Euclid preparation. Three-dimensional galaxy clustering in configuration space: Three-point correlation function estimation
Abstract
Higher-order correlation functions are firmly established as a fundamental tool for the statistical analysis of clustering in modern galaxy surveys. It was demonstrated that they greatly enrich the information content extracted by two-point statistics, allowing us to break the degeneracies between model parameters and constrain departures from Gaussianity. This paper presents the statistical estimators adopted to evaluate the galaxy three-point correlation function and its numerical implementation within the data analysis pipeline of the Euclid Science Ground Segment. Two different algorithms are adopted to count triplets: a direct and exact counting method capable of providing a robust three-point correlation function measurement for any triangular configuration, and a more efficient method based on spherical harmonic decomposition, designed to address the computational challenges of measuring the three-point statistics for data sets as large as those of the final Euclid survey. The spherical harmonic decomposition estimates the Legendre coefficients of the three-point correlation function up to a finite expansion order. Despite being an approximation, the three-point function measured with this approach satisfies the scientific requirements of the mission. We also introduce, implement, and validate the random split technique, which reduces the computational cost of counting triplets in the reference random sample by a factor of 10, without significantly compromising numerical accuracy. We evaluated the robustness, precision, and accuracy of the numerical estimates through an extensive campaign of validation tests, the results of which are presented. Finally, we quantify the computational requirements and their scaling with the expected size of Euclid data set, showing that a complete three-point analysis of the final Euclid survey is within computational reach.
Authors 99
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Brera Astronomical Observatory · Istituto Nazionale di Fisica Nucleare, Sezione di Genova · University of Genoa
Affiliation as printed
INAF-Osservatorio Astronomico di Brera, Via Brera 28, 20122 Milano, Italy
INFN-Sezione di Genova, Via Dodecaneso 33, 16146, Genova, Italy
Dipartimento di Fisica, Università di Genova, Via Dodecaneso 33, 16146, Genova, Italy
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Osservatorio di Astrofisica e Scienza dello Spazio · National Institute for Astrophysics · University of Bologna
Affiliation as printed
Dipartimento di Fisica e Astronomia "Augusto Righi" - Alma Mater Studiorum Università di Bologna, via Piero Gobetti 93/2, 40129 Bologna, Italy
INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy
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Istituto Nazionale di Fisica Nucleare, Sezione di Bologna · Osservatorio di Astrofisica e Scienza dello Spazio · National Institute for Astrophysics · University of Bologna
Affiliation as printed
Dipartimento di Fisica e Astronomia "Augusto Righi" - Alma Mater Studiorum Università di Bologna, via Piero Gobetti 93/2, 40129 Bologna, Italy
INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy
INFN-Sezione di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy
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Brera Astronomical Observatory · Istituto Nazionale di Fisica Nucleare, Sezione di Genova · University of Genoa
Affiliation as printed
Dipartimento di Fisica, Università di Genova, Via Dodecaneso 33, 16146, Genova, Italy
INFN-Sezione di Genova, Via Dodecaneso 33, 16146, Genova, Italy
INAF-Osservatorio Astronomico di Brera, Via Brera 28, 20122 Milano, Italy
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Osservatorio di Astrofisica e Scienza dello Spazio · National Institute for Astrophysics · University of Bologna
Affiliation as printed
Dipartimento di Fisica e Astronomia, Università di Bologna, Via Gobetti 93/2, 40129 Bologna, Italy
INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy
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Brera Astronomical Observatory · Istituto Nazionale di Fisica Nucleare, Sezione di Genova · University of Genoa
Affiliation as printed
Dipartimento di Fisica, Università di Genova, Via Dodecaneso 33, 16146, Genova, Italy
INAF-Osservatorio Astronomico di Brera, Via Brera 28, 20122 Milano, Italy
INFN-Sezione di Genova, Via Dodecaneso 33, 16146, Genova, Italy
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Affiliation as printed
Universität Bonn, Argelander-Institut für Astronomie, Auf dem Hügel 71, 53121 Bonn, Germany
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Trieste Astronomical Observatory · Istituto Nazionale di Fisica Nucleare, Sezione di Trieste · Institute for Fundamental Physics of the Universe
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INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34143 Trieste, Italy
IFPU, Institute for Fundamental Physics of the Universe, via Beirut 2, 34151 Trieste, Italy
INFN, Sezione di Trieste, Via Valerio 2, 34127 Trieste TS, Italy
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Trieste Astronomical Observatory
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INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34143 Trieste, Italy
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Trieste Astronomical Observatory
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INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34143 Trieste, Italy
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Trieste Astronomical Observatory
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INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34143 Trieste, Italy
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Centre National de la Recherche Scientifique · Aix-Marseille Université
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Aix-Marseille Université, CNRS, CNES, LAM, Marseille, France
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Affiliation as printed
Universität Bonn, Argelander-Institut für Astronomie, Auf dem Hügel 71, 53121 Bonn, Germany
