Deep-learning based reconstruction of the shower maximum X$_{max}$ using the water-Cherenkov detectors of the Pierre Auger Observatory

Repository KITopen (Karlsruhe Institute of Technology)

Abstract

The atmospheric depth of the air shower maximum Xmax is an observable commonly used for the determination of the nuclear mass composition of ultra-high energy cosmic rays. Direct measurements of Xmax are performed using observations of the longitudinal shower development with fluorescence telescopes. At the same time, several methods have been proposed for an indirect estimation of Xmax from the characteristics of the shower particles registered with surface detector arrays. In this paper, we present a deep neural network (DNN) for the estimation of Xmax. The reconstruction relies on the signals induced by shower particles in the ground based water-Cherenkov detectors of the Pierre Auger Observatory. The network architecture features recurrent long short-term memory layers to process the temporal structure of signals and hexagonal convolutions to exploit the symmetry of the surface detector array. We evaluate the performance of the network using air showers simulated with three different hadronic interaction models. Thereafter, we account for long-term detector effects and calibrate the reconstructed Xmax using fluorescence measurements. Finally, we show that the event-by-event resolution in the reconstruction of the shower maximum improves with increasing shower energy and reaches less than 25 g/cm2 at energies above 2 × 1019 eV.

Authors 95

1. A. Aab

   Radboud University Nijmegen

   Affiliation as printed

   IMAPP, Radboud University Nijmegen, Nijmegen, The Netherlands

2. P. Abreu

   University of Lisbon · LIP - Laboratory of Instrumentation and Experimental Particle Physics · Instituto Superior Técnico

   Affiliation as printed

   Laboratório de Instrumentação e Física Experimental de Partículas — LIP and Instituto Superior Técnico — IST, Universidade de Lisboa — UL, Lisboa, Portugal

3. M. Aglietta

   Istituto Nazionale di Fisica Nucleare, Sezione di Torino · Osservatorio Astrofisico di Torino · National Institute for Astrophysics

   Affiliation as printed

   INFN, Sezione di Torino, Torino, Italy

   Osservatorio Astrofisico di Torino (INAF), Torino, Italy

4. Justin M. Albury

   The University of Adelaide

   Affiliation as printed

   University of Adelaide, Adelaide, S.A., Australia

5. I. Allekotte

   Consejo Nacional de Investigaciones Científicas y Técnicas · Balseiro Institute · Bariloche Atomic Centre

   Affiliation as printed

   Centro Atómico Bariloche and Instituto Balseiro (CNEA-UNCuyo-CONICET), San Carlos de Bariloche, Argentina

6. Alejandro Almela

   National Technological University · Consejo Nacional de Investigaciones Científicas y Técnicas · National University of General San Martín · Instituto de Tecnologías en Detección y Astropartículas

   Affiliation as printed

   Instituto de Tecnologías en Detección y Astropartículas (CNEA, CONICET, UNSAM), Buenos Aires, Argentina

   Universidad Tecnológica Nacional — Facultad Regional Buenos Aires, Buenos Aires, Argentina

7. Jaime Álvarez-Muñiz

   Universidade de Santiago de Compostela

   Affiliation as printed

   Instituto Galego de Física de Altas Enerxías (IGFAE), Universidade de Santiago de Compostela, Santiago de Compostela, Spain

8. Rafael Alves Batista

   Radboud University Nijmegen

   Affiliation as printed

   IMAPP, Radboud University Nijmegen, Nijmegen, The Netherlands

9. Gioacchino Alex Anastasi

   Istituto Nazionale di Fisica Nucleare, Sezione di Torino · University of Turin

   Affiliation as printed

   INFN, Sezione di Torino, Torino, Italy

   Università Torino, Dipartimento di Fisica, Torino, Italy

10. Luis A. Anchordoqui

    Lehman College · City University of New York

    Affiliation as printed

    Department of Physics and Astronomy, Lehman College, City University of New York, Bronx, NY, U.S.A

11. Belén Andrada

    Consejo Nacional de Investigaciones Científicas y Técnicas · National University of General San Martín · Instituto de Tecnologías en Detección y Astropartículas

    Affiliation as printed

    Instituto de Tecnologías en Detección y Astropartículas (CNEA, CONICET, UNSAM), Buenos Aires, Argentina

