Euclid preparation

LXXXIII. The impact of redshift interlopers on the two-point correlation function analysis

¹ INAF-Osservatorio Astronomico di Brera, Via Brera 28, 20122 Milano, Italy
² INFN-Sezione di Genova, Via Dodecaneso 33, 16146 Genova, Italy
³ Dipartimento di Fisica, Università di Genova, Via Dodecaneso 33, 16146 Genova, Italy
⁴ Aix-Marseille Université, CNRS, CNES, LAM, Marseille, France
⁵ SISSA, International School for Advanced Studies, Via Bonomea 265, 34136 Trieste TS, Italy
⁶ ICSC – Centro Nazionale di Ricerca in High Performance Computing, Big Data e Quantum Computing, Via Magnanelli 2 Bologna Italy
⁷ INFN, Sezione di Trieste, Via Valerio 2, 34127 Trieste, TS, Italy
⁸ Dipartimento di Fisica - Sezione di Astronomia, Università di Trieste, Via Tiepolo 11, 34131 Trieste, Italy
⁹ INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34143 Trieste, Italy
¹⁰ IFPU, Institute for Fundamental Physics of the Universe, via Beirut 2, 34151 Trieste, Italy
¹¹ Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive Pasadena, CA 91109, USA
¹² Johns Hopkins University, 3400 North Charles Street Baltimore, MD 21218, USA
¹³ California Institute of Technology, 1200 E California Blvd Pasadena, CA 91125, USA
¹⁴ INAF-IASF Milano, Via Alfonso Corti 12, 20133 Milano, Italy
¹⁵ Institut d’Astrophysique de Paris, UMR 7095, CNRS, and Sorbonne Université, 98 bis boulevard Arago, 75014 Paris, France
¹⁶ Institute of Space Sciences (ICE, CSIC), Campus UAB, Carrer de Can Magrans s/n, 08193 Barcelona, Spain
¹⁷ Dipartimento di Fisica, Università degli studi di Genova, and INFN-Sezione di Genova, via Dodecaneso 33, 16146 Genova, Italy
¹⁸ Dipartimento di Fisica e Astronomia “G. Galilei”, Università di Padova, Via Marzolo 8, 35131 Padova, Italy
¹⁹ INFN-Padova, Via Marzolo 8, 35131 Padova, Italy
²⁰ Waterloo Centre for Astrophysics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
²¹ Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
²² Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada
²³ Minnesota Institute for Astrophysics, University of Minnesota, 116 Church St SE Minneapolis, MN 55455, USA
²⁴ Infrared Processing and Analysis Center, California Institute of Technology, Pasadena, CA 91125, USA
²⁵ Université Paris-Saclay, CNRS, Institut d’astrophysique spatiale, 91405 Orsay, France
²⁶ ESAC/ESA, Camino Bajo del Castillo s/n. Urb. Villafranca del Castillo, 28692 Villanueva de la Cañada, Madrid, Spain
²⁷ School of Mathematics and Physics, University of Surrey, Guildford, Surrey GU2 7XH, UK
²⁸ INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy
²⁹ Dipartimento di Fisica e Astronomia, Università di Bologna, Via Gobetti 93/2, 40129 Bologna, Italy
³⁰ INFN-Sezione di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy
³¹ INAF-Osservatorio Astronomico di Padova, Via dell’Osservatorio 5, 35122 Padova, Italy
³² Space Science Data Center, Italian Space Agency, via del Politecnico snc, 00133 Roma, Italy
³³ INAF-Osservatorio Astrofisico di Torino, Via Osservatorio 20, 10025 Pino Torinese, (TO), Italy
³⁴ Department of Physics “E. Pancini”, University Federico II, Via Cinthia 6, 80126 Napoli, Italy
³⁵ INAF-Osservatorio Astronomico di Capodimonte, Via Moiariello 16, 80131 Napoli, Italy