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University of Helsinki · Helsinki Institute of Physics
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Department of Physics and Helsinki Institute of Physics, Gustaf Hällströmin katu 2, University of Helsinki, 00014 Helsinki, Finland
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Scuola Internazionale Superiore di Studi Avanzati · Trieste Astronomical Observatory · Istituto Nazionale di Fisica Nucleare, Sezione di Trieste · Institute for Fundamental Physics of the Universe · Fondazione ICSC Centro Nazionale di Ricerca in High Performance Computing, Big Data e Quantum Computing
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IFPU, Institute for Fundamental Physics of the Universe, via Beirut 2, 34151 Trieste, Italy
INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34143 Trieste, Italy
SISSA, International School for Advanced Studies, Via Bonomea 265, 34136 Trieste TS, Italy
INFN, Sezione di Trieste, Via Valerio 2, 34127 Trieste TS, Italy
ICSC - Centro Nazionale di Ricerca in High Performance Computing, Big Data e Quantum Computing, Via Magnanelli 2, Bologna, Italy
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Centre National de la Recherche Scientifique · Université Paris-Saclay · Institut d'Astrophysique Spatiale
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Université Paris-Saclay, CNRS, Institut d'astrophysique spatiale, 91405, Orsay, France
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European Space Astronomy Centre
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ESAC/ESA, Camino Bajo del Castillo, s/n., Urb. Villafranca del Castillo, 28692 Villanueva de la Cañada, Madrid, Spain
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Brera Astronomical Observatory
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INAF-Osservatorio Astronomico di Brera, Via Brera 28, 20122 Milano, Italy
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Osservatorio di Astrofisica e Scienza dello Spazio · National Institute for Astrophysics
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INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy
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Scuola Internazionale Superiore di Studi Avanzati · Trieste Astronomical Observatory · Istituto Nazionale di Fisica Nucleare, Sezione di Trieste · Institute for Fundamental Physics of the Universe
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IFPU, Institute for Fundamental Physics of the Universe, via Beirut 2, 34151 Trieste, Italy
INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34143 Trieste, Italy
INFN, Sezione di Trieste, Via Valerio 2, 34127 Trieste TS, Italy
SISSA, International School for Advanced Studies, Via Bonomea 265, 34136 Trieste TS, Italy
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Istituto Nazionale di Fisica Nucleare, Sezione di Bologna · Osservatorio di Astrofisica e Scienza dello Spazio · National Institute for Astrophysics · University of Bologna
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Dipartimento di Fisica e Astronomia, Università di Bologna, Via Gobetti 93/2, 40129 Bologna, Italy
INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy
INFN-Sezione di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy
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Osservatorio di Astrofisica e Scienza dello Spazio · National Institute for Astrophysics
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INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy
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Osservatorio di Astrofisica e Scienza dello Spazio · National Institute for Astrophysics
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INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy
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Trieste Astronomical Observatory · Institute for Fundamental Physics of the Universe
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INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34143 Trieste, Italy
IFPU, Institute for Fundamental Physics of the Universe, via Beirut 2, 34151 Trieste, Italy
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Astronomical Observatory of Capodimonte · University of Naples Federico II
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Department of Physics "E. Pancini", University Federico II, Via Cinthia 6, 80126, Napoli, Italy
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Istituto Nazionale di Fisica Nucleare, Sezione di Torino · Osservatorio Astrofisico di Torino · University of Turin · National Institute for Astrophysics
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Dipartimento di Fisica, Università degli Studi di Torino, Via P. Giuria 1, 10125 Torino, Italy
INFN-Sezione di Torino, Via P. Giuria 1, 10125 Torino, Italy
INAF-Osservatorio Astrofisico di Torino, Via Osservatorio 20, 10025 Pino Torinese
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Leiden University · Royal Observatory · Leiden Observatory · University of Edinburgh
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Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ, UK
Leiden Observatory, Leiden University, Einsteinweg 55, 2333 CC Leiden, The Netherlands
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Osservatorio Astrofisico di Torino · National Institute for Astrophysics
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National Institute for Astrophysics
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INAF-IASF Milano, Via Alfonso Corti 12, 20133 Milano, Italy
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Astronomical Observatory of Rome · Istituto Nazionale di Fisica Nucleare, Sezione di Roma I · National Institute for Astrophysics
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INAF-Osservatorio Astronomico di Roma, Via Frascati 33, 00078 Monteporzio Catone, Italy
INFN-Sezione di Roma, Piazzale Aldo Moro, 2 - c/o Dipartimento di Fisica, Edificio G. Marconi, 00185 Roma, Italy
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Port d'Informació Científica · Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas
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Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas
Port d'Informació Científica, Campus UAB, C. Albareda s/n, 08193 Bellaterra
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Deutsches Zentrum für Luft- und Raumfahrt e. V. (DLR)
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Institute for Theoretical Particle Physics and Cosmology
Deutsches Zentrum für Luft- und Raumfahrt e. V
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Astronomical Observatory of Rome · National Institute for Astrophysics
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INAF-Osservatorio Astronomico di Roma, Via Frascati 33, 00078 Monteporzio Catone, Italy
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Osservatorio di Astrofisica e Scienza dello Spazio · National Institute for Astrophysics
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INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy
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Astronomical Observatory of Capodimonte · Istituto Nazionale di Fisica Nucleare, Sezione di Napoli
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INAF-Osservatorio Astronomico di Capodimonte, Via Moiariello 16, 80131 Napoli, Italy
INFN section of Naples, Via Cinthia 6, 80126, Napoli, Italy
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University of Hawaiʻi at Mānoa · University of Hawaii System
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Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu, HI 96822, USA
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Affiliation as printed
Dipartimento di Fisica e Astronomia "Augusto Righi" - Alma Mater Studiorum Università di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy
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Instituto de Astrofísica de Canarias
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Instituto de Astrofísica de Canarias, E-38205 La Laguna, Tenerife, Spain
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Affiliation as printed
Jodrell Bank Centre for Astrophysics, Department of Physics and Astronomy, University of Manchester, Oxford Road, Manchester M13 9PL, UK
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European Space Agency · European Space Astronomy Centre · European Space Research Institute
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European Space Agency/ESRIN, Largo Galileo Galilei 1, 00044 Frascati, Roma, Italy
ESAC/ESA, Camino Bajo del Castillo, s/n., Urb. Villafranca del Castillo, 28692 Villanueva de la Cañada, Madrid, Spain
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Lyon 1 Université · Centre National de la Recherche Scientifique · Institut National de Physique Nucléaire et de Physique des Particules · Institut de Physique des 2 Infinis de Lyon
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Université Claude Bernard Lyon 1, CNRS/IN2P3, IP2I Lyon, UMR 5822, Villeurbanne, F-69100, France
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Institució Catalana de Recerca i Estudis Avançats · Institute of Space Sciences · Institut de Ciències del Cosmos
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Institut de Ciències del Cosmos
Institució Catalana de Recerca i Estudis Avançats
Institut de Ciencies de l'Espai
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Lyon 1 Université · Centre National de la Recherche Scientifique · Institut National de Physique Nucléaire et de Physique des Particules · Institut de Physique des 2 Infinis de Lyon
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UCB Lyon 1, CNRS/IN2P3, IUF, IP2I Lyon, 4 rue Enrico Fermi, 69622 Villeurbanne, France
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University of Lisbon · Institute of Astrophysics and Space Sciences
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Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, Edifício C8, Campo Grande, PT1749-016 Lisboa, Portugal
Instituto de Astrofísica e Ciências do Espaço, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, 1749-016 Lisboa, Portugal
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Affiliation as printed
Department of Astronomy, University of Geneva, ch. d'Ecogia 16, 1290 Versoix, Switzerland
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Trieste Astronomical Observatory
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INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34143 Trieste, Italy
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Centre National de la Recherche Scientifique · Université Paris-Saclay · Institut d'Astrophysique Spatiale
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Université Paris-Saclay, CNRS, Institut d'astrophysique spatiale, 91405, Orsay, France
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Department of Astronomy, University of Geneva, ch. d'Ecogia 16, 1290 Versoix, Switzerland
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European Space Astronomy Centre
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ESAC/ESA, Camino Bajo del Castillo, s/n., Urb. Villafranca del Castillo, 28692 Villanueva de la Cañada, Madrid, Spain
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Istituto Nazionale di Fisica Nucleare, Sezione di Padova
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INFN-Padova, Via Marzolo 8, 35131 Padova, Italy
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Centre National de la Recherche Scientifique · Aix-Marseille Université · Centre de physique des particules de Marseille · Institut National de Physique Nucléaire et de Physique des Particules
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Aix-Marseille Université, CNRS/IN2P3, CPPM, Marseille, France
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Institute for Space Astrophysics and Planetology · National Institute for Astrophysics
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INAF-Istituto di Astrofisica e Planetologia Spaziali, via del Fosso del Cavaliere, 100, 00100 Roma, Italy
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Osservatorio di Astrofisica e Scienza dello Spazio · National Institute for Astrophysics
