Euclid preparation. LXXII. Three-dimensional galaxy clustering in configuration space. 1. Two-point correlation function estimation

Euclid Collaboration; de la Torre, S.; Marulli, F.; Keihänen, E.; Viitanen, A.; Viel, M.; Veropalumbo, A.; Branchini, E.; Tavagnacco, D.; Rizzo, F.; Valiviita, J.; Lindholm, V.; Allevato, V.; Parimbelli, G.; Sarpa, E.; Ghaffari, Z.; Amara, A.; Andreon, S.; Auricchio, N.; Baccigalupi, C.; Baldi, M.; Bardelli, S.; Basset, A.; Bonino, D.; Brescia, M.; Brinchmann, J.; Caillat, A.; Camera, S.; Capobianco, V.; Carbone, C.; Carretero, J.; Casas, S.; Castander, F.J.; Castellano, M.; Castignani, G.; Cavuoti, S.; Cimatti, A.; Colodro-Conde, C.; Congedo, G.; Conselice, C.J.; Conversi, L.; Copin, Y.; Courbin, F.; Courtois, H.M.; Crocce, M.; Da Silva, A.; Degaudenzi, H.; De Lucia, G.; Di Giorgio, A.M.; Dinis, J.; Dubath, F.; Duncan, C.A.J.; Dupac, X.; Dusini, S.; Farina, M.; Farrens, S.; Faustini, F.; Ferriol, S.; Fourmanoit, N.; Frailis, M.; Franceschi, E.; Franzetti, P.; Fumana, M.; Galeotta, S.; George, K.; Gillard, W.; Gillis, B.; Giocoli, C.; Gómez-Alvarez, P.; Granett, B.R.; Grazian, A.; Grupp, F.; Guzzo, L.; Haugan, S.V.H.; Holmes, W.; Hormuth, F.; Hornstrup, A.; Ilić, S.; Jahnke, K.; Jhabvala, M.; Joachimi, B.; Kermiche, S.; Kiessling, A.; Kilbinger, M.; Kubik, B.; Kunz, M.; Kurki-Suonio, H.; Ligori, S.; Lilje, P.B.; Lloro, I.; Mainetti, G.; Maino, D.; Maiorano, E.; Mansutti, O.; Marggraf, O.; Markovic, K.; Martinelli, M.; Martinet, N.; Massey, R.; Maurogordato, S.; Medinaceli, E.; Mei, S.; Melchior, M.; Mellier, Y.; Meneghetti, M.; Merlin, E.; Meylan, G.; Moresco, M.; Morin, B.; Moscardini, L.; Munari, E.; Neissner, C.; Niemi, S.-M.; Padilla, C.; Paltani, S.; Pasian, F.; Pedersen, K.; Percival, W.J.; Pettorino, V.; Pires, S.; Polenta, G.; Poncet, M.; Pozzetti, L.; Raison, F.; Renzi, A.; Rhodes, J.; Riccio, G.; Romelli, E.; Roncarelli, M.; Rossetti, E.; Saglia, R.; Sakr, Z.; Sánchez, A.G.; Sapone, D.; Sartoris, B.; Schneider, P.; Schrabback, T.; Scodeggio, M.; Secroun, A.; Sefusatti, E.; Seidel, G.; Seiffert, M.; Serrano, S.; Sirignano, C.; Sirri, G.; Stanco, L.; Steinwagner, J.; Surace, C.; Tallada-Crespí, P.; Taylor, A.N.; Tereno, I.; Toledo-Moreo, R.; Torradeflot, F.; Tsyganov, A.; Tutusaus, I.; Valenziano, L.; Vassallo, T.; Wang, Y.; Weller, J.; Zacchei, A.; Zamorani, G.; Zucca, E.; Biviano, A.; Bolzonella, M.; Bozzo, E.; Burigana, C.; Calabrese, M.; Di