# Search for High-Energy Neutrinos from Ultra-Luminous Infrared Galaxies with
IceCube

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  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  C.
Alispach  Département de physique nucléaire et corpusculaire, Université de
Genève, CH-1211 Genève, Switzerland  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  R. An  Department of Physics
and Laboratory for Particle Physics and Cosmology, Harvard University,
Cambridge, MA 02138, USA  K. Andeen  Department of Physics, Marquette
University, Milwaukee, WI, 53201, USA  T. Anderson  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. Ashida  Dept. of Physics and Wisconsin IceCube
Particle Astrophysics Center, University of Wisconsin–Madison, Madison, WI
53706, USA  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  A. Barbano Département de physique
nucléaire et corpusculaire, Université de Genève, CH-1211 Genève, Switzerland
S. W. Barwick Dept. of Physics and Astronomy, University of California,
Irvine, CA 92697, USA  B. Bastian  DESY, D-15738 Zeuthen, Germany  V. Basu
Dept. of Physics and Wisconsin IceCube Particle Astrophysics Center,
University of Wisconsin–Madison, Madison, WI 53706, USA  S. Baur Université
Libre de Bruxelles, Science Faculty CP230, B-1050 Brussels, Belgium  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  C.
Bellenghi  Physik-department, Technische Universität München, D-85748
Garching, Germany  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
also at National Research Nuclear University, Moscow Engineering Physics
Institute (MEPhI), Moscow 115409, Russia  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  M. Boddenberg  III. Physikalisches Institut, RWTH Aachen
University, D-52057 Aachen, Germany  F. Bontempo  Karlsruhe Institute of
Technology, Institute for Astroparticle Physics, D-76021 Karlsruhe, Germany
J. Borowka  III. Physikalisches Institut, RWTH Aachen University, D-52057
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-52057 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  S. Bron  Département
de physique nucléaire et corpusculaire, Université de Genève, CH-1211 Genève,
Switzerland  J. Brostean-Kaiser  DESY, D-15738 Zeuthen, Germany  S. Browne
Karlsruhe Institute of Technology, Institute of Experimental Particle Physics,
D-76021 Karlsruhe, Germany  A. Burgman Dept. of Physics and Astronomy, Uppsala
University, Box 516, S-75120 Uppsala, Sweden  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  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  K. Clark Dept. of Physics,
Engineering Physics, and Astronomy, Queen’s University, Kingston, ON K7L 3N6,
Canada  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  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  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-52057 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, Pennsylvania State University, University Park, PA
16802, 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  S. De Ridder  Dept. of Physics and Astronomy, University of Gent,
B-9000 Gent, Belgium  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 Vrije Universiteit Brussel (VUB), Dienst ELEM, B-1050 Brussels,
Belgium  M. de With  Institut für Physik, Humboldt-Universität zu Berlin,
D-12489 Berlin, Germany  T. DeYoung Dept. of Physics and Astronomy, Michigan
State University, East Lansing, MI 48824, USA  S. Dharani  III. Physikalisches
Institut, RWTH Aachen University, D-52057 Aachen, Germany  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. Dunkman  Dept. of
Physics, Pennsylvania State University, University Park, PA 16802, USA  M. A.
DuVernois Dept. of Physics and Wisconsin IceCube Particle Astrophysics Center,
University of Wisconsin–Madison, Madison, WI 53706, USA  E. Dvorak  Physics
Department, South Dakota School of Mines and Technology, Rapid City, SD 57701,
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-52057 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  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  K. Filimonov  Dept. of
Physics, University of California, Berkeley, CA 94720, 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-52057 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-52057 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  A.
Goldschmidt  Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
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  M. Gündüz  Fakultät für
Physik & Astronomie, Ruhr-Universität Bochum, D-44780 Bochum, Germany  C.
Günther  III. Physikalisches Institut, RWTH Aachen University, D-52057 Aachen,
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-52057 Aachen,
Germany  F. Halzen Dept. of Physics and Wisconsin IceCube Particle
Astrophysics Center, University of Wisconsin–Madison, Madison, WI 53706, 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 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  A. Haungs Karlsruhe Institute of Technology, Institute
for Astroparticle Physics, D-76021 Karlsruhe, Germany  S. Hauser  III.
Physikalisches Institut, RWTH Aachen University, D-52057 Aachen, Germany  D.
Hebecker  Institut für Physik, Humboldt-Universität zu Berlin, D-12489 Berlin,
Germany  K. Helbing Dept. of Physics, University of Wuppertal, D-42119
Wuppertal, Germany  F. Henningsen Physik-department, Technische Universität
München, D-85748 Garching, Germany  E. C. Hettinger  Dept. of Physics and
Astronomy, Michigan State University, East Lansing, MI 48824, USA  S. Hickford
Dept. of Physics, University of Wuppertal, D-42119 Wuppertal, Germany  J.
Hignight  Dept. of Physics, University of Alberta, Edmonton, Alberta, Canada
T6G 2E1  C. Hill Dept. of Physics and Institute for Global Prominent Research,
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  R. Hoffmann
Dept. of Physics, University of Wuppertal, D-42119 Wuppertal, Germany  T.
Hoinka  Dept. of Physics, TU Dortmund University, D-44221 Dortmund, Germany
B. Hokanson-Fasig  Dept. of Physics and Wisconsin IceCube Particle
Astrophysics Center, University of Wisconsin–Madison, Madison, WI 53706, 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
F. Huang Dept. of Physics, Pennsylvania State University, University Park, PA
16802, USA  M. Huber  Physik-department, Technische Universität München,
D-85748 Garching, 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  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 Institute for Global
Prominent Research, 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
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  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  M. Kellermann  III. Physikalisches Institut, RWTH
Aachen University, D-52057 Aachen, Germany  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 Institute for Global Prominent Research, Chiba University,
Chiba 263-8522, Japan  T. Kintscher  DESY, D-15738 Zeuthen, Germany  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  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  S. Kopper
Dept. of Physics and Astronomy, University of Alabama, Tuscaloosa, AL 35487,
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. 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  J. L. Lanfranchi  Dept. of
Physics, Pennsylvania State University, University Park, PA 16802, USA  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 Karlsruhe Institute
of Technology, Institute of Experimental Particle Physics, D-76021 Karlsruhe,
Germany  Y. Li  Dept. of Physics, Pennsylvania State University, University
Park, PA 16802, 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. 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  I. C. Mariş Université Libre de
Bruxelles, Science Faculty CP230, B-1050 Brussels, Belgium  R. Maruyama Dept.
of Physics, Yale University, New Haven, CT 06520, USA  K. Mase  Dept. of
Physics and Institute for Global Prominent Research, Chiba University, Chiba
263-8522, Japan  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  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 Institute for Global
Prominent Research, Chiba University, Chiba 263-8522, Japan  S. Meighen-Berger
Physik-department, Technische Universität München, D-85748 Garching, Germany
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, Massachusetts Institute of Technology, Cambridge,
MA 02139, USA  R. Naab DESY, D-15738 Zeuthen, Germany  R. Nagai Dept. of
Physics and Institute for Global Prominent Research, 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  L. V.
Nguyễn  Dept. of Physics and Astronomy, Michigan State University, East
Lansing, MI 48824, USA  H. Niederhausen Physik-department, Technische
Universität München, D-85748 Garching, Germany  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  D. R. Nygren  Lawrence Berkeley National Laboratory,
Berkeley, CA 94720, 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
A. Olivas  Dept. of Physics, University of Maryland, College Park, MD 20742,
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-52057 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-52057 Aachen, Germany  D. Pieloth  Dept.
of Physics, TU Dortmund University, D-44221 Dortmund, Germany  S. Pieper
Dept. of Physics, University of Wuppertal, D-42119 Wuppertal, Germany  M.
Pittermann  Karlsruhe Institute of Technology, Institute of Experimental
Particle Physics, D-76021 Karlsruhe, Germany  A. Pizzuto Dept. of Physics and
Wisconsin IceCube Particle Astrophysics Center, University of
Wisconsin–Madison, Madison, WI 53706, USA  M. Plum Department of Physics,
Marquette University, Milwaukee, WI, 53201, 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
P. B. Price  Dept. of Physics, University of California, Berkeley, CA 94720,
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  A. Raissi  Dept. of Physics
and Astronomy, University of Canterbury, Private Bag 4800, Christchurch, New
Zealand  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  I. C. Rea
Physik-department, Technische Universität München, D-85748 Garching, Germany
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  R.
Reimann III. Physikalisches Institut, RWTH Aachen University, D-52057 Aachen,
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  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  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  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  J. Sandroos
Institute of Physics, University of Mainz, Staudinger Weg 7, D-55099 Mainz,
Germany  M. Santander Dept. of Physics and Astronomy, University of Alabama,
Tuscaloosa, AL 35487, USA  S. Sarkar Dept. of Physics, University of Oxford,
Parks Road, Oxford OX1 3PU, UK  S. Sarkar Dept. of Physics, University of
Alberta, Edmonton, Alberta, Canada T6G 2E1  K. Satalecka DESY, D-15738
Zeuthen, Germany  M. Scharf  III. Physikalisches Institut, RWTH Aachen
University, D-52057 Aachen, Germany  M. Schaufel  III. Physikalisches
Institut, RWTH Aachen University, D-52057 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  P. Schlunder  Dept. of Physics, TU Dortmund University, D-44221
Dortmund, Germany  T. Schmidt  Dept. of Physics, University of Maryland,
College Park, MD 20742, USA  A. Schneider Dept. of Physics and Wisconsin
IceCube Particle Astrophysics Center, University of Wisconsin–Madison,
Madison, WI 53706, 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-52057 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  M. Silva Dept. of Physics and Wisconsin IceCube
Particle Astrophysics Center, University of Wisconsin–Madison, Madison, WI
53706, 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  D. Soldin  Bartol Research
Institute and Dept. of Physics and Astronomy, University of Delaware, Newark,
DE 19716, USA  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 also at National
Research Nuclear University, Moscow Engineering Physics Institute (MEPhI),
Moscow 115409, Russia  DESY, D-15738 Zeuthen, Germany  J. Stachurska  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  J. Stettner III. Physikalisches Institut, RWTH
Aachen University, D-52057 Aachen, Germany  A. Steuer  Institute of Physics,
University of Mainz, Staudinger Weg 7, D-55099 Mainz, 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  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  F.
Tenholt Fakultät für Physik & Astronomie, Ruhr-Universität Bochum, D-44780
Bochum, Germany  S. Ter-Antonyan Dept. of Physics, Southern University, Baton
Rouge, LA 70813, USA  S. Tilav  Bartol Research Institute and Dept. of Physics
and Astronomy, University of Delaware, Newark, DE 19716, USA  F. Tischbein
III. Physikalisches Institut, RWTH Aachen University, D-52057 Aachen, Germany
K. Tollefson Dept. of Physics and Astronomy, Michigan State University, East
Lansing, MI 48824, USA  L. Tomankova Fakultät für Physik & Astronomie, Ruhr-
Universität Bochum, D-44780 Bochum, Germany  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  M. Tselengidou  Erlangen Centre for Astroparticle
Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg, D-91058 Erlangen,
Germany  C. F. Tung School of Physics and Center for Relativistic
Astrophysics, Georgia Institute of Technology, Atlanta, GA 30332, USA  A.
Turcati  Physik-department, Technische Universität München, D-85748 Garching,
Germany  R. Turcotte  Karlsruhe Institute of Technology, Institute for
Astroparticle Physics, D-76021 Karlsruhe, Germany  C. F. Turley Dept. of
Physics, Pennsylvania State University, University Park, PA 16802, USA  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  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  S.
Verpoest Dept. of Physics and Astronomy, University of Gent, B-9000 Gent,
Belgium  M. Vraeghe  Dept. of Physics and Astronomy, University of Gent,
B-9000 Gent, Belgium  C. Walck  Oskar Klein Centre and Dept. of Physics,
Stockholm University, SE-10691 Stockholm, Sweden  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  M. J. Weiss  Dept. of Physics,
Pennsylvania State University, University Park, PA 16802, USA  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 of Experimental
Particle 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-52057 Aachen,
Germany  D. R. Williams  Dept. of Physics and Astronomy, University of
Alabama, Tuscaloosa, AL 35487, USA  M. Wolf Physik-department, Technische
Universität München, D-85748 Garching, Germany  K. Woschnagg  Dept. of
Physics, University of California, Berkeley, CA 94720, 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  Y. Xu  Dept. of
Physics and Astronomy, Stony Brook University, Stony Brook, NY 11794-3800, USA
J. P. Yanez  Dept. of Physics, University of Alberta, Edmonton, Alberta,
Canada T6G 2E1  S. Yoshida Dept. of Physics and Institute for Global Prominent
Research, 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

