The Astrophysical Journal Letters, 762:L13 (8pp), 2013 January 1 doi:10.1088/2041-8205/762/1/L13
C
°
2013. The American Astronomical Society. All rights reserved. Printed in the U.S.A.
CONSTRAINTS ON THE ORIGIN OF COSMIC RAYS ABOVE 10
18
eV FROM LARGE-SCALE
ANISOTROPY SEARCHES IN DATA OF THE PIERRE AUGER OBSERVATORY
The Pierre Auger Collaboration
95
,
P. Abreu
1
, M. Aglietta
2
, M. Ahlers
3
,E.J.Ahn
4
, I. F. M. Albuquerque
5
, D. Allard
6
, I. Allekotte
7
, J. Allen
8
,
P. Allison
9
, A. Almela
10,11
, J. Alvarez Castillo
12
, J. Alvarez-Mu
˜
niz
13
, R. Alves Batista
14
, M. Ambrosio
15
,
A. Aminaei
16
, L. Anchordoqui
17
, S. Andringa
1
,T.Anti
ˇ
ci’c
18
,C.Aramo
15
, E. Arganda
19,20
, F. Arqueros
20
, H. Asorey
7
,
P. Assis
1
, J. Aublin
21
,M.Ave
22
, M. Avenier
23
, G. Avila
24
, A. M. Badescu
25
, M. Balzer
26
, K. B. Barber
27
,
A. F. Barbosa
28,96
, R. Bardenet
29
, S. L. C. Barroso
30
, B. Baughman
9,97
,J.B
¨
auml
31
,C.Baus
22
, J. J. Beatty
9
,
K. H. Becker
32
, A. Bell
´
etoile
33
, J. A. Bellido
27
,S.BenZvi
3
, C. Berat
23
, X. Bertou
7
, P. L. Biermann
34
,
P. Billoir
21
, F. Blanco
20
, M. Blanco
21,35
, C. Bleve
32
,H.Bl
¨
umer
22,31
,M.Boh
´
a
ˇ
cov
´
a
36
, D. Boncioli
37
,
C. Bonifazi
21,38
,R.Bonino
2
, N. Borodai
39
, J. Brack
40
, I. Brancus
41
, P. Brogueira
1
,W.C.Brown
42
,R.Bruijn
43,98
,
P. Buchholz
44
, A. Bueno
45
, L. Buroker
17
, R. E. Burton
46
, K. S. Caballero-Mora
47
, B. Caccianiga
48
, L. Caramete
34
,
R. Caruso
49
, A. Castellina
2
, O. Catalano
50
, G. Cataldi
51
, L. Cazon
1
, R. Cester
52
, J. Chauvin
23
,S.H.Cheng
47
,
A. Chiavassa
2
, J. A. Chinellato
14
, J. Chirinos Diaz
53
, J. Chudoba
36
,M.Cilmo
15
,R.W.Clay
27
, G. Cocciolo
51
,
L. Collica
48
, M. R. Coluccia
51
, R. Concei¸c
˜
ao
1
, F. Contreras
54
, H. Cook
43
, M. J. Cooper
27
, J. Coppens
16,55
, A. Cordier
29
,
S. Coutu
47
, C. E. Covault
46
, A. Creusot
6
,A.Criss
47
, J. Cronin
56
, A. Curutiu
34
, S. Dagoret-Campagne
29
, R. Dallier
33
,
B. Daniel
14
,S.Dasso
57,58
, K. Daumiller
31
,B.R.Dawson
27
, R. M. de Almeida
59
, M. De Domenico
49
, C. De Donato
12
,
S. J. de Jong
16,55
, G. De La Vega
60
, W. J. M. de Mello Junior
14
, J. R. T. de Mello Neto
38
,I.DeMitri
51
, V. de Souza
61
,
K. D. de Vries
62
, L. del Peral
35
, M. del R
´
ıo
37,54
, O. Deligny
63
, H. Dembinski
22
,N.Dhital
53
,C.DiGiulio
37,64
,
M. L. D
´
ıaz Castro
28
,P.N.Diep
65
,F.Diogo
1
, C. Dobrigkeit
14
, W. Docters
62
,J.C.D’Olivo
12
,P.N.Dong
63,65
,
A. Dorofeev
40
,J.C.dosAnjos
28
,M.T.Dova
19
,D.D’Urso
15
, I. Dutan
34
,J.Ebr
36
, R. Engel
31
, M. Erdmann
66
,
C. O. Escobar
