
of Physics, University of Adelaide, Adelaide, 5005, Australia  K. D. Hoffman
Dept. of Physics, University of Maryland, College Park, MD 20742, USA  K.
Hoshina  also at Earthquake Research Institute, University of Tokyo, Bunkyo,
Tokyo 113-0032, Japan  Dept. of Physics and Wisconsin IceCube Particle
Astrophysics Center, University of Wisconsin–Madison, Madison, WI 53706, USA
W. Hou  Karlsruhe Institute of Technology, Institute for Astroparticle
Physics, D-76021 Karlsruhe, Germany  T. Huber Karlsruhe Institute of
Technology, Institute for Astroparticle Physics, D-76021 Karlsruhe, Germany
K. Hultqvist Oskar Klein Centre and Dept. of Physics, Stockholm University,
SE-10691 Stockholm, Sweden  M. Hünnefeld  Dept. of Physics, TU Dortmund
University, D-44221 Dortmund, Germany  R. Hussain  Dept. of Physics and
Wisconsin IceCube Particle Astrophysics Center, University of
Wisconsin–Madison, Madison, WI 53706, USA  K. Hymon  Dept. of Physics, TU
Dortmund University, D-44221 Dortmund, Germany  S. In  Dept. of Physics,
Sungkyunkwan University, Suwon 16419, Korea  N. Iovine Université Libre de
Bruxelles, Science Faculty CP230, B-1050 Brussels, Belgium  A. Ishihara  Dept.
of Physics and The International Center for Hadron Astrophysics, Chiba
University, Chiba 263-8522, Japan  M. Jansson  Oskar Klein Centre and Dept. of
Physics, Stockholm University, SE-10691 Stockholm, Sweden  G. S. Japaridze
CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA  M. Jeong  Dept. of
Physics, Sungkyunkwan University, Suwon 16419, Korea  M. Jin Department of
Physics and Laboratory for Particle Physics and Cosmology, Harvard University,
Cambridge, MA 02138, USA  B. J. P. Jones Dept. of Physics, University of Texas
at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX
76019, USA  D. Kang Karlsruhe Institute of Technology, Institute for
Astroparticle Physics, D-76021 Karlsruhe, Germany  W. Kang Dept. of Physics,
Sungkyunkwan University, Suwon 16419, Korea  X. Kang  Dept. of Physics, Drexel
University, 3141 Chestnut Street, Philadelphia, PA 19104, USA  A. Kappes
Institut für Kernphysik, Westfälische Wilhelms-Universität Münster, D-48149
Münster, Germany  D. Kappesser  Institute of Physics, University of Mainz,
Staudinger Weg 7, D-55099 Mainz, Germany  L. Kardum  Dept. of Physics, TU
Dortmund University, D-44221 Dortmund, Germany  T. Karg DESY, D-15738 Zeuthen,
Germany  M. Karl Physik-department, Technische Universität München, D-85748
Garching, Germany  A. Karle Dept. of Physics and Wisconsin IceCube Particle
Astrophysics Center, University of Wisconsin–Madison, Madison, WI 53706, USA
U. Katz Erlangen Centre for Astroparticle Physics, Friedrich-Alexander-
Universität Erlangen-Nürnberg, D-91058 Erlangen, Germany  M. Kauer Dept. of
Physics and Wisconsin IceCube Particle Astrophysics Center, University of
Wisconsin–Madison, Madison, WI 53706, USA  J. L. Kelley Dept. of Physics and
Wisconsin IceCube Particle Astrophysics Center, University of
Wisconsin–Madison, Madison, WI 53706, USA  A. Kheirandish Dept. of Physics,
Pennsylvania State University, University Park, PA 16802, USA  K. Kin  Dept.
of Physics and The International Center for Hadron Astrophysics, Chiba
University, Chiba 263-8522, Japan  J. Kiryluk  Dept. of Physics and Astronomy,
Stony Brook University, Stony Brook, NY 11794-3800, USA  S. R. Klein Dept. of
Physics, University of California, Berkeley, CA 94720, USA  Lawrence Berkeley
National Laboratory, Berkeley, CA 94720, USA  A. Kochocki Dept. of Physics and
Astronomy, Michigan State University, East Lansing, MI 48824, USA  R. Koirala
Bartol Research Institute and Dept. of Physics and Astronomy, University of
Delaware, Newark, DE 19716, USA  H. Kolanoski Institut für Physik, Humboldt-
Universität zu Berlin, D-12489 Berlin, Germany  T. Kontrimas  Physik-
department, Technische Universität München, D-85748 Garching, Germany  L.
Köpke  Institute of Physics, University of Mainz, Staudinger Weg 7, D-55099
Mainz, Germany  C. Kopper Dept. of Physics and Astronomy, Michigan State
University, East Lansing, MI 48824, USA  D. J. Koskinen Niels Bohr Institute,
University of Copenhagen, DK-2100 Copenhagen, Denmark  P. Koundal Karlsruhe
Institute of Technology, Institute for Astroparticle Physics, D-76021
Karlsruhe, Germany  M. Kovacevich Dept. of Physics, Drexel University, 3141
Chestnut Street, Philadelphia, PA 19104, USA  M. Kowalski Institut für Physik,
Humboldt-Universität zu Berlin, D-12489 Berlin, Germany  DESY, D-15738
Zeuthen, Germany  T. Kozynets  Niels Bohr Institute, University of Copenhagen,
DK-2100 Copenhagen, Denmark  E. Krupczak  Dept. of Physics and Astronomy,
Michigan State University, East Lansing, MI 48824, USA  E. Kun  Fakultät für
Physik & Astronomie, Ruhr-Universität Bochum, D-44780 Bochum, Germany  N.
Kurahashi Dept. of Physics, Drexel University, 3141 Chestnut Street,
Philadelphia, PA 19104, USA  N. Lad  DESY, D-15738 Zeuthen, Germany  C.
Lagunas Gualda DESY, D-15738 Zeuthen, Germany  M. J. Larson Dept. of Physics,
University of Maryland, College Park, MD 20742, USA  F. Lauber Dept. of
Physics, University of Wuppertal, D-42119 Wuppertal, Germany  J. P. Lazar
Department of Physics and Laboratory for Particle Physics and Cosmology,
Harvard University, Cambridge, MA 02138, USA  Dept. of Physics and Wisconsin
IceCube Particle Astrophysics Center, University of Wisconsin–Madison,
Madison, WI 53706, USA  J. W. Lee Dept. of Physics, Sungkyunkwan University,
Suwon 16419, Korea  K. Leonard Dept. of Physics and Wisconsin IceCube Particle
Astrophysics Center, University of Wisconsin–Madison, Madison, WI 53706, USA
A. Leszczyńska Bartol Research Institute and Dept. of Physics and Astronomy,
University of Delaware, Newark, DE 19716, USA  M. Lincetto  Fakultät für
Physik & Astronomie, Ruhr-Universität Bochum, D-44780 Bochum, Germany  Q. R.
Liu Dept. of Physics and Wisconsin IceCube Particle Astrophysics Center,
University of Wisconsin–Madison, Madison, WI 53706, USA  M. Liubarska  Dept.
of Physics, University of Alberta, Edmonton, Alberta, Canada T6G 2E1  E.
Lohfink  Institute of Physics, University of Mainz, Staudinger Weg 7, D-55099
Mainz, Germany  C. Love  Dept. of Physics, Drexel University, 3141 Chestnut
Street, Philadelphia, PA 19104, USA  C. J. Lozano Mariscal  Institut für
Kernphysik, Westfälische Wilhelms-Universität Münster, D-48149 Münster,
Germany  L. Lu Dept. of Physics and Wisconsin IceCube Particle Astrophysics
Center, University of Wisconsin–Madison, Madison, WI 53706, USA  F. Lucarelli
Département de physique nucléaire et corpusculaire, Université de Genève,
CH-1211 Genève, Switzerland  A. Ludwig Dept. of Physics and Astronomy,
Michigan State University, East Lansing, MI 48824, USA  Department of Physics
and Astronomy, UCLA, Los Angeles, CA 90095, USA  W. Luszczak Dept. of Physics
and Wisconsin IceCube Particle Astrophysics Center, University of
Wisconsin–Madison, Madison, WI 53706, USA  Y. Lyu Dept. of Physics, University
of California, Berkeley, CA 94720, USA  Lawrence Berkeley National Laboratory,
Berkeley, CA 94720, USA  W. Y. Ma DESY, D-15738 Zeuthen, Germany  J. Madsen
Dept. of Physics and Wisconsin IceCube Particle Astrophysics Center,
University of Wisconsin–Madison, Madison, WI 53706, USA  K. B. M. Mahn  Dept.
of Physics and Astronomy, Michigan State University, East Lansing, MI 48824,
USA  Y. Makino  Dept. of Physics and Wisconsin IceCube Particle Astrophysics
Center, University of Wisconsin–Madison, Madison, WI 53706, USA  S. Mancina
Dept. of Physics and Wisconsin IceCube Particle Astrophysics Center,
University of Wisconsin–Madison, Madison, WI 53706, USA  W. Marie Sainte
Dept. of Physics and Wisconsin IceCube Particle Astrophysics Center,
University of Wisconsin–Madison, Madison, WI 53706, USA  I. C. Mariş
Université Libre de Bruxelles, Science Faculty CP230, B-1050 Brussels, Belgium
S. Márka  Dept. of Physics, Columbia University, New York, NY 10027, USA  Z.
Márka  Dept. of Physics, Columbia University, New York, NY 10027, USA  M.
Marsee  Dept. of Physics and Astronomy, University of Alabama, Tuscaloosa, AL
35487, USA  I. Martinez-Soler  Department of Physics and Laboratory for
Particle Physics and Cosmology, Harvard University, Cambridge, MA 02138, USA
R. Maruyama Dept. of Physics, Yale University, New Haven, CT 06520, USA  T.
McElroy  Dept. of Physics, University of Alberta, Edmonton, Alberta, Canada
T6G 2E1  F. McNally Department of Physics, Mercer University, Macon, GA
31207-0001, USA  J. V. Mead  Niels Bohr Institute, University of Copenhagen,
