# Searches for Neutrinos from LHAASO ultra-high-energy $\gamma$-ray sources
using the IceCube Neutrino Observatory

R. Abbasi Department of Physics, Loyola University Chicago, Chicago, IL 60660,
USA  M. Ackermann DESY, D-15738 Zeuthen, Germany  J. Adams  Dept. of Physics
and Astronomy, University of Canterbury, Private Bag 4800, Christchurch, New
Zealand  N. Aggarwal  Dept. of Physics, University of Alberta, Edmonton,
Alberta, Canada T6G 2E1  J. A. Aguilar Université Libre de Bruxelles, Science
Faculty CP230, B-1050 Brussels, Belgium  M. Ahlers Niels Bohr Institute,
University of Copenhagen, DK-2100 Copenhagen, Denmark  J.M. Alameddine Dept.
of Physics, TU Dortmund University, D-44221 Dortmund, Germany  A. A. Alves Jr
Karlsruhe Institute of Technology, Institute for Astroparticle Physics,
D-76021 Karlsruhe, Germany  N. M. Amin  Bartol Research Institute and Dept. of
Physics and Astronomy, University of Delaware, Newark, DE 19716, USA  K.
Andeen  Department of Physics, Marquette University, Milwaukee, WI, 53201, USA
T. Anderson  Dept. of Astronomy and Astrophysics, Pennsylvania State
University, University Park, PA 16802, USA  Dept. of Physics, Pennsylvania
State University, University Park, PA 16802, USA  G. Anton Erlangen Centre for
Astroparticle Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg,
D-91058 Erlangen, Germany  C. Argüelles Department of Physics and Laboratory
for Particle Physics and Cosmology, Harvard University, Cambridge, MA 02138,
USA  Y. Ashida  Dept. of Physics and Wisconsin IceCube Particle Astrophysics
Center, University of Wisconsin–Madison, Madison, WI 53706, USA  S.
Athanasiadou  DESY, D-15738 Zeuthen, Germany  S. N. Axani Bartol Research
Institute and Dept. of Physics and Astronomy, University of Delaware, Newark,
DE 19716, USA  X. Bai Physics Department, South Dakota School of Mines and
Technology, Rapid City, SD 57701, USA  A. Balagopal V. Dept. of Physics and
Wisconsin IceCube Particle Astrophysics Center, University of
Wisconsin–Madison, Madison, WI 53706, USA  M. Baricevic  Dept. of Physics and
Wisconsin IceCube Particle Astrophysics Center, University of
Wisconsin–Madison, Madison, WI 53706, USA  S. W. Barwick Dept. of Physics and
Astronomy, University of California, Irvine, CA 92697, USA  V. Basu Dept. of
Physics and Wisconsin IceCube Particle Astrophysics Center, University of
Wisconsin–Madison, Madison, WI 53706, USA  R. Bay  Dept. of Physics,
University of California, Berkeley, CA 94720, USA  J. J. Beatty Dept. of
Astronomy, Ohio State University, Columbus, OH 43210, USA  Dept. of Physics
and Center for Cosmology and Astro-Particle Physics, Ohio State University,
Columbus, OH 43210, USA  K.-H. Becker  Dept. of Physics, University of
Wuppertal, D-42119 Wuppertal, Germany  J. Becker Tjus Fakultät für Physik &
Astronomie, Ruhr-Universität Bochum, D-44780 Bochum, Germany  J. Beise Dept.
of Physics and Astronomy, Uppsala University, Box 516, S-75120 Uppsala, Sweden
C. Bellenghi  Physik-department, Technische Universität München, D-85748
Garching, Germany  S. Benda  Dept. of Physics and Wisconsin IceCube Particle
Astrophysics Center, University of Wisconsin–Madison, Madison, WI 53706, USA
S. BenZvi Dept. of Physics and Astronomy, University of Rochester, Rochester,
NY 14627, USA  D. Berley  Dept. of Physics, University of Maryland, College
Park, MD 20742, USA  E. Bernardini Dipartimento di Fisica e Astronomia Galileo
Galilei, Università Degli Studi di Padova, 35122 Padova PD, Italy  D. Z.
Besson  Dept. of Physics and Astronomy, University of Kansas, Lawrence, KS
66045, USA  G. Binder  Dept. of Physics, University of California, Berkeley,
CA 94720, USA  Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
D. Bindig  Dept. of Physics, University of Wuppertal, D-42119 Wuppertal,
Germany  E. Blaufuss Dept. of Physics, University of Maryland, College Park,
MD 20742, USA  S. Blot DESY, D-15738 Zeuthen, Germany  F. Bontempo  Karlsruhe
Institute of Technology, Institute for Astroparticle Physics, D-76021
Karlsruhe, Germany  J. Y. Book Department of Physics and Laboratory for
Particle Physics and Cosmology, Harvard University, Cambridge, MA 02138, USA
J. Borowka  III. Physikalisches Institut, RWTH Aachen University, D-52056
Aachen, Germany  C. Boscolo Meneguolo Dipartimento di Fisica e Astronomia
Galileo Galilei, Università Degli Studi di Padova, 35122 Padova PD, Italy  S.
Böser Institute of Physics, University of Mainz, Staudinger Weg 7, D-55099
Mainz, Germany  O. Botner Dept. of Physics and Astronomy, Uppsala University,
Box 516, S-75120 Uppsala, Sweden  J. Böttcher  III. Physikalisches Institut,
RWTH Aachen University, D-52056 Aachen, Germany  E. Bourbeau  Niels Bohr
Institute, University of Copenhagen, DK-2100 Copenhagen, Denmark  J. Braun
Dept. of Physics and Wisconsin IceCube Particle Astrophysics Center,
University of Wisconsin–Madison, Madison, WI 53706, USA  B. Brinson  School of
Physics and Center for Relativistic Astrophysics, Georgia Institute of
Technology, Atlanta, GA 30332, USA  J. Brostean-Kaiser  DESY, D-15738 Zeuthen,
Germany  R. T. Burley  Department of Physics, University of Adelaide,
Adelaide, 5005, Australia  R. S. Busse  Institut für Kernphysik, Westfälische
Wilhelms-Universität Münster, D-48149 Münster, Germany  M. A. Campana Dept. of
Physics, Drexel University, 3141 Chestnut Street, Philadelphia, PA 19104, USA
E. G. Carnie-Bronca  Department of Physics, University of Adelaide, Adelaide,
5005, Australia  Y. L. Chang  Tsung-Dao Lee Institute, Shanghai Jiao Tong
University, Shanghai 201210, China  C. Chen School of Physics and Center for
Relativistic Astrophysics, Georgia Institute of Technology, Atlanta, GA 30332,
USA  Z. Chen  Dept. of Physics and Astronomy, Stony Brook University, Stony
Brook, NY 11794-3800, USA  D. Chirkin Dept. of Physics and Wisconsin IceCube
Particle Astrophysics Center, University of Wisconsin–Madison, Madison, WI
53706, USA  K. Choi  Dept. of Physics, Sungkyunkwan University, Suwon 16419,
Korea  B. A. Clark Dept. of Physics and Astronomy, Michigan State University,
East Lansing, MI 48824, USA  L. Classen  Institut für Kernphysik, Westfälische
Wilhelms-Universität Münster, D-48149 Münster, Germany  A. Coleman Bartol
Research Institute and Dept. of Physics and Astronomy, University of Delaware,
Newark, DE 19716, USA  G. H. Collin  Dept. of Physics, Massachusetts Institute
of Technology, Cambridge, MA 02139, USA  A. Connolly  Dept. of Astronomy, Ohio
State University, Columbus, OH 43210, USA  Dept. of Physics and Center for
Cosmology and Astro-Particle Physics, Ohio State University, Columbus, OH
43210, USA  J. M. Conrad Dept. of Physics, Massachusetts Institute of
Technology, Cambridge, MA 02139, USA  P. Coppin Vrije Universiteit Brussel
(VUB), Dienst ELEM, B-1050 Brussels, Belgium  P. Correa Vrije Universiteit
Brussel (VUB), Dienst ELEM, B-1050 Brussels, Belgium  S. Countryman  Columbia
Astrophysics and Nevis Laboratories, Columbia University, New York, NY 10027,
USA  D. F. Cowen  Dept. of Astronomy and Astrophysics, Pennsylvania State
University, University Park, PA 16802, USA  Dept. of Physics, Pennsylvania
State University, University Park, PA 16802, USA  C. Dappen  III.
Physikalisches Institut, RWTH Aachen University, D-52056 Aachen, Germany  P.
Dave School of Physics and Center for Relativistic Astrophysics, Georgia
Institute of Technology, Atlanta, GA 30332, USA  C. De Clercq Vrije
Universiteit Brussel (VUB), Dienst ELEM, B-1050 Brussels, Belgium  J. J.
DeLaunay Dept. of Physics and Astronomy, University of Alabama, Tuscaloosa, AL
35487, USA  D. Delgado López Department of Physics and Laboratory for Particle
Physics and Cosmology, Harvard University, Cambridge, MA 02138, USA  H.
Dembinski Bartol Research Institute and Dept. of Physics and Astronomy,
University of Delaware, Newark, DE 19716, USA  K. Deoskar  Oskar Klein Centre
and Dept. of Physics, Stockholm University, SE-10691 Stockholm, Sweden  A.
Desai Dept. of Physics and Wisconsin IceCube Particle Astrophysics Center,
University of Wisconsin–Madison, Madison, WI 53706, USA  P. Desiati Dept. of
Physics and Wisconsin IceCube Particle Astrophysics Center, University of
Wisconsin–Madison, Madison, WI 53706, USA  K. D. de Vries Vrije Universiteit
Brussel (VUB), Dienst ELEM, B-1050 Brussels, Belgium  G. de Wasseige Centre
for Cosmology, Particle Physics and Phenomenology - CP3, Université catholique
de Louvain, Louvain-la-Neuve, Belgium  T. DeYoung Dept. of Physics and
Astronomy, Michigan State University, East Lansing, MI 48824, USA  A. Diaz
Dept. of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139,
USA  J. C. Díaz-Vélez Dept. of Physics and Wisconsin IceCube Particle
Astrophysics Center, University of Wisconsin–Madison, Madison, WI 53706, USA
M. Dittmer  Institut für Kernphysik, Westfälische Wilhelms-Universität
Münster, D-48149 Münster, Germany  H. Dujmovic Karlsruhe Institute of
Technology, Institute for Astroparticle Physics, D-76021 Karlsruhe, Germany
M. A. DuVernois Dept. of Physics and Wisconsin IceCube Particle Astrophysics
Center, University of Wisconsin–Madison, Madison, WI 53706, USA  T. Ehrhardt
Institute of Physics, University of Mainz, Staudinger Weg 7, D-55099 Mainz,
Germany  P. Eller Physik-department, Technische Universität München, D-85748
Garching, Germany  R. Engel  Karlsruhe Institute of Technology, Institute for
Astroparticle Physics, D-76021 Karlsruhe, Germany  Karlsruhe Institute of
Technology, Institute of Experimental Particle Physics, D-76021 Karlsruhe,
Germany  H. Erpenbeck  III. Physikalisches Institut, RWTH Aachen University,
D-52056 Aachen, Germany  J. Evans  Dept. of Physics, University of Maryland,
College Park, MD 20742, USA  P. A. Evenson  Bartol Research Institute and
Dept. of Physics and Astronomy, University of Delaware, Newark, DE 19716, USA
K. L. Fan  Dept. of Physics, University of Maryland, College Park, MD 20742,
USA  A. R. Fazely Dept. of Physics, Southern University, Baton Rouge, LA
70813, USA  A. Fedynitch Institute of Physics, Academia Sinica, Taipei, 11529,
Taiwan  N. Feigl  Institut für Physik, Humboldt-Universität zu Berlin, D-12489
Berlin, Germany  S. Fiedlschuster  Erlangen Centre for Astroparticle Physics,