4,14
, J. Espadanal
1
, A. Etchegoyen
10,11
, P. Facal San Luis
56
, H. Falcke
16,55,67
, K. Fang
56
, G. Farrar
8
,
A. C. Fauth
14
, N. Fazzini
4
, A. P. Ferguson
46
,B.Fick
53
,J.M.Figueira
11
, A. Filevich
11
, A. Filip
ˇ
ci
ˇ
c
68,69
, S. Fliescher
66
,
C. E. Fracchiolla
40
, E. D. Fraenkel
62
, O. Fratu
25
,U.Fr
¨
ohlich
44
, B. Fuchs
22
,R.Gaior
21
, R. F. Gamarra
11
, S. Gambetta
70
,
B. Garc
´
ıa
60
, S. T. Garcia Roca
13
, D. Garcia-Gamez
29
, D. Garcia-Pinto
20
, G. Garilli
49
, A. Gascon Bravo
45
, H. Gemmeke
26
,
P. L. Ghia
21
, M. Giller
71
, J. Gitto
60
, H. Glass
4
,M.S.Gold
72
,G.Golup
7
, F. Gomez Albarracin
19
,M.G
´
omez Berisso
7
,
P. F. G
´
omez Vitale
24
,P.Gon¸calves
1
, J. G. Gonzalez
31
, B. Gookin
40
, A. Gorgi
2
, P. Gouffon
5
, E. Grashorn
9
, S. Grebe
16,55
,
N. Griffith
9
, A. F. Grillo
73
, Y. Guardincerri
58
, F. Guarino
15
, G. P. Guedes
74
,P.Hansen
19
, D. Harari
7
, T. A. Harrison
27
,
J. L. Harton
40
,A.Haungs
31
, T. Hebbeker
66
,D.Heck
31
, A. E. Herve
27
,G.C.Hill
27
, C. Hojvat
4
, N. Hollon
56
,
V. C. Holmes
27
, P. Homola
39
,J.R.H
¨
orandel
16,55
, P. Horvath
75
, M. Hrabovsk
´
y
36,75
,D.Huber
22
, T. Huege
31
,A.Insolia
49
,
F. Ionita
56
, A. Italiano
49
,S.Jansen
16,55
, C. Jarne
19
, S. Jiraskova
16
, M. Josebachuili
11
, K. Kadija
18
, K. H. Kampert
32
,
P. Karhan
76
, P. Kasper
4
, I. Katkov
22
,B.K
´
egl
29
, B. Keilhauer
31
, A. Keivani
77
, J. L. Kelley
16
,E.Kemp
14
,
R. M. Kieckhafer
53
, H. O. Klages
31
, M. Kleifges
26
, J. Kleinfeller
31,54
, J. Knapp
43
, D.-H. Koang
23
, K. Kotera
56
,
N. Krohm
32
,O.Kr
¨
omer
26
, D. Kruppke-Hansen
32
, D. Kuempel
44,66
, J. K. Kulbartz
78
, N. Kunka
26
,G.LaRosa
50
,
C. Lachaud
6
,D.LaHurd
46
, L. Latronico
2
,R.Lauer
72
, P. Lautridou
33
,S.LeCoz
23
,M.S.A.B.Le
˜
ao
79
, D. Lebrun
23
,
P. Lebrun
4
, M. A. Leigui de Oliveira
79
, A. Letessier-Selvon
21
, I. Lhenry-Yvon
63
,K.Link
22
,R.L
´
opez
80
,
A. Lopez Ag
¨
uera
13
, K. Louedec
23,29
, J. Lozano Bahilo
45
,L.Lu
43
, A. Lucero
11
, M. Ludwig
22
, H. Lyberis
38,63
,
M. C. Maccarone
50
, C. Macolino
21
, S. Maldera
2
, J. Maller
33
, D. Mandat
36
, P. Mantsch
4
, A. G. Mariazzi
19
,J.Marin
2,54
,
V. Marin
33
,I.C.Maris
21
, H. R. Marquez Falcon
81
, G. Marsella
51
, D. Martello
51
, L. Martin
33
, H. Martinez
82
,
O. Mart
´
ınez Bravo
80
, D. Martraire
63
,J.J.Mas
´
ıas Meza
58
, H. J. Mathes
31
, J. Matthews
77
, J. A. J. Matthews
72
,
G. Matthiae
37
, D. Maurel
31
, D. Maurizio
28,52
,P.O.Mazur
4
, G. Medina-Tanco
12
, M. Melissas
22
, D. Melo
11
,
E. Menichetti
52
, A. Menshikov
26
, P. Mertsch
83