Ferdinando, D.; Escartin Vigo, J.A.; Farinelli, R.; Finelli, F.; Gabarra, L.; Gracia-Carpio, J.; Matthew, S.; Mauri, N.; Mora, A.; Pezzotta, A.; Pöntinen, M.; Scottez, V.; Simon, P.; Spurio Mancini, A.; Tenti, M.; Wiesmann, M.; Akrami, Y.; Andika, I.T.; Anselmi, S.; Archidiacono, M.; Atrio-Barandela, F.; Balaguera-Antolinez, A.; Bertacca, D.; Bethermin, M.; Blanchard, A.; Blot, L.; Böhringer, H.; Borgani, S.; Brown, M.L.; Bruton, S.; Cabanac, R.; Calabro, A.; Camacho Quevedo, B.; Cañas-Herrera, G.; Cappi, A.; Caro, F.; Carvalho, C.S.; Castro, T.; Chambers, K.C.; Cogato, F.; Contarini, S.; Cooray, A.R.; Cucciati, O.; Davini, S.; De Paolis, F.; Desprez, G.; Díaz-Sánchez, A.; Di Domizio, S.; Dole, H.; Escoffier, S.; Ferrari, A.G.; Ferreira, P.G.; Finoguenov, A.; Fontana, A.; Ganga, K.; García-Bellido, J.; Gasparetto, T.; Gautard, V.; Gaztanaga, E.; Giacomini, F.; Gianotti, F.; Gozaliasl, G.; Gregorio, A.; Guidi, M.; Gutierrez, C.M.; Hall, A.; Hemmati, S.; Hildebrandt, H.; Hjorth, J.; Jimenez Muñoz, A.; Joudaki, S.; Kajava, J.E.; Kang, Y.; Kansal, V.; Karagiannis, D.; Kirkpatrick, C.; Kruk, S.; Lattanzi, M.; Le Brun, A.M.C.; Lee, S.; Le Graet, J.; Legrand, L.; Lembo, M.; Lesgourgues, J.; Liaudat, T.I.; Loureiro, A.; Macias-Perez, J.; Magliocchetti, M.; Mannucci, F.; Maoli, R.; Martín-Fleitas, J.; Martins, C.J.A.P.; Maurin, L.; Metcalf, R.B.; Miluzio, M.; Monaco, P.; Moretti, C.; Morgante, G.; Murray, C.; Nadathur, S.; Naidoo, K.; Navarro-Alsina, A.; Nesseris, S.; Paterson, K.; Patrizii, L.; Pisani, A.; Popa, V.; Potter, D.; Reimberg, P.; Risso, I.; Rocci, P.-F.; Sahlén, M.; Schneider, A.; Schultheis, M.; Sciotti, D.; Sellentin, E.; Sereno, M.; Silvestri, A.; Smith, L.C.; Tanidis, K.; Tao, C.; Tessore, N.; Testera, G.; Teyssier, R.; Toft, S.; Tosi, S.; Troja, A.; Tucci, M.; Valieri, C.; Vergani, D.; Verza, G.; Vielzeuf, P.; Walton, N.A.