###### Abstract

Ultra-luminous infrared galaxies (ULIRGs) have infrared luminosities
$L_{\mathrm{IR}}\geq 10^{12}L_{\odot}$, making them the most luminous objects
in the infrared sky. These dusty objects are generally powered by starbursts
with star-formation rates that exceed $100~{}M_{\odot}~{}\mathrm{yr}^{-1}$,
possibly combined with a contribution from an active galactic nucleus. Such
environments make ULIRGs plausible sources of astrophysical high-energy
neutrinos, which can be observed by the IceCube Neutrino Observatory at the
South Pole. We present a stacking search for high-energy neutrinos from a
representative sample of 75 ULIRGs with redshift $z\leq 0.13$ using 7.5 years
of IceCube data. The results are consistent with a background-only
observation, yielding upper limits on the neutrino flux from these 75 ULIRGs.
For an unbroken $E^{-2.5}$ power-law spectrum, we report an upper limit on the
stacked flux $\Phi_{\nu_{\mu}+\bar{\nu}_{\mu}}^{90\%}=3.24\times
10^{-14}~{}\mathrm{TeV^{-1}~{}cm^{-2}~{}s^{-1}}~{}(E/10~{}\mathrm{TeV})^{-2.5}$
at 90% confidence level. In addition, we constrain the contribution of the
ULIRG source population to the observed diffuse astrophysical neutrino flux as
well as model predictions.

††journal: ApJ

##  1 Introduction

The observation of high-energy astrophysical neutrinos with IceCube (Aartsen
et al., 2013, 2014) marked the birth of neutrino astronomy. Numerous studies
have been performed searching for the sources of these astrophysical
neutrinos, which are cosmic messengers that represent a smoking-gun signature
of hadronic acceleration. So far, the blazar TXS 0506+056 (Aartsen et al.,
2018a, b) is the sole neutrino source candidate that has been identified with
a significance at the $3\sigma$ level, and the first indications of neutrino
emission have been found from the starburst galaxy NGC 1068 (Aartsen et al.,
2020a). Studies from the community have also shown indications of
astrophysical neutrinos correlated with the tidal disruption event AT2019dsg
(Stein et al., 2021) and radio-bright active galactic nuclei (AGN; Plavin et
al., 2020). However, these results are insufficient to explain the origin of
the observed diffuse astrophysical neutrino flux (Aartsen et al., 2015, 2016,
2020b; Abbasi et al., 2020a). Constraints from IceCube studies imply that if
the neutrino sky is dominated by a single source population, this population
likely consists of relatively numerous, low-luminosity sources (Lipari, 2008;
Silvestri & Barwick, 2010; Murase et al., 2012; Ahlers & Halzen, 2014;
Kowalski, 2015; Murase & Waxman, 2016; Aartsen et al., 2019a, b; Ackermann et
al., 2019). In particular, the study of Aartsen et al. (2017a) constrains the
diffuse neutrino contribution of blazars in the 2LAC catalog of the Fermi
Large Area Telescope (LAT; Atwood et al., 2009; Ackermann et al., 2011).
Furthermore, Fermi-LAT observations provide an upper bound on the contribution
of non-blazar sources to the extragalactic gamma-ray background (EGB;
Ackermann et al., 2015, 2016). This bound implies constraints on the non-
blazar source populations that could be responsible for the diffuse neutrino
flux (e.g. Bechtol et al., 2017). In particular, the non-blazar EGB bound
hints towards neutrino sources that are gamma-ray opaque (Murase et al., 2016;
Vereecken & de Vries, 2020).

In this work we investigate ultra-luminous infrared galaxies (ULIRGs; see
Lonsdale et al. 2006 for a review) as neutrino source candidates. These
objects are characterized by a rest-frame infrared (IR) luminosity111Note that
in this work we do not distinguish hyper-luminous infrared galaxies (HyLIRGs;
$L_{\mathrm{IR}}\geq 10^{13}L_{\odot}$) from the ULIRG source class.
$L_{\mathrm{IR}}\geq 10^{12}L_{\odot}$ between 8–1000 $\mu$m. ULIRG
morphologies typically contain features of spiral-galaxy mergers (e.g. Hung et
al., 2014), indicating that they correspond to an evolutionary phase of such
systems (e.g. Larson et al., 2016). The local source density of ULIRGs is
${\sim}10^{-7}\text{--}10^{-6}~{}\mathrm{Mpc^{-3}}$, although the abundance of
ULIRGs increases rapidly up to a redshift $z\sim 1$ (Kim & Sanders, 1998;
Blain et al., 1999; Cowie et al., 2004; Le Floc’h et al., 2005; Hopkins et
al., 2006; Magnelli et al., 2009; Clements et al., 2010; Goto et al., 2011;
Magnelli et al., 2011; Casey et al., 2012). ULIRGs and their less luminous but
more numerous counterparts, the luminous infrared galaxies (LIRGs;
$10^{11}L_{\odot}\leq L_{\mathrm{IR}}<10^{12}L_{\odot}$), become the main
contributors to the IR energy density at redshifts $z\sim 2\text{--}3$ (Genzel
& Cesarsky, 2000; Chapman et al., 2005; Reddy et al., 2008).

ULIRGs are predominantly powered by starbursts with star-formation rates
$\gtrsim 100~{}M_{\odot}~{}\mathrm{yr^{-1}}$ (Lonsdale et al., 2006; Rieke et
al., 2009; da Cunha et al., 2010; Piqueras López et al., 2016). The strong
thermal IR emission of ULIRGs is the result of abundant dust and gas
reprocessing higher-frequency radiation. In addition, can show signs of AGN
activity (Nagar et al., 2003; Lonsdale et al., 2006; Clements et al., 2010;
Fadda et al., 2010). The fraction of ULIRGs containing an AGN is $\gtrsim
40\%$, with higher values reported as a function of increasing infrared
luminosity (Veilleux et al., 1995; Kim et al., 1998; Veilleux et al., 1999;
Goto, 2005; Imanishi et al., 2008; Hou et al., 2009). The AGN contribution to
the infrared luminosity is typically of the order of $\sim$10%, although AGN
can become the dominant contributors for ULIRGs with a stronger infrared
output (Farrah et al., 2003; Veilleux et al., 2009; Imanishi et al., 2010;
Nardini et al., 2010; Yuan et al., 2010). Lonsdale et al. (2006) also note
that the AGN power could be underestimated due to strong obscuration of the
AGN. This result is consistent with the work of Nardini & Risaliti (2011), who
find that AGN in a sample of local ULIRGs are Compton-thick, i.e. the AGN are
obscured by dust clouds with column densities $N_{H}\gtrsim 1.5\times
10^{24}~{}\mathrm{cm^{-2}}$ (Comastri, 2004). Observations of Arp 220, i.e.
the closest ULIRG, indicate that a possible AGN hosted by this object should
be Compton-thick with $N_{H}\gtrsim 10^{25}~{}\mathrm{cm^{-2}}$ (Wilson et
al., 2014; Scoville et al., 2017).