12. S. Andringa

    University of Lisbon · LIP - Laboratory of Instrumentation and Experimental Particle Physics · Instituto Superior Técnico

    Affiliation as printed

    Laboratório de Instrumentação e Física Experimental de Partículas — LIP and Instituto Superior Técnico — IST, Universidade de Lisboa — UL, Lisboa, Portugal

13. C. Aramo

    Istituto Nazionale di Fisica Nucleare, Sezione di Napoli

    Affiliation as printed

    INFN, Sezione di Napoli, Napoli, Italy

14. Paulo Ricardo Araújo Ferreira Aachen III. Physikalisches Institut A

    RWTH Aachen University

    Affiliation as printed

    RWTH Aachen University, III. Physikalisches Institut A, Aachen, Germany

15. Juan Carlos Arteaga Velázquez

    Universidad Michoacana de San Nicolás de Hidalgo

    Affiliation as printed

    Universidad Michoacana de San Nicolás de Hidalgo, Morelia, Michoacán, México

16. H. Asorey

    Consejo Nacional de Investigaciones Científicas y Técnicas · National University of General San Martín · Instituto de Tecnologías en Detección y Astropartículas

    Affiliation as printed

    Instituto de Tecnologías en Detección y Astropartículas (CNEA, CONICET, UNSAM), Buenos Aires, Argentina

17. Pedro Assis

    University of Lisbon · LIP - Laboratory of Instrumentation and Experimental Particle Physics · Instituto Superior Técnico

    Affiliation as printed

    Laboratório de Instrumentação e Física Experimental de Partículas — LIP and Instituto Superior Técnico — IST, Universidade de Lisboa — UL, Lisboa, Portugal

18. G. Ávila

    Pierre Auger Observatory · Comisión Nacional de Energía Atómica

    Affiliation as printed

    Observatorio Pierre Auger and Comisión Nacional de Energía Atómica, Malargüe, Argentina

19. Alina Mihaela Badescu

    Universitatea Națională de Știință și Tehnologie Politehnica București

    Affiliation as printed

    University Politehnica of Bucharest, Bucharest, Romania

20. Alena Bakalová

    FZU - Institute of Physics of the Czech Academy of Sciences

    Affiliation as printed

    Institute of Physics of the Czech Academy of Sciences, Prague, Czech Republic

21. Alexandru Balaceanu

    Horia Hulubei National Institute for R and D in Physics and Nuclear Engineering

    Affiliation as printed

    “Horia Hulubei” National Institute for Physics and Nuclear Engineering, Bucharest-Magurele, Romania

22. Felicia Carla Tiziana Barbato

    Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali del Gran Sasso · Gran Sasso Science Institute

    Affiliation as printed

    Gran Sasso Science Institute, L'Aquila, Italy

    INFN Laboratori Nazionali del Gran Sasso, Assergi (L'Aquila), Italy

23. Ricardo Jorge Barreira Luz

    University of Lisbon · LIP - Laboratory of Instrumentation and Experimental Particle Physics · Instituto Superior Técnico

    Affiliation as printed

    Laboratório de Instrumentação e Física Experimental de Partículas — LIP and Instituto Superior Técnico — IST, Universidade de Lisboa — UL, Lisboa, Portugal

24. K.H. Becker

    University of Wuppertal

    Affiliation as printed

    Bergische Universität Wuppertal, Department of Physics, Wuppertal, Germany

25. Jose A. Bellido

    Universidad Nacional de San Agustin de Arequipa · The University of Adelaide

    Affiliation as printed

    Universidad Nacional de San Agustin de Arequipa, Facultad de Ciencias Naturales y Formales, Arequipa, Peru

    University of Adelaide, Adelaide, S.A., Australia

26. Corinne Bérat

    Centre National de la Recherche Scientifique · Institut National de Physique Nucléaire et de Physique des Particules · Université Grenoble Alpes

    Affiliation as printed

    Univ. Grenoble Alpes, CNRS, Grenoble Institute of Engineering Univ. Grenoble Alpes, LPSC-IN2P3, 38000 Grenoble, France