DK-2100 Copenhagen, Denmark  K. Meagher Dept. of Physics and Wisconsin IceCube
Particle Astrophysics Center, University of Wisconsin–Madison, Madison, WI
53706, USA  S. Mechbal  DESY, D-15738 Zeuthen, Germany  A. Medina  Dept. of
Physics and Center for Cosmology and Astro-Particle Physics, Ohio State
University, Columbus, OH 43210, USA  M. Meier Dept. of Physics and The
International Center for Hadron Astrophysics, Chiba University, Chiba
263-8522, Japan  S. Meighen-Berger Physik-department, Technische Universität
München, D-85748 Garching, Germany  Y. Merckx  Vrije Universiteit Brussel
(VUB), Dienst ELEM, B-1050 Brussels, Belgium  J. Micallef  Dept. of Physics
and Astronomy, Michigan State University, East Lansing, MI 48824, USA  D.
Mockler  Université Libre de Bruxelles, Science Faculty CP230, B-1050
Brussels, Belgium  T. Montaruli Département de physique nucléaire et
corpusculaire, Université de Genève, CH-1211 Genève, Switzerland  R. W. Moore
Dept. of Physics, University of Alberta, Edmonton, Alberta, Canada T6G 2E1  R.
Morse  Dept. of Physics and Wisconsin IceCube Particle Astrophysics Center,
University of Wisconsin–Madison, Madison, WI 53706, USA  M. Moulai Dept. of
Physics and Wisconsin IceCube Particle Astrophysics Center, University of
Wisconsin–Madison, Madison, WI 53706, USA  T. Mukherjee  Karlsruhe Institute
of Technology, Institute for Astroparticle Physics, D-76021 Karlsruhe, Germany
R. Naab DESY, D-15738 Zeuthen, Germany  R. Nagai Dept. of Physics and The
International Center for Hadron Astrophysics, Chiba University, Chiba
263-8522, Japan  U. Naumann  Dept. of Physics, University of Wuppertal,
D-42119 Wuppertal, Germany  J. Necker DESY, D-15738 Zeuthen, Germany  M.
Neumann  Institut für Kernphysik, Westfälische Wilhelms-Universität Münster,
D-48149 Münster, Germany  H. Niederhausen Dept. of Physics and Astronomy,
Michigan State University, East Lansing, MI 48824, USA  M. U. Nisa Dept. of
Physics and Astronomy, Michigan State University, East Lansing, MI 48824, USA
S. C. Nowicki  Dept. of Physics and Astronomy, Michigan State University, East
Lansing, MI 48824, USA  A. Obertacke Pollmann Dept. of Physics, University of
Wuppertal, D-42119 Wuppertal, Germany  M. Oehler  Karlsruhe Institute of
Technology, Institute for Astroparticle Physics, D-76021 Karlsruhe, Germany
B. Oeyen Dept. of Physics and Astronomy, University of Gent, B-9000 Gent,
Belgium  A. Olivas  Dept. of Physics, University of Maryland, College Park, MD
20742, USA  R. Orsoe  Physik-department, Technische Universität München,
D-85748 Garching, Germany  J. Osborn  Dept. of Physics and Wisconsin IceCube
Particle Astrophysics Center, University of Wisconsin–Madison, Madison, WI
53706, USA  E. O’Sullivan Dept. of Physics and Astronomy, Uppsala University,
Box 516, S-75120 Uppsala, Sweden  H. Pandya Bartol Research Institute and
Dept. of Physics and Astronomy, University of Delaware, Newark, DE 19716, USA
D. V. Pankova  Dept. of Physics, Pennsylvania State University, University
Park, PA 16802, USA  N. Park Dept. of Physics, Engineering Physics, and
Astronomy, Queen’s University, Kingston, ON K7L 3N6, Canada  G. K. Parker
Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science
Hall Rm 108, Box 19059, Arlington, TX 76019, USA  E. N. Paudel Bartol Research
Institute and Dept. of Physics and Astronomy, University of Delaware, Newark,
DE 19716, USA  L. Paul  Department of Physics, Marquette University,
Milwaukee, WI, 53201, USA  C. Pérez de los Heros Dept. of Physics and
Astronomy, Uppsala University, Box 516, S-75120 Uppsala, Sweden  L. Peters
III. Physikalisches Institut, RWTH Aachen University, D-52056 Aachen, Germany
J. Peterson  Dept. of Physics and Wisconsin IceCube Particle Astrophysics
Center, University of Wisconsin–Madison, Madison, WI 53706, USA  S. Philippen
III. Physikalisches Institut, RWTH Aachen University, D-52056 Aachen, Germany
S. Pieper  Dept. of Physics, University of Wuppertal, D-42119 Wuppertal,
Germany  A. Pizzuto Dept. of Physics and Wisconsin IceCube Particle
Astrophysics Center, University of Wisconsin–Madison, Madison, WI 53706, USA
M. Plum Physics Department, South Dakota School of Mines and Technology, Rapid
City, SD 57701, USA  Y. Popovych  Institute of Physics, University of Mainz,
Staudinger Weg 7, D-55099 Mainz, Germany  A. Porcelli Dept. of Physics and
Astronomy, University of Gent, B-9000 Gent, Belgium  M. Prado Rodriguez  Dept.
of Physics and Wisconsin IceCube Particle Astrophysics Center, University of
Wisconsin–Madison, Madison, WI 53706, USA  B. Pries  Dept. of Physics and
Astronomy, Michigan State University, East Lansing, MI 48824, USA  G. T.
Przybylski  Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA  C.
Raab Université Libre de Bruxelles, Science Faculty CP230, B-1050 Brussels,
Belgium  J. Rack-Helleis  Institute of Physics, University of Mainz,
Staudinger Weg 7, D-55099 Mainz, Germany  M. Rameez Niels Bohr Institute,
University of Copenhagen, DK-2100 Copenhagen, Denmark  K. Rawlins  Dept. of
Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr.,
Anchorage, AK 99508, USA  Z. Rechav  Dept. of Physics and Wisconsin IceCube
Particle Astrophysics Center, University of Wisconsin–Madison, Madison, WI
53706, USA  A. Rehman Bartol Research Institute and Dept. of Physics and
Astronomy, University of Delaware, Newark, DE 19716, USA  P. Reichherzer
Fakultät für Physik & Astronomie, Ruhr-Universität Bochum, D-44780 Bochum,
Germany  G. Renzi  Université Libre de Bruxelles, Science Faculty CP230,
B-1050 Brussels, Belgium  E. Resconi Physik-department, Technische Universität
München, D-85748 Garching, Germany  S. Reusch  DESY, D-15738 Zeuthen, Germany
W. Rhode Dept. of Physics, TU Dortmund University, D-44221 Dortmund, Germany
M. Richman  Dept. of Physics, Drexel University, 3141 Chestnut Street,
Philadelphia, PA 19104, USA  B. Riedel Dept. of Physics and Wisconsin IceCube
Particle Astrophysics Center, University of Wisconsin–Madison, Madison, WI
53706, USA  E. J. Roberts  Department of Physics, University of Adelaide,
Adelaide, 5005, Australia  S. Robertson  Dept. of Physics, University of
California, Berkeley, CA 94720, USA  Lawrence Berkeley National Laboratory,
Berkeley, CA 94720, USA  S. Rodan  Dept. of Physics, Sungkyunkwan University,
Suwon 16419, Korea  G. Roellinghoff  Dept. of Physics, Sungkyunkwan
University, Suwon 16419, Korea  M. Rongen Institute of Physics, University of
Mainz, Staudinger Weg 7, D-55099 Mainz, Germany  C. Rott Department of Physics
and Astronomy, University of Utah, Salt Lake City, UT 84112, USA  Dept. of
Physics, Sungkyunkwan University, Suwon 16419, Korea  T. Ruhe  Dept. of
Physics, TU Dortmund University, D-44221 Dortmund, Germany  L. Ruohan  Physik-
department, Technische Universität München, D-85748 Garching, Germany  D.
Ryckbosch  Dept. of Physics and Astronomy, University of Gent, B-9000 Gent,
Belgium  D. Rysewyk Cantu Dept. of Physics and Astronomy, Michigan State
University, East Lansing, MI 48824, USA  I. Safa Department of Physics and
Laboratory for Particle Physics and Cosmology, Harvard University, Cambridge,
MA 02138, USA  Dept. of Physics and Wisconsin IceCube Particle Astrophysics
Center, University of Wisconsin–Madison, Madison, WI 53706, USA  J. Saffer
Karlsruhe Institute of Technology, Institute of Experimental Particle Physics,
D-76021 Karlsruhe, Germany  D. Salazar-Gallegos Dept. of Physics and
Astronomy, Michigan State University, East Lansing, MI 48824, USA  P.
Sampathkumar  Karlsruhe Institute of Technology, Institute for Astroparticle
Physics, D-76021 Karlsruhe, Germany  S. E. Sanchez Herrera  Dept. of Physics
and Astronomy, Michigan State University, East Lansing, MI 48824, USA  A.
Sandrock Dept. of Physics, TU Dortmund University, D-44221 Dortmund, Germany
M. Santander Dept. of Physics and Astronomy, University of Alabama,
Tuscaloosa, AL 35487, USA  S. Sarkar Dept. of Physics, University of Alberta,
Edmonton, Alberta, Canada T6G 2E1  S. Sarkar Dept. of Physics, University of
Oxford, Parks Road, Oxford OX1 3PU, UK  K. Satalecka DESY, D-15738 Zeuthen,
Germany  M. Schaufel  III. Physikalisches Institut, RWTH Aachen University,
D-52056 Aachen, Germany  H. Schieler  Karlsruhe Institute of Technology,
Institute for Astroparticle Physics, D-76021 Karlsruhe, Germany  S. Schindler
Erlangen Centre for Astroparticle Physics, Friedrich-Alexander-Universität
Erlangen-Nürnberg, D-91058 Erlangen, Germany  B. Schlueter  Institut für
Kernphysik, Westfälische Wilhelms-Universität Münster, D-48149 Münster,