Hadronic acceleration, and hence neutrino production, could occur both in
starburst reservoirs (e.g. Tamborra et al., 2014; Peretti et al., 2019;
Ambrosone et al., 2021) and in AGN (e.g. Murase, 2017; Inoue et al., 2019;
Kheirandish et al., 2021). Since ULIRGs host such environments, this implies
that ULIRGs are candidate sources of astrophysical neutrinos. He et al. (2013)
have constructed a reservoir model of the starburst regions of ULIRGs, where
the enhanced hypernova rates are responsible for hadronic acceleration. They
predict a PeV diffuse neutrino flux from ULIRGs that can explain a significant
fraction of the diffuse IceCube observations. The generic reservoir model of
Palladino et al. (2019) considers a neutrino flux from hadronically-powered
gamma-ray galaxies (HAGS), which include ULIRGs and starburst galaxies with
$L_{\mathrm{IR}}<10^{12}L_{\odot}$. For power-law spectra
($\Phi_{\nu+\bar{\nu}}\propto E^{-\gamma}$) with spectral indices $\gamma\leq
2.12$, this model can partially explain the diffuse neutrino observations
while remaining consistent with the non-blazar EGB bound above 50 GeV
(Ackermann et al., 2016; Lisanti et al., 2016; Zechlin et al., 2016). In
particular, a population of HAGS could be the dominant contributor to the
diffuse neutrino flux above 100 TeV, and it could be responsible for roughly
half of the diffuse neutrino flux between 10–100 TeV. In contrast with such
reservoir scenarios, Vereecken & de Vries (2020) model the neutrino production
in ULIRGs through a beam dump of hadrons accelerated in a Compton-thick AGN.
They find that if the AGN is obscured by column densities $N_{H}\gtrsim
5\times 10^{25}~{}\mathrm{cm^{-2}}$, ULIRGs could fit the diffuse neutrino
observations without violating the Fermi-LAT non-blazar EGB bound above 50 GeV
(Ackermann et al., 2016).

This paper presents an IceCube search for high-energy astrophysical neutrinos
originating from ULIRGs. In Section 2 we describe the source selection, the
IceCube dataset, and the analysis method used in this search. The results of
the analysis are presented in Section 3. The interpretation of these results
is given in Section 4, where we discuss the implications for the neutrino flux
from the ULIRG source population, and where we compare our results to the
models of He et al. (2013), Palladino et al. (2019), and Vereecken & de Vries
(2020). Finally, we present our conclusions in Section 5. In this work, we
assume a $\Lambda$CDM cosmology using the Planck 2015 results (Ade et al.,
2016), $H_{0}=67.8~{}\mathrm{km~{}s^{-1}~{}Mpc^{-1}}$, $\Omega_{m}=0.31$, and
$\Omega_{\Lambda}=0.69$.

##  2 Search for Neutrino Emission from ULIRGs

###  2.1 Selection of ULIRGs

The ULIRGs for this analysis are obtained from three different catalogs,
primarily based on data from the Infrared Astronomical Satellite (IRAS;
Neugebauer et al., 1984), listed below. The infrared luminosity
$L_{\mathrm{IR}}$ listed in the catalogs is determined using the IRAS flux
measurements at 12 $\mu$m, 25 $\mu$m, 60 $\mu$m, and 100 $\mu$m (see e.g.
Sanders & Mirabel, 1996). The three catalogs are:

  1. 1.

The IRAS Revised Bright Galaxy Sample (RBGS; Sanders et al., 2003). This
catalog contains the brightest extragalactic sources observed by IRAS. These
RBGS objects are sources with a 60 $\mu$m infrared flux
$f_{60}>5.24~{}\mathrm{Jy}$ and a Galactic latitude $\left|b\right|>5^{\circ}$
to exclude the Galactic Plane. The RBGS provides the total infrared luminosity
between 8–1000 $\mu$m for all objects in the sample, containing 21 ULIRGs.

  2. 2.

The IRAS 1 Jy Survey of ULIRGs (Kim & Sanders, 1998) selected from the IRAS
Faint Source Catalog (FSC; Moshir et al., 1992) contains sources with
$f_{60}>1~{}\mathrm{Jy}$. The survey required the ULIRGs to have a Galactic
latitude $\left|b\right|>30^{\circ}$ to avoid strong contamination from the
Galactic Plane. Furthermore, in order to have accessible redshift information
from observatories located at Mauna Kea, Hawaii, this survey is restricted to
declinations $\delta>-40^{\circ}$. The resulting selection is a set of 118
ULIRGs.

  3. 3.

The ULIRG sample used by Nardini et al. (2010). Their selection is primarily
based on the redshift survey (Saunders et al., 2000) of the IRAS Point Source
Catalog (PSC; Beichman et al., 1988). This catalog contains objects with
$f_{60}\gtrsim 0.6~{}\mathrm{Jy}$ and covers 84% of the sky. In addition, the
authors require the ULIRGs to be observed by the Infrared Spectograph (IRS;
Houck et al., 2004) on the Spitzer Space Telescope (Werner et al., 2004). As
such, they obtain a sample of 164 ULIRGs.

There exists some overlap between the ULIRGs of the above three catalogs.
Therefore, the NASA/IPAC Extragalactic Database222Available at
ned.ipac.caltech.edu. (NED) is used to cross-identify these sources. This
cross-identification was done by obtaining the NED source list of each
catalog, and then cross-identifying sources with the same NED information in
each list. The result is a selection of 189 unique ULIRGs. For uniformity, NED
is also used to obtain the equatorial coordinates and redshift for each
object. Since $L_{\mathrm{IR}}$ values depend on IRAS flux measurements, which
are optimized separately for the different IRAS surveys, they are taken in the
following order:

  * •

From Catalog 1 if available;

  * •

From Catalog 2 if not available in Catalog 1;

  * •

From Catalog 3 if not available in Catalog 1 or 2.

Note that Catalog 3 is the only catalog that provides uncertainties on these
values. We therefore include all objects from this catalog that are consistent
with $L_{\mathrm{IR}}=10^{12}L_{\odot}$ within one standard deviation333The
NED identifications (with $\log_{10}(L_{\mathrm{IR}}/L_{\odot})$ values) of
these objects are UGC 05101 ($11.99\pm 0.02$), IRAS 18588+3517 ($11.97\pm
0.04$), and 2MASX J23042114+3421477 ($11.99\pm 0.04$)..

To obtain a representative sample of the local ULIRG population, which we
define as a sample of ULIRGs that is complete up to a given redshift, we place
a cut on the redshifts in our initial ULIRG selection. We find that keeping
only those objects with $z\leq 0.13$ allows the least luminous ULIRGs (i.e.
$L_{\mathrm{IR}}=10^{12}L_{\odot}$) to be observed, given a conservative IRAS
sensitivity $f_{60}=1~{}\mathrm{Jy}$ (see Appendix A, where we also take into
account the effect of the limited sky coverage of Catalog 2). The result is a
representative sample of 75 ULIRGs with $z\leq 0.13$, shown in Fig. 1. Table 3
lists their NED identification, equatorial coordinates, redshifts, fluxes at
60 $\mu$m, and total IR luminosities.

###  2.2 Detector and Data Set

The IceCube Neutrino Observatory is a $1~{}\mathrm{km}^{3}$ optical Cherenkov
detector located at the geographic South Pole (Aartsen et al., 2017b). The
detector is buried in the ice at depths between 1450 m and 2450 m below the
surface. It consists of 5160 digital optical modules (DOMs), which are
distributed over 86 vertical strings. Each DOM contains a photomultiplier tube
and on-board read-out electronics (Abbasi et al., 2009, 2010). When a high-
energy neutrino interacts with the ice or the bedrock in the vicinity of the
detector, secondary relativistic particles are produced that emit Cherenkov
radiation, which can be registered by the DOMs. The number of photons
collected by the DOMs gives a measure of the energy deposited by these
secondary charged particles. This feature combined with the arrival time of
the light at the DOMs is used to reconstruct the particle trajectories, which
are subsequently used to determine the arrival direction of the original
neutrino.

Figure 1: Sky distribution of the representative sample of 75 ULIRGs with
redshift $z\leq 0.13$ selected for this IceCube search.

IceCube is sensitive to all neutrino flavors, although neutrinos and
antineutrinos can generally not be distinguished. Neutral-current interactions
of the three flavors, and charged-current interactions of electron neutrinos
($\nu_{e}+\bar{\nu}_{e}$) and tau neutrinos ($\nu_{\tau}+\bar{\nu}_{\tau}$)
are observed by means of their particle cascades. These cascades lead to a
rather spherical pattern of recorded photons inside the detector, with a
relatively poor angular resolution ($\gtrsim 8^{\circ}$; see Aartsen et al.,
2019c). However, charged-current interactions of muon neutrinos
($\nu_{\mu}+\bar{\nu}_{\mu}$) produce muons, which can leave extended track-
like signatures in the detector444Tracks can also be the signature of taus
produced in charged-current interactions of tau neutrinos. However, such
tracks only become detectable at the highest tau energies $E_{\tau}$, since
the decay length of the tau is roughly
$\mathrm{50~{}m}\times(E_{\tau}/\mathrm{PeV})$ (see also Abbasi et al.,
2020b). The typical angular resolution of these tracks is $\lesssim 1^{\circ}$
for muons with energies $\gtrsim 1~{}\mathrm{TeV}$ (Aartsen et al., 2017c,
2020a).

For this analysis we use the IceCube gamma-ray follow-up (GFU) data sample
(Aartsen et al., 2017c), which contains well-reconstructed muon tracks with
$4\pi$ sky coverage. The track selection is performed separately for both
hemispheres due to their differing background characteristics. The background
for astrophysical neutrinos originates from cosmic-ray induced particle
cascades in Earth’s atmosphere. Atmospheric neutrinos produced in such
cascades are able to reach the detector from both hemispheres, leading to a
background event rate at the mHz level. Compared to astrophysical neutrinos,
atmospheric neutrinos have a relatively soft spectrum that dominates at
energies $\lesssim 100~{}\mathrm{TeV}$ (Abbasi et al., 2011; Aartsen et al.,
2015, 2016, 2020b; Abbasi et al., 2020a). Atmospheric muons produced in the
Northern hemisphere are attenuated by Earth before reaching IceCube. In the
Southern hemisphere, however, they are able to penetrate the Antarctic ice and
leave track signatures in the detector. These atmospheric muons have a median
event rate of 2.7 kHz, requiring a more stringent event selection in the
Southern sky. The event selection criteria result in a GFU track sample at the
atmospheric neutrino level, with an all-sky event rate of 6.6 mHz. Note that
this is still various orders of magnitude above the expected rate of
astrophysical neutrinos at the $\mu$Hz level. The selection efficiency of the
GFU sample is determined by simulating signal neutrinos according to an
unbroken power-law spectrum $\Phi_{\nu+\bar{\nu}}\propto E_{\nu}^{-2}$ between
$100~{}\mathrm{GeV}<E_{\nu}<1~{}\mathrm{EeV}$. In the Northern hemisphere, the
selection efficiency is $\sim$50% at $E_{\nu}\sim 100~{}\mathrm{GeV}$ and
reaches $\sim$95% for $E_{\nu}\gtrsim 100~{}\mathrm{TeV}$. In the Southern
hemisphere, the selection efficiency is $\sim$5% at $E_{\nu}\sim
10~{}\mathrm{TeV}$ and exceeds 70% for $E_{\nu}\gtrsim 1~{}\mathrm{PeV}$. The
GFU data used in this search contains over $1.5\times 10^{6}$ events, spanning
a livetime of 2615.97 days $\sim$ 7.5 years of the full 86-string IceCube
configuration between 2011–2018.

