Euclid: Photometric redshift calibration with self-organising maps^★

¹ Max Planck Institute for Extraterrestrial Physics, Giessenbachstr. 1, 85748 Garching, Germany
² Ruhr University Bochum, Faculty of Physics and Astronomy, Astronomical Institute (AIRUB), German Centre for Cosmological Lensing (GCCL), 44780 Bochum, Germany
³ Universität Bonn, Argelander-Institut für Astronomie, Auf dem Hügel 71, 53121 Bonn, Germany
⁴ Aix-Marseille Université, CNRS, CNES, LAM, Marseille, France
⁵ Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Campus UAB, 08193 Bellaterra, (Barcelona), Spain
⁶ Serra Húnter Fellow, Departament de Física, Universitat Autònoma de Barcelona, E-08193 Bellaterra, Spain
⁷ INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy
⁸ Infrared Processing and Analysis Center, California Institute of Technology, Pasadena, CA 91125, USA
⁹ Department of Astronomy, University of Geneva, Ch. d’Ecogia 16, 1290 Versoix, Switzerland
¹⁰ Leiden Observatory, Leiden University, Einsteinweg 55, 2333 CC Leiden, The Netherlands
¹¹ ESAC/ESA, Camino Bajo del Castillo, s/n, Urb. Villafranca del Castillo, 28692 Villanueva de la Cañada, Madrid, Spain
¹² School of Mathematics and Physics, University of Surrey, Guildford, Surrey GU2 7XH, UK
¹³ INAF-Osservatorio Astronomico di Brera, Via Brera 28, 20122 Milano, Italy
¹⁴ IFPU, Institute for Fundamental Physics of the Universe, Via Beirut 2, 34151 Trieste, Italy
¹⁵ INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34143 Trieste, Italy
¹⁶ INFN, Sezione di Trieste, Via Valerio 2, 34127 Trieste, TS, Italy
¹⁷ SISSA, International School for Advanced Studies, Via Bonomea 265, 34136 Trieste, TS, Italy
¹⁸ Dipartimento di Fisica e Astronomia, Università di Bologna, Via Gobetti 93/2, 40129 Bologna, Italy
¹⁹ INFN-Sezione di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy
²⁰ INAF-Osservatorio Astronomico di Padova, Via dell’Osservatorio 5, 35122 Padova, Italy
²¹ Universitäts-Sternwarte München, Fakultät für Physik, Ludwig-Maximilians-Universität München, Scheinerstrasse 1, 81679 München, Germany
²² Dipartimento di Fisica, Università di Genova, Via Dodecaneso 33, 16146 Genova, Italy
²³ INFN-Sezione di Genova, Via Dodecaneso 33, 16146 Genova, Italy
²⁴ Department of Physics “E. Pancini”, University Federico II, Via Cinthia 6, 80126 Napoli, Italy
²⁵ INAF-Osservatorio Astronomico di Capodimonte, Via Moiariello 16, 80131 Napoli, Italy
²⁶ Dipartimento di Fisica, Università degli Studi di Torino, Via P. Giuria 1, 10125 Torino, Italy
²⁷ INFN-Sezione di Torino, Via P. Giuria 1, 10125 Torino, Italy
²⁸ INAF-Osservatorio Astrofisico di Torino, Via Osservatorio 20, 10025 Pino Torinese, (TO), Italy
²⁹ European Space Agency/ESTEC, Keplerlaan 1, 2201 AZ, Noordwijk, The Netherlands
³⁰ Institute Lorentz, Leiden University, Niels Bohrweg 2, 2333 CA, Leiden, The Netherlands
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 Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas (CIEMAT), Avenida Complutense 40, 28040 Madrid, Spain
³⁵ Port d’Informació Científica, Campus UAB, C. Albareda s/n, 08193 Bellaterra, (Barcelona), Spain
³⁶ Institut d’Estudis Espacials de Catalunya (IEEC), Edifici RDIT, Campus UPC, 08860 Castelldefels, Barcelona, Spain
³⁷ Institute of Space Sciences (ICE, CSIC), Campus UAB, Carrer de Can Magrans, s/n, 08193 Barcelona, Spain
³⁸ Institute for Theoretical Particle Physics and Cosmology (TTK), RWTH Aachen University, 52056 Aachen, Germany
³⁹ INFN Section of Naples, Via Cinthia 6, 80126 Napoli, Italy
⁴⁰ Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu, HI 96822, USA
⁴¹ Dipartimento di Fisica e Astronomia “Augusto Righi” – Alma Mater Studiorum Università di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy
⁴² Instituto de Astrofísica de Canarias, Vía Láctea, 38205 La Laguna, Tenerife, Spain
⁴³ Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh, EH9 3HJ, UK