Germany  T. Schmidt  Dept. of Physics, University of Maryland, College Park,
MD 20742, USA  J. Schneider Erlangen Centre for Astroparticle Physics,
Friedrich-Alexander-Universität Erlangen-Nürnberg, D-91058 Erlangen, Germany
F. G. Schröder Karlsruhe Institute of Technology, Institute for Astroparticle
Physics, D-76021 Karlsruhe, Germany  Bartol Research Institute and Dept. of
Physics and Astronomy, University of Delaware, Newark, DE 19716, USA  L.
Schumacher  Physik-department, Technische Universität München, D-85748
Garching, Germany  G. Schwefer  III. Physikalisches Institut, RWTH Aachen
University, D-52056 Aachen, Germany  S. Sclafani Dept. of Physics, Drexel
University, 3141 Chestnut Street, Philadelphia, PA 19104, USA  D. Seckel
Bartol Research Institute and Dept. of Physics and Astronomy, University of
Delaware, Newark, DE 19716, USA  S. Seunarine  Dept. of Physics, University of
Wisconsin, River Falls, WI 54022, USA  A. Sharma  Dept. of Physics and
Astronomy, Uppsala University, Box 516, S-75120 Uppsala, Sweden  S. Shefali
Karlsruhe Institute of Technology, Institute of Experimental Particle Physics,
D-76021 Karlsruhe, Germany  N. Shimizu  Dept. of Physics and The International
Center for Hadron Astrophysics, Chiba University, Chiba 263-8522, Japan  M.
Silva Dept. of Physics and Wisconsin IceCube Particle Astrophysics Center,
University of Wisconsin–Madison, Madison, WI 53706, USA  A. C. Silva Oliveira
Dept. of Physics, Columbia University, New York, NY 10027, USA  B. Skrzypek
Department of Physics and Laboratory for Particle Physics and Cosmology,
Harvard University, Cambridge, MA 02138, USA  B. Smithers Dept. of Physics,
University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box
19059, Arlington, TX 76019, USA  R. Snihur  Dept. of Physics and Wisconsin
IceCube Particle Astrophysics Center, University of Wisconsin–Madison,
Madison, WI 53706, USA  J. Soedingrekso  Dept. of Physics, TU Dortmund
University, D-44221 Dortmund, Germany  A. Sogaard  Niels Bohr Institute,
University of Copenhagen, DK-2100 Copenhagen, Denmark  D. Soldin Karlsruhe
Institute of Technology, Institute of Experimental Particle Physics, D-76021
Karlsruhe, Germany  C. Spannfellner  Physik-department, Technische Universität
München, D-85748 Garching, Germany  G. M. Spiczak Dept. of Physics, University
of Wisconsin, River Falls, WI 54022, USA  C. Spiering DESY, D-15738 Zeuthen,
Germany  M. Stamatikos  Dept. of Physics and Center for Cosmology and Astro-
Particle Physics, Ohio State University, Columbus, OH 43210, USA  T. Stanev
Bartol Research Institute and Dept. of Physics and Astronomy, University of
Delaware, Newark, DE 19716, USA  R. Stein DESY, D-15738 Zeuthen, Germany  T.
Stezelberger Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
T. Stürwald  Dept. of Physics, University of Wuppertal, D-42119 Wuppertal,
Germany  T. Stuttard Niels Bohr Institute, University of Copenhagen, DK-2100
Copenhagen, Denmark  A. G. Sullivan  Dept. of Physics, Columbia University,
New York, NY 10027, USA  G. W. Sullivan Dept. of Physics, University of
Maryland, College Park, MD 20742, USA  I. Taboada School of Physics and Center
for Relativistic Astrophysics, Georgia Institute of Technology, Atlanta, GA
30332, USA  S. Ter-Antonyan Dept. of Physics, Southern University, Baton
Rouge, LA 70813, USA  W. G. Thompson Department of Physics and Laboratory for
Particle Physics and Cosmology, Harvard University, Cambridge, MA 02138, USA
J. Thwaites  Dept. of Physics and Wisconsin IceCube Particle Astrophysics
Center, University of Wisconsin–Madison, Madison, WI 53706, USA  S. Tilav
Bartol Research Institute and Dept. of Physics and Astronomy, University of
Delaware, Newark, DE 19716, USA  K. Tollefson Dept. of Physics and Astronomy,
Michigan State University, East Lansing, MI 48824, USA  C. Tönnis  Institute
of Basic Science, Sungkyunkwan University, Suwon 16419, Korea  S. Toscano
Université Libre de Bruxelles, Science Faculty CP230, B-1050 Brussels, Belgium
D. Tosi  Dept. of Physics and Wisconsin IceCube Particle Astrophysics Center,
University of Wisconsin–Madison, Madison, WI 53706, USA  A. Trettin  DESY,
D-15738 Zeuthen, Germany  C. F. Tung School of Physics and Center for
Relativistic Astrophysics, Georgia Institute of Technology, Atlanta, GA 30332,
USA  R. Turcotte  Karlsruhe Institute of Technology, Institute for
Astroparticle Physics, D-76021 Karlsruhe, Germany  J. P. Twagirayezu  Dept. of
Physics and Astronomy, Michigan State University, East Lansing, MI 48824, USA
B. Ty  Dept. of Physics and Wisconsin IceCube Particle Astrophysics Center,
University of Wisconsin–Madison, Madison, WI 53706, USA  M. A. Unland
Elorrieta Institut für Kernphysik, Westfälische Wilhelms-Universität Münster,
D-48149 Münster, Germany  K. Upshaw  Dept. of Physics, Southern University,
Baton Rouge, LA 70813, USA  N. Valtonen-Mattila  Dept. of Physics and
Astronomy, Uppsala University, Box 516, S-75120 Uppsala, Sweden  J.
Vandenbroucke Dept. of Physics and Wisconsin IceCube Particle Astrophysics
Center, University of Wisconsin–Madison, Madison, WI 53706, USA  N. van
Eijndhoven Vrije Universiteit Brussel (VUB), Dienst ELEM, B-1050 Brussels,
Belgium  D. Vannerom  Dept. of Physics, Massachusetts Institute of Technology,
Cambridge, MA 02139, USA  J. van Santen DESY, D-15738 Zeuthen, Germany  J.
Vara  Institut für Kernphysik, Westfälische Wilhelms-Universität Münster,
D-48149 Münster, Germany  J. Veitch-Michaelis  Dept. of Physics and Wisconsin
IceCube Particle Astrophysics Center, University of Wisconsin–Madison,
Madison, WI 53706, USA  S. Verpoest Dept. of Physics and Astronomy, University
of Gent, B-9000 Gent, Belgium  D. Veske Dept. of Physics, Columbia University,
New York, NY 10027, USA  C. Walck  Oskar Klein Centre and Dept. of Physics,
Stockholm University, SE-10691 Stockholm, Sweden  W. Wang  Dept. of Physics
and Wisconsin IceCube Particle Astrophysics Center, University of
Wisconsin–Madison, Madison, WI 53706, USA  T. B. Watson Dept. of Physics,
University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box
19059, Arlington, TX 76019, USA  C. Weaver Dept. of Physics and Astronomy,
Michigan State University, East Lansing, MI 48824, USA  P. Weigel  Dept. of
Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA  A.
Weindl  Karlsruhe Institute of Technology, Institute for Astroparticle
Physics, D-76021 Karlsruhe, Germany  J. Weldert  Institute of Physics,
University of Mainz, Staudinger Weg 7, D-55099 Mainz, Germany  C. Wendt Dept.
of Physics and Wisconsin IceCube Particle Astrophysics Center, University of
Wisconsin–Madison, Madison, WI 53706, USA  J. Werthebach  Dept. of Physics, TU
Dortmund University, D-44221 Dortmund, Germany  M. Weyrauch  Karlsruhe
Institute of Technology, Institute for Astroparticle Physics, D-76021
Karlsruhe, Germany  N. Whitehorn Dept. of Physics and Astronomy, Michigan
State University, East Lansing, MI 48824, USA  Department of Physics and
Astronomy, UCLA, Los Angeles, CA 90095, USA  C. H. Wiebusch III.
Physikalisches Institut, RWTH Aachen University, D-52056 Aachen, Germany  N.
Willey  Dept. of Physics and Astronomy, Michigan State University, East
Lansing, MI 48824, USA  D. R. Williams  Dept. of Physics and Astronomy,
University of Alabama, Tuscaloosa, AL 35487, USA  M. Wolf Dept. of Physics and
Wisconsin IceCube Particle Astrophysics Center, University of
Wisconsin–Madison, Madison, WI 53706, USA  G. Wrede  Erlangen Centre for
Astroparticle Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg,
D-91058 Erlangen, Germany  J. Wulff  Fakultät für Physik & Astronomie, Ruhr-
Universität Bochum, D-44780 Bochum, Germany  X. W. Xu  Dept. of Physics,
Southern University, Baton Rouge, LA 70813, USA  J. P. Yanez  Dept. of
Physics, University of Alberta, Edmonton, Alberta, Canada T6G 2E1  E. Yildizci
Dept. of Physics and Wisconsin IceCube Particle Astrophysics Center,
University of Wisconsin–Madison, Madison, WI 53706, USA  S. Yoshida Dept. of
Physics and The International Center for Hadron Astrophysics, Chiba
University, Chiba 263-8522, Japan  S. Yu  Dept. of Physics and Astronomy,
Michigan State University, East Lansing, MI 48824, USA  T. Yuan Dept. of
Physics and Wisconsin IceCube Particle Astrophysics Center, University of
Wisconsin–Madison, Madison, WI 53706, USA  Z. Zhang  Dept. of Physics and
Astronomy, Stony Brook University, Stony Brook, NY 11794-3800, USA  P. Zhelnin
Department of Physics and Laboratory for Particle Physics and Cosmology,
Harvard University, Cambridge, MA 02138, USA