27. Mario Edoardo Bertaina

    Istituto Nazionale di Fisica Nucleare, Sezione di Torino · University of Turin

    Affiliation as printed

    INFN, Sezione di Torino, Torino, Italy

    Università Torino, Dipartimento di Fisica, Torino, Italy

28. X. Bertou

    Consejo Nacional de Investigaciones Científicas y Técnicas · Balseiro Institute · Bariloche Atomic Centre

    Affiliation as printed

    Centro Atómico Bariloche and Instituto Balseiro (CNEA-UNCuyo-CONICET), San Carlos de Bariloche, Argentina

29. Peter L. Biermann

    Max Planck Institute for Radio Astronomy

    Affiliation as printed

    Max-Planck-Institut für Radioastronomie, Bonn, Germany

30. Teresa Bister Aachen III. Physikalisches Institut A

    RWTH Aachen University

    Affiliation as printed

    RWTH Aachen University, III. Physikalisches Institut A, Aachen, Germany

31. Jonathan Biteau

    Centre National de la Recherche Scientifique · Université Paris-Saclay · Institut National de Physique Nucléaire et de Physique des Particules · Laboratoire de Physique des 2 Infinis Irène Joliot-Curie

    Affiliation as printed

    Université Paris-Saclay, CNRS/IN2P3, IJCLab, Orsay, France

32. Jiří Blažek

    FZU - Institute of Physics of the Czech Academy of Sciences

    Affiliation as printed

    Institute of Physics of the Czech Academy of Sciences, Prague, Czech Republic

33. C. Bleve

    Centre National de la Recherche Scientifique · Institut National de Physique Nucléaire et de Physique des Particules · Université Grenoble Alpes

    Affiliation as printed

    Univ. Grenoble Alpes, CNRS, Grenoble Institute of Engineering Univ. Grenoble Alpes, LPSC-IN2P3, 38000 Grenoble, France

34. Denise Boncioli

    University of L'Aquila · Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali del Gran Sasso

    Affiliation as printed

    INFN Laboratori Nazionali del Gran Sasso, Assergi (L'Aquila), Italy

    Università dell'Aquila, Dipartimento di Scienze Fisiche e Chimiche, L'Aquila, Italy

35. C. Bonifazi

    Universidade Federal do Rio de Janeiro

    Affiliation as printed

    Universidade Federal do Rio de Janeiro, Instituto de Física, Rio de Janeiro, RJ, Brazil

36. Luan Bonneau Arbeletche

    Universidade de São Paulo

    Affiliation as printed

    Universidade de São Paulo, Instituto de Física, São Paulo, SP, Brazil

37. Nataliia Borodai

    Institute of Nuclear Physics, Polish Academy of Sciences

    Affiliation as printed

    Institute of Nuclear Physics PAN, Krakow, Poland

38. Ana Martina Botti

    Consejo Nacional de Investigaciones Científicas y Técnicas · National University of General San Martín · Instituto de Tecnologías en Detección y Astropartículas

    Affiliation as printed

    Instituto de Tecnologías en Detección y Astropartículas (CNEA, CONICET, UNSAM), Buenos Aires, Argentina

39. J. Brack

    Colorado State University

    Affiliation as printed

    Colorado State University, Fort Collins, CO, U.S.A

40. T. Bretz Aachen III. Physikalisches Institut A

    RWTH Aachen University

    Affiliation as printed

    RWTH Aachen University, III. Physikalisches Institut A, Aachen, Germany

41. P. Gabriel Brichetto Orchera

    Consejo Nacional de Investigaciones Científicas y Técnicas · National University of General San Martín · Instituto de Tecnologías en Detección y Astropartículas

    Affiliation as printed

    Instituto de Tecnologías en Detección y Astropartículas (CNEA, CONICET, UNSAM), Buenos Aires, Argentina

42. Florian Lukas Briechle Aachen III. Physikalisches Institut A

    RWTH Aachen University

    Affiliation as printed

    RWTH Aachen University, III. Physikalisches Institut A, Aachen, Germany

43. Peter Buchholz

    University of Siegen

    Affiliation as printed

    Universität Siegen, Department Physik — Experimentelle Teilchenphysik, Siegen, Germany

