Euclid preparation

LXXII. Three-dimensional galaxy clustering in configuration space: Two-point correlation function estimation

¹ Aix-Marseille Université, CNRS, CNES, LAM, Marseille, France
² Dipartimento di Fisica e Astronomia “Augusto Righi” – Alma Mater Studiorum Università di Bologna, via Piero Gobetti 93/2, 40129 Bologna, Italy
³ INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy
⁴ INFN-Sezione di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy
⁵ Department of Physics and Helsinki Institute of Physics, Gustaf Hällströmin katu 2, 00014 University of Helsinki, Helsinki, Finland
⁶ INAF-Osservatorio Astronomico di Roma, Via Frascati 33, 00078 Monteporzio Catone, Italy
⁷ IFPU, Institute for Fundamental Physics of the Universe, via Beirut 2, 34151 Trieste, Italy
⁸ INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34143 Trieste, Italy
⁹ SISSA, International School for Advanced Studies, Via Bonomea 265, 34136 Trieste, TS, Italy
¹⁰ INFN, Sezione di Trieste, Via Valerio 2, 34127 Trieste TS, Italy
¹¹ ICSC – Centro Nazionale di Ricerca in High Performance Computing, Big Data e Quantum Computing, Via Magnanelli 2, Bologna, Italy
¹² INAF-Osservatorio Astronomico di Brera, Via Brera 28, 20122 Milano, Italy
¹³ INFN-Sezione di Genova, Via Dodecaneso 33, 16146 Genova, Italy
¹⁴ Dipartimento di Fisica, Università degli studi di Genova, and INFN-Sezione di Genova, via Dodecaneso 33, 16146 Genova, Italy
¹⁵ Dipartimento di Fisica, Università di Genova, Via Dodecaneso 33, 16146 Genova, Italy
¹⁶ Department of Physics, P.O. Box 64 00014 University of Helsinki, Helsinki, Finland
¹⁷ Helsinki Institute of Physics, Gustaf Hällströmin katu 2, University of Helsinki, Helsinki, Finland
¹⁸ INAF-Osservatorio Astronomico di Capodimonte, Via Moiariello 16, 80131 Napoli, Italy
¹⁹ Institute of Space Sciences (ICE, CSIC), Campus UAB, Carrer de Can Magrans, s/n, 08193 Barcelona, Spain
²⁰ School of Mathematics and Physics, University of Surrey, Guildford, Surrey GU2 7XH, UK
²¹ Dipartimento di Fisica e Astronomia, Università di Bologna, Via Gobetti 93/2, 40129 Bologna, Italy
²² Centre National d’Etudes Spatiales – Centre spatial de Toulouse, 18 avenue Edouard Belin, 31401 Toulouse Cedex 9, France
²³ INAF-Osservatorio Astrofisico di Torino, Via Osservatorio 20, 10025 Pino Torinese (TO), Italy
²⁴ Department of Physics “E. Pancini”, University Federico II, Via Cinthia 6, 80126 Napoli, Italy
²⁵ INFN section of Naples, Via Cinthia 6, 80126 Napoli, Italy
²⁶ Instituto de Astrofísica e Ciências do Espaço, Universidade do Porto, CAUP, Rua das Estrelas, PT4150-762 Porto, Portugal
²⁷ Faculdade de Ciências da Universidade do Porto, Rua do Campo de Alegre, 4150-007 Porto, Portugal
²⁸ Dipartimento di Fisica, Università degli Studi di Torino, Via P. Giuria 1, 10125 Torino, Italy
²⁹ INFN-Sezione di Torino, Via P. Giuria 1, 10125 Torino, Italy
³⁰ INAF-IASF Milano, Via Alfonso Corti 12, 20133 Milano, Italy
³¹ Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas (CIEMAT), Avenida Complutense 40, 28040 Madrid, Spain
³² Port d’Informació Científica, Campus UAB, C. Albareda s/n, 08193 Bellaterra (Barcelona), Spain
³³ Institute for Theoretical Particle Physics and Cosmology (TTK), RWTH Aachen University, 52056 Aachen, Germany
³⁴ Institute of Cosmology and Gravitation, University of Portsmouth, Portsmouth PO1 3FX, UK
³⁵ Institut d’Estudis Espacials de Catalunya (IEEC), Edifici RDIT, Campus UPC, 08860 Castelldefels, Barcelona, Spain
³⁶ Dipartimento di Fisica e Astronomia “Augusto Righi” – Alma Mater Studiorum Università di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy
³⁷ Instituto de Astrofísica de Canarias, Calle Vía Láctea s/n, 38204 San Cristóbal de La Laguna, Tenerife, Spain
³⁸ Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ, UK
³⁹ Jodrell Bank Centre for Astrophysics, Department of Physics and Astronomy, University of Manchester, Oxford Road, Manchester M13 9PL, UK
⁴⁰ European Space Agency/ESRIN, Largo Galileo Galilei 1, 00044 Frascati, Roma, Italy
⁴¹ ESAC/ESA, Camino Bajo del Castillo, s/n., Urb. Villafranca del Castillo, 28692 Villanueva de la Cañada, Madrid, Spain
⁴² Université Claude Bernard Lyon 1, CNRS/IN2P3, IP2I Lyon, UMR 5822, Villeurbanne F-69100, France
⁴³ Institut de Ciències del Cosmos (ICCUB), Universitat de Barcelona (IEEC-UB), Martí i Franquès 1, 08028 Barcelona, Spain
⁴⁴ Institució Catalana de Recerca i Estudis Avançats (ICREA), Passeig de Lluís Companys 23, 08010 Barcelona, Spain
⁴⁵ UCB Lyon 1, CNRS/IN2P3, IUF, IP2I Lyon, 4 rue Enrico Fermi, 69622 Villeurbanne, France
⁴⁶ Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, Edifício C8, Campo Grande, PT1749-016 Lisboa, Portugal
⁴⁷ Instituto de Astrofísica e Ciências do Espaço, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, 1749-016 Lisboa, Portugal
⁴⁸ Department of Astronomy, University of Geneva, ch. d’Ecogia 16, 1290 Versoix, Switzerland
⁴⁹ INAF-Istituto di Astrofisica e Planetologia Spaziali, via del Fosso del Cavaliere, 100, 00100 Roma, Italy
⁵⁰ INFN-Padova, Via Marzolo 8, 35131 Padova, Italy
⁵¹ Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM, 91191 Gif-sur-Yvette, France
⁵² Space Science Data Center, Italian Space Agency, via del Politecnico snc, 00133 Roma, Italy
⁵³ Aix-Marseille Université, CNRS/IN2P3, CPPM, Marseille, France
⁵⁴ Universitäts-Sternwarte München, Fakultät für Physik, Ludwig-Maximilians-Universität München, Scheinerstrasse 1, 81679 München, Germany
⁵⁵ FRACTAL S.L.N.E., calle Tulipán 2, Portal 13 1A, 28231 Las Rozas de Madrid, Spain
⁵⁶ INAF-Osservatorio Astronomico di Padova, Via dell’Osservatorio 5, 35122 Padova, Italy
⁵⁷ Max Planck Institute for Extraterrestrial Physics, Giessenbachstr. 1, 85748 Garching, Germany
⁵⁸ Dipartimento di Fisica “Aldo Pontremoli”, Università degli Studi di Milano, Via Celoria 16, 20133 Milano, Italy
⁵⁹ Institute of Theoretical Astrophysics, University of Oslo, P.O. Box 1029 Blindern 0315 Oslo, Norway
⁶⁰ Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA
⁶¹ Felix Hormuth Engineering, Goethestr. 17, 69181 Leimen, Germany
⁶² Technical University of Denmark, Elektrovej 327, 2800 Kgs. Lyngby, Denmark
⁶³ Cosmic Dawn Center (DAWN), Copenhagen, Denmark
⁶⁴ Université Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France
⁶⁵ Institut de Recherche en Astrophysique et Planétologie (IRAP), Université de Toulouse, CNRS, UPS, CNES, 14 Av. Edouard Belin, 31400 Toulouse, France
⁶⁶ Max-Planck-Institut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany
⁶⁷ NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA
⁶⁸ Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK
⁶⁹ Université de Genève, Département de Physique Théorique and Centre for Astroparticle Physics, 24 quai Ernest-Ansermet, CH-1211 Genève 4, Switzerland
⁷⁰ NOVA optical infrared instrumentation group at ASTRON, Oude Hoogeveensedijk 4, 7991PD Dwingeloo, The Netherlands
⁷¹ Centre de Calcul de l’IN2P3/CNRS, 21 avenue Pierre de Coubertin, 69627 Villeurbanne Cedex, France
⁷² INFN-Sezione di Milano, Via Celoria 16, 20133 Milano, Italy
⁷³ Universität Bonn, Argelander-Institut für Astronomie, Auf dem Hügel 71, 53121 Bonn, Germany
⁷⁴ INFN-Sezione di Roma, Piazzale Aldo Moro, 2 – c/o Dipartimento di Fisica, Edificio G. Marconi, 00185 Roma, Italy
