# Cosmic-ray anisotropies in right ascension
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 (IGFAE), Universidade de Santiago de Compostela,
Santiago de Compostela, Spain , G.A. Anastasi5858affiliation: Università
Torino, Dipartimento di Fisica, Torino, Italy 4949affiliation: INFN, Sezione
di Torino, Torino, Italy , L. Anchordoqui8282affiliation: 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 , P.R. Araújo Ferreira3939affiliation: RWTH Aachen
University, III. Physikalisches Institut A, Aachen, Germany , H.
Asorey88affiliation: Instituto de Tecnologías en Detección y Astropartículas
(CNEA, CONICET, UNSAM), Buenos Aires, Argentina , 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. Bakalova3030affiliation:
Institute of Physics of the Czech Academy of Sciences, Prague, Czech Republic
, 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 , 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 , T. Bister3939affiliation: RWTH Aachen
University, III. Physikalisches Institut A, Aachen, Germany , J.
Biteau3232affiliation: Institut de Physique Nucléaire d’Orsay (IPNO),
Université Paris-Sud, Univ. Paris/Saclay, CNRS-IN2P3, Orsay, France , 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. Bleve3434affiliation:
Univ. Grenoble Alpes, CNRS, Grenoble Institute of Engineering Univ. Grenoble
Alpes, LPSC-IN2P3, 38000 Grenoble, France, France , M.
Boháčová3030affiliation: Institute of Physics of the Czech Academy of
Sciences, Prague, Czech Republic , D. Boncioli5353affiliation: Università
dell’Aquila, Dipartimento di Scienze Fisiche e Chimiche, L’Aquila, Italy
4343affiliation: INFN Laboratori Nazionali del Gran Sasso, Assergi (L’Aquila),
Italy , C. Bonifazi2424affiliation: Universidade Federal do Rio de Janeiro,
Instituto de Física, Rio de Janeiro, RJ, Brazil , L. Bonneau
Arbeletche1919affiliation: Universidade de São Paulo, Instituto de Física, São
Paulo, SP, 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 , 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 , I.
Caracas3535affiliation: Bergische Universität Wuppertal, Department of
Physics, Wuppertal, Germany , 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 , M. Cerda99affiliation:
Observatorio Pierre Auger, Malargüe, Argentina , J.A.
Chinellato2020affiliation: Universidade Estadual de Campinas, IFGW, Campinas,
SP, Brazil , K. Choi1313affiliation: Université Libre de Bruxelles (ULB),
Brussels, Belgium , 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. Coleman8888affiliation: University of Delaware,
Department of Physics and Astronomy, Bartol Research Institute, Newark, DE,
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 , A.
Condorelli4242affiliation: Gran Sasso Science Institute, L’Aquila, Italy
4343affiliation: INFN Laboratori Nazionali del Gran Sasso, Assergi (L’Aquila),
Italy , 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 , F.
Convenga5252affiliation: Università del Salento, Dipartimento di Matematica e
Fisica “E. De Giorgi”, Lecce, Italy 4545affiliation: INFN, Sezione di Lecce,
Lecce, Italy , C.E. Covault8080affiliation: Case Western Reserve University,
Cleveland, OH, USA 10071007affiliation: also at Radboud Universtiy Nijmegen,
Nijmegen, The Netherlands , 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 , J. de Jesús88affiliation: Instituto de Tecnologías en
Detección y Astropartículas (CNEA, CONICET, UNSAM), Buenos Aires, Argentina
3737affiliation: Karlsruhe Institute of Technology, Institut für Kernphysik,
Karlsruhe, Germany , 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 , D. de Oliveira
Franco2020affiliation: Universidade Estadual de Campinas, IFGW, Campinas, SP,
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 , M. del Río1010affiliation: Observatorio Pierre
Auger and Comisión Nacional de Energía Atómica, Malargüe, Argentina , 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 , A.
Di Matteo4949affiliation: INFN, Sezione di Torino, Torino, Italy , M.L. Díaz
Castro2020affiliation: Universidade Estadual de Campinas, IFGW, Campinas, SP,
Brazil , 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 , J.
Ebr3030affiliation: Institute of Physics of the Czech Academy of Sciences,
Prague, Czech Republic , R. Engel3636affiliation: Karlsruhe Institute of
Technology, Institute for Experimental Particle Physics (ETP), Karlsruhe,
Germany 3737affiliation: Karlsruhe Institute of Technology, Institut für
Kernphysik, Karlsruhe, Germany , I. Epicoco5252affiliation: Università del
Salento, Dipartimento di Matematica e Fisica “E. De Giorgi”, Lecce, Italy
4545affiliation: INFN, Sezione di Lecce, Lecce, Italy , 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.
Farmer8787affiliation: University of Chicago, Enrico Fermi Institute, Chicago,
IL, USA , G. Farrar8585affiliation: 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 , B.
Fick8484affiliation: Michigan Technological University, Houghton, MI, USA ,
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. Fujii8787affiliation: University of Chicago, Enrico Fermi
Institute, Chicago, IL, USA 10051005affiliation: now at Hakubi Center for
Advanced Research and Graduate School of Science, Kyoto University, Kyoto,
Japan , 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 , C. Galea7575affiliation: IMAPP, Radboud
University Nijmegen, Nijmegen, The Netherlands , C. Galelli5555affiliation:
Università di Milano, Dipartimento di Fisica, Milano, Italy 4646affiliation:
INFN, Sezione di Milano, Milano, Italy , B. García77affiliation: Instituto de
Tecnologías en Detección y Astropartículas (CNEA, CONICET, UNSAM), and
Universidad Tecnológica Nacional – Facultad Regional Mendoza (CONICET/CNEA),
Mendoza, Argentina , A.L. Garcia Vegas3939affiliation: RWTH Aachen University,
III. Physikalisches Institut A, Aachen, Germany , H. Gemmeke3838affiliation:
Karlsruhe Institute of Technology, Institut für Prozessdatenverarbeitung und
Elektronik, Karlsruhe, Germany , F. Gesualdi88affiliation: Instituto de
Tecnologías en Detección y Astropartículas (CNEA, CONICET, UNSAM), Buenos
Aires, Argentina 3737affiliation: Karlsruhe Institute of Technology, Institut
für Kernphysik, 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. Giaccari7575affiliation: IMAPP, Radboud University Nijmegen,
Nijmegen, The Netherlands , M. Giammarchi4646affiliation: INFN, Sezione di
Milano, Milano, Italy , M. Giller6565affiliation: University of Łódź, Faculty
of Astrophysics, Łódź, Poland , J. Glombitza3939affiliation: RWTH Aachen
University, III. Physikalisches Institut A, Aachen, Germany , F.
Gobbi99affiliation: Observatorio Pierre Auger, Malargüe, Argentina , 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 , J.P. Gongora99affiliation: Observatorio Pierre
Auger, 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 , S. Hahn3737affiliation: Karlsruhe Institute of Technology, Institut
für Kernphysik, Karlsruhe, Germany 88affiliation: Instituto de Tecnologías en
Detección y Astropartículas (CNEA, CONICET, UNSAM), Buenos Aires, Argentina ,
R. Halliday8080affiliation: 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 ,
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 , G.C. Hill1212affiliation: University of
Adelaide, Adelaide, S.A., Australia , C. Hojvat10021002affiliation: Fermi
National Accelerator Laboratory, USA , 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 , J.A. Johnsen8181affiliation: Colorado School of Mines,
Golden, CO, USA , 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 , 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 , M.
Köpke3636affiliation: Karlsruhe Institute of Technology, Institute for
Experimental Particle Physics (ETP), Karlsruhe, 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.
LaHurd8080affiliation: Case Western Reserve University, Cleveland, OH, USA ,
R.G. Lang1818affiliation: Universidade de São Paulo, Instituto de Física de
São Carlos, São Carlos, SP, Brazil , 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 (IGFAE), Universidade de Santiago de
Compostela, Santiago de Compostela, Spain , R. Lorek8080affiliation: Case
Western Reserve University, Cleveland, OH, USA , Q. Luce3636affiliation:
Karlsruhe Institute of Technology, Institute for Experimental Particle Physics
(ETP), Karlsruhe, Germany , A. Lucero88affiliation: Instituto de Tecnologías
en Detección y Astropartículas (CNEA, CONICET, UNSAM), Buenos Aires, Argentina
, A. Machado Payeras2020affiliation: Universidade Estadual de Campinas, IFGW,
Campinas, SP, Brazil , M. Malacari8787affiliation: University of Chicago,
Enrico Fermi Institute, Chicago, IL, USA , 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 , B.C. Manning1212affiliation: University of Adelaide,
Adelaide, S.A., Australia , J. Manshanden4040affiliation: Universität Hamburg,
II. Institut für Theoretische Physik, Hamburg, Germany , 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. Martinez1818affiliation: Universidade de São Paulo,
