Euclid preparation

XI. Mean redshift determination from galaxy redshift probabilities for cosmic shear tomography

¹ Aix-Marseille Univ., CNRS, CNES, LAM, Marseille, France
e-mail: olivier.ilbert@lam.fr
² Ruhr-Universität Bochum, Astronomisches Institut, German Centre for Cosmological Lensing, Universitätsstr. 150, 44801 Bochum, Germany
³ Department of Astronomy, University of Geneva, Ch. d’Écogia 16, 1290 Versoix, Switzerland
⁴ Institut d’Astrophysique de Paris, 98bis boulevard Arago, 75014 Paris, France
⁵ Cosmic Dawn Center (DAWN), Niels Bohr Institute, University of Copenhagen, Vibenshuset, Lyngbyvej 2, 2100 Copenhagen, Denmark
⁶ Infrared Processing and Analysis Center, California Institute of Technology, Pasadena, CA 91125, USA
⁷ Institute of Cosmology and Gravitation, University of Portsmouth, Portsmouth PO1 3FX, UK
⁸ Jodrell Bank Centre for Astrophysics, School of Physics and Astronomy, University of Manchester, Oxford Road, Manchester M13 9PL, UK
⁹ INAF-Osservatorio Astronomico di Brera, Via Brera 28, 20122 Milano, Italy
¹⁰ INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy
¹¹ Mullard Space Science Laboratory, University College London, Holmbury St Mary, Dorking, Surrey RH5 6NT, UK
¹² IFPU, Institute for Fundamental Physics of the Universe, Via Beirut 2, 34151 Trieste, Italy
¹³ SISSA, International School for Advanced Studies, Via Bonomea 265, 34136 Trieste, TS, Italy
¹⁴ INFN, Sezione di Trieste, Via Valerio 2, 34127 Trieste, TS, Italy
¹⁵ INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34131 Trieste, Italy
¹⁶ Universidad de la Laguna, 38206 San Cristóbal de La Laguna, Tenerife, Spain
¹⁷ Instituto de Astrofísica de Canarias, Calle Vía Làctea s/n, 38204 San Cristóbal de la Laguna, Tenerife, Spain
¹⁸ Dipartimento di Fisica e Astronomia, Universitá 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 Max Planck Institute for Extraterrestrial Physics, Giessenbachstr. 1, 85748 Garching, Germany
²³ INAF-Osservatorio Astrofisico di Torino, Via Osservatorio 20, 10025 Pino Torinese, TO, Italy
²⁴ Dipartimento di Fisica – Sezione di Astronomia, Universitá di Trieste, Via Tiepolo 11, 34131 Trieste, Italy
²⁵ Université de Paris, CNRS, Astroparticule et Cosmologie, 75006 Paris, France
²⁶ INFN-Sezione di Roma Tre, Via della Vasca Navale 84, 00146 Roma, Italy
²⁷ Department of Mathematics and Physics, Roma Tre University, Via della Vasca Navale 84, 00146 Rome, Italy
²⁸ INAF-Osservatorio Astronomico di Roma, Via Frascati 33, 00078 Monteporzio Catone, Italy
²⁹ INAF-Osservatorio Astronomico di Capodimonte, Via Moiariello 16, 80131 Napoli, Italy
³⁰ INFN-Bologna, Via Irnerio 46, 40126 Bologna, Italy
³¹ Dipartimento di Fisica e Scienze della Terra, Universitá degli Studi di Ferrara, Via Giuseppe Saragat 1, 44122 Ferrara, Italy
³² INAF, Istituto di Radioastronomia, Via Piero Gobetti 101, 40129 Bologna, Italy
³³ Institut de Recherche en Astrophysique et Planétologie (IRAP), Université de Toulouse, CNRS, UPS, CNES, 14 Av. Edouard Belin, 31400 Toulouse, France
³⁴ INFN-Sezione di Torino, Via P. Giuria 1, 10125 Torino, Italy
³⁵ Dipartimento di Fisica, Universitá degli Studi di Torino, Via P. Giuria 1, 10125 Torino, Italy
³⁶ Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS, Laboratoire Lagrange, Bd de l’Observatoire, CS 34229, 06304 Nice Cedex 4, France
³⁷ INAF-IASF Milano, Via Alfonso Corti 12, 20133 Milano, Italy
³⁸ Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Campus UAB, 08193 Bellaterra, Barcelona, Spain
³⁹ Instituto de Astrofísica e Ciências do Espaço, Faculdade de Ciências, Universidade de Lisboa, Tapada da Ajuda, 1349-018 Lisboa, Portugal
⁴⁰ AIM, CEA, CNRS, Université Paris-Saclay, Université Paris Diderot, Sorbonne Paris Cité, 91191 Gif-sur-Yvette, France
⁴¹ Institute of Space Sciences (ICE, CSIC), Campus UAB, Carrer de Can Magrans, s/n, 08193 Barcelona, Spain
⁴² Institut d’Estudis Espacials de Catalunya (IEEC), Carrer Gran Capitá 2-4, 08034 Barcelona, Spain
⁴³ Observatoire de Sauverny, Ecole Polytechnique Fédérale de Lau- sanne, 1290 Versoix, Switzerland
