Euclid: Improving redshift distribution reconstruction using a deep-to-wide transfer function^★

¹ Department of Astronomy, University of Geneva, ch. d’Ecogia 16, 1290 Versoix, Switzerland
² INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy
³ Ruhr University Bochum, Faculty of Physics and Astronomy, Astronomical Institute (AIRUB), German Centre for Cosmological Lensing (GCCL), 44780 Bochum, Germany
⁴ Institute of Space Sciences (ICE, CSIC), Campus UAB, Carrer de Can Magrans, s/n, 08193 Barcelona, Spain
⁵ Institut d’Estudis Espacials de Catalunya (IEEC), Edifici RDIT, Campus UPC, 08860 Castelldefels, Barcelona, Spain
⁶ Infrared Processing and Analysis Center, California Institute of Technology, Pasadena, CA 91125, USA
⁷ Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Campus UAB, 08193 Bellaterra (Barcelona), Spain
⁸ Aix-Marseille Université, CNRS, CNES, LAM, Marseille, France
⁹ Serra Húnter Fellow, Departament de Física, Universitat Autònoma de Barcelona, E-08193 Bellaterra, Spain
¹⁰ Max Planck Institute for Extraterrestrial Physics, Giessenbachstr. 1, 85748 Garching, Germany
¹¹ Department of Physics and Astronomy, University of California, Davis, CA 95616, USA
¹² Université Paris-Saclay, CNRS, Institut d’astrophysique spatiale, 91405 Orsay, France
¹³ ESAC/ESA, Camino Bajo del Castillo, s/n., Urb. Villafranca del Castillo, 28692 Villanueva de la Cañada, Madrid, Spain
¹⁴ INAF-Osservatorio Astronomico di Brera, Via Brera 28, 20122 Milano, Italy
¹⁵ Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM, 91191 Gif-sur-Yvette, France
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 Dipartimento di Fisica e Astronomia, Università di Bologna, Via Gobetti 93/2, 40129 Bologna, Italy
²¹ INFN-Sezione di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy
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 Instituto de Astrofísica e Ciências do Espaço, Universidade do Porto, CAUP, Rua das Estrelas, PT4150-762 Porto, Portugal
²⁷ Faculdade de Ciências da Universidade do Porto, Rua do Campo de Alegre, 4150-007 Porto, Portugal
²⁸ European Southern Observatory, Karl-Schwarzschild-Str. 2, 85748 Garching, Germany
²⁹ Dipartimento di Fisica, Università degli Studi di Torino, Via P. Giuria 1, 10125 Torino, Italy
³⁰ INFN-Sezione di Torino, Via P. Giuria 1, 10125 Torino, Italy
³¹ INAF-Osservatorio Astrofisico di Torino, Via Osservatorio 20, 10025 Pino Torinese (TO), Italy
³² Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ, UK
³³ Leiden Observatory, Leiden University, Einsteinweg 55, 2333 CC, Leiden, The Netherlands
³⁴ INAF-IASF Milano, Via Alfonso Corti 12, 20133 Milano, Italy
³⁵ INAF-Osservatorio Astronomico di Roma, Via Frascati 33, 00078 Monteporzio Catone, Italy
³⁶ INFN-Sezione di Roma, Piazzale Aldo Moro, 2 – c/o Dipartimento di Fisica, Edificio G. Marconi, 00185 Roma, Italy
³⁷ Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas (CIEMAT), Avenida Complutense 40, 28040 Madrid, Spain
³⁸ Port d’Informació Científica, Campus UAB, C. Albareda s/n, 08193 Bellaterra (Barcelona), Spain
³⁹ Institute for Theoretical Particle Physics and Cosmology (TTK), RWTH Aachen University, 52056 Aachen, Germany
⁴⁰ Deutsches Zentrum für Luft- und Raumfahrt e. V. (DLR), Linder Höhe, 51147 Köln, Germany
⁴¹ INFN section of Naples, Via Cinthia 6, 80126 Napoli, Italy
⁴² Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu, HI 96822, USA
⁴³ Dipartimento di Fisica e Astronomia “Augusto Righi” – Alma Mater Studiorum Università di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy
⁴⁴ Instituto de Astrofísica de Canarias, E-38205 La Laguna, Tenerife, Spain
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 Institut de Ciencies de l’Espai (IEEC-CSIC), Campus UAB, Carrer de Can Magrans, s/n Cerdanyola del Vallés, 08193 Barcelona, Spain