Friedrich-Alexander-Universität Erlangen-Nürnberg, D-91058 Erlangen, Germany
A. T. Fienberg  Dept. of Physics, Pennsylvania State University, University
Park, PA 16802, USA  C. Finley Oskar Klein Centre and Dept. of Physics,
Stockholm University, SE-10691 Stockholm, Sweden  L. Fischer  DESY, D-15738
Zeuthen, Germany  D. Fox Dept. of Astronomy and Astrophysics, Pennsylvania
State University, University Park, PA 16802, USA  A. Franckowiak Fakultät für
Physik & Astronomie, Ruhr-Universität Bochum, D-44780 Bochum, Germany  E.
Friedman  Dept. of Physics, University of Maryland, College Park, MD 20742,
USA  A. Fritz  Institute of Physics, University of Mainz, Staudinger Weg 7,
D-55099 Mainz, Germany  P. Fürst  III. Physikalisches Institut, RWTH Aachen
University, D-52056 Aachen, Germany  T. K. Gaisser Bartol Research Institute
and Dept. of Physics and Astronomy, University of Delaware, Newark, DE 19716,
USA  J. Gallagher  Dept. of Astronomy, University of Wisconsin–Madison,
Madison, WI 53706, USA  E. Ganster III. Physikalisches Institut, RWTH Aachen
University, D-52056 Aachen, Germany  A. Garcia Department of Physics and
Laboratory for Particle Physics and Cosmology, Harvard University, Cambridge,
MA 02138, USA  S. Garrappa DESY, D-15738 Zeuthen, Germany  L. Gerhardt
Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA  A. Ghadimi
Dept. of Physics and Astronomy, University of Alabama, Tuscaloosa, AL 35487,
USA  C. Glaser  Dept. of Physics and Astronomy, Uppsala University, Box 516,
S-75120 Uppsala, Sweden  T. Glauch Physik-department, Technische Universität
München, D-85748 Garching, Germany  T. Glüsenkamp Erlangen Centre for
Astroparticle Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg,
D-91058 Erlangen, Germany  N. Goehlke  Karlsruhe Institute of Technology,
Institute of Experimental Particle Physics, D-76021 Karlsruhe, Germany  J. G.
Gonzalez  Bartol Research Institute and Dept. of Physics and Astronomy,
University of Delaware, Newark, DE 19716, USA  S. Goswami  Dept. of Physics
and Astronomy, University of Alabama, Tuscaloosa, AL 35487, USA  D. Grant
Dept. of Physics and Astronomy, Michigan State University, East Lansing, MI
48824, USA  S. J. Gray Dept. of Physics, University of Maryland, College Park,
MD 20742, USA  T. Grégoire  Dept. of Physics, Pennsylvania State University,
University Park, PA 16802, USA  S. Griswold Dept. of Physics and Astronomy,
University of Rochester, Rochester, NY 14627, USA  C. Günther  III.
Physikalisches Institut, RWTH Aachen University, D-52056 Aachen, Germany  P.
Gutjahr Dept. of Physics, TU Dortmund University, D-44221 Dortmund, Germany
C. Haack  Physik-department, Technische Universität München, D-85748 Garching,
Germany  A. Hallgren Dept. of Physics and Astronomy, Uppsala University, Box
516, S-75120 Uppsala, Sweden  R. Halliday  Dept. of Physics and Astronomy,
Michigan State University, East Lansing, MI 48824, USA  L. Halve III.
Physikalisches Institut, RWTH Aachen University, D-52056 Aachen, Germany  F.
Halzen Dept. of Physics and Wisconsin IceCube Particle Astrophysics Center,
University of Wisconsin–Madison, Madison, WI 53706, USA  H. Hamdaoui  Dept. of
Physics and Astronomy, Stony Brook University, Stony Brook, NY 11794-3800, USA
M. Ha Minh  Physik-department, Technische Universität München, D-85748
Garching, Germany  K. Hanson  Dept. of Physics and Wisconsin IceCube Particle
Astrophysics Center, University of Wisconsin–Madison, Madison, WI 53706, USA
J. Hardin  Dept. of Physics, Massachusetts Institute of Technology, Cambridge,
MA 02139, USA  Dept. of Physics and Wisconsin IceCube Particle Astrophysics
Center, University of Wisconsin–Madison, Madison, WI 53706, USA  A. A.
Harnisch  Dept. of Physics and Astronomy, Michigan State University, East
Lansing, MI 48824, USA  P. Hatch  Dept. of Physics, Engineering Physics, and
Astronomy, Queen’s University, Kingston, ON K7L 3N6, Canada  A. Haungs
Karlsruhe Institute of Technology, Institute for Astroparticle Physics,
D-76021 Karlsruhe, Germany  K. Helbing Dept. of Physics, University of
Wuppertal, D-42119 Wuppertal, Germany  J. Hellrung  III. Physikalisches
Institut, RWTH Aachen University, D-52056 Aachen, Germany  F. Henningsen
Physik-department, Technische Universität München, D-85748 Garching, Germany
L. Heuermann  III. Physikalisches Institut, RWTH Aachen University, D-52056
Aachen, Germany  S. Hickford  Dept. of Physics, University of Wuppertal,
D-42119 Wuppertal, Germany  A. Hidvegi  Oskar Klein Centre and Dept. of
Physics, Stockholm University, SE-10691 Stockholm, Sweden  C. Hill Dept. of
Physics and The International Center for Hadron Astrophysics, Chiba
University, Chiba 263-8522, Japan  G. C. Hill  Department of Physics,
University of Adelaide, Adelaide, 5005, Australia  K. D. Hoffman  Dept. of
Physics, University of Maryland, College Park, MD 20742, USA  K. Hoshina  also
at Earthquake Research Institute, University of Tokyo, Bunkyo, Tokyo 113-0032,
Japan  Dept. of Physics and Wisconsin IceCube Particle Astrophysics Center,
University of Wisconsin–Madison, Madison, WI 53706, USA  W. Hou Karlsruhe
Institute of Technology, Institute for Astroparticle Physics, D-76021
Karlsruhe, Germany  T. Huber Karlsruhe Institute of Technology, Institute for
Astroparticle Physics, D-76021 Karlsruhe, Germany  K. Hultqvist Oskar Klein
Centre and Dept. of Physics, Stockholm University, SE-10691 Stockholm, Sweden
M. Hünnefeld  Dept. of Physics, TU Dortmund University, D-44221 Dortmund,
Germany  R. Hussain  Dept. of Physics and Wisconsin IceCube Particle
Astrophysics Center, University of Wisconsin–Madison, Madison, WI 53706, USA
K. Hymon  Dept. of Physics, TU Dortmund University, D-44221 Dortmund, Germany
S. In  Dept. of Physics, Sungkyunkwan University, Suwon 16419, Korea  N.
Iovine Université Libre de Bruxelles, Science Faculty CP230, B-1050 Brussels,
Belgium  A. Ishihara  Dept. of Physics and The International Center for Hadron
Astrophysics, Chiba University, Chiba 263-8522, Japan  M. Jansson  Oskar Klein
Centre and Dept. of Physics, Stockholm University, SE-10691 Stockholm, Sweden
G. S. Japaridze CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA  M.
Jeong  Dept. of Physics, Sungkyunkwan University, Suwon 16419, Korea  M. Jin
Department of Physics and Laboratory for Particle Physics and Cosmology,
Harvard University, Cambridge, MA 02138, USA  B. J. P. Jones Dept. of Physics,
University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box
19059, Arlington, TX 76019, USA  D. Kang Karlsruhe Institute of Technology,
Institute for Astroparticle Physics, D-76021 Karlsruhe, Germany  W. Kang Dept.
of Physics, Sungkyunkwan University, Suwon 16419, Korea  X. Kang  Dept. of
Physics, Drexel University, 3141 Chestnut Street, Philadelphia, PA 19104, USA
A. Kappes Institut für Kernphysik, Westfälische Wilhelms-Universität Münster,
D-48149 Münster, Germany  D. Kappesser  Institute of Physics, University of
Mainz, Staudinger Weg 7, D-55099 Mainz, Germany  L. Kardum  Dept. of Physics,
TU Dortmund University, D-44221 Dortmund, Germany  T. Karg DESY, D-15738
Zeuthen, Germany  M. Karl Physik-department, Technische Universität München,
D-85748 Garching, Germany  A. Karle Dept. of Physics and Wisconsin IceCube
Particle Astrophysics Center, University of Wisconsin–Madison, Madison, WI
53706, USA  U. Katz Erlangen Centre for Astroparticle Physics, Friedrich-
Alexander-Universität Erlangen-Nürnberg, D-91058 Erlangen, Germany  M. Kauer
Dept. of Physics and Wisconsin IceCube Particle Astrophysics Center,
University of Wisconsin–Madison, Madison, WI 53706, USA  J. L. Kelley Dept. of
Physics and Wisconsin IceCube Particle Astrophysics Center, University of
Wisconsin–Madison, Madison, WI 53706, USA  A. Kheirandish Department of
Physics & Astronomy, University of Nevada, Las Vegas, NV, 89154, USA  Nevada
Center for Astrophysics, University of Nevada, Las Vegas, NV 89154, USA  K.
Kin  Dept. of Physics and The International Center for Hadron Astrophysics,
Chiba University, Chiba 263-8522, Japan  J. Kiryluk Dept. of Physics and
Astronomy, Stony Brook University, Stony Brook, NY 11794-3800, USA  S. R.
Klein Dept. of Physics, University of California, Berkeley, CA 94720, USA
Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA  A. Kochocki
Dept. of Physics and Astronomy, Michigan State University, East Lansing, MI
48824, USA  R. Koirala Bartol Research Institute and Dept. of Physics and
Astronomy, University of Delaware, Newark, DE 19716, USA  H. Kolanoski
Institut für Physik, Humboldt-Universität zu Berlin, D-12489 Berlin, Germany
T. Kontrimas  Physik-department, Technische Universität München, D-85748
Garching, Germany  L. Köpke  Institute of Physics, University of Mainz,
Staudinger Weg 7, D-55099 Mainz, Germany  C. Kopper Dept. of Physics and
Astronomy, Michigan State University, East Lansing, MI 48824, USA  D. J.
Koskinen Niels Bohr Institute, University of Copenhagen, DK-2100 Copenhagen,
Denmark  P. Koundal Karlsruhe Institute of Technology, Institute for
Astroparticle Physics, D-76021 Karlsruhe, Germany  M. Kovacevich Dept. of
Physics, Drexel University, 3141 Chestnut Street, Philadelphia, PA 19104, USA
M. Kowalski Institut für Physik, Humboldt-Universität zu Berlin, D-12489
Berlin, Germany  DESY, D-15738 Zeuthen, Germany  T. Kozynets  Niels Bohr
Institute, University of Copenhagen, DK-2100 Copenhagen, Denmark  K. Kruiswijk
Centre for Cosmology, Particle Physics and Phenomenology - CP3, Université
catholique de Louvain, Louvain-la-Neuve, Belgium  E. Krupczak  Dept. of
Physics and Astronomy, Michigan State University, East Lansing, MI 48824, USA
E. Kun  Fakultät für Physik & Astronomie, Ruhr-Universität Bochum, D-44780
Bochum, Germany  N. Kurahashi Dept. of Physics, Drexel University, 3141
Chestnut Street, Philadelphia, PA 19104, USA  N. Lad  DESY, D-15738 Zeuthen,
Germany  C. Lagunas Gualda DESY, D-15738 Zeuthen, Germany  M. Lamoureux
Centre for Cosmology, Particle Physics and Phenomenology - CP3, Université
catholique de Louvain, Louvain-la-Neuve, Belgium  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 DeHolton Dept. of Physics and Wisconsin IceCube
Particle Astrophysics Center, University of Wisconsin–Madison, Madison, WI