³⁶ Instituto de Astrofísica e Ciências do Espaço, Universidade do Porto, CAUP, Rua das Estrelas, PT4150-762 Porto, Portugal
³⁷ Faculdade de Ciências da Universidade do Porto, Rua do Campo de Alegre, 4150-007 Porto, Portugal
³⁸ Dipartimento di Fisica, Università degli Studi di Torino, Via P. Giuria 1, 10125 Torino, Italy
³⁹ INFN-Sezione di Torino, Via P. Giuria 1, 10125 Torino, Italy
⁴⁰ European Space Agency/ESTEC, Keplerlaan 1, 2201 AZ Noordwijk, The Netherlands
⁴¹ Institute Lorentz, Leiden University, Niels Bohrweg 2, 2333 CA Leiden, The Netherlands
⁴² Leiden Observatory, Leiden University, Einsteinweg 55, 2333, CC Leiden, The Netherlands
⁴³ INAF-Osservatorio Astronomico di Roma, Via Frascati 33, 00078 Monteporzio Catone, Italy
⁴⁴ INFN-Sezione di Roma, Piazzale Aldo Moro, 2 – c/o Dipartimento di Fisica Edificio G. Marconi, 00185 Roma, Italy
⁴⁵ Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas (CIEMAT), Avenida Complutense 40, 28040 Madrid, Spain
⁴⁶ Port d’Informació Científica, Campus UAB, C. Albareda s/n, 08193 Bellaterra, (Barcelona), Spain
⁴⁷ Institute for Theoretical Particle Physics and Cosmology (TTK), RWTH Aachen University, 52056 Aachen, Germany
⁴⁸ INFN section of Naples, Via Cinthia 6, 80126 Napoli, Italy
⁴⁹ Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive Honolulu, HI 96822, USA
⁵⁰ Dipartimento di Fisica e Astronomia “Augusto Righi” – Alma Mater Studiorum Università di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy
⁵¹ Instituto de Astrofísica de Canarias, Vía Láctea, 38205 La Laguna, Tenerife, Spain
⁵² Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill Edinburgh, EH9 3HJ, UK
⁵³ Jodrell Bank Centre for Astrophysics, Department of Physics and Astronomy, University of Manchester, Oxford Road Manchester, M13 9PL, UK
⁵⁴ European Space Agency/ESRIN, Largo Galileo Galilei 1, 00044, Frascati Roma, Italy
⁵⁵ Université Claude Bernard Lyon 1, CNRS/IN2P3, IP2I Lyon, UMR 5822, Villeurbanne, F-69100, France
⁵⁶ Institut de Ciències del Cosmos (ICCUB), Universitat de Barcelona (IEEC-UB), Martí i Franquès 1, 08028 Barcelona, Spain
⁵⁷ Institució Catalana de Recerca i Estudis Avançats (ICREA), Passeig de Lluís Companys 23, 08010 Barcelona, Spain
⁵⁸ UCB Lyon 1, CNRS/IN2P3, IUF, IP2I Lyon, 4 rue Enrico Fermi, 69622 Villeurbanne, France
⁵⁹ Institut d’Estudis Espacials de Catalunya (IEEC), Edifici RDIT, Campus UPC, 08860 Castelldefels, Barcelona, Spain
⁶⁰ Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, Edifício C8, Campo Grande, PT1749-016 Lisboa, Portugal
⁶¹ Instituto de Astrofísica e Ciências do Espaço, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, 1749-016 Lisboa, Portugal
⁶² Department of Astronomy, University of Geneva, ch. d’Ecogia 16, 1290 Versoix, Switzerland
⁶³ INAF-Istituto di Astrofisica e Planetologia Spaziali, via del Fosso del Cavaliere 100, 00100 Roma, Italy
⁶⁴ Aix-Marseille Université, CNRS/IN2P3, CPPM, Marseille, France
⁶⁵ INFN-Bologna, Via Irnerio 46, 40126 Bologna, Italy
⁶⁶ School of Physics, HH Wills Physics Laboratory, University of Bristol, Tyndall Avenue Bristol, BS8 1TL, UK
⁶⁷ Universitäts-Sternwarte München, Fakultät für Physik, Ludwig-Maximilians-Universität München, Scheinerstrasse 1, 81679 München, Germany