###  2.3 Analysis Method

In this work, we search for an astrophysical component in the IceCube data
which is spatially correlated with our representative sample of 75 ULIRGs.
This astrophysical signal would be characterized by an excess of neutrino
events above the background of atmospheric muons and atmospheric neutrinos. To
search for this excess, a time-integrated unbinned maximum likelihood analysis
is performed (Braun et al., 2008). In addition, the ULIRGs are stacked in
order to enhance the sensitivity of the analysis (see Achterberg et al.,
2006).

The unbinned likelihood for a search stacking $M$ candidate point sources
using $N$ data events is given by

$\mathcal{L}(n_{s},\gamma)=\prod_{i=1}^{N}\left[\frac{n_{s}}{N}\sum_{k=1}^{M}w_{k}\mathcal{S}_{i}^{k}(\gamma)+\left(1-\frac{n_{s}}{N}\right)\mathcal{B}_{i}\right].$
(1)

Here, $n_{s}$ denotes the number of signal events, and $\gamma$ denotes the
spectral index of the signal energy distribution, which is assumed to follow
an unbroken power-law spectrum, $\Phi_{\nu+\bar{\nu}}\propto E^{-\gamma}$.
These fit parameters are restricted to $n_{s}\geq 0$ and $\gamma\in[1,4]$ but
allowed to float otherwise. For each event $i$, the probability density
functions (PDFs) of the background, $\mathcal{B}_{i}$, and the signal for
source $k$, $\mathcal{S}_{i}^{k}$, are evaluated. The parameter $w_{k}$
represents the stacking weight of source $k$.

Both the signal PDF and background PDF are separated into spatial and energy
components. The background PDF is evaluated as
$\mathcal{B}_{i}=B(\delta_{i})/2\pi\times\mathcal{E}_{\mathcal{B}}(E_{i})$,
with $\delta_{i}$ and $E_{i}$ the reconstructed declination and energy of
event $i$, respectively. The spatial component is uniform in right ascension
due to the rotation of the IceCube detector with Earth’s axis, resulting in a
factor $1/2\pi$. The spatial PDF, $B$, and the energy PDF,
$\mathcal{E}_{\mathcal{B}}$, are constructed from experimentally obtained
background data in reconstructed declination and energy. Analogously, the
signal PDF of candidate point source $k$ is evaluated as
$\mathcal{S}_{i}^{k}(\gamma)=S(\textbf{x}_{k},\textbf{x}_{i},\sigma_{i})\times\mathcal{E}_{\mathcal{S}}(E_{i},\gamma)$.
For the spatial PDF of the signal, $S$, we take a two-dimensional Gaussian
centered around the location of the source, $\textbf{x}_{k}$. The Gaussian is
evaluated using the reconstructed location of event $i$, $\textbf{x}_{i}$, and
its angular uncertainty, $\sigma_{i}$, as the standard deviation. The
estimation of the angular uncertainty does not take into account systematic
effects, such that we follow Aartsen et al. (2020a) and impose a lower bound
$\sigma_{i}\geq 0.2^{\circ}$. Since $\sigma_{i}$ is much larger than the
uncertainty on the source location, the latter may safely be neglected. The
energy PDF of the signal, $\mathcal{E}_{\mathcal{S}}$, is modeled using an
unbroken power-law spectrum with spectral index $\gamma\in[1,4]$. We assume
that all candidate sources have identical accelerator properties, and we
therefore use a single spectral index $\gamma$ to represent the neutrino
spectrum of all ULIRGs.

The stacking weight of source $k\in\\{1,2,...,M\\}$ is constructed as
$w_{k}=r_{k}t_{k}/\sum_{j=1}^{M}r_{j}t_{j}$. Firstly, it depends on the
detector response for an unbroken $E^{-\gamma}$ power-law spectrum at the
source declination $\delta_{k}$. This dependence is reflected by the weight
term $r_{k}\propto\int A_{\mathrm{eff}}(E,\delta_{k})E^{-\gamma}\mathrm{d}E$,
where $A_{\mathrm{eff}}$ is the effective area of the detector (Aartsen et
al., 2017c). Secondly, the stacking weight depends on a theoretical weight
$t_{k}$, which is modeled according to the hypothesis tested by the analysis.
In this work, we make the generic assumption that the total IR luminosity
between 8–1000 $\mu$m, $L_{\mathrm{IR}}$, is representative for the power of a
possible hadronic accelerator in ULIRGs. This assumption is motivated by the
fact that the total IR luminosity is directly related to the star-formation
rate (see e.g. Rieke et al., 2009), and that a possible AGN contribution
likely increases with IR luminosity (see e.g. Nardini et al., 2010).
Additionally, we assume that the neutrino production is identical in all
candidate sources. Hence, we set $t_{k}=F_{\mathrm{IR},k}$, which is the total
IR flux (8-1000 $\mu$m) of ULIRG $k$. The total infrared flux is computed as
$F_{\mathrm{IR}}=L_{\mathrm{IR}}/(4\pi d_{L}^{2})$, where $L_{\mathrm{IR}}$ is
taken from the respective ULIRG catalog (see Section 2.1), and where $d_{L}$
is the luminosity distance determined from the redshift measurements.

Subsequently, a test statistic is constructed as
$\mathrm{TS}=2\log\mathcal{L}(n_{s}=\hat{n}_{s},\gamma=\hat{\gamma})/\log\mathcal{L}(n_{s}=0)$.
Here, $\hat{n}_{s}$ and $\hat{\gamma}$ are those values that maximize the
likelihood given in Eq. (1), where a single $\hat{\gamma}$ is fitted for the
full ULIRG sample. This TS is used to differentiate data containing a signal
component from data being compatible with background. The background-only TS
distribution is determined by randomizing the IceCube data in right ascension
$10^{5}$ times, and calculating the TS in each iteration, which is called a
trial. However, ${\sim}10^{8}$ trials are required to obtain a background-only
TS distribution that is accurate up to the $5\sigma$ significance level. As
this is computationally unfeasible, we use a $\chi^{2}$ PDF to approximate the
background-only distribution (Wilks, 1938). This PDF is then used to compute
the one-sided p-value corresponding with a certain observed
$\mathrm{TS_{obs}}$. The p-value reflects the compatibility of a certain
$\mathrm{TS_{obs}}$ with the background-only scenario. This p-value is
determined by evaluating the background-only survival function at
$\mathrm{TS_{obs}}$, i.e. the integral of the background-only PDF over all
$\mathrm{TS\geq TS_{obs}}$.

Figure 2: Sensitivity, $3\sigma$, and $5\sigma$ discovery potentials as a
function of the spectral index $\gamma$, for injected pseudo-signal following
an unbroken $E^{-\gamma}$ power-law spectrum. Panel (a) shows these quantities
in terms of the flux at the normalization energy $E_{0}=10~{}\mathrm{TeV}$.
Panel (b) shows them in terms of the mean number of injected pseudo-signal
events. This number is found by convolving the injection spectrum with the
effective area of the detector, and integrating it over energy and detector
livetime.

To test the performance of the analysis, we simulate muon neutrinos with a
true direction exactly at the location of our 75 selected ULIRGs. The relative
number of neutrinos simulated from an ULIRG location is proportional to the
stacking weight of that source. These neutrinos, with energies
$100~{}\mathrm{GeV}<E_{\nu}<100~{}\mathrm{PeV}$, are generated from an
unbroken power-law spectrum,
$\Phi_{\nu_{\mu}+\bar{\nu}_{\mu}}(E_{\nu})=\Phi_{\nu_{\mu}+\bar{\nu}_{\mu}}(E_{0})(E_{\nu}/E_{0})^{-\gamma}$,
which is normalized at an energy555Note that for all spectra considered in
this work, the analysis is sensitive to neutrinos with an energy
$E_{0}=10~{}\mathrm{TeV}$. $E_{0}=10~{}\mathrm{TeV}$. In such a simulation,
the neutrino produces a track signature in the detector, i.e. a pseudo-signal
event. The angle between the reconstructed direction of the track and the true
direction of the neutrino creates a spread of these pseudo-signal events
centered around the ULIRG locations. The number of pseudo-signal events are
drawn from a Poisson distribution with a given mean. For various values of
this mean pseudo-signal, we determine the corresponding TS distribution by
performing $10^{3}$ trials. We define the sensitivity of the analysis at 90%
confidence level as the mean number of pseudo-signal events required to obtain
a p-value $\leq 0.5$ in 90% of the trials. In addition, we define the
$3\sigma$ (resp. $5\sigma$) discovery potential as the mean number of pseudo-
signal events required to obtain a p-value $\leq 2.70\times 10^{-3}$ (resp.
$\leq 5.73\times 10^{-7}$) in 50% of the trials. Panel (a) of Fig. 2 shows
these quantities in terms of the stacked muon-neutrino flux evaluated at666The
shape of the sensitivity and discovery potentials plotted in panel (a) of Fig.
2 is a direct consequence of the evaluation of the flux at
$E_{0}=10~{}\mathrm{TeV}$. $E_{0}=10~{}\mathrm{TeV}$ as a function of the
spectral index $\gamma$. Panel (b) shows the same quantities in terms of the
total mean number of pseudo-signal events. We determine this number by
integrating the injection spectrum, after convolving it with the detector
effective area, over energy and detector lifetime. We find that the
sensitivity and discovery potentials are more competitive for harder spectra.
This dependence is expected since harder spectra are more easily distinguished
from the atmospheric background.

