# Large-scale cosmic-ray anisotropies above 4 EeV measured by
the Pierre Auger Observatory

A. Aab7575affiliation: IMAPP, Radboud University Nijmegen, Nijmegen, The
Netherlands , P. Abreu6767affiliation: Laboratório de Instrumentação e Física
Experimental de Partículas – LIP and Instituto Superior Técnico – IST,
Universidade de Lisboa – UL, Lisboa, Portugal , M. Aglietta5050affiliation:
Osservatorio Astrofisico di Torino (INAF), Torino, Italy 4949affiliation:
INFN, Sezione di Torino, Torino, Italy , I.F.M. Albuquerque1919affiliation:
Universidade de São Paulo, Instituto de Física, São Paulo, SP, Brazil , J.M.
Albury1212affiliation: University of Adelaide, Adelaide, S.A., Australia , I.
Allekotte11affiliation: Centro Atómico Bariloche and Instituto Balseiro (CNEA-
UNCuyo-CONICET), San Carlos de Bariloche, Argentina , A. Almela88affiliation:
Instituto de Tecnologías en Detección y Astropartículas (CNEA, CONICET,
UNSAM), Buenos Aires, Argentina 1111affiliation: Universidad Tecnológica
Nacional – Facultad Regional Buenos Aires, Buenos Aires, Argentina , J.
Alvarez Castillo6363affiliation: Universidad Nacional Autónoma de México,
México, D.F., México , J. Alvarez-Muñiz7474affiliation: Instituto Galego de
Física de Altas Enerxías (I.G.F.A.E.), Universidad de Santiago de Compostela,
Santiago de Compostela, Spain , G.A. Anastasi4242affiliation: Gran Sasso
Science Institute, L’Aquila, Italy 4343affiliation: INFN Laboratori Nazionali
del Gran Sasso, Assergi (L’Aquila), Italy , L. Anchordoqui8181affiliation:
Department of Physics and Astronomy, Lehman College, City University of New
York, Bronx, NY, USA , B. Andrada88affiliation: Instituto de Tecnologías en
Detección y Astropartículas (CNEA, CONICET, UNSAM), Buenos Aires, Argentina ,
S. Andringa6767affiliation: Laboratório de Instrumentação e Física
Experimental de Partículas – LIP and Instituto Superior Técnico – IST,
Universidade de Lisboa – UL, Lisboa, Portugal , C. Aramo4747affiliation: INFN,
Sezione di Napoli, Napoli, Italy , H. Asorey11affiliation: Centro Atómico
Bariloche and Instituto Balseiro (CNEA-UNCuyo-CONICET), San Carlos de
Bariloche, Argentina 2828affiliation: Universidad Industrial de Santander,
Bucaramanga, Colombia , P. Assis6767affiliation: Laboratório de Instrumentação
e Física Experimental de Partículas – LIP and Instituto Superior Técnico –
IST, Universidade de Lisboa – UL, Lisboa, Portugal , G. Avila99affiliation:
Observatorio Pierre Auger, Malargüe, Argentina 1010affiliation: Observatorio
Pierre Auger and Comisión Nacional de Energía Atómica, Malargüe, Argentina ,
A.M. Badescu7070affiliation: University Politehnica of Bucharest, Bucharest,
Romania , A. Balaceanu6868affiliation: “Horia Hulubei” National Institute for
Physics and Nuclear Engineering, Bucharest-Magurele, Romania , F.
Barbato5656affiliation: Università di Napoli “Federico II”, Dipartimento di
Fisica “Ettore Pancini”, Napoli, Italy 4747affiliation: INFN, Sezione di
Napoli, Napoli, Italy , R.J. Barreira Luz6767affiliation: Laboratório de
Instrumentação e Física Experimental de Partículas – LIP and Instituto
Superior Técnico – IST, Universidade de Lisboa – UL, Lisboa, Portugal , S.
Baur3737affiliation: Karlsruhe Institute of Technology, Institut für
Kernphysik, Karlsruhe, Germany , K.H. Becker3535affiliation: Bergische
Universität Wuppertal, Department of Physics, Wuppertal, Germany , J.A.
Bellido1212affiliation: University of Adelaide, Adelaide, S.A., Australia , C.
Berat3434affiliation: Univ. Grenoble Alpes, CNRS, Grenoble Institute of
Engineering Univ. Grenoble Alpes, LPSC-IN2P3, 38000 Grenoble, France, France ,
M.E. Bertaina5858affiliation: Università Torino, Dipartimento di Fisica,
Torino, Italy 4949affiliation: INFN, Sezione di Torino, Torino, Italy , X.
Bertou11affiliation: Centro Atómico Bariloche and Instituto Balseiro (CNEA-
UNCuyo-CONICET), San Carlos de Bariloche, Argentina , P.L.
Biermann10011001affiliation: Max-Planck-Institut für Radioastronomie, Bonn,
Germany , J. Biteau3232affiliation: Institut de Physique Nucléaire d’Orsay
(IPNO), Université Paris-Sud, Univ. Paris/Saclay, CNRS-IN2P3, Orsay, France ,
S.G. Blaess1212affiliation: University of Adelaide, Adelaide, S.A., Australia
, A. Blanco6767affiliation: Laboratório de Instrumentação e Física
Experimental de Partículas – LIP and Instituto Superior Técnico – IST,
Universidade de Lisboa – UL, Lisboa, Portugal , J. Blazek3030affiliation:
Institute of Physics of the Czech Academy of Sciences, Prague, Czech Republic
, C. Bleve5252affiliation: Università del Salento, Dipartimento di Matematica
e Fisica “E. De Giorgi”, Lecce, Italy 4545affiliation: INFN, Sezione di Lecce,
Lecce, Italy , M. Boháčová3030affiliation: Institute of Physics of the Czech
Academy of Sciences, Prague, Czech Republic , C. Bonifazi2424affiliation:
Universidade Federal do Rio de Janeiro, Instituto de Física, Rio de Janeiro,
RJ, Brazil , N. Borodai6464affiliation: Institute of Nuclear Physics PAN,
Krakow, Poland , A.M. Botti88affiliation: Instituto de Tecnologías en
Detección y Astropartículas (CNEA, CONICET, UNSAM), Buenos Aires, Argentina
3737affiliation: Karlsruhe Institute of Technology, Institut für Kernphysik,
Karlsruhe, Germany , J. Brack10041004affiliation: Colorado State University,
Fort Collins, CO, USA , T. Bretz3939affiliation: RWTH Aachen University, III.
Physikalisches Institut A, Aachen, Germany , A. Bridgeman3636affiliation:
Karlsruhe Institute of Technology, Institute for Experimental Particle Physics
(ETP), Karlsruhe, Germany , F.L. Briechle3939affiliation: RWTH Aachen
University, III. Physikalisches Institut A, Aachen, Germany , P.
Buchholz4141affiliation: Universität Siegen, Fachbereich 7 Physik –
Experimentelle Teilchenphysik, Siegen, Germany , A. Bueno7373affiliation:
Universidad de Granada and C.A.F.P.E., Granada, Spain , S.
Buitink1414affiliation: Vrije Universiteit Brussels, Brussels, Belgium , M.
Buscemi5454affiliation: Università di Catania, Dipartimento di Fisica e
Astronomia, Catania, Italy 4444affiliation: INFN, Sezione di Catania, Catania,
Italy , K.S. Caballero-Mora6262affiliation: Universidad Autónoma de Chiapas,
Tuxtla Gutiérrez, Chiapas, México , L. Caccianiga5555affiliation: Università
di Milano, Dipartimento di Fisica, Milano, Italy , L. Calcagni44affiliation:
IFLP, Universidad Nacional de La Plata and CONICET, La Plata, Argentina , A.
Cancio1111affiliation: Universidad Tecnológica Nacional – Facultad Regional
Buenos Aires, Buenos Aires, Argentina 88affiliation: Instituto de Tecnologías
en Detección y Astropartículas (CNEA, CONICET, UNSAM), Buenos Aires, Argentina
, F. Canfora7575affiliation: IMAPP, Radboud University Nijmegen, Nijmegen, The
Netherlands 7777affiliation: Nationaal Instituut voor Kernfysica en Hoge
Energie Fysica (NIKHEF), Science Park, Amsterdam, The Netherlands , J.M.
Carceller7373affiliation: Universidad de Granada and C.A.F.P.E., Granada,
Spain , R. Caruso5454affiliation: Università di Catania, Dipartimento di
Fisica e Astronomia, Catania, Italy 4444affiliation: INFN, Sezione di Catania,
Catania, Italy , A. Castellina5050affiliation: Osservatorio Astrofisico di
Torino (INAF), Torino, Italy 4949affiliation: INFN, Sezione di Torino, Torino,
Italy , F. Catalani1717affiliation: Universidade de São Paulo, Escola de
Engenharia de Lorena, Lorena, SP, Brazil , G. Cataldi4545affiliation: INFN,
Sezione di Lecce, Lecce, Italy , L. Cazon6767affiliation: Laboratório de
Instrumentação e Física Experimental de Partículas – LIP and Instituto
Superior Técnico – IST, Universidade de Lisboa – UL, Lisboa, Portugal , J.A.
Chinellato2020affiliation: Universidade Estadual de Campinas, IFGW, Campinas,
SP, Brazil , J. Chudoba3030affiliation: Institute of Physics of the Czech
Academy of Sciences, Prague, Czech Republic , L. Chytka3131affiliation:
Palacky University, RCPTM, Olomouc, Czech Republic , R.W. Clay1212affiliation:
University of Adelaide, Adelaide, S.A., Australia , A.C. Cobos
Cerutti77affiliation: Instituto de Tecnologías en Detección y Astropartículas
(CNEA, CONICET, UNSAM), and Universidad Tecnológica Nacional – Facultad
Regional Mendoza (CONICET/CNEA), Mendoza, Argentina , R.
Colalillo5656affiliation: Università di Napoli “Federico II”, Dipartimento di
Fisica “Ettore Pancini”, Napoli, Italy 4747affiliation: INFN, Sezione di
Napoli, Napoli, Italy , A. Coleman8585affiliation: Pennsylvania State
University, University Park, PA, USA , M.R. Coluccia5252affiliation:
Università del Salento, Dipartimento di Matematica e Fisica “E. De Giorgi”,
Lecce, Italy 4545affiliation: INFN, Sezione di Lecce, Lecce, Italy , R.
Conceição6767affiliation: Laboratório de Instrumentação e Física Experimental
de Partículas – LIP and Instituto Superior Técnico – IST, Universidade de
Lisboa – UL, Lisboa, Portugal , G. Consolati4646affiliation: INFN, Sezione di
Milano, Milano, Italy 5151affiliation: Politecnico di Milano, Dipartimento di
Scienze e Tecnologie Aerospaziali , Milano, Italy , F. Contreras99affiliation:
Observatorio Pierre Auger, Malargüe, Argentina 1010affiliation: Observatorio
Pierre Auger and Comisión Nacional de Energía Atómica, Malargüe, Argentina ,
M.J. Cooper1212affiliation: University of Adelaide, Adelaide, S.A., Australia
, S. Coutu8585affiliation: Pennsylvania State University, University Park, PA,
USA , C.E. Covault7979affiliation: Case Western Reserve University, Cleveland,
OH, USA , B. Daniel2020affiliation: Universidade Estadual de Campinas, IFGW,
Campinas, SP, Brazil , S. Dasso55affiliation: Instituto de Astronomía y Física
del Espacio (IAFE, CONICET-UBA), Buenos Aires, Argentina 33affiliation:
Departamento de Física and Departamento de Ciencias de la Atmósfera y los
Océanos, FCEyN, Universidad de Buenos Aires and CONICET, Buenos Aires,
Argentina , K. Daumiller3737affiliation: Karlsruhe Institute of Technology,
Institut für Kernphysik, Karlsruhe, Germany , B.R. Dawson1212affiliation:
University of Adelaide, Adelaide, S.A., Australia , J.A. Day1212affiliation:
University of Adelaide, Adelaide, S.A., Australia , R.M. de
Almeida2626affiliation: Universidade Federal Fluminense, EEIMVR, Volta
Redonda, RJ, Brazil , S.J. de Jong7575affiliation: IMAPP, Radboud University
Nijmegen, Nijmegen, The Netherlands 7777affiliation: Nationaal Instituut voor
Kernfysica en Hoge Energie Fysica (NIKHEF), Science Park, Amsterdam, The
Netherlands , G. De Mauro7575affiliation: IMAPP, Radboud University Nijmegen,
Nijmegen, The Netherlands 7777affiliation: Nationaal Instituut voor Kernfysica
en Hoge Energie Fysica (NIKHEF), Science Park, Amsterdam, The Netherlands ,
J.R.T. de Mello Neto2424affiliation: Universidade Federal do Rio de Janeiro,
Instituto de Física, Rio de Janeiro, RJ, Brazil 2525affiliation: Universidade
Federal do Rio de Janeiro (UFRJ), Observatório do Valongo, Rio de Janeiro, RJ,
Brazil , I. De Mitri4242affiliation: Gran Sasso Science Institute, L’Aquila,
Italy 4343affiliation: INFN Laboratori Nazionali del Gran Sasso, Assergi
(L’Aquila), Italy , J. de Oliveira2626affiliation: Universidade Federal
Fluminense, EEIMVR, Volta Redonda, RJ, Brazil , V. de Souza1818affiliation:
Universidade de São Paulo, Instituto de Física de São Carlos, São Carlos, SP,
Brazil , J. Debatin3636affiliation: Karlsruhe Institute of Technology,
Institute for Experimental Particle Physics (ETP), Karlsruhe, Germany , O.
Deligny3232affiliation: Institut de Physique Nucléaire d’Orsay (IPNO),
Université Paris-Sud, Univ. Paris/Saclay, CNRS-IN2P3, Orsay, France , N.
Dhital6464affiliation: Institute of Nuclear Physics PAN, Krakow, Poland , M.L.
Díaz Castro2020affiliation: Universidade Estadual de Campinas, IFGW, Campinas,
SP, Brazil , F. Diogo6767affiliation: Laboratório de Instrumentação e Física
Experimental de Partículas – LIP and Instituto Superior Técnico – IST,
Universidade de Lisboa – UL, Lisboa, Portugal , C. Dobrigkeit2020affiliation:
Universidade Estadual de Campinas, IFGW, Campinas, SP, Brazil , J.C.
D’Olivo6363affiliation: Universidad Nacional Autónoma de México, México, D.F.,
México , Q. Dorosti4141affiliation: Universität Siegen, Fachbereich 7 Physik –
Experimentelle Teilchenphysik, Siegen, Germany , R.C. dos
Anjos2323affiliation: Universidade Federal do Paraná, Setor Palotina,
Palotina, Brazil , M.T. Dova44affiliation: IFLP, Universidad Nacional de La
Plata and CONICET, La Plata, Argentina , A. Dundovic4040affiliation:
Universität Hamburg, II. Institut für Theoretische Physik, Hamburg, Germany ,
J. Ebr3030affiliation: Institute of Physics of the Czech Academy of Sciences,
Prague, Czech Republic , R. Engel3737affiliation: Karlsruhe Institute of
Technology, Institut für Kernphysik, Karlsruhe, Germany , M.
Erdmann3939affiliation: RWTH Aachen University, III. Physikalisches Institut
A, Aachen, Germany , C.O. Escobar10021002affiliation: Fermi National
Accelerator Laboratory, USA , A. Etchegoyen88affiliation: Instituto de
Tecnologías en Detección y Astropartículas (CNEA, CONICET, UNSAM), Buenos
Aires, Argentina 1111affiliation: Universidad Tecnológica Nacional – Facultad
Regional Buenos Aires, Buenos Aires, Argentina , H. Falcke7575affiliation:
IMAPP, Radboud University Nijmegen, Nijmegen, The Netherlands 7878affiliation:
Stichting Astronomisch Onderzoek in Nederland (ASTRON), Dwingeloo, The
Netherlands 7777affiliation: Nationaal Instituut voor Kernfysica en Hoge
Energie Fysica (NIKHEF), Science Park, Amsterdam, The Netherlands , J.
Farmer8686affiliation: University of Chicago, Enrico Fermi Institute, Chicago,
IL, USA , G. Farrar8484affiliation: New York University, New York, NY, USA ,
A.C. Fauth2020affiliation: Universidade Estadual de Campinas, IFGW, Campinas,
SP, Brazil , N. Fazzini10021002affiliation: Fermi National Accelerator
Laboratory, USA , F. Feldbusch3838affiliation: Karlsruhe Institute of
Technology, Institut für Prozessdatenverarbeitung und Elektronik, Karlsruhe,
Germany , F. Fenu5858affiliation: Università Torino, Dipartimento di Fisica,
Torino, Italy 4949affiliation: INFN, Sezione di Torino, Torino, Italy , L.P.
Ferreyro88affiliation: Instituto de Tecnologías en Detección y Astropartículas
(CNEA, CONICET, UNSAM), Buenos Aires, Argentina , J.M. Figueira88affiliation:
Instituto de Tecnologías en Detección y Astropartículas (CNEA, CONICET,
UNSAM), Buenos Aires, Argentina , A. Filipčič7272affiliation: Experimental
Particle Physics Department, J. Stefan Institute, Ljubljana, Slovenia
7171affiliation: Center for Astrophysics and Cosmology (CAC), University of
Nova Gorica, Nova Gorica, Slovenia , M.M. Freire66affiliation: Instituto de
Física de Rosario (IFIR) – CONICET/U.N.R. and Facultad de Ciencias Bioquímicas
y Farmacéuticas U.N.R., Rosario, Argentina , T. Fujii8686affiliation:
University of Chicago, Enrico Fermi Institute, Chicago, IL, USA
10051005affiliation: now at Institute for Cosmic Ray Research, University of
Tokyo , A. Fuster88affiliation: Instituto de Tecnologías en Detección y
Astropartículas (CNEA, CONICET, UNSAM), Buenos Aires, Argentina
1111affiliation: Universidad Tecnológica Nacional – Facultad Regional Buenos
Aires, Buenos Aires, Argentina , B. García77affiliation: Instituto de
Tecnologías en Detección y Astropartículas (CNEA, CONICET, UNSAM), and
Universidad Tecnológica Nacional – Facultad Regional Mendoza (CONICET/CNEA),
Mendoza, Argentina , H. Gemmeke3838affiliation: Karlsruhe Institute of
Technology, Institut für Prozessdatenverarbeitung und Elektronik, Karlsruhe,
Germany , A. Gherghel-Lascu6868affiliation: “Horia Hulubei” National Institute
for Physics and Nuclear Engineering, Bucharest-Magurele, Romania , P.L.
Ghia3232affiliation: Institut de Physique Nucléaire d’Orsay (IPNO), Université
Paris-Sud, Univ. Paris/Saclay, CNRS-IN2P3, Orsay, France , U.
Giaccari2424affiliation: Universidade Federal do Rio de Janeiro, Instituto de
Física, Rio de Janeiro, RJ, Brazil 1515affiliation: Centro Brasileiro de
Pesquisas Fisicas, Rio de Janeiro, RJ, Brazil , M. Giammarchi4646affiliation:
INFN, Sezione di Milano, Milano, Italy , M. Giller6565affiliation: University
of Łódź, Faculty of Astrophysics, Łódź, Poland , D. Głas6666affiliation:
University of Łódź, Faculty of High-Energy Astrophysics,Łódź, Poland , J.
Glombitza3939affiliation: RWTH Aachen University, III. Physikalisches Institut
A, Aachen, Germany , G. Golup11affiliation: Centro Atómico Bariloche and
Instituto Balseiro (CNEA-UNCuyo-CONICET), San Carlos de Bariloche, Argentina ,
M. Gómez Berisso11affiliation: Centro Atómico Bariloche and Instituto Balseiro
(CNEA-UNCuyo-CONICET), San Carlos de Bariloche, Argentina , P.F. Gómez
Vitale99affiliation: Observatorio Pierre Auger, Malargüe, Argentina
1010affiliation: Observatorio Pierre Auger and Comisión Nacional de Energía
Atómica, Malargüe, Argentina , N. González88affiliation: Instituto de
Tecnologías en Detección y Astropartículas (CNEA, CONICET, UNSAM), Buenos
Aires, Argentina , I. Goos11affiliation: Centro Atómico Bariloche and
Instituto Balseiro (CNEA-UNCuyo-CONICET), San Carlos de Bariloche, Argentina
3737affiliation: Karlsruhe Institute of Technology, Institut für Kernphysik,
Karlsruhe, Germany , D. Góra6464affiliation: Institute of Nuclear Physics PAN,
Krakow, Poland , A. Gorgi5050affiliation: Osservatorio Astrofisico di Torino
(INAF), Torino, Italy 4949affiliation: INFN, Sezione di Torino, Torino, Italy
, M. Gottowik3535affiliation: Bergische Universität Wuppertal, Department of
Physics, Wuppertal, Germany , T.D. Grubb1212affiliation: University of
Adelaide, Adelaide, S.A., Australia , F. Guarino5656affiliation: Università di
Napoli “Federico II”, Dipartimento di Fisica “Ettore Pancini”, Napoli, Italy
4747affiliation: INFN, Sezione di Napoli, Napoli, Italy , G.P.
Guedes2121affiliation: Universidade Estadual de Feira de Santana, Feira de
Santana, Brazil , E. Guido4949affiliation: INFN, Sezione di Torino, Torino,
Italy 5858affiliation: Università Torino, Dipartimento di Fisica, Torino,
Italy , R. Halliday7979affiliation: Case Western Reserve University,
Cleveland, OH, USA , M.R. Hampel88affiliation: Instituto de Tecnologías en
Detección y Astropartículas (CNEA, CONICET, UNSAM), Buenos Aires, Argentina ,
P. Hansen44affiliation: IFLP, Universidad Nacional de La Plata and CONICET, La
Plata, Argentina , D. Harari11affiliation: Centro Atómico Bariloche and
Instituto Balseiro (CNEA-UNCuyo-CONICET), San Carlos de Bariloche, Argentina ,
T.A. Harrison1212affiliation: University of Adelaide, Adelaide, S.A.,
Australia , V.M. Harvey1212affiliation: University of Adelaide, Adelaide,
S.A., Australia , A. Haungs3737affiliation: Karlsruhe Institute of Technology,
Institut für Kernphysik, Karlsruhe, Germany , T. Hebbeker3939affiliation: RWTH
Aachen University, III. Physikalisches Institut A, Aachen, Germany , D.
Heck3737affiliation: Karlsruhe Institute of Technology, Institut für
Kernphysik, Karlsruhe, Germany , P. Heimann4141affiliation: Universität
Siegen, Fachbereich 7 Physik – Experimentelle Teilchenphysik, Siegen, Germany
, G.C. Hill1212affiliation: University of Adelaide, Adelaide, S.A., Australia
, C. Hojvat10021002affiliation: Fermi National Accelerator Laboratory, USA ,
E.M. Holt3636affiliation: Karlsruhe Institute of Technology, Institute for
Experimental Particle Physics (ETP), Karlsruhe, Germany 88affiliation:
Instituto de Tecnologías en Detección y Astropartículas (CNEA, CONICET,
UNSAM), Buenos Aires, Argentina , P. Homola6464affiliation: Institute of
Nuclear Physics PAN, Krakow, Poland , J.R. Hörandel7575affiliation: IMAPP,
Radboud University Nijmegen, Nijmegen, The Netherlands 7777affiliation:
Nationaal Instituut voor Kernfysica en Hoge Energie Fysica (NIKHEF), Science
Park, Amsterdam, The Netherlands , P. Horvath3131affiliation: Palacky
University, RCPTM, Olomouc, Czech Republic , M. Hrabovský3131affiliation:
Palacky University, RCPTM, Olomouc, Czech Republic , T. Huege3737affiliation:
Karlsruhe Institute of Technology, Institut für Kernphysik, Karlsruhe, Germany
1414affiliation: Vrije Universiteit Brussels, Brussels, Belgium , J.
Hulsman88affiliation: Instituto de Tecnologías en Detección y Astropartículas
(CNEA, CONICET, UNSAM), Buenos Aires, Argentina 3737affiliation: Karlsruhe
Institute of Technology, Institut für Kernphysik, Karlsruhe, Germany , A.
Insolia5454affiliation: Università di Catania, Dipartimento di Fisica e
Astronomia, Catania, Italy 4444affiliation: INFN, Sezione di Catania, Catania,
Italy , P.G. Isar6969affiliation: Institute of Space Science, Bucharest-
Magurele, Romania , I. Jandt3535affiliation: Bergische Universität Wuppertal,
Department of Physics, Wuppertal, Germany , J.A. Johnsen8080affiliation:
Colorado School of Mines, Golden, CO, USA , M. Josebachuili88affiliation:
Instituto de Tecnologías en Detección y Astropartículas (CNEA, CONICET,
UNSAM), Buenos Aires, Argentina , J. Jurysek3030affiliation: Institute of
Physics of the Czech Academy of Sciences, Prague, Czech Republic , A.
Kääpä3535affiliation: Bergische Universität Wuppertal, Department of Physics,
Wuppertal, Germany , K.H. Kampert3535affiliation: Bergische Universität
Wuppertal, Department of Physics, Wuppertal, Germany , B.
Keilhauer3737affiliation: Karlsruhe Institute of Technology, Institut für
Kernphysik, Karlsruhe, Germany , N. Kemmerich1919affiliation: Universidade de
São Paulo, Instituto de Física, São Paulo, SP, Brazil , J.
Kemp3939affiliation: RWTH Aachen University, III. Physikalisches Institut A,
Aachen, Germany , H.O. Klages3737affiliation: Karlsruhe Institute of
Technology, Institut für Kernphysik, Karlsruhe, Germany , M.
Kleifges3838affiliation: Karlsruhe Institute of Technology, Institut für
Prozessdatenverarbeitung und Elektronik, Karlsruhe, Germany , J.
Kleinfeller99affiliation: Observatorio Pierre Auger, Malargüe, Argentina , R.
Krause3939affiliation: RWTH Aachen University, III. Physikalisches Institut A,
Aachen, Germany , D. Kuempel3535affiliation: Bergische Universität Wuppertal,
Department of Physics, Wuppertal, Germany , G. Kukec Mezek7171affiliation:
Center for Astrophysics and Cosmology (CAC), University of Nova Gorica, Nova
Gorica, Slovenia , A. Kuotb Awad3636affiliation: Karlsruhe Institute of
Technology, Institute for Experimental Particle Physics (ETP), Karlsruhe,
Germany , B.L. Lago1616affiliation: Centro Federal de Educação Tecnológica
Celso Suckow da Fonseca, Nova Friburgo, Brazil , D. LaHurd7979affiliation:
Case Western Reserve University, Cleveland, OH, USA , R.G.
Lang1818affiliation: Universidade de São Paulo, Instituto de Física de São
Carlos, São Carlos, SP, Brazil , R. Legumina6565affiliation: University of
Łódź, Faculty of Astrophysics, Łódź, Poland , M.A. Leigui de
Oliveira2222affiliation: Universidade Federal do ABC, Santo André, SP, Brazil
, V. Lenok3737affiliation: Karlsruhe Institute of Technology, Institut für
Kernphysik, Karlsruhe, Germany , A. Letessier-Selvon3333affiliation:
Laboratoire de Physique Nucléaire et de Hautes Energies (LPNHE), Universités
Paris 6 et Paris 7, CNRS-IN2P3, Paris, France , I. Lhenry-Yvon3232affiliation:
Institut de Physique Nucléaire d’Orsay (IPNO), Université Paris-Sud, Univ.
Paris/Saclay, CNRS-IN2P3, Orsay, France , D. Lo Presti5454affiliation:
Università di Catania, Dipartimento di Fisica e Astronomia, Catania, Italy
4444affiliation: INFN, Sezione di Catania, Catania, Italy , L.
Lopes6767affiliation: Laboratório de Instrumentação e Física Experimental de
Partículas – LIP and Instituto Superior Técnico – IST, Universidade de Lisboa
– UL, Lisboa, Portugal , R. López5959affiliation: Benemérita Universidad
Autónoma de Puebla, Puebla, México , A. López Casado7474affiliation: Instituto
Galego de Física de Altas Enerxías (I.G.F.A.E.), Universidad de Santiago de
Compostela, Santiago de Compostela, Spain , R. Lorek7979affiliation: Case
Western Reserve University, Cleveland, OH, USA , Q. Luce3232affiliation:
Institut de Physique Nucléaire d’Orsay (IPNO), Université Paris-Sud, Univ.
Paris/Saclay, CNRS-IN2P3, Orsay, France , A. Lucero88affiliation: Instituto de
Tecnologías en Detección y Astropartículas (CNEA, CONICET, UNSAM), Buenos
Aires, Argentina , M. Malacari8686affiliation: University of Chicago, Enrico
Fermi Institute, Chicago, IL, USA , M. Mallamaci5555affiliation: Università di
Milano, Dipartimento di Fisica, Milano, Italy 4646affiliation: INFN, Sezione
di Milano, Milano, Italy , G. Mancarella5252affiliation: Università del
Salento, Dipartimento di Matematica e Fisica “E. De Giorgi”, Lecce, Italy
4545affiliation: INFN, Sezione di Lecce, Lecce, Italy , D.
Mandat3030affiliation: Institute of Physics of the Czech Academy of Sciences,
Prague, Czech Republic , P. Mantsch10021002affiliation: Fermi National
Accelerator Laboratory, USA , A.G. Mariazzi44affiliation: IFLP, Universidad
Nacional de La Plata and CONICET, La Plata, Argentina , I.C.
Mariş1313affiliation: Université Libre de Bruxelles (ULB), Brussels, Belgium ,
G. Marsella5252affiliation: Università del Salento, Dipartimento di Matematica
e Fisica “E. De Giorgi”, Lecce, Italy 4545affiliation: INFN, Sezione di Lecce,
Lecce, Italy , D. Martello5252affiliation: Università del Salento,
Dipartimento di Matematica e Fisica “E. De Giorgi”, Lecce, Italy
4545affiliation: INFN, Sezione di Lecce, Lecce, Italy , H.
Martinez6060affiliation: Centro de Investigación y de Estudios Avanzados del
IPN (CINVESTAV), México, D.F., México , O. Martínez Bravo5959affiliation:
Benemérita Universidad Autónoma de Puebla, Puebla, México , H.J.
Mathes3737affiliation: Karlsruhe Institute of Technology, Institut für
Kernphysik, Karlsruhe, Germany , S. Mathys3535affiliation: Bergische
Universität Wuppertal, Department of Physics, Wuppertal, Germany , J.
Matthews8282affiliation: Louisiana State University, Baton Rouge, LA, USA , G.
Matthiae5757affiliation: Università di Roma “Tor Vergata”, Dipartimento di
Fisica, Roma, Italy 4848affiliation: INFN, Sezione di Roma “Tor Vergata”,
Roma, Italy , E. Mayotte3535affiliation: Bergische Universität Wuppertal,
Department of Physics, Wuppertal, Germany , P.O. Mazur10021002affiliation:
Fermi National Accelerator Laboratory, USA , G. Medina-Tanco6363affiliation:
Universidad Nacional Autónoma de México, México, D.F., México , D.
Melo88affiliation: Instituto de Tecnologías en Detección y Astropartículas
(CNEA, CONICET, UNSAM), Buenos Aires, Argentina , A. Menshikov3838affiliation:
Karlsruhe Institute of Technology, Institut für Prozessdatenverarbeitung und
Elektronik, Karlsruhe, Germany , K.-D. Merenda8080affiliation: Colorado School
of Mines, Golden, CO, USA , S. Michal3131affiliation: Palacky University,
RCPTM, Olomouc, Czech Republic , M.I. Micheletti66affiliation: Instituto de
Física de Rosario (IFIR) – CONICET/U.N.R. and Facultad de Ciencias Bioquímicas
y Farmacéuticas U.N.R., Rosario, Argentina , L. Middendorf3939affiliation:
RWTH Aachen University, III. Physikalisches Institut A, Aachen, Germany , L.
Miramonti5555affiliation: Università di Milano, Dipartimento di Fisica,
Milano, Italy 4646affiliation: INFN, Sezione di Milano, Milano, Italy , B.
Mitrica6868affiliation: “Horia Hulubei” National Institute for Physics and
Nuclear Engineering, Bucharest-Magurele, Romania , D. Mockler3636affiliation:
Karlsruhe Institute of Technology, Institute for Experimental Particle Physics
(ETP), Karlsruhe, Germany , S. Mollerach11affiliation: Centro Atómico
Bariloche and Instituto Balseiro (CNEA-UNCuyo-CONICET), San Carlos de
Bariloche, Argentina , F. Montanet3434affiliation: Univ. Grenoble Alpes, CNRS,
Grenoble Institute of Engineering Univ. Grenoble Alpes, LPSC-IN2P3, 38000
Grenoble, France, France , C. Morello5050affiliation: Osservatorio Astrofisico
di Torino (INAF), Torino, Italy 4949affiliation: INFN, Sezione di Torino,
Torino, Italy , G. Morlino4242affiliation: Gran Sasso Science Institute,
L’Aquila, Italy 4343affiliation: INFN Laboratori Nazionali del Gran Sasso,
Assergi (L’Aquila), Italy , M. Mostafá8585affiliation: Pennsylvania State
University, University Park, PA, USA , A.L. Müller88affiliation: Instituto de
Tecnologías en Detección y Astropartículas (CNEA, CONICET, UNSAM), Buenos
Aires, Argentina 3737affiliation: Karlsruhe Institute of Technology, Institut
für Kernphysik, Karlsruhe, Germany , M.A. Muller2020affiliation: Universidade
Estadual de Campinas, IFGW, Campinas, SP, Brazil 10031003affiliation: also at
Universidade Federal de Alfenas, Poços de Caldas, Brazil , S.
Müller3636affiliation: Karlsruhe Institute of Technology, Institute for
Experimental Particle Physics (ETP), Karlsruhe, Germany 88affiliation:
Instituto de Tecnologías en Detección y Astropartículas (CNEA, CONICET,
UNSAM), Buenos Aires, Argentina , R. Mussa4949affiliation: INFN, Sezione di
Torino, Torino, Italy , L. Nellen6363affiliation: Universidad Nacional
Autónoma de México, México, D.F., México , P.H. Nguyen1212affiliation:
University of Adelaide, Adelaide, S.A., Australia , M. Niculescu-
Oglinzanu6868affiliation: “Horia Hulubei” National Institute for Physics and
Nuclear Engineering, Bucharest-Magurele, Romania , M.
Niechciol4141affiliation: Universität Siegen, Fachbereich 7 Physik –
Experimentelle Teilchenphysik, Siegen, Germany , D. Nitz8383affiliation:
Michigan Technological University, Houghton, MI, USA 10061006affiliation: also
at Karlsruhe Institute of Technology, Karlsruhe, Germany , D.
Nosek2929affiliation: Charles University, Faculty of Mathematics and Physics,
Institute of Particle and Nuclear Physics, Prague, Czech Republic , V.
Novotny2929affiliation: Charles University, Faculty of Mathematics and
Physics, Institute of Particle and Nuclear Physics, Prague, Czech Republic ,
L. Nožka3131affiliation: Palacky University, RCPTM, Olomouc, Czech Republic ,
A Nucita5252affiliation: Università del Salento, Dipartimento di Matematica e
Fisica “E. De Giorgi”, Lecce, Italy 4545affiliation: INFN, Sezione di Lecce,
Lecce, Italy , L.A. Núñez2828affiliation: Universidad Industrial de Santander,
Bucaramanga, Colombia , A. Olinto8686affiliation: University of Chicago,
Enrico Fermi Institute, Chicago, IL, USA , M. Palatka3030affiliation:
Institute of Physics of the Czech Academy of Sciences, Prague, Czech Republic
, J. Pallotta22affiliation: Centro de Investigaciones en Láseres y
Aplicaciones, CITEDEF and CONICET, Villa Martelli, Argentina , P.
Papenbreer3535affiliation: Bergische Universität Wuppertal, Department of
Physics, Wuppertal, Germany , G. Parente7474affiliation: Instituto Galego de
Física de Altas Enerxías (I.G.F.A.E.), Universidad de Santiago de Compostela,
Santiago de Compostela, Spain , A. Parra5959affiliation: Benemérita
Universidad Autónoma de Puebla, Puebla, México , M. Pech3030affiliation:
Institute of Physics of the Czech Academy of Sciences, Prague, Czech Republic
, F. Pedreira7474affiliation: Instituto Galego de Física de Altas Enerxías
(I.G.F.A.E.), Universidad de Santiago de Compostela, Santiago de Compostela,
Spain , J. Pȩkala6464affiliation: Institute of Nuclear Physics PAN, Krakow,
Poland , R. Pelayo6161affiliation: Unidad Profesional Interdisciplinaria en
Ingeniería y Tecnologías Avanzadas del Instituto Politécnico Nacional (UPIITA-
IPN), México, D.F., México , J. Peña-Rodriguez2828affiliation: Universidad
Industrial de Santander, Bucaramanga, Colombia , L.A.S.
Pereira2020affiliation: Universidade Estadual de Campinas, IFGW, Campinas, SP,
Brazil , M. Perlin88affiliation: Instituto de Tecnologías en Detección y
Astropartículas (CNEA, CONICET, UNSAM), Buenos Aires, Argentina , L.
Perrone5252affiliation: Università del Salento, Dipartimento di Matematica e
Fisica “E. De Giorgi”, Lecce, Italy 4545affiliation: INFN, Sezione di Lecce,
Lecce, Italy , C. Peters3939affiliation: RWTH Aachen University, III.
Physikalisches Institut A, Aachen, Germany , S. Petrera4242affiliation: Gran
Sasso Science Institute, L’Aquila, Italy 4343affiliation: INFN Laboratori
Nazionali del Gran Sasso, Assergi (L’Aquila), Italy , J.