⁴⁴ Jodrell Bank Centre for Astrophysics, Department of Physics and Astronomy, University of Manchester, Oxford Road, Manchester, M13 9PL, UK
⁴⁵ European Space Agency/ESRIN, Largo Galileo Galilei 1, 00044 Frascati, Roma, Italy
⁴⁶ Université Claude Bernard Lyon 1, CNRS/IN2P3, IP2I Lyon, UMR 5822, Villeurbanne, F-69100, France
⁴⁷ Institut de Ciències del Cosmos (ICCUB), Universitat de Barcelona (IEEC-UB), Martí i Franquès 1, 08028 Barcelona, Spain
⁴⁸ Institució Catalana de Recerca i Estudis Avançats (ICREA), Passeig de Lluís Companys 23, 08010 Barcelona, Spain
⁴⁹ UCB Lyon 1, CNRS/IN2P3, IUF, IP2I Lyon, 4 Rue Enrico Fermi, 69622 Villeurbanne, France
⁵⁰ Mullard Space Science Laboratory, University College London, Holmbury St Mary, Dorking, Surrey RH5 6NT, UK
⁵¹ Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, Edifício C8, Campo Grande, PT1749-016 Lisboa, Portugal
⁵² Instituto de Astrofísica e Ciências do Espaço, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, 1749-016 Lisboa, Portugal
⁵³ INFN-Padova, Via Marzolo 8, 35131 Padova, Italy
⁵⁴ Aix-Marseille Université, CNRS/IN2P3, CPPM, Marseille, France
⁵⁵ INAF-Istituto di Astrofisica e Planetologia Spaziali, Via del Fosso del Cavaliere, 100, 00100 Roma, Italy
⁵⁶ Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM, 91191 Gif-sur-Yvette, France
⁵⁷ Space Science Data Center, Italian Space Agency, Via del Politecnico snc, 00133 Roma, Italy
⁵⁸ INFN-Bologna, Via Irnerio 46, 40126 Bologna, Italy
⁵⁹ University Observatory, LMU Faculty of Physics, Scheinerstrasse 1, 81679 Munich, Germany
⁶⁰ Institute of Theoretical Astrophysics, University of Oslo, P.O. Box 1029 Blindern, 0315 Oslo, Norway
⁶¹ Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA
⁶² Felix Hormuth Engineering, Goethestr. 17, 69181 Leimen, Germany
⁶³ Technical University of Denmark, Elektrovej 327, 2800 Kgs. Lyngby, Denmark
⁶⁴ Cosmic Dawn Center (DAWN), Denmark
⁶⁵ Institut d’Astrophysique de Paris, UMR 7095, CNRS, and Sorbonne Université, 98 bis Boulevard Arago, 75014 Paris, 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 Department of Physics and Helsinki Institute of Physics, Gustaf Hällströmin katu 2, 00014 University of Helsinki, Finland
⁷⁰ Department of Physics, P.O. Box 64, 00014 University of Helsinki, Finland
⁷¹ Helsinki Institute of Physics, Gustaf Hällströmin katu 2, University of Helsinki, Helsinki, Finland
⁷² Laboratoire d’etude de l’Univers et des phenomenes eXtremes, Observatoire de Paris, Université PSL, Sorbonne Université, CNRS, 92190 Meudon, France
⁷³ SKA Observatory, Jodrell Bank, Lower Withington, Macclesfield, Cheshire SK11 9FT, UK
⁷⁴ Dipartimento di Fisica “Aldo Pontremoli”, Università degli Studi di Milano, Via Celoria 16, 20133 Milano, Italy
⁷⁵ INFN-Sezione di Milano, Via Celoria 16, 20133 Milano, Italy
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 Université Paris Cité, CNRS, Astroparticule et Cosmologie, 75013 Paris, France
⁷⁹ CNRS-UCB International Research Laboratory, Centre Pierre Binétruy, IRL2007, CPB-IN2P3, Berkeley, USA
⁸⁰ University of Applied Sciences and Arts of Northwestern Switzerland, School of Engineering, 5210 Windisch, Switzerland
⁸¹ Institut d’Astrophysique de Paris, 98bis Boulevard Arago, 75014 Paris, France
⁸² Institute of Physics, Laboratory of Astrophysics, Ecole Polytechnique Fédérale de Lausanne (EPFL), Observatoire de Sauverny, 1290 Versoix, Switzerland
⁸³ 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
⁸⁴ DARK, Niels Bohr Institute, University of Copenhagen, Jagtvej 155, 2200 Copenhagen, Denmark
⁸⁵ Centre National d’Etudes Spatiales – Centre spatial de Toulouse, 18 Avenue Edouard Belin, 31401 Toulouse Cedex 9, France
⁸⁶ Institute of Space Science, Str. Atomistilor, Nr. 409 Măgurele, Ilfov, 077125, Romania
⁸⁷ Consejo Superior de Investigaciones Cientificas, Calle Serrano 117, 28006 Madrid, Spain