⁶⁸ Max Planck Institute for Extraterrestrial Physics, Giessenbachstr. 1, 85748 Garching, Germany
⁶⁹ Dipartimento di Fisica “Aldo Pontremoli”, Università degli Studi di Milano, Via Celoria 16, 20133 Milano, Italy
⁷⁰ INFN-Sezione di Milano, Via Celoria 16, 20133 Milano, Italy
⁷¹ Institute of Theoretical Astrophysics, University of Oslo, P.O. Box 1029 Blindern, 0315, Oslo, Norway
⁷² Felix Hormuth Engineering, Goethestr. 17, 69181 Leimen, Germany
⁷³ Technical University of Denmark, Elektrovej 327, 2800 Kgs. Lyngby, Denmark
⁷⁴ Cosmic Dawn Center (DAWN), Denmark
⁷⁵ Max-Planck-Institut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany
⁷⁶ NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA
⁷⁷ Department of Physics and Astronomy, University College London, Gower Street London, WC1E 6BT, UK
⁷⁸ Department of Physics and Helsinki Institute of Physics, Gustaf Hällströmin katu 2, 00014 University of Helsinki, Finland
⁷⁹ Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM, 91191 Gif-sur-Yvette, France
⁸⁰ Université de Genève, Département de Physique Théorique and Centre for Astroparticle Physics, 24 quai Ernest-Ansermet, CH-1211 Genève 4, Switzerland
⁸¹ Department of Physics, P.O. Box 64, 00014 University of Helsinki, Finland
⁸² Helsinki Institute of Physics, Gustaf Hällströmin katu 2 University of Helsinki Helsinki, Finland
⁸³ Laboratoire d’etude de l’Univers et des phenomenes eXtremes, Observatoire de Paris, Université PSL, Sorbonne Université, CNRS, 92190 Meudon, France
⁸⁴ Mullard Space Science Laboratory, University College London, Holmbury St Mary, Dorking, Surrey, RH5 6NT, UK
⁸⁵ NOVA optical infrared instrumentation group at ASTRON, Oude Hoogeveensedijk 4, 7991PD Dwingeloo, The Netherlands
⁸⁶ Centre de Calcul de l’IN2P3/CNRS, 21 avenue Pierre de Coubertin, 69627 Villeurbanne Cedex, France
⁸⁷ University of Applied Sciences and Arts of Northwestern Switzerland, School of Computer Science, 5210 Windisch, Switzerland
⁸⁸ Universität Bonn, Argelander-Institut für Astronomie, Auf dem Hügel 71, 53121 Bonn, Germany
⁸⁹ Dipartimento di Fisica e Astronomia “Augusto Righi” – Alma Mater Studiorum Università di Bologna, via Piero Gobetti 93/2, 40129 Bologna, Italy
⁹⁰ Department of Physics, Institute for Computational Cosmology, Durham University, South Road Durham, DH1 3LE, UK
⁹¹ Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS, Laboratoire Lagrange, Bd de l’Observatoire CS 34229, 06304 Nice cedex 4, France
⁹² Université Paris Cité, CNRS, Astroparticule et Cosmologie, 75013 Paris, France
⁹³ CNRS-UCB International Research Laboratory, Centre Pierre Binétruy, IRL2007, CPB-IN2P3 Berkeley, USA
⁹⁴ University of Applied Sciences and Arts of Northwestern Switzerland, School of Engineering, 5210 Windisch, Switzerland
⁹⁵ Institut d’Astrophysique de Paris, 98bis Boulevard Arago, 75014 Paris, France
⁹⁶ Institute of Physics, Laboratory of Astrophysics, Ecole Polytechnique Fédérale de Lausanne (EPFL), Observatoire de Sauverny, 1290 Versoix, Switzerland
⁹⁷ Aurora Technology for European Space Agency (ESA), Camino bajo del Castillo s/n Urbanizacion Villafranca del Castillo Villanueva de la Cañada, 28692, Madrid, Spain
⁹⁸ Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Campus UAB, 08193 Bellaterra (Barcelona), Spain