Phuntsok8585affiliation: Pennsylvania State University, University Park, PA,
USA , T. Pierog3737affiliation: Karlsruhe Institute of Technology, Institut
für Kernphysik, Karlsruhe, Germany , M. Pimenta6767affiliation: Laboratório de
Instrumentação e Física Experimental de Partículas – LIP and Instituto
Superior Técnico – IST, Universidade de Lisboa – UL, Lisboa, Portugal , V.
Pirronello5454affiliation: Università di Catania, Dipartimento di Fisica e
Astronomia, Catania, Italy 4444affiliation: INFN, Sezione di Catania, Catania,
Italy , M. Platino88affiliation: Instituto de Tecnologías en Detección y
Astropartículas (CNEA, CONICET, UNSAM), Buenos Aires, Argentina , J.
Poh8686affiliation: University of Chicago, Enrico Fermi Institute, Chicago,
IL, USA , B. Pont7575affiliation: IMAPP, Radboud University Nijmegen,
Nijmegen, The Netherlands , C. Porowski6464affiliation: Institute of Nuclear
Physics PAN, Krakow, Poland , R.R. Prado1818affiliation: Universidade de São
Paulo, Instituto de Física de São Carlos, São Carlos, SP, Brazil , P.
Privitera8686affiliation: University of Chicago, Enrico Fermi Institute,
Chicago, IL, USA , M. Prouza3030affiliation: Institute of Physics of the Czech
Academy of Sciences, Prague, Czech Republic , A. Puyleart8383affiliation:
Michigan Technological University, Houghton, MI, USA , S.
Querchfeld3535affiliation: Bergische Universität Wuppertal, Department of
Physics, Wuppertal, Germany , S. Quinn7979affiliation: Case Western Reserve
University, Cleveland, OH, USA , R. Ramos-Pollan2828affiliation: Universidad
Industrial de Santander, Bucaramanga, Colombia , J. Rautenberg3535affiliation:
Bergische Universität Wuppertal, Department of Physics, Wuppertal, Germany ,
D. Ravignani88affiliation: Instituto de Tecnologías en Detección y
Astropartículas (CNEA, CONICET, UNSAM), Buenos Aires, Argentina , M.
Reininghaus3737affiliation: Karlsruhe Institute of Technology, Institut für
Kernphysik, Karlsruhe, Germany , J. Ridky3030affiliation: Institute of Physics
of the Czech Academy of Sciences, Prague, Czech Republic , F.
Riehn6767affiliation: Laboratório de Instrumentação e Física Experimental de
Partículas – LIP and Instituto Superior Técnico – IST, Universidade de Lisboa
– UL, Lisboa, Portugal , M. Risse4141affiliation: Universität Siegen,
Fachbereich 7 Physik – Experimentelle Teilchenphysik, Siegen, Germany , P.
Ristori22affiliation: Centro de Investigaciones en Láseres y Aplicaciones,
CITEDEF and CONICET, Villa Martelli, Argentina , V. Rizi5353affiliation:
Università dell’Aquila, Dipartimento di Scienze Fisiche e Chimiche, L’Aquila,
Italy 4343affiliation: INFN Laboratori Nazionali del Gran Sasso, Assergi
(L’Aquila), Italy , W. Rodrigues de Carvalho1919affiliation: Universidade de
São Paulo, Instituto de Física, São Paulo, SP, Brazil , J. Rodriguez
Rojo99affiliation: Observatorio Pierre Auger, Malargüe, Argentina , M.J.
Roncoroni88affiliation: Instituto de Tecnologías en Detección y
Astropartículas (CNEA, CONICET, UNSAM), Buenos Aires, Argentina , M.
Roth3737affiliation: Karlsruhe Institute of Technology, Institut für
Kernphysik, Karlsruhe, Germany , E. Roulet11affiliation: Centro Atómico
Bariloche and Instituto Balseiro (CNEA-UNCuyo-CONICET), San Carlos de
Bariloche, Argentina , A.C. Rovero55affiliation: Instituto de Astronomía y
Física del Espacio (IAFE, CONICET-UBA), Buenos Aires, Argentina , P.
Ruehl4141affiliation: Universität Siegen, Fachbereich 7 Physik –
Experimentelle Teilchenphysik, Siegen, Germany , S.J. Saffi1212affiliation:
University of Adelaide, Adelaide, S.A., Australia , A. Saftoiu6868affiliation:
“Horia Hulubei” National Institute for Physics and Nuclear Engineering,
Bucharest-Magurele, Romania , F. Salamida5353affiliation: Università
dell’Aquila, Dipartimento di Scienze Fisiche e Chimiche, L’Aquila, Italy
4343affiliation: INFN Laboratori Nazionali del Gran Sasso, Assergi (L’Aquila),
Italy , H. Salazar5959affiliation: Benemérita Universidad Autónoma de Puebla,
Puebla, México , A. Saleh7171affiliation: Center for Astrophysics and
Cosmology (CAC), University of Nova Gorica, Nova Gorica, Slovenia , G.
Salina4848affiliation: INFN, Sezione di Roma “Tor Vergata”, Roma, Italy , F.
Sánchez88affiliation: Instituto de Tecnologías en Detección y Astropartículas
(CNEA, CONICET, UNSAM), Buenos Aires, Argentina , E.M. Santos1919affiliation:
Universidade de São Paulo, Instituto de Física, São Paulo, SP, Brazil , E.
Santos3030affiliation: Institute of Physics of the Czech Academy of Sciences,
Prague, Czech Republic , F. Sarazin8080affiliation: Colorado School of Mines,
Golden, CO, USA , R. Sarmento6767affiliation: Laboratório de Instrumentação e
Física Experimental de Partículas – LIP and Instituto Superior Técnico – IST,
Universidade de Lisboa – UL, Lisboa, Portugal , C. Sarmiento-
Cano88affiliation: Instituto de Tecnologías en Detección y Astropartículas
(CNEA, CONICET, UNSAM), Buenos Aires, Argentina , R. Sato99affiliation:
Observatorio Pierre Auger, Malargüe, Argentina , P. Savina5252affiliation:
Università del Salento, Dipartimento di Matematica e Fisica “E. De Giorgi”,
Lecce, Italy 4545affiliation: INFN, Sezione di Lecce, Lecce, Italy , M.
Schauer3535affiliation: Bergische Universität Wuppertal, Department of
Physics, Wuppertal, Germany , V. Scherini4545affiliation: INFN, Sezione di
Lecce, Lecce, Italy , H. Schieler3737affiliation: Karlsruhe Institute of
Technology, Institut für Kernphysik, Karlsruhe, Germany , M.
Schimassek3636affiliation: Karlsruhe Institute of Technology, Institute for
Experimental Particle Physics (ETP), Karlsruhe, Germany , M.
Schimp3535affiliation: Bergische Universität Wuppertal, Department of Physics,
Wuppertal, Germany , D. Schmidt3636affiliation: Karlsruhe Institute of
Technology, Institute for Experimental Particle Physics (ETP), Karlsruhe,
Germany , O. Scholten7676affiliation: KVI – Center for Advanced Radiation
Technology, University of Groningen, Groningen, The Netherlands
1414affiliation: Vrije Universiteit Brussels, Brussels, Belgium , P.
Schovánek3030affiliation: Institute of Physics of the Czech Academy of
Sciences, Prague, Czech Republic , F.G. Schröder3636affiliation: Karlsruhe
Institute of Technology, Institute for Experimental Particle Physics (ETP),
Karlsruhe, Germany , S. Schröder3535affiliation: Bergische Universität
Wuppertal, Department of Physics, Wuppertal, Germany , J.
Schumacher3939affiliation: RWTH Aachen University, III. Physikalisches
Institut A, Aachen, Germany , S.J. Sciutto44affiliation: IFLP, Universidad
Nacional de La Plata and CONICET, La Plata, Argentina , R.C.
Shellard1515affiliation: Centro Brasileiro de Pesquisas Fisicas, Rio de
Janeiro, RJ, Brazil , G. Sigl4040affiliation: Universität Hamburg, II.
Institut für Theoretische Physik, Hamburg, Germany , G. Silli88affiliation:
Instituto de Tecnologías en Detección y Astropartículas (CNEA, CONICET,
UNSAM), Buenos Aires, Argentina 3737affiliation: Karlsruhe Institute of
Technology, Institut für Kernphysik, Karlsruhe, Germany , O.
Sima6868affiliation: “Horia Hulubei” National Institute for Physics and
Nuclear Engineering, Bucharest-Magurele, Romania 10071007affiliation: also at
University of Bucharest, Physics Department, Bucharest, Romania , R.
Šmída3939affiliation: RWTH Aachen University, III. Physikalisches Institut A,
Aachen, Germany , G.R. Snow8787affiliation: University of Nebraska, Lincoln,
NE, USA , P. Sommers8585affiliation: Pennsylvania State University, University
Park, PA, USA , J.F. Soriano8181affiliation: Department of Physics and
Astronomy, Lehman College, City University of New York, Bronx, NY, USA , J.
Souchard3434affiliation: Univ. Grenoble Alpes, CNRS, Grenoble Institute of
Engineering Univ. Grenoble Alpes, LPSC-IN2P3, 38000 Grenoble, France, France ,
R. Squartini99affiliation: Observatorio Pierre Auger, Malargüe, Argentina , D.
Stanca6868affiliation: “Horia Hulubei” National Institute for Physics and
Nuclear Engineering, Bucharest-Magurele, Romania , S. Stanič7171affiliation:
Center for Astrophysics and Cosmology (CAC), University of Nova Gorica, Nova
Gorica, Slovenia , J. Stasielak6464affiliation: Institute of Nuclear Physics
PAN, Krakow, Poland , P. Stassi3434affiliation: Univ. Grenoble Alpes, CNRS,
Grenoble Institute of Engineering Univ. Grenoble Alpes, LPSC-IN2P3, 38000
Grenoble, France, France , M. Stolpovskiy3434affiliation: Univ. Grenoble
Alpes, CNRS, Grenoble Institute of Engineering Univ. Grenoble Alpes, LPSC-
IN2P3, 38000 Grenoble, France, France , A. Streich3636affiliation: Karlsruhe
Institute of Technology, Institute for Experimental Particle Physics (ETP),
Karlsruhe, Germany , F. Suarez88affiliation: Instituto de Tecnologías en
Detección y Astropartículas (CNEA, CONICET, UNSAM), Buenos Aires, Argentina
1111affiliation: Universidad Tecnológica Nacional – Facultad Regional Buenos
Aires, Buenos Aires, Argentina , M. Suárez-Durán2828affiliation: Universidad
Industrial de Santander, Bucaramanga, Colombia , T. Sudholz1212affiliation:
University of Adelaide, Adelaide, S.A., Australia , T.
Suomijärvi3232affiliation: Institut de Physique Nucléaire d’Orsay (IPNO),
Université Paris-Sud, Univ. Paris/Saclay, CNRS-IN2P3, Orsay, France , A.D.
Supanitsky88affiliation: Instituto de Tecnologías en Detección y
Astropartículas (CNEA, CONICET, UNSAM), Buenos Aires, Argentina , J.
Šupík3131affiliation: Palacky University, RCPTM, Olomouc, Czech Republic , Z.
Szadkowski6666affiliation: University of Łódź, Faculty of High-Energy
Astrophysics,Łódź, Poland , A. Taboada3737affiliation: Karlsruhe Institute of
Technology, Institut für Kernphysik, Karlsruhe, Germany , O.A.
Taborda11affiliation: Centro Atómico Bariloche and Instituto Balseiro (CNEA-
UNCuyo-CONICET), San Carlos de Bariloche, Argentina , A. Tapia2727affiliation:
Universidad de Medellín, Medellín, Colombia , C. Timmermans7777affiliation:
Nationaal Instituut voor Kernfysica en Hoge Energie Fysica (NIKHEF), Science
Park, Amsterdam, The Netherlands 7575affiliation: IMAPP, Radboud University
Nijmegen, Nijmegen, The Netherlands , C.J. Todero Peixoto1717affiliation:
Universidade de São Paulo, Escola de Engenharia de Lorena, Lorena, SP, Brazil
, B. Tomé6767affiliation: Laboratório de Instrumentação e Física Experimental
de Partículas – LIP and Instituto Superior Técnico – IST, Universidade de
Lisboa – UL, Lisboa, Portugal , G. Torralba Elipe7474affiliation: Instituto
Galego de Física de Altas Enerxías (I.G.F.A.E.), Universidad de Santiago de
Compostela, Santiago de Compostela, Spain , P. Travnicek3030affiliation:
Institute of Physics of the Czech Academy of Sciences, Prague, Czech Republic
, M. Trini7171affiliation: Center for Astrophysics and Cosmology (CAC),
University of Nova Gorica, Nova Gorica, Slovenia , M. Tueros44affiliation:
IFLP, Universidad Nacional de La Plata and CONICET, La Plata, Argentina , R.
Ulrich3737affiliation: Karlsruhe Institute of Technology, Institut für
Kernphysik, Karlsruhe, Germany , M. Unger3737affiliation: Karlsruhe Institute
of Technology, Institut für Kernphysik, Karlsruhe, Germany , M.
Urban3939affiliation: RWTH Aachen University, III. Physikalisches Institut A,
Aachen, Germany , J.F. Valdés Galicia6363affiliation: Universidad Nacional
Autónoma de México, México, D.F., México , I. Valiño7474affiliation: Instituto
Galego de Física de Altas Enerxías (I.G.F.A.E.), Universidad de Santiago de
Compostela, Santiago de Compostela, Spain , L. Valore5656affiliation:
Università di Napoli “Federico II”, Dipartimento di Fisica “Ettore Pancini”,
Napoli, Italy 4747affiliation: INFN, Sezione di Napoli, Napoli, Italy , P. van
Bodegom1212affiliation: University of Adelaide, Adelaide, S.A., Australia ,
A.M. van den Berg7676affiliation: KVI – Center for Advanced Radiation
Technology, University of Groningen, Groningen, The Netherlands , A. van
Vliet7575affiliation: IMAPP, Radboud University Nijmegen, Nijmegen, The
Netherlands , E. Varela5959affiliation: Benemérita Universidad Autónoma de
Puebla, Puebla, México , B. Vargas Cárdenas6363affiliation: Universidad
Nacional Autónoma de México, México, D.F., México , R.A.
Vázquez7474affiliation: Instituto Galego de Física de Altas Enerxías
(I.G.F.A.E.), Universidad de Santiago de Compostela, Santiago de Compostela,
Spain , D. Veberič3737affiliation: Karlsruhe Institute of Technology, Institut
für Kernphysik, Karlsruhe, Germany , C. Ventura2525affiliation: Universidade
Federal do Rio de Janeiro (UFRJ), Observatório do Valongo, Rio de Janeiro, RJ,
Brazil , I.D. Vergara Quispe44affiliation: IFLP, Universidad Nacional de La
Plata and CONICET, La Plata, Argentina , V. Verzi4848affiliation: INFN,
Sezione di Roma “Tor Vergata”, Roma, Italy , J. Vicha3030affiliation:
Institute of Physics of the Czech Academy of Sciences, Prague, Czech Republic
, L. Villaseñor5959affiliation: Benemérita Universidad Autónoma de Puebla,
Puebla, México , S. Vorobiov7171affiliation: Center for Astrophysics and
Cosmology (CAC), University of Nova Gorica, Nova Gorica, Slovenia , H.
Wahlberg44affiliation: IFLP, Universidad Nacional de La Plata and CONICET, La
Plata, Argentina , O. Wainberg88affiliation: Instituto de Tecnologías en
Detección y Astropartículas (CNEA, CONICET, UNSAM), Buenos Aires, Argentina
1111affiliation: Universidad Tecnológica Nacional – Facultad Regional Buenos
Aires, Buenos Aires, Argentina , A.A. Watson10001000affiliation: School of
Physics and Astronomy, University of Leeds, Leeds, United Kingdom , M.
Weber3838affiliation: Karlsruhe Institute of Technology, Institut für
Prozessdatenverarbeitung und Elektronik, Karlsruhe, Germany , A.
Weindl3737affiliation: Karlsruhe Institute of Technology, Institut für
Kernphysik, Karlsruhe, Germany , M. Wiedeński6666affiliation: University of
Łódź, Faculty of High-Energy Astrophysics,Łódź, Poland , L.
Wiencke8080affiliation: Colorado School of Mines, Golden, CO, USA , H.
Wilczyński6464affiliation: Institute of Nuclear Physics PAN, Krakow, Poland ,
M. Wirtz3939affiliation: RWTH Aachen University, III. Physikalisches Institut
A, Aachen, Germany , D. Wittkowski3535affiliation: Bergische Universität
Wuppertal, Department of Physics, Wuppertal, Germany , B.
Wundheiler88affiliation: Instituto de Tecnologías en Detección y
Astropartículas (CNEA, CONICET, UNSAM), Buenos Aires, Argentina , L.
Yang7171affiliation: Center for Astrophysics and Cosmology (CAC), University
of Nova Gorica, Nova Gorica, Slovenia , A. Yushkov3030affiliation: Institute
of Physics of the Czech Academy of Sciences, Prague, Czech Republic , E.
Zas7474affiliation: Instituto Galego de Física de Altas Enerxías (I.G.F.A.E.),
Universidad de Santiago de Compostela, Santiago de Compostela, Spain , D.
Zavrtanik7171affiliation: Center for Astrophysics and Cosmology (CAC),
University of Nova Gorica, Nova Gorica, Slovenia 7272affiliation: Experimental
Particle Physics Department, J. Stefan Institute, Ljubljana, Slovenia , M.
Zavrtanik7272affiliation: Experimental Particle Physics Department, J. Stefan
Institute, Ljubljana, Slovenia 7171affiliation: Center for Astrophysics and
Cosmology (CAC), University of Nova Gorica, Nova Gorica, Slovenia , L.
Zehrer7171affiliation: Center for Astrophysics and Cosmology (CAC), University
of Nova Gorica, Nova Gorica, Slovenia , A. Zepeda6060affiliation: Centro de
Investigación y de Estudios Avanzados del IPN (CINVESTAV), México, D.F.,
México , B. Zimmermann3838affiliation: Karlsruhe Institute of Technology,
Institut für Prozessdatenverarbeitung und Elektronik, Karlsruhe, Germany , M.
Ziolkowski4141affiliation: Universität Siegen, Fachbereich 7 Physik –
Experimentelle Teilchenphysik, Siegen, Germany , Z. Zong3232affiliation:
Institut de Physique Nucléaire d’Orsay (IPNO), Université Paris-Sud, Univ.
Paris/Saclay, CNRS-IN2P3, Orsay, France , F. Zuccarello5454affiliation:
Università di Catania, Dipartimento di Fisica e Astronomia, Catania, Italy
4444affiliation: INFN, Sezione di Catania, Catania, Italy