44. Antonio Bueno

    Universidad de Granada

    Affiliation as printed

    Universidad de Granada and C.A.F.P.E., Granada, Spain

45. S. Buitink

    Vrije Universiteit Brussel

    Affiliation as printed

    Vrije Universiteit Brussels, Brussels, Belgium

46. Mario Buscemi

    Istituto Nazionale di Fisica Nucleare, Sezione di Catania

    Affiliation as printed

    INFN, Sezione di Catania, Catania, Italy

47. Karen Salomé Caballero-Mora

    Universidad Autónoma de Chiapas

    Affiliation as printed

    Universidad Autónoma de Chiapas, Tuxtla Gutiérrez, Chiapas, México

48. Lorenzo Caccianiga

    University of Milan · Istituto Nazionale di Fisica Nucleare, Sezione di Milano

    Affiliation as printed

    INFN, Sezione di Milano, Milano, Italy

    Università di Milano, Dipartimento di Fisica, Milano, Italy

49. Fabrizia Canfora

    Radboud University Nijmegen · National Institute for Subatomic Physics

    Affiliation as printed

    IMAPP, Radboud University Nijmegen, Nijmegen, The Netherlands

    Nationaal Instituut voor Kernfysica en Hoge Energie Fysica (NIKHEF), Science Park, Amsterdam, The Netherlands

50. Ioana Caracas

    University of Wuppertal

    Affiliation as printed

    Bergische Universität Wuppertal, Department of Physics, Wuppertal, Germany

51. Jose Miguel Carceller

    Universidad de Granada

    Affiliation as printed

    Universidad de Granada and C.A.F.P.E., Granada, Spain

52. Rossella Caruso

    University of Catania · Istituto Nazionale di Fisica Nucleare, Sezione di Catania

    Affiliation as printed

    INFN, Sezione di Catania, Catania, Italy

    Università di Catania, Dipartimento di Fisica e Astronomia, Catania, Italy

53. A. Castellina

    Istituto Nazionale di Fisica Nucleare, Sezione di Torino · Osservatorio Astrofisico di Torino · National Institute for Astrophysics

    Affiliation as printed

    INFN, Sezione di Torino, Torino, Italy

    Osservatorio Astrofisico di Torino (INAF), Torino, Italy

54. Fernando Catalani

    Universidade de São Paulo

    Affiliation as printed

    Universidade de São Paulo, Escola de Engenharia de Lorena, Lorena, SP, Brazil

55. G. Cataldi

    Istituto Nazionale di Fisica Nucleare, Sezione di Lecce

    Affiliation as printed

    INFN, Sezione di Lecce, Lecce, Italy

56. Lorenzo Cazon

    University of Lisbon · LIP - Laboratory of Instrumentation and Experimental Particle Physics · Instituto Superior Técnico

    Affiliation as printed

    Laboratório de Instrumentação e Física Experimental de Partículas — LIP and Instituto Superior Técnico — IST, Universidade de Lisboa — UL, Lisboa, Portugal

57. M. Cerda

    Pierre Auger Observatory

    Affiliation as printed

    Observatorio Pierre Auger, Malargüe, Argentina

58. Jose Augusto Chinellato

    Universidade Estadual de Campinas (UNICAMP)

    Affiliation as printed

    Universidade Estadual de Campinas, IFGW, Campinas, SP, Brazil

59. Koun Choi

    Université Libre de Bruxelles

    Affiliation as printed

    Université Libre de Bruxelles (ULB), Brussels, Belgium

60. Jiří Chudoba

    FZU - Institute of Physics of the Czech Academy of Sciences

    Affiliation as printed

    Institute of Physics of the Czech Academy of Sciences, Prague, Czech Republic

61. L. Chytka

    Palacký University Olomouc

    Affiliation as printed

    Palacky University, RCPTM, Olomouc, Czech Republic

62. R. W. Clay

    The University of Adelaide

    Affiliation as printed

    University of Adelaide, Adelaide, S.A., Australia

63. Agustín Cobos Cerutti

    National Technological University · Consejo Nacional de Investigaciones Científicas y Técnicas · National University of General San Martín · Instituto de Tecnologías en Detección y Astropartículas