⁷⁵ Department of Physics, Institute for Computational Cosmology, Durham University, South Road, Durham DH1 3LE, UK
⁷⁶ Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS, Laboratoire Lagrange, Bd de l’Observatoire, CS 34229, 06304 Nice cedex 4, France
⁷⁷ Université Paris Cité, CNRS, Astroparticule et Cosmologie, 75013 Paris, France
⁷⁸ University of Applied Sciences and Arts of Northwestern Switzerland, School of Engineering, 5210 Windisch, Switzerland
⁷⁹ Institut d’Astrophysique de Paris, 98bis Boulevard Arago, 75014 Paris, France
⁸⁰ Institut d’Astrophysique de Paris, UMR 7095, CNRS, and Sorbonne Université, 98 bis boulevard Arago, 75014 Paris, France
⁸¹ Institute of Physics, Laboratory of Astrophysics, Ecole Polytechnique Fédérale de Lausanne (EPFL), Observatoire de Sauverny, 1290 Versoix, Switzerland
⁸² Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Campus UAB, 08193 Bellaterra (Barcelona), Spain
⁸³ European Space Agency/ESTEC, Keplerlaan 1, 2201 AZ Noordwijk, The Netherlands
⁸⁴ DARK, Niels Bohr Institute, University of Copenhagen, Jagtvej 155, 2200 Copenhagen, Denmark
⁸⁵ Waterloo Centre for Astrophysics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
⁸⁶ Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
⁸⁷ Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada
⁸⁸ Dipartimento di Fisica e Astronomia “G. Galilei”, Università di Padova, Via Marzolo 8, 35131 Padova, Italy
⁸⁹ Institut für Theoretische Physik, University of Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany
⁹⁰ Université St Joseph, Faculty of Sciences, Beirut, Lebanon
⁹¹ Departamento de Física, FCFM, Universidad de Chile, Blanco Encalada 2008, Santiago, Chile
⁹² Universität Innsbruck, Institut für Astro- und Teilchenphysik, Technikerstr. 25/8, 6020 Innsbruck, Austria
⁹³ Satlantis, University Science Park, Sede Bld 48940, Leioa-Bilbao, Spain
⁹⁴ Instituto de Astrofísica e Ciências do Espaço, Faculdade de Ciências, Universidade de Lisboa, Tapada da Ajuda, 1349-018 Lisboa, Portugal
⁹⁵ Universidad Politécnica de Cartagena, Departamento de Electrónica y Tecnología de Computadoras, Plaza del Hospital 1, 30202 Cartagena, Spain
⁹⁶ Centre for Information Technology, University of Groningen, P.O. Box 11044 9700 CA Groningen, The Netherlands
⁹⁷ INFN-Bologna, Via Irnerio 46, 40126 Bologna, Italy
⁹⁸ Infrared Processing and Analysis Center, California Institute of Technology, Pasadena, CA 91125, USA
⁹⁹ INAF, Istituto di Radioastronomia, Via Piero Gobetti 101, 40129 Bologna, Italy
¹⁰⁰ Astronomical Observatory of the Autonomous Region of the Aosta Valley (OAVdA), Loc. Lignan 39, I-11020 Nus (Aosta Valley), Italy
¹⁰¹ Department of Physics, Oxford University, Keble Road, Oxford OX1 3RH, UK
¹⁰² Aurora Technology for European Space Agency (ESA), Camino bajo del Castillo, s/n, Urbanizacion Villafranca del Castillo, Villanueva de la Cañada, 28692 Madrid, Spain
¹⁰³ ICL, Junia, Université Catholique de Lille, LITL, 59000 Lille, France
¹⁰⁴ Department of Physics, Royal Holloway, University of London, London TW20 0EX, UK
¹⁰⁵ Mullard Space Science Laboratory, University College London, Holmbury St Mary, Dorking, Surrey RH5 6NT, UK
¹⁰⁶ Instituto de Física Teórica UAM-CSIC, Campus de Cantoblanco, 28049 Madrid, Spain
¹⁰⁷ CERCA/ISO, Department of Physics, Case Western Reserve University, 10900 Euclid Avenue, Cleveland, OH 44106, USA
¹⁰⁸ Technical University of Munich, TUM School of Natural Sciences, Physics Department, James-Franck-Str. 1, 85748 Garching, Germany
¹⁰⁹ Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85748 Garching, Germany
¹¹⁰ Laboratoire Univers et Théorie, Observatoire de Paris, Université PSL, Université Paris Cité, CNRS, 92190 Meudon, France