53706, USA  A. Leszczyńska Bartol Research Institute and Dept. of Physics and
Astronomy, University of Delaware, Newark, DE 19716, USA  M. Lincetto
Fakultät für Physik & Astronomie, Ruhr-Universität Bochum, D-44780 Bochum,
Germany  Q. R. Liu Dept. of Physics and Wisconsin IceCube Particle
Astrophysics Center, University of Wisconsin–Madison, Madison, WI 53706, USA
M. Liubarska  Dept. of Physics, University of Alberta, Edmonton, Alberta,
Canada T6G 2E1  E. Lohfink  Institute of Physics, University of Mainz,
Staudinger Weg 7, D-55099 Mainz, Germany  C. Love  Dept. of Physics, Drexel
University, 3141 Chestnut Street, Philadelphia, PA 19104, USA  C. J. Lozano
Mariscal  Institut für Kernphysik, Westfälische Wilhelms-Universität Münster,
D-48149 Münster, Germany  L. Lu Dept. of Physics and Wisconsin IceCube
Particle Astrophysics Center, University of Wisconsin–Madison, Madison, WI
53706, USA  F. Lucarelli Département de physique nucléaire et corpusculaire,
Université de Genève, CH-1211 Genève, Switzerland  A. Ludwig Department of
Physics and Astronomy, UCLA, Los Angeles, CA 90095, USA  W. Luszczak 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  Dept. of Physics and Wisconsin IceCube Particle
Astrophysics Center, University of Wisconsin–Madison, Madison, WI 53706, USA
Y. Lyu Dept. of Physics, University of California, Berkeley, CA 94720, USA
Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA  W. Y. Ma DESY,
D-15738 Zeuthen, Germany  J. Madsen Dept. of Physics and Wisconsin IceCube
Particle Astrophysics Center, University of Wisconsin–Madison, Madison, WI
53706, USA  K. B. M. Mahn  Dept. of Physics and Astronomy, Michigan State
University, East Lansing, MI 48824, USA  Y. Makino  Dept. of Physics and
Wisconsin IceCube Particle Astrophysics Center, University of
Wisconsin–Madison, Madison, WI 53706, USA  S. Mancina  Dept. of Physics and
Wisconsin IceCube Particle Astrophysics Center, University of
Wisconsin–Madison, Madison, WI 53706, USA  W. Marie Sainte  Dept. of Physics
and Wisconsin IceCube Particle Astrophysics Center, University of
Wisconsin–Madison, Madison, WI 53706, USA  I. C. Mariş Université Libre de
Bruxelles, Science Faculty CP230, B-1050 Brussels, Belgium  S. Marka  Columbia
Astrophysics and Nevis Laboratories, Columbia University, New York, NY 10027,
USA  Z. Marka  Columbia Astrophysics and Nevis Laboratories, Columbia
University, New York, NY 10027, USA  M. Marsee  Dept. of Physics and
Astronomy, University of Alabama, Tuscaloosa, AL 35487, USA  I. Martinez-Soler
Department of Physics and Laboratory for Particle Physics and Cosmology,
Harvard University, Cambridge, MA 02138, USA  R. Maruyama Dept. of Physics,
Yale University, New Haven, CT 06520, USA  F. Mayhew  Dept. of Physics and
Astronomy, Michigan State University, East Lansing, MI 48824, USA  T. McElroy
Dept. of Physics, University of Alberta, Edmonton, Alberta, Canada T6G 2E1  F.
McNally Department of Physics, Mercer University, Macon, GA 31207-0001, USA
J. V. Mead  Niels Bohr Institute, University of Copenhagen, DK-2100
Copenhagen, Denmark  K. Meagher Dept. of Physics and Wisconsin IceCube
Particle Astrophysics Center, University of Wisconsin–Madison, Madison, WI
53706, USA  S. Mechbal  DESY, D-15738 Zeuthen, Germany  A. Medina  Dept. of
Physics and Center for Cosmology and Astro-Particle Physics, Ohio State
University, Columbus, OH 43210, USA  M. Meier Dept. of Physics and The
International Center for Hadron Astrophysics, Chiba University, Chiba
263-8522, Japan  S. Meighen-Berger Physik-department, Technische Universität
München, D-85748 Garching, Germany  Y. Merckx  Vrije Universiteit Brussel
(VUB), Dienst ELEM, B-1050 Brussels, Belgium  J. Micallef  Dept. of Physics
and Astronomy, Michigan State University, East Lansing, MI 48824, USA  D.
Mockler  Université Libre de Bruxelles, Science Faculty CP230, B-1050
Brussels, Belgium  T. Montaruli Département de physique nucléaire et
corpusculaire, Université de Genève, CH-1211 Genève, Switzerland  R. W. Moore
Dept. of Physics, University of Alberta, Edmonton, Alberta, Canada T6G 2E1  R.
Morse  Dept. of Physics and Wisconsin IceCube Particle Astrophysics Center,
University of Wisconsin–Madison, Madison, WI 53706, USA  M. Moulai Dept. of
Physics and Wisconsin IceCube Particle Astrophysics Center, University of
Wisconsin–Madison, Madison, WI 53706, USA  T. Mukherjee  Karlsruhe Institute
of Technology, Institute for Astroparticle Physics, D-76021 Karlsruhe, Germany
R. Naab DESY, D-15738 Zeuthen, Germany  R. Nagai Dept. of Physics and The
International Center for Hadron Astrophysics, Chiba University, Chiba
263-8522, Japan  U. Naumann  Dept. of Physics, University of Wuppertal,
D-42119 Wuppertal, Germany  A. Nayerhoda Dipartimento di Fisica e Astronomia
Galileo Galilei, Università Degli Studi di Padova, 35122 Padova PD, Italy  J.
Necker DESY, D-15738 Zeuthen, Germany  M. Neumann  Institut für Kernphysik,
Westfälische Wilhelms-Universität Münster, D-48149 Münster, Germany  H.
Niederhausen Dept. of Physics and Astronomy, Michigan State University, East
Lansing, MI 48824, USA  M. U. Nisa Dept. of Physics and Astronomy, Michigan
State University, East Lansing, MI 48824, USA  A. Noell  III. Physikalisches
Institut, RWTH Aachen University, D-52056 Aachen, Germany  S. C. Nowicki
Dept. of Physics and Astronomy, Michigan State University, East Lansing, MI
48824, USA  A. Obertacke Pollmann Dept. of Physics, University of Wuppertal,
D-42119 Wuppertal, Germany  M. Oehler  Karlsruhe Institute of Technology,
Institute for Astroparticle Physics, D-76021 Karlsruhe, Germany  B. Oeyen
Dept. of Physics and Astronomy, University of Gent, B-9000 Gent, Belgium  A.
Olivas  Dept. of Physics, University of Maryland, College Park, MD 20742, USA
R. Orsoe  Physik-department, Technische Universität München, D-85748 Garching,
Germany  J. Osborn  Dept. of Physics and Wisconsin IceCube Particle
Astrophysics Center, University of Wisconsin–Madison, Madison, WI 53706, USA
E. O’Sullivan Dept. of Physics and Astronomy, Uppsala University, Box 516,
S-75120 Uppsala, Sweden  H. Pandya Bartol Research Institute and Dept. of
Physics and Astronomy, University of Delaware, Newark, DE 19716, USA  D. V.
Pankova  Dept. of Physics, Pennsylvania State University, University Park, PA
16802, USA  N. Park Dept. of Physics, Engineering Physics, and Astronomy,
Queen’s University, Kingston, ON K7L 3N6, Canada  G. K. Parker  Dept. of
Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108,
Box 19059, Arlington, TX 76019, USA  E. N. Paudel Bartol Research Institute
and Dept. of Physics and Astronomy, University of Delaware, Newark, DE 19716,
USA  L. Paul  Department of Physics, Marquette University, Milwaukee, WI,
53201, USA  C. Pérez de los Heros Dept. of Physics and Astronomy, Uppsala
University, Box 516, S-75120 Uppsala, Sweden  J. Peterson  Dept. of Physics
and Wisconsin IceCube Particle Astrophysics Center, University of
Wisconsin–Madison, Madison, WI 53706, USA  S. Philippen  III. Physikalisches
Institut, RWTH Aachen University, D-52056 Aachen, Germany  S. Pieper  Dept. of
Physics, University of Wuppertal, D-42119 Wuppertal, Germany  A. Pizzuto Dept.
of Physics and Wisconsin IceCube Particle Astrophysics Center, University of
Wisconsin–Madison, Madison, WI 53706, USA  M. Plum Physics Department, South
Dakota School of Mines and Technology, Rapid City, SD 57701, USA  Y. Popovych
Institute of Physics, University of Mainz, Staudinger Weg 7, D-55099 Mainz,
Germany  A. Porcelli Dept. of Physics and Astronomy, University of Gent,
B-9000 Gent, Belgium  M. Prado Rodriguez  Dept. of Physics and Wisconsin
IceCube Particle Astrophysics Center, University of Wisconsin–Madison,
Madison, WI 53706, USA  B. Pries Dept. of Physics and Astronomy, Michigan
State University, East Lansing, MI 48824, USA  R. Procter-Murphy  Dept. of
Physics, University of Maryland, College Park, MD 20742, USA  G. T. Przybylski
Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA  C. Raab
Université Libre de Bruxelles, Science Faculty CP230, B-1050 Brussels, Belgium
J. Rack-Helleis  Institute of Physics, University of Mainz, Staudinger Weg 7,
D-55099 Mainz, Germany  M. Rameez Niels Bohr Institute, University of
Copenhagen, DK-2100 Copenhagen, Denmark  K. Rawlins  Dept. of Physics and
Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK
99508, USA  Z. Rechav  Dept. of Physics and Wisconsin IceCube Particle
Astrophysics Center, University of Wisconsin–Madison, Madison, WI 53706, USA
A. Rehman Bartol Research Institute and Dept. of Physics and Astronomy,
University of Delaware, Newark, DE 19716, USA  P. Reichherzer  Fakultät für
Physik & Astronomie, Ruhr-Universität Bochum, D-44780 Bochum, Germany  G.
Renzi  Université Libre de Bruxelles, Science Faculty CP230, B-1050 Brussels,
Belgium  E. Resconi Physik-department, Technische Universität München, D-85748
Garching, Germany  S. Reusch  DESY, D-15738 Zeuthen, Germany  W. Rhode Dept.
of Physics, TU Dortmund University, D-44221 Dortmund, Germany  M. Richman
Dept. of Physics, Drexel University, 3141 Chestnut Street, Philadelphia, PA
19104, USA  B. Riedel Dept. of Physics and Wisconsin IceCube Particle
Astrophysics Center, University of Wisconsin–Madison, Madison, WI 53706, USA
E. J. Roberts  Department of Physics, University of Adelaide, Adelaide, 5005,
Australia  S. Robertson  Dept. of Physics, University of California, Berkeley,
CA 94720, USA  Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
S. Rodan  Dept. of Physics, Sungkyunkwan University, Suwon 16419, Korea  G.
Roellinghoff  Dept. of Physics, Sungkyunkwan University, Suwon 16419, Korea
M. Rongen Institute of Physics, University of Mainz, Staudinger Weg 7, D-55099
Mainz, Germany  C. Rott Department of Physics and Astronomy, University of
Utah, Salt Lake City, UT 84112, USA  Dept. of Physics, Sungkyunkwan
University, Suwon 16419, Korea  T. Ruhe  Dept. of Physics, TU Dortmund
University, D-44221 Dortmund, Germany  L. Ruohan  Physik-department,
Technische Universität München, D-85748 Garching, Germany  D. Ryckbosch  Dept.
of Physics and Astronomy, University of Gent, B-9000 Gent, Belgium  D. Rysewyk
Cantu Dept. of Physics and Astronomy, Michigan State University, East Lansing,