⁸⁸ Universidad de La Laguna, Departamento de Astrofísica, 38206 La Laguna, Tenerife, Spain
⁸⁹ Dipartimento di Fisica e Astronomia “G. Galilei”, Università di Padova, Via Marzolo 8, 35131 Padova, Italy
⁹⁰ Institut für Theoretische Physik, University of Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany
⁹¹ Institut de Recherche en Astrophysique et Planétologie (IRAP), Université de Toulouse, CNRS, UPS, CNES, 14 Av. Edouard Belin, 31400 Toulouse, France
⁹² Université St Joseph; Faculty of Sciences, Beirut, Lebanon
⁹³ Departamento de Física, FCFM, Universidad de Chile, Blanco Encalada 2008 Santiago, Chile
⁹⁴ Universität Innsbruck, Institut für Astro- und Teilchenphysik, Technikerstr. 25/8, 6020 Innsbruck, Austria
⁹⁵ Satlantis, University Science Park, Sede Bld 48940 Leioa-Bilbao, Spain
⁹⁶ Centre for Electronic Imaging, Open University, Walton Hall, Milton Keynes, MK7 6AA, UK
⁹⁷ Instituto de Astrofísica e Ciências do Espaço, Faculdade de Ciências, Universidade de Lisboa, Tapada da Ajuda, 1349-018 Lisboa, Portugal
⁹⁸ Niels Bohr Institute, University of Copenhagen, Jagtvej 128, 2200 Copenhagen, Denmark
⁹⁹ Universidad Politécnica de Cartagena, Departamento de Electrónica y Tecnología de Computadoras, Plaza del Hospital 1, 30202 Cartagena, Spain
¹⁰⁰ Kapteyn Astronomical Institute, University of Groningen, PO Box 800, 9700 AV, Groningen, The Netherlands
¹⁰¹ INAF, Istituto di Radioastronomia, Via Piero Gobetti 101, 40129 Bologna, Italy
¹⁰² Department of Physics, Oxford University, Keble Road, Oxford, OX1 3RH, UK
¹⁰³ ICL, Junia, Université Catholique de Lille, LITL, 59000 Lille, France

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Received: 13 August 2025
Accepted: 2 December 2025

Abstract

The Euclid large-scale weak-lensing survey aims to trace the evolution of cosmic structures up to redshift z ∼ 3 and beyond. Its success depends critically on obtaining highly accurate mean redshifts for ensembles of galaxies n(z) in all tomographic bins, essential for deriving robust cosmological constraints. However, photometric redshifts (photo-zs) are affected by systematic biases, arising from various sources of uncertainty and dominated by selection effects of the spectroscopic sample used for calibration. To address these challenges, we utilised self-organising maps (SOMs) with mock samples resembling the Euclid Wide Survey (EWS) from the Flagship2 simulation, to validate Euclid’s uncertainty requirement of |Δ⟨z⟩| = ⟨z_est⟩−⟨z⟩≤0.002(1 + z) per tomographic bin, assuming DR3-level data. Consequently, we identify the most effective galaxy selection for our tomographic bins, while systematically examining the implementation of quality control cuts to reduce sources of uncertainty. In particular, we observe that defining the redshift tomography using the mean spectroscopic redshift (spec-z) per SOM cell, results in none of the ten tomographic redshift bins satisfying the requirement. In contrast, the redshift tomography on the photo-zs of the EWS-like sample yields superior results, with eight out of ten bins [0 < z ≤ 2.5] meeting the Euclid requirement. To enhance the realism of our study, we morph our calibration sample to mimic the C3R2 survey in incremental steps. In this context, a maximum of six out of ten bins meet the requirement, strongly advocating the adoption of a redshift tomography defined by the photo-zs of individual galaxies rather than the commonly used mean spec-z of SOM cells. To examine the impact on the expected biases for Ω_m, σ₈, and Δw₀ measured by Euclid, we perform a Fisher forecast for cosmic shear only, based on our redshift uncertainties. Here, we find that even under an evaluation of the uncertainty where the impact of the redshift bias is substantial, most absolute biases remain below 0.1σ in the idealised scenario and below 0.3σ in the more realistic case.