,S.Messina
62
, C. Meurer
66
, R. Meyhandan
84
, S. Mi’canovi’c
18
,
M. I. Micheletti
85
,I.A.Minaya
20
, L. Miramonti
48
, L. Molina-Bueno
45
, S. Mollerach
7
, M. Monasor
56
,
D. Monnier Ragaigne
29
, F. Montanet
23
, B. Morales
12
, C. Morello
2
, E. Moreno
80
, J. C. Moreno
19
, M. Mostaf
´
a
40
,
C. A. Moura
79
, M. A. Muller
14
,G.M
¨
uller
66
,M.M
¨
unchmeyer
21
, R. Mussa
52
, G. Navarra
2,96
, J. L. Navarro
45
, S. Navas
45
,
P. Necesal
36
, L. Nellen
12
, A. Nelles
16,55
,J.Neuser
32
, P. T. Nhung
65
, M. Niechciol
44
,L.Niemietz
32
, N. Nierstenhoefer
32
,
D. Nitz
53
,D.Nosek
76
,L.No
ˇ
zka
36
, J. Oehlschl
¨
ager
31
,A.Olinto
56
, M. Ortiz
20
, N. Pacheco
35
, D. Pakk Selmi-Dei
14
,
M. Palatka
36
, J. Pallotta
86
, N. Palmieri
22
, G. Parente
13
, E. Parizot
6
, A. Parra
13
, S. Pastor
87
, T. Paul
88
, M. Pech
36
,
J. P¸ekala
39
, R. Pelayo
13,80
, I. M. Pepe
89
, L. Perrone
51
, R. Pesce
70
, E. Petermann
90
, S. Petrera
64
, A. Petrolini
70
,
Y. Petrov
40
, C. Pfendner
3
, R. Piegaia
58
, T. Pierog
31
, P. Pieroni
58
, M. Pimenta
1
, V. Pirronello
49
, M. Platino
11
,M.Plum
66
,
V. H. Ponce
7
, M. Pontz
44
, A. Porcelli
31
, P. Privitera
56
, M. Prouza
36
,E.J.Quel
86
, S. Querchfeld
32
, J. Rautenberg
32
,
O. Ravel
33
, D. Ravignani
11
, B. Revenu
33
, J. Ridky
36
, S. Riggi
13
, M. Risse
44
, P. Ristori
86
, H. Rivera
48
,V.Rizi
64
, J. Roberts
8
,
W. Rodrigues de Carvalho
13
, G. Rodriguez
13
, I. Rodriguez Cabo
13
, J. Rodriguez Martino
54
, J. Rodriguez Rojo
54
,
M. D. Rodr
´
ıguez-Fr
´
ıas
35
,G.Ros
35
, J. Rosado
20
, T. Rossler
75
, M. Roth
31
,B.Rouill
´
e-d’Orfeuil
56
, E. Roulet
7
,
A. C. Rovero
57
,C.R
¨
uhle
26
, A. Saftoiu
41
, F. Salamida
63
, H. Salazar
80
, F. Salesa Greus
40
, G. Salina
37
,F.S
´
anchez
11
,
C. E. Santo
1
, E. Santos
1
, E. M. Santos
38
, F. Sarazin
91
, B. Sarkar
32
, S. Sarkar
83
, R. Sato
54
, N. Scharf
66
, V. Scherini
48
,
1
The Astrophysical Journal Letters, 762:L13 (8pp), 2013 January 1 Abreu et al.
H. Schieler
31
, P. Schiffer
66,78
, A. Schmidt
26
, O. Scholten
62
, H. Schoorlemmer
16,55
, J. Schovancova
36
, P. Schov
´
anek
36
,
F. Schr
¨
oder
31
, D. Schuster
91
, S. J. Sciutto
19
, M. Scuderi
49
, A. Segreto
50
, M. Settimo
44
, A. Shadkam
77
, R. C. Shellard
28
,
I. Sidelnik
11
,G.Sigl
78
, H. H. Silva Lopez
12
,O.Sima
92
,A.’Smia
ł
lkowski
71
,R.
ˇ
Sm
´
ıda
31
,G.R.Snow
90
, P. Sommers
47
,
J. Sorokin
27
, H. Spinka
4,93
, R. Squartini
54
, Y. N. Srivastava
88
, S. Stanic
69
, J. Stapleton
9
, J. Stasielak
39
, M. Stephan
66
,
A. Stutz
23
, F. Suarez
11
, T. Suomij
¨
arvi
63
,A.D.Supanitsky
57
,T.
