Euclid: Photometric redshift calibration performance with the clustering-redshifts technique in the Flagship 2 simulation^⋆

¹ Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Campus UAB, 08193 Bellaterra (Barcelona), Spain
² Serra Húnter Fellow, Departament de Física, Universitat Autònoma de Barcelona, E-08193 Bellaterra, Spain
³ Aix-Marseille Université, CNRS, CNES, LAM, Marseille, France
⁴ Ruhr University Bochum, Faculty of Physics and Astronomy, Astronomical Institute (AIRUB), German Centre for Cosmological Lensing (GCCL), 44780 Bochum, Germany
⁵ Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain
⁶ Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas (CIEMAT), Avenida Complutense 40, 28040 Madrid, Spain
⁷ Port d’Informació Científica, Campus UAB, C. Albareda s/n, 08193 Bellaterra (Barcelona), Spain
⁸ Max Planck Institute for Extraterrestrial Physics, Giessenbachstr. 1, 85748 Garching, Germany
⁹ Department of Astronomy, University of Geneva, ch. d’Ecogia 16, 1290 Versoix, Switzerland
¹⁰ Institute of Cosmology and Gravitation, University of Portsmouth, Portsmouth PO1 3FX, UK
¹¹ Institució Catalana de Recerca i Estudis Avançats (ICREA), Passeig de Lluís Companys 23, 08010 Barcelona, Spain
¹² ESAC/ESA, Camino Bajo del Castillo, s/n., Urb. Villafranca del Castillo, 28692 Villanueva de la Cañada, Madrid, Spain
¹³ School of Mathematics and Physics, University of Surrey, Guildford, Surrey GU2 7XH, UK
¹⁴ INAF-Osservatorio Astronomico di Brera, Via Brera 28, 20122 Milano, Italy
¹⁵ INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy
¹⁶ IFPU, Institute for Fundamental Physics of the Universe, Via Beirut 2, 34151 Trieste, Italy
¹⁷ INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34143 Trieste, Italy
¹⁸ INFN, Sezione di Trieste, Via Valerio 2, 34127 Trieste TS, Italy
¹⁹ SISSA, International School for Advanced Studies, Via Bonomea 265, 34136 Trieste TS, Italy
²⁰ Centre National d’Etudes Spatiales – Centre spatial de Toulouse, 18 avenue Edouard Belin, 31401 Toulouse Cedex 9, France
²¹ Dipartimento di Fisica e Astronomia, Università di Bologna, Via Gobetti 93/2, 40129 Bologna, Italy
²² INFN-Sezione di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy
²³ INAF-Osservatorio Astronomico di Padova, Via dell’Osservatorio 5, 35122 Padova, Italy
²⁴ Dipartimento di Fisica, Università di Genova, Via Dodecaneso 33, 16146 Genova, Italy
²⁵ INFN-Sezione di Genova, Via Dodecaneso 33, 16146 Genova, Italy
²⁶ Department of Physics "E. Pancini", University Federico II, Via Cinthia 6, 80126 Napoli, Italy
²⁷ INAF-Osservatorio Astronomico di Capodimonte, Via Moiariello 16, 80131 Napoli, Italy
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-Osservatorio Astrofisico di Torino, Via Osservatorio 20, 10025 Pino Torinese (TO), Italy
³¹ INAF-IASF Milano, Via Alfonso Corti 12, 20133 Milano, Italy
³² INAF-Osservatorio Astronomico di Roma, Via Frascati 33, 00078 Monteporzio Catone, Italy
³³ INFN-Sezione di Roma, Piazzale Aldo Moro, 2 – c/o Dipartimento di Fisica, Edificio G. Marconi, 00185 Roma, Italy
³⁴ Institute for Theoretical Particle Physics and Cosmology (TTK), RWTH Aachen University, 52056 Aachen, Germany
³⁵ Institute of Space Sciences (ICE, CSIC), Campus UAB, Carrer de Can Magrans, s/n, 08193 Barcelona, Spain
³⁶ Institut d’Estudis Espacials de Catalunya (IEEC), Edifici RDIT, Campus UPC, 08860 Castelldefels, Barcelona, Spain
³⁷ INFN section of Naples, Via Cinthia 6, 80126 Napoli, Italy
³⁸ Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu, HI 96822, USA
³⁹ Dipartimento di Fisica e Astronomia “Augusto Righi” – Alma Mater Studiorum Università di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy
⁴⁰ Instituto de Astrofísica de Canarias, Vía Láctea, 38205 La Laguna, Tenerife, Spain
⁴¹ Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ, UK
⁴² Jodrell Bank Centre for Astrophysics, Department of Physics and Astronomy, University of Manchester, Oxford Road, Manchester M13 9PL, UK
⁴³ European Space Agency/ESRIN, Largo Galileo Galilei 1, 00044 Frascati, Roma, Italy
⁴⁴ Université Claude Bernard Lyon 1, CNRS/IN2P3, IP2I Lyon, UMR 5822, Villeurbanne, F-69100, France
⁴⁵ Institut de Ciències del Cosmos (ICCUB), Universitat de Barcelona (IEEC-UB), Martí i Franquès 1, 08028 Barcelona, Spain
⁴⁶ UCB Lyon 1, CNRS/IN2P3, IUF, IP2I Lyon, 4 rue Enrico Fermi, 69622 Villeurbanne, France
⁴⁷ Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, Edifício C8, Campo Grande, PT1749-016 Lisboa, Portugal
⁴⁸ Instituto de Astrofísica e Ciências do Espaço, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, 1749-016 Lisboa, Portugal
⁴⁹ Université Paris-Saclay, CNRS, Institut d’astrophysique spatiale, 91405 Orsay, France
⁵⁰ Aix-Marseille Université, CNRS/IN2P3, CPPM, Marseille, France
⁵¹ INAF-Istituto di Astrofisica e Planetologia Spaziali, via del Fosso del Cavaliere, 100, 00100 Roma, Italy
⁵² Space Science Data Center, Italian Space Agency, via del Politecnico snc, 00133 Roma, Italy
⁵³ INFN-Bologna, Via Irnerio 46, 40126 Bologna, Italy
⁵⁴ School of Physics, HH Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, UK
⁵⁵ Universitäts-Sternwarte München, Fakultät für Physik, Ludwig-Maximilians-Universität München, Scheinerstrasse 1, 81679 München, Germany
⁵⁶ FRACTAL S.L.N.E., calle Tulipán 2, Portal 13 1A, 28231 Las Rozas de Madrid, Spain
⁵⁷ Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA
⁵⁸ Department of Physics, Lancaster University, Lancaster LA1 4YB, UK