MI 48824, USA  I. Safa Department of Physics and Laboratory for Particle
Physics and Cosmology, Harvard University, Cambridge, MA 02138, USA  Dept. of
Physics and Wisconsin IceCube Particle Astrophysics Center, University of
Wisconsin–Madison, Madison, WI 53706, USA  J. Saffer  Karlsruhe Institute of
Technology, Institute of Experimental Particle Physics, D-76021 Karlsruhe,
Germany  D. Salazar-Gallegos Dept. of Physics and Astronomy, Michigan State
University, East Lansing, MI 48824, USA  P. Sampathkumar  Karlsruhe Institute
of Technology, Institute for Astroparticle Physics, D-76021 Karlsruhe, Germany
S. E. Sanchez Herrera  Dept. of Physics and Astronomy, Michigan State
University, East Lansing, MI 48824, USA  A. Sandrock Dept. of Physics, TU
Dortmund University, D-44221 Dortmund, Germany  M. Santander Dept. of Physics
and Astronomy, University of Alabama, Tuscaloosa, AL 35487, USA  S. Sarkar
Dept. of Physics, University of Alberta, Edmonton, Alberta, Canada T6G 2E1  S.
Sarkar Dept. of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, UK
J. Savelberg  III. Physikalisches Institut, RWTH Aachen University, D-52056
Aachen, Germany  M. Schaufel  III. Physikalisches Institut, RWTH Aachen
University, D-52056 Aachen, Germany  H. Schieler  Karlsruhe Institute of
Technology, Institute for Astroparticle Physics, D-76021 Karlsruhe, Germany
S. Schindler Erlangen Centre for Astroparticle Physics, Friedrich-Alexander-
Universität Erlangen-Nürnberg, D-91058 Erlangen, Germany  B. Schlueter
Institut für Kernphysik, Westfälische Wilhelms-Universität Münster, D-48149
Münster, Germany  T. Schmidt  Dept. of Physics, University of Maryland,
College Park, MD 20742, USA  J. Schneider Erlangen Centre for Astroparticle
Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg, D-91058 Erlangen,
Germany  F. G. Schröder Karlsruhe Institute of Technology, Institute for
Astroparticle Physics, D-76021 Karlsruhe, Germany  Bartol Research Institute
and Dept. of Physics and Astronomy, University of Delaware, Newark, DE 19716,
USA  L. Schumacher  Physik-department, Technische Universität München, D-85748
Garching, Germany  G. Schwefer  III. Physikalisches Institut, RWTH Aachen
University, D-52056 Aachen, Germany  S. Sclafani Dept. of Physics, Drexel
University, 3141 Chestnut Street, Philadelphia, PA 19104, USA  D. Seckel
Bartol Research Institute and Dept. of Physics and Astronomy, University of
Delaware, Newark, DE 19716, USA  S. Seunarine  Dept. of Physics, University of
Wisconsin, River Falls, WI 54022, USA  A. Sharma  Dept. of Physics and
Astronomy, Uppsala University, Box 516, S-75120 Uppsala, Sweden  S. Shefali
Karlsruhe Institute of Technology, Institute of Experimental Particle Physics,
D-76021 Karlsruhe, Germany  N. Shimizu  Dept. of Physics and The International
Center for Hadron Astrophysics, Chiba University, Chiba 263-8522, Japan  M.
Silva Dept. of Physics and Wisconsin IceCube Particle Astrophysics Center,
University of Wisconsin–Madison, Madison, WI 53706, USA  B. Skrzypek
Department of Physics and Laboratory for Particle Physics and Cosmology,
Harvard University, Cambridge, MA 02138, USA  B. Smithers Dept. of Physics,
University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box
19059, Arlington, TX 76019, USA  R. Snihur  Dept. of Physics and Wisconsin
IceCube Particle Astrophysics Center, University of Wisconsin–Madison,
Madison, WI 53706, USA  J. Soedingrekso  Dept. of Physics, TU Dortmund
University, D-44221 Dortmund, Germany  A. Søgaard  Niels Bohr Institute,
University of Copenhagen, DK-2100 Copenhagen, Denmark  D. Soldin Karlsruhe
Institute of Technology, Institute of Experimental Particle Physics, D-76021
Karlsruhe, Germany  C. Spannfellner  Physik-department, Technische Universität
München, D-85748 Garching, Germany  G. M. Spiczak Dept. of Physics, University
of Wisconsin, River Falls, WI 54022, USA  C. Spiering DESY, D-15738 Zeuthen,
Germany  M. Stamatikos  Dept. of Physics and Center for Cosmology and Astro-
Particle Physics, Ohio State University, Columbus, OH 43210, USA  T. Stanev
Bartol Research Institute and Dept. of Physics and Astronomy, University of
Delaware, Newark, DE 19716, USA  R. Stein DESY, D-15738 Zeuthen, Germany  T.
Stezelberger Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
T. Stürwald  Dept. of Physics, University of Wuppertal, D-42119 Wuppertal,
Germany  T. Stuttard Niels Bohr Institute, University of Copenhagen, DK-2100
Copenhagen, Denmark  G. W. Sullivan Dept. of Physics, University of Maryland,
College Park, MD 20742, USA  I. Taboada School of Physics and Center for
Relativistic Astrophysics, Georgia Institute of Technology, Atlanta, GA 30332,
USA  S. Ter-Antonyan Dept. of Physics, Southern University, Baton Rouge, LA
70813, USA  W. G. Thompson Department of Physics and Laboratory for Particle
Physics and Cosmology, Harvard University, Cambridge, MA 02138, USA  J.
Thwaites  Dept. of Physics and Wisconsin IceCube Particle Astrophysics Center,
University of Wisconsin–Madison, Madison, WI 53706, USA  S. Tilav  Bartol
Research Institute and Dept. of Physics and Astronomy, University of Delaware,
Newark, DE 19716, USA  K. Tollefson Dept. of Physics and Astronomy, Michigan
State University, East Lansing, MI 48824, USA  C. Tönnis  Dept. of Physics,
Sungkyunkwan University, Suwon 16419, Korea  S. Toscano Université Libre de
Bruxelles, Science Faculty CP230, B-1050 Brussels, Belgium  D. Tosi  Dept. of
Physics and Wisconsin IceCube Particle Astrophysics Center, University of
Wisconsin–Madison, Madison, WI 53706, USA  A. Trettin  DESY, D-15738 Zeuthen,
Germany  C. F. Tung School of Physics and Center for Relativistic
Astrophysics, Georgia Institute of Technology, Atlanta, GA 30332, USA  R.
Turcotte  Karlsruhe Institute of Technology, Institute for Astroparticle
Physics, D-76021 Karlsruhe, Germany  J. P. Twagirayezu  Dept. of Physics and
Astronomy, Michigan State University, East Lansing, MI 48824, USA  B. Ty
Dept. of Physics and Wisconsin IceCube Particle Astrophysics Center,
University of Wisconsin–Madison, Madison, WI 53706, USA  M. A. Unland
Elorrieta Institut für Kernphysik, Westfälische Wilhelms-Universität Münster,
D-48149 Münster, Germany  K. Upshaw  Dept. of Physics, Southern University,
Baton Rouge, LA 70813, USA  N. Valtonen-Mattila  Dept. of Physics and
Astronomy, Uppsala University, Box 516, S-75120 Uppsala, Sweden  J.
Vandenbroucke Dept. of Physics and Wisconsin IceCube Particle Astrophysics
Center, University of Wisconsin–Madison, Madison, WI 53706, USA  N. van
Eijndhoven Vrije Universiteit Brussel (VUB), Dienst ELEM, B-1050 Brussels,
Belgium  D. Vannerom  Dept. of Physics, Massachusetts Institute of Technology,
Cambridge, MA 02139, USA  J. van Santen DESY, D-15738 Zeuthen, Germany  J.
Vara  Institut für Kernphysik, Westfälische Wilhelms-Universität Münster,
D-48149 Münster, Germany  J. Veitch-Michaelis  Dept. of Physics and Wisconsin
IceCube Particle Astrophysics Center, University of Wisconsin–Madison,
Madison, WI 53706, USA  S. Verpoest Dept. of Physics and Astronomy, University
of Gent, B-9000 Gent, Belgium  D. Veske  Columbia Astrophysics and Nevis
Laboratories, Columbia University, New York, NY 10027, USA  C. Walck  Oskar
Klein Centre and Dept. of Physics, Stockholm University, SE-10691 Stockholm,
Sweden  W. Wang  Dept. of Physics and Wisconsin IceCube Particle Astrophysics
Center, University of Wisconsin–Madison, Madison, WI 53706, USA  T. B. Watson
Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science
Hall Rm 108, Box 19059, Arlington, TX 76019, USA  C. Weaver Dept. of Physics
and Astronomy, Michigan State University, East Lansing, MI 48824, USA  P.
Weigel  Dept. of Physics, Massachusetts Institute of Technology, Cambridge, MA
02139, USA  A. Weindl  Karlsruhe Institute of Technology, Institute for
Astroparticle Physics, D-76021 Karlsruhe, Germany  J. Weldert  Institute of
Physics, University of Mainz, Staudinger Weg 7, D-55099 Mainz, Germany  C.
Wendt Dept. of Physics and Wisconsin IceCube Particle Astrophysics Center,
University of Wisconsin–Madison, Madison, WI 53706, USA  J. Werthebach  Dept.
of Physics, TU Dortmund University, D-44221 Dortmund, Germany  M. Weyrauch
Karlsruhe Institute of Technology, Institute for Astroparticle Physics,
D-76021 Karlsruhe, Germany  N. Whitehorn Dept. of Physics and Astronomy,
Michigan State University, East Lansing, MI 48824, USA  Department of Physics
and Astronomy, UCLA, Los Angeles, CA 90095, USA  C. H. Wiebusch III.
Physikalisches Institut, RWTH Aachen University, D-52056 Aachen, Germany  N.
Willey  Dept. of Physics and Astronomy, Michigan State University, East
Lansing, MI 48824, USA  D. R. Williams  Dept. of Physics and Astronomy,
University of Alabama, Tuscaloosa, AL 35487, USA  M. Wolf Dept. of Physics and
Wisconsin IceCube Particle Astrophysics Center, University of
Wisconsin–Madison, Madison, WI 53706, USA  G. Wrede  Erlangen Centre for
Astroparticle Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg,
D-91058 Erlangen, Germany  J. Wulff  Fakultät für Physik & Astronomie, Ruhr-
Universität Bochum, D-44780 Bochum, Germany  D. L. Xu  Tsung-Dao Lee
Institute, Shanghai Jiao Tong University, Shanghai 201210, China  X. W. Xu
Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA  J. P. Yanez
Dept. of Physics, University of Alberta, Edmonton, Alberta, Canada T6G 2E1  M.
Yasutsugu  Dept. of Physics and The International Center for Hadron
Astrophysics, Chiba University, Chiba 263-8522, Japan  E. Yildizci  Dept. of
Physics and Wisconsin IceCube Particle Astrophysics Center, University of
Wisconsin–Madison, Madison, WI 53706, USA  S. Yoshida Dept. of Physics and The
International Center for Hadron Astrophysics, Chiba University, Chiba
263-8522, Japan  S. Yu  Dept. of Physics and Astronomy, Michigan State
University, East Lansing, MI 48824, USA  T. Yuan Dept. of Physics and
Wisconsin IceCube Particle Astrophysics Center, University of
Wisconsin–Madison, Madison, WI 53706, USA  Z. Zhang  Dept. of Physics and
Astronomy, Stony Brook University, Stony Brook, NY 11794-3800, USA  P. Zhelnin
Department of Physics and Laboratory for Particle Physics and Cosmology,
Harvard University, Cambridge, MA 02138, USA