ˇ
Su
ˇ
sa
18
, M. S. Sutherland
77
,J.Swain
88
, Z. Szadkowski
71
,
M. Szuba
31
, A. Tapia
11
, M. Tartare
23
,O.Ta¸sc
˘
au
32
, R. Tcaciuc
44
,N.T.Thao
65
, D. Thomas
40
, J. Tiffenberg
58
,
C. Timmermans
16,55
, W. Tkaczyk
71,96
, C. J. Todero Peixoto
61
,G.Toma
41
, L. Tomankova
36
,B.Tom
´
e
1
, A. Tonachini
52
,
G. Torralba Elipe
13
, P. Travnicek
36
, D. B. Tridapalli
5
, G. Tristram
6
, E. Trovato
49
, M. Tueros
13
, R. Ulrich
31
,
M. Unger
31
, M. Urban
29
,J.F.Vald
´
es Galicia
12
,I.Vali
˜
no
13
, L. Valore
15
,G.vanAar
16
, A. M. van den Berg
62
,
S. van Velzen
16
, A. van Vliet
78
, E. Varela
80
, B. Vargas C
´
ardenas
12
,J.R.V
´
azquez
20
,R.A.V
´
azquez
13
, D. Veberi
ˇ
c
68,69
,
V. Verzi
37
,J.Vicha
36
, M. Videla
60
, L. Villase
˜
nor
81
, H. Wahlberg
19
, P. Wahrlich
27
, O. Wainberg
10,11
,D.Walz
66
,
A. A. Watson
43
, M. Weber
26
, K. Weidenhaupt
66
,A.Weindl
31
, F. Werner
31
, S. Westerhoff
3
, B. J. Whelan
27,47
,
A. Widom
88
, G. Wieczorek
71
,L.Wiencke
91
, B. Wilczy
´
nska
39
, H. Wilczy
´
nski
39
,M.Will
31
, C. Williams
56
,T.Winchen
66
,
M. Wommer
31
, B. Wundheiler
11
, T. Yamamoto
56,99
, T. Yapici
53
, P. Younk
44,94
,G.Yuan
77
, A. Yushkov
13
,
B. Zamorano Garcia
45
,E.Zas
13
, D. Zavrtanik
68,69
, M. Zavrtanik
68,69
,I.Zaw
8,100
, A. Zepeda
82,101
, J. Zhou
56
, Y. Zhu
26
,
M. Zimbres Silva
14,32
, and M. Ziolkowski
44
1
LIP and Instituto Superior T
´
ecnico, Technical University of Lisbon, Portugal
2
Istituto di Fisica dello Spazio Interplanetario (INAF), Universit
`
a di Torino and Sezione INFN, Torino, Italy
3
University of Wisconsin, Madison, WI, USA
4
Fermilab, Batavia, IL, USA
5
Universidade de S
˜
ao Paulo, Instituto de F
´
ısica, S
˜
ao Paulo, SP, Brazil
6
Laboratoire AstroParticule et Cosmologie (APC), Universit
´
e Paris 7, CNRS-IN2P3, Paris, France
7
Centro At
´
omico Bariloche and Instituto Balseiro (CNEA-UNCuyo-CONICET), San Carlos de Bariloche, Argentina
8
New York University, New York, NY, USA
9
Ohio State University, Columbus, OH, USA
10
Universidad Tecnol
´
ogica Nacional - Facultad Regional Buenos Aires, Buenos Aires, Argentina
11
Instituto de Tecnolog
´
ıas en Detecci
´
on y Astropart
´
ıculas (CNEA, CONICET, UNSAM), Buenos Aires, Argentina
12
Universidad Nacional Autonoma de Mexico, Mexico, D.F., Mexico
13
Universidad de Santiago de Compostela, Spain
14
Universidade Estadual de Campinas, IFGW, Campinas, SP, Brazil
15
Universit
`
a di Napoli “Federico II” and Sezione INFN, Napoli, Italy
16
IMAPP, Radboud University Nijmegen, The Netherlands
17
University of Wisconsin, Milwaukee, WI, USA
18
Rudjer Bo
ˇ
skovi’c Institute, 10000 Zagreb, Croatia
19
IFLP, Universidad Nacional de La Plata and CONICET, La Plata, Argentina
20
Universidad Complutense de Madrid, Madrid, Spain
21
Laboratoire de Physique Nucl
´
eaire et de Hautes Energies (LPNHE), Universit
´
es Paris 6 et Paris 7, CNRS-IN2P3, Paris, France
22
Karlsruhe Institute of Technology - Campus South - Institut f
¨
ur Experimentelle Kernphysik (IEKP), Karlsruhe, Germany
23
Laboratoire de Physique Subatomique et de Cosmologie (LPSC), Universit
´
e Joseph Fourier Grenoble, CNRS-IN2P3, Grenoble INP, France
24
Observatorio Pierre Auger and Comisi
´
on Nacional de Energ
´
ıa At
´
omica, Malarg
¨
ue, Argentina
25
University Politehnica of Bucharest, Romania
26
Karlsruhe Institute of Technology - Campus North - Institut f
¨
ur Prozessdatenverarbeitung und Elektronik, Karlsruhe, Germany
27
University of Adelaide, Adelaide, S.A., Australia
28
Centro Brasileiro de Pesquisas Fisicas, Rio de Janeiro, RJ, Brazil
29
Laboratoire de l’Acc
´
el
´
erateur Lin
´
eaire (LAL), Universit
´
e Paris 11, CNRS-IN2P3, France
30
Universidade Estadual do Sudoeste da Bahia, Vitoria da Conquista, BA, Brazil
31
Karlsruhe Institute of Technology - Campus North - Institut f
¨
ur Kernphysik, Karlsruhe, Germany
32
Bergische Universit
¨
at Wuppertal, Wuppertal, Germany
33
SUBATECH,
´
Ecole des Mines de Nantes, CNRS-IN2P3, Universit
´
e de Nantes, France
34
Max-Planck-Institut f
¨
ur Radioastronomie, Bonn, Germany
35
Universidad de Alcal
´
a, Alcal
´
a de Henares (Madrid), Spain
36
Institute of Physics of the Academy of Sciences of the Czech Republic, Prague, Czech Republic