Instituto de Física de São Carlos, São Carlos, SP, Brazil , O. Martínez
Bravo5959affiliation: Benemérita Universidad Autónoma de Puebla, Puebla,
México , M. Mastrodicasa5353affiliation: Università dell’Aquila, Dipartimento
di Scienze Fisiche e Chimiche, L’Aquila, Italy 4343affiliation: INFN
Laboratori Nazionali del Gran Sasso, Assergi (L’Aquila), Italy , H.J.
Mathes3737affiliation: Karlsruhe Institute of Technology, Institut für
Kernphysik, Karlsruhe, Germany , J. Matthews8383affiliation: 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.
Merenda8181affiliation: 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. Miramonti5555affiliation: Università di Milano,
Dipartimento di Fisica, Milano, Italy 4646affiliation: INFN, Sezione di
Milano, Milano, Italy , D. Mockler1313affiliation: Université Libre de
Bruxelles (ULB), Brussels, Belgium , 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. Mostafá8686affiliation: 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 2424affiliation:
Universidade Federal do Rio de Janeiro, Instituto de Física, Rio de Janeiro,
RJ, Brazil , S. Müller3636affiliation: Karlsruhe Institute of Technology,
Institute for Experimental Particle Physics (ETP), Karlsruhe, Germany , R.
Mussa4949affiliation: INFN, Sezione di Torino, Torino, Italy , M.
Muzio8585affiliation: New York University, New York, NY, USA , W.M.
Namasaka3535affiliation: Bergische Universität Wuppertal, Department of
Physics, Wuppertal, Germany , L. Nellen6363affiliation: Universidad Nacional
Autónoma de México, México, D.F., México , 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. Nitz8484affiliation:
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 , 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 , M.P. Panetta5252affiliation: Università del
Salento, Dipartimento di Matematica e Fisica “E. De Giorgi”, Lecce, Italy
4545affiliation: INFN, Sezione di Lecce, Lecce, Italy , P.
Papenbreer3535affiliation: Bergische Universität Wuppertal, Department of
Physics, Wuppertal, Germany , G. Parente7474affiliation: Instituto Galego de
Física de Altas Enerxías (IGFAE), Universidade 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
(IGFAE), Universidade 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 , J. Perez Armand1919affiliation: Universidade de São Paulo, Instituto
de Física, São Paulo, SP, Brazil , M. Perlin88affiliation: Instituto de
Tecnologías en Detección y Astropartículas (CNEA, CONICET, UNSAM), Buenos
Aires, Argentina 3737affiliation: Karlsruhe Institute of Technology, Institut
für Kernphysik, Karlsruhe, Germany , 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 , 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 , B. Pont7575affiliation: IMAPP, Radboud University Nijmegen,
Nijmegen, The Netherlands , M. Pothast7777affiliation: Nationaal Instituut
voor Kernfysica en Hoge Energie Fysica (NIKHEF), Science Park, Amsterdam, The
Netherlands 7575affiliation: IMAPP, Radboud University Nijmegen, Nijmegen, The
Netherlands , P. Privitera8787affiliation: University of Chicago, Enrico Fermi
Institute, Chicago, IL, USA , M. Prouza3030affiliation: Institute of Physics
of the Czech Academy of Sciences, Prague, Czech Republic , A.
Puyleart8484affiliation: Michigan Technological University, Houghton, MI, USA
, S. Querchfeld3535affiliation: Bergische Universität Wuppertal, Department of
Physics, Wuppertal, Germany , 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 88affiliation: Instituto de Tecnologías en
Detección y Astropartículas (CNEA, CONICET, UNSAM), Buenos Aires, Argentina ,
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 , G. Salina4848affiliation: INFN, Sezione di Roma “Tor
Vergata”, Roma, Italy , J.D. Sanabria Gomez2828affiliation: Universidad
Industrial de Santander, Bucaramanga, Colombia , 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. Sarazin8181affiliation: 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
3232affiliation: Institut de Physique Nucléaire d’Orsay (IPNO), Université
Paris-Sud, Univ. Paris/Saclay, CNRS-IN2P3, Orsay, France , C.
Schäfer3737affiliation: Karlsruhe Institute of Technology, Institut für
Kernphysik, Karlsruhe, 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 88affiliation:
Instituto de Tecnologías en Detección y Astropartículas (CNEA, CONICET,
UNSAM), Buenos Aires, Argentina , M. Schimp3535affiliation: Bergische
Universität Wuppertal, Department of Physics, Wuppertal, Germany , F.
Schlüter3737affiliation: Karlsruhe Institute of Technology, Institut für
Kernphysik, Karlsruhe, Germany 88affiliation: Instituto de Tecnologías en
Detección y Astropartículas (CNEA, CONICET, UNSAM), Buenos Aires, Argentina ,
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. Schröder8888affiliation: University of Delaware, Department of Physics
and Astronomy, Bartol Research Institute, Newark, DE, USA 3737affiliation:
Karlsruhe Institute of Technology, Institut für Kernphysik, Karlsruhe, Germany
, S. Schröder3535affiliation: Bergische Universität Wuppertal, Department of
Physics, Wuppertal, Germany , S.J. Sciutto44affiliation: IFLP, Universidad
Nacional de La Plata and CONICET, La Plata, Argentina , M.
Scornavacche88affiliation: Instituto de Tecnologías en Detección y
Astropartículas (CNEA, CONICET, UNSAM), Buenos Aires, Argentina
3737affiliation: Karlsruhe Institute of Technology, Institut für Kernphysik,
Karlsruhe, Germany , 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
Radboud Universtiy Nijmegen, Nijmegen, The Netherlands , R.
Šmída8787affiliation: University of Chicago, Enrico Fermi Institute, Chicago,
IL, USA , P. Sommers8686affiliation: Pennsylvania State University, University
Park, PA, USA , J.F. Soriano8282affiliation: 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 , M.
Stadelmaier3737affiliation: Karlsruhe Institute of Technology, Institut für
Kernphysik, Karlsruhe, Germany 88affiliation: Instituto de Tecnologías en
Detección y Astropartículas (CNEA, CONICET, UNSAM), Buenos Aires, 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 , A. Streich3636affiliation: 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 , 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. Taboada3636affiliation: 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 , 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 , P. Tobiska3030affiliation: Institute of
Physics of the Czech Academy of Sciences, Prague, Czech Republic , 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
(IGFAE), Universidade de Santiago de Compostela, Santiago de Compostela, Spain
, A. Travaini99affiliation: Observatorio Pierre Auger, Malargüe, Argentina ,
P. Travnicek3030affiliation: Institute of Physics of the Czech Academy of
Sciences, Prague, Czech Republic , C. Trimarelli5353affiliation: Università
dell’Aquila, Dipartimento di Scienze Fisiche e Chimiche, L’Aquila, Italy
4343affiliation: INFN Laboratori Nazionali del Gran Sasso, Assergi (L’Aquila),
Italy , M. Trini7171affiliation: Center for Astrophysics and Cosmology (CAC),
University of Nova Gorica, Nova Gorica, Slovenia 10071007affiliation: also at
Radboud Universtiy Nijmegen, Nijmegen, The Netherlands , 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 , L.
Vaclavek3131affiliation: Palacky University, RCPTM, Olomouc, Czech Republic ,
J.F. Valdés Galicia6363affiliation: Universidad Nacional Autónoma de México,
México, D.F., México , I. Valiño4242affiliation: Gran Sasso Science Institute,
L’Aquila, Italy 4343affiliation: INFN Laboratori Nazionali del Gran Sasso,
Assergi (L’Aquila), Italy , L. Valore5656affiliation: Università di Napoli
“Federico II”, Dipartimento di Fisica “Ettore Pancini”, Napoli, Italy
4747affiliation: INFN, Sezione di Napoli, Napoli, Italy , 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 , A. Vásquez-
Ramírez2828affiliation: Universidad Industrial de Santander, Bucaramanga,
Colombia , 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 , J. Vink7979affiliation: Universiteit van
Amsterdam, Faculty of Science, Amsterdam, The Netherlands , 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 , 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 , L. Wiencke8181affiliation:
Colorado School of Mines, Golden, CO, USA , H. Wilczyński6464affiliation:
Institute of Nuclear Physics PAN, Krakow, Poland , T. Winchen1414affiliation:
Vrije Universiteit Brussels, Brussels, Belgium , 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 , A. Yushkov3030affiliation: Institute of Physics of the
Czech Academy of Sciences, Prague, Czech Republic , E. Zas7474affiliation:
Instituto Galego de Física de Altas Enerxías (IGFAE), Universidade 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 , M.
Ziolkowski4141affiliation: Universität Siegen, Fachbereich 7 Physik –
Experimentelle Teilchenphysik, Siegen, Germany , F. Zuccarello5454affiliation:
Università di Catania, Dipartimento di Fisica e Astronomia, Catania, Italy
4444affiliation: INFN, Sezione di Catania, Catania, Italy