⁹⁹ School of Mathematics, Statistics and Physics, Newcastle University, Herschel Building, Newcastle-upon-Tyne, NE1 7RU, UK
¹⁰⁰ DARK, Niels Bohr Institute, University of Copenhagen, Jagtvej 155, 2200 Copenhagen, Denmark
¹⁰¹ Centre National d’Etudes Spatiales – Centre spatial de Toulouse, 18 avenue Edouard Belin, 31401 Toulouse Cedex 9, France
¹⁰² Institute of Space Science, Str. Atomistilor, nr. 409 Măgurele Ilfov, 077125, Romania
¹⁰³ Consejo Superior de Investigaciones Cientificas, Calle Serrano 117, 28006, Madrid, Spain
¹⁰⁴ Universidad de La Laguna, Departamento de Astrofísica, 38206 La Laguna, Tenerife, Spain
¹⁰⁵ Institut für Theoretische Physik, University of Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany
¹⁰⁶ Institut de Recherche en Astrophysique et Planétologie (IRAP), Université de Toulouse, CNRS, UPS, CNES, 14 Av. Edouard Belin, 31400 Toulouse, France
¹⁰⁷ Université St Joseph; Faculty of Sciences, Beirut, Lebanon
¹⁰⁸ Departamento de Física, FCFM, Universidad de Chile, Blanco Encalada 2008 Santiago, Chile
¹⁰⁹ Universität Innsbruck, Institut für Astro- und Teilchenphysik, Technikerstr. 25/8, 6020 Innsbruck, Austria
¹¹⁰ Satlantis, University Science Park, Sede Bld, 48940 Leioa-Bilbao, Spain
¹¹¹ Instituto de Astrofísica e Ciências do Espaço, Faculdade de Ciências, Universidade de Lisboa, Tapada da Ajuda, 1349-018 Lisboa, Portugal
¹¹² Cosmic Dawn Center (DAWN)
¹¹³ Niels Bohr Institute, University of Copenhagen, Jagtvej 128, 2200 Copenhagen, Denmark
¹¹⁴ Universidad Politécnica de Cartagena, Departamento de Electrónica y Tecnología de Computadoras, Plaza del Hospital 1, 30202 Cartagena, Spain
¹¹⁵ Kapteyn Astronomical Institute, University of Groningen, PO Box 800, 9700 AV Groningen, The Netherlands
¹¹⁶ Dipartimento di Fisica e Scienze della Terra, Università degli Studi di Ferrara, Via Giuseppe Saragat 1, 44122 Ferrara, Italy
¹¹⁷ Istituto Nazionale di Fisica Nucleare, Sezione di Ferrara, Via Giuseppe Saragat 1, 44122 Ferrara, Italy
¹¹⁸ INAF, Istituto di Radioastronomia, 40129 Bologna, Italy
¹¹⁹ Department of Physics, Oxford University, Keble Road Oxford, OX1 3RH, UK
¹²⁰ INAF – Osservatorio Astronomico di Brera, via Emilio Bianchi 46, 23807 Merate, Italy
¹²¹ ICL, Junia, Université Catholique de Lille, LITL, 59000 Lille, France
¹²² Instituto de Física Teórica UAM-CSIC, Campus de Cantoblanco, 28049 Madrid, Spain
¹²³ CERCA/ISO, Department of Physics, Case Western Reserve University, 10900 Euclid Avenue Cleveland, OH 44106, USA
¹²⁴ Technical University of Munich, TUM School of Natural Sciences, Physics Department, James-Franck-Str. 1, 85748 Garching, Germany
¹²⁵ Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85748 Garching, Germany
¹²⁶ Departamento de Física Fundamental. Universidad de Salamanca. Plaza de la Merced s/n., 37008 Salamanca, Spain
¹²⁷ Instituto de Astrofísica de Canarias (IAC); Departamento de Astrofísica, Universidad de La Laguna (ULL), 38200 La Laguna, Tenerife, Spain
¹²⁸ Université de Strasbourg, CNRS, Observatoire astronomique de Strasbourg, UMR 7550, 67000 Strasbourg, France
¹²⁹ Center for Data-Driven Discovery, Kavli IPMU (WPI), UTIAS, The University of Tokyo, Kashiwa, Chiba 277-8583, Japan
¹³⁰ Ludwig-Maximilians-University, Schellingstrasse 4, 80799 Munich, Germany