37
Universit
`
a di Roma II “Tor Vergata” and Sezione INFN, Roma, Italy
38
Universidade Federal do Rio de Janeiro, Instituto de F
´
ısica, Rio de Janeiro, RJ, Brazil
39
Institute of Nuclear Physics PAN, Krakow, Poland
40
Colorado State University, Fort Collins, CO, USA
41
“Horia Hulubei” National Institute for Physics and Nuclear Engineering, Bucharest- Magurele, Romania
42
Colorado State University, Pueblo, CO, USA
43
School of Physics and Astronomy, University of Leeds, UK
44
Universit
¨
at Siegen, Siegen, Germany
45
Universidad de Granada & C.A.F.P.E., Granada, Spain
46
Case Western Reserve University, Cleveland, OH, USA
47
Pennsylvania State University, University Park, PA, USA
48
Universit
`
a di Milano and Sezione INFN, Milan, Italy
49
Universit
`
a di Catania and Sezione INFN, Catania, Italy
50
Istituto di Astrofisica Spaziale e Fisica Cosmica di Palermo (INAF), Palermo, Italy
51
Dipartimento di Matematica e Fisica “E. De Giorgi” dell’Universit
`
a del Salento and Sezione INFN, Lecce, Italy
52
Universit
`
a di Torino and Sezione INFN, Torino, Italy
53
Michigan Technological University, Houghton, MI, USA
2
The Astrophysical Journal Letters, 762:L13 (8pp), 2013 January 1 Abreu et al.
54
Observatorio Pierre Auger, Malarg
¨
ue, Argentina
55
Nikhef, Science Park, Amsterdam, The Netherlands
56
University of Chicago, Enrico Fermi Institute, Chicago, IL, USA
57
Instituto de Astronom
´
ıa y F
´
ısica del Espacio (CONICET-UBA), Buenos Aires, Argentina
58
Departamento de F
´
ısica, FCEyN, Universidad de Buenos Aires y CONICET, Argentina
59
Universidade Federal Fluminense, EEIMVR, Volta Redonda, RJ, Brazil
60
National Technological University, Faculty Mendoza (CONICET/CNEA), Mendoza, Argentina
61
Universidade de S
˜
ao Paulo, Instituto de F
´
ısica, S
˜
ao Carlos, SP, Brazil
62
Kernfysisch Versneller Instituut, University of Groningen, Groningen, The Netherlands
63
Institut de Physique Nucl
´
eaire d’Orsay (IPNO), Universit
´
e Paris 11, CNRS-IN2P3, Orsay, France
64
Universit
`
a dell’Aquila and INFN, L’Aquila, Italy
65
Institute for Nuclear Science and Technology (INST), Hanoi, Vietnam
66
RWTH Aachen University, III. Physikalisches Institut A, Aachen, Germany
67
ASTRON, Dwingeloo, The Netherlands
68
J. Stefan Institute, Ljubljana, Slovenia
69
Laboratory for Astroparticle Physics, University of Nova Gorica, Slovenia
70
Dipartimento di Fisica dell’Universit
`
a and INFN, Genova, Italy
71
University of Ł
´
od
´
z, Ł
´
od
´
z, Poland
72
University of New Mexico, Albuquerque, NM, USA
73
INFN, Laboratori Nazionali del Gran Sasso, Assergi (L’Aquila), Italy
74
Universidade Estadual de Feira de Santana, Brazil
75
Palacky University, RCPTM, Olomouc, Czech Republic
76
Charles University, Faculty of Mathematics and Physics, Institute of Particle and Nuclear Physics, Prague, Czech Republic
77
Louisiana State University, Baton Rouge, LA, USA
78
Universit
¨
at Hamburg, Hamburg, Germany
79
Universidade Federal do ABC, Santo Andr
´
e, SP, Brazil
80
Benem
´
erita Universidad Aut
´
onoma de Puebla, Puebla, Mexico
81
Universidad Michoacana de San Nicolas de Hidalgo, Morelia, Michoacan, Mexico
82
Centro de Investigaci
´
on y de Estudios Avanzados del IPN (CINVESTAV), M
´
exico, Mexico
83
Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford, UK
84
University of Hawaii, Honolulu, HI, USA
85
Instituto de F
´
ısica de Rosario (IFIR) - CONICET/U.N.R. and Facultad de Ciencias Bioqu
´
ımicas y Farmac
´
euticas U.N.R., Rosario, Argentina
86
Centro de Investigaciones en L
´
aseres y Aplicaciones, CITEDEF and CONICET, Argentina
87
Instituto de F
´
ısica Corpuscular, CSIC-Universitat de Val
`
encia, Valencia, Spain
88
Northeastern University, Boston, MA, USA
89
Universidade Federal da Bahia, Salvador, BA, Brazil
90
University of Nebraska, Lincoln, NE, USA
91
Colorado School of Mines, Golden, CO, USA
92
University of Bucharest, Physics Department, Romania
93
Argonne National Laboratory, Argonne, IL, USA
94
Los Alamos National Laboratory, Los Alamos, NM, USA
Received 2012 October 22; accepted 2012 November 25; published 2012 December 12
ABSTRACT
