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.
Cite
@article{arxiv.2605.03012,
title = {Euclid preparation. Three-dimensional galaxy clustering in configuration space: Three-point correlation function estimation},
author = {Euclid Collaboration and A. Veropalumbo and M. Moresco and F. Marulli and E. Branchini and M. Guidi and A. Farina and A. Pugno and E. Sefusatti and D. Tavagnacco and F. Rizzo and E. Romelli and S. de la Torre and A. Eggemeier and E. Sihvola and M. Viel and N. Aghanim and B. Altieri and S. Andreon and N. Auricchio and C. Baccigalupi and M. Baldi and S. Bardelli and P. Battaglia and A. Biviano and M. Brescia and S. Camera and G. Cañas-Herrera and V. Capobianco and C. Carbone and V. F. Cardone and J. Carretero and S. Casas and M. Castellano and G. Castignani and S. Cavuoti and K. C. Chambers and A. Cimatti and C. Colodro-Conde and G. Congedo and C. J. Conselice and L. Conversi and Y. Copin and F. Courbin and H. M. Courtois and A. Da Silva and H. Degaudenzi and G. De Lucia and H. Dole and F. Dubath and X. Dupac and S. Dusini and S. Escoffier and M. Farina and R. Farinelli and F. Faustini and S. Ferriol and F. Finelli and P. Fosalba and S. Fotopoulou and M. Frailis and E. Franceschi and M. Fumana and S. Galeotta and K. George and W. Gillard and B. Gillis and C. Giocoli and P. Gómez-Alvarez and J. Gracia-Carpio and A. Grazian and F. Grupp and L. Guzzo and W. Holmes and F. Hormuth and A. Hornstrup and K. Jahnke and M. Jhabvala and B. Joachimi and S. Kermiche and A. Kiessling and B. Kubik and M. Kunz and H. Kurki-Suonio and A. M. C. Le Brun and S. Ligori and P. B. Lilje and V. Lindholm and I. Lloro and G. Mainetti and D. Maino and E. Maiorano and O. Mansutti and S. Marcin and O. Marggraf and M. Martinelli and N. Martinet and R. J. Massey and E. Medinaceli and S. Mei and M. Melchior and Y. Mellier and M. Meneghetti and E. Merlin and G. Meylan and A. Mora and L. Moscardini and C. Neissner and S. -M. Niemi and J. W. Nightingale and C. Padilla and S. Paltani and F. Pasian and K. Pedersen and W. J. Percival and V. Pettorino and S. Pires and G. Polenta and M. Poncet and L. A. Popa and L. Pozzetti and F. Raison and A. Renzi and J. Rhodes and G. Riccio and M. Roncarelli and R. Saglia and Z. Sakr and D. Sapone and B. Sartoris and P. Schneider and T. Schrabback and A. Secroun and G. Seidel and S. Serrano and P. Simon and C. Sirignano and G. Sirri and L. Stanco and J. Steinwagner and P. Tallada-Crespí and A. N. Taylor and I. Tereno and N. Tessore and S. Toft and R. Toledo-Moreo and F. Torradeflot and I. Tutusaus and L. Valenziano and J. Valiviita and T. Vassallo and G. Verdoes Kleijn and Y. Wang and J. Weller and G. Zamorani and F. M. Zerbi and E. Zucca and V. Allevato and M. Ballardini and C. Benoist and M. Bolzonella and E. Bozzo and C. Burigana and R. Cabanac and M. Calabrese and A. Cappi and T. Castro and J. A. Escartin Vigo and L. Gabarra and J. García-Bellido and V. Gautard and J. Macias-Perez and R. Maoli and J. Martín-Fleitas and N. Mauri and R. B. Metcalf and P. Monaco and A. Pezzotta and M. Pöntinen and I. Risso and V. Scottez and M. Sereno and M. Tenti and M. Tucci and M. Wiesmann and Y. Akrami and G. Alguero and I. T. Andika and G. Angora and S. Anselmi and M. Archidiacono and F. Atrio-Barandela and E. Aubourg and L. Bazzanini and J. Bel and D. Bertacca and M. Bethermin and F. Beutler and A. Blanchard and L. Blot and H. Böhringer and M. Bonici and S. Borgani and M. L. Brown and S. Bruton and A. Calabro and B. Camacho Quevedo and F. Caro and C. S. Carvalho and F. Cogato and S. Conseil and A. R. Cooray and O. Cucciati and S. Davini and G. Desprez and A. Díaz-Sánchez and S. Di Domizio and J. M. Diego and V. Duret and M. Y. Elkhashab and A. Enia and Y. Fang and A. G. Ferrari and A. Finoguenov and F. Fontanot and A. Franco and K. Ganga and T. Gasparetto and E. Gaztanaga and F. Giacomini and F. Gianotti and G. Gozaliasl and A. Gruppuso and C. M. Gutierrez and A. Hall and H. Hildebrandt and J. Hjorth and S. Joudaki and J. J. E. Kajava and Y. Kang and V. Kansal and D. Karagiannis and K. Kiiveri and J. Kim and C. C. Kirkpatrick and S. Kruk and M. Lattanzi and L. Legrand and M. Lembo and F. Lepori and G. Leroy and G. F. Lesci and J. Lesgourgues and T. I. Liaudat and S. J. Liu and A. Loureiro and M. Magliocchetti and F. Mannucci and C. J. A. P. Martins and L. Maurin and M. Migliaccio and M. Miluzio and C. Moretti and G. Morgante and S. Nadathur and K. Naidoo and P. Natoli and A. Navarro-Alsina and S. Nesseris and L. Pagano and D. Paoletti and F. Passalacqua and K. Paterson and L. Patrizii and R. Paviot and A. Pisani and D. Potter and G. W. Pratt and S. Quai and M. Radovich and K. Rojas and W. Roster and S. Sacquegna and M. Sahlén and D. B. Sanders and E. Sarpa and A. Schneider and D. Sciotti and E. Sellentin and L. C. Smith and J. G. Sorce and K. Tanidis and C. Tao and F. Tarsitano and G. Testera and R. Teyssier and S. Tosi and A. Troja and A. Venhola and D. Vergani and F. Vernizzi and G. Verza and P. Vielzeuf and S. Vinciguerra and N. A. Walton and A. H. Wright},
journal= {arXiv preprint arXiv:2605.03012},
year = {2026}
}
Comments
20 pages, 9 Figures