###### Abstract

We present measurements of the large-scale cosmic-ray anisotropies in right
ascension, using data collected by the surface detector array of the Pierre
Auger Observatory over more than 14 years. We determine the equatorial dipole
component, $\vec{d}_{\perp}$, through a Fourier analysis in right ascension
that includes weights for each event so as to account for the main detector-
induced systematic effects. For the energies at which the trigger efficiency
of the array is small, the “East-West” method is employed. Besides using the
data from the array with detectors separated by 1500 m, we also include data
from the smaller but denser sub-array of detectors with 750 m separation,
which allows us to extend the analysis down to $\sim 0.03$ EeV. The most
significant equatorial dipole amplitude obtained is that in the cumulative bin
above 8 EeV, $d_{\perp}=6.0^{+1.0}_{-0.9}$%, which is inconsistent with
isotropy at the 6$\sigma$ level. In the bins below 8 EeV, we obtain 99% CL
upper-bounds on $d_{\perp}$ at the level of 1 to 3 percent. At energies below
1 EeV, even though the amplitudes are not significant, the phases determined
in most of the bins are not far from the right ascension of the Galactic
center, at $\alpha_{\rm GC}=-94^{\circ}$, suggesting a predominantly Galactic
origin for anisotropies at these energies. The reconstructed dipole phases in
the energy bins above 4 EeV point instead to right ascensions that are almost
opposite to the Galactic center one, indicative of an extragalactic cosmic ray
origin.

The Pierre Auger Collaboration

††affiliationtext: —–

##  1 Introduction

The distribution of cosmic-ray (CR) arrival directions is expected to provide
essential clues to understanding the CR origin. Being charged particles, they
are significantly deflected by the magnetic fields present in our galaxy
(Haverkorn, 2015) and, for those arriving from outside it, also by the
extragalactic magnetic fields (Feretti et al., 2012). Since the deflections
get smaller for increasing rigidities, it is only at the highest energies that
one may hope to observe localized flux excesses associated with individual CR
sources. On the other hand, as the energies lower and the deflections become
large, the propagation eventually becomes diffusive and it is likely that only
large-scale patterns, such as a dipolar flux modulation, may be detectable.
However, the small amplitudes of these anisotropies make their observation
quite challenging.

Due to the Earth’s rotation, cosmic-ray observatories running for long periods
of time have an almost uniform exposure in right ascension. This enables them
to achieve a high sensitivity to the modulation of the flux in this angular
coordinate. In particular, for a dipolar cosmic-ray flux the first-harmonic
modulation in right ascension provides a direct measurement of the projection
of the dipole in the equatorial plane, $\vec{d}_{\perp}$. The possible sources
of systematic uncertainties that could affect these measurements, such as
those from remaining non-uniformities of the exposure or those related to the
effects of atmospheric variations, can often be accounted for. Even when this
is not possible, as can happen when the trigger efficiency of the array is
small, methods that are insensitive to these systematic effects can be adopted
to reconstruct $\vec{d}_{\perp}$, although they have a somewhat reduced
sensitivity to the modulations. On the other hand, at low energies the number
of events detected is large, what tends to enhance the statistical sensitivity
of the measurements.

The projection of the dipole along the Earth rotation axis $d_{z}$ can, in
principle, be reconstructed from the study of the azimuthal modulation of the
CR fluxes. This requires accounting in detail for the effects of the
geomagnetic field on the air showers, which can affect the reconstruction of
the CR energies in an azimuthally dependent way. Also, the presence of a tilt
of the array can induce a spurious contribution to $d_{z}$. When the trigger
efficiency of the array is small, these effects may lead to systematic
uncertainties that cannot be totally corrected for, particularly given the
azimuthal dependence of the trigger efficiency arising from the actual
geometry of the surface detector array of the Pierre Auger Observatory. Due to
these limitations, we will here restrict our analysis to the determination of
$\vec{d}_{\perp}$ through the study of the distribution in right ascension of
the events recorded in different energy bins. We note that the determination
of $d_{z}$ for energies $E\geq 4$ EeV, for which that detector has full
efficiency for zenith angles up to 80∘, was discussed in detail in The Pierre
Auger Collaboration (2015a, 2017a, 2018).

At $E\geq 8$ EeV, a significant first-harmonic modulation in right ascension,
corresponding to an amplitude $d_{\perp}\sim 6$%, has been detected by the
Pierre Auger Observatory (The Pierre Auger Collaboration, 2017a). The
reconstructed direction of the three-dimensional dipole suggests a predominant
extragalactic origin of the CR anisotropies at energies above 4 EeV, and the
dipolar amplitudes obtained in different bins show a growing trend with
increasing energies (The Pierre Auger Collaboration, 2017a, 2018).