⁵⁹ Technical University of Denmark, Elektrovej 327, 2800 Kgs. Lyngby, Denmark
⁶⁰ Cosmic Dawn Center (DAWN), Denmark
⁶¹ Max-Planck-Institut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany
⁶² NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA
⁶³ Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK
⁶⁴ Department of Physics and Helsinki Institute of Physics, Gustaf Hällströmin katu 2, 00014 University of Helsinki, Finland
⁶⁵ Université de Genève, Département de Physique Théorique and Centre for Astroparticle Physics, 24 quai Ernest-Ansermet, CH-1211 Genève 4, Switzerland
⁶⁶ Department of Physics, P.O. Box 64 00014 University of Helsinki, Finland
⁶⁷ Helsinki Institute of Physics, Gustaf Hällströmin katu 2, University of Helsinki, Helsinki, Finland
⁶⁸ Laboratoire d’etude de l’Univers et des phenomenes eXtremes, Observatoire de Paris, Université PSL, Sorbonne Université, CNRS, 92190 Meudon, France
⁶⁹ Institute of Theoretical Astrophysics, University of Oslo, P.O. Box 1029 Blindern 0315 Oslo, Norway
⁷⁰ SKA Observatory, Jodrell Bank, Lower Withington, Macclesfield, Cheshire SK11 9FT, UK
⁷¹ Centre de Calcul de l’IN2P3/CNRS, 21 avenue Pierre de Coubertin, 69627 Villeurbanne Cedex, France
⁷² Dipartimento di Fisica “Aldo Pontremoli”, Università degli Studi di Milano, Via Celoria 16, 20133 Milano, Italy
⁷³ INFN-Sezione di Milano, Via Celoria 16, 20133 Milano, Italy
⁷⁴ University of Applied Sciences and Arts of Northwestern Switzerland, School of Computer Science, 5210 Windisch, Switzerland
⁷⁵ Universität Bonn, Argelander-Institut für Astronomie, Auf dem Hügel 71, 53121 Bonn, Germany
⁷⁶ Dipartimento di Fisica e Astronomia “Augusto Righi” – Alma Mater Studiorum Università di Bologna, via Piero Gobetti 93/2, 40129 Bologna, Italy
⁷⁷ Department of Physics, Institute for Computational Cosmology, Durham University, South Road, Durham DH1 3LE, UK
⁷⁸ Infrared Processing and Analysis Center, California Institute of Technology, Pasadena, CA 91125, USA
⁷⁹ Université Paris Cité, CNRS, Astroparticule et Cosmologie, 75013 Paris, France
⁸⁰ CNRS-UCB International Research Laboratory, Centre Pierre Binétruy, IRL2007, CPB-IN2P3, Berkeley, USA
⁸¹ University of Applied Sciences and Arts of Northwestern Switzerland, School of Engineering, 5210 Windisch, Switzerland
⁸² Institut d’Astrophysique de Paris, 98bis Boulevard Arago, 75014 Paris, France
⁸³ Institut d’Astrophysique de Paris, UMR 7095, CNRS, and Sorbonne Université, 98 bis boulevard Arago, 75014 Paris, France
⁸⁴ Institute of Physics, Laboratory of Astrophysics, Ecole Polytechnique Fédérale de Lausanne (EPFL), Observatoire de Sauverny, 1290 Versoix, Switzerland
⁸⁵ Telespazio UK S.L. for European Space Agency (ESA), Camino bajo del Castillo, s/n, Urbanizacion Villafranca del Castillo, Villanueva de la Cañada, 28692 Madrid, Spain
⁸⁶ European Space Agency/ESTEC, Keplerlaan 1, 2201 AZ Noordwijk, The Netherlands
⁸⁷ DARK, Niels Bohr Institute, University of Copenhagen, Jagtvej 155, 2200 Copenhagen, Denmark
⁸⁸ Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM, 91191 Gif-sur-Yvette, France
⁸⁹ Institute of Space Science, Str. Atomistilor, nr. 409 Măgurele, Ilfov 077125, Romania
⁹⁰ Consejo Superior de Investigaciones Cientificas, Calle Serrano 117, 28006 Madrid, Spain
⁹¹ Universidad de La Laguna, Departamento de Astrofísica, 38206 La Laguna, Tenerife, Spain
⁹² Dipartimento di Fisica e Astronomia “G. Galilei”, Università di Padova, Via Marzolo 8, 35131 Padova, Italy
⁹³ INFN-Padova, Via Marzolo 8, 35131 Padova, Italy
⁹⁴ Institut für Theoretische Physik, University of Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany
⁹⁵ Institut de Recherche en Astrophysique et Planétologie (IRAP), Université de Toulouse, CNRS, UPS, CNES, 14 Av. Edouard Belin, 31400 Toulouse, France
⁹⁶ Université St Joseph; Faculty of Sciences, Beirut, Lebanon
⁹⁷ Departamento de Física, FCFM, Universidad de Chile, Blanco Encalada 2008, Santiago, Chile
⁹⁸ Universität Innsbruck, Institut für Astro- und Teilchenphysik, Technikerstr. 25/8, 6020 Innsbruck, Austria
⁹⁹ Satlantis, University Science Park, Sede Bld 48940, Leioa-Bilbao, Spain
¹⁰⁰ Department of Physics, Royal Holloway, University of London, TW20 0EX, UK
¹⁰¹ Instituto de Astrofísica e Ciências do Espaço, Faculdade de Ciências, Universidade de Lisboa, Tapada da Ajuda, 1349-018 Lisboa, Portugal
¹⁰² Cosmic Dawn Center (DAWN)
¹⁰³ Niels Bohr Institute, University of Copenhagen, Jagtvej 128, 2200 Copenhagen, Denmark
¹⁰⁴ Universidad Politécnica de Cartagena, Departamento de Electrónica y Tecnología de Computadoras, Plaza del Hospital 1, 30202 Cartagena, Spain
¹⁰⁵ Centre for Information Technology, University of Groningen, PO Box 11044 9700 CA Groningen, The Netherlands
¹⁰⁶ Kapteyn Astronomical Institute, University of Groningen, PO Box 800 9700 AV Groningen, The Netherlands
¹⁰⁷ INAF, Istituto di Radioastronomia, Via Piero Gobetti 101, 40129 Bologna, Italy
¹⁰⁸ Department of Physics, Oxford University, Keble Road, Oxford OX1 3RH, UK
¹⁰⁹ Aurora Technology for European Space Agency (ESA), Camino bajo del Castillo, s/n, Urbanizacion Villafranca del Castillo, Villanueva de la Cañada, 28692 Madrid, Spain
¹¹⁰ INAF-Osservatorio Astronomico di Brera, Via Brera 28, 20122 Milano, Italy, and INFN-Sezione di Genova, Via Dodecaneso 33, 16146 Genova, Italy
¹¹¹ ICL, Junia, Université Catholique de Lille, LITL, 59000 Lille, France
¹¹² ICSC – Centro Nazionale di Ricerca in High Performance Computing, Big Data e Quantum Computing, Via Magnanelli 2, Bologna, Italy