###### Abstract

Using data from the IceCube Neutrino Observatory, we searched for high-energy
neutrino emission from the gravitational-wave events detected by advanced LIGO
and Virgo detectors during their third observing run. We did a low-latency
follow-up on the public candidate events released during the detectors’ third
observing run and an archival search on the 80 confident events reported in
GWTC-2.1 and GWTC-3 catalogs. An extended search was also conducted for
neutrino emission on longer timescales from neutron star containing mergers.
Follow-up searches on the candidate optical counterpart of GW190521 were also
conducted. We used two methods; an unbinned maximum likelihood analysis and a
Bayesian analysis using astrophysical priors, both of which were previously
used to search for high-energy neutrino emission from gravitational-wave
events. No significant neutrino emission was observed by any analysis and
upper limits were placed on the time-integrated neutrino flux as well as the
total isotropic equivalent energy emitted in high-energy neutrinos.

high-energy astrophysics, neutrino astronomy, multi-messenger astrophysics

##  1 Introduction

Since the initial discoveries of astrophysical high-energy neutrinos in 2013
(Aartsen et al., 2013, 2014) and gravitational waves (GWs) in 2015 (Abbott et
al., 2016a), we have entered an exciting era of multi-messenger astronomy. We
now have over 10 years of IceCube neutrino data from the full detector
configuration (Aartsen et al., 2017) and 90 reported GW events with high
astrophysical probability by the LIGO Scientific, Virgo and KAGRA
Collaborations (LVK) (Abbott et al., 2019, 2021a, 2021b). This abundance of
multi-messenger data allows for statistically robust searches for common
sources of GWs and high-energy neutrinos. Searches dating back before the
individual confident discoveries of astrophysical GWs and high-energy
neutrinos have not found a significant joint emission (Aso et al., 2008; van
Elewyck et al., 2009; Bartos et al., 2011; Baret et al., 2012; Adrián-Martínez
et al., 2013; Aartsen et al., 2014a; Adrián-Martínez et al., 2016). Following
the first confident GW observation (Abbott et al., 2016b), several attempts
from IceCube and ANTARES have not found significant emission of coincident
high energy neutrinos (Albert et al., 2017a, b, 2020; Aartsen et al., 2020;
Veske et al., 2021b). Searches for neutrinos in the low-energy regime have
also been conducted by IceCube (Abbasi et al., 2021), Super-Kamiokande (Abe et
al., 2021a), KamLAND (Abe et al., 2021b), and Borexino (Agostini et al.,
2017).

The discovery of such a joint emission would provide important information
about physics of the source and improve our understanding of the sources of
the individual messengers. Currently, the emission of high-energy neutrinos
from a GW source is expected to come from formed jets during the GW emission,
which accelerates charged particles (Ando et al., 2013). These charged
particles would produce mesons. From their decays and the decays of their
secondaries, high-energy neutrino emission is expected (Fang & Metzger, 2017;
Kimura et al., 2018). Moreover, the inclusion of neutrino information to the
gravitational-wave observation would help in constraining the location of the
source more precisely in the sky, enabling more explorations to be done on it
via the telescopes with narrow field of views. These motivations keep the
search efforts vibrant despite the estimated low chance for joint detections
with the current detectors (Bartos et al., 2011; Baret et al., 2012; Fang &
Metzger, 2017).

In this article, we present our low-latency follow-up searches and archival
searches for high-energy neutrino emission from the GW events detected during
the complete third observing run of advanced LIGO and Virgo detectors (O3). In
Section 2, we describe the IceCube detector and its neutrino data used for
this analysis, and the GW detector runs followed up in this paper. In Section
3, we provide relevant details about the searches done by two main analysis
methods; unbinned maximum likelihood (UML) and Low Latency Algorithm for
Multi-messenger Astrophysics (LLAMA). More detailed discussions on the methods
can also be found in our previous publication (Aartsen et al., 2020). Section
4 describes the low-latency operation of the pipelines for following-up the
candidate GW event alerts reported during the O3 run at the Gravitational-wave
Candidate Event Database (GraceDB) 111https://gracedb.ligo.org/, and
summarizes the results. In Section 5, we present the results of our archival
searches using both LLAMA and UML methods. These archival searches were
performed on the 44 confident GW events from GWTC-2.1 (Abbott et al., 2021a)
222Most of the events in GWTC-2.1 were already reported in the catalog GWTC-2
(Abbott et al., 2021c). These were previously analyzed by both LLAMA and UML
searches (Veske et al., 2021b). The LLAMA pipeline reanalyzed them with a
refined background distribution, while the UML results remained the same. and
36 GW events from GWTC-3 (Abbott et al., 2021b). These analyses include a
search within a time window of $\pm$500 s around the GW events, a dedicated
follow-up on the candidate optical flare from GW190521 (Abbott et al., 2020a;
Graham et al., 2020), and an extended two-week search on the neutron star
containing events by the UML pipeline.

##  2 The Neutrino and Gravitational Wave Observations

###  2.1 The IceCube Detector

The IceCube Neutrino Observatory is a cubic-kilometer detector array located
at the geographic South Pole (Aartsen et al., 2017). The detector consists of
86 strings drilled deep into ice. These strings hold 60 Digital Optical
Modules (DOMs) between depths of 1.5 km and 2.5 km in the Antarctic ice. The
main component of the DOMs are photomultiplier tubes used to detect the
Cherenkov light emitted by charged particles produced when neutrinos interact
in ice.

There are two main event topologies seen within IceCube data: tracks and
cascades. Tracks are produced when muon neutrinos undergo charged-current
interactions and produce muons that travel along a straight line and deposit
Cherenkov light along its path. Cascades, which mainly consist of
electromagnetic showers, are generated via charged-current interactions of
electron neutrinos and neutral-current interactions of neutrinos of all
flavors within the ice. Tracks are excellent for pointing towards various
astrophysical sources since they have an angular resolution of
$\lesssim\,1^{\circ}$, which is much better than the pointing resolution of
cascades ($\gtrsim\,10^{\circ}$)(Aartsen et al., 2014b, c).

The analyses presented here use neutrino data from a low-latency data stream
known as the Gamma-ray Follow-Up (GFU) Online event stream. The GFU Online
event selection is able to rapidly reconstruct neutrino events observed in the
IceCube detector and the data is made available within roughly 30 s, allowing
for rapid neutrino follow-ups. The GFU dataset uses track events detected with
IceCube, since their pointing resolutions are well suited for follow-up
analyses. The details of the selection can be found in Aartsen et al. (2016)
and the online version of the dataset, which we use in this article, is
described further in Kintscher (2016).

The dataset consists of through-going muon tracks originating primarily from
cosmic-ray backgrounds from the atmosphere. In the southern sky, the sample is
dominated by the atmospheric muons while in the northern sky, the sample is
dominated by atmospheric neutrinos. Atmospheric muons do not contribute to the
rate in the northern sky due to Earth absorption. The all-sky neutrino event
rate ranges from 6-7 mHz depending on seasonal variation of atmospheric
neutrinos (Heix et al., 2020). Overall the rate of astrophysical neutrinos is
roughly three orders of magnitude lower than that of the atmospheric
backgrounds (Aartsen et al., 2016).

###  2.2 The third observing run of ground-based gravitational-wave detectors

On April 1st 2019 at 15:00 UTC the LIGO and Virgo detectors network (Aasi et
al., 2015; Acernese et al., 2014) started their third observing run with an
increased sensitivity enabling the detection of gravitational waves from
compact binary coalescences at a rate of greater than 1 merger per week
(Abbott et al., 2021a, b). During the period of October 1st 15:00 UTC to
November 1st 15:00 UTC the detectors were not collecting data, thus separating
the observation run to two segments, O3a followed by O3b, which ended on March
27th 2020 at 17:00 UTC. The near-realtime analysis of LIGO-Virgo data by the
LIGO Scientific and Virgo Collaborations (LVC) allows for the broadcasting of
open public alerts. On the other hand, an in-depth offline analysis provides
an update to the catalog of GW events.

Figure 1: A comparison of the sky localizations of the 90 % probability
regions of the GW skymaps (orange) and the 90 % contours of the neutrino
localizations (blue). The skymaps shown here include all 91 GW events from O1,
O2 and O3. It can be seen that we are mainly limited by the large areas of the
GW skymaps, which reduces if three detectors from LVC detect the event
simultaneously.

In this paper, since a combination of the events from IceCube and the GW
events from O3 are used, the analyses becomes dependent on the localizations
of both the neutrino and the GW events. Figure 1 compares the sky
localizations of the skymaps of the candidate GW events published in the GW
catalogs (O1 to O3) and the neutrino events detected by IceCube, within the
GFU dataset. The 90% localizations of both are used to make the comparison. It
is seen that we are mainly limited by the localization uncertainties of the GW
skymaps. These uncertainties are expected to reduce within the future runs of
the ground-based gravitational-wave detectors (Abbott et al., 2018).

##  3 Methods

There are two main searches that we employed: the UML and LLAMA searches. Both
the UML and LLAMA analyses performed short time scale follow-ups for each
reported GW event. The analyses searched for neutrino emission within a
$\pm$500 s time window centered around the GW merger time. This time window
was used both in the realtime and archival searches. The time window is a
conservative empirical estimate of the delay between the GW and neutrino
emission for a model based on gamma-ray bursts (Baret et al., 2011).

Additionally, the UML analysis performed a long time scale analysis on all
binary neutron star (BNS) and neutron star-black hole (NSBH) candidates. This
search, called the 2-week follow-up, is motivated by models which predict
neutrino emission on longer time scales from binaries with at least one
neutron star (Fang & Metzger, 2017; Decoene et al., 2020). We searched within
a time period of [-0.1,+14] days around the GW merger times.

Both analyses also performed a neutrino follow-up search on the candidate
optical counterpart to the binary black hole (BBH) merger GW190521 observed by
Zwicky Transient Facility (ZTF) (Graham et al., 2020). ZTF observed a flaring
active galactic nuclei (AGN), J124942.3+344929, which coincided with the 90%
credible region of the GW event’s sky localization. This flare can be
explained by the accretion of the gas in the AGN disk to the kicked final
black hole of the merger (McKernan et al., 2019). The motivation for the
neutrino follow-up was the expected formation of a jet accelerating particles
due to the chaotic accretion dynamics around the kicked black hole travelling
through the AGN disk.

###  3.1 Unbinned Maximum Likelihood

The unbinned maximum likelihood (UML) method tests for a point-like neutrino
source coincident with the GW localization region. The likelihood takes into
account the direction, angular error, and reconstructed energy of each
neutrino on the sky. The sky is divided into equal area bins using the Healpix
pixelization scheme (Górski et al., 2005). We then perform a likelihood ratio
test where the test statistic (TS) is the log-likelihood ratio. The TS is
computed at each pixel in the sky by maximizing the log-likelihood ratio and
weighting the result by the GW localization probability in the given pixel.
The pixel with the largest TS value is taken to be the best-fit location for a
joint GW-neutrino source and the associated TS is considered the final
observed TS for the analysis. For a full detailed description of the
likelihood and TS used here, see Hussain et al. (2019).