¹¹¹ Departamento de Física Fundamental, Universidad de Salamanca, Plaza de la Merced s/n, 37008 Salamanca, Spain
¹¹² Departamento de Astrofísica, Universidad de La Laguna, 38206 La Laguna, Tenerife, Spain
¹¹³ Université de Strasbourg, CNRS, Observatoire astronomique de Strasbourg, UMR 7550, 67000 Strasbourg, France
¹¹⁴ Center for Data-Driven Discovery, Kavli IPMU (WPI), UTIAS, The University of Tokyo, Kashiwa, Chiba 277-8583, Japan
¹¹⁵ Ludwig-Maximilians-University, Schellingstrasse 4, 80799 Munich, Germany
¹¹⁶ Max-Planck-Institut für Physik, Boltzmannstr. 8, 85748 Garching, Germany
¹¹⁷ Dipartimento di Fisica – Sezione di Astronomia, Università di Trieste, Via Tiepolo 11, 34131 Trieste, Italy
¹¹⁸ California institute of Technology, 1200 E California Blvd, Pasadena, CA 91125, USA
¹¹⁹ Institute Lorentz, Leiden University, Niels Bohrweg 2, 2333 CA Leiden, The Netherlands
¹²⁰ Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu HI 96822, USA
¹²¹ Department of Physics & Astronomy, University of California Irvine, Irvine, CA 92697, USA
¹²² Department of Mathematics and Physics E. De Giorgi, University of Salento, Via per Arnesano, CP-I93, 73100 Lecce, Italy
¹²³ INFN, Sezione di Lecce, Via per Arnesano, CP-193, 73100 Lecce, Italy
¹²⁴ INAF-Sezione di Lecce, c/o Dipartimento Matematica e Fisica, Via per Arnesano, 73100 Lecce, Italy
¹²⁵ Kapteyn Astronomical Institute, University of Groningen, PO Box 800 9700 AV Groningen, The Netherlands
¹²⁶ Departamento Física Aplicada, Universidad Politécnica de Cartagena, Campus Muralla del Mar, 30202 Cartagena, Murcia, Spain
¹²⁷ Université Paris-Saclay, CNRS, Institut d’astrophysique spatiale, 91405 Orsay, France
¹²⁸ CEA Saclay, DFR/IRFU, Service d’Astrophysique, Bat. 709, 91191 Gif-sur-Yvette, France
¹²⁹ Department of Computer Science, Aalto University, PO Box 15400 Espoo FI-00 076, Finland
¹³⁰ Instituto de Astrofísica de Canarias, c/ Via Lactea s/n, La Laguna E-38200, Spain. Departamento de Astrofísica de la Universidad de La Laguna, Avda. Francisco Sanchez, La Laguna E-38200, Spain
¹³¹ Caltech/IPAC, 1200 E. California Blvd., Pasadena, CA 91125, USA
¹³² Ruhr University Bochum, Faculty of Physics and Astronomy, Astronomical Institute (AIRUB), German Centre for Cosmological Lensing (GCCL), 44780 Bochum, Germany
¹³³ Univ. Grenoble Alpes, CNRS, Grenoble INP, LPSC-IN2P3, 53, Avenue des Martyrs, 38000 Grenoble, France
¹³⁴ Department of Physics and Astronomy, Vesilinnantie 5, 20014 University of Turku, Turku, Finland
¹³⁵ Serco for European Space Agency (ESA), Camino bajo del Castillo, s/n, Urbanizacion Villafranca del Castillo, Villanueva de la Cañada, 28692 Madrid, Spain
¹³⁶ ARC Centre of Excellence for Dark Matter Particle Physics, Melbourne, Australia
¹³⁷ Centre for Astrophysics & Supercomputing, Swinburne University of Technology, Hawthorn, Victoria 3122, Australia
¹³⁸ Dipartimento di Fisica e Scienze della Terra, Università degli Studi di Ferrara, Via Giuseppe Saragat 1, 44122 Ferrara, Italy
¹³⁹ Department of Physics and Astronomy, University of the Western Cape, Bellville, Cape Town 7535, South Africa
¹⁴⁰ Istituto Nazionale di Fisica Nucleare, Sezione di Ferrara, Via Giuseppe Saragat 1, 44122 Ferrara, Italy
¹⁴¹ DAMTP, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, UK
¹⁴² Kavli Institute for Cosmology Cambridge, Madingley Road, Cambridge CB3 0HA, UK
¹⁴³ IRFU, CEA, Université Paris-Saclay, 91191 Gif-sur-Yvette Cedex, France
¹⁴⁴ Oskar Klein Centre for Cosmoparticle Physics, Department of Physics, Stockholm University, Stockholm SE-106 91, Sweden
¹⁴⁵ Astrophysics Group, Blackett Laboratory, Imperial College London, London SW7 2AZ, UK