The phase in right ascension of the dipolar modulation of the flux determined
above 8 EeV is $\alpha_{d}\simeq 100^{\circ}$. This is nearly opposite to the
phases measured at PeV energies by IceCube and IceTop (IceCube Collaboration,
2012, 2016), which lie not far from the Galactic center direction which is at
$\alpha_{\rm GC}=-94^{\circ}$. Also the KASCADE-Grande measurements, involving
CR energies from few PeV up to few tens of PeV, lead to phases lying close to
the right ascension of the Galactic center, even though the measured
amplitudes are not statistically significant (KASCADE-Grande Collaboration,
2019).111Hints of anisotropies on smaller angular scales were also found
recently in a reanalysis of KASCADE-Grande data (Ahlers, 2019). All this is in
agreement with the expectation that for energies above that of the knee of the
CR spectrum, which corresponds to the steepening taking place at $\sim 4$ PeV,
the outward diffusive escape of the CRs produced in the Galaxy should give
rise to a dipolar flux component having its maximum not far from the Galactic
center direction. Also at energies above few EeV, where the propagation would
become more rectilinear, a continuous distribution of Galactic sources should
give rise to a dipolar component not far from the GC direction (The Pierre
Auger Collaboration, 2018). Departures from these behaviors could however
result if the CR source distribution is not symmetric with respect to the
Galactic center (such as in the presence of a powerful nearby CR source), in
the presence of drift motions caused by the regular Galactic magnetic field
components (Ptuskin et al., 1993), or when the contribution from the
extragalactic component becomes sizable. Note that the expected direction of a
dipole of extragalactic origin will depend on the (unknown) distribution of
the CR sources and on the effects of the deflections caused by the Galactic
magnetic field, as was discussed in detail in The Pierre Auger Collaboration
(2018).

The change from a Galactic CR origin towards a predominantly extragalactic
origin is expected to take place somewhere above the knee. More precise
measurements of the large-scale anisotropies, filling the gap between the
IceCube/IceTop or KASCADE-Grande measurements and the dipole determined by the
Pierre Auger Observatory above 8 EeV, should provide information about this
transition. In fact, although at energies below 8 EeV the reported dipolar
amplitudes are not significant, indications that a change in the phase of the
anisotropies in right ascension takes place around few EeV are apparent in the
Pierre Auger Observatory measurements (The Pierre Auger Collaboration, 2011a,
2012, 2013; Sidelnik, 2013; Al Samarai, 2015). One has to keep in mind in this
discussion that the energy at which the total anisotropy becomes of
predominantly extragalactic origin may be different from the energy at which
the CR flux becomes of predominantly extragalactic origin, since the intrinsic
anisotropies of each component are likely different.

We present here an update of the measurements of the large-scale anisotropies
that are sensitive to the equatorial component of a dipole, for the whole
energy range from $\sim 0.03$ EeV up to $\geq 32$ EeV, covering more than
three decades of energy. The results above 4 EeV are an update of those
presented in The Pierre Auger Collaboration (2018), including two more years
of data, corresponding to an increase in the exposure by 20%. At lower
energies, we provide a major update of the latest published results (Al
Samarai, 2015), with 50% more exposure for the SD1500 array and twice as much
for the SD750 array. At energies below 2 EeV, possible systematic effects
related to the reduced trigger efficiency could be significant. To study the
modulation in right ascension in this regime we have then to resort to the
“East-West” method, which has larger associated uncertainties but is not
affected by most of the systematic effects (Nagashima et al., 1989; Bonino et
al., 2011). At energies below 0.25 EeV, it proves convenient to use the data
from the sub-array of detectors with 750 m spacing which, although being much
smaller, can detect a larger number of events at these energies.

##  2 The Observatory and the dataset

The Pierre Auger Observatory (The Pierre Auger Collaboration, 2015b), located
near the city of Malargüe in western Argentina (at latitude $35.2^{\circ}$
South), is the largest existing CR observatory. Its surface detector array
(SD) consists of water-Cherenkov detectors having each one 12 tonnes of ultra-
pure water viewed by three 9 inch phototubes. The main array, SD1500, consists
of detectors distributed on a triangular grid with separations of 1,500 m that
span an area of 3,000 km2. A smaller sub-array, SD750, covers an area of 23
km2 with detectors separated by 750 m, making it sensitive also to smaller CR
energies. These arrays sample the secondary particles of the air showers
reaching ground level. In addition, the fluorescence detector (FD) consists of
27 telescopes that overlook the SD array. The FD can determine the
longitudinal development of the air showers by observing the UV light emitted
by atmospheric nitrogen molecules excited by the passage of the charged
particles of the shower. This fluorescence light can be detected during clear
moonless nights, with a corresponding duty cycle of about 15% (The Pierre
Auger Collaboration, 2015b). The SD arrays have instead a continuous
operation, detecting events with a duty cycle close to 100%. They also have a
more uniform (and simpler to evaluate) exposure. This is why the studies of
the large-scale anisotropies that we perform here are based on the much larger
number of events recorded by the surface arrays.

For the SD1500 array, the dataset considered in this work includes events with
energies above 0.25 EeV that were detected from 2004 January 1 up to 2018
August 31. For energies below 4 EeV, it includes events with zenith angles up
to $60^{\circ}$, allowing coverage of 71% of the sky, and the quality trigger
applied requires that all the six detectors surrounding the one with the
largest signal be active at the time the event is detected. For energies above
4 EeV, more inclined events can be reliably reconstructed (The Pierre Auger
Collaboration, 2014b) and hence the zenith-angle range is extended up to
$80^{\circ}$, allowing coverage of 85% of the sky. Moreover, given that at
these energies the number of detectors triggered by each shower is large (4 or
more detectors for more than 99% of the events), we also include in this case
events passing a relaxed trigger condition, allowing that one of the six
detectors that are neighbors to the one with the largest signal be missing or
not functioning, provided that the reconstructed shower core be contained
inside a triangle of nearby active detectors (The Pierre Auger Collaboration,
2017a). The integrated exposure of the array for $\theta\leq 60^{\circ}$ and
using the strict trigger selection is 60,700 km2 sr yr, while that for
$\theta\leq 80^{\circ}$ and relaxing the trigger is 92,500 km2 sr yr.

The CR arrival directions are reconstructed from the timing of the signals in
the different triggered stations, and the angular resolution is better than
1.6∘ (The Pierre Auger Collaboration, 2015b), so that it has negligible impact
on the reconstruction of the dipole. The energies of the events with
$\theta\leq 60^{\circ}$ are assigned in terms of the reconstructed signals at
a reference distance from the shower core of 1000 m. They are corrected for
atmospheric effects, accounting for the pressure and air density variations
following The Pierre Auger Collaboration (2017b), as well as for geomagnetic
effects, following The Pierre Auger Collaboration (2011b). The inclined
events, whose signals are dominantly produced by the muonic component of the
showers, have a negligible dependence on atmospheric variations, while
geomagnetic effects are already taken into account in their reconstruction
(The Pierre Auger Collaboration, 2014b). Their energies are assigned in terms
of the estimated muon number at ground level. The SD1500 array has full
trigger efficiency for $E\geq 2.5$ EeV if one considers events with
$\theta\leq 60^{\circ}$, and for $E\geq 4$ EeV for events with $\theta\leq
80^{\circ}$. The energies of the CRs are calibrated using the hybrid events
measured simultaneously by the SD and FD detectors, in the regimes of full
trigger efficiency. For lower energies, in which case we consider events with
$\theta\leq 60^{\circ}$, the energy assignment is performed using the
extrapolation of the corresponding calibration curve. The energy resolution
for events with $\theta\leq 60^{\circ}$ is about 7% above 10 EeV, and degrades
for lower energies, reaching about 20% at 1 EeV, while the systematic
uncertainty in the energy scale is 14% (see Verzi (2019) for details). The
more inclined events have an energy resolution of 19%, with a similar
systematic uncertainty (The Pierre Auger Collaboration, 2014b).