###### Abstract

We present a detailed study of the large-scale anisotropies of cosmic rays
with energies above 4 EeV measured using the Pierre Auger Observatory. For the
energy bins [4, 8] EeV and $E\geq 8$ EeV, the most significant signal is a
dipolar modulation in right ascension at energies above 8 EeV, as previously
reported. In this paper we further scrutinize the highest-energy bin by
splitting it into three energy ranges. We find that the amplitude of the
dipole increases with energy above 4 EeV. The growth can be fitted with a
power law with index $\beta=0.79\pm 0.19$. The directions of the dipoles are
consistent with an extragalactic origin of these anisotropies at all the
energies considered. Additionally we have estimated the quadrupolar components
of the anisotropy: they are not statistically significant. We discuss the
results in the context of the predictions from different models for the
distribution of ultrahigh-energy sources and cosmic magnetic fields.

astroparticle physics — cosmic rays

††slugcomment: Published in Astrophys. J as DOI:
10.3847/1538-4357/aae689††affiliationtext: —–

##  1 Introduction

The distribution of the arrival directions of cosmic rays (CR) with ultrahigh
energies is expected to play a major role in the quest to unveil the origin of
these particles. Hints of anisotropies at intermediate ($\sim 10^{\circ}$–
$20^{\circ}$) angular scales have been reported at the highest energies, above
$\sim 40$ EeV (where 1 ${\rm EeV}\equiv 10^{18}$ eV), by searching for a
localized excess in the cosmic-ray flux or for correlations with catalogs of
candidate populations of astrophysical sources (The Pierre Auger
Collaboration, 2015a, 2018; Matthews, 2017). None of these results has a
large-enough statistical significance to claim a detection. At $E\geq 8$ EeV,
a first-harmonic modulation in right ascension was detected with a
significance of more than 5.2$\sigma$ (The Pierre Auger Collaboration, 2017a).
The amplitude of the three-dimensional dipolar component that was determined
in this energy bin is $\sim 6.5$%, with its direction lying $\sim 125^{\circ}$
away from the Galactic center direction and hence indicating an extragalactic
origin for this flux.