    Affiliation as printed

    Instituto de Tecnologías en Detección y Astropartículas (CNEA, CONICET, UNSAM), and Universidad Tecnológica Nacional — Facultad Regional Mendoza (CONICET/CNEA), Mendoza, Argentina

64. Roberta Colalillo

    Istituto Nazionale di Fisica Nucleare, Sezione di Napoli · University of Naples Federico II

    Affiliation as printed

    INFN, Sezione di Napoli, Napoli, Italy

    Università di Napoli “Federico II”, Dipartimento di Fisica “Ettore Pancini”, Napoli, Italy

65. Alan Coleman

    University of Delaware

    Affiliation as printed

    University of Delaware, Department of Physics and Astronomy, Bartol Research Institute, Newark, DE, U.S.A

66. M. R. Coluccia

    Istituto Nazionale di Fisica Nucleare, Sezione di Lecce

    Affiliation as printed

    INFN, Sezione di Lecce, Lecce, Italy

67. R. Conceição

    University of Lisbon · LIP - Laboratory of Instrumentation and Experimental Particle Physics · Instituto Superior Técnico

    Affiliation as printed

    Laboratório de Instrumentação e Física Experimental de Partículas — LIP and Instituto Superior Técnico — IST, Universidade de Lisboa — UL, Lisboa, Portugal

68. Antonio Condorelli

    Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali del Gran Sasso · Gran Sasso Science Institute

    Affiliation as printed

    Gran Sasso Science Institute, L'Aquila, Italy

    INFN Laboratori Nazionali del Gran Sasso, Assergi (L'Aquila), Italy

69. Giovanni Consolati

    Istituto Nazionale di Fisica Nucleare, Sezione di Milano · Politecnico di Milano

    Affiliation as printed

    INFN, Sezione di Milano, Milano, Italy

    Politecnico di Milano, Dipartimento di Scienze e Tecnologie Aerospaziali , Milano, Italy

70. F. Contreras

    Pierre Auger Observatory · Comisión Nacional de Energía Atómica

    Affiliation as printed

    Observatorio Pierre Auger and Comisión Nacional de Energía Atómica, Malargüe, Argentina

71. Fabio Convenga

    University of Salento · Istituto Nazionale di Fisica Nucleare, Sezione di Lecce

    Affiliation as printed

    INFN, Sezione di Lecce, Lecce, Italy

    Università del Salento, Dipartimento di Matematica e Fisica “E. De Giorgi”, Lecce, Italy

72. Diego Correia dos Santos

    Universidade Federal Fluminense

    Affiliation as printed

    Universidade Federal Fluminense, EEIMVR, Volta Redonda, RJ, Brazil

73. Corbin E. Covault

    Case Western Reserve University

    Affiliation as printed

    Case Western Reserve University, Cleveland, OH, U.S.A

74. Sergio Dasso

    Consejo Nacional de Investigaciones Científicas y Técnicas · Universidad de Buenos Aires · Institute of Astronomy and Space Physics

    Affiliation as printed

    Departamento de Física and Departamento de Ciencias de la Atmósfera y los Océanos, FCEyN, Universidad de Buenos Aires and CONICET, Buenos Aires, Argentina

    Instituto de Astronomía y Física del Espacio (IAFE, CONICET-UBA), Buenos Aires, Argentina

75. K. Daumiller

    Karlsruhe Institute of Technology

    Affiliation as printed

    Karlsruhe Institute of Technology (KIT), Institute for Astroparticle Physics, Karlsruhe, Germany

76. Bruce R. Dawson

    The University of Adelaide

    Affiliation as printed

    University of Adelaide, Adelaide, S.A., Australia

77. J.A. Day

    The University of Adelaide

    Affiliation as printed

    University of Adelaide, Adelaide, S.A., Australia

78. R. M. de Almeida

    Universidade Federal Fluminense

    Affiliation as printed

    Universidade Federal Fluminense, EEIMVR, Volta Redonda, RJ, Brazil

79. Joaquín de Jesús

    Karlsruhe Institute of Technology · Consejo Nacional de Investigaciones Científicas y Técnicas · National University of General San Martín · Instituto de Tecnologías en Detección y Astropartículas

    Affiliation as printed

    Instituto de Tecnologías en Detección y Astropartículas (CNEA, CONICET, UNSAM), Buenos Aires, Argentina