doi:10.1051/0004-6361/202553927

Published August 2025 | Version Published

Journal Article Open

Euclid preparation. LXXII. Three-dimensional galaxy clustering in configuration space. 1. Two-point correlation function estimation

1. French National Centre for Scientific Research
2. University of Bologna
3. INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129, Bologna, Italy
4. INFN Sezione di Bologna
5. University of Helsinki
6. INAF-Osservatorio Astronomico di Roma, Via Frascati 33, 00078, Monteporzio Catone, Italy
7. Institute for Fundamental Physics of the Universe
8. Trieste Astronomical Observatory
9. International School for Advanced Studies
10. INFN Sezione di Trieste
11. ICSC – Centro Nazionale di Ricerca in High Performance Computing, Big Data e Quantum Computing, Via Magnanelli 2, Bologna, Italy
12. Brera Astronomical Observatory
13. INFN Sezione di Genova
14. University of Genoa
15. Helsinki Institute of Physics
16. Astronomical Observatory of Capodimonte
17. Institute of Space Sciences
18. University of Surrey
19. Centre National d'Études Spatiales
20. Osservatorio Astrofisico di Torino
21. University of Naples Federico II
22. INFN Sezione di Napoli
23. University of Porto
24. University of Turin
25. INFN Sezione di Torino
26. Istituto di Astrofisica Spaziale e Fisica Cosmica di Milano
27. Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas
28. RWTH Aachen University
29. University of Portsmouth
30. Institut d'Estudis Espacials de Catalunya
31. Instituto de Astrofísica de Canarias
32. University of Edinburgh
33. University of Manchester
34. European Space Research Institute
35. European Space Astronomy Centre
36. Claude Bernard University Lyon 1
37. University of Barcelona
38. Institució Catalana de Recerca i Estudis Avançats
39. UCB Lyon 1, CNRS/IN2P3, IUF, IP2I Lyon, 4 rue Enrico Fermi, 69622, Villeurbanne, France
40. University of Lisbon
41. University of Geneva
42. Institute for Space Astrophysics and Planetology
43. INFN Sezione di Padova
44. University of Paris
45. Agenzia Spaziale Italiana
46. Center for Particle Physics of Marseilles
47. Ludwig-Maximilians-Universität München
48. FRACTAL S.L.N.E., calle Tulipán 2, Portal 13 1A, 28231, Las Rozas de Madrid, Spain
49. Osservatorio Astronomico di Padova
50. Max Planck Institute for Extraterrestrial Physics
51. University of Milan
52. University of Oslo
53. Jet Propulsion Lab
54. Felix Hormuth Engineering, Goethestr. 17, 69181, Leimen, Germany
55. Technical University of Denmark
56. University of Copenhagen
57. Laboratoire de Physique des 2 Infinis Irène Joliot-Curie
58. Research Institute in Astrophysics and Planetology
59. Max Planck Institute for Astronomy
60. Goddard Space Flight Center
61. University College London
62. Netherlands Institute for Radio Astronomy
63. Centre de Calcul de l'IN2P3/CNRS, 21 avenue Pierre de Coubertin, 69627, Villeurbanne Cedex, France
64. INFN Sezione di Milano
65. University of Bonn
66. INFN Sezione di Roma I
67. Durham University
68. Lagrange Laboratory
69. Astroparticle and Cosmology Laboratory
70. University of Applied Sciences and Arts Northwestern Switzerland
71. Institut d'Astrophysique de Paris
72. École Polytechnique Fédérale de Lausanne
73. Institute for High Energy Physics
74. European Space Research and Technology Centre
75. University of Waterloo
76. Perimeter Institute
77. University of Padua
78. Heidelberg University
79. Université St Joseph, Faculty of Sciences, Beirut, Lebanon
80. University of Chile
81. Universität Innsbruck
82. Satlantis, University Science Park, Sede Bld 48940, Leioa-Bilbao, Spain
83. Polytechnic University of Cartagena
84. University of Groningen
85. Infrared Processing and Analysis Center
86. National Institute for Astrophysics
87. Astronomical Observatory of the Autonomous Region of the Aosta Valley (OAVdA), Loc. Lignan 39, I-11020, Nus (Aosta Valley), Italy
88. University of Oxford
89. Aurora Technology for European Space Agency (ESA), Camino bajo del Castillo, s/n, Urbanizacion Villafranca del Castillo, Villanueva de la Cañada, 28692, Madrid, Spain
90. ICL, Junia, Université Catholique de Lille, LITL, 59000, Lille, France
91. Royal Holloway University of London
92. Institute for Theoretical Physics
93. Case Western Reserve University
94. Technical University of Munich
95. Max Planck Institute for Astrophysics
96. University of Salamanca
97. University of La Laguna
98. Observatory of Strasbourg
99. University of Tokyo
100. Max Planck Institute for Physics
101. University of Trieste
102. California Institute of Technology
103. Leiden University
104. University of Hawaii at Manoa
105. University of California, Irvine
106. University of Salento
107. INFN Sezione di Lecce
108. INAF-Sezione di Lecce, c/o Dipartimento Matematica e Fisica, Via per Arnesano, 73100, Lecce, Italy
109. Institut d'Astrophysique Spatiale
110. CEA Saclay
111. Aalto University
112. Ruhr University Bochum
113. Grenoble Institute of Technology
114. University of Turku
115. Serco for European Space Agency (ESA), Camino bajo del Castillo, s/n, Urbanizacion Villafranca del Castillo, Villanueva de la Cañada, 28692, Madrid, Spain
116. Swinburne University of Technology
117. University of Ferrara
118. University of the Western Cape
119. INFN Sezione di Ferrara
120. University of Cambridge
121. Institut de Recherche sur les Lois Fondamentales de l'Univers
122. Stockholm University
123. Imperial College London
124. Arcetri Astrophysical Observatory
125. Sapienza University of Rome
126. HE Space for European Space Agency (ESA), Camino bajo del Castillo, s/n, Urbanizacion Villafranca del Castillo, Villanueva de la Cañada, 28692, Madrid, Spain
127. Princeton University
128. Institute of Space Science
129. University of Zurich
130. Uppsala University
131. Center for Computational Astrophysics, Flatiron Institute, 162 5th Avenue, 10010, New York, NY, USA