For energies below 0.25 EeV, and down to $\sim 0.03$ EeV (below which the
trigger efficiency is tiny), we use the events from the denser and smaller
SD750 array, since the accumulated statistics is larger. The dataset comprises
events with zenith angles up to $55^{\circ}$ detected from 2012 January 1 up
to 2018 August 31. The trigger applied requires that all six detectors around
the one with the largest signal be functioning and the associated exposure is
234 km2 sr yr. The energies are assigned in terms of the reconstructed signals
at a reference distance from the shower core of 450 m. They are corrected for
atmospheric effects following The Pierre Auger Collaboration (2017b). The
SD750 array has full trigger efficiency for $E\geq 0.3$ EeV if one considers
events with $\theta\leq 55^{\circ}$ (The Pierre Auger Collaboration, 2015b).
The energies are calibrated with hybrid events observed in the regime of full
trigger efficiency and below that threshold the energy assignment is performed
on the basis of the extrapolation of the corresponding calibration curve. At
0.3 EeV the energy resolution is about 18% (Coleman, 2019).

##  3 The analysis method

The weighted first-harmonic analysis in the right ascension angle $\alpha$,
often referred to as Rayleigh analysis, provides the Fourier coefficients as

$a=\frac{2}{\mathcal{N}}\sum_{i=1}^{N}w_{i}\cos\alpha_{i},~{}~{}~{}~{}~{}~{}b=\frac{2}{\mathcal{N}}\sum_{i=1}^{N}w_{i}\sin\alpha_{i},$
(1)

where the sums run over all $N$ detected events. The weights $w_{i}$, which
are of order unity, account for the effects of the non-uniformities in the
exposure as a function of time, with the normalization factor being
${\mathcal{N}}\equiv\sum_{i}w_{i}$. The amplitude and phase of the first-
harmonic modulation are given by $r=\sqrt{a^{2}+b^{2}}$ and
$\varphi=\arctan(b/a)$. The probability to obtain an amplitude larger than the
one measured as a result of a fluctuation from an isotropic distribution is
$P(\geq r)=\exp(-\mathcal{N}r^{2}/4)$. To obtain the weights, we permanently
monitor the number of active unitary detector cells, corresponding to the
number of active detectors that are surrounded by an hexagon of working
detectors or, when considering the relaxed trigger condition above 4 EeV, we
also account for detector configurations with only five active detectors
around the central one. We obtain from this the exposure of the Auger
Observatory in bins of right ascension of the zenith of the array,
$\alpha^{0}$. This angle is given by $\alpha^{0}(t_{i})\equiv 2\pi
t_{i}/T_{s}~{}(\mathrm{mod}~{}2\pi)$, with the origin of time being taken such
that $\alpha^{0}(0)=0$. The sidereal-time period, $T_{s}\simeq 23.934$ h,
corresponds to one extra cycle per year with respect to the solar frequency.
The fraction of the total exposure that is associated to a given $\alpha^{0}$
bin, taken to be of 1.25∘ width (5 minutes), is proportional to the total
number of unitary cells in that bin, $N_{\mathrm{cell}}(\alpha^{0})$. The
weights $w_{i}$ account for the relative variations of $N_{\mathrm{cell}}$ as
a function of $\alpha^{0}$, i.e.

$w_{i}=\left(\frac{N_{\mathrm{cell}}(\alpha^{0}(t_{i}))}{\langle
N_{\mathrm{cell}}\rangle}\right)^{-1},$ (2)

with $\langle
N_{\mathrm{cell}}\rangle=1/(2\pi)\int_{0}^{2\pi}\mathrm{d}\alpha^{0}~{}N_{\mathrm{cell}}(\alpha^{0})$.
Including these weights in the Fourier coefficients eliminates the spurious
contribution to the amplitudes associated to the non-uniform exposure in right
ascension.

We note that if one were to consider periods of only a few months, the
resulting modulation of $N_{\mathrm{cell}}(\alpha^{0})$ could amount to an
effect of a few percent on the modulation in right ascension of the event
rates. However, after considering several years, the modulations that appear
on shorter time scales tend to get averaged out, with the surviving effects
being now typically at the level of about $\pm 0.5$%. The effects of the tilt
of the SD array (The Pierre Auger Collaboration, 2012), which is inclined on
average by $\sim 0.2^{\circ}$ towards $\phi\simeq-30^{\circ}$ (i.e. towards
the South-East), can also be accounted for by adding an extra factor in the
weights (The Pierre Auger Collaboration, 2018). However, this is actually only
relevant when performing the Fourier analysis in the azimuth variable $\phi$,
something we will not perform here.

When the triggering of the array is not fully efficient, there are additional
systematic effects related to the interplay between the atmospheric effects in
the air-shower development and the energy-dependent trigger efficiency. In
particular, changes in the air density modify the Molière radius determining
the lateral spread of the electromagnetic component of the showers. The fall-
off of the signal at ground level is preferentially harder under hot weather
conditions and steeper under cold ones. The detection efficiency of the SD is
thus expected to follow these variations to some extent, being on average
larger when the weather is hot than when it is cold. As a consequence, one
could expect that, at energies below full trigger efficiency, a spurious
modulation could appear at the solar frequency.

Moreover, we have found that the amplitude of the modulation of the rates at
the antisidereal frequency, which is that corresponding to one cycle less per
year than the solar frequency, suggests that spurious unaccounted effects
become relevant below 2 EeV. In particular, the Fourier amplitude
corresponding to the antisidereal time period $T_{\rm as}=24.066$ h in the bin
[1, 2] EeV is $r=0.005$. This has a probability of arising as a fluctuation of
less than 0.1%. A non-negligible antisidereal amplitude could for instance
appear in the presence of daily and seasonal systematic effects which are not
totally accounted for. Since in this case comparable spurious amplitudes could
be expected in the sidereal and antisidereal sidebands (Farley & Storey,
1954), we only use the Rayleigh method described before in the bins above 2
EeV. We have checked that in the bins above 2 EeV the amplitudes at both the
solar and antisidereal frequencies are consistent with being just due to
fluctuations, so that there are no signs indicating that surviving systematic
effects could be present at the sidereal frequency at these energies (see
Table 2 in the Appendix).222Given that, for events with zenith angles smaller
than 60∘, the trigger efficiency is larger than $\sim 95$% above 2 EeV, the
efficiency related systematic effects are negligible above this threshold.
Alternatively, one can use for the energies below 2 EeV the differential East-
West (EW) method (Bonino et al., 2011), which is based on the difference
between the counting rates of the events measured from the East sector and
those from the West sector. Since the exposure is the same for events coming
from the East and for those coming from the West333A possible tilt of the
array in the East-West direction, giving just a constant term in the East-West
rate difference, does not affect the determination of the first-harmonic
modulation., and also the spurious modulations due to the atmospheric effects
are the same in both sectors, the relative difference between both rates,
$(E-W)/(E+W)$, is not sensitive to these experimental and atmospheric
systematic effects. This allows one to reconstruct in a clean way the
modulation of the rate itself, without the need to apply any correction but at
the expense of a reduced sensitivity to the amplitude of the CR flux
modulations.