¹³¹ Max-Planck-Institut für Physik, Boltzmannstr. 8, 85748 Garching, Germany
¹³² Department of Physics & Astronomy, University of California Irvine, Irvine, CA 92697, USA
¹³³ Department of Mathematics and Physics E. De Giorgi, University of Salento, Via per Arnesano CP-I93, 73100 Lecce, Italy
¹³⁴ INFN, Sezione di Lecce, Via per Arnesano CP-193, 73100 Lecce, Italy
¹³⁵ INAF-Sezione di Lecce, c/o Dipartimento Matematica e Fisica, Via per Arnesano, 73100 Lecce, Italy
¹³⁶ Departamento Física Aplicada, Universidad Politécnica de Cartagena, Campus Muralla del Mar, 30202 Cartagena, Murcia, Spain
¹³⁷ Instituto de Física de Cantabria, Edificio Juan Jordá, Avenida de los Castros, 39005 Santander, Spain
¹³⁸ Observatorio Nacional, Rua General Jose Cristino, 77-Bairro Imperial de Sao Cristovao, Rio de Janeiro, 20921-400, Brazil
¹³⁹ CEA Saclay, DFR/IRFU, Service d’Astrophysique, Bat. 709, 91191 Gif-sur-Yvette, France
¹⁴⁰ Institute of Cosmology and Gravitation, University of Portsmouth, Portsmouth, PO1 3FX, UK
¹⁴¹ Department of Computer Science, Aalto University, PO Box 15400 Espoo, FI-00 076, Finland
¹⁴² Instituto de Astrofísica de Canarias, c/ Via Lactea s/n, La Laguna 38200, Spain. Departamento de Astrofísica de la Universidad de La Laguna, Avda. Francisco Sanchez, La Laguna, 38200, Spain
¹⁴³ Caltech/IPAC, 1200 E. California Blvd. Pasadena, CA 91125, USA
¹⁴⁴ Ruhr University Bochum, Faculty of Physics and Astronomy, Astronomical Institute (AIRUB), German Centre for Cosmological Lensing (GCCL), 44780 Bochum, Germany
¹⁴⁵ Department of Physics and Astronomy, Vesilinnantie 5, 20014 University of Turku, Finland
¹⁴⁶ Serco for European Space Agency (ESA), Camino bajo del Castillo s/n Urbanizacion Villafranca del Castillo Villanueva de la Cañada, 28692, Madrid, Spain
¹⁴⁷ ARC Centre of Excellence for Dark Matter Particle Physics, Melbourne, Australia
¹⁴⁸ Centre for Astrophysics & Supercomputing, Swinburne University of Technology, Hawthorn, Victoria 3122, Australia
¹⁴⁹ Department of Physics and Astronomy, University of the Western Cape, Bellville, Cape Town, 7535, South Africa
¹⁵⁰ DAMTP, Centre for Mathematical Sciences, Wilberforce Road Cambridge, CB3 0WA, UK
¹⁵¹ Kavli Institute for Cosmology Cambridge, Madingley Road Cambridge, CB3 0HA, UK
¹⁵² Department of Astrophysics, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland
¹⁵³ Department of Physics, Centre for Extragalactic Astronomy, Durham University, South Road Durham, DH1 3LE, UK
¹⁵⁴ IRFU, CEA, Université Paris-Saclay, 91191 Gif-sur-Yvette Cedex, France
¹⁵⁵ Oskar Klein Centre for Cosmoparticle Physics, Department of Physics, Stockholm University, Stockholm, SE-106 91, Sweden
¹⁵⁶ Astrophysics Group, Blackett Laboratory, Imperial College London, London, SW7 2AZ, UK
¹⁵⁷ Univ. Grenoble Alpes, CNRS, Grenoble INP, LPSC-IN2P3, 53 Avenue des Martyrs, 38000 Grenoble, France
¹⁵⁸ INAF-Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, 50125 Firenze, Italy
¹⁵⁹ Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 2, 00185 Roma, Italy
¹⁶⁰ Centro de Astrofísica da Universidade do Porto, Rua das Estrelas, 4150-762 Porto, Portugal
¹⁶¹ HE Space for European Space Agency (ESA), Camino bajo del Castillo s/n Urbanizacion Villafranca del Castillo Villanueva de la Cañada 28692 Madrid, Spain