A thorough search for large-scale anisotropies in the distribution of arrival directions of cosmic rays detected
above 10
18
eV at the Pierre Auger Observatory is reported. For the first time, these large-scale anisotropy searches
are performed as a function of both the right ascension and the declination and expressed in terms of dipole and
quadrupole moments. Within the systematic uncertainties, no significant deviation from isotropy is revealed. Upper
limits on dipole and quadrupole amplitudes are derived under the hypothesis that any cosmic ray anisotropy is
dominated by such moments in this energy range. These upper limits provide constraints on the production of
cosmic rays above 10
18
eV, since they allow us to challenge an origin from stationary galactic sources densely
distributed in the galactic disk and emitting predominantly light particles in all directions.
Key words: astroparticle physics – cosmic rays
Online-only material: color figures
The large-scale distribution of arrival directions of Ultra-High
Energy Cosmic Rays (UHECRs) as a function of the energy is a
key observable to provide further understanding of their origin.
Above '0.25 EeV, the most stringent bounds ever obtained
on the dipole component in the equatorial plane were recently
reported, being below 2% at 99% CL for EeV energies (Pierre
95
Av. San Mart
´
ın Norte 306, 5613 Malarg
¨
ue, Mendoza, Argentina;
www.auger.org.
96
Deceased.
97
Now at University of Maryland.
98
Now at Universit
´
edeLausanne.
99
At Konan University, Kobe, Japan.
100
Now at NYU Abu Dhabi.
101
Now at the Universidad Autonoma de Chiapas on leave of absence from
Cinvestav.
Auger Collaboration 2011a). Such a sensitivity provides some
constraints upon scenarios in which dipolar anisotropies could
be imprinted in the distribution of arrival directions as the result
of the escape of UHECRs from the Galaxy up to the ankle
energy (Ptuskin et al. 1993; Candia et al. 2003; Giacinti et al.
2012). On the other hand, if UHECRs above 1 EeV already have
a predominant extragalactic origin (Hillas 1967; Blumenthal
1970; Berezinsky et al. 2006, 2004), their angular distribution is
expected to be isotropic to a high level. Thus, the study of large-
scale anisotropies at EeV energies would help in establishing
whether the origin of UHECRs is galactic or extragalactic in
this energy range.
The upper limits aforementioned are based on first harmonic
analyses of the right ascension distributions in several energy
3
The Astrophysical Journal Letters, 762:L13 (8pp), 2013 January 1 Abreu et al.
ranges. The analyses benefit from the almost uniform directional
exposure in right ascension of any ground-based observatory
operating with high duty cycle, but are not sensitive to a dipole
component along the Earth rotation axis. In contrast, using the
large amount of data collected by the surface detector array of the
Pierre Auger Observatory, in this Letter we report on searches
for dipole and quadrupole patterns significantly standing out
above the background noise whose components are functions
of both the right ascension and the declination (a detailed
description of the present analysis can be found in Pierre Auger
Collaboration 2012).
The Pierre Auger Observatory is located in Malarg
¨
ue,
Argentina, at a mean latitude of 35.
◦
2 S, a mean longitude of
69.
◦
5 W, and a mean altitude of 1400 m above sea level. It exploits
two available techniques to detect extensive air showers initiated
by UHECRs: a surface detector (SD) array and a fluorescence
detector (FD). The SD array consists of 1660 water-Cherenkov
detectors laid out over about 3000 km
2
on a triangular grid with
1.5 km spacing, sensitive to the light emitted in their volume by
the secondary particles of the showers. At the perimeter of this
array, the atmosphere is overlooked on dark nights by 27 opti-
cal telescopes grouped in 5 buildings. These telescopes record
the number of secondary charged particles in the air shower as a
function of depth in the atmosphere by measuring the amount of
nitrogen fluorescence caused by those particles along the track
of the shower. At the lowest energies observed, the angular res-
olution of the SD is about 2.