^⋆⋆ Corresponding author: wdoumerg@ifae.es

Received: 16 May 2025
Accepted: 28 July 2025

Abstract

Aims. The precision of cosmological constraints from imaging surveys hinges on an accurately estimated redshift distribution n(z) of the tomographic bins, especially their mean redshifts. We assess the effectiveness of the clustering-redshifts technique in constraining Euclid tomographic redshift bins to meet the target uncertainty of σ(⟨z⟩) < 0.002(1 + z). We inferred these mean redshifts from the small-scale angular clustering of Euclid galaxies, which were distributed into bins with spectroscopic samples localised in narrow redshift slices.

Methods. We generated spectroscopic mocks from the Flagship2 simulation for the Baryon Oscillation Spectroscopic Survey (BOSS), the Dark Energy Spectroscopic Instrument (DESI), and the Euclid Near-Infrared Spectrometer and Photometer (NISP) spectroscopic survey. We evaluated and optimised the clustering-redshifts pipeline, and we introduced a new method for measuring the photometric galaxy bias (clustering), which is the primary limitation of this technique.

Results. We have successfully constrained the means and standard deviations of the redshift distributions for all of the tomographic bins (with a maximum photometric redshift of 1.6). We achieved precision beyond the required thresholds. We have identified the main sources of bias, particularly the impact of the one-halo galaxy distribution, which imposed the minimal separation scale to be larger than 1.5 Mpc for evaluating cross-correlations. These results demonstrate that clustering-redshifts can meet the precision requirements for Euclid, and we highlighted several avenues for future improvements.