The observation of a significant dipole, together with the lack of significant
anisotropies at small angular scales, implies that the Galactic and/or
extragalactic magnetic fields have a non-negligible effect on ultrahigh-energy
cosmic-ray (UHECR) trajectories. This is in fact expected in scenarios with
mixed composition where the CRs are heavier for increasing energies, in
agreement with the trends in the composition that have been inferred for
energies above a few EeV (The Pierre Auger Collaboration, 2014a, b, 2016,
2017d). Extragalactic magnetic fields can significantly spread the arrival
directions of heavy CR nuclei up to the highest energies observed, even for
nearby extragalactic sources, washing out small-scale anisotropies while still
leading to anisotropies at large (and eventually intermediate) angular
scales.111The root-mean square deflection of a particle of charge $Z$ and
energy $E$ in a homogeneous turbulent magnetic field with root mean square
amplitude $B$ and coherence length $l_{c}$ is $\delta_{rms}\simeq
30^{\circ}(B/{\rm nG})(4Z\,{\rm EeV}/E)\sqrt{l_{c}/{\rm Mpc}}\sqrt{L/10\,{\rm
Mpc}}$. For instance, oxygen nuclei with 30 EeV coming from a distance
$L\simeq 10$ Mpc are deflected by about $30^{\circ}$ for an extragalactic
field of 1 nG, which is consistent with the bounds from cosmic background
radiation and Faraday rotation measures (Durrer & Neronov, 2013). The Galactic
magnetic field is also expected to further modify the arrival directions of
extragalactic CRs, affecting both the amplitude and the direction of the
dipolar contribution to their flux and also inducing some higher multipolar
components when the deflections become sizable. It is not yet clear whether
the dipolar anisotropy observed arises from the diffusive propagation from
powerful sources in a few nearby galaxies or is instead reflecting the known
anisotropy in the distribution of galaxies within few hundred Mpc (Giler et
al., 1980; Berezinsky et al., 1990; Harari et al., 2014, 2015). A detailed
study of the amplitude and phase of the dipole as a function of energy, as
well as the possible emergence of structures at smaller angular scales, should
shed light on the distribution of the sources and on the strength and
structure of the magnetic fields responsible for the deflections.

We present here an extension of the analysis of the large-scale anisotropies
measured by the Pierre Auger Observatory for energies above 4 EeV. We obtain
both the dipolar and quadrupolar components in the two energy ranges that were
discussed in The Pierre Auger Collaboration (2015b, 2017a), i.e. [4, 8] EeV
and $E\geq 8$ EeV. We further analyze the bin above 8 EeV by splitting it into
three so as to explore how the amplitude and phase of the dipole changes with
energy. We then discuss the results obtained in the frame of scenarios
proposed for the origin of the large-scale anisotropies.

##  2 The Observatory and the dataset

The Pierre Auger Observatory, located near Malargüe, Argentina (The Pierre
Auger Collaboration, 2015c), has an array of surface detectors (SD) that
covers an area of 3000 km2. The array contains 1660 water-Cherenkov detectors,
1600 of which are deployed on a triangular grid with 1500 m spacing with the
remainder on a lattice of 750 m covering 23.5 km2. The array is overlooked by
27 fluorescence telescopes (FD) that are used to monitor the longitudinal
development of the air showers during moonless and clear nights, with a duty
cycle of about $13\%$. The SD has a duty cycle of about $100\%$ so that it
provides the vast majority of the events, and it is hence adopted for the
present study. The energy of these events is calibrated using hybrid events
measured simultaneously by both SD and FD.

The dataset analyzed in this work is the same one as that considered in The
Pierre Auger Collaboration (2017a), including events from the SD array with
1500 m separation detected from 2004 January 1 up to 2016 August 31. We retain
events with zenith angles up to $80^{\circ}$ and energies in excess of 4 EeV,
for which the array is fully efficient over the full zenith angle range
considered.222The smaller but denser sub-array with 750 m spacing among
detectors is fully efficient down to $\sim 0.3$ EeV for events with
$\theta<55^{\circ}$. The large-scale anisotropy results that can be obtained
using it will be presented elsewhere. The events with zenith angles
$\theta\leq 60^{\circ}$, referred to as vertical, have a different
reconstruction and calibration from the ones having $60^{\circ}<\theta\leq
80^{\circ}$, referred to as inclined events. The energies of the vertical
sample are corrected for atmospheric effects (The Pierre Auger Collaboration,
2017b), since, otherwise, systematic modulations of the rates as a function of
the hour of the day or of the season, and hence also as a function of right
ascension, could be induced. These effects arise from the dependence on the
atmospheric conditions of the longitudinal and lateral attenuation of the
electromagnetic component of the extended air showers. The energies are also
corrected for geomagnetic effects (The Pierre Auger Collaboration, 2011)
since, otherwise, systematic modulations in the azimuthal distribution could
result. Results from the inclined sample, for which the signal from the muonic
component of the extended air showers is dominant, have negligible dependence
on the atmospheric effects while the geomagnetic field effects are already
accounted for in the reconstruction. We include events for which at least 5 of
the 6 neighboring stations to the one with the largest signal are active at
the time at which the event is recorded (The Pierre Auger Collaboration,
2017a). Adopting this cut, the total integrated exposure of the array in the
period considered is 76,800 km2 sr yr. Selecting events with zenith angles up
to $80^{\circ}$ allows us to explore all the directions with declinations
between $-90^{\circ}\leq\delta\leq 45^{\circ}$, covering $85\%$ of the sky.
The total number of recorded events above the energy threshold of 4 EeV is
113,888.

##  3 Large-scale anisotropy results

Above full trigger efficiency for the SD array, which is achieved for $E\geq
4$ EeV when zenith angles up to $80^{\circ}$ are considered, the systematic
effects relevant for the distributions of the events in right ascension
($\alpha$) and in the azimuth angle ($\phi$) are well under control (see
Section 4). One can hence obtain a reliable estimate of the three-dimensional
dipole components, and eventually also higher multipoles, from the Fourier
analysis in these two angular coordinates after including appropriate weights
to account for known systematic effects (The Pierre Auger Collaboration,
2015b). The method adopted, based on the harmonic analyses on $\alpha$ and
$\phi$, does not require to have a detailed knowledge of the distribution of
the event directions that would be expected for an isotropic flux after all
detector, calibration and atmospheric effects are included. It thus has the
advantage of being largely insensitive to possible distortions in the zenith-
angle distribution of the events, such as those that could result from a
difference in the relative energy calibration of the vertical and inclined
samples.

The harmonic amplitudes of order $k$ are given by

$a_{k}^{x}=\frac{2}{\mathcal{N}}\sum_{i=1}^{N}w_{i}\cos(kx_{i})\ \ \ ,\ \ \
b_{k}^{x}=\frac{2}{\mathcal{N}}\sum_{i=1}^{N}w_{i}\sin(kx_{i}),$ (1)

with $x=\alpha$ or $\phi$. The sums run over the number of events $N$ in the
energy range considered and the normalization factor is
$\mathcal{N}=\sum_{i=1}^{N}w_{i}$. The weight factors $w_{i}$ take into
account the modulation in the exposure due to dead times of the detectors and
also account for the effects of the tilt of the array, which on average is
inclined $0.2^{\circ}$ towards $\phi_{0}\simeq-30^{\circ}$ (being the azimuth
measured anti-clockwise from the East direction). The weights, which are of
order unity, are given by (The Pierre Auger Collaboration, 2015b)

$\displaystyle w_{i}$ $\displaystyle=$ $\displaystyle\left[\Delta N_{\rm
cell}(\alpha_{i}^{0})(1+0.003\tan\theta_{i}\cos(\phi_{i}-\phi_{0}))\right]^{-1},$
(2)

with the factor $\Delta N_{\rm cell}(\alpha_{i}^{0})$ being the relative
variation of the total number of active detector cells for a given right
ascension of the zenith of the observatory $\alpha^{0}$, evaluated at the time
$t_{i}$ at which the $i$-th event is detected,
$\alpha_{i}^{0}=\alpha^{0}(t_{i})$, and $\phi_{i}$ and $\theta_{i}$ are the
azimuth and the zenith angle of the event, respectively.

The amplitude $r_{k}^{x}$ and phase $\varphi_{k}^{x}$ of the event rate
modulation are given by

$r_{k}^{x}=\sqrt{(a_{k}^{x})^{2}+(b_{k}^{x})^{2}},\hskip
20.0pt\varphi_{k}^{x}=\frac{1}{k}\arctan\frac{b_{k}^{x}}{a_{k}^{x}}.$ (3)

The probability that an amplitude equal to or larger than $r_{k}^{x}$ arises
as a fluctuation from an isotropic distribution is given by $P(\geq
r_{k}^{x})=\exp(-\mathcal{N}(r_{k}^{x})^{2}/4)$ (Linsley, 1975).

In this work we will focus on the first two harmonics. Note that the first-
harmonic amplitudes, corresponding to $k=1$, are the only ones present when
the flux is purely dipolar. The second order harmonics, with $k=2$, are also
relevant in the case of a flux with a non-vanishing quadrupolar contribution.

###  3.1 Harmonic analysis in right ascension and azimuth

Table 1 contains the results of the first and second harmonic analyses in
right ascension for the two energy bins that were considered in previous
publications, [4, 8] EeV and $E\geq 8$ EeV. The statistical uncertainties in
the harmonic coefficients are $\sqrt{2/\mathcal{N}}$. No significant harmonic
amplitude is observed in the first bin, while for energies above 8 EeV the
$p$-value for the first harmonic is $2.6\times 10^{-8}$. The results for the
first harmonics were already presented in The Pierre Auger Collaboration
(2017a).

Table 1: Results of the first and second harmonic analyses in right ascension. Energy [EeV] | events | $k$ | $a_{k}^{\alpha}$ | $b_{k}^{\alpha}$ | $r_{k}^{\alpha}$ | $\varphi_{k}^{\alpha}[^{\circ}]$ | $P(\geq r_{k}^{\alpha})$
---|---|---|---|---|---|---|---
4 - 8 | 81,701 | 1 | $0.001\pm 0.005$ | $0.005\pm 0.005$ | 0.005 | $80\pm 60$ | 0.60
|  | 2 | $-0.001\pm 0.005$ | $0.001\pm 0.005$ | 0.002 | $70\pm 80$ | 0.94
$\geq$ 8 | 32,187 | 1 | $-0.008\pm 0.008$ | $0.046\pm 0.008$ | 0.047 | $100\pm 10$ | $2.6\times 10^{-8}$
|  | 2 | $0.013\pm 0.008$ | $0.012\pm 0.008$ | 0.018 | $21\pm 12$ | 0.065

In Fig. 1, we display the distribution in right ascension of the normalized
rates in the energy bin $E\geq 8$ EeV. We also show with a black solid line
the first-harmonic modulation obtained through the Rayleigh analysis and the
distribution corresponding to a first plus second harmonic, with the
amplitudes and phases reported in Table 1.

Figure 1: Distribution in right ascension of the normalized rates of events
with energy above 8 EeV. The black (solid) and the blue (dashed) lines show
the distributions obtained from the weighted Fourier analysis corresponding to
a first harmonic ($\chi^{2}/{\rm dof}=1.02$, for 10 degrees of freedom) and
first plus second harmonics ($\chi^{2}/{\rm dof}=0.44$, for 8 degrees of
freedom), respectively.

In Table 2, we report the results of the harmonic analysis in the azimuth
angle. The $a_{1}^{\phi}$ amplitudes, that give a measure of the difference
between the flux coming from the East and that coming from the West,
integrated over time, should vanish if there are no spurious modulations
affecting the azimuth distribution. The values obtained are in fact compatible
with zero in the two bins. The $b_{1}^{\phi}$ amplitudes, that give a measure
of the flux modulation in the North-South direction, can be used to estimate
the component of the CR dipole along the Earth rotation axis. The most
significant amplitude is obtained for energies between 4 and 8 EeV and is
$b_{1}^{\phi}=-0.013\pm 0.005$, corresponding to an excess CR flux from the
South, that has a chance probability to arise from an isotropic distribution
of $0.009$. Regarding the second harmonic, none of the amplitudes found are
significantly different from zero.