◦
2 and reaches ∼1
◦
at the highest
energies. This is sufficient to perform searches for large-scale
anisotropies. The statistical fluctuation in energy measurement
amounts to about 15%, while the absolute energy scale is given
by the FD measurements and has a systematic uncertainty of
22% (Pierre Auger Collaboration 2008).
In the analyses presented in this Letter, the data set consists
of events recorded by the SD array from 2004 January 1 to
2011 December 31, with zenith angles less than 55
◦
. To ensure
good reconstruction, an event is accepted only if all six nearest
neighbors of the water-Cherenkov detector with the highest
signal were operational at the time of the event (Pierre Auger
Collaboration 2010a). Based on this fiducial cut, any active
water-Cherenkov detector with six active neighbors defines an
active elemental cell. In these conditions, and above the energy
at which the detection efficiency saturates, 3 EeV (Pierre Auger
Collaboration 2010a), the total exposure of the SD array is
23,520 km
2
yr sr.
Due to the steepness of the energy spectrum, any mild bias in
the estimate of the shower energy with time or zenith angle can
lead to significant distortions of the event counting rate above a
given energy. It is thus critical to control the energy estimate in
searching for anisotropies. The procedure followed to obtain an
unbiased estimate of the shower energy consists in correcting
measurements of shower signals for the influences of weather
effects (Pierre Auger Collaboration 2009) and the geomagnetic
field (Pierre Auger Collaboration 2011b). Using the constant
intensity cut method (Hersil 1961), the shower signal is then
converted to the value that would have been expected had the
shower arrived at a zenith angle of 38
◦
. This reference shower
signal is finally converted into energy using a calibration curve
based on hybrid events measured simultaneously by the SD array
and FD telescopes, since the latter can provide a calorimetric
measurement of the energy (Pierre Auger Collaboration 2008).
In searching for anisotropies, it is also critical to know
accurately the effective time-integrated collecting area for a
flux from each direction of the sky, or in other words, the
directional exposure ω of the Observatory. For each elemental
cell, this is obtained through the integration over local sidereal
time (LST) α
0
of x
(i)
(α
0
) × a
cell
(θ) × ²(θ,ϕ,E), with x
(i)
(α
0
)
the total operational time of the cell (i)atLSTα
0
, a
cell
(θ) =
1.95 cos θ km
2
the geometric aperture of each elemental cell
under incidence zenith angle θ (Pierre Auger Collaboration
2010a), and ²(θ,ϕ,E) the detection efficiency under incidence
zenith angle θ and azimuth angle ϕ at energy E.Inthesameway
as in Pierre Auger Collaboration (2011a), the small modulation
of the exposure in α
0
due to the variations of x
(i)
can be
accounted for by re-weighting the events with the number of
elemental cells at the LST of each event k, ΔN
cell
(α
0
k
). Since both
θ and ϕ depend only on the difference α − α
0
, the integration
over α
0
can then be substituted for an integration over the hour
angle α
0
= α − α
0
so that the directional exposure actually does
not depend on right ascension when the x
(i)
areassumedtobe
independent of the LST:
ω(δ, E) =
n
cell
X
i=1
x
(i)
Z
24h
0
dα
0
× a
cell
(θ(α
0
,δ))²(θ (α
0
,δ),ϕ(α
0
,δ),E). (1)
The zenithal dependence of the detection efficiency ²(θ,ϕ,E)
can be obtained directly from the data in an empirical way
(Pierre Auger Collaboration 2012). Additional effects have
an impact on ω, such as the azimuthal dependence of the
efficiency due to geomagnetic effects, the corrections to both
the geometric aperture of each elemental cell and the detection
efficiency due to the tilt of the array, and the corrections due
to the spatial extension of the array. Accounting for all these
effects, the resulting dependence of ω on declination can be
found in Pierre Auger Collaboration (2012). For a wide range
of declinations between '−89
◦
and '−20
◦
, the directional
exposure is '2500 km
2
yr at 1 EeV, and '3500 km
2
yr for
any energy above full efficiency. Then, at higher declinations, it
smoothly falls to zero, with no exposure above 20
◦
declination.
The detection of significant dipole or quadrupole moments
above EeV energies would be of considerable interest. Dipole
and quadrupole patterns are encoded in the low-order a
1m
and
a
2m
coefficients of the multipolar expansion of any angular
distribution over the sphere Φ(n):
Φ(n) =
X
`>0
`
X
m=−`
a
`m
Y
`m
(n), (2)
where n denotes a unit vector taken in equatorial coordinates.