##  3 Results

We report the results of the stacking search for neutrino emission from our
representative sample of 75 ULIRGs using 7.5 years of IceCube data, with the
total IR flux of each individual source as a stacking weight. The analysis
yields a best fit for the number of signal events $\hat{n}_{s}=0$, such that
the best fit for the spectral index, $\hat{\gamma}$, remains undetermined. The
fitted results correspond with a $\mathrm{TS}=0$, and p-value $=1$. These
observations are consistent with the hypothesis that the data is compatible
with background. We therefore set upper limits on the stacked muon-neutrino
flux of the 75 ULIRGs considered. Since the analysis yields a $\mathrm{TS}=0$,
the upper limits at 90% confidence level (CL) are set equal to the 90%
sensitivity, shown in Fig. 2 for unbroken $E^{-\gamma}$ power-law spectra.
Table 1 lists the upper limits, $\Phi_{\nu_{\mu}+\bar{\nu}_{\mu}}^{90\%}$, for
some specific values of the spectral index $\gamma$ at the normalization
energy $E_{0}=10~{}\mathrm{TeV}$.

Table 1: Resulting flux upper limits at 90% confidence level of the ULIRG
stacking analysis.

Spectral index $\gamma$ | $\Phi_{\nu_{\mu}+\bar{\nu}_{\mu}}^{90\%}~{}\mathrm{at}~{}E_{0}=10~{}\mathrm{TeV}$
---|---
| $\mathrm{10^{-14}\times TeV^{-1}~{}cm^{-2}~{}s^{-1}}$
2.0 | 1.23
2.28 | 2.40
2.5 | 3.24
2.87 | 3.62
3.0 | 3.34

Note. — The spectral index $\gamma=2.28$ corresponds to the best fit of the
diffuse neutrino flux in Stettner (2020). The spectral index $\gamma=2.87$
corresponds to the best fit in Abbasi et al. (2020a).

##  4 Discussion

###  4.1 Limits on the ULIRG Source Population

The upper limits $\Phi_{\nu_{\mu}+\bar{\nu}_{\mu}}^{90\%}$ of the ULIRG
stacking analysis can be translated into an upper limit on the diffuse muon-
neutrino flux originating from all ULIRGs with redshift $z\leq 0.13$, computed
as $\Phi_{\nu_{\mu}+\bar{\nu}_{\mu}}^{z\leq
0.13}=\epsilon_{c}\Phi_{\nu_{\mu}+\bar{\nu}_{\mu}}^{90\%}/(4\pi~{}\mathrm{sr})$.
Here, $\epsilon_{c}=1.1$ which corrects for the completeness of the ULIRG
sample (see Appendix A for more details). This result can be extrapolated to
an upper limit on the contribution of the total ULIRG source population to the
diffuse neutrino flux. For this extrapolation we assume that all ULIRGs have
identical properties of hadronic acceleration and neutrino production over
cosmic history. We follow the method presented in Ahlers & Halzen (2014) to
estimate the neutrino flux of all ULIRGs up to a redshift $z_{\max}$ as

$\Phi_{\nu_{\mu}+\bar{\nu}_{\mu}}^{z\leq
z_{\max}}=\frac{\xi_{z=z_{\max}}}{\xi_{z=0.13}}\Phi_{\nu_{\mu}+\bar{\nu}_{\mu}}^{z\leq
0.13}.$ (2)

The redshift evolution factor $\xi_{z}$ effectively integrates the source
luminosity function over cosmic history up to a redshift $z$. For an unbroken
$E^{-\gamma}$ power-law spectrum, $\xi_{z}$ becomes energy-independent. It can
then be computed directly given a parameterization $\mathcal{H}(z)$ of the
source evolution with redshift (Vereecken & de Vries, 2020). More details and
numerical values of $\xi_{z}$ are provided in Appendix B.

The ULIRG luminosity function has been a topic of several studies (Kim &
Sanders, 1998; Blain et al., 1999; Genzel & Cesarsky, 2000; Cowie et al.,
2004; Chapman et al., 2005; Le Floc’h et al., 2005; Hopkins et al., 2006;
Lonsdale et al., 2006; Caputi et al., 2007; Reddy et al., 2008; Magnelli et
al., 2009; Clements et al., 2010; Goto et al., 2011; Magnelli et al., 2011;
Casey et al., 2012; Gruppioni et al., 2013). Qualitatively, it is observed
that ULIRGs have a rapidly increasing source evolution up to a redshift $z\sim
1$, followed by a relative flattening of the source evolution at higher
redshifts. Unless stated otherwise, in this work we follow Vereecken & de
Vries (2020) by parameterizing the ULIRG redshift evolution as
$\mathcal{H}(z)\propto(1+z)^{m}$, with $m=4$ for $z\leq 1$ and $m=0$ (i.e. a
flat source evolution) for $1<z\leq 4$.

Using Eq. (2), we are now able to determine the upper limits at 90% CL on the
diffuse muon-neutrino flux of the ULIRG population up to a redshift
$z_{\max}=4.0$, which is chosen following Palladino et al. (2019). The
integral limits for unbroken $E^{-2.0}$, $E^{-2.5}$, and $E^{-3.0}$ power-law
spectra are shown in panel (a) of Fig. 3. Each of these limits is plotted in
their respective 90% central energy region, defined as the energy range in
which events contribute to 90% of the total sensitivity777The 90% central
energy range of the sensitivity is determined by reducing (resp. increasing)
the maximum (resp. minimum) allowed energy of injected pseudo-signal events in
steps of $\log_{10}(E/\mathrm{GeV})=0.2$, and computing the sensitivity in
each step. The maximum energy bound (resp. minimum energy bound) is the value
for which the sensitivity flux increases with 5% compared to the sensitivity
flux integrated over all energies.. We find that the limits under the
$E^{-2.0}$ and $E^{-2.5}$ assumptions exclude ULIRGs as the sole contributors
to the diffuse neutrino observations up to energies of $\sim$3 PeV and
$\sim$600 TeV, respectively. The $E^{-3.0}$ limit mostly constrains the
diffuse ULIRG flux at energies below the diffuse observations. Panel (b) of
Fig. 3 shows the quasi-differential limits on the diffuse neutrino flux from
ULIRGs. These quasi-differential limits are determined by computing the
$E^{-2.0}$ limit in each bin of energy decade between 100 GeV and 10 PeV. We
find that the quasi-differential limits constrain ULIRGs as the sole
contributors to the diffuse neutrino observations in the 10–100 TeV and 0.1–1
PeV bins, respectively.

Figure 3: Panel (a) presents the integral limits at 90% confidence level on
the contribution of the ULIRG population up to a redshift $z_{\max}=4.0$ to
the observed diffuse muon-neutrino flux. These integral limits are shown for
unbroken $E^{-2.0}$ (dashed blue line), $E^{-2.5}$ (dash-dotted dark magenta
line), and $E^{-3.0}$ (dotted light magenta line) power-law spectra. The
integral limits are plotted within their respective 90% central energy ranges.
Panel (b) presents the quasi-differential limits at 90% confidence level
(dashed blue line), found by determining the limit for an $E^{-2.0}$ spectrum
in each decade of energy. In each panel, the diffuse neutrino observations are
shown in terms of the 7.5 year differential per-flavor measurements using the
high-energy starting event (HESE) sample (black data points; Abbasi et al.,
2020a) and the 9.5 year best-fit unbroken power-law spectrum of astrophysical
muon neutrinos from the Northern hemisphere (red band; Stettner, 2020).

The above results do not constrain the possible contribution of LIRGs
($10^{11}L_{\odot}\leq L_{\mathrm{IR}}<10^{12}L_{\odot}$) to the diffuse
neutrino flux. Within $z<1$, the IR luminosity density of LIRGs evolves
roughly the same with redshift as the IR luminosity density of ULIRGs,
although the former is $\sim$10–50 times larger (Le Floc’h et al., 2005;
Caputi et al., 2007; Magnelli et al., 2009; Goto et al., 2011; Casey et al.,
2012). Assuming that the correlation between the total IR and neutrino
luminosities holds down to $L_{\mathrm{IR}}\geq 10^{11}L_{\odot}$, the
contribution of LIRGs to the neutrino flux is expected to dominate with
respect to ULIRGs. However, we note that a possible AGN contribution to the
total IR luminosity seems to increase for ULIRGs (Nardini et al., 2010). This
increase in AGN contribution suggests that the hadronic acceleration
properties of ULIRGs may differ from those of LIRGs. A dedicated study
searching for high-energy neutrinos from LIRGs would provide further insights
on the possible acceleration mechanisms within these objects.

###  4.2 Comparison with Model Predictions

First, we compare our results with the cosmic-ray reservoir model developed by
He et al. (2013). They consider hypernovae as hadronic accelerators which are
able to produce $\mathcal{O}(100~{}\mathrm{PeV})$ protons. He et al. (2013)
suggest that the enhanced star-formation rate in ULIRGs leads to an enhanced
hypernova rate. This enhanced hypernova rate results in ULIRG neutrino
emission consistent with an $E^{-2.0}$ power-law spectrum, with a cutoff at
$\sim$2 PeV. They predict a diffuse neutrino flux originating from ULIRGs up
to a redshift $z_{\max}=2.3$. Hence, we compare the prediction by He et al.
(2013) to our $E^{-2.0}$ upper limit (90% CL) on the diffuse ULIRG neutrino
flux up to a redshift $z_{\max}=2.3$. This comparison is presented in panel
(a) of Fig. 4. We find that our upper limit at 90% CL using 7.5 years of
IceCube data is at the level of the predicted flux of He et al. (2013). A
follow-up study using additional years of data is required to further
investigate the validity of this model.

Figure 4: Panel (a) shows the prediction by He et al. (2013) of a diffuse
neutrino flux from hypernovae in ULIRGs (full magenta line) and the $E^{-2.0}$
upper limit at 90% confidence level of this search (dashed blue line). For
comparison, an ULIRG source evolution is assumed and integrated up to a
redshift $z_{\max}=2.3$. The model prediction is in tension with the obtained
limit. Panel (b) shows the prediction by Palladino et al. (2019) of a diffuse
neutrino flux, normalized to the IceCube observations, from hadronically
powered gamma-ray galaxies (HAGS; full magenta line) and the $E^{-2.12}$ upper
limit at 90% confidence level of this search (dashed blue line). For
comparison, a source evolution according to the star-formation rate is assumed
and integrated up to a redshift $z_{\max}=4.0$. The obtained limit excludes
ULIRGs as the sole HAGS that can explain the diffuse neutrino observations.
The diffuse neutrino observations are described in Fig. 3.