⁵⁰ UCB Lyon 1, CNRS/IN2P3, IUF, IP2I Lyon, 4 rue Enrico Fermi, 69622 Villeurbanne, France
⁵¹ Mullard Space Science Laboratory, University College London, Holmbury St Mary, Dorking, Surrey RH5 6NT, UK
⁵² INFN-Padova, Via Marzolo 8, 35131 Padova, Italy
⁵³ Aix-Marseille Université, CNRS/IN2P3, CPPM, Marseille, France
⁵⁴ INAF-Istituto di Astrofisica e Planetologia Spaziali, via del Fosso del Cavaliere, 100, 00100 Roma, Italy
⁵⁵ Space Science Data Center, Italian Space Agency, via del Politecnico snc, 00133 Roma, Italy
⁵⁶ INFN-Bologna, Via Irnerio 46, 40126 Bologna, Italy
⁵⁷ University Observatory, LMU Faculty of Physics, Scheinerstr. 1, 81679 Munich, Germany
⁵⁸ INAF-Osservatorio Astronomico di Padova, Via dell’Osservatorio 5, 35122 Padova, Italy
⁵⁹ Universitäts-Sternwarte München, Fakultät für Physik, Ludwig-Maximilians-Universität München, Scheinerstr. 1, 81679 München, 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, University of Helsinki, 00014 Helsinki, Finland
⁷⁰ Université de Genève, Département de Physique Théorique and Centre for Astroparticle Physics, 24 quai Ernest-Ansermet, CH-1211 Genève 4, Switzerland
⁷¹ Department of Physics, P.O. Box 64, University of Helsinki, 00014 Helsinki, Finland
⁷² Helsinki Institute of Physics, Gustaf Hällströmin katu 2, University of Helsinki, 00014 Helsinki, Finland
⁷³ Kapteyn Astronomical Institute, University of Groningen, PO Box 800, 9700 AV, Groningen, The Netherlands
⁷⁴ Laboratoire d’etude de l’Univers et des phenomenes eXtremes, Observatoire de Paris, Université PSL, Sorbonne Université, CNRS, 92190 Meudon, France
⁷⁵ SKAO, Jodrell Bank, Lower Withington, Macclesfield SK11 9FT, UK
⁷⁶ Centre de Calcul de l’IN2P3/CNRS, 21 avenue Pierre de Coubertin, 69627 Villeurbanne Cedex, France
⁷⁷ Dipartimento di Fisica “Aldo Pontremoli”, Università degli Studi di Milano, Via Celoria 16, 20133 Milano, Italy
⁷⁸ INFN-Sezione di Milano, Via Celoria 16, 20133 Milano, Italy
⁷⁹ University of Applied Sciences and Arts of Northwestern Switzerland, School of Computer Science, 5210 Windisch, Switzerland
⁸⁰ Universität Bonn, Argelander-Institut für Astronomie, Auf dem Hügel 71, 53121 Bonn, Germany
⁸¹ Dipartimento di Fisica e Astronomia “Augusto Righi” – Alma Mater Studiorum Università di Bologna, via Piero Gobetti 93/2, 40129 Bologna, Italy
⁸² Department of Physics, Institute for Computational Cosmology, Durham University, South Road, Durham DH1 3LE, UK
⁸³ Université Paris Cité, CNRS, Astroparticule et Cosmologie, 75013 Paris, France
⁸⁴ CNRS-UCB International Research Laboratory, Centre Pierre Binétruy, IRL2007, CPB-IN2P3, Berkeley, USA
⁸⁵ Institut d’Astrophysique de Paris, 98bis Boulevard Arago, 75014 Paris, France
⁸⁶ Institute of Physics, Laboratory of Astrophysics, Ecole Polytechnique Fédérale de Lausanne (EPFL), Observatoire de Sauverny, 1290 Versoix, Switzerland
⁸⁷ 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
⁸⁸ European Space Agency/ESTEC, Keplerlaan 1, 2201 AZ, Noordwijk, The Netherlands
⁸⁹ DARK, Niels Bohr Institute, University of Copenhagen, Jagtvej 155, 2200 Copenhagen, Denmark
⁹⁰ Centre National d’Etudes Spatiales – Centre spatial de Toulouse, 18 avenue Edouard Belin, 31401 Toulouse Cedex 9, France
⁹¹ Institute of Space Science, Str. Atomistilor, nr. 409 Măgurele, Ilfov 077125, Romania
⁹² Dipartimento di Fisica e Astronomia “G. Galilei”, Università di Padova, Via Marzolo 8, 35131 Padova, Italy
⁹³ Institut für Theoretische Physik, University of Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany
⁹⁴ Institut de Recherche en Astrophysique et Planétologie (IRAP), Université de Toulouse, CNRS, UPS, CNES, 14 Av. Edouard Belin, 31400 Toulouse, France
⁹⁵ Université St Joseph, Faculty of Sciences, Beirut, Lebanon
⁹⁶ Departamento de Física, FCFM, Universidad de Chile, Blanco Encalada 2008, Santiago, Chile