To compute the significance for each GW follow-up, we perform 30,000 pseudo-
experiments with scrambled neutrino data to generate a background TS
distribution. Then scrambling is carried out by randomly assigning a time for
the neutrinos, which is equivalent to a scramble in right ascension, while
maintaining the declination dependence of the data. The final observed TS for
a given GW event is then compared to its background distribution to compute a
$p$-value.

In the case where the observed TS is consistent with background, we place 90%
confidence level (CL) upper limits (ULs) on the time-integrated neutrino flux,
$E^{2}F$, assuming an $E^{-2}$ spectrum, where $F\,=\,dN/dE\,dA$. The limits
are computed by injecting simulated signal neutrinos into the sky according to
the GW localization probability. We then follow the all-sky scan procedure
described above to compute a TS for a given value of injected neutrino flux.
We run 500 trials for a given injected neutrino flux with a random injection
location chosen for each trial. The 90% UL on the neutrino flux is then
defined as the flux for which 90% of trials produce a TS value greater than
the observed TS value for the GW event.

Upper limits to the isotropical equivalent energy ($E_{\rm iso}$ ULs) are
computed in a similar manner. Once again we assume an $E^{-2}$ spectrum and
convert our injected $E_{\rm iso}$ into a flux at Earth by sampling a location
on the sky as well as a distance to the GW source according the the 3D
localization probability provided by LIGO/Virgo. The flux is then converted to
an expected number of events observed at IceCube using the dataset’s
declination dependence and effective area.

Note that all reported ULs are only valid within a certain range of energies.
The energy range of our data sample depends strongly on declination. The
central 68% energy range in the southern hemisphere is roughly 5 $\times$ 105
GeV - 107 GeV and in the northern hemisphere ranges from roughly 5 $\times$
103 GeV to 105 GeV.

For the follow-up of the potential optical counterpart of GW190521, AGN
J124942.3+344929, we do not include any of the GW spatial information because
we are testing for neutrino emission from the precise location of the AGN
rather than the full GW contour. We search for neutrinos correlated with the
location of the AGN in a 112 day time window after the merger, which is a
conservative estimate based on the time profile of the optical flare. This is
done in a model independent manner, with no assumptions on the emission
profile in the entire time window. This method is equivalent to the full all-
sky scan method described above except the localization skymap is a delta
function at the single pixel containing the AGN.

###  3.2 Low Latency Algorithm for Multi-messenger Astrophysics (LLAMA)

The LLAMA analysis is based on the calculation of Bayesian probabilities of
the observed coincidences of GWs and high-energy neutrinos (Bartos et al.,
2019). The odds ratio of the coincidence arising from a joint astrophysical
emission of GWs and neutrinos being unrelated, considering any of them being
not astrophysical as well, is used as a test statistic. For the analysis of
confirmed GW detections followed up in this study, the GW events are assumed
to be certainly astrophysical. The origins of the neutrinos are quantified for
astrophysical or background scenarios. This requires the effective area of
IceCube, past triggers of the GFU stream (which are predominantly of
atmospheric origin), and the reconstructed energies of the neutrinos and their
sky localizations. In addition to this, an $E^{-2}$ astrophysical spectrum is
assumed. The relation between the GW and neutrinos are quantified via the
difference between their detection times, their respective sky localizations,
and the mean distance reconstruction of the GW event. Together with the
astrophysical emission energy $E_{\mathrm{iso}}$, which is log-uniform between
$10^{46}-10^{51}$ erg, the distance reconstruction of the GW event accounts
for the propagation of the neutrinos in space.

Precomputed background distributions are used for calculating the $p$-values.
In order to include the distance information of the GW events appropriately,
different background distributions are constructed for different source types
(BNS, NSBH, BBH coalescences). For this purpose, GW events are simulated for
each source category and they are randomly matched with scrambled past GFU
detections. The number of neutrinos matched with each GW event is drawn
according to a Poisson distribution with a mean corresponding to the average
GFU trigger count in 1000 s. The 90% CL upper limits (frequentist limits) on
the time-integrated neutrino flux are calculated as described in the appendix
of Aartsen et al. (2020).

The neutrino follow-up on the candidate optical counterpart of GW190521 in the
LLAMA analysis follows the assumed emission model described in Graham et al.
(2020). The model assumes a linearly decreasing gas density around the active
galactic nuclei. The kicked black hole from the merger travels through and
accretes gas from the AGN disk. For our neutrino search, we hypothesized a
neutrino emission from the particle accelerating jets which are expected to
form due to the accretion. Hence, the intensity of the expected neutrino
emission is assumed to be proportional to the accretion rate, which is assumed
to be a linearly decreasing emission intensity over time in this model. The
start and end times of the accretion were found from the observed light curves
by following the same model, which also includes an optical diffusion delay
obeying a Maxwell-Boltzmann distribution. The least-squares estimations for
the start and end times of the accretion were found to be 23 and 80 days after
the merger respectively, the same as that found in Graham et al. (2020). So,
we searched for a neutrino emission from a point source located at the AGN’s
position, free of any diffusion effect, which starts 23 days after the BBH
merger and linearly decreases for the following 57 days until it ends.

##  4 Low-Latency Operation

Both UML (Aartsen et al., 2020) and LLAMA (Countryman et al., 2019; Bartos et
al., 2019) analyses deployed low-latency pipelines designed to perform
automated neutrino follow-up searches after receiving notices from LVC through
the Gamma-ray Coordinates Network (GCN) (Keivani et al., 2019; Hussain et al.,
2019).

Figure 2: Latency of IceCube GCN circulars relative to GW merger times for all
56 events reported during the O3 observing run444All of the GCN notices of
these GW events can be found at https://gcn.gsfc.nasa.gov/lvc_events.html..
The outlier near 20 hours is S190421ar, where the LVC GCN notice was not
received until roughly 19 hours after the GW merger. This plot only shows the
follow-ups which were triggered automatically via GCN notices sent by LVC.

These pipelines allow for rapid neutrino follow-ups and the dissemination of
results to the astronomical community via GCN circulars. Low-latency neutrino
information can help inform the observing strategies of electromagnetic
observatories searching for electromagnetic counterparts to GW events. For
example, observatories such as Swift-XRT were able to use IceCube’s neutrino
follow-up results to narrow the search region for several GW events (Keivani
et al., 2021). While no electromagnetic counterparts were found during the O3
observing run, these pipelines show the discovery potential of low-latency
multi-messenger astronomy in identifying joint sources of photons, GWs, and
neutrinos.

Both analyses take advantage of the GCN notices to receive information about a
given GW event and trigger a dedicated neutrino follow-up search. The
pipelines use a python package, PyGCN (Singer, 2021), to continuously monitor
the GCN system for GCN notices sent by LVC. Due to the low-latency of the GFU
Online stream ($\sim$30 s) and the speed of the follow-up analyses ($\sim$56
min), IceCube was able to rapidly circulate results from neutrino follow-ups
to the astronomical community by using subsequent GCN circulars. Figure 4
shows the distribution of response times between the IceCube GCN circulars and
the GW merger time. The latency shown in the figure takes into account the
time taken by LVC to send the initial GCN notice. Also included in the latency
is the final vetting of the IceCube results by the collaboration’s Realtime
Oversight Committee (ROC) before sending the IceCube follow-up results via GCN
circulars. Follow-ups with observed $p$-value $\leq$ 1% in either pipeline or
any follow-ups that were deemed interesting to the astronomical community by
the ROC, resulted in releasing the directional information of the potentially
significant neutrino candidate via GCN circulars.

During O3, there were a total of 56 non-retracted candidate GW events that
were publicly shared. We ran follow-ups on these events and 4 of them resulted
in the release of the directional information of a neutrino to the
astronomical community. These released coincidences were further followed-up
by different telescopes and observatories, e.g. Swift-XRT (Page et al., 2020;
Keivani et al., 2021) and Karl G. Jansky Very Large Array (Bhakta et al.,
2021). For each of these events, the LVC GCN notices and the GCN circular
archives are linked. The archives show all follow-ups performed by each
observatory, including the follow-ups that use IceCube information. These
events were the following:

Figure 3: Evolution of the localization skymap for S190728q
666https://gcn.gsfc.nasa.gov/notices_l/S190728q.lvc and the associated follow-
up results from each pipeline which were sent via GCN circulars. As the
localization is refined, the $p$-values from both pipeline become more
significant. The colormap in the figure represents the probability per pixel
in the skymap and the green crosses show the neutrino observations.

  * •

S190517h777GW event GCN notice
https://gcn.gsfc.nasa.gov/notices_l/S190517h.lvc, 888GCN circular archive
https://gcn.gsfc.nasa.gov/other/GW190517h.gcn3: This candidate BBH merger
event had one neutrino located in the 90% credible sky region of the GW
localization. Due to this spatial coincidence the neutrino’s localization was
shared with the community 999https://gcn.gsfc.nasa.gov/gcn/gcn3/24573.gcn3,
despite its low statistical significance.

  * •

S190728q101010GW event GCN notice
https://gcn.gsfc.nasa.gov/notices_l/S190728q.lvc, 111111GCN circular archive
https://gcn.gsfc.nasa.gov/other/GW190728q.gcn3: This candidate BBH merger
event originally had a two-detector localization which did not yield any
significant neutrino coincidence. The localization was later improved by the
incorporation of the Virgo data, which increased the significance of one of
the neutrinos. With the final online skymap the coincidence had the $p$-values
1.0% and 1.6% for the LLAMA and UML searches,
respectively121212https://gcn.gsfc.nasa.gov/gcn/gcn3/25210.gcn3. Figure 6
shows the various localization skymaps sent by LVC and the associated results
from each pipeline, which were reported in low-latency via GCN circulars. The
skymaps were refined over a period of roughly 14 hours following the initial
GCN notice sent by LVC. It is seen that the $p$-values from both pipelines
become more significant as the localization is refined, since the neutrino
candidate 3 remains within the high probability region of the skymap as the GW
localization shrinks. Figure 4 shows the zoomed in updated skymap of
GW190728_064510 with the coincident neutrino overlaid.