Second, we consider the work of Palladino et al. (2019). Their study applies a
multimessenger approach to construct a generic cosmic-ray reservoir model of
hadronically powered gamma-ray galaxies (HAGS). Candidate HAGS include ULIRGs
and starburst galaxies with $L_{\mathrm{IR}}<10^{12}L_{\odot}$. Palladino et
al. (2019) model the diffuse neutrino and gamma-ray emission of a population
of HAGS up to a redshift $z_{\max}=4.0$ according to a power-law spectrum with
an exponential cutoff. This spectrum is fitted to the diffuse IceCube
observations given in Haack & Wiebusch (2018). They find that spectra with
indices $\gamma\leq 2.12$ are able to explain a significant fraction of the
diffuse neutrino observations without violating the non-blazar EGB bound above
50 GeV (Ackermann et al., 2016; Lisanti et al., 2016; Zechlin et al., 2016).
In panel (b) of Fig. 4 we compare the baseline HAGS model with spectral index
$\gamma=2.12$ to our $E^{-2.12}$ upper limit (90% CL) on the diffuse ULIRG
neutrino flux up to a redshift $z_{\max}=4.0$. To determine this limit, we
follow Palladino et al. (2019) and parameterize the ULIRG source evolution
according to the star-formation rate, $\mathcal{H}(z)\propto(1+z)^{m}$, with
$m=3.4$ for $z\leq 1$ and $m=-0.5$ for $1<z\leq 4$ (Hopkins & Beacom, 2006;
Yüksel et al., 2008). We find that our limits exclude ULIRGs at 90% CL as the
sole HAGS that can be responsible for the diffuse neutrino observations.
However, it should be noted that this result does not have any implications
for other candidate HAGS, such as starburst galaxies with
$L_{\mathrm{IR}}<10^{12}L_{\odot}$.

Last, we make a comparison with the beam-dump model of Vereecken & de Vries
(2020). This model considers Compton-thick AGN, i.e. AGN obscured by clouds of
matter with hydrogen column densities $N_{H}\gtrsim 1.5\times
10^{24}~{}\mathrm{cm^{-2}}$ (Comastri, 2004), as hadronic accelerators. The
neutrino production is modeled through the $pp$-interactions of accelerated
hadrons with cloud nuclei. Vereecken & de Vries (2020) predict a diffuse
neutrino flux from ULIRGs, for which they consider two methods to normalize
the proton luminosity. In one approach, it is normalized to the IceCube
observations of Kopper (2018). The authors find that ULIRGs can fit the
IceCube data without exceeding the Fermi-LAT non-blazar EGB bound above 50 GeV
(Ackermann et al., 2016) for column densities $N_{H}\gtrsim 5\times
10^{25}~{}\mathrm{cm^{-2}}$. A second approach is found by normalizing the
ULIRG proton luminosity to the radio luminosity using the observed ULIRG
radio-infrared relation (Sargent et al., 2010). In this case, the modeling
mainly depends on the electron-to-proton luminosity ratio, $f_{e}$ (see e.g.
Merten et al., 2017).

Here, we fit the results of Vereecken & de Vries (2020) for an $E^{-2.0}$
spectrum to our $E^{-2.0}$ upper limit (90% CL) on the diffuse neutrino flux
from ULIRGs up to a redshift $z_{\max}=4.0$. Subsequently, we use the method
presented in Vereecken & de Vries (2020) to estimate the ULIRG radio
luminosity using the radio-infrared relation of Sargent et al. (2010). For
this estimation, we take a conservative value
$L_{\mathrm{IR}}=10^{12}L_{\odot}$, and we assume that AGN contribute to 10%
of this infrared luminosity based on the results of Nardini et al. (2010).
This allows us to set a lower limit on the electron-to-proton luminosity
ratio, $f_{e}\gtrsim 10^{-3}$, by fixing all other parameters in the model of
Vereecken & de Vries (2020). It should be noted that among these parameters
are quantities with large uncertainties, such as the electron-to-radio
luminosity ratio (Becker Tjus et al., 2014). Hence, the lower limit
$f_{e}\gtrsim 10^{-3}$ should be regarded as an order-of-magnitude estimation.
Nevertheless, we point out that this limit on the electron-to-proton
luminosity ratio lies within the same order of magnitude as the lower limits
provided by Vereecken & de Vries (2020) for several obscured flat-spectrum
radio AGN that were also studied with IceCube (Maggi et al., 2016, 2018).

##  5 Conclusions

ULIRGs have IR luminosities $L_{\mathrm{IR}}\geq 10^{12}L_{\odot}$, making
them the most luminous objects in the IR sky. They are mainly powered by
starbursts, possibly combined with an AGN contribution that likely increases
with IR luminosity. These starburst and AGN environments are plausible hosts
of hadronic accelerators, suggesting that neutrino production occurs in such
environments. ULIRGs are therefore candidate sources of high-energy
astrophysical neutrinos. Studies by He et al. (2013), Palladino et al. (2019),
and Vereecken & de Vries (2020) suggest that the ULIRG population could be
responsible for a significant fraction of the diffuse astrophysical neutrino
flux observed with the IceCube Neutrino Observatory at the South Pole.

In this work, we presented a stacking search for astrophysical neutrinos from
ULIRGs using 7.5 years of IceCube data. A representative sample of 75 ULIRGs
with redshifts $z\leq 0.13$ was obtained from three catalogs based on IRAS
data (Kim & Sanders, 1998; Sanders et al., 2003; Nardini et al., 2010). An
unbinned maximum likelihood analysis was performed with the IceCube data to
search for an excess of an astrophysical signal from ULIRGs above the
atmospheric background. No such excess has been found. The analysis yields a
$\text{p-value}=1$, which is consistent with the hypothesis that the data is
compatible with background. Hence, we report upper limits (90% CL) on the
neutrino flux originating from these 75 ULIRGs. The stacked flux upper limit
for an unbroken $E^{-2.5}$ power-law spectrum is
$\Phi_{\nu_{\mu}+\bar{\nu}_{\mu}}^{90\%}=3.24\times
10^{-14}~{}\mathrm{TeV^{-1}~{}cm^{-2}~{}s^{-1}}~{}(E/10~{}\mathrm{TeV})^{-2.5}$.

We studied the implication of our null result on the contribution of the ULIRG
source population to the IceCube diffuse neutrino observations. The integral
limits for unbroken $E^{-2.0}$ and $E^{-2.5}$ power-law spectra exclude ULIRGs
as the sole contributors to the diffuse neutrino flux up to energies of
$\sim$3 PeV and $\sim$600 TeV, respectively. The quasi-differential limits
exclude ULIRGs as the sole contributors to the diffuse neutrino flux in the
10–100 TeV and 0.1–1 PeV energy bins. We remark that these results do not
constrain the possible diffuse neutrino contribution of the less luminous but
more numerous LIRGs ($10^{11}L_{\odot}\leq L_{\mathrm{IR}}<10^{12}L_{\odot}$),
which have physical properties that are similar to those of ULIRGs (see e.g.
Lonsdale et al., 2006).

Finally, we compared our upper limits at 90% CL with three models that predict
a diffuse neutrino flux from ULIRGs. First, the prediction of He et al. (2013)
is in tension with our $E^{-2.0}$ upper limit, although a follow-up study with
additional years of data is required to test the validity of this model.
Second, our $E^{-2.12}$ upper limit excludes ULIRGs as the sole population of
HAGS, proposed by Palladino et al. (2019), that are responsible for the
diffuse neutrino observations. We note that this result does not constrain the
possible diffuse neutrino contribution from other candidate HAGS, such as
starburst galaxies with $L_{\mathrm{IR}}<10^{12}L_{\odot}$. Third, we report a
lower limit on the electron-to-proton luminosity ratio (Merten et al., 2017),
$f_{e}\gtrsim 10^{-3}$, in the beam-dump model of Vereecken & de Vries (2020).
This lower limit was determined by fitting the model to our $E^{-2.0}$ upper
limit, while fixing all other model parameters. These parameters include
quantities with large uncertainties, such as the electron-to-radio luminosity
ratio (Becker Tjus et al., 2014). Therefore, the lower limit on the electron-
to-proton luminosity ratio presented here should be regarded as an order-of-
magnitude estimation. A dedicated search for high-energy neutrinos from
Compton-thick AGN could provide more insights on the possible neutrino
production in such beam-dump scenarios.

## Acknowledgments

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.

##  Appendix A Completeness of the ULIRG Selection

A representative sample of the local ULIRG population is found by determining
the redshift up to which the least luminous ULIRGs (i.e.
$L_{\mathrm{IR}}=10^{12}L_{\odot}$) can be observed, given a conservative IRAS
sensitivity $f_{60}=1~{}\mathrm{Jy}$. For this redshift determination we use
the observed correlation between $f_{60}$ and the total IR flux
$F_{\mathrm{IR}}=L_{\mathrm{IR}}/(4\pi d_{L}^{2})$ of our initial ULIRG
selection (see Section 2.1), which is shown in Fig. 5. Here, $d_{L}$ is the
luminosity distance, which is determined from the redshift measurements. Since
the $f_{60}$ measurements are optimized separately for the different IRAS
surveys, these are taken in the following order:

  * •

From the RBGS (Sanders et al., 2003) if available;

  * •

From the FSC (Moshir et al., 1992) if not available in the RBGS;

  * •

From the PSC (Beichman et al., 1988) if not available in the RBGS or FSC.

Note that the data from the FSC and PSC are obtained from NED.