Due to the non-uniform and incomplete coverage of the sky
at the Pierre Auger Observatory, the estimated coefficients
a
`m
are determined in a two-step procedure. First, from any
event set with arrival directions {n
1
,...,n
N
} recorded at LST
{α
0
1
,...,α
0
N
}, the multipolar coefficients of the angular distri-
bution coupled to the exposure function are estimated through
b
`m
=
N
X
k=1
Y
`m
(n
k
)
ΔN
cell
¡
α
0
k
¢
. (3)
ΔN
cell
(α
0
k
) corrects for the slightly non-uniform directional
exposure in right ascension. Then, assuming that the multipolar
expansion of the angular distribution Φ(n)isbounded to `
max
,
the first b
`m
coefficients with ` 6 `
max
are related to the
4
The Astrophysical Journal Letters, 762:L13 (8pp), 2013 January 1 Abreu et al.
E [EeV]
1 10
Amplitude, r
-3
10
-2
10
-1
10
1
Figure 1. Reconstructed amplitude of the dipole as a function of the energy. The
dotted line stands for the 99% CL upper bounds on the amplitudes that would
result from fluctuations of an isotropic distribution.
non-vanishing a
`m
through
b
`m
=
`
max
X
`
0
=0
`
0
X
m
0
=−`
0
[K]
`
0
m
0
`m
a
`
0
m
0
, (4)
where the matrix K is entirely determined by the directional
exposure:
[K]
`
0
m
0
`m
=
Z
ΔΩ
dΩω(n)Y
`m
(n)Y
`
0
m
0
(n). (5)
Inverting Equation (4) allows us to recover the underlying a
`m
,
with a resolution proportional to ([K
−1
]
`m
`m
a
00
)
0.5
(Billoir &
Deligny 2008). As a consequence of the incomplete coverage of
the sky, this resolution deteriorates by a factor larger than two
each time `
max
is incremented by 1. With our present statistics,
this prevents the recovery of each coefficient with good accuracy
as soon as `
max
> 3, which is why we restrict ourselves to dipole
and quadrupole searches.
We first assume that the angular distribution of cosmic rays is
modulated by a pure dipole and parameterize the intensity Φ(n)
in any direction as
Φ(n) =
Φ
0
4π
(1 + rd · n), (6)
where d denotes the dipole unit vector. The dipole pattern is
here fully characterized by a declination δ
d
, a right ascension
α
d
, and an amplitude r corresponding to the maximal anisotropy
contrast: r = (Φ
max
− Φ
min
)/(Φ
max
+ Φ
min
). The estimation of
these three coefficients is straightforward from the estimated
spherical harmonic coefficients a
1m
. The reconstructed ampli-
tudes r are shown in Figure 1 as a function of the energy. The
99% CL upper bounds on the amplitudes that would result from
fluctuations of an isotropic distribution are indicated by the dot-
ted line. One can see that within the statistical uncertainties,
there is no evidence of any significant signal. In Figure 2,the
corresponding directions are shown in orthographic projection
with the associated uncertainties, as a function of the energy.
Both angles are expected to be randomly distributed in the case
of independent samples whose parent distribution is isotropic.
It is thus interesting to note that all reconstructed declinations
are in the equatorial southern hemisphere, and to note also the
intriguing smooth alignment of the phases in right ascension as
a function of the energy. In our previous report on first harmonic
°=-90δ
°=-60δ
°=-30δ
°=0δ
°=30δ
°=330α
°=0α
°=30α
°=60α
°=90α
1<E[EeV]<2
2<E[EeV]<4
4<E[EeV]<8
E[EeV]>8
Figure 2. Reconstructed declination and right ascension of the dipole with
corresponding uncertainties, as a function of the energy, in orthographic
projection.
(A color version of this figure is available in the online journal.)
E [EeV]
1 10
]°Right Ascension [
0
60
120
180
300
240
180
Figure 3. Reconstructed right ascension of the dipole as a function of the energy.
The smooth fit to the data of Pierre Auger Collaboration (2011a)isshownas
the dashed line (see the text).
(A color version of this figure is available in the online journal.)
analysis in right ascension (Pierre Auger Collaboration 2011a),
we already pointed out this alignment, and stressed that such a
consistency of phases in adjacent energy intervals is expected
with a smaller number of events than the detection of ampli-
tudes standing out significantly above the background noise in
the case of a real underlying anisotropy. This motivated us to
design a prescription aimed at establishing at 99% CL whether
this consistency in phases is real, using the exact same analy-
sis as the one reported in Pierre Auger Collaboration (2011a).
The prescribed test will end once the total exposure since 2011
June 25 reaches 21,000 km
2
yr sr. The smooth fit to the data
of Pierre Auger Collaboration (2011a) is shown as a dashed
line in Figure 3, restricted to the energy range considered here.
Though the phase between 4 and 8 EeV is poorly determined
due to the corresponding direction in declination pointing close
to the equatorial south pole, it is noteworthy that a consistently
5