    Karlsruhe Institute of Technology (KIT), Institute for Astroparticle Physics, Karlsruhe, Germany

80. S. J. de Jong

    Radboud University Nijmegen · National Institute for Subatomic Physics

    Affiliation as printed

    IMAPP, Radboud University Nijmegen, Nijmegen, The Netherlands

    Nationaal Instituut voor Kernfysica en Hoge Energie Fysica (NIKHEF), Science Park, Amsterdam, The Netherlands

81. G. De Mauro

    Radboud University Nijmegen · National Institute for Subatomic Physics

    Affiliation as printed

    IMAPP, Radboud University Nijmegen, Nijmegen, The Netherlands

    Nationaal Instituut voor Kernfysica en Hoge Energie Fysica (NIKHEF), Science Park, Amsterdam, The Netherlands

82. I. De Mitri

    Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali del Gran Sasso · Gran Sasso Science Institute

    Affiliation as printed

    Gran Sasso Science Institute, L'Aquila, Italy

    INFN Laboratori Nazionali del Gran Sasso, Assergi (L'Aquila), Italy

83. Jaime de Souza Oliveira

    Universidade Federal Fluminense

    Affiliation as printed

    Universidade Federal Fluminense, EEIMVR, Volta Redonda, RJ, Brazil

84. Danelise de Oliveira Franco

    Universidade Estadual de Campinas (UNICAMP)

    Affiliation as printed

    Universidade Estadual de Campinas, IFGW, Campinas, SP, Brazil

85. Emanuele De Vito

    University of Salento · Istituto Nazionale di Fisica Nucleare, Sezione di Lecce

    Affiliation as printed

    INFN, Sezione di Lecce, Lecce, Italy

    Università del Salento, Dipartimento di Matematica e Fisica “E. De Giorgi”, Lecce, Italy

86. Olivier Deligny

    Centre National de la Recherche Scientifique · Université Paris-Saclay · Institut National de Physique Nucléaire et de Physique des Particules · Laboratoire de Physique des 2 Infinis Irène Joliot-Curie

    Affiliation as printed

    CNRS/IN2P3, IJCLab, Université Paris-Saclay, Orsay, France

87. Armando di Matteo

    Istituto Nazionale di Fisica Nucleare, Sezione di Torino

    Affiliation as printed

    INFN, Sezione di Torino, Torino, Italy

88. C. Dobrigkeit

    Universidade Estadual de Campinas (UNICAMP)

    Affiliation as printed

    Universidade Estadual de Campinas, IFGW, Campinas, SP, Brazil

89. J. C. D’Olivo

    Universidad Nacional Autónoma de México

    Affiliation as printed

    Universidad Nacional Autónoma de México, México, D.F., México

90. R. C. dos Anjos

    Universidade Federal do Paraná

    Affiliation as printed

    Universidade Federal do Paraná, Setor Palotina, Palotina, Brazil

91. M. T. Dova

    Consejo Nacional de Investigaciones Científicas y Técnicas · Instituto de Física La Plata · Universidad Nacional de La Plata

    Affiliation as printed

    IFLP, Universidad Nacional de La Plata and CONICET, La Plata, Argentina

92. Jan Ebr

    FZU - Institute of Physics of the Czech Academy of Sciences

    Affiliation as printed

    Institute of Physics of the Czech Academy of Sciences, Prague, Czech Republic

93. Robert Engel

    Karlsruhe Institute of Technology

    Affiliation as printed

    Karlsruhe Institute of Technology (KIT), Institute for Astroparticle Physics, Karlsruhe, Germany

    Karlsruhe Institute of Technology (KIT), Institute for Experimental Particle Physics, Karlsruhe, Germany

94. Italo Epicoco

    University of Salento · Istituto Nazionale di Fisica Nucleare, Sezione di Lecce

    Affiliation as printed

    INFN, Sezione di Lecce, Lecce, Italy

    Università del Salento, Dipartimento di Matematica e Fisica “E. De Giorgi”, Lecce, Italy

95. Martin Erdmann Aachen III. Physikalisches Institut A

    RWTH Aachen University

    Affiliation as printed

    RWTH Aachen University, III. Physikalisches Institut A, Aachen, Germany