¹⁴⁶ INAF-Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, 50125 Firenze, Italy
¹⁴⁷ Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 2, 00185 Roma, Italy
¹⁴⁸ Centro de Astrofísica da Universidade do Porto, Rua das Estrelas, 4150-762 Porto, Portugal
¹⁴⁹ HE Space for European Space Agency (ESA), Camino bajo del Castillo, s/n, Urbanizacion Villafranca del Castillo, Villanueva de la Cañada, 28692 Madrid, Spain
¹⁵⁰ Department of Astrophysical Sciences, Peyton Hall, Princeton University, Princeton, NJ 08544, USA
¹⁵¹ Institute of Space Science, Str. Atomistilor, nr. 409 Măgurele, Ilfov 077125, Romania
¹⁵² Department of Astrophysics, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland
¹⁵³ INAF-Osservatorio Astronomico di Brera, Via Brera 28, 20122 Milano, Italy, and INFN-Sezione di Genova, Via Dodecaneso 33, 16146 Genova, Italy
¹⁵⁴ Theoretical astrophysics, Department of Physics and Astronomy, Uppsala University, Box 515 751 20 Uppsala, Sweden
¹⁵⁵ Mathematical Institute, University of Leiden, Niels Bohrweg 1, 2333 CA Leiden, The Netherlands
¹⁵⁶ Leiden Observatory, Leiden University, Einsteinweg 55, 2333 CC Leiden, The Netherlands
¹⁵⁷ Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK
¹⁵⁸ Niels Bohr Institute, University of Copenhagen, Jagtvej 128, 2200 Copenhagen, Denmark
¹⁵⁹ Center for Computational Astrophysics, Flatiron Institute, 162 5th Avenue, 10010 New York, NY, USA

^⋆ Corresponding author: sylvain.delatorre@lam.fr

Received: 28 January 2025
Accepted: 18 June 2025

Abstract

The two-point correlation function of the galaxy spatial distribution is a major cosmological observable that enables constraints on the dynamics and geometry of the Universe. The Euclid mission is aimed at performing an extensive spectroscopic survey of approximately 20–30 million Hα-emitting galaxies up to a redshift of about 2. This ambitious project seeks to elucidate the nature of dark energy by mapping the three-dimensional clustering of galaxies over a significant portion of the sky. This paper presents the methodology and software developed for estimating the three-dimensional two-point correlation function within the Euclid Science Ground Segment. The software is designed to overcome the significant challenges posed by the large and complex Euclid dataset, which involves millions of galaxies. The key challenges include efficient pair counting, managing computational resources, and ensuring the accuracy of the correlation function estimation. The software leverages advanced algorithms, including k-d tree, octree, and linked-list data partitioning strategies, to optimise the pair-counting process. These methods are crucial for handling the massive volume of data efficiently. The implementation also includes parallel processing capabilities using shared-memory open multi-processing to further enhance performance and reduce computation times. Extensive validation and performance testing of the software are presented. Those have been performed by using various mock galaxy catalogues to ensure that it meets the stringent accuracy requirement of the Euclid mission. The results indicate that the software is robust and can reliably estimate the two-point correlation function, which is essential for deriving cosmological parameters with high precision. Furthermore, the paper discusses the expected performance of the software during different stages of Euclid Wide Survey observations and forecasts how the precision of the correlation function measurements will improve over the mission’s timeline, highlighting the software’s capability to handle large datasets efficiently.