Table 2: Results of the first and second harmonic analyses in azimuth. Energy [EeV] | $k$ | $a_{k}^{\phi}$ | $b_{k}^{\phi}$ | $P(\geq\mid a_{k}^{\phi}\mid)$ | $P(\geq\mid b_{k}^{\phi}\mid)$
---|---|---|---|---|---
4 - 8 | 1 | $-0.010\pm 0.005$ | $-0.013\pm 0.005$ | 0.045 | 0.009
| 2 | $0.002\pm 0.005$ | $-0.002\pm 0.005$ | 0.69 | 0.69
$\geq$ 8 | 1 | $-0.007\pm 0.008$ | $-0.014\pm 0.008$ | 0.38 | 0.08
| 2 | $-0.002\pm 0.008$ | $0.006\pm 0.008$ | 0.80 | 0.45

Figure 2 displays the maps, in equatorial coordinates, of the exposure-
weighted average of the flux inside a top-hat window of radius $45^{\circ}$,
so as to better appreciate the large-scale features, for the energy bins [4,
8] EeV and $E\geq 8$ EeV. An excess in the flux from the southern directions
is the predominant feature at energies between 4 and 8 EeV, while above 8 EeV
the excess comes from a region with right ascensions close to $100^{\circ}$,
with a corresponding deficit in the opposite direction, in accordance with the
results from the harmonic analyses in right ascension and azimuth.

Figure 2: Maps in equatorial coordinates of the CR flux, smoothed in windows of 45∘, for the energy bins [4, 8] EeV (left) and $E\geq 8$ EeV (right). The Galactic plane is represented with a dashed line and the Galactic center is indicated with a star. Table 3: Results of the first-harmonic analysis in right ascension in the three bins above 8 EeV. Energy [EeV] | events | $a_{1}^{\alpha}$ | $b_{1}^{\alpha}$ | $r_{1}^{\alpha}$ |  $\varphi_{1}^{\alpha}$ [∘] | $P(\geq r_{1}^{\alpha})$
---|---|---|---|---|---|---
8 - 16 | 24,070 | $-0.011\pm 0.009$ | $\phantom{-}0.044\pm 0.009$ | 0.046 | $104\pm 11$ | $3.7\times 10^{-6}$
16 - 32 | 6,604 | $\phantom{-}0.007\pm 0.017$ | $\phantom{-}0.050\pm 0.017$ | 0.051 | $82\pm 20$ | $0.014$
$\geq 32$ | 1,513 | $-0.03\pm 0.04$ | $0.05\pm 0.04$ | 0.06 | $115\pm 35$ | $0.26$
Table 4: Results of the first-harmonic analysis in azimuth in the three bins above 8 EeV. Energy [EeV] | $a_{1}^{\phi}$ | $b_{1}^{\phi}$ | $P(\geq|a_{1}^{\phi}|)$ | $P(\geq|b_{1}^{\phi}|)$
---|---|---|---|---
8 - 16 | $-0.013\pm 0.009$ | $-0.004\pm 0.009$ | 0.15 | 0.66
16 - 32 | $\phantom{-}0.003\pm 0.017$ | $-0.042\pm 0.017$ | 0.86 | 0.013
$\geq 32$ | $\phantom{-}0.05\pm 0.04$ | $-0.04\pm 0.04$ | 0.21 | 0.32

Given the significant first-harmonic modulation in right ascension that was
found in the bin with $E\geq 8$ EeV, we now divide this higher energy bin into
three to study the possible energy dependence of this signal. For this, we use
energy boundaries scaled by factors of two, i.e. considering the bins [8, 16]
EeV, [16, 32] EeV and $E\geq 32$ EeV. Table 3 reports the results for the
right ascension analysis in these new energy bins. The $p$-values for the
first-harmonic modulation in right ascension are $3.7\times 10^{-6}$ in the
[8, 16] EeV range, 0.014 in the [16, 32] EeV bin and 0.26 for energies above
32 EeV. Table 4 reports the results for the corresponding azimuth analysis in
these new energy bins.

###  3.2 Reconstruction of the CR dipole

We now convert the harmonic coefficients in right ascension and in azimuth
into anisotropy parameters on the sphere, assuming first that the dominant
component of the anisotropy is the dipole $\vec{d}$. The flux distribution can
then be parametrized as a function of the CR arrival direction ${\hat{u}}$ as

$\Phi({\hat{u}})=\Phi_{0}(1+{\vec{d}}\cdot{\hat{u}}).$ (4)

In this case, the amplitude of the dipole component along the rotation axis of
the Earth, $d_{z}$, that in the equatorial plane, $d_{\perp}$, and the right
ascension and declination of the dipole direction, ($\alpha_{d},\delta_{d})$,
are related to the first-harmonic amplitudes in right ascension and azimuth
through (The Pierre Auger Collaboration, 2015b)

$\displaystyle d_{z}$ $\displaystyle\simeq$
$\displaystyle\frac{b_{1}^{\phi}}{\cos\ell_{\rm
obs}\langle\sin\theta\rangle},$ $\displaystyle d_{\perp}$
$\displaystyle\simeq$
$\displaystyle\frac{r_{1}^{\alpha}}{\langle\cos\delta\rangle},$
$\displaystyle\alpha_{d}$ $\displaystyle=$
$\displaystyle\varphi_{1}^{\alpha},$ $\displaystyle\delta_{d}$
$\displaystyle=$ $\displaystyle\arctan\left(\frac{d_{z}}{d_{\perp}}\right),$
(5)

where $\langle\cos\delta\rangle\simeq 0.7814$ is the mean cosine of the
declinations of the events, $\langle\sin\theta\rangle\simeq 0.6525$ the mean
sine of the event zenith angles, and $\ell_{\rm obs}\simeq-35.2^{\circ}$ is
the latitude of the Observatory. Note that, as is well known, when the
coverage of the sky is not complete a coupling between the reconstructed
multipoles can occur. The dipole parameters inferred from this set of
relations can thus receive extra contributions from higher-order multipoles,
something that will be explicitly checked in the next subsection in the case
of a non-negligible quadrupolar contribution to the flux.

Table 5: Three-dimensional dipole reconstruction for energies above 4 EeV. We show the results obtained for the two bins previously reported (The Pierre Auger Collaboration, 2017a), i.e. between 4 and 8 EeV and above 8 EeV, as well as dividing the high-energy range into three bins. Energy [EeV] | $d_{\perp}$ | $d_{z}$ | $d$ |  $\alpha_{d}$ [∘] |  $\delta_{d}$ [∘]
---|---|---|---|---|---
interval | median |  |  |  |  |
4 - 8 | 5.0 | $0.006^{+0.007}_{-0.003}$ | $-0.024\pm 0.009$ | $0.025^{+0.010}_{-0.007}$ | $80\pm 60$ | $-75^{+17}_{-8}$
$\geq 8$ | 11.5 | $0.060^{+0.011}_{-0.010}$ | $-0.026\pm 0.015$ | $0.065^{+0.013}_{-0.009}$ | $100\pm 10$ | $-24^{+12}_{-13}$
8 - 16 | 10.3 | $0.058^{+0.013}_{-0.011}$ | $-0.008\pm 0.017$ | $0.059^{+0.015}_{-0.008}$ | $104\pm 11$ | $-8^{+16}_{-16}$
16 - 32 | 20.2 | $0.065^{+0.025}_{-0.018}$ | $-0.08\pm 0.03$ | $0.10^{+0.03}_{-0.02}$ | $82\pm 20$ | $-50^{+15}_{-14}$
$\geq 32$ | 39.5 | $0.08^{+0.05}_{-0.03}$ | $-0.08\pm 0.07$ | $0.11^{+0.07}_{-0.03}$ | $115\pm 35$ | $-46^{+28}_{-26}$

In the two upper rows of Table 5, we show the reconstructed dipole components
for the energy bins previously studied, [4, 8] EeV and $E\geq 8$ EeV. The
results for the three new bins above 8 EeV are reported in the lower three
rows. The uncertainties in the amplitude and phase correspond to the $68\%$
confidence level of the marginalized probability distribution functions.

In Table 5 a growth of the dipolar amplitude $d$ with increasing energies is
observed. Adopting for the energy dependence of the dipole amplitude a power-
law behavior $d(E)=d_{10}\times(E/10~{}\rm{EeV})^{\beta}$, we perform a
maximum-likelihood fit to the values measured in the four bins above 4 EeV. We
consider a likelihood function ${\cal
L}(d_{10},\beta)=\prod_{i=1}^{4}f(\vec{d}_{i};d_{10},\beta)$, where in each
energy bin $f$ is given by a three-dimensional Gaussian for the dipole vector
$\vec{d}=d(E)(\cos\delta\cos\alpha,\cos\delta\sin\alpha,\sin\delta)$, centered
at the measured dipole values and with the dispersions
$\sigma_{x}=\sigma_{y}=\sqrt{2/\mathcal{N}}/\langle\cos\delta\rangle$ and
$\sigma_{z}=\sqrt{2/\mathcal{N}}/(\langle\sin\theta\rangle\cos\ell_{\rm
obs})$, marginalized over the angular variables $\alpha$ and $\delta$. The fit
leads to a reference amplitude $d_{10}=0.055\pm 0.008$ and a power-law index
$\beta=0.79\pm 0.19$.333Regarding the goodness of the fit, we have checked
that, for a model in which the dipole amplitude follows the power-law
obtained, a better agreement than the one found with the actual data is
expected to result in about 50% of the realizations. A fit with an energy-
independent dipole amplitude ($\beta=0$) is disfavored at the level of
3.7$\sigma$ by a likelihood-ratio test.

Figure 3: Evolution with energy of the amplitude (left panel) and direction
(right panel) of the three-dimensional dipole determined in different energy
bins above 4 EeV. In the sky map in Galactic coordinates of the right panel
the dots represent the direction towards the galaxies in the 2MRS catalog that
lie within 100 Mpc and the cross indicates the direction towards the flux-
weighted dipole inferred from that catalog.

The left panel of Fig. 3 shows the amplitude of the dipole as a function of
the energy, with the data points centered at the median energy in each of the
four bins above 4 EeV, as well as the power-law fit. The right panel is a map,
in Galactic coordinates, showing the 68% CL sky regions for the dipole
direction in the same bins. They all point towards a similar region of the
sky, and in order of increasing energies they are centered at Galactic
coordinates ($\ell,b)=(287^{\circ},-32^{\circ})$, $(221^{\circ},-3^{\circ})$,
$(257^{\circ},-33^{\circ})$ and $(259^{\circ},-11^{\circ})$, respectively.
With the present accuracy no clear trend in the change of the dipole direction
as a function of energy can be identified. In the background of Fig. 3, we
indicate with dots the location of the observed galaxies from the 2MRS catalog
that lie within 100 Mpc and also show with a cross the reconstructed 2MRS
flux-weighted dipole direction (Erdogdu et al., 2006), which could be expected
to be related to the CR dipole direction if the galaxies were to trace the
distribution of the UHECR sources and the effects of the magnetic field
deflections were ignored.

Figure 4 shows sky maps, in Galactic coordinates, of the ratio between the
observed flux and that expected for an isotropic distribution, averaged in
angular windows of 45∘ radius, for the different energy bins above 4 EeV. The
location of the main overdense regions can be observed. Note that the color
scale is kept fixed, so as to better appreciate the increase in the amplitude
of the flux variations with increasing energies.

Figure 4: Maps in Galactic coordinates of the ratio between the number of
observed events in windows of 45∘ over those expected for an isotropic
distribution of arrival directions, for the four energy bins above 4 EeV.

###  3.3 Reconstruction of a dipole plus quadrupole pattern

In order to quantify the amplitude of the quadrupolar moments and their
effects on the dipole reconstruction, we assume now that the angular
distribution of the CR flux can be well approximated by the combination of a
dipole plus a quadrupole. In this case, the flux can be parametrized as

$\Phi({\hat{u}})=\Phi_{0}\left(1+{\vec{d}}\cdot{\hat{u}}+\frac{1}{2}\sum_{i,j}Q_{ij}u_{i}u_{j}\right),$
(6)

with $Q_{ij}$ being the symmetric and traceless quadrupole tensor.

Table 6: Results of the first harmonic in right ascension, separating the events in those arriving from the southern (S) and northern (N) hemispheres. Energy [EeV] | Hemisphere | $N$ | $a_{1}^{\alpha}$ | $b_{1}^{\alpha}$ | $r_{1}^{\alpha}$ |  $\varphi_{1}^{\alpha}$ [∘]
---|---|---|---|---|---|---
4 - 8 | S | 65,183 | $0.003\pm 0.005$ | $0.005\pm 0.005$ | $0.006$ | $60\pm 50$
| N | 16,518 | $-0.009\pm 0.011$ | $0.003\pm 0.011$ | $0.010$ | $160\pm 60$
$\geq$ 8 | S | 25,823 | $-0.011\pm 0.009$ | $0.047\pm 0.009$ | $0.048$ | $103\pm 10$
| N | 6,364 | $0.0024\pm 0.018$ | $0.041\pm 0.018$ | $0.041$ | $87\pm 25$

The components of the dipole and of the quadrupole can be estimated as in The
Pierre Auger Collaboration (2015b). They are obtained from the first and
second harmonics in right ascension and azimuth, given in Tables 1 and 2, as
well as considering the first harmonic in right ascension of the events coming
from the northern and southern hemispheres separately, which are reported in
Table 6. From these results we obtained the three dipole components and the
five independent quadrupole components that are reported in Table 7, for the
two energy bins [4, 8] EeV and $E\geq 8$ EeV. The only non-vanishing
correlation coefficients between the quantities reported in Table 7 are
$\rho(d_{x},Q_{xz})=\rho(d_{y},Q_{yz})=0.63$ and $\rho(d_{z},Q_{zz})=0.91$.
The nine components of the quadrupole tensor can be readily obtained from
those in Table 7 exploiting the condition that the tensor be symmetric and
traceless. None of the the quadrupole components is statistically significant
and the reconstructed dipoles are consistent with those obtained before under
the assumption that no higher multipoles are present. They are also consistent
with results obtained in past analyses in The Pierre Auger Collaboration
(2015b) and The Pierre Auger & Telescope Array Collaborations (2014). Note
that allowing for the presence of a quadrupole leads to larger uncertainties
in the reconstructed dipole components, specially in the one along the Earth
rotation axis due to the incomplete sky coverage present around the North
celestial pole. Indeed, in both energy bins the uncertainties in the
equatorial dipole components increase by $\sim 30$% while those on $d_{z}$
increase by a factor of about 2.7.