¹⁶² Department of Astrophysical Sciences, Peyton Hall, Princeton University, Princeton, NJ 08544, USA
¹⁶³ Theoretical astrophysics, Department of Physics and Astronomy, Uppsala University, Box 515, 751 20 Uppsala, Sweden
¹⁶⁴ Mathematical Institute, University of Leiden, Einsteinweg 55, 2333 CA Leiden, The Netherlands
¹⁶⁵ Institute of Astronomy, University of Cambridge, Madingley Road Cambridge, CB3 0HA, UK
¹⁶⁶ Univ. Lille, CNRS, Centrale Lille, UMR 9189 CRIStAL, 59000 Lille, France
¹⁶⁷ Space physics and astronomy research unit, University of Oulu, Pentti Kaiteran katu 1, FI-90014 Oulu, Finland
¹⁶⁸ Center for Computational Astrophysics, Flatiron Institute, 162 5th Avenue, 10010 New York, NY, USA

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Received: 6 May 2025
Accepted: 23 November 2025

Abstract

Context. The Euclid galaxy survey is designed to measure the spectroscopic redshift of emission-line galaxies (ELGs) by identifying the Hα emission line in their slitless spectra. The efficacy of this approach crucially depends on the signal-to-noise ratio (S/N) of the line, as sometimes noise fluctuations in the spectrum continuum can be misidentified as Hα. In addition, other genuine strong emission lines can be mistaken for Hα, depending on the redshift of the source. Both effects lead to ambiguities in the redshift measurement that can result in catastrophic redshift errors and the inclusion of ‘interloper’ galaxies in the sample.

Aims. This paper forecasts the impact on the galaxy clustering analysis of the expected redshift errors in the Euclid spectroscopic sample. Specifically, it investigates the effect of the redshift interloper contamination on the galaxy two-point correlation function (2PCF) and, in turn, on the inferred growth rate of structure fσ₈ and Alcock–Paczynski (AP) parameters α_∥ and α_⊥.

Methods. This work is based on the analysis of 1000 synthetic spectroscopic catalogues, the EuclidLargeMocks, which mimic the area and selection function of the Euclid Data Release 1 (DR1) sample. We estimated the 2PCF of contaminated catalogues and separated the different contributions, particularly those coming from galaxies with correctly measured redshift and from contaminants. We explored different models of increasing complexity to describe the measured 2PCF at a fixed cosmology, with the aim of identifying the most efficient model to reproduce the data. Finally, we performed a cosmological inference and evaluated the systematic error on the inferred fσ₈, α_∥, and α_⊥ values associated with different models.

Results. Our results demonstrate that a minimal modelling approach, which only accounts for an attenuation of the clustering signal regardless of the type of contaminants, is sufficient to recover the correct values of fσ₈, α_∥, and α_⊥ at DR1. The accuracy and precision of the estimated AP parameters are largely insensitive to the presence of interlopers. The adoption of a minimal modelling induces a 1%–3% systematic error on the growth rate of structure estimation, depending on the considered redshift. However, this error remains smaller than the statistical error expected for the Euclid DR1 analysis.