Figure 4: Skymap of GW190728_064510 overlaid with the coincident neutrino. The
red region represents the GW localization probability per pixel. The blue
cross shows the best-fit neutrino direction with the circle showing the 90%
containment angular error region. The neutrino arrived 360 s before the GW
merger. The final pre-trial $p$-values for this event are $p=0.013$ and
$p=0.04$ with the LLAMA and UML analyses, respectively. The GCN circular
describing this event was also sent in realtime
(https://gcn.gsfc.nasa.gov/gcn3/25210.gcn3).

  * •

S191216ap131313GW event GCN notice
https://gcn.gsfc.nasa.gov/notices_l/S191216ap.lvc,  141414GCN circular archive
https://gcn.gsfc.nasa.gov/other/GW191216ap.gcn3: This candidate BBH merger
event was one of the events for which the results of the two analyses
disagreed. It was located relatively close, at $\sim 400$ Mpc. Due to this
atypically close distance for a BBH merger, the neutrino-GW coincidence was
favored by the LLAMA search which assigned a $p$-value of 0.6%, whereas the
UML search obtained a $p$-value of 22%
151515https://gcn.gsfc.nasa.gov/gcn/gcn3/26460.gcn3. The most interesting
response to our GCN notices came after the release of the neutrino coinciding
with this event. HAWC observatory sent out another notice saying their most
significant _subthreshold_ gamma-ray trigger coincides both with the neutrino
and GW’s localizations 161616https://gcn.gsfc.nasa.gov/gcn/gcn3/26472.gcn3. No
further counterpart was found from the region and due to the uncertain nature
of the gamma-ray trigger the state of the triple coincidence remained
inconclusive.

  * •

S200213t171717GW event GCN notice
https://gcn.gsfc.nasa.gov/notices_l/S200213t.lvc, 181818GCN circular archive
https://gcn.gsfc.nasa.gov/other/GW200213t.gcn3: This event was the only
candidate BNS merger for which a coincident neutrino was released. However, it
was excluded in the published GW catalogs, since it did not meet the threshold
requirements in the offline analysis from LVC (Abbott et al., 2021b). The UML
and LLAMA searches obtained $p$-values of 0.3% and 1.7% respectively for the
neutrino coincidence191919https://gcn.gsfc.nasa.gov/gcn/gcn3/27043.gcn3.

Both of these low-latency pipelines are being prepared to continue neutrino
follow-ups during the fourth observing run of LIGO, Virgo and KAGRA detectors,
planned to start in 2023.

##  5 Archival Searches on Catalogs

Once the catalogs containing the confident GW detections were published by
LVC, we performed archival searches on these events. There were several GW
events added or subtracted in the catalog when compared to the the candidate
events shared with the community by LVC during the O3 run. Initially, LVC
released the catalog GWTC-2 (Abbott et al., 2021c), which contained 39 events
from the first half of O3. These events were analyzed using both UML and LLAMA
methods and no significant neutrino emission was found (Veske et al., 2021b).
Later, this catalog was renewed by LVC resulting in the publication of
GWTC-2.1(Abbott et al., 2021a), which has an updated statistic used for the
classification of the events as confident detections. This updated catalog has
44 GW events out of which 8 were new when compared to GWTC-2. Three events
from GWTC-2 were retracted in the updated catalog. Here, we present the
results of the 44 confident events in GWTC-2.1. The 36 common events were
reanalyzed by the LLAMA search with a renewed background distribution, which
was generated with the latest population estimates for the binary black holes.
No appreciable change was found with the previous analysis. The results of the
UML analysis for the common events stayed the same. Finally, LVC also
published GWTC-3 (Abbott et al., 2021b), a catalog containing the confident GW
events observed during the second half of the O3 run (Abbott et al., 2021b).
These events were also analyzed as a part of the archival search.

First, we present the results of the searches for neutrino emission within a
time window of $\pm$500 s around the 80 mergers in GWTC-2.1 and GWTC-3. We did
not observe a significant neutrino emission from any GW event by any analysis.
ULs were placed on the time-integrated, energy scaled neutrino flux, $E^{2}F$,
as well as the $E_{\rm iso}$, emitted in high-energy muon neutrinos. Table 1
summarizes the results for each follow-up of GW events in GWTC-2.1 performed
by both analyses. Similarly, Table 2 shows the results for the GW events in
GWTC-3. Figure 5 shows the histogram of the $p$-values for the collection of
GW events from GWTC-1 (Abbott et al., 2019), GWTC-2.1 (Abbott et al., 2021a)
and GWTC-3 (Abbott et al., 2021b) from both analyses and the background
expectations. The set of events did not show any significant sign of emission.
The shown background expectation for the UML analysis was derived from the
background TS distributions of each GW. The LLAMA analysis’ background
$p$-value distribution is seen to be uniform for all kinds of events. The
different results for the LLAMA and the UML analyses arise from the inherent
differences in the statistical approaches of the two — one being a Bayesian
approach including priors of the GW source and the other being a purely
frequentist approach. This is also true for the $p$-values obtained in the
low-latency search described in section 4.

Figure 5: $p$-value distribution for the LLAMA (top panel) and UML (bottom
panel) analyses of the 11 events in GWTC-1 (Abbott et al., 2019), 44 GW events
in GWTC-2.1 (Abbott et al., 2021a), and the 36 GW events in GWTC-3 (Abbott et
al., 2021b). The distributions are consistent with background expectations.
The $p$-value distributions obtained for the events in GWTC-1 were already
published in Aartsen et al. (2020). The LLAMA background expectations shown
here is taken from that of one representative GW, and scaled to 91 GW events.
The orange and blue bands represent the Poisson errors on the observed
distribution of LLAMA and UML $p$-values, respectively.

Figure 6 shows the $E_{\rm iso}$ ULs for all GW events in GWTC-1, GWTC-2.1 and
GWTC-3 along with the total rest mass energy of the initial compact objects
and the total energy radiated by the system post-merger. The total radiated
energy is computed by taking the difference of the total rest mass energy of
the two progenitors and the final remnant object.

Figure 6: $E_{\rm iso}$ ULs for 91 GW candidates in GWTC-1, GWTC 2.1 and
GWTC-3. The blue, green, and orange triangles show the BBH, BNS and NSBH
events, respectively. Note that the 36 GW candidates present in both GWTC-2
and GWTC-2.1 do not have updated skymaps available so the results shown here
are using the GWTC-2 skymaps. The black crosses represent the total rest mass
energy of the progenitors of the binary merger. The grey plusses represent the
total energy radiated by the binary system. Also shown for reference is the
observed $E_{\rm iso}$ in photons by $Fermi$ GBM for GW170817 (red star)
(Abbott et al., 2017). The grey band represents the best and worst median UL
that IceCube can place based on a point source hypothesis. The $E_{\rm iso}$
ULs for the 11 GW events from GWTC-1 remain the same as those published in
Aartsen et al. (2020).

No significant neutrino emission was observed in the second archival search
presented here, which is the 2-week follow-up. There are only 3 GW events in
GWTC-2.1 which may have at least one neutron star in the binary system:
GW190425, GW190814, and GW190917_114630. Also 4 NSBH events were published in
the GWTC-3 catalog: GW191219_163120, GW200105_162426 (marginal event),
GW200115_042309, GW200210_092254. All of these events have at least one
progenitor object with a mass estimate lower than 3 M⊙ (Abbott et al., 2021a,
b). The 2-week follow-up is performed on these 7 GW events. Once again, we
place 90% ULs on the time-integrated neutrino emission from each of the 7 GWs
tested here. Table 3 shows the $p$-values and ULs for these events and Fig. 7
shows the final test statistic maps for these events. There was no difference
between the neutron star containing events in GWTC-2 and GWTC-2.1.

Finally, no significant neutrino emission was found for the follow-ups on the
candidate optical counterpart of GW190521 by both analysis methods. The
modelled search of LLAMA yielded a $p$-value of 0.79, 90% CL upper limit on
the $E^{2}F$ of 0.05 GeV cm-2 and 90% CL upper limit on $E_{\rm iso}$ of
8$\times 10^{53}$ erg. The UML analysis found a $p$-value of 0.25, with a 90%
CL upper limit on the time-integrated flux of $E^{2}F$=0.081 GeV cm-2.

##  6 Conclusion

Finding joint sources of GWs and high-energy neutrinos can help shed light on
the sources of the highest energy neutrinos and cosmic rays (Murase & Bartos,
2019). Studying these joint sources will also further expand our understanding
of energetic outflows from the mergers of compact objects. The completion of
the O3 realtime observing run and the release of the update to the second GW
catalog, GWTC-2.1, followed by the release of GWTC-3 have provided a
substantial increase in the number of reported GW candidates available for
follow-up searches.

We developed low-latency pipelines which ran automated neutrino follow-ups for
all GW events reported by LVC during the O3 observing run. Two different
analyses, UML and LLAMA, both ran in low-latency and followed up each of the
56 candidate events reported during the O3 run. Four of the follow-up searches
resulted in the release of the neutrino candidate’s direction to the public
via GCN circulars. This information prompted follow-up searches in
electromagnetic observatories such as Swift-XRT, demonstrating the power of
low-latency multi-messenger observations in informing the observing strategies
of other observatories. The unresolved triple coincidence for GW191216,
involving a subthreshold gamma-ray trigger from HAWC observatory, triggered
the development of general multi-messenger search methods for many messengers
(Veske et al., 2021a).

In addition to the low-latency follow-ups, we performed three offline analyses
of the GW events reported in GWTC-2.1 and GWTC-3. The first analysis searched
for neutrino emission within a $\pm$500 s time window centered around the GW
merger time. Both the UML and LLAMA methods performed this search and no
significant neutrino emission was observed in either search.

The second analysis was a 2-week follow-up of all BNS and NSBH candidate
events with the UML search. All the GW events followed up in this analysis had
at least one progenitor object with a mass estimate of $<$3 M⊙. No significant
neutrino emission was observed and 90% ULs were placed on the time-integrated
neutrino flux from each source.

The third analysis searched for neutrino emission from the potential optical
counterpart of the BBH merger GW190521 reported by ZTF. The UML analysis
tested a time window of 112 days following the GW merger time which covers the
entire flare in the optical light curve. The UML analysis assumed a uniform
neutrino emission within the time window. The LLAMA analysis assumed linearly
decreasing neutrino emission in a 57 day time window according to the
contemplated emission scenario for the optical flare. No significant neutrino
emission was observed in both analysis methods and we derived 90% ULs on the
time-integrated flux and the $E_{\mathrm{iso}}$ from the AGN J124942.3+344929.