In this approach (Bonino et al., 2011), the first-harmonic amplitude and phase
are calculated using a slightly modified Fourier analysis that accounts for
the subtraction of the Western sector from the Eastern one. The Fourier
coefficients are defined as

$a_{\rm
EW}=\frac{2}{N}\sum_{i=1}^{N}\cos(\alpha^{0}(t_{i})-\xi_{i}),~{}~{}~{}~{}~{}~{}b_{\rm
EW}=\frac{2}{N}\sum_{i=1}^{N}\sin(\alpha^{0}(t_{i})-\xi_{i}),$ (3)

where $\xi_{i}=0$ for events coming from the East and $\xi_{i}=\pi$ for those
coming from the West, so as to easily implement the subtraction of data from
the two hemispheres.

In the case in which the dominant contribution to the flux modulation is
purely dipolar, the amplitude $r_{\rm EW}=\sqrt{a_{\rm EW}^{2}+b_{\rm
EW}^{2}}$ and phase $\varphi_{\rm EW}=\arctan(b_{\rm EW}/a_{\rm EW})$ obtained
with this method are related to the ones from the Rayleigh formalism through
$r=\frac{\pi\langle\cos\delta\rangle}{2\langle\sin\theta\rangle}r_{\rm EW}$
and $\varphi=\varphi_{\rm EW}+\pi/2$, where $\langle\cos\delta\rangle$ is the
average of the cosine of the declination of the events and similarly
$\langle\sin\theta\rangle$ is the average of the sine of their zenith angles
(Bonino et al., 2011). The probability to obtain an amplitude larger than the
one measured as a result of a fluctuation from an isotropic distribution is
$P(\geq r_{\rm EW})=\exp(-Nr_{\rm EW}^{2}/4)$.

The amplitude of the equatorial dipole component is related to the amplitude
of the first-harmonic modulation through $d_{\perp}\simeq
r/\langle\cos\delta\rangle$, and its phase $\alpha_{d}$ coincides with the
first-harmonic phase $\varphi$.

##  4 Right ascension modulation from 0.03 EeV up to $E\geq 32$ EeV

In Table 1, we report the results for the reconstructed equatorial dipole in
different energy bins, covering the range from $\sim 0.03$ EeV up to $E\geq
32$ EeV. The energies defining the boundaries of the bins are $2^{n}$ EeV,
with $n=-5,-4,...,4,5$. As mentioned previously, the results are obtained from
the study of the right ascension modulation using different methods and
datasets. We use the weighted Rayleigh analysis in the energy bins above 2
EeV, for which the systematic effects associated with the non-saturated
detector efficiency and to the effects related to atmospheric variations are
well under control. When this is not the case, we report the results of the
East-West method which, although having larger uncertainties, is quite
insensitive to most sources of systematic effects in the right ascension
distribution. For energies above 0.25 EeV, we report the results obtained with
the data from the SD1500 array, while for lower energies we use the dataset
from the SD750 array since, having a lower threshold, it leads to a larger
number of events despite the reduced size of the array. In that case, given
that the SD750 array is not fully efficient below 0.3 EeV, we just use the
East-West method.

|  $E$ [EeV] |  $E_{\rm med}$ [EeV] | $N$ |  $d_{\perp}$ [%] |  $\sigma_{x,y}$ [%] | $\alpha_{d}[^{\circ}]$ | $P(\geq d_{\perp})$ |  $d_{\perp}^{\rm UL}$ [%]
---|---|---|---|---|---|---|---|---
East-West | 1/32 - 1/16 | 0.051 | 432,155 | $1.0^{+1.0}_{-0.4}$ | 0.91 | $112\pm 71$ | 0.54 | 3.3
(SD750) | 1/16 - 1/8 | 0.088 | 924,856 | $0.6^{+0.6}_{-0.3}$ | 0.52 | $-44\pm 68$ | 0.50 | 2.0
| 1/8 - 1/4 | 0.161 | 488,752 | $0.2^{+0.8}_{-0.2}$ | 0.63 | $-31\pm 108$ | 0.94 | 2.0
East-West | 1/4 - 1/2 | 0.43 | 770,316 | $0.6^{+0.5}_{-0.3}$ | 0.48 | $-135\pm 64$ | 0.45 | 1.8
(SD1500) | 1/2 - 1 | 0.70 | 2,388,467 | $0.5^{+0.3}_{-0.2}$ | 0.27 | $-99\pm 43$ | 0.20 | 1.1
| 1 - 2 | 1.28 | 1,243,103 | $0.18^{+0.47}_{-0.02}$ | 0.35 | $-69\pm 100$ | 0.87 | 1.1
Rayleigh | 2 - 4 | 2.48 | 283,074 | $0.5^{+0.4}_{-0.2}$ | 0.34 | $-11\pm 55$ | 0.34 | 1.4
(SD1500) | 4 - 8 | 5.1 | 88,325 | $1.0^{+0.7}_{-0.4}$ | 0.61 | $69\pm 46$ | 0.23 | 2.6
| 8 - 16 | 10.3 | 27,271 | $5.6^{+1.2}_{-1.0}$ | 1.1 | $97\pm 12$ | $2.3\times 10^{-6}$ | –
| 16 - 32 | 20.3 | 7,664 | $7.5^{+2.3}_{-1.8}$ | 2.1 | $80\pm 17$ | $1.5\times 10^{-3}$ | –
| $\geq 32$ | 40 | 1,993 | $13^{+5}_{-3}$ | 4.1 | $152\pm 19$ | $5.3\times 10^{-3}$ | –
| $\geq 8$ | 11.5 | 36,928 | $6.0^{+1.0}_{-0.9}$ | 0.94 | $98\pm 9$ | $1.4\times 10^{-9}$ | –

Table 1: Equatorial dipole reconstruction in different energy bins. Indicated
are the median energies in each bin $E_{\rm med}$, number of events $N$,
amplitude of $d_{\perp}$, uncertainty
$\sigma_{x,y}=\sigma/\langle\cos\delta\rangle$ of the components $d_{x}$ or
$d_{y}$, right ascension phase, probability to get a larger amplitude from
fluctuations of an isotropic distribution and 99% CL upper limit on the
amplitude.

Figure 1: Reconstructed equatorial-dipole amplitude (left) and phase (right).
The upper limits at 99% CL are shown for all the energy bins in which the
measured amplitude has a chance probability greater than 1%. The gray bands
indicate the amplitude and phase for the energy bin $E\geq 8$ EeV. Results
from other experiments are shown for comparison (IceCube Collaboration, 2012,
2016; KASCADE-Grande Collaboration, 2019).

For each energy bin, we report in Table 1 the number of events $N$, the
amplitude $d_{\perp}$, the uncertainty $\sigma_{x,y}$ of the components
$d_{x}$ or $d_{y}$, the right ascension phase of the dipolar modulation
$\alpha_{d}$, the chance probability $P(\geq d_{\perp})$ and, when the
measured amplitude has a probability larger than 1%, we also report the 99% CL
upper limit on the amplitude of the equatorial dipole $d_{\perp}^{\rm\small
UL}$. The upper limits on the first-harmonic amplitude at a given confidence
level CL (${\rm CL}=0.99$ for 99% CL) are derived from the distribution for a
dipolar anisotropy of unknown amplitude, marginalized over the dipole phase,
requiring that

$\int_{0}^{r^{\rm\small
UL}}\mathrm{d}r\,\frac{r}{\sigma^{2}}\exp\left[-\frac{r^{2}+s^{2}}{2\sigma^{2}}\right]I_{0}\left(\frac{rs}{\sigma^{2}}\right)={\rm
CL},$ (4)

with $I_{0}(x)$ the zero-order modified Bessel function, $s$ the measured
amplitude and the dispersion being $\sigma=\sqrt{2/\mathcal{N}}$ for the
Rayleigh analysis while
$\sigma=(\pi\langle\cos\delta\rangle/2\langle\sin\theta\rangle)\sqrt{2/N}$ for
the East-West method. These bounds on the first-harmonic amplitude are then
converted into the corresponding upper limit for the amplitude of the
equatorial dipole using that $d_{\perp}^{\rm\small UL}=r^{\rm\small
UL}/\langle\cos\delta\rangle$. For the uncertainties in the phase, we use the
two-dimensional distribution marginalized instead over the dipole amplitude
$r$ (Linsley, 1975). In Table 3 in the Appendix we also report the results
obtained above 2 EeV with the East-West method, which are consistent with
those obtained with the Fourier analysis in Table 1 but have larger
uncertainties.