To determine the $F_{\mathrm{IR}}$ value corresponding with
$f_{60}=1~{}\mathrm{Jy}$, we perform a log-linear fit on the $f_{60}$ and
$F_{\mathrm{IR}}$ catalog data of the form

$\log_{10}\left(\frac{f_{60}}{\mathrm{Jy}}\right)=a\log_{10}\left(\frac{F_{\mathrm{IR}}}{\mathrm{W~{}m^{-2}}}\right)+b,$
(A1)

with best-fit parameters $a=(95.85\pm 0.81)\times 10^{-2}$ and $b=12.645\pm
0.094$. This fit is shown in Fig. 5. Subsequently, using Eq. (A1), the
luminosity distance $d_{L}$ can be determined for which
$L_{\mathrm{IR}}=10^{12}L_{\odot}$ given $f_{60}=1~{}\mathrm{Jy}$. We find
that $d_{L}\sim 700~{}\mathrm{Mpc}$, which corresponds to a redshift $z\sim
0.143$. However, the uncertainties on $L_{\mathrm{IR}}$ were not taken into
account, since they are not provided by Catalogs 1 & 2\. Therefore, a
conservative redshift $z=0.13$ is adopted up to which we are confident that
the ULIRG selection is representative for the local ULIRG population. This
conservative redshift cut results in a final selection of 75 ULIRGs with
$z\leq 0.13$.

Figure 5: Correlation between the flux density at 60 $\mu$m, $f_{60}$, and the
total IR flux between 8–1000 $\mu$m, $F_{\mathrm{IR}}$, for our initial
selection of 189 ULIRGs. The log-linear fit through these data points is also
shown.

The redshift cut at $z=0.13$ effectively corresponds with a flux constraint
$f_{60}\gtrsim 1~{}\mathrm{Jy}$. However, the final sample of 75 ULIRGs likely
misses sources with $1~{}\mathrm{Jy}\leq f_{60}<5.24~{}\mathrm{Jy}$, called
“1-Jy sources” hereafter. This lack of sources is due the fact that Catalog 2,
although complete, only covers 40% of the sky. In addition, the required
Spitzer observations limit the coverage of Catalog 3. The final ULIRG sample
contains 37 1-Jy sources from Catalog 2, and 15 1-Jy sources from Catalog 3
which are located in the complementary 60% of the sky. Hence, we likely miss
$\sim$40 1-Jy sources in our final ULIRG selection.

The effect of these missing 1-Jy sources is estimated by computing their
contribution to the cumulative stacking weight of the analysis (see Section
2.3). For this estimation, 40 1-Jy sources are simulated evenly over the part
of the sky not covered by Catalog 2, where each declination will directly
determine the corresponding detector response. Each of these sources is given
a theoretical weight equal to the median value of the total IR flux of the 37
ULIRGs taken from Catalog 2. After repeating this simulation $10^{4}$ times,
we find that the median contribution of 40 missing 1-Jy sources to the
cumulative stacking weight is roughly 10% for all spectra considered in this
work. Our sample of 75 ULIRGs can therefore still be regarded as a
representative sample of the local ULIRG population. We compute the upper
limit on the diffuse neutrino flux from all ULIRGs within $z\leq 0.13$ as
$\Phi_{\nu_{\mu}+\bar{\nu}_{\mu}}^{z\leq
0.13}=\epsilon_{c}\Phi_{\nu_{\mu}+\bar{\nu}_{\mu}}^{90\%}/(4\pi~{}\mathrm{sr})$.
Here, $\Phi_{\nu_{\mu}+\bar{\nu}_{\mu}}^{\mathrm{90\%}}$ is the upper limit on
the stacked flux from the 75 analyzed ULIRGs (see e.g. Table 1), while the
completeness correction factor $\epsilon_{c}=1.1$ takes into account the
missing contribution of $\sim$40 missing 1-Jy sources.

##  Appendix B Redshift Evolution Factor

A redshift evolution factor $\xi_{z}$ (Ahlers & Halzen, 2014) was introduced
to estimate the muon-neutrino flux corresponding with a certain fraction of
the ULIRG source population (see Section 4.1). For an unbroken $E^{-\gamma}$
power-law spectrum, it takes the energy-independent form (e.g. Vereecken & de
Vries, 2020)

$\xi_{z}(\gamma)=\int_{0}^{z}\frac{\mathcal{H}(z^{\prime})(1+z^{\prime})^{-\gamma}}{\sqrt{\Omega_{m}(1+z^{\prime})^{3}+\Omega_{\Lambda}}}\mathrm{d}z^{\prime}.$
(B1)

Table 2 lists the values of $\xi_{z}$ for different combinations of the
redshift $z$ up to which Eq. (B1) is integrated and the spectral index
$\gamma$. These values are given for three parameterizations of the source
evolution $\mathcal{H}(z)\propto(1+z)^{m}$:

  * •

ULIRG evolution, where $m=4$ for $z\leq 1$ and $m=0$ for $1<z\leq 4$
(Vereecken & de Vries, 2020).

  * •

Star-forming evolution, where $m=3.4$ for $z\leq 1$ and $m=-0.3$ for $1<z\leq
4$ (Hopkins & Beacom, 2006; Yüksel et al., 2008).

  * •

Flat evolution, where $m=0$ for all $z$.

Table 2: Values of the redshift evolution factor $\xi_{z}$ for different
unbroken $E^{-\gamma}$ power-law spectra and source evolutions.

Source evolution | Spectral index $\gamma$ | $\xi_{z=0.13}$ | $\xi_{z=2.3}$ | $\xi_{z=4.0}$
---|---|---|---|---
| 2.0 | 0.14 | 3.0 | 3.4 |
ULIRG | 2.5 | 0.14 | 2.2 | 2.5 |
| 3.0 | 0.13 | 1.7 | 1.8 |
| 2.0 | 0.14 | 2.2 | 2.4 |
Star formation | 2.5 | 0.13 | 1.6 | 1.7 |
| 3.0 | 0.13 | 1.2 | 1.3 |
| 2.0 | 0.11 | 0.49 | 0.53 |
Flat | 2.5 | 0.11 | 0.41 | 0.43 |
| 3.0 | 0.11 | 0.35 | 0.36 |

Note. — The parameterizations of the considered source evolutions are
described in the text.

Table 3: ULIRGs used in this IceCube search.