###### Abstract

Galactic PeVatrons are Galactic sources theorized to accelerate cosmic rays up
to PeV in energy. The accelerated cosmic rays are expected to interact
hadronically with nearby ambient gas or the interstellar medium, resulting in
$\gamma$-rays and neutrinos. Recently, the Large High Altitude Air Shower
Observatory (LHAASO) identified 12 $\gamma$-ray sources with emissions above
100 TeV, making them candidates for PeV cosmic-ray accelerators (PeVatrons).
While at these high energies the Klein-Nishina effect suppresses exponentially
leptonic emission from Galactic sources, evidence for neutrino emission would
unequivocally confirm hadronic acceleration. Here, we present the results of a
search for neutrinos from these $\gamma$-ray sources and stacking searches
testing for excess neutrino emission from all 12 sources as well as their
subcatalogs of supernova remnants and pulsar wind nebulae with 11 years of
track events from the IceCube Neutrino Observatory. No significant emissions
were found. Based on the resulting limits, we place constraints on the
fraction of $\gamma$-ray flux originating from the hadronic processes in the
Crab Nebula and LHAASO J2226+6057.

##  1 Introduction

The origin of the high-energy cosmic rays (CRs) is a longstanding question in
particle astrophysics. The cosmic-ray spectrum is typically parametrized with
an E-2.7 power law up to its “knee”, ${\rm E}_{\rm CR}\sim 3$ PeV, above which
the spectrum softens (Abbasi et al., 2018). The CRs with energy up to the
“knee” are generally believed to be confined and accelerated in the Milky Way,
implying the presence of PeV accelerators known as PeVatrons that accelerate
the particles to energy $>1$ PeV within our Galaxy. In addition to propelling
CRs to PeV energies, Galactic PeVatrons are expected to emit $\gamma$-rays and
neutrinos through associate pion decays (Ahlers et al., 2016). High energy
$\gamma$-rays may also originate from leptonic processes like inverse Compton
scattering and bremsstrahlung; however, at ${\rm E}_{\gamma}\gtrsim 50$ TeV,
inverse Compton scattering is inefficient due to Klein-Nishina suppression
(Cristofari, 2021; Hinton & Hofmann, 2009; Moderski et al., 2005). As inverse
Compton scattering is the primary mechanism for electrons to emit
$\gamma$-rays (Blumenthal & Gould, 1970), $\gamma$-ray emission from leptonic
processes is dramatically suppressed. Ultra-high-energy (UHE, $>100$ TeV)
$\gamma$-ray sources, especially those with observed spectra following a
simple power law to at least tens of TeV, are suspected to be indicators of
PeVatrons. Testify that the acceleration of hadrons is taking place for those
TeV sources is of importance to pinpoint the PeV CR sources.

Supernova remnants (SNRs) are widely considered candidate Galactic PeVatrons.
SNRs are generally believed to be the primary candidates of hadronic sources
in the Galaxy, with particles being accelerated by diffusive shock
acceleration (DSA) in expanding shocks. According to the SNR hypothesis, 10%
of the total explosion energy of the supernova progenitor is converted into
CRs, compatible with the observed intensity of CRs and their estimated
confinement time in the Galaxy (Blandford & Ostriker, 1978). The DSA mechanism
and strong magnetic field amplification close to the shocks in SNRs also can
explain the observed power-law spectrum of CRs (Cristofari et al., 2018).
Apart from that, molecular clouds located within $100$ parsec of the SNRs
could be effective sites for $>$ TeV $\gamma$-ray production (Gabici &
Aharonian, 2007). The highest-energy particles would quickly escape SNRs and
diffuse faster in the interstellar medium (ISM), arriving at nearby molecular
clouds earlier than the lower energy CRs and producing neutrinos and
$\gamma$-rays there. CR might also be accelerated in young massive star
clusters (YMCs) and pulsar wind nebulae (PWNe). Although the $\gamma$-ray
emission from PWNe is widely expected to be leptonic, several studies suggest
that the presence of relativistic hadrons in the pulsar winds might also be
possible (Di Palma et al., 2017). From the Hillas criterion, the magnetic
fields of PWNe could effectively trap particles with energy ${\rm E}\lesssim
3$ PeV (Hillas, 1984). Therefore, a large amount of energy of PWNe could be
stored in relativistic protons if they are continuously produced. In hadronic
scenarios, CRs might be accelerated at the termination shocks (Di Palma et
al., 2017) or by the shocks of SNRs which confined the diffuse nebulae (Ohira
et al., 2018).

Albert et al. (2021) reported that the TeV $\gamma$-ray spectrum of HAWC
J1825-134 has no indication for a cut-off up to 200 TeV, implying that the
source might be a possible PeVatron. HAWC J1825-134 may be associated with a
giant molecular cloud, and the YMC located inside the molecular cloud is
thought to accelerate CRs to PeV energies. Evidence of a PeVatron at the
center of the Galaxy has also been reported by the HESS Collaboration by
observing $\gamma$-rays from collisions of a young population of CRs with
close by molecular clouds, with a hard $\gamma$-ray spectrum observed up to
${\rm E}_{\gamma}\sim 40$ TeV (Abramowski et al., 2016). Detection of
astrophysical neutrinos (${\rm E}_{\nu}\gtrsim 100$ TeV) would be a smoking
gun for the existence of Galactic PeVatrons. The IceCube Neutrino Observatory
has previously searched for Galactic neutrino emission from individual
sources, stacked similar objects (PWNe, SNRs, etc.), and the Galactic plane
(Aartsen et al., 2017, 2019, 2020a, 2020b). Joint analyses with data from the
ANTARES Neutrino Telescope were also performed to search for neutrinos from
the Galactic plane and the southern sky (Albert et al., 2018, 2020a),
exploiting the advantageous field of view of ANTARES and large volume and high
statistics of IceCube. No significant Galactic neutrino sources were found
from those searches, and the contribution of Galactic sources to the all-sky
isotropic astrophysical neutrino flux has been constrained to $\leq 14\%$
(Aartsen et al., 2017).

Recently, the LHAASO Collaboration reported the detection of a dozen Galactic
${\rm E}_{\gamma}\geq 100$ TeV $\gamma$-ray sources with $>7\sigma$ detection
(Cao et al., 2021a). This is the first LHAASO catalog and the largest list of
UHE $\gamma$-ray sources published to date. Searching for neutrino emission
from those LHAASO UHE sources will enable differentiation between leptonic and
hadronic mechanisms that contribute to UHE $\gamma$-ray flux. In this letter,
we perform a stacking analysis and a catalog search to probe the hadronic
nature of these potential PeVatrons. We divide the LHAASO sources into 3
groups according to their possible association (all UHE sources, all possible
PWNe, and all possible SNRs) in the stacking analysis, providing flux limits
to constrain the total fraction of Galactic CRs that come from the UHE
$\gamma$-ray SNRs and PWNe above 100 TeV. Section 2 briefly introduces the
IceCube Observatory, the LHAASO detector arrays, the neutrino dataset, and the
source list of 12 UHE sources. Analysis methods are shown in Section 3. In
Section 4 and Section 5, we discuss and summarize the results.

##  2 IceCube and LHAASO detectors and datasets

###  2.1 IceCube neutrino sample

The IceCube Neutrino Observatory is a cubic kilometer array of 5160 digital
optical modules (DOMs) located in the geographic South Pole (Abbasi et al.,
2009). These DOMs are arranged along 86 readout and support cables (”strings”)
that instrument the glacial ice at a depth between 1.45 to 2.45 km. Each DOM
is equipped with a 10-inch photomultiplier tube in a pressure-resistant sphere
along with the necessary electronics for read-out of signal (Abbasi et al.,
2009). These DOMs are designed to observe the Cherenkov light induced by
energetic charged particles traveling in ice. These energetic charged
particles are produced by charged-current (CC) interaction or neutral-current
(NC) interaction from neutrinos of all flavors (Abbasi et al., 2010). The
track-like (from CC interaction from muon neutrino) and cascade-like (from
other NC and CC interaction) events are recorded by DOMs and analyzed in terms
of the direction and energy of the primary neutrino. IceCube also includes
DeepCore, a GeV-scale neutrino sub-detector (Abbasi et al., 2012) and IceTop,
an air shower array (Abbasi et al., 2013), which are not used in this study.

The dataset used in this analysis comprises 11 years of IceCube track-like
data from April 6, 2008 to May 29, 2020. Track-like events have a better
angular resolution (a typical $\sim$ TeV neutrino has angular uncertainty
$\sim 1^{\circ}$) compared to cascade-like events because of the long lever
arm, providing better sensitivity to astrophysical point sources. The data
taken from April 6, 2008 to May 13, 2011 are from the partially built detector
with 40, 59 and 79 strings (IC40, IC59, and IC79) (Aartsen et al., 2020a) and
the rest of the data are taken from the the full detector configuration of 86
strings (Aartsen et al., 2014). The dominant source of background is
atmospheric neutrinos and atmospheric muons originating from air showers
induced by cosmic-ray interactions in the atmosphere. Appendix A shows the
details of the dataset used and the relevant energy range.

The dataset also incorporates the improved in-situ calibration of the single-
photoelectron charge distributions (Aartsen et al., 2020c) and other
improvements in reconstruction, further boosting the sensitivity relative to
the previous analyses (Aartsen et al., 2020a). Sensitivity and 5$\sigma$
discovery potential of the dataset are shown in Figure 1.

###  2.2 LHAASO ultra-high-energy $\gamma$-ray sources

The Large High Altitude Air Shower Observatory (LHAASO) is a complex of
extensive air shower detector arrays aims to study $\gamma$-rays and cosmic
rays. Located in the Sichuan province of China with an elevation of $4410~{}m$
a.s.l., LHAASO consists of the three components Kilometer Square Array (KM2A),
Water Cherenkov Detector Array (WCDA), and Wield Field-of-view Cherenkov
Telescope Array (WFCTA). LHAASO-KM2A focuses on Galactic $\gamma$-ray sources
above $30$ TeV in the Northern sky and has been operating since December 2019.
The KM2A comprises uniformly distributed electromagnetic particle detectors
(ED) and muon detectors (MD) over $1.3~{}{\rm km}^{2}$. The vast area of
scintillation counters together with the MD array would effectively suppress
the background from CR-induced hadronic showers for $\gamma$-rays above $\sim
50$ TeV, yielding a sensitivity of the full KM2A approaching $\sim 1\%$ for a
Crab-like source with a 1-year observation at 100 TeV (Liu et al., 2016; Cui
et al., 2014). The angular and energy resolution of the KM2A are $0.4^{\circ}$
and $28\%$ at 30 TeV, respectively. We note that at 1 PeV, the angular
resolution of the KM2A would reach $0.2^{\circ}$ (Cao et al., 2019).

The half-completed LHAASO-KM2A has already detected twelve UHE $\gamma$-ray
sources above 100 TeV with statistical significance $\geq 7\sigma$, from
December 2019 to October 2021 (Cao et al., 2021a, Table 1). All these
potential PeVatrons appear to be located in our Galaxy. Among these twelve
sources, three sources (eHWCJ1825-134, eHWCJ1907+063, and eHWCJ2019+368) are
also in the HAWC’s high energy source list (Abeysekara et al., 2019a) with
conclusive evidences of $\geq 100$ TeV emission. Except for LHAASO J0534+2202,
which is the Crab Nebula, all the other LHAASO UHE sources have no firm
association, with several known TeV counterparts nearby. Table 2 in Cao et al.
(2021a) lists all the possible TeV associations close to these twelve UHE
sources, suggesting that majority of them might be associated with PWNe or
SNRs.

##  3 Analysis Method

###  3.1 Catalog search

A maximum likelihood ratio test is performed following the technique described
in Abbasi et al. (2011) and Braun et al. (2008). The same method was also used
in the previous IceCube 10 years time-integrated point source search (Aartsen
et al., 2020a). The first LHAASO catalog consists of 12 UHE $\gamma$-ray
sources detected above 100 TeV with $>7\sigma$ (Cao et al., 2021a). Only two
of the LHAASO sources (LHAASO J0534+2202 and LHAASO J2108+5157) are considered
point sources with regard to LHAASO’s angular resolution. For the remaining
ten sources, significant angular extensions in $\gamma$-ray are detected by
LHAASO and a 0.3 degree Gaussian emission template is used to measure the
$\gamma$-ray flux. Hence, a 0.3 degree Gaussian extent is assumed for the
remaining ten sources to match assumptions used in the LHAASO analysis (Cao et
al., 2021a). We model the spatial signal likelihood as a 2D Gaussian in
tangent plane coordinates which is valid for a sufficiently small angular
extension. The angular uncertainty of each event is obtained directly from the
reconstruction. Source extensions and estimated angular uncertainties for
events are added in quadrature when estimating spatial likelihoods for each
event. We assume a power-law spectrum with spectral index $\Gamma$ for the
signal hypothesis. The normalization and spectral index $1<\Gamma<4$ of the
signal flux are optimized in a maximum likelihood analysis. A detailed
description of the likelihood can be found in Appendix B.

Figure 1 shows the sensitivity and 5$\sigma$ discovery potential as a function
of declination of this search method for $\Gamma=2$ and $\Gamma=3$.
Sensitivity is the neutrino flux required for 90% of the trials to yield a
p-value less than 0.5. The 5 $\sigma$ discovery potential is the neutrino flux
required for 50% of trials with simulated signal to yield a p-value less than
$2.87\times 10^{-7}$(5 $\sigma$ significance in one-tail Gaussian test). In
our analyses, we use 50 TeV as the pivot energy when calculating the neutrino
flux, given that 100 TeV $\gamma$-rays from pion decay would be accompanied by
neutrinos at 50 TeV (Ahlers & Murase (2014), see Appendix C for more detail).