Fig. 1 shows the equatorial dipole amplitude (left panel) and phase (right
panel) that were determined in all the energy bins considered, as reported in
Table 1. Also shown are the results obtained by the IceCube, IceTop and
KASCADE-Grande experiments in the 1–30 PeV range (IceCube Collaboration, 2012,
2016; KASCADE-Grande Collaboration, 2019). We also show the 99% CL upper limit
$d_{\perp}^{\rm UL}$ in the cases in which the measured amplitude has more
than 1% probability to be a fluctuation from an isotropic distribution. The
results for the integral bin with $E\geq 8$ EeV, that was considered in The
Pierre Auger Collaboration (2017a), is shown as a gray band.

A trend of increasing amplitudes for increasing energies is observed, with
values going from $d_{\perp}\simeq 0.1$% at PeV energies, to $\sim 1$% at EeV
energies and reaching $\sim 10$% at 30 EeV. Regarding the phases, a transition
between values lying close to the right ascension of the Galactic center,
$\alpha_{d}\simeq\alpha_{\rm GC}$, towards values in a nearly opposite
direction, $\alpha_{d}\simeq 100^{\circ}$, is observed to take place around a
few EeV.

Figure 2: Components of the dipole in the equatorial plane for different
energy bins above 0.25 EeV (left panel) and below 1 EeV (right panel). The
horizontal axis corresponds to the component along the direction $\alpha=0$
while the vertical axis to that along $\alpha=90^{\circ}$. The radius of each
circle corresponds to the 1$\sigma$ uncertainty in $d_{x}$ and $d_{y}$. The
Galactic center direction is also indicated. The measurements from IceCube
(IC) and IceTop (IT) at PeV energies are also indicated in the right panel
(IceCube Collaboration, 2012, 2016).

The overall behavior of the amplitudes and phases in the $d_{x}$–$d_{y}$ plane
is depicted in Fig. 2. The left panel includes the energies above 0.25 EeV
while the right panel those below 1 EeV. In these plots, the right ascension
$\alpha_{d}$ is the polar angle, measured anti-clockwise from the x-axis (so
that $d_{x}=d_{\perp}\cos\alpha_{d}$ and $d_{y}=d_{\perp}\sin\alpha_{d}$). The
circles shown have a radius equal to the 1$\sigma$ uncertainties
$\sigma_{x,y}$ in the dipole components $d_{x,y}$ (reported in the Table 1),
effectively including $\sim 39$% of the two-dimensional confidence region. One
can appreciate in this plot how the amplitudes decrease for decreasing
energies, and how the phases change as a function of the energy, pointing
almost in the opposite direction of the Galactic center above 4 EeV and not
far from it below 1 EeV.

The values of the anisotropy parameters obtained above are based, by
construction, on the event content in the energy intervals under scrutiny. The
finite resolution on the energies induces bin-to-bin migration of events. Due
to the steepness of the energy spectrum, the migration happens especially from
lower to higher energy bins. This influences the energy dependence of the
recovered parameters. However, given that the size of the energy bins chosen
here is much larger than the resolution, the migration of events remains small
enough to avoid significant distortions for the recovered values above full
efficiency. For instance, given the energy resolution of the SD1500 array
(Verzi, 2019) and assuming a dipole amplitude scaling as $E^{0.8}$, as was
found in The Pierre Auger Collaboration (2018) to approximately hold above 4
EeV, the impact of the migrations remains below an order of magnitude smaller
than the statistical uncertainties associated to the recovered parameters. In
the energy range below full efficiency, additional systematic effects enter
into play on the energy estimate. We note that forward-folding simulations of
the response function effects into an injected anisotropy show that the
recovered parameters are not impacted by more than their current statistical
uncertainties. A complete unfolding of these effects is left for future
studies. It requires an accurate knowledge of the response function of the SD
arrays down to low energies, which is not available at the moment.

##  5 Discussion and conclusions

We have updated the searches for anisotropies on large angular scales using
the cosmic rays detected by the Pierre Auger Observatory. The analysis covered
more than three orders of magnitude in energy, including events with $E\geq
0.03$ EeV and hence encompassing the expected transition between Galactic and
extragalactic origins of the cosmic rays. This was achieved by studying the
first-harmonic modulation in right ascension of the CR fluxes determined with
the SD1500 and the SD750 surface detector arrays. This allowed us to determine
the equatorial component of a dipolar modulation, $\vec{d}_{\perp}$, or
eventually to set strict upper-bounds on it.

For the inclusive bin above 8 EeV, the first-harmonic modulation in right
ascension leads to an equatorial dipole amplitude
$d_{\perp}=0.060^{+0.010}_{-0.009}$, which has a probability to arise by
chance from an isotropic distribution of $1.4\times 10^{-9}$, corresponding to
a two-sided Gaussian significance of 6$\sigma$. The phase of the maximum of
this modulation is at $\alpha_{d}=98^{\circ}\pm 9^{\circ}$, indicating an
extragalactic origin for these CRs. When splitting the bin above 8 EeV, as
originally done in The Pierre Auger Collaboration (2018), one finds
indications of an increasing amplitude with increasing energies, and the
direction of the dipole suggests that it has an extragalactic origin in all
the three bins considered. A growing dipole amplitude for increasing energies
could for instance be associated with the larger relative contribution to the
flux that arises at high energies from nearby sources, that are more
anisotropically distributed than the integrated flux from the distant ones. A
suppression of the more isotropic contribution from distant sources is
expected to result from the strong attenuation of the CR flux that should take
place at the highest energies as a consequence of their interactions with the
background radiation (Greisen, 1966; Zatsepin & Kuzmin, 1966).