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INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy
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Astronomical Observatory of Rome · Agenzia Spaziale Italiana · National Institute for Astrophysics
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INAF-Osservatorio Astronomico di Roma, Via Frascati 33, 00078 Monteporzio Catone, Italy
Space Science Data Center, Italian Space Agency, via del Politecnico snc, 00133 Roma, Italy
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Lyon 1 Université · Centre National de la Recherche Scientifique · Institut National de Physique Nucléaire et de Physique des Particules · Institut de Physique des 2 Infinis de Lyon
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Université Claude Bernard Lyon 1, CNRS/IN2P3, IP2I Lyon, UMR 5822, Villeurbanne, F-69100, France
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Istituto Nazionale di Fisica Nucleare, Sezione di Bologna · Osservatorio di Astrofisica e Scienza dello Spazio · National Institute for Astrophysics
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INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy
INFN-Bologna, Via Irnerio 46, 40126 Bologna, Italy
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Institut d'Estudis Espacials de Catalunya
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Institut d'Estudis Espacials de Catalunya
Institute of Space Sciences
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Affiliation as printed
School of Physics, HH Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol, BS8 1TL, UK
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Trieste Astronomical Observatory
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INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34143 Trieste, Italy
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Osservatorio di Astrofisica e Scienza dello Spazio · National Institute for Astrophysics
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INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy
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National Institute for Astrophysics
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INAF-IASF Milano, Via Alfonso Corti 12, 20133 Milano, Italy
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Trieste Astronomical Observatory
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INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34143 Trieste, Italy
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Ludwig-Maximilians-Universität München
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University Observatory, LMU Faculty of Physics, Scheinerstr. 1, 81679 Munich, Germany
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Centre National de la Recherche Scientifique · Aix-Marseille Université · Centre de physique des particules de Marseille · Institut National de Physique Nucléaire et de Physique des Particules
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Aix-Marseille Université, CNRS/IN2P3, CPPM, Marseille, France
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Royal Observatory · University of Edinburgh
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Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ, UK
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Istituto Nazionale di Fisica Nucleare, Sezione di Bologna · Osservatorio di Astrofisica e Scienza dello Spazio · National Institute for Astrophysics
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INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy
INFN-Sezione di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy
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European Space Astronomy Centre
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FRACTAL S.L.N.E., calle Tulipán 2, Portal 13 1A, 28231, Las Rozas de Madrid, Spain
ESAC/ESA, Camino Bajo del Castillo, s/n., Urb. Villafranca del Castillo, 28692 Villanueva de la Cañada, Madrid, Spain
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Max Planck Institute for Extraterrestrial Physics
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Max Planck Institute for Extraterrestrial Physics, Giessenbachstr. 1, 85748 Garching, Germany
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Osservatorio Astronomico di Padova
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INAF-Osservatorio Astronomico di Padova, Via dell'Osservatorio 5, 35122 Padova, Italy
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Max Planck Institute for Extraterrestrial Physics · Ludwig-Maximilians-Universität München
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Max Planck Institute for Extraterrestrial Physics, Giessenbachstr. 1, 85748 Garching, Germany
Universitäts-Sternwarte München, Fakultät für Physik, Ludwig-Maximilians-Universität München, Scheinerstr. 1, 81679 München, Germany
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University of Milan · Brera Astronomical Observatory · Istituto Nazionale di Fisica Nucleare, Sezione di Milano
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Dipartimento di Fisica "Aldo Pontremoli", Università degli Studi di Milano, Via Celoria 16, 20133 Milano, Italy
INAF-Osservatorio Astronomico di Brera, Via Brera 28, 20122 Milano, Italy
INFN-Sezione di Milano, Via Celoria 16, 20133 Milano, Italy
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Affiliation as printed
Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA, 91109, USA
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Felix Hormuth Engineering, Goethestr. 17, 69181 Leimen, Germany
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Technical University of Denmark
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Technical University of Denmark, Elektrovej 327, 2800 Kgs. Lyngby, Denmark
Cosmic Dawn Center
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Max Planck Institute for Astronomy
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Max-Planck-Institut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany
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Affiliation as printed
NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA
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Affiliation as printed
Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK
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Centre National de la Recherche Scientifique · Aix-Marseille Université · Centre de physique des particules de Marseille · Institut National de Physique Nucléaire et de Physique des Particules
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Aix-Marseille Université, CNRS/IN2P3, CPPM, Marseille, France
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Affiliation as printed
Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA, 91109, USA
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Lyon 1 Université · Centre National de la Recherche Scientifique · Institut National de Physique Nucléaire et de Physique des Particules · Institut de Physique des 2 Infinis de Lyon
Affiliation as printed
Université Claude Bernard Lyon 1, CNRS/IN2P3, IP2I Lyon, UMR 5822, Villeurbanne, F-69100, France
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Affiliation as printed
Université de Genève, Département de Physique Théorique and Centre for Astroparticle Physics, 24 quai Ernest-Ansermet, CH-1211 Genève 4, Switzerland
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University of Helsinki · Helsinki Institute of Physics
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Department of Physics, P.O. Box 64, University of Helsinki, 00014 Helsinki, Finland
Helsinki Institute of Physics, Gustaf Hällströmin katu 2, University of Helsinki, 00014 Helsinki, Finland
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Centre National de la Recherche Scientifique · Université Paris Sciences et Lettres · Observatoire de Paris · Sorbonne Université · Laboratoire d'Étude de l'Univers et des Phénomènes Extrêmes
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Laboratoire d'etude de l'Univers et des phenomenes eXtremes, Observatoire de Paris, Université PSL, Sorbonne Université, CNRS, 92190 Meudon, France
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Osservatorio Astrofisico di Torino · National Institute for Astrophysics
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INAF-Osservatorio Astrofisico di Torino, Via Osservatorio 20, 10025 Pino Torinese
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Affiliation as printed
Institute of Theoretical Astrophysics, University of Oslo, P.O. Box 1029 Blindern, 0315 Oslo, Norway
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University of Helsinki · Helsinki Institute of Physics
Affiliation as printed
Department of Physics, P.O. Box 64, University of Helsinki, 00014 Helsinki, Finland
Helsinki Institute of Physics, Gustaf Hällströmin katu 2, University of Helsinki, 00014 Helsinki, Finland
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Affiliation as printed
SKAO, Jodrell Bank, Lower Withington, Macclesfield SK11 9FT, UK
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Centre National de la Recherche Scientifique · Centre de Calcul de l’Institut National de Physique Nucléaire et de Physique des Particules
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Centre de Calcul de l'IN2P3/CNRS, 21 avenue Pierre de Coubertin 69627 Villeurbanne Cedex, France
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University of Milan · Istituto Nazionale di Fisica Nucleare, Sezione di Milano · National Institute for Astrophysics
Affiliation as printed
Dipartimento di Fisica "Aldo Pontremoli", Università degli Studi di Milano, Via Celoria 16, 20133 Milano, Italy
INAF-IASF Milano, Via Alfonso Corti 12, 20133 Milano, Italy
INFN-Sezione di Milano, Via Celoria 16, 20133 Milano, Italy
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Osservatorio di Astrofisica e Scienza dello Spazio · National Institute for Astrophysics
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INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy
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Trieste Astronomical Observatory
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INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34143 Trieste, Italy
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FHNW University of Applied Sciences and Arts Northwestern Switzerland
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University of Applied Sciences and Arts of Northwestern Switzerland, School of Computer Science, 5210 Windisch, Switzerland
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Affiliation as printed
Universität Bonn, Argelander-Institut für Astronomie, Auf dem Hügel 71, 53121 Bonn, Germany
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Astronomical Observatory of Rome · Istituto Nazionale di Fisica Nucleare, Sezione di Roma I · National Institute for Astrophysics
Affiliation as printed
INAF-Osservatorio Astronomico di Roma, Via Frascati 33, 00078 Monteporzio Catone, Italy
INFN-Sezione di Roma, Piazzale Aldo Moro, 2 - c/o Dipartimento di Fisica, Edificio G. Marconi, 00185 Roma, Italy
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Centre National de la Recherche Scientifique · Aix-Marseille Université
Affiliation as printed
Aix-Marseille Université, CNRS, CNES, LAM, Marseille, France
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Affiliation as printed
Department of Physics, Institute for Computational Cosmology, Durham University, South Road, Durham, DH1 3LE, UK
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Osservatorio di Astrofisica e Scienza dello Spazio · National Institute for Astrophysics
Affiliation as printed
INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy
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Centre National de la Recherche Scientifique · Université Paris Cité · Institut National de Physique Nucléaire et de Physique des Particules · Centre Pierre Binétruy · University of California, Berkeley
Affiliation as printed
Université Paris Cité, CNRS, Astroparticule et Cosmologie, 75013 Paris, France
CNRS-UCB International Research Laboratory, Centre Pierre Binétruy, IRL2007, CPB-IN2P3, Berkeley, USA
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