###  3.2 Stacking search

A total of six stacking analyses are performed combing three catalogues - all
LHAASO sources, sources potentially associated with SNRs, and sources
potentially associated with PWNe - and two weighting schemes - equal neutrino
flux at Earth and neutrino flux proportional to the $\gamma$-ray flux at 100
TeV reported by LHAASO (Cao et al., 2021a). The source hypothesis in the
stacking analysis is the same as in the catalog search, with sources
considered to have 0.3 degree Gaussian extension except for LHAASO J0534+2202
and LHAASO J2108+5157. According to the association proposed by Cao et al.
(2021a), nine sources are included in the PWN stacking search, and six sources
are included in the SNR stacking search. There are four gamma-ray sources in
common between the SNR and PWN stacking searches. Table 1 shows the source
type of the potential association of the LHAASO sources. We assume that all
the sources in each stacking scheme have a universal unbroken power-law energy
spectrum with the same spectral index. The spectral index and the total number
of signal neutrinos are fitted as free parameters during the maximization of
the likelihood. For the equal-weight cases, the relative weight of each source
is $\frac{1}{N}$ where N is the number of sources in the catalog. For the
flux-weighted cases, the relative weight of each source i is
$\frac{\phi_{i}}{\sum_{j}\phi_{j}}$ where $\phi_{i}$ is the LHAASO
$\gamma$-ray flux at 100 TeV (Cao et al., 2021a). We generate $10^{5}$
background trials by scrambling the right ascension coordinates of the track
sample. The stacking search is performed on each background trial, identifying
the source with the lowest pre-trial p-value in each. The distribution of
these p-values is used to correct for the look-elsewhere effect. The post-
trial p-value is computed by comparing the pre-trial p-value obtained from the
real data and the distribution of the lowest pre-trial p-values (Aartsen et
al., 2020a).

##  4 Results and discussion

###  4.1 Catalog search and Stacking search results

Table 1 shows the result of the catalog search, including the best-fit number
of neutrino events, best-fit power law index and pre-trial p-value. The 90%
confidence interval (C.I.) flux upper limit for each source at 50 TeV assuming
a spectral index $\Gamma=2$ is shown in the last column. We find no
significant correlation between the observed neutrinos and the newly
identified LHAASO UHE (${\rm E}_{\gamma}>100$ TeV) sources in our searches.
Figure 1 shows 90% flux limits for $\Gamma=2$ and $\Gamma=3$, comparing with
the sensitivity from IceCube’s 11 years dataset and ANTARES’s 13 years dataset
(Illuminati, 2021). Appendix C explains the detail of the estimation of the
neutrino flux from the observed gamma-ray flux (Ahlers & Murase, 2014). Here
we assume that the full $\gamma$-ray flux is produced via proton-proton
interaction.

Source | R.A. | Dec |  $\gamma$-ray flux[CU] | Possible association | $n_{s}$ | $\Gamma$ | TS | pre-trial p-value | $\phi_{90\%}$
---|---|---|---|---|---|---|---|---|---
LHAASOJ1825-1326 | 276.45 |  $-$13.45 | 3.57 | PWN | 1.00 | 3.33 | 0.02 | 0.42 | 4.0
LHAASOJ1839-0545 | 279.95 |  $-$5.75 | 0.7 | PWN | 9.34 | 3.12 | 1.43 | 0.46 | 1.8
LHAASOJ1843-0338 | 280.75 |  $-$3.65 | 0.73 | SNR | 0.00 | — | 0.00 | 1.0 | 0.99
LHAASOJ1849-0003 | 282.35 |  $-$0.05 | 0.74 |  PWN/YMC | 0.00 | — | 0.00 | 1.0 | 0.90
LHAASOJ1908+0621 | 287.05 | 6.35 | 1.36 | SNR/PWN | 6.83 | 2.11 | 4.06 | 0.046 | 2.5
LHAASOJ1929+1745 | 292.25 | 17.75 | 0.38 | SNR/PWN | 16.0 | 2.63 | 1.34 | 0.18 | 2.3
LHAASOJ0534+2202 | 83.55 | 22.05 | 1.0 | PWN | 14.0 | 4.0 | 1.22 | 0.19 | 2.0
LHAASOJ1956+2845 | 299.05 | 28.75 | 0.41 | SNR | 17.6 | 3.05 | 1.16 | 0.21 | 2.5
LHAASOJ2018+3651 | 304.75 | 36.85 | 0.5 |  PWN/YMC | 18.7 | 2.67 | 3.62 | 0.045 | 4.5
LHAASOJ2032+4102 | 308.05 | 41.05 | 0.54 |  SNR/PWN/YMC | 24.8 | 3.98 | 2.81 | 0.075 | 4.1
LHAASOJ2108+5157 | 317.15 | 51.95 | 0.38 | - | 10.6 | 2.96 | 0.84 | 0.26 | 2.4
LHAASOJ2226+6057 | 336.75 | 60.95 | 1.05 | SNR/PWN | 0.00 | — | 0.00 | 1.0 | 2.9
Table 1: Table of best-fit parameters with corresponding test statistic (TS)
and p-value of catalog search. The $\gamma$-ray flux is the $\gamma$-ray flux
of the source at 100 TeV in Crab units (CU) ($6.1\times 10^{-17}~{}{\rm
TeV}^{-1}~{}{\rm cm}^{-2}~{}{\rm s}^{-1}$) reported by LHAASO (Cao et al.,
2021a). The neutrino 90% C.I. flux upper-limit ($\phi_{90\%}$) is
parameterized as:
$\frac{dN_{\nu_{\mu}+\nu_{\bar{\mu}}}}{dE_{\nu}}=\phi_{90\%}\cdot(\frac{E_{\nu}}{50{\rm
TeV}})^{-2}\times 10^{-16}~{}{\rm TeV}^{-1}~{}{\rm cm}^{-2}~{}{\rm s}^{-1}$.
The relevant energy range of the flux upper limit can be found in Appendix C.
The two smallest pre-trial p-values of 0.046 and 0.045 observed for two
sources correspond to a post-trial p-value of 0.42 with the assumption that
those 12 sources are independent given their large separation.

Figure 1: The blue solid and blue dashed lines are the per-source IceCube
5$\sigma$ discovery potential and sensitivity for 0.3 degree extension and
$\Gamma=2$ spectrum (a), and the orange solid and dashed lines are those for
0.3 degree extension and $\Gamma=3$ spectrum (b) of this analysis. The green
solid and green dashed lines on the left plot are the 5$\sigma$ discovery
potential and sensitivity of a $E^{-2}$ spectrum of ANTARES point source
analysis (Illuminati, 2021). The red stars represent the neutrino flux
predicted from the LHAASO measurement if photon flux is assumed to be 100% of
hadronic origin (Ahlers & Murase, 2014). The blue and orange triangles
represent the 90% flux limits obtained from this analysis for $E^{-2}$ and
$E^{-3}$ spectrum, respectively. The green crosses are the ANTARES 90% flux
limits (Illuminati, 2021).

The two lowest p-value sources are LHAASO J1908+0621 and LHAASO J2018+3651.
LHAASO J1908+0621 is thought to be the UHE counterpart of MGRO J1908+06, which
is also the lowest p-value Galactic source in the source list of the IceCube
10-year point-source search (Aartsen et al., 2020a). LHAASO J2018+3651 might
be associated with MGRO J2019+37, and an HII region, Sh $2-104$, is located to
the west. The region Sh $2-104$ comprises several YMCs with diffuse X-ray
emission probably from the colliding winds of young stars (Gotthelf et al.,
2016).

Ten of the LHAASO UHE sources with $\delta<42^{\circ}$ are in the source list
for the ANTARES 13-year point-source search (Illuminati, 2021). LHAASO
J2018+3651 is the only LHAASO source with reported pre-trial p-value of 0.14.
LHAASO J1908+0621, LHAASO J1929+1745, and LHAASO J2032+4102 have p-values
$\lesssim 0.06$ in the searches of Huang & Li (2021) with 10 years of IceCube
track events (Abbasi et al., 2021). The pre-trial p-values of LHAASO
J1929+1745 and LHAASO J2032+4102 are $\sim 0.03$ and $\sim 0.04$ with an
extension of 0.6 degree, while that of LHAASO J1908+0621 is $\sim 0.06$ for
the point-source hypothesis. LHAASO J2032+4132 is the third significant source
in our catalog search with a pre-trial p-value of 0.075. The differences
between the significance level for LHAASO J2018+3651 and LHAASO J1929+1745 in
our analysis and that in Huang & Li (2021) might result from the differences
in datasets’ livetime and in track reconstruction approaches or from the
limitations of the public dataset.

Table 2 shows the result of the stacking searches, including the best-fit
total number of signal events, best-fit power law index, and pre-trial p-value
for each stacking scheme. The 90% C.I. flux upper limit at 50 TeV for each
tested weighting scheme assuming a spectral index of 2 is shown in the last
column. No significant emission is found from all 6 stacking schemes, with the
lowest p-value results found from all possible LHAASO PWNe and all LHAASO UHE
sources weighted equally. The 90% flux upper limits for each weighting schemes
tested as a function of spectral index is shown in Figure 2.

Sample | Weighting scheme | $n_{s}$ | $\Gamma$ | TS | Pre-trial p-value | $\phi_{90\%}$
---|---|---|---|---|---|---
All sources | flux-weighted | 38.7 | 2.58 | 3.11 | 0.068 | 7.2
All sources | equal-weighted | 79.7 | 2.81 | 4.83 | 0.022 | 7.8
SNR | flux-weighted | 8.74 | 2.21 | 1.85 | 0.14 | 4.1
SNR | equal-weighted | 22.3 | 2.56 | 1.42 | 0.16 | 4.2
PWN | flux-weighted | 33.4 | 2.46 | 4.15 | 0.042 | 8.0
PWN | equal-weighted | 59.2 | 2.62 | 5.42 | 0.022 | 8.1
Table 2: Table of best-fit parameters for the stacking analyses. The 90% flux
upper-limit ($\phi_{90\%}$) is parameterized as
:$\frac{dN_{\nu_{\mu}+\nu_{\bar{\mu}}}}{dE_{\nu}}=\phi_{90\%}\cdot(\frac{E_{\nu}}{50{\rm
TeV}})^{-2}\times 10^{-16}~{}{\rm TeV}^{-1}~{}{\rm cm}^{-2}~{}{\rm s}^{-1}$.
The smallest pre-trial p-value of 0.022 observed in the two stacking
hypotheses corresponds to a post-trial p-value of 0.06.

Figure 2: Our 90% flux upper limits on neutrino emission at 50 TeV from (a)
all 12 LHAASO sources, (b) sources that could be associated with SNRs, and (c)
sources that could be associated with PWNe. The orange line represents the
equal-weight case and the blue line represents the flux-weighted case. The
hadronic flux prediction assumes that the flux measured by LHAASO is of purely
hadronic origin.

###  4.2 Hadronic constrains

In this section, we try to constrain the fraction of $\gamma$-ray emission
from hadronic processes in the LHAASO sources. To obtain meaningful hadronic
constraints based on the non-observation of neutrinos, we look up the observed
$\gamma$-ray indexes for LHAASO sources from the literature in order to
estimate a more realistic $\gamma$-ray spectrum for the 90% C.I. upper limits.
Considering the observed TeV $\gamma$-ray spectra and comparing the
theoretically predicted neutrino flux (the estimation detail is described in
Appendix C) with $90\%$ upper-limit flux calculated using the TeV spectral
parameters, we are able to constrain the hadronic contributions to the
$\gamma$-ray flux for three of the LHAASO UHE sources: LHAASO J0534+2202,
LHAASO J1849-0003, and LHAASO J2226+6057. The hadronic constraints, neutrino
upper limits, and expected neutrino fluxes for the three LHAASO sources are
shown in Table 3. We note that the constraints illustrated here are the best
possible bounds we could obtain as we assume that the $\gamma$-ray emissions
are completely hadronic. The limits would be weaker if part of the UHE
$\gamma$-rays from the sources originated from leptonic processes.