⁴⁴ Department of Physics “E. Pancini”, University Federico II, Via Cinthia 6, 80126 Napoli, Italy
⁴⁵ INFN Section of Naples, Via Cinthia 6, 80126 Napoli, Italy
⁴⁶ INAF-Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, 50125 Firenze, Italy
⁴⁷ Centre National d’Etudes Spatiales, Toulouse, France
⁴⁸ Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ, UK
⁴⁹ European Space Agency/ESRIN, Largo Galileo Galilei 1, 00044 Frascati, Roma, Italy
⁵⁰ ESAC/ESA, Camino Bajo del Castillo s/n, Urb. Villafranca del Castillo, 28692 Villanueva de la Cañada, Madrid, Spain
⁵¹ Univ. Lyon, Univ. Claude Bernard Lyon 1, CNRS/IN2P3, IP2I Lyon, UMR 5822, 69622 Villeurbanne, France
⁵² Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, Edifício C8, Campo Grande, 1749-016 Lisboa, Portugal
⁵³ Instituto de Astrofísica e Ciências do Espaço, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, 1749-016 Lisboa, Portugal
⁵⁴ Department of Physics, Oxford University, Keble Road Oxford OX1 3RH, UK
⁵⁵ INFN-Padova, Via Marzolo 8, 35131 Padova, Italy
⁵⁶ University of Lyon, UCB Lyon 1, CNRS/IN2P3, IUF, IP2I, Lyon, France
⁵⁷ School of Physics, HH Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, UK
⁵⁸ Aix-Marseille Univ., CNRS/IN2P3, CPPM, Marseille, France
⁵⁹ Department of Physics, University of Helsinki, PO Box 64, 00014 Helsinki, Finland
⁶⁰ Dipartimento di Fisica “Aldo Pontremoli”, Universitá degli Studi di Milano, Via Celoria 16, 20133 Milano, Italy
⁶¹ INFN-Sezione di Milano, Via Celoria 16, 20133 Milano, Italy
⁶² Institute of Theoretical Astrophysics, University of Oslo, PO Box 1029, Blindern, 0315 Oslo, Norway
⁶³ Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA
⁶⁴ von Hoerner & Sulger GmbH, SchloßPlatz 8, 68723 Schwetzingen, Germany
⁶⁵ Max-Planck-Institut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany
⁶⁶ Department of Physics and Helsinki Institute of Physics, University of Helsinki, Gustaf Hällströmin Katu 2, 00014 Helsinki, Finland
⁶⁷ Université de Genève, Département de Physique Théorique and Centre for Astroparticle Physics, 24 Quai Ernest-Ansermet, 1211 Genève 4, Switzerland
⁶⁸ NOVA Optical Infrared Instrumentation Group at ASTRON, Oude Hoogeveensedijk 4, 7991 PD Dwingeloo, The Netherlands
⁶⁹ Argelander-Institut für Astronomie, Universität Bonn, Auf dem Hügel 71, 53121 Bonn, Germany
⁷⁰ Institute for Computational Cosmology, Department of Physics, Durham University, South Road, Durham DH1 3LE, UK
⁷¹ Institut für Theoretische Physik, University of Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany
⁷² Zentrum für Astronomie, Universität Heidelberg, Philosophenweg 12, 69120 Heidelberg, Germany
⁷³ INAF-IASF Bologna, Via Piero Gobetti 101, 40129 Bologna, Italy
⁷⁴ Université de Paris, 75013 Paris, France
⁷⁵ LERMA, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Université, 75014 Paris, France
⁷⁶ CEA Saclay, DFR/IRFU, Service d’Astrophysique, Bât. 709, 91191 Gif-sur-Yvette, France
⁷⁷ IRFU, CEA, Université Paris-Saclay, 91191 Gif-sur-Yvette Cedex, France
⁷⁸ ICC&CEA, Department of Physics, Durham University, South Road, DH1 3LE Durham, UK
⁷⁹ Department of Physics and Astronomy, University of Aarhus, Ny Munkegade 120, 8000 Aarhus C, Denmark
⁸⁰ Space Science Data Center, Italian Space Agency, Via del Politecnico snc, 00133 Roma, Italy
⁸¹ Institute of Space Science, Bucharest 077125, Romania
⁸² Institute for Computational Science, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland
⁸³ Dipartimento di Fisica e Astronomia “G. Galilei”, Universitá di Padova, Via Marzolo 8, 35131 Padova, Italy
⁸⁴ Departamento de Física, FCFM, Universidad de Chile, Blanco Encalada 2008, Santiago, Chile
⁸⁵ Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas (CIEMAT), Avenida Complutense 40, 28040 Madrid, Spain
⁸⁶ Universidad Politécnica de Cartagena, Departamento de Electrónica y Tecnología de Computadoras, 30202 Cartagena, Spain
⁸⁷ Kapteyn Astronomical Institute, University of Groningen, PO Box 800, 9700 AV Groningen, The Netherlands
⁸⁸ Department of Physics, University of Jyväskylä, PO Box 35 (YFL), 40014 Jyväskylä, Finland
⁸⁹ Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK

Received: 24 December 2020
Accepted: 2 January 2021

Abstract

The analysis of weak gravitational lensing in wide-field imaging surveys is considered to be a major cosmological probe of dark energy. Our capacity to constrain the dark energy equation of state relies on an accurate knowledge of the galaxy mean redshift ⟨z⟩. We investigate the possibility of measuring ⟨z⟩ with an accuracy better than 0.002 (1 + z) in ten tomographic bins spanning the redshift interval 0.2 < z < 2.2, the requirements for the cosmic shear analysis of Euclid. We implement a sufficiently realistic simulation in order to understand the advantages and complementarity, as well as the shortcomings, of two standard approaches: the direct calibration of ⟨z⟩ with a dedicated spectroscopic sample and the combination of the photometric redshift probability distribution functions (zPDFs) of individual galaxies. We base our study on the Horizon-AGN hydrodynamical simulation, which we analyse with a standard galaxy spectral energy distribution template-fitting code. Such a procedure produces photometric redshifts with realistic biases, precisions, and failure rates. We find that the current Euclid design for direct calibration is sufficiently robust to reach the requirement on the mean redshift, provided that the purity level of the spectroscopic sample is maintained at an extremely high level of > 99.8%. The zPDF approach can also be successful if the zPDF is de-biased using a spectroscopic training sample. This approach requires deep imaging data but is weakly sensitive to spectroscopic redshift failures in the training sample. We improve the de-biasing method and confirm our finding by applying it to real-world weak-lensing datasets (COSMOS and KiDS+VIKING-450).