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.

Copyright and License

© The Authors 2025. Open Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Acknowledgement

The authors would like to thank Jean-Charles Lambert for his help in using and extracting reliable computational measures from the LAM computer cluster. This work was supported by the ASI/INAF agreement n. 2018-23-HH.0 “Scientific activity for Euclid mission, Phase D”, the MIUR, PRIN 2017 research grant ‘From Darklight to DM: understanding the galaxy/matter connection to measure the Universe’ and the INFN project “InDark”. FM acknowledges the financial contribution from the grant PRIN-MUR 2022 20227RNLY3 ‘The concordance cosmological model: stress-tests with galaxy clusters’ supported by Next Generation EU and from the grant ASI n. 2024-10-HH.0 ‘Attività scientifiche per la missione Euclid – fase E’. This work has made use of CosmoHub. CosmoHub is developed and maintained by PIC, IFAE, CIEMAT, in collaboration with ICE-CSIC. It is partially financed by the European Union NextGenerationEU(PRTR-C17.I1) and by Generalitat de Catalunya, as well as by the grant EQC2021-007479-P funded by MCIN/AEI/10.13039/501100011033 and by the “European Union NextGenerationEU/PRTR”. The Euclid Consortium acknowledges the European Space Agency and a number of agencies and institutes that have supported the development of Euclid, in particular the Agenzia Spaziale Italiana, the Austrian Forschungsförderungsgesellschaft funded through BMK, the Belgian Science Policy, the Canadian Euclid Consortium, the Deutsches Zentrum für Luft- und Raumfahrt, the DTU Space and the Niels Bohr Institute in Denmark, the French Centre National d’Etudes Spatiales, the Fundação para a Ciência e a Tecnologia, the Hungarian Academy of Sciences, the Ministerio de Ciencia, Innovación y Universidades, the National Aeronautics and Space Administration, the National Astronomical Observatory of Japan, the Netherlandse Onderzoekschool Voor Astronomie, the Norwegian Space Agency, the Research Council of Finland, the Romanian Space Agency, the State Secretariat for Education, Research, and Innovation (SERI) at the Swiss Space Office (SSO), and the United Kingdom Space Agency. A complete and detailed list is available on the Euclid web site (https://www.euclid-ec.org).

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Euclid preparation. LXXII. Three-dimensional galaxy clustering in configuration space. 1. Two-point correlation function estimation

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