LHAASO name | TeV counterpart | Index / $\alpha$ | $\beta$ | Energy range | Extension | $\phi_{90\%}$ | $\phi_{\rm Predicted}$ | Constraints | Refs
---|---|---|---|---|---|---|---|---|---
|  |  |  | [TeV] | [deg.] |  |  |  |
J1849$-$0003 | HESSJ1849$-$000 | 1.99 | — | $0.4-100$ | 0.09 | 0.85 | 0.90 |  $<$94% | [a]
J0534+2202 | Crab Nebula. | 3.12 | — | $10-1600$ | 0.00 | 0.70 | 1.2 |  $<$59% | [b]
|  | 2.79 | 0.1 | $1-177$ | 0.00 | 1.0 | 1.2 |  $<$84% | [c]
J2226+6057 | SNR G106.3+02.7 | 3.01 | — | $20-500$ | 0.36 | 0.60 | 1.3 |  $<$47% | [d]
|  | 1.56 | 0.88 | $20-500$ | 0.36 | 2.1 | 1.3 | — | [d]
Table 3: Table of TeV spectral parameters and the corresponding hadronic
constraints, neutrino upper limits, and expected neutrino fluxes at 50 TeV.
The parameter $\phi_{90\%}$ represents the neutrino $90\%$ C.I. flux limits
parameterized as
:$\frac{dN_{\nu_{\mu}+\nu_{\bar{\mu}}}}{dE_{\nu}}=\phi_{90\%}\cdot(\frac{E_{\nu}}{50{\rm
TeV}})^{{-\alpha}-\beta\cdot\log\frac{E_{\nu}}{50{\rm TeV}}}\times
10^{-16}~{}{\rm TeV}^{-1}~{}{\rm cm}^{-2}~{}{\rm s}^{-1}$. The parameter
$\phi_{\rm Predicted}$ is the predicted neutrino flux with the assumption of
$\gamma$-ray s are entirely hadronic. Hadronic constraints correspond to the
ratio $\phi_{90\%}/\phi_{\rm Predicted}$ at 50 TeV calculated with fixed
spectral parameters. The TeV spectral and morphology information (columns
$3-6$) is taken from [a] Huang & Li (2021), [b] Cao et al. (2021b), [c]
Abeysekara et al. (2019b), and [d] Cao et al. (2021a).

The strongest hadronic constraint is put on LHAASO J2226+6057 with a limit of
$\lesssim 47\%$, with the assumption that the neutrino spectrum follows a
simple power law with an index of $3.01$ reported by LHAASO. The UHE source
may be associated with SNR G106.3+02.7, suggested as a potential PeVatron by
Albert et al. (2020b) and Amenomori et al. (2021). The observations of HAWC
and Tibet AS$\gamma$ for the SNR indicate an unbroken hard TeV spectrum
extends up to at least 100 TeV. Amenomori et al. (2021) suggested that the VHE
protons might be accelerated and trapped in the SNR given the hard spectral
index. On the other hand, the UHE $\gamma$-ray flux of J2226+6057 detected by
LHAASO from 20 to 500 TeV is better described with log-parabola rather than a
single power-law (Cao et al., 2021a). However, the hadronic component of
J2226+6057’s $\gamma$-ray flux cannot be constrained when applying the log-
parabola model to calculate the neutrino flux limits.

For LHAASO J0534+2202, which is the UHE counterpart of the Crab Nebula, we
constrain the hadronic UHE $\gamma$-ray emission to $\lesssim 59\%$ of the
total, assuming a power law of $\Gamma=3.12$ as reported by LHAASO. Applying
the log-parabola model by HAWC, the hadronic constraint on the Crab is
$\lesssim 84\%$, compared to $\lesssim 70\%$ reported previously by Huang & Li
(2021). Although a 1.12 PeV $\gamma$-induced shower was detected by LHAASO-
KM2A from the direction of the Crab, the hadronic origin of TeV $\gamma$-rays
from it is considered to be less likely (Cao et al., 2021b). If the UHE
emission from the Crab is hadronic, CRs should be accelerated in the pulsar’s
magnetosphere or at the wind termination shock. An alternative scenario
proposed by Cheng et al. (1990) suggests that the CRs could be accelerated in
the outer gap of the pulsar.

We could only marginally constrain the hadronic fraction of the $\gamma$-ray
flux for LHAASO J1849$-$0003 to $\lesssim 94\%$, with a power-law index of
1.99 (Huang & Li, 2021).

##  5 Conclusions and outlook

In this study, we have performed catalog and stacking searches on twelve
LHAASO UHE $\gamma$-ray sources. We have found no significant neutrino
emission, with the smallest post-trial p-value of 0.06 in PWN equal-weight
stacking search. The resulting 90% neutrino flux upper limits for an $E^{-2}$
spectrum are given. For LHAASO J1849-0003, LHAASO J0534+2202, and LHAASO
J2226+6057, we are able to constrain the hadronic $\gamma$-ray emission
tailored to the available spectral information of these sources. Joint fits
between $\gamma$-rays and neutrinos (Fan et al., 2021) and physics-motivated
lepto-hadronic modeling of the spectrum of each individual source may provide
a better and more accurate limit. Future detectors should also improve our
understanding of these potential PeVatrons. The planned IceCube-Gen2 detector
(Aartsen et al., 2021), with an increased effective area relative to IceCube
and improved angular resolution, is expected to become up to five times more
sensitivity for Galactic neutrino sources compared to IceCube.

The IceCube collaboration acknowledges the significant contributions to this
manuscript from Yu-Ling Chang, Kwok Lung Fan and Michael Larson. We also
acknowledge support from: 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), Advanced Cyberinfrastructure
Coordination Ecosystem: Services & Support (ACCESS), 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;
European Union – EGI Advanced Computing for research; 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, Carlsberg Foundation,
and European Commission; 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 IceCube track-like neutrino dataset

Table 4 shows the event counts, livetime, start and end date of each detector
configuration of the track-like neutrino dataset used in the analysis. Figure
3 shows the distribution of events as a function of reconstructed declination
and estimated energy and also the 90% energy range for data and MC signal with
a spectral index of 2 and 3.

Figure 3: The 2D distribution of events in data taken in 2019 with full 86 strings as a function of reconstructed declination and estimated energy. The 90% energy range for the data is shown in the black solid line. Simulated astrophysical signal Monte Carlo (MC) for an $E^{-2}$ and an $E^{-3}$ spectrum is shown in purple and orange respectively as a guide for the relevant energy range of IceCube Data | Total number of events | Total livetime (days) | Start date | Stop date
---|---|---|---|---
IC40 | 36900 | 376 | 6/4/2008 | 20/5/2009
IC59 | 107011 | 354 | 20/5/2009 | 31/5/2010
IC79 | 101972 | 313 | 1/6/2010 | 13/5/2011
IC86 | 1294410 | 3635 | 13/5/2011 | 22/8/2021
Table 4: IceCube configuration, number of events, livetime, start and end
date.

##  Appendix B Likelihood

For a single-source analysis, the likelihood is

$L=\prod_{i}^{N}L_{i}(\vec{\theta},\vec{D_{i}})=\prod_{i}^{N}(\frac{n_{s}}{N}S(\vec{\theta},\vec{D_{i}})+\frac{N-n_{s}}{N}B(\vec{D_{i}})),$
(B1)

where $L_{i}$ is the likelihood of the event i, $\vec{\theta}$ is the source
properties including location, morphology, and spectrum. The parameter vector
$\vec{D_{i}}$ stands for the reconstruction information of the event i,
including reconstructed direction, energy, and estimated angular error. $N$ is
the total number of events and $n_{s}$ is the best-fit number of signal
neutrino. $S$ and $B$ are the signal probability distribution function (PDF)
and background probability distribution function, each consisting of a product
of a spatial likelihood and an energy likelihood.
Our test statistic (TS) is the log-likelihood ratio:

$TS=2\sum_{i}^{N}log\left(\frac{L_{i}(\vec{\theta},\vec{D_{i}})}{L_{i}(n_{s}=0,\vec{D_{i}}))}\right)\\\
=2\sum_{i}^{N}log\left(\frac{n_{s}}{N}(\frac{S(\vec{D_{i}},\vec{\theta})}{B(\vec{D_{i}})}-1)+1\right).$
(B2)

The signal spatial likelihood of the point source is modeled as 2D Gaussian in
the tangent plane which is valid for a sufficiently small angular extension

$S_{spatial}(\vec{r},\vec{r}_{\nu},\sigma)=\frac{1}{2\pi\sigma^{2}}e^{-\frac{(\vec{r}-\vec{r}_{\nu})^{2}}{2\sigma^{2}}}.$
(B3)

Here, the parameters $\vec{r},\vec{r}_{\nu},\sigma$ correspond to the source
location, reconstructed direction and estimated angular error.
The signal’s spatial likelihood term for Gaussian extended sources is a
modified version of the standard 2D Gaussian used for point sources.

$S_{spatial}(\vec{r}_{src},\vec{r},\sigma,\sigma_{A})=\frac{1}{2\pi(\sigma^{2}+\sigma_{A}^{2})}e^{{-\frac{(\vec{r}_{src}-\vec{r})^{2}}{2(\sigma^{2}+\sigma_{A}^{2})}}},$
(B4)

with the $\sigma_{A}$ being the extension of the source. The background
spatial likelihood is

$B_{spatial}(\vec{r}_{events})=\frac{1}{2\pi}p(d),$ (B5)

where $d$ is the reconstructed declination of the event and $p$ is the
declination PDF of the background. The energy-dependent part in the signal and
background PDFs are modeled after the distributions of Monte Carlo and real
data in terms of reconstructed energy and zenith.

For the stacking analysis, the likelihood is

$L=\prod_{i}^{N}\frac{n_{s}}{N}(\sum_{j}^{M}w_{j}S(\vec{\theta_{j}},\vec{D_{i}})+\frac{N-n_{s}}{N}B(\vec{D_{i}})),$
(B6)

where $w_{j}$ is the product of the assumed source weight and energy-
integrated effective area at the source declination. The weight $w_{j}$ is
normalized as $\sum_{j}^{M}w_{j}=1$ with M being the total number of
sources(Abbasi et al., 2011). Hence the TS is

$TS=2\sum_{i}^{N}log\left(\frac{n_{s}}{N}(\frac{\sum_{j}^{M}w_{j}S(\vec{D_{i}},\vec{\theta_{j}})}{B(\vec{D_{i}})}-1)+1\right).$
(B7)

##  Appendix C Connection between gamma-ray flux and neutrino flux

In pp interactions, protons interact with nearby material and produce charged
and neutral pions with a ratio of about 2 to 1 (Ahlers & Murase, 2014).
Charged pion decay to neutrinos and other products, and the resulting
neutrinos carry roughly 1/4 the energy of the pion. Neutral pion decay into
two $\gamma$-rays, each with 1/2 of the energy (Ahlers & Murase, 2014). On
Earth, the flux observed is

$E_{\gamma}J_{\gamma}(E_{\gamma})\approx
e^{\frac{-d}{\lambda_{\gamma\gamma}}}\frac{1}{3}\sum_{\nu_{\alpha}}E_{\nu}J_{\nu_{\alpha}}(E_{\nu}),$
(C1)

where $J_{\gamma}(E_{\gamma})$ and $J_{\nu_{\alpha}}(E_{\nu})$ are the gamma-
ray differential particle flux and neutrino differential particle flux for
neutrino favor $\alpha$ . Assuming the absorption of gamma-rays is negligible
and equal flux from each neutrino flavor due to oscillations, relationship
between $\gamma$-rayand neutrino fluxes is then

$J_{\nu_{\mu}}(E_{\nu_{\mu}})=2J_{\gamma}(E_{\nu_{\mu}}/2).$ (C2)

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is negative for $a\leq 2$. Thus, we identify $a_{s}=2$ as the minimum value of
$a$ for which Eq. 1 of the main text is valid. For each country, $\ell_{s}$ is
determined by direct averaging as described in Sec. S.5.4

Figure S9: Robustness check for $\bar{f}(a,\ell)$ for different values of
$\Delta t_{s}$ for the ITn cohort. The main text shows $\Delta t_{s}=50$ days.
The results are consistent across the range of values.