NED identification | R.A. | Dec. | Redshift | $d_{L}$ | $f_{60}$ | $\sigma_{f_{60}}$ | $\log_{10}\left(L_{\mathrm{IR}}\right)$ | ULIRG catalog
---|---|---|---|---|---|---|---|---
| deg | deg |  | Mpc | Jy | Jy | $L_{\odot}$ |
2MASX J00002427-5250313 | 0.10 | -52.84 | 0.125 | 604 | 1.89 | 0.13 | 12.20 | Nardini et al. (2010) |  |  |  |
2MASX J00114330-0722073 | 2.93 | -7.37 | 0.118 | 570 | 2.63 | 0.18 | 12.19 | Kim & Sanders (1998) |  |  |  |
2MASX J00212652-0839261 | 5.36 | -8.66 | 0.128 | 622 | 2.59 | 0.23 | 12.33 | Kim & Sanders (1998) |  |  |  |
2MASX J00220698-7409418 | 5.53 | -74.16 | 0.096 | 457 | 4.16 | 0.21 | 12.33 | Nardini et al. (2010) |  |  |  |
2MASX J00480675-2848187 | 12.03 | -28.81 | 0.110 | 526 | 2.60 | 0.18 | 12.12 | Kim & Sanders (1998) |  |  |  |
GALEXASC J005040.35-270440.6 | 12.67 | -27.08 | 0.129 | 626 | 1.13 | 0.14 | 12.00 | Kim & Sanders (1998) |  |  |  |
GALEXASC J010250.01-222157.4 | 15.71 | -22.37 | 0.118 | 567 | 2.29 | 0.16 | 12.24 | Kim & Sanders (1998) |  |  |  |
2MASX J01190760-0829095 | 19.78 | -8.49 | 0.118 | 569 | 1.74 | 0.10 | 12.03 | Kim & Sanders (1998) |  |  |  |
2MASX J01405591-4602533 | 25.23 | -46.05 | 0.090 | 426 | 2.91 | 0.20 | 12.12 | Nardini et al. (2010) |  |  |  |
2MASX J02042730-2049413 | 31.11 | -20.83 | 0.116 | 557 | 1.45 | 0.12 | 12.01 | Kim & Sanders (1998) |  |  |  |
2MASX J03274981+1616594 | 51.96 | 16.28 | 0.129 | 625 | 1.38 | 0.08 | 12.06 | Kim & Sanders (1998) |  |  |  |
2MASX J04121945-2830252 | 63.08 | -28.51 | 0.117 | 565 | 1.82 | 0.09 | 12.15 | Kim & Sanders (1998) |  |  |  |
2MASX J04124420-5109402 | 63.18 | -51.16 | 0.125 | 602 | 2.09 | 0.10 | 12.26 | Nardini et al. (2010) |  |  |  |
2MASX J05210136-2521450 | 80.26 | -25.36 | 0.043 | 194 | 13.25 | 0.03 | 12.11 | Sanders et al. (2003) |  |  |  |
2MASX J05583717-7716393 | 89.65 | -77.28 | 0.117 | 562 | 1.42 | 0.06 | 12.05 | Nardini et al. (2010) |  |  |  |
2MASX J06025406-7103104 | 90.73 | -71.05 | 0.079 | 373 | 5.13 | 0.15 | 12.23 | Nardini et al. (2010) |  |  |  |
2MASX J06210118-6317238 | 95.26 | -63.29 | 0.092 | 437 | 3.96 | 0.12 | 12.22 | Nardini et al. (2010) |  |  |  |
2MASX J07273754-0254540 | 111.91 | -2.92 | 0.088 | 413 | 6.49 | 0.03 | 12.32 | Sanders et al. (2003) |  |  |  |
2MASX J08380365+5055090 | 129.52 | 50.92 | 0.097 | 459 | 2.14 | 0.11 | 12.01 | Nardini et al. (2010) |  |  |  |
IRAS 08572+3915 | 135.11 | 39.07 | 0.058 | 270 | 7.30 | 0.03 | 12.10 | Sanders et al. (2003) |  |  |  |
2MASX J09041268-3627007 | 136.05 | -36.45 | 0.060 | 276 | 11.64 | 0.06 | 12.26 | Sanders et al. (2003) |  |  |  |
2MASX J09063400+0451271 | 136.64 | 4.86 | 0.125 | 605 | 1.48 | 0.09 | 12.07 | Kim & Sanders (1998) |  |  |  |
2MASX J09133888-1019196 | 138.41 | -10.32 | 0.054 | 249 | 6.75 | 0.04 | 12.00 | Sanders et al. (2003) |  |  |  |
UGC 05101 | 143.96 | 61.35 | 0.039 | 179 | 11.54 | 0.81 | 11.99 | Nardini et al. (2010) |  |  |  |
2MASX J09452133+1737533 | 146.34 | 17.63 | 0.128 | 621 | 0.89 | 0.06 | 12.08 | Nardini et al. (2010) |  |  |  |
GALEXASC J095634.42+084306.0 | 149.14 | 8.72 | 0.129 | 624 | 1.44 | 0.10 | 12.03 | Kim & Sanders (1998) |  |  |  |
IRAS 10190+1322 | 155.43 | 13.12 | 0.077 | 358 | 3.33 | 0.27 | 12.00 | Kim & Sanders (1998) |  |  |  |
2MASX J10522356+4408474 | 163.10 | 44.15 | 0.092 | 435 | 3.53 | 0.21 | 12.13 | Kim & Sanders (1998) |  |  |  |
2MASX J10591815+2432343 | 164.83 | 24.54 | 0.043 | 197 | 12.10 | 0.03 | 12.02 | Sanders et al. (2003) |  |  |  |
LCRS B110930.3-023804 | 168.01 | -2.91 | 0.107 | 509 | 3.25 | 0.16 | 12.20 | Kim & Sanders (1998) |  |  |  |
2MASX J11531422+1314276 | 178.31 | 13.24 | 0.127 | 616 | 2.58 | 0.15 | 12.28 | Kim & Sanders (1998) |  |  |  |
IRAS 12071-0444 | 182.44 | -5.02 | 0.128 | 621 | 2.46 | 0.15 | 12.35 | Kim & Sanders (1998) |  |  |  |
IRAS 12112+0305 | 183.44 | 2.81 | 0.073 | 342 | 8.18 | 0.03 | 12.28 | Sanders et al. (2003) |  |  |  |
Mrk 0231 | 194.06 | 56.87 | 0.042 | 193 | 30.80 | 0.04 | 12.51 | Sanders et al. (2003) |  |  |  |
WKK 2031 | 198.78 | -55.16 | 0.031 | 139 | 41.11 | 0.07 | 12.26 | Sanders et al. (2003) |  |  |  |
IRAS 13335-2612 | 204.09 | -26.46 | 0.125 | 604 | 1.40 | 0.11 | 12.06 | Kim & Sanders (1998) |  |  |  |
Mrk 0273 | 206.18 | 55.89 | 0.038 | 172 | 22.51 | 0.04 | 12.14 | Sanders et al. (2003) |  |  |  |
4C +12.50 | 206.89 | 12.29 | 0.122 | 587 | 1.92 | 0.21 | 12.28 | Kim & Sanders (1998) |  |  |  |
IRAS 13454-2956 | 207.08 | -30.20 | 0.129 | 625 | 2.16 | 0.11 | 12.21 | Kim & Sanders (1998) |  |  |  |
2MASX J13561001+2905355 | 209.04 | 29.09 | 0.108 | 518 | 1.83 | 0.13 | 12.00 | Kim & Sanders (1998) |  |  |  |
2MASXJ 14081899+2904474 | 212.08 | 29.08 | 0.117 | 561 | 1.61 | 0.16 | 12.03 | Kim & Sanders (1998) |  |  |  |
IRAS 14348-1447 | 219.41 | -15.01 | 0.083 | 390 | 6.82 | 0.04 | 12.30 | Sanders et al. (2003) |  |  |  |
2MASX J14405901-3704322 | 220.25 | -37.08 | 0.068 | 315 | 6.72 | 0.04 | 12.15 | Sanders et al. (2003) |  |  |  |
2MASX J14410437+5320088 | 220.27 | 53.34 | 0.105 | 498 | 1.95 | 0.08 | 12.04 | Kim & Sanders (1998) |  |  |  |
2MASX J15155520-2009172 | 228.98 | -20.15 | 0.109 | 520 | 1.92 | 0.13 | 12.09 | Kim & Sanders (1998) |  |  |  |
SDSS J152238.10+333135.8 | 230.66 | 33.53 | 0.124 | 601 | 1.77 | 0.09 | 12.18 | Kim & Sanders (1998) |  |  |  |
IRAS 15250+3609 | 231.75 | 35.98 | 0.055 | 254 | 7.10 | 0.04 | 12.02 | Sanders et al. (2003) |  |  |  |
Arp 220 | 233.74 | 23.50 | 0.018 | 81 | 104.09 | 0.11 | 12.21 | Sanders et al. (2003) |  |  |  |
IRAS 15462-0450 | 237.24 | -4.99 | 0.100 | 474 | 2.92 | 0.20 | 12.16 | Kim & Sanders (1998) |  |  |  |
2MASX J16491420+3425096 | 252.31 | 34.42 | 0.111 | 534 | 2.27 | 0.11 | 12.11 | Kim & Sanders (1998) |  |  |  |
SBS 1648+547 | 252.45 | 54.71 | 0.104 | 494 | 2.88 | 0.12 | 12.12 | Kim & Sanders (1998) |  |  |  |
2MASX J17034196+5813443 | 255.92 | 58.23 | 0.106 | 506 | 2.43 | 0.15 | 12.10 | Kim & Sanders (1998) |  |  |  |
2MASX J17232194-0017009 | 260.84 | -0.28 | 0.043 | 196 | 32.13 | 0.06 | 12.39 | Sanders et al. (2003) |  |  |  |
2MASX J18383543+3552197 | 279.65 | 35.87 | 0.116 | 558 | 2.23 | 0.13 | 12.29 | Nardini et al. (2010) |  |  |  |
IRAS 18588+3517 | 285.17 | 35.36 | 0.107 | 510 | 1.47 | 0.10 | 11.97 | Nardini et al. (2010) |  |  |  |
Superantennae | 292.84 | -72.66 | 0.062 | 286 | 5.48 | 0.22 | 12.10 | Nardini et al. (2010) |  |  |  |
2MASX J19322229-0400010 | 293.09 | -4.00 | 0.086 | 404 | 7.32 | 0.11 | 12.37 | Sanders et al. (2003) |  |  |  |
IRAS 19458+0944 | 297.07 | 9.87 | 0.100 | 475 | 3.95 | 0.40 | 12.37 | Nardini et al. (2010) |  |  |  |
IRAS 19542+1110 | 299.15 | 11.32 | 0.065 | 301 | 6.18 | 0.04 | 12.04 | Sanders et al. (2003) |  |  |  |
2MASX J20112386-0259503 | 302.85 | -3.00 | 0.106 | 504 | 4.70 | 0.28 | 12.44 | Nardini et al. (2010) |  |  |  |
2MASX J20132950-4147354 | 303.37 | -41.79 | 0.130 | 628 | 5.23 | 0.31 | 12.64 | Nardini et al. (2010) |  |  |  |
IRAS 20414-1651 | 311.08 | -16.67 | 0.087 | 410 | 4.36 | 0.26 | 12.14 | Kim & Sanders (1998) |  |  |  |
ESO 286-IG 019 | 314.61 | -42.65 | 0.043 | 196 | 12.19 | 0.03 | 12.00 | Sanders et al. (2003) |  |  |  |
IRAS 21208-0519 | 320.87 | -5.12 | 0.130 | 630 | 1.17 | 0.07 | 12.01 | Kim & Sanders (1998) |  |  |  |
$\mathrm{\left[HB89\right]}$ 2121-179 | 321.17 | -17.75 | 0.112 | 536 | 1.07 | 0.09 | 12.06 | Kim & Sanders (1998) |  |  |  |
2MASX J21354580-2332359 | 323.94 | -23.54 | 0.125 | 604 | 1.65 | 0.08 | 12.09 | Kim & Sanders (1998) |  |  |  |
2MASX J22074966+3039393 | 331.96 | 30.66 | 0.127 | 614 | 1.87 | 0.36 | 12.29 | Nardini et al. (2010) |  |  |  |
IRAS 22491-1808 | 342.96 | -17.87 | 0.078 | 364 | 5.54 | 0.04 | 12.11 | Sanders et al. (2003) |  |  |  |
2MASX J23042114+3421477 | 346.09 | 34.36 | 0.108 | 516 | 1.42 | 0.10 | 11.99 | Nardini et al. (2010) |  |  |  |
ESO 148-IG 002 | 348.94 | -59.05 | 0.045 | 204 | 10.94 | 0.04 | 12.00 | Sanders et al. (2003) |  |  |  |
2MASX J23254938+2834208 | 351.46 | 28.57 | 0.114 | 547 | 1.26 | 0.13 | 12.00 | Kim & Sanders (1998) |  |  |  |
2MASX J23255611+1002500 | 351.48 | 10.05 | 0.128 | 619 | 1.56 | 0.09 | 12.05 | Kim & Sanders (1998) |  |  |  |
2MASX J23260362-6910185 | 351.52 | -69.17 | 0.107 | 509 | 3.74 | 0.15 | 12.31 | Nardini et al. (2010) |  |  |  |
2MASX J23351192+2930000 | 353.80 | 29.50 | 0.107 | 511 | 2.10 | 0.13 | 12.06 | Kim & Sanders (1998) |  |  |  |
2MASX J23390127+3621087 | 354.76 | 36.35 | 0.064 | 299 | 7.44 | 0.05 | 12.13 | Sanders et al. (2003) |  |  |  |

Note. — Column (1): Primary name identification in the NASA/IPAC Extragalactic
Database (NED). Columns (2)–(4): Equatorial J2000 coordinates and redshift
taken from NED. Column (5): Luminosity distance determined from the redshift
measurements using the cosmological parameters in Ade et al. (2016). Columns
(6)-(7): Infrared flux at 60 $\mu$m and its uncertainty. Taken from the IRAS
Revised Bright Galaxy Sample (RBGS; Sanders et al., 2003) if available; taken
from the IRAS Faint Source Catalog (FSC; Moshir et al., 1992) if not available
in the RBGS; taken from the IRAS Point Source Catalog (PSC; Beichman et al.,
1988) if not available in the RBGS or FSC. Data from the FSC and PSC is
obtained from NED. Columns (8)–(9): Total infrared luminosity between 8–1000
$\mu$m and the ULIRG catalog from which this value is taken.

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