From the components of the quadrupole tensor it is possible to define an
average quadrupole amplitude, $Q\equiv\sqrt{\sum_{ij}Q_{ij}^{2}/9}$. This
amplitude is directly related to the usual angular power-spectrum moments
$C_{\ell}$ through $Q^{2}=(50/3)C_{2}/C_{0}$, and it is hence a rotationally
invariant quantity. From the results given in Table 7 one obtains that
$Q=0.012\pm 0.009$ for $4\leq E/{\rm EeV}<8$ and $Q=0.032\pm 0.014$ for $E\geq
8$ EeV. We note that for isotropic realizations, 95% of the values of $Q$
would be below 0.037 and 0.060, respectively, showing that the quadrupole
amplitude is consistent with isotropic expectations.

Table 7: Reconstructed dipole and quadrupole components in the two energy bins. The $x$ axis lies in the direction $\alpha=0$. Energy [EeV] | $d_{i}$ | $Q_{ij}$
---|---|---
4 - 8 | $d_{x}=-0.005\pm 0.008$ | $Q_{zz}=-0.01\pm 0.04$
| $d_{y}=0.005\pm 0.008$ | $Q_{xx}-Q_{yy}=-0.007\pm 0.029$
| $d_{z}=-0.032\pm 0.024$ | $Q_{xy}=0.004\pm 0.015$
|  | $Q_{xz}=-0.020\pm 0.019$
|  | $Q_{yz}=-0.005\pm 0.019$
$\geq 8$ | $d_{x}=-0.003\pm 0.013$ | $Q_{zz}=0.02\pm 0.06$
| $d_{y}=0.050\pm 0.013$ | $Q_{xx}-Q_{yy}=0.08\pm 0.05$
| $d_{z}=-0.02\pm 0.04$ | $Q_{xy}=0.038\pm 0.024$
|  | $Q_{xz}=0.02\pm 0.03$
|  | $Q_{yz}=-0.03\pm 0.03$

##  4 On the dipole uncertainties

Let us now discuss the impact of the different systematic effects that we have
accounted for. The variations in the array size with time and the atmospheric
variations are the two systematic effects that could influence the estimation
of the equatorial component of the dipole. Had we neglected the changes in the
array size with time it would have changed $d_{\perp}$, with the dataset
considered, by less than $4\times 10^{-4}$, and not performing the atmospheric
corrections would have changed $d_{\perp}$ by less than $10^{-3}$ (the precise
amount of the change in these two cases depends on the particular phase of
$d_{\perp}$ in each energy bin). The small values of the effects due to
atmospheric corrections and changes in the exposure are mostly due to the fact
that for the present dataset they are averaged over a period of more than 12
years. On the other hand, the tilt of the array and the effects of the
geomagnetic field on the shower development can influence the estimation of
the North-South dipole component. The net effect of including the tilt of the
array when performing observations up to zenith angles of 80∘ is to change
$d_{z}$ by +0.004, which is small since the Observatory site is in a very flat
location. The largest effect is that associated to the geomagnetic
corrections, which change $d_{z}$ by +0.011. Since these corrections are known
with an uncertainty of about 25% (The Pierre Auger Collaboration, 2011), they
leave as a remnant a systematic uncertainty on $d_{z}$ of about 0.003.

A standard check to verify that all the systematic effects that can influence
the right-ascension distribution are accurately accounted for, in particular
those arising from atmospheric effects or from the variations in the exposure
of the array with time, is to look at the Fourier amplitude at the solar and
anti-sidereal frequencies (Farley & Storey, 1954). No significant physical
modulation of cosmic rays should be present at these frequencies for an
anisotropy of astrophysical origin. We report in Table 8 the results of the
first-harmonic analysis at these two frequencies. One can see that the flux
modulations at both the solar and anti-sidereal frequencies, having amplitudes
with a sizable chance probability, are in fact compatible with zero for the
two energy ranges considered.

Table 8: First-harmonic amplitude, and probability for it to arise as a fluctuation of an isotropic distribution, at the solar and anti-sidereal frequencies. Energy | solar | anti-sidereal
---|---|---
$[$EeV$]$ | $r_{1}$ | $P(\geq r_{1})$ | $r_{1}$ | $P(\geq r_{1})$
4 - 8 | $0.006$ | 0.48 | $0.004$ | 0.76
$\geq 8$ | $0.007$ | 0.69 | $0.011$ | 0.36

Regarding the effects of possible systematic distortions in the zenith-angle
distributions, such as those that could arise for instance from a mismatch
between the energy calibration of vertical and inclined events, they could
affect the dipole components by modifying the quantities
$\langle\sin\theta\rangle$ or $\langle\cos\delta\rangle$ entering in Eq. (5).
Considering for instance the $E\geq 8$ EeV bin, we note that for these events
$\langle\sin\theta\rangle=0.6525$ while the expected value that is obtained
from simulations with a dipolar distribution with amplitude and direction
similar to the reconstructed one and the same number of events is
$\langle\sin\theta\rangle=0.6558\pm 0.0013$ (while an isotropic distribution
would lead to a central value $\langle\sin\theta\rangle=0.6565$). If the
difference between the observed and the expected values of
$\langle\sin\theta\rangle$, which is less than 1%, were attributed to
systematic effects in the zenith distribution, the impact that this would have
on the inferred dipole component $d_{z}$ would be negligible in comparison to
its statistical uncertainty, which is about 50%. Similarly, the value of the
average declination cosine in the data is $\langle\cos\delta\rangle=0.7814$,
while that expected for the inferred dipole obtained through simulations is
$0.7811\pm 0.0013$, showing that possible systematic effects on $d_{\perp}$
arising from this quantity are even smaller. This is a verification that the
method adopted is largely insensitive to possible systematic distortions in
the zenith or declination distribution of the events.

##  5 Discussion

The most significant anisotropy in the distribution of cosmic rays observed in
the studies performed above 4 EeV is the large-scale dipolar modulation of the
flux at energies above 8 EeV. The maximum of this modulation lies in Galactic
coordinates at $(l,b)=(233^{\circ},-13^{\circ})$, with an uncertainty of about
15∘. This is $~{}125^{\circ}$ away from the Galactic center direction,
indicating an extragalactic origin for these ultrahigh-energy particles. As
examples of the large-scale anisotropies expected from a Galactic CR
component, we show in Fig. 5 the direction of the dipole that would result for
cosmic rays coming from sources distributed as the luminous matter in the
Galaxy, taken as a bulge and an exponential disk modeled as in Weber & Boer
(2010). The CRs are propagated through the Galactic magnetic field, described
with the models proposed in Jansson & Farrar (2012) and Pshirkov et al.
(2011), for different values of the CR rigidity, $R=E/eZ$ (with $eZ$ the
charge of the CR nucleus). The results are obtained by actually backtracking
the trajectories of antiparticles leaving the Earth (Thielheim & Langhoff,
1968) from a dense grid of equally spaced directions and obtaining the
associated weight for each direction by integrating the matter density along
their path through the Galaxy (Karakula et al., 1972). We obtain in this way
an estimation of the flux that would arrive at the Earth from a continuous
distribution of sources isotropically emitting cosmic rays and with a density
proportional to that of the luminous matter. The points in the plot indicate
the direction of the reconstructed dipolar component of the flux maps
obtained. The direction of the resulting dipoles lie very close to the
Galactic center for particles with the highest rigidities considered, and as
the rigidity decreases they slowly move away from it towards increasing
Galactic longitudes (closer to the direction of the inner spiral arm which is
at $(l,b)\simeq(80^{\circ},0^{\circ})$). Note that at 10 EeV the inferred
average values of the CR charges is $Z\sim 1.7$ to 5, depending on the
hadronic models adopted for the analysis, while in the lower energy bin the
inferred charges are actually smaller (The Pierre Auger Collaboration, 2014b),
justifying the range of rigidities considered. The resulting dipole directions
obtained in these Galactic scenarios are quite different from the dipole
direction observed above 8 EeV, clearly showing that in a standard scenario
the dominant contribution to the dipolar modulation at these energies cannot
arise from a Galactic component. Besides the dipole direction, let us note
that the amplitude of the dipole (and also the amplitudes of the quadrupole)
turns out to be large in the models of purely Galactic cosmic rays depicted in
the figure. In particular, we find that $d>0.8$ for all the rigidities
considered, showing that the dominant component at these energies needs to be
much more isotropic, and hence of likely extragalactic origin.

Figure 5: Map in Galactic coordinates of the direction of the dipolar
component of the flux for different particle rigidities for cosmic rays coming
from Galactic sources and propagating in the Galactic magnetic-field model of
Jansson & Farrar (2012) (blue points) and the bisymmetric model of Pshirkov et
al. (2011) (red points). The points show the results for the following
rigidities: 64 EV, 32 EV, 16 EV, 8 EV, 4 EV and 2 EV (with increasing distance
from the Galactic center). We also show in purple the observed direction of
the dipole for $E\geq 8$ EeV and the $68\%$ CL region for it. The background
in gray indicates the integrated matter density profile assumed for the
Galactic source distribution (Weber & Boer, 2010).

Regarding the possible origin of the dipolar CR anisotropy, we note that the
relative motion of the observer with respect to the rest frame of cosmic rays
is expected to give rise to a dipolar modulation of the flux, known as the
Compton–Getting effect (Compton & Getting, 1935). For particles with a power-
law energy spectrum d$\Phi/{\rm d}E\propto E^{-\gamma}$, the resulting dipolar
amplitude is $d_{\rm CG}=(v/c)(\gamma+2)$, with $v/c$ the velocity of the
observer normalized to the speed of light. In particular, if the rest frame of
the cosmic rays were the same as that of the cosmic microwave background, the
dipole amplitude would be $d_{\rm CG}\simeq 0.006$ (Kachelriess & Serpico,
2006), an order of magnitude smaller than the observed dipole above 8 EeV.
Thus, the Compton–Getting effect is predicted to give only a sub-dominant
contribution to the dipole measured for energies above 8 EeV.

Plausible explanations for the observed dipolar-like distribution include the
diffusive propagation from the closest extragalactic source(s) or that it be
due to the inhomogeneous distribution of the sources in our cosmic
neighborhood (Giler et al., 1980; Berezinsky et al., 1990; Harari et al.,
2014, 2015). The expected amplitude of the resulting dipole depends in these
cases mostly on the number density of the source distribution, $\rho$, with
only a mild dependence on the amplitude of the extragalactic magnetic
field.444This is because, as the value of the magnetic field is increased, for
any given nearby source closer than the magnetic horizon its contribution to
the CR density increases as it gets enhanced by the diffusion while, on the
other hand, the value of the dipolar component of its anisotropy decreases in
such a way that both changes compensate for each other to a large extent. For
homogeneous source distributions with $\rho\sim(10^{-5}-10^{-3})$ Mpc-3,
spanning the range between densities of galaxy clusters, jetted radio-
galaxies, Seyfert galaxies and starburst galaxies, the dipole amplitude turns
out to be at the level of few percent at $E\sim 10$ EeV, both for scenarios
with light (Harari et al., 2014) and with mixed CR compositions (Harari et
al., 2015). A density of sources smaller by a factor of ten leads on average
to a dipolar amplitude larger by approximately a factor of two. An enhanced
anisotropy could result if the sources were to follow the inhomogeneous
distribution of the local galaxies, with a dipole amplitude larger by a factor
of about two with respect to the case of a uniform distribution of the same
source density. The expected behavior is exemplified in Figure 6 where we have
included the observed dipole amplitude values together with the predictions
from Harari et al. (2015) for a scenario with five representative mass
components (H, He, C, Si and Fe) having an $E^{-2}$ spectrum with a sharp
rigidity cutoff at 6 EV and adopting a source density $\rho=10^{-4}\,{\rm
Mpc}^{-3}$ (ignoring the effects of the Galactic magnetic field). The data
show indications of a growth in the amplitude with increasing energy that is
similar to the one obtained in the models. Note that this kind of scenario is
also in line with the composition favored by Pierre Auger Observatory data
(The Pierre Auger Collaboration, 2017c).

Figure 6: Comparison of the dipole amplitude as a function of energy with
predictions from models (Harari et al., 2015) with mixed composition and a
source density $\rho=10^{-4}\,{\rm Mpc}^{-3}$. Cosmic rays are propagated in
an isotropic turbulent extragalactic magnetic field with rms amplitude of 1 nG
and a Kolmogorov spectrum with coherence length equal to 1 Mpc (with the
results having only mild dependence on the magnetic-field strength adopted).
The gray line indicates the mean value for simulations with uniformly
distributed sources, while the blue one shows the mean value for realizations
with sources distributed as the galaxies in the 2MRS catalog. The bands
represent the dispersion for different realizations of the source
distribution. The steps observed reflect the rigidity cutoff of the different
mass components.

Regarding the direction of the dipolar modulation, it is important to take
into account the effect of the Galactic magnetic field on the trajectories of
extragalactic cosmic rays reaching the Earth.555These deflections can not only
lead to a significant change in the dipole direction and in its amplitude, but
they also generate some higher order harmonics even if pure dipolar modulation
is only present outside the Galaxy (Harari et al., 2010). The facts that the
Galactic magnetic field model is not well known and that the CR composition is
still uncertain make it difficult to infer the dipole direction associated to
the flux outside the Galaxy from the measured one. As an example, we show in
Fig. 7 the change in the direction of an originally dipolar distribution after
traversing a particular Galactic magnetic field, modeled in this example
following Jansson & Farrar (2012). The arrows start in a grid of initial
directions for the dipole outside the Galaxy and indicate the dipole
directions that would be reconstructed at the Earth for different CR
rigidities. The points along the lines indicate the directions for rigidities
of 32 EV, 16 EV, 8 EV and the tip of the arrow those for 4 EV, respectively.
We see that after traversing the Galactic magnetic field the extragalactic
dipoles originally pointing in one half of the sky, essentially that of
positive Galactic longitudes, tend to have their directions aligned closer to
the inner spiral arm, at $(l,b)\simeq(80^{\circ},0^{\circ})$ (indicated with
an I in the plot). On the other hand, those originally pointing to the
opposite half tend to align their directions towards the outer spiral arm, at
$(l,b)\simeq(-100^{\circ},0^{\circ})$ (indicated with an O in the plot). The
measured dipole direction for $E\geq 8$ EeV is indicated with the shaded area
and one can see that it lies not far from the outer spiral arm direction. The
line color shows the resulting suppression factor of the dipole amplitude
after the effects of the Galactic magnetic field deflections are taken into
account. Qualitatively similar results, showing a tendency for the direction
of the dipolar component to align with the spiral arm directions, are also
obtained when adopting instead the Galactic magnetic field from Pshirkov et
al. (2011).