Figure S10: Scatter plots showing the association between the added duration
of phone calls in a relationship, and their total number. Results are
presented a log-log scale and show a strong positive correlation, with the
coefficients presented in the supplementary text.

Figure S11: $b(\ell)$ as a function of $\ell$ obtained through the Mann-
Kendall method, cohort by cohort. The vertical axis is in logarithmic scale.
Clearly, $b(\ell)$ has an increasing trend with respect to $\ell$, with minor
exceptions. This result, remarkably similar to Fig. 2 in the main paper,
highlights the consistency between the Mann-Kendall and stable region average
methods.

Figure S12: Visual comparison of a sample of $\bar{f_{i}}(a,\ell)$ curves
(light color) with their respective cohort average $\bar{f}(a,\ell)$ (dark
color). Cohorts are indicated in each plot. As expected, individual egos
exhibit larger fluctuations than their cohort average, yet the fluctuations
are generally centered around the averages, providing evidence that the
general behavior of individual egos is qualitatively similar to that of the
cohort average with respect to monotonicity with respect to $\ell$, and
steadiness with respect to $a$. More quantitative evidence for these features
being present in the $\bar{f}_{i}$ is provided by the Kolmogorov-Smirnov test
shown in the main text, Fig. 3, as well as below in Fig. S14

Figure S13: Distribution of $b_{i}(\ell)$ per cohort (indicated in each plot),
with both axes in logarithmic scale. These distributions show that the average
stable call volume of egos to their alters does not vary much given a
lifetime, supporting the point that $b(\ell)$ and $b_{i}(\ell)$ are similar
given $\ell$. In order to show all information in logarithmic scale, all
values with frequency 0 are shown with frequency $10^{-2.5}$. Also, since no
ego has a value of $b_{i}(\ell)=0$, no information was lost due to the scaling
of the horizontal axes in any of the plots. All plots to the left use the
stable average region method of estimation of $b_{i}(\ell)$, and the right
column shows the estimation using the Mann-Kendall test for trends. The
averages of $b_{i}(\ell)$ over the egos of a cohort are displayed for each
cohort and lifetime group with a vertical dashed line.

Figure S14: Averages (circles) and standard deviations (lines-whiskers) of
$b_{i}(\ell)$ over egos, determined through the Mann-Kendall method, separated
by cohorts and lifetime groups (medium and long). This figure is equivalent to
Fig. 3B of the main text, generated with the alternative plateau finding
method. The $\times$ symbol represents the value of $b(\ell)$ per cohort and
lifetime group. The results support both the point that volume of calls
increases with $\ell$, and that $b(\ell)$ is a reasonable approximation for
the behavior of individual ego patterns of communication with their alters of
a given lifetime group.

Figure S15: Distribution of $p$-values obtained from applying the Kolomogorov-
Smirnov test to each individual curve $\bar{f_{i}}$. Each $p$-value is
generated by dividing $\bar{f_{i}}$ into two equal-sized ranges of $a$ and
comparing the values of $\bar{f_{i}}(a,\ell)$ between the two halves. Medium
and long lifetime groups are chosen per cohort and are consistent with those
chosen in the main text (cohorts are indicated in the plots). The
distributions shown use $10$ equal-sized bins for the $p$-values. Due to the
logarithmic scale in the vertical axis of each plot, in order to show all
information, values with frequency 0 are shown with frequency $10^{-1}$. In
all plots, purple and teal dashed lines represent the average of the
distribution for alters with medium and long lifetimes, respectively,
calculated from the raw data that generates the distributions (values reported
in Sec. S.5.3). The black vertical line represents $p=0.05$. The significance
of the plots is that they show that the time series $\bar{f}_{i}(a,\ell)$ for
the different cohorts and medium and long lifetimes of Fig. 1 do not have
decaying or increasing trends.

Figure S16: Distribution of $\ell_{s}$ plotted with logarithmic vertical
scale. Panel A corresponds to the distribution of $\ell_{s}$ of all combined
ego-alter pairs over all cohorts. The distribution is displayed with symbols,
and the line crossing the distribution is the least-squares fit line for Eq.
7. Estimations of the average $\ell_{s}$ under the assumption that Eq. 7 is a
good approximation as well as the average calculated directly from the data
are given within the text of this Supplementary Information and in Tab. S3
(which also contains per cohort averages from panel B of this figure). Panel B
shows the distributions of $\ell_{s}$ separated by cohort. For the individual
cohorts as well as the combined cohort, $\ell_{s}$ is obtained for all
relationships for which the calculation of $b_{i}(\ell)$ converges.

Cohort | average $\ell_{s}$ |  |
---|---|---|---
UK | 51.13 |  |
ITn | 66.14 |  |
IT | 56.49 |  |
US | 56.51 |  |
UK, Italy, and US combined | 55.94 |  |
Exponential fit | $\ell_{s,\min{}}$ | $\upsilon$ | Estimated average $\ell_{s}$
UK, Italy, and US combined | 14 | 48.70 | 62.38
Table S3: Calculation/estimation of average $\ell_{s}$ by cohort, all cohorts
combined, and exponential fit for all cohorts combined (Eq. 7). When all
cohorts are combined, results are obtained from an ordinary least square (OLS)
estimation (Fig. S16A). For the individual cohorts as well as the combined
cohort, averages are obtained directly from the $\ell_{s}$ of all
relationships for which the calculation of $b_{i}(\ell)$ converges. Their
distributions are shown in Fig S16B.

Figure S17: Distribution of $g$ for transient alters, measured between a
starting and ending elapsed duration of relationships $a_{o}$ and $a_{f}$.
Panel A uses $a_{o}=0$ and $a_{f}=\mathcal{L}_{\mathcal{E}}$ which means all
calls for each ego-alter transient relationship with the
$\mathcal{L}_{\mathcal{E}}$ is taken into account; Panel B uses $a_{o}=30$ and
$a_{f}=60$, the values used in Figs. 3 and 4 of the main text.

Figure S18: Survival probabilities $P(a\mid a_{o},a_{f},\gamma)$ of transient
alters to duration of at least $a$ for different bins $\gamma$ of amount of
mobile phone calls between $a_{o}=30$ and $a_{f}=60$ days. Each plot
corresponds to a single cohort (indicated in each plot), in contrast to the
main text which includes UK, IT, and US. The smaller samples that make up each
cohort do lead to noisier results as well as step-wise jumps on the plots. The
bins represented by $\gamma$ as the exponent in $3^{\gamma}\leq
g<3^{\gamma+1}$ are $\gamma=0,1,2,3$. As $\gamma$ increases, and even though
the plots display noisier behavior than in Fig. 4 of the main text, the
probability of survival also increases in all cohorts, i.e. for
$\gamma^{\prime}>\gamma$, $P(a\mid a_{o},a_{f},\gamma^{\prime})>P(a\mid
a_{o},a_{f},\gamma)$, consistent with the conclusions of the main text.

Figure S19: Exploration of survival probabilities $P(a\mid a_{o},a_{f},\gamma)$ of transient alters to duration of at least $a$ for different bins $\gamma$ of amount of mobile phone calls between $a_{o}$ and $a_{f}$ days. To explore the effects of $a_{o}$ and $a_{f}$, we proceed in a systematic way: each row of plots fixes the value of $a_{f}-a_{o}$, while increasing $a_{o}$; while each column fixes $a_{o}$ while increasing $a_{f}-a_{o}$. The values of $a_{f}-a_{o}$ in order of rows, from top to bottom, are $15$, $30$, $45$, and $60$ days; the values of $a_{o}$ in order of columns, from left to right, are $0$, $30$, and $60$ days. We use the combined data for UK, Italy and US, and therefore, we only look at relationships active for $\ell<\mathcal{L}_{{\rm US}}=220$ days or less, in order to include data for all three cohorts. The bins represented by $\gamma$ as the exponent in $3^{\gamma}\leq g<3^{\gamma+1}$ are $\gamma=0,1,2,3$. The most important effects observed are that if $a_{o}$ is chosen early in the relationship (say $a_{o}=0$), survival curves are closer together and even show inconsistency for the smallest call bin $\gamma=0$. Also, curves with increasing $\gamma$ do not separate as broadly. Larger $a_{f}-a_{o}$, on the other hand, leads to greater separation between curves of increasing $\gamma$, although increasing the window of observation is somehow antithetical to the idea of using $g$ measured in a small time window to predict relationship lifetime. In any case, for reasonable $a_{o}$ (one that is not too small) we still find, as in the main text, that as $\gamma$ increases the probability of survival also increases, i.e. for $\gamma^{\prime}>\gamma$, $P(a\mid a_{o},a_{f},\gamma^{\prime})>P(a\mid a_{o},a_{f},\gamma)$. $\gamma$ | A | B | C | D | E | F | G | H | I | J | K | L
---|---|---|---|---|---|---|---|---|---|---|---|---
0 | 3820 | 1186 | 964 | 3053 | 1624 | 1335 | 2531 | 1902 | 1588 | 2094 | 2032 | 1716
1 | 3462 | 381 | 275 | 4058 | 638 | 500 | 4425 | 850 | 704 | 4764 | 1039 | 857
2 | 299 | 107 | 52 | 431 | 151 | 94 | 546 | 183 | 138 | 625 | 228 | 179
3 | 38 | 10 | 12 | 72 | 41 | 33 | 102 | 61 | 45 | 113 | 75 | 55
Table S4: Number of alters used at each series $\gamma$ in Fig. S19. Every
column corresponds to a panel in Fig. S19. There is a noticeable decrease in
the number of alters, as $\gamma$ increases. Just as for Fig. S19, a
combination of the three countries was used for this Table

Figure S20: Version of Fig. 5 from the main paper with contours created using
US and Italian cohorts and the points correspond to the UK cohort. In the
spirit of the main text, the color background represents ranges of $P_{{\rm
IT+US}}(a\mid a_{o},a_{f},\gamma)$, namely $[0,0.25)$ (red), $[0.25,0.5)$
(teal), $[0.5,0.75)$ (purple), and $[0.75,1]$ (yellow). Panel A shows the
symbol $\blacksquare$ for $P_{{\rm UK}}(a\mid a_{o},a_{f},\gamma)$ in the
interval $[0,0.25)$, panel B shows the symbol $\diamond$ for the interval
$[0.25,0.5)$, panel C uses the symbol $\bullet$ for the interval $[0.5,0.75)$,
and panel D uses the symbol $\blacktriangle$ for the interval $[0.75,1)$ The
match in location between the symbols and the colored regions is reasonable
throughout values of the probability. However, quality is degraded slightly in
comparison to the main text, Fig. 5, as the sample for the UK cohort is
considerably smaller than the one for Italy (which forms the symbols of the
main text). Overall, the qualitative trend of the results presented is still
consistent with those of the main text.

Figure S21: Version of Fig. 5 from the main paper with contours created using
UK and Italian cohorts and the symbols correspond to the US cohort. In the
spirit of the main text, the color background represents ranges of $P_{{\rm
UK+IT}}(a\mid a_{o},a_{f},\gamma)$, namely $[0,0.25)$ (red), $[0.25,0.5)$
(teal), $[0.5,0.75)$ (purple), and $[0.75,1]$ (yellow). Panel A shows the
symbol $\blacksquare$ for $P_{{\rm US}}(a\mid a_{o},a_{f},\gamma)$ in the
interval $[0,0.25)$, panel B shows the symbol $\diamond$ for the interval
$[0.25,0.5)$, panel C uses the symbol $\bullet$ for the interval $[0.5,0.75)$,
and panel D uses the symbol $\blacktriangle$ for the interval $[0.75,1)$. The
match in location between the symbols and the colored regions is best achieved
for largest probabilities, i.e. dark yellow and purple regions. For lower
probability regions, the match is not as good although it has the correct
trend of dependence of survival with respect to $g$, namely, more calling
means longer survival. The smaller size of the US cohort plays a role.
Overall, the qualitative trend of the results presented is still consistent
with those of the main text.