Apart from the analyses presented here, there also exists a gravitational wave
follow-up analysis with neutrinos of a few 10 -100s of GeV energies detected
by IceCube (Balagopal V. et al., 2022). This upcoming analysis will provide
additional information, complimentary to the analyses with high-energy
neutrinos presented here. Additionally, a search for extremely low energy
neutrinos, with 0.5-5 GeV energies, from IceCube was conducted, and found no
significant emission of neutrinos (Abbasi et al., 2021).

The low-latency and archival searches will continue to function during the
upcoming O4 run of LVK. It is expected that the O4 operational run will
demonstrate enhanced performance, thereby increasing the rate of expected
mergers. This would provide more opportunities to conduct multi-messenger
studies which may lead to a potential discovery of neutrino and gravitational
wave correlations. Additionally, the inclusion of more detectors from LVK will
reduce the area of the sky localizations of the GW skymaps. This is also
expected to contribute towards higher significances in case of coincident
detections (Abbott et al., 2018).

Future GW detectors like the Einstein Telescope (ET Science Team, 2011) and
Cosmic Explorer (Reitze et al., 2019) aim at achieving improved sensitivities
and lowering their frequency regime of operation. These improved detectors are
expected to enhance the rate of observed merger events with better precision,
which will in turn boost the capabilities of multi-messenger observations of
these sources (Kalogera et al., 2019). The next generation of the IceCube
Neutrino Observatory, IceCube-Gen2, is planned to be an 8-fold extension to
the instrumented volume of the current detector array. It is expected to
extend the current energy range of IceCube to several 100s of PeV (Aartsen et
al., 2021). IceCube-Gen2 can potentially help in addressing the question of
joint emission of neutrinos and GWs, when used in tandem with the future GW
detectors.

GWTC-2.1 | LLAMA | UML
---|---|---
|  | Area |  |  $E{{}^{2}F}$ UL |  |  $E{{}^{2}F}$ UL |
Event | Type | [deg2] | $p$-value | [GeVcm-2] | $p$-value | [GeVcm-2] | $E_{\rm iso}$ UL [erg]
GW190403_051519 | BBH | 5589.4 | 0.51 | 0.14 | 0.46 | 0.101 | 1.86 $\times$ 1055
GW190408_181802 | BBH | 148.8 | 0.22 | 0.048 | 0.17 | 0.0512 | 4.85 $\times$ 1053
GW190412 | BBH | 20.9 | 0.27 | 0.041 | 0.13 | 0.0459 | 8.31 $\times$ 1052
GW190413_052954 | BBH | 1484.5 | 0.30 | 0.087 | 0.28 | 0.133 | 7.01 $\times$ 1054
GW190413_134308 | BBH | 730.6 | 0.27 | 0.34 | 0.34 | 0.270 | 2.84 $\times$ 1055
GW190421_213856 | BBH | 1211.5 | 0.81 | 0.46 | 0.56 | 0.393 | 1.40 $\times$ 1055
GW190425 | BNS | 9958.2 | 0.16 | 0.22 | 0.94 | 0.176 | 1.66 $\times$ 1052
GW190426_190642 | BBH | 8214.5 | 0.42 | 0.17 | 0.18 | 0.282 | 1.25 $\times$ 1055
GW190503_185404 | BBH | 94.4 | 0.94 | 0.54 | 0.34 | 0.584 | 4.99 $\times$ 1054
GW190512_180714 | BBH | 218.0 | 0.81 | 0.23 | 0.85 | 0.199 | 1.74 $\times$ 1054
GW190513_205428 | BBH | 518.4 | 0.99 | 0.043 | 0.94 | 0.0514 | 6.73 $\times$ 1053
GW190514_065416 | BBH | 3009.7 | 0.25 | 0.089 | 0.44 | 0.0453 | 3.96 $\times$ 1054
GW190517_055101 | BBH | 473.3 | 0.21 | 0.48 | 0.26 | 0.366 | 6.05 $\times$ 1054
GW190519_153544 | BBH | 857.1 | 0.067 | 0.15 | 0.21 | 0.0914 | 3.20 $\times$ 1054
GW190521 | BBH | 1008.2 | 0.62 | 0.37 | 0.63 | 0.359 | 1.90 $\times$ 1055
GW190521_074359 | BBH | 546.5 | 0.11 | 0.049 | 0.15 | 0.0451 | 2.36 $\times$ 1053
GW190527_092055 | BBH | 3662.4 | 0.65 | 0.41 | 0.88 | 0.326 | 1.01 $\times$ 1055
GW190602_175927 | BBH | 694.5 | 0.31 | 0.34 | 0.17 | 0.370 | 9.73 $\times$ 1054
GW190620_030421 | BBH | 7202.1 | 0.20 | 0.36 | 0.23 | 0.121 | 4.13 $\times$ 1054
GW190630_185205 | BBH | 1216.9 | 0.64 | 0.15 | 0.81 | 0.427 | 5.31 $\times$ 1053
GW190701_203306 | BBH | 46.1 | 1.0 | 0.039 | 0.87 | 0.0385 | 7.65 $\times$ 1053
GW190706_222641 | BBH | 653.8 | 0.99 | 0.036 | 0.92 | 0.0356 | 3.17 $\times$ 1054
GW190707_093326 | BBH | 1346. | 0.43 | 0.24 | 0.63 | 0.202 | 4.74 $\times$ 1053
GW190708_232457 | BBH | 13675.4 | 0.11 | 0.11 | 0.56 | 0.0720 | 1.62 $\times$ 1053
GW190719_215514 | BBH | 2890.1 | 0.83 | 0.054 | 0.91 | 0.0512 | 4.90 $\times$ 1054
GW190720_000836 | BBH | 463.4 | 0.99 | 0.13 | 0.94 | 0.0872 | 5.34 $\times$ 1053
GW190725_174728 | BBH | 2292.5 | 0.048 | 0.19 | 0.59 | 0.0918 | 4.04 $\times$ 1053
GW190727_060333 | BBH | 833.8 | 0.89 | 0.38 | 0.74 | 0.324 | 1.53 $\times$ 1055
GW190728_064510 | BBH | 395.5 | 0.0084 | 0.89 | 0.04 | 0.315 | 6.36 $\times$ 1053
GW190731_140936 | BBH | 3387.3 | 0.25 | 0.93 | 0.61 | 0.385 | 1.81 $\times$ 1055
GW190803_022701 | BBH | 1519.5 | 0.31 | 0.037 | 0.64 | 0.0354 | 1.69 $\times$ 1054
GW190805_211137 | BBH | 3949.1 | 0.74 | 0.20 | 0.93 | 0.180 | 2.56 $\times$ 1055
GW190814 | BBH* | 19.3 | 1.0 | 0.24 | 1.0 | 0.259 | 5.68 $\times$ 1052
GW190828_063405 | BBH | 520.1 | 0.93 | 0.21 | 0.98 | 0.178 | 2.74 $\times$ 1054
GW190828_065509 | BBH | 664.0 | 0.84 | 0.38 | 0.84 | 0.368 | 3.73 $\times$ 1054
GW190910_112807 | BBH | 10880.3 | 0.22 | 0.45 | 0.77 | 0.177 | 1.90 $\times$ 1054
GW190915_235702 | BBH | 396.9 | 0.56 | 0.036 | 0.44 | 0.0354 | 3.61 $\times$ 1053
GW190916_200658 | BBH | 4499.2 | 0.52 | 0.16 | 0.85 | 0.108 | 1.22 $\times$ 1055
GW190917_114630 | NSBH* | 2050.6 | 0.20 | 0.19 | 0.72 | 0.203 | 6.37 $\times$ 1053
GW190924_021846 | BBH | 357.9 | 0.031 | 0.037 | 0.23 | 0.0346 | 4.46 $\times$ 1052
GW190925_232845 | BBH | 1233.5 | 0.39 | 0.11 | 0.59 | 0.0908 | 3.41 $\times$ 1053
GW190926_050336 | BBH | 2505.9 | 0.13 | 0.78 | 0.33 | 0.280 | 2.30 $\times$ 1055
GW190929_012149 | BBH | 2219.3 | 0.11 | 0.34 | 0.22 | 0.276 | 1.85 $\times$ 1055
GW190930_133541 | BBH | 1679.6 | 0.14 | 0.038 | 0.31 | 0.0427 | 1.05 $\times$ 1053
Table 1: Results for the events in GWTC-2.1 (Abbott et al., 2021a) for the 1000 s follow-up. GW190814 is labelled as a BBH merger here although the type of the lighter object with $\sim 2.6$ M⊙ is unknown (Abbott et al., 2020b). GW190917_114630 is labelled as NSBH since its estimated source properties are more like that of an NSBH event although the event was found to be significant by a BBH template. The table also shows the area on the sky containing 90% probabilities from the GW skymap. GWTC-3 | LLAMA | UML
---|---|---
|  | Area |  |  $E{{}^{2}F}$ UL |  |  $E{{}^{2}F}$ UL |
Event | Type | [deg2] | $p$-value | [GeVcm-2] | $p$-value | [GeVcm-2] | $E_{\rm iso}$ UL [erg]
GW191103_012549 | BBH | 2519.6 | 0.53 | 0.049 | 0.71 | 0.049 | $1.96\,\times\,10^{53}$
GW191105_143521 | BBH | 728.7 | 0.27 | 0.28 | 0.54 | 0.267 | $1.28\,\times\,10^{54}$
GW191109_010717 | BBH | 1784.3 | 0.14 | 0.48 | 0.05 | 0.508 | $5.03\,\times\,10^{54}$
GW191113_071753 | BBH | 2993.3 | 0.076 | 0.52 | 0.19 | 0.441 | $3.12\,\times\,10^{54}$
GW191126_115259 | BBH | 1514.5 | 0.77 | 0.13 | 1.00 | 0.138 | $1.42\,\times\,10^{54}$
GW191127_050227 | BBH | 1499.2 | 0.38 | 0.078 | 0.83 | 0.081 | $2.96\,\times\,10^{54}$
GW191129_134029 | BBH | 848.3 | 0.25 | 0.35 | 0.30 | 0.425 | $8.95\,\times\,10^{53}$
GW191204_110529 | BBH | 4747.7 | 0.16 | 0.36 | 0.49 | 0.085 | $1.46\,\times\,10^{54}$
GW191204_171526 | BBH | 344.9 | 0.97 | 0.26 | 1.00 | 0.280 | $3.96\,\times\,10^{53}$
GW191215_223052 | BBH | 595.8 | 0.98 | 0.26 | 1.00 | 0.211 | $2.98\,\times\,10^{54}$
GW191216_213338 | BBH | 480.1 | 0.0049 | 0.093 | 0.10 | 0.071 | $2.57\,\times\,10^{52}$
GW191219_163120 | NSBH | 2232.1 | 0.09 | 0.26 | 0.71 | 0.219 | $2.80\,\times\,10^{53}$
GW191222_033537 | BBH | 2299.2 | 0.95 | 0.36 | 1.00 | 0.375 | $1.1\,\times\,10^{55}$
GW191230_180458 | BBH | 1012.2 | 0.37 | 0.36 | 0.28 | 0.488 | $3.18\,\times\,10^{55}$
GW200105_162426 | NSBH | 7881.8 | 0.20 | 0.13 | 0.81 | 0.095 | $2.98\,\times\,10^{52}$
GW200112_155838 | BBH | 4250.4 | 0.58 | 0.18 | 0.79 | 0.133 | $8.43\,\times\,10^{53}$
GW200115_042309 | NSBH | 511.9 | 0.34 | 0.038 | 0.45 | 0.045 | $2.12\,\times\,10^{52}$
GW200128_022011 | BBH | 2677.5 | 0.46 | 0.25 | 0.47 | 0.243 | $9.31\,\times\,10^{54}$
GW200129_065458 | BBH | 81.8 | 0.033 | 0.041 | 0.05 | 0.406 | $1.73\,\times\,10^{53}$
GW200202_154313 | BBH | 159.3 | 0.0057 | 0.039 | 0.06 | 0.038 | $2.43\,\times\,10^{52}$
GW200208_130117 | BBH | 38.0 | 0.94 | 0.33 | 1.00 | 0.518 | $9.25\,\times\,10^{54}$
GW200208_222617 | BBH | 1889.2 | 0.41 | 0.045 | 0.90 | 0.043 | $4.98\,\times\,10^{54}$
GW200209_085452 | BBH | 924.5 | 0.84 | 0.50 | 1.00 | 0.041 | $1.81\,\times\,10^{54}$
GW200210_092254 | BBH | 1830.7 | 0.28 | 0.071 | 0.79 | 0.081 | $2.51\,\times\,10^{53}$
GW200216_220804 | BBH | 3009.5 | 0.065 | 0.066 | 0.46 | 0.236 | $2.82\,\times\,10^{54}$
GW200219_094415 | BBH | 702.1 | 0.98 | 0.23 | 1.00 | 0.035 | $9.57\,\times\,10^{54}$
GW200220_061928 | BBH | 3484.7 | 0.23 | 0.22 | 0.05 | 0.357 | $4.23\,\times\,10^{55}$
GW200220_124850 | BBH | 3168.9 | 0.42 | 0.13 | 0.53 | 0.118 | $6.31\,\times\,10^{54}$
GW200224_222234 | BBH | 49.9 | 0.90 | 0.068 | 1.00 | 0.079 | $9.33\,\times\,10^{53}$
GW200225_060421 | BBH | 509.0 | 0.0048 | 0.10 | 0.20 | 0.055 | $3.03\,\times\,10^{53}$
GW200302_015811 | BBH | 7010.8 | 0.16 | 0.67 | 0.21 | 0.531 | $4.34\,\times\,10^{54}$
GW200306_093714 | BBH | 4371.2 | 0.15 | 0.074 | 0.57 | 0.046 | $9.99\,\times\,10^{53}$
GW200308_173609 | BBH | 18705.7 | 0.24 | 0.38 | 0.29 | 0.326 | $7.18\,\times\,10^{55}$
GW200311_115853 | BBH | 35.6 | 1.0 | 0.047 | 1.00 | 0.076 | $4.38\,\times\,10^{53}$
GW200316_215756 | BBH | 410.4 | 0.17 | 0.066 | 0.04 | 0.110 | $5.19\,\times\,10^{53}$
GW200322_091133 | BBH | 31571.1 | 0.23 | 0.18 | 0.87 | 0.148 | $4.39\,\times\,10^{55}$
Table 2: Results for the events in GWTC-3 (Abbott et al., 2021b) for the 1000 s follow-up. The central 68% energy range of the events contributing to the limits shown here ranges from $5\,\times$ 105 GeV - 107 GeV in the southern hemisphere and $5\,\times$ 103 GeV - 105 GeV in the northern hemisphere. Event | Type |  $p$-value |  $E{{}^{2}F}$ UL [GeVcm-2]
---|---|---|---
GW190425 | BNS | 0.43 | 0.661
GW190917_114630 | NSBH | 0.84 | 0.442
GW190814 | BBH | 0.59 | 0.309
GW191219_163120 | NSBH | 0.67 | 0.347
GW200105_162426 | NSBH | 0.47 | 0.382
GW200115_042309 | NSBH | 0.68 | 0.078
GW200210_092254 | NSBH | 0.13 | 0.303
Table 3: Results for the 2 week follow-up analysis using the UML method. 3
events from GWTC-2.1 (Abbott et al., 2021a) and 4 events from GWTC-3 (Abbott
et al., 2021b) were followed up as they were the only potential BNS/NSBH
candidates.