Figure 7: Change of the direction of the dipolar component of an extragalactic
flux after traversing the Galactic magnetic field, modeled as in Jansson &
Farrar (2012). We consider a grid (black circles) corresponding to the
directions of a purely dipolar flux outside the Galaxy. Points along the lines
indicate the reconstructed directions for different values of the particle
rigidity: 32 EV, 16 EV, 8 EV and, at the tip of the arrow, 4 EV, respectively.
The line color indicates the resulting fractional change of the dipole
amplitude. The observed direction of the dipole for energies $E\geq 8$ EeV is
indicated by the gray cross, with the shaded area indicating the $68\%$ CL
region. The labels I and O indicate the directions towards the inner and outer
spiral arms, respectively.

The detection of large-scale anisotropies could open the possibility to
jointly probe the distribution of UHECR sources and that of extragalactic
magnetic fields (Sigl et al., 2004). In particular, the growth of the dipole
with energy is reproduced in the scenarios considered in Wittkowski & Kampert
(2018), di Matteo & Tinyakov (2018) and Hackstein et al. (2018), which further
investigate the expected strength of the quadrupolar moments, none of which is
found to be significant in our study. In Wittkowski & Kampert (2018) actually
the full angular power spectrum $C_{l}$ up to $l=32$ is obtained considering
the mixed CR composition scenarios with a common maximum rigidity at the
sources that best fit the Pierre Auger Observatory results (Wittkowski, 2017).
They found that only for $l=1$, corresponding to the dipole, is the $C_{l}$
expected to be greater than the 5$\sigma$ CL range of isotropy when a number
of events like that recorded by the Pierre Auger Observatory is considered. In
di Matteo & Tinyakov (2018) the dipole and quadrupole amplitudes are examined
under several assumptions on the mass composition, for a scenario of sources
distributed as in the 2MASS Galaxy Redshift Catalog. The amplitudes of the
dipole moment reported in the present work can be well reproduced in their
scenario with intermediate mass nuclei. In Hackstein et al. (2018) pure proton
or pure iron compositions and different magnetogenesis and source distribution
scenarios are considered. For the proton case, the first multipole above 8 EeV
is generally lower than the measured value (see also Hackstein et al. (2016)),
while a value closer to the observed one is obtained for the pure iron case.
It is also concluded that UHECR large-scale anisotropies do not carry much
information on the genesis and distribution of extragalactic magnetic fields.
The dependence of the dipolar anisotropies on the root mean square amplitude
and coherence length of a turbulent homogeneous intergalactic magnetic field
was studied in Globus & Piran (2017), for proton, He and CNO source models.
They found that the dipole amplitudes for $E\geq 8$ EeV turn out to be of the
order of the one observed for a range of magnetic-field parameters and their
model is consistent with an increase of the dipole amplitude with energy. In
summary, the dipolar amplitude mostly depends on the large scale distribution
of the sources and their density, but it is not very sensitive to the details
of the extragalactic magnetic field. Information on the extragalactic magnetic
field parameters may eventually be obtained from the determination of
anisotropies on smaller angular scales, for which a larger number of events
would be needed.

##  6 Conclusions

We have extended the analysis of the large angular scale anisotropies of the
cosmic rays detected by the Pierre Auger Observatory for energies above 4 EeV.
The harmonic analyses both in right ascension and in azimuth allowed us to
reconstruct the three components of the dipole under the assumption that the
higher multipoles are sub-dominant. As already described in The Pierre Auger
Collaboration (2017a), for the bin above 8 EeV the first-harmonic modulation
in right ascension has a $p$-value of $2.6\times 10^{-8}$. The amplitude of
the three-dimensional reconstructed dipole is $d=0.065^{+0.013}_{-0.009}$ for
$E\geq 8$ EeV, pointing towards Galactic coordinates
$(l,b)=(233^{\circ},-13^{\circ})$, suggestive of an extragalactic origin for
these CRs. For $4\,{\rm EeV}\leq E<8$ EeV the dipole amplitude is
$d=0.025^{+0.010}_{-0.007}$. Allowing for the presence of a quadrupolar
modulation in the distribution of arrival directions, we determined here the
three dipolar and the five quadrupolar components in the [4, 8] EeV and $E\geq
8$ EeV bins. None of the quadrupolar components turned out to be statistically
significant and the dipolar components are consistent with the dipole-only
results.

We also split the bin above 8 EeV into three to study a possible dependence of
the dipole with energy. The direction of the dipole suggests an extragalactic
origin for the cosmic-ray anisotropies in each energy bin. We find that the
amplitude increases with energy above 4 EeV, with a constant amplitude being
disfavored at the 3.7$\sigma$ level. A growing amplitude of the dipole with
increasing energies is expected due to the smaller deflections suffered by
cosmic rays at higher rigidities. The dipole amplitude is also enhanced for
increasing energies due to the increased attenuation suffered by the CR from
distant sources, which implies an increase in the relative contribution to the
flux arising from the nearby sources, leading to a more anisotropic flux
distribution.

Further clues to understand the origin of the UHECRs are expected to result
from the study of the anisotropies at small or intermediate angular scales for
energy thresholds even higher than those considered here. Also the extension
of the studies of anisotropies at large angular scales to lower energies may
provide crucial information to understand the transition between the Galactic
and extragalactic origins of cosmic rays.

## Acknowledgments

The successful installation, commissioning, and operation of the Pierre Auger
Observatory would not have been possible without the strong commitment and
effort from the technical and administrative staff in Malargüe. We are very
grateful to the following agencies and organizations for financial support:

Argentina – Comisión Nacional de Energía Atómica; Agencia Nacional de
Promoción Científica y Tecnológica (ANPCyT); Consejo Nacional de
Investigaciones Científicas y Técnicas (CONICET); Gobierno de la Provincia de
Mendoza; Municipalidad de Malargüe; NDM Holdings and Valle Las Leñas; in
gratitude for their continuing cooperation over land access; Australia – the
Australian Research Council; Brazil – Conselho Nacional de Desenvolvimento
Científico e Tecnológico (CNPq); Financiadora de Estudos e Projetos (FINEP);
Fundação de Amparo à Pesquisa do Estado de Rio de Janeiro (FAPERJ); São Paulo
Research Foundation (FAPESP) Grants No. 2010/07359-6 and No. 1999/05404-3;
Ministério da Ciência, Tecnologia, Inovações e Comunicações (MCTIC); Czech
Republic – Grant No. MSMT CR LTT18004, LO1305, LM2015038 and
CZ.02.1.01/0.0/0.0/16_013/0001402; France – Centre de Calcul IN2P3/CNRS;
Centre National de la Recherche Scientifique (CNRS); Conseil Régional Ile-de-
France; Département Physique Nucléaire et Corpusculaire (PNC-IN2P3/CNRS);
Département Sciences de l’Univers (SDU-INSU/CNRS); Institut Lagrange de Paris
(ILP) Grant No. LABEX ANR-10-LABX-63 within the Investissements d’Avenir
Programme Grant No. ANR-11-IDEX-0004-02; Germany – Bundesministerium für
Bildung und Forschung (BMBF); Deutsche Forschungsgemeinschaft (DFG);
Finanzministerium Baden-Württemberg; Helmholtz Alliance for Astroparticle
Physics (HAP); Helmholtz-Gemeinschaft Deutscher Forschungszentren (HGF);
Ministerium für Innovation, Wissenschaft und Forschung des Landes Nordrhein-
Westfalen; Ministerium für Wissenschaft, Forschung und Kunst des Landes Baden-
Württemberg; Italy – Istituto Nazionale di Fisica Nucleare (INFN); Istituto
Nazionale di Astrofisica (INAF); Ministero dell’Istruzione, dell’Universitá e
della Ricerca (MIUR); CETEMPS Center of Excellence; Ministero degli Affari
Esteri (MAE); México – Consejo Nacional de Ciencia y Tecnología (CONACYT) No.
167733; Universidad Nacional Autónoma de México (UNAM); PAPIIT DGAPA-UNAM; The
Netherlands – Ministry of Education, Culture and Science; Netherlands
Organisation for Scientific Research (NWO); Dutch national e-infrastructure
with the support of SURF Cooperative; Poland – National Centre for Research
and Development, Grant No. ERA-NET-ASPERA/02/11; National Science Centre,
Grants No. 2013/08/M/ST9/00322, No. 2016/23/B/ST9/01635 and No. HARMONIA
5–2013/10/M/ST9/00062, UMO-2016/22/M/ST9/00198; Portugal – Portuguese national
funds and FEDER funds within Programa Operacional Factores de Competitividade
through Fundação para a Ciência e a Tecnologia (COMPETE); Romania – Romanian
Ministry of Research and Innovation CNCS/CCCDI-UESFISCDI, projects PN-
III-P1-1.2-PCCDI-2017-0839/19PCCDI/2018, PN-III-P2-2.1-PED-2016-1922, PN-
III-P2-2.1-PED-2016-1659 and PN18090102 within PNCDI III; Slovenia – Slovenian
Research Agency; Spain – Comunidad de Madrid; Fondo Europeo de Desarrollo
Regional (FEDER) funds; Ministerio de Economía y Competitividad; Xunta de
Galicia; European Community 7th Framework Program Grant No.
FP7-PEOPLE-2012-IEF-328826; USA – Department of Energy, Contracts No. DE-
AC02-07CH11359, No. DE-FR02-04ER41300, No. DE-FG02-99ER41107 and No. DE-
SC0011689; National Science Foundation, Grant No. 0450696; The Grainger
Foundation; Marie Curie-IRSES/EPLANET; European Particle Physics Latin
American Network; European Union 7th Framework Program, Grant No.
PIRSES-2009-GA-246806; and UNESCO.

## References

  * Berezinsky et al. (1990) Berezinsky, V., Grigorieva, S.I., Dogiel, V.A. 1990, A&A, 232, 582
  * Compton & Getting (1935) Compton, A.H., Getting, I.A. 1935, Phys. Rev., 47, 817
  * di Matteo & Tinyakov (2018) di Matteo, A., Tinyakov, P. 2018, MNRAS, 476, 715
  * Durrer & Neronov (2013) Durrer, R., Neronov, A. 2013, Astron. Astrophys. Rev. 21, 62
  * Erdogdu et al. (2006) Erdogdu, P., et al. 2006, MNRAS, 368, 1515
  * Farley & Storey (1954) Farley, F. J. M., Storey, J. R., 1954, Proc. Phys. Soc. A, 67, 996
  * Giler et al. (1980) Giler, M., Wdowczyk, J., Wolfendale, A.W. 1980, J. Phys. G: Nucl. Phys., 6, 1561
  * Globus & Piran (2017) Globus, N., Piran, T. 2017, ApJ, 850, L25
  * Hackstein et al. (2016) Hackstein, S., et al. 2016,MNRAS, 462, 3660
  * Hackstein et al. (2018) Hackstein, S., et al. 2018,MNRAS, 475, 2519
  * Harari et al. (2010) Harari, D., Mollerach, S., Roulet, E. 2010, JCAP, 11 033
  * Harari et al. (2014) Harari, D., Mollerach, S., Roulet, E. 2014, PRD, 89, 123001
  * Harari et al. (2015) Harari, D., Mollerach, S., Roulet, E. 2015, PRD, 92, 063014
  * Jansson & Farrar (2012) Jansson, R., Farrar, G.R. 2012, ApJ, 757, 14
  * Kachelriess & Serpico (2006) Kachelriess, M., Serpico, P.D. 2006, Phys. Lett. B, 640, 225
  * Karakula et al. (1972) Karakula, S., Osborne, J., Roberts, E., Tkaczyk, W. 1972, J. Phys. A5, 904
  * Linsley (1975) Linsley, J. 1975, PRL, 34, 1530
  * Matthews (2017) Matthews, J. N. for the Telescope Array Collaboration 2017, PoS ICRC2017, 1096
  * Pshirkov et al. (2011) Pshirkov, M.S., Tinyakov, P.G., Kronberg, P.P., Newton-McGee, K.J. 2011, ApJ, 738, 192
  * Sigl et al. (2004) Sigl, G., Miniati, F., Ensslin, T.A. 2004, PRD, 70, 043007
  * The Pierre Auger Collaboration (2011) The Pierre Auger Collaboration 2011, JCAP, 11, 022
  * The Pierre Auger Collaboration (2012) The Pierre Auger Collaboration 2012, ApJS, 203, 34
  * The Pierre Auger Collaboration (2013) The Pierre Auger Collaboration 2013, ApJ, 762, L13
  * The Pierre Auger Collaboration (2014a) The Pierre Auger Collaboration 2014a, PRD, 90, 122005
  * The Pierre Auger Collaboration (2014b) The Pierre Auger Collaboration 2014b, PRD, 90, 122006
  * The Pierre Auger Collaboration (2015a) The Pierre Auger Collaboration 2015a, ApJ, 804, 15
  * The Pierre Auger Collaboration (2015b) The Pierre Auger Collaboration 2015b, ApJ, 802, 111
  * The Pierre Auger Collaboration (2015c) The Pierre Auger Collaboration 2015c, NIM A, 798, 172
  * The Pierre Auger Collaboration (2016) The Pierre Auger Collaboration 2016, Phys. Lett. B, 762, 288
  * The Pierre Auger Collaboration (2017a) The Pierre Auger Collaboration 2017a, Science, 357, 1266
  * The Pierre Auger Collaboration (2017b) The Pierre Auger Collaboration 2017b, JINST, 12, P02006
  * The Pierre Auger Collaboration (2017c) The Pierre Auger Collaboration 2017c, JCAP, 1704
  * The Pierre Auger Collaboration (2017d) The Pierre Auger Collaboration 2017d, PRD, 96, 122003
  * The Pierre Auger Collaboration (2018) The Pierre Auger Collaboration 2018, ApJ, 853, L29
  * The Pierre Auger & Telescope Array Collaborations (2014) The Pierre Auger and Telescope Array Collaborations 2014, ApJ, 794, 172
  * Thielheim & Langhoff (1968) Thielheim, K.O., Langhoff, W. 1968, J. Phys. A, 2, 694
  * Weber & Boer (2010) Weber, M., de Boer, W. 2010, A&A, 509, 25
  * Wittkowski (2017) Wittkowski, D. for the Pierre Auger Collaboration 2017, PoS ICRC2017, 563
  * Wittkowski & Kampert (2018) Wittkowski, D., Kampert, K.-H. 2018, ApJ, 854, L3