⁹⁷ Universität Innsbruck, Institut für Astro- und Teilchenphysik, Technikerstr. 25/8, 6020 Innsbruck, Austria
⁹⁸ Satlantis, University Science Park, Sede Bld, 48940 Leioa-Bilbao, Spain
⁹⁹ Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, Edifício C8, Campo Grande, PT1749-016 Lisboa, Portugal
¹⁰⁰ Instituto de Astrofísica e Ciências do Espaço, Faculdade de Ciências, Universidade de Lisboa, Tapada da Ajuda, 1349-018 Lisboa, Portugal
¹⁰¹ Cosmic Dawn Center (DAWN)
¹⁰² Niels Bohr Institute, University of Copenhagen, Jagtvej 128, 2200 Copenhagen, Denmark
¹⁰³ Universidad Politécnica de Cartagena, Departamento de Electrónica y Tecnología de Computadoras, Plaza del Hospital 1, 30202 Cartagena, Spain
¹⁰⁴ Caltech/IPAC, 1200 E. California Blvd., Pasadena, CA 91125, USA
¹⁰⁵ Astronomisches Rechen-Institut, Zentrum für Astronomie der Universität Heidelberg, Mönchhofstr. 12-14, 69120 Heidelberg, Germany
¹⁰⁶ Instituto de Física Teórica UAM-CSIC, Campus de Cantoblanco, 28049 Madrid, Spain
¹⁰⁷ Aurora Technology for European Space Agency (ESA), Camino bajo del Castillo, s/n, Urbanizacion Villafranca del Castillo, Villanueva de la Cañada, 28692 Madrid, Spain
¹⁰⁸ ICL, Junia, Université Catholique de Lille, LITL, 59000 Lille, France
¹⁰⁹ ICSC – Centro Nazionale di Ricerca in High Performance Computing, Big Data e Quantum Computing, Via Magnanelli 2, Bologna, Italy
¹¹⁰ Department of Astrophysical Sciences, Peyton Hall, Princeton University, Princeton, NJ 08544, USA

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Received: 5 January 2026
Accepted: 3 March 2026

Abstract

The Euclid mission of the European Space Agency seeks to understand the Universe’s expansion history and the nature of dark energy, through measurements of cosmic shear. This requires a very accurate estimate of the true redshift distribution of the galaxies, with the systematic error in the mean redshift satisfying σ_⟨z⟩ < 0.002(1 + z) per tomographic bin. Achieving this accuracy relies on reference samples with spectroscopic redshifts, together with a procedure to match them to survey sources for which only photometric redshifts are available. One important source of systematic uncertainty is the mismatch in photometric properties between galaxies in the Euclid survey and the reference objects. We develop a method to degrade the photometry of objects with deep photometry to match the properties of any shallower survey in the multi-band photometric space, preserving all the correlations between the fluxes and their uncertainties. We compare our transfer method with more demanding image-based methods, such as Balrog from the Dark Energy Survey Collaboration. According to our metrics, our method outperforms Balrog. We implement our method in the redshift distribution reconstruction, based on the self-organising map approach, and test it using a realistic sample from the Euclid Flagship Mock Galaxy Simulation. We find that the key ingredient is to ensure that the reference objects are distributed in the colour space the same way as the wide-survey objects, which can be efficiently achieved with our transfer method. In our best implementation, the mean redshift biases are consistently reduced across the tomographic bins, bringing a significant fraction of them within the Euclid accuracy requirements in all tomographic bins. Equally importantly, the tests allow us to pinpoint which step in the calibration pipeline has the strongest impact on achieving the required accuracy. Our approach also reproduces the overall redshift distributions, which are crucial for applications such as angular clustering. The agreement between the reconstructed and true distributions demonstrates both the feasibility and robustness of the approach. This implementation is sufficient for Euclid Data Release 1 and provides a solid foundation for subsequent data releases.