## Acknowledgements

The IceCube collaboration acknowledges the significant contributions to this
manuscript from Aswathi Balagopal V., Raamis Hussain and Doğa Veske. The
authors gratefully acknowledge the support from the following agencies and
institutions: USA – U.S. National Science Foundation-Office of Polar Programs,
U.S. National Science Foundation-Physics Division, U.S. National Science
Foundation-EPSCoR, Wisconsin Alumni Research Foundation, Center for High
Throughput Computing (CHTC) at the University of Wisconsin–Madison, Open
Science Grid (OSG), Extreme Science and Engineering Discovery Environment
(XSEDE), Frontera computing project at the Texas Advanced Computing Center,
U.S. Department of Energy-National Energy Research Scientific Computing
Center, Particle astrophysics research computing center at the University of
Maryland, Institute for Cyber-Enabled Research at Michigan State University,
and Astroparticle physics computational facility at Marquette University;
Belgium – Funds for Scientific Research (FRS-FNRS and FWO), FWO Odysseus and
Big Science programmes, and Belgian Federal Science Policy Office (Belspo);
Germany – Bundesministerium für Bildung und Forschung (BMBF), Deutsche
Forschungsgemeinschaft (DFG), Helmholtz Alliance for Astroparticle Physics
(HAP), Initiative and Networking Fund of the Helmholtz Association, Deutsches
Elektronen Synchrotron (DESY), and High Performance Computing cluster of the
RWTH Aachen; Sweden – Swedish Research Council, Swedish Polar Research
Secretariat, Swedish National Infrastructure for Computing (SNIC), and Knut
and Alice Wallenberg Foundation; Australia – Australian Research Council;
Canada – Natural Sciences and Engineering Research Council of Canada, Calcul
Québec, Compute Ontario, Canada Foundation for Innovation, WestGrid, and
Compute Canada; Denmark – Villum Fonden and Carlsberg Foundation; New Zealand
– Marsden Fund; Japan – Japan Society for Promotion of Science (JSPS) and
Institute for Global Prominent Research (IGPR) of Chiba University; Korea –
National Research Foundation of Korea (NRF); Switzerland – Swiss National
Science Foundation (SNSF); United Kingdom – Department of Physics, University
of Oxford.

This research has made use of data or software obtained from the Gravitational
Wave Open Science Center (gw-openscience.org) (Abbott et al., 2021d), a
service of LIGO Laboratory, the LIGO Scientific Collaboration, the Virgo
Collaboration, and KAGRA. LIGO Laboratory and Advanced LIGO are funded by the
United States National Science Foundation (NSF) 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. Virgo is funded, through the European Gravitational
Observatory (EGO), by the French Centre National de Recherche Scientifique
(CNRS), the Italian Istituto Nazionale di Fisica Nucleare (INFN) and the Dutch
Nikhef, with contributions by institutions from Belgium, Germany, Greece,
Hungary, Ireland, Japan, Monaco, Poland, Portugal, Spain. The construction and
operation of KAGRA are funded by Ministry of Education, Culture, Sports,
Science and Technology (MEXT), and Japan Society for the Promotion of Science
(JSPS), National Research Foundation (NRF) and Ministry of Science and ICT
(MSIT) in Korea, Academia Sinica (AS) and the Ministry of Science and
Technology (MoST) in Taiwan.

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##  Appendix A Skymaps

This appendix includes the skymaps obtained in the context of this analysis.
Figure 7 shows the TS maps for the two-week follow-up analysis. Figures 8 and
9 show the skymaps with the GW probabilities and the observed neutrinos within
the 1000 s time window in the archival search.

Figure 7: Final test statistic maps for the 3 BNS and NSBH candidates in
GWTC-2.1 (Abbott et al., 2021a), and the 4 NSBH candidates in GWTC-3 (Abbott
et al., 2021b). The pixel with highest test statistic in the sky is shown in
the blue crosshairs. The color scale shows the test statistic weighted by the
GW localization information. Here $w$ = $P_{\mathrm{\rm GW}}(\Omega)/A_{\rm
pix}$ where $P_{\rm GW}(\Omega)$ is the probability of the GW source being in
a given pixel and $A_{\rm pix}$ is the pixel area. Figure 8: Skymaps for the
1000 s follow-up of all events from the GWTC-2.1 (Abbott et al., 2021a)
catalog. Shown in red is the localization probability of the GW event with the
black contour representing the 90% containment region of the GW localization.
The blue crosses show the best fit neutrino candidate directions with the blue
circles representing the 90% angular error region of the neutrino candidates.
Figure 9: Skymaps for the 1000 s follow-up of all events from the GWTC-3
(Abbott et al., 2021b) catalog.