At energies below 8 EeV, none of the amplitudes are significant, and we set
99% CL upper bounds on $d_{\perp}$ at the level of 1 to 3%. The phases
measured in most of the bins below 1 EeV are not far from the direction
towards the Galactic center. All this suggests that the origin of these
dipolar anisotropies changes from a predominantly Galactic one to an
extragalactic one somewhere in the range between 1 EeV and few EeV. The small
size of the dipolar amplitudes in this energy range, combined with the
indications that the composition is relatively light (The Pierre Auger
Collaboration, 2014a), disfavor a predominant flux component of Galactic
origin at $E>1$ EeV (The Pierre Auger Collaboration, 2013). Models of Galactic
CRs relying on a mixed mass composition, with rigidity dependent spectra, have
been proposed to explain the knee (at $\sim 4$ PeV) and second-knee (at $\sim
0.1$ EeV) features in the spectrum (Candia et al., 2003). The predicted
anisotropies depend on the details of the Galactic magnetic field model
considered and, below 0.5 EeV, they are consistent with the upper bounds we
obtained. An extrapolation of these models, considering that there is no
cutoff in the Galactic component, would predict dipolar anisotropies at the
several percent level beyond the EeV, in tension with the upper bounds in this
range. The conflict is even stronger for Galactic models (Calvez et al., 2010)
having a light CR composition that extends up to the ankle energy (at $\sim 5$
EeV). The presence of a more isotropic extragalactic component making a
significant contribution already at EeV energies could dilute the anisotropy
of Galactic origin, so as to be consistent with the bounds obtained. Note that
even if the extragalactic component were completely isotropic in some
reference frame, the motion of the Earth with respect to that system could
give rise to a dipolar anisotropy through the Compton-Getting effect (Compton
& Getting, 1935). For instance, for a CR distribution that is isotropic in the
CMB rest frame, the resulting Compton-Getting dipole amplitude would be about
0.6% (Kachelriess & Serpico, 2006). This amplitude depends on the relative
velocity and on the CR spectral slope, but not directly on the particle
charge. The deflections of the extragalactic CRs caused by the Galactic
magnetic field are expected to further reduce this amplitude, and also to
generate higher harmonics, in a rigidity dependent way, so that the exact
predictions are model dependent. The Compton-Getting extragalactic
contribution to the dipolar anisotropy is hence below the upper limits
obtained.

More data, as well as analyses exploiting the discrimination between the
different cosmic-ray mass components that will become feasible with the
upgrade of the Pierre Auger Observatory currently being implemented
(Castellina, 2019), will be crucial to understand in depth the origin of the
cosmic rays at these energies and to learn how their anisotropies are
produced.

## 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 -Ministry of Science and Higher
Education, grant No. DIR/WK/2018/11; 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 and PN18090102 within PNCDI III;
Slovenia – Slovenian Research Agency, grants P1-0031, P1-0385, I0-0033,
N1-0111; Spain – Ministerio de Economía, Industria y Competitividad
(FPA2017-85114-P and FPA2017-85197-P), Xunta de Galicia (ED431C 2017/07),
Junta de Andalucía (SOMM17/6104/UGR), Feder Funds, RENATA Red Nacional
Temática de Astropartículas (FPA2015-68783-REDT) and María de Maeztu Unit of
Excellence (MDM-2016-0692); 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; and UNESCO.

In Table 2 we report the amplitudes and probabilities obtained with the SD1500
array at the solar and antisidereal frequencies, in all bins above 2 EeV for
which the Rayleigh analysis was applied at the sidereal frequency. One can see
that all these amplitudes are consistent with being fluctuations, showing then
no signs of remaining systematic effects. We also report in Table 3 the
equatorial dipole amplitudes and phases obtained with the East-West method
above 2 EeV, and compare them with the results for the same datasets that were
obtained with the Rayleigh method (reported in Table 1). The inferred
equatorial dipole amplitudes turn out to be consistent, although the
statistical uncertainty obtained with the East-West method is larger by a
factor $\pi\langle\cos\delta\rangle/2\langle\sin\theta\rangle$ (Bonino et al.,
2011). Given that above full trigger efficiency one has that
$\langle\sin\theta\rangle\simeq 0.58$ when considering $\theta<60^{\circ}$, as
we do for $E<4$ EeV, or $\langle\sin\theta\rangle\simeq 0.65$ when considering
$\theta<80^{\circ}$, as we do for $E\geq 4$ EeV, and that
$\langle\cos\delta\rangle\simeq 0.78$ in both zenith ranges, the statistical
uncertainties obtained in the East-West analysis are larger by a factor of
about 2.1 than those obtained with the Rayleigh analysis for
$\theta<60^{\circ}$, or by a factor of about 1.9 for $\theta<80^{\circ}$, as
can be seen in Table 3.

|  | solar | antisidereal
---|---|---|---
$E$ [EeV] | $N$ |  $r$ [%] | $P(\geq r)$ |  $r$ [%] | $P(\geq r)$
2 - 4 | 283,074 | $0.6^{+0.3}_{-0.2}$ | 0.07 | $0.5^{+0.3}_{-0.2}$ | 0.20
4 - 8 | 88,325 | $0.8^{+0.5}_{-0.3}$ | 0.24 | $0.5^{+0.5}_{-0.2}$ | 0.59
8 - 16 | 27,271 | $0.6^{+1.1}_{-0.2}$ | 0.79 | $0.5^{+1.1}_{-0.1}$ | 0.83
16 - 32 | 7,664 | $1.1^{+2.0}_{-0.3}$ | 0.79 | $3.1^{+1.9}_{-1.1}$ | 0.16
$\geq 32$ | 1,993 | $1.5^{+4.4}_{-0.1}$ | 0.90 | $1.3^{+4.6}_{-0.0}$ | 0.92
$\geq 8$ | 36,928 | $0.3^{+1.1}_{-0.0}$ | 0.93 | $1.0^{+0.8}_{-0.4}$ | 0.39
Table 2: Fourier amplitudes at the solar and antisidereal frequencies, and the probabilities to get larger values from statistical fluctuations of an isotropic distribution, for the different energy bins above 2 EeV. |  | East-West (SD1500) | Rayleigh (SD1500)
---|---|---|---
$E$ [EeV] | $N$ |  $d_{\perp}$ [%] |  $\sigma_{x,y}$ [%] | $\alpha_{d}[^{\circ}]$ | $P(\geq d_{\perp})$ |  $d_{\perp}$ [%] |  $\sigma_{x,y}$ [%] | $\alpha_{d}[^{\circ}]$
2 - 4 | 283,074 | $0.2^{+0.9}_{-0.2}$ | 0.72 | $-16\pm 167$ | 0.94 | $0.5^{+0.4}_{-0.2}$ | 0.34 | $-11\pm 55$
4 - 8 | 88,325 | $1.7^{+1.3}_{-0.7}$ | 1.1 | $41\pm 38$ | 0.33 | $1.0^{+0.7}_{-0.4}$ | 0.61 | $69\pm 46$
8 - 16 | 27,271 | $6.4^{+2.3}_{-1.7}$ | 2.1 | $147\pm 18$ | $8.3\times 10^{-3}$ | $5.6^{+1.2}_{-1.0}$ | 1.1 | $97\pm 12$
16 - 32 | 7,664 | $9.3^{+4.5}_{-3.0}$ | 3.9 | $67\pm 24$ | $5.8\times 10^{-2}$ | $7.5^{+2.3}_{-1.8}$ | 2.1 | $80\pm 17$
$\geq 32$ | 1,993 | $25^{+9}_{-6}$ | 7.6 | $151\pm 17$ | $4.1\times 10^{-3}$ | $13^{+5}_{-3}$ | 4.1 | $152\pm 19$
$\geq 8$ | 36,928 | $6.6^{+2.0}_{-1.5}$ | 1.8 | $132\pm 15$ | $8.6\times 10^{-4}$ | $6.0^{+1.0}_{-0.9}$ | 0.94 | $98\pm 9$
Table 3: Equatorial dipole reconstruction above 2 EeV obtained using the East-
West method. Indicated are the number of events, amplitude of $d_{\perp}$,
uncertainty $\sigma_{x,y}=\sigma/\langle\cos\delta\rangle$ of the components
$d_{x}$ or $d_{y}$, right ascension phase $\alpha_{d}$ and probability $P(\geq
d_{\perp})$ to get a larger amplitude from fluctuations of an isotropic
distribution. For comparison we also include in the last two columns the
values of $d_{\perp}$ and $\alpha_{d}$ that were obtained in the Rayleigh
analysis (reported in Table 1).

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