Euclid preparation

LXIX. The impact of relativistic redshift-space distortions on two-point clustering statistics from the Euclid wide spectroscopic survey

¹ INFN-Padova, Via Marzolo 8, 35131 Padova, Italy
² Dipartimento di Fisica e Astronomia “G. Galilei”, Università di Padova, Via Marzolo 8, 35131 Padova, Italy
³ INAF-Osservatorio Astronomico di Padova, Via dell’Osservatorio 5, 35122 Padova, Italy
⁴ Universität Bonn, Argelander-Institut für Astronomie, Auf dem Hügel 71, 53121 Bonn, Germany
⁵ Dipartimento di Fisica – Sezione di Astronomia, Università di Trieste, Via Tiepolo 11, 34131 Trieste, Italy
⁶ INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34143 Trieste, Italy
⁷ IFPU, Institute for Fundamental Physics of the Universe, Via Beirut 2, 34151 Trieste, Italy
⁸ INFN, Sezione di Trieste, Via Valerio 2, 34127 Trieste, TS, Italy
⁹ Université Paris-Saclay, CNRS, Institut d’astrophysique spatiale, 91405 Orsay, France
¹⁰ School of Mathematics and Physics, University of Surrey, Guildford, Surrey GU2 7XH, UK
¹¹ INAF-Osservatorio Astronomico di Brera, Via Brera 28, 20122 Milano, Italy
¹² INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy
¹³ SISSA, International School for Advanced Studies, Via Bonomea 265, 34136 Trieste, TS, Italy
¹⁴ Dipartimento di Fisica e Astronomia, Università di Bologna, Via Gobetti 93/2, 40129 Bologna, Italy
¹⁵ INFN-Sezione di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy
¹⁶ Max Planck Institute for Extraterrestrial Physics, Giessenbachstr. 1, 85748 Garching, Germany
¹⁷ INAF-Osservatorio Astrofisico di Torino, Via Osservatorio 20, 10025 Pino Torinese (TO), Italy
¹⁸ Dipartimento di Fisica, Università di Genova, Via Dodecaneso 33, 16146 Genova, Italy
¹⁹ INFN-Sezione di Genova, Via Dodecaneso 33, 16146 Genova, Italy
²⁰ Department of Physics “E. Pancini”, University Federico II, Via Cinthia 6, 80126 Napoli, Italy
²¹ INAF-Osservatorio Astronomico di Capodimonte, Via Moiariello 16, 80131 Napoli, Italy
²² INFN section of Naples, Via Cinthia 6, 80126 Napoli, Italy
²³ Instituto de Astrofísica e Ciências do Espaço, Universidade do Porto, CAUP, Rua das Estrelas, PT4150-762 Porto, Portugal
²⁴ Dipartimento di Fisica, Università degli Studi di Torino, Via P. Giuria 1, 10125 Torino, Italy
²⁵ INFN-Sezione di Torino, Via P. Giuria 1, 10125 Torino, Italy
²⁶ INAF-IASF Milano, Via Alfonso Corti 12, 20133 Milano, Italy
²⁷ INAF-Osservatorio Astronomico di Roma, Via Frascati 33, 00078 Monteporzio Catone, Italy
²⁸ INFN-Sezione di Roma, Piazzale Aldo Moro, 2 – c/o Dipartimento di Fisica, Edificio G. Marconi, 00185 Roma, Italy
²⁹ Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas (CIEMAT), Avenida Complutense 40, 28040 Madrid, Spain
³⁰ Port d’Informació Científica, Campus UAB, C. Albareda s/n, 08193 Bellaterra (Barcelona), Spain
³¹ Institut d’Estudis Espacials de Catalunya (IEEC), Edifici RDIT, Campus UPC, 08860 Castelldefels, Barcelona, Spain
³² Institute of Space Sciences (ICE, CSIC), Campus UAB, Carrer de Can Magrans, s/n, 08193 Barcelona, Spain
³³ Institute for Theoretical Particle Physics and Cosmology (TTK), RWTH Aachen University, 52056 Aachen, Germany
³⁴ Dipartimento di Fisica e Astronomia “Augusto Righi” – Alma Mater Studiorum Università di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy
³⁵ Instituto de Astrofísica de Canarias, Calle Vía Láctea s/n, 38204 San Cristóbal de La Laguna, Tenerife, Spain
³⁶ Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ, UK
³⁷ Jodrell Bank Centre for Astrophysics, Department of Physics and Astronomy, University of Manchester, Oxford Road, Manchester M13 9PL, UK
³⁸ European Space Agency/ESRIN, Largo Galileo Galilei 1, 00044 Frascati, Roma, Italy
³⁹ ESAC/ESA, Camino Bajo del Castillo, s/n., Urb. Villafranca del Castillo, 28692 Villanueva de la Cañada, Madrid, Spain
⁴⁰ Université Claude Bernard Lyon 1, CNRS/IN2P3, IP2I Lyon, UMR 5822, Villeurbanne F-69100, France
⁴¹ Institute of Physics, Laboratory of Astrophysics, Ecole Polytechnique Fédérale de Lausanne (EPFL), Observatoire de Sauverny, 1290 Versoix, Switzerland
⁴² UCB Lyon 1, CNRS/IN2P3, IUF, IP2I Lyon, 4 rue Enrico Fermi, 69622 Villeurbanne, France
⁴³ Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, Edifício C8, Campo Grande, PT1749-016 Lisboa, Portugal
⁴⁴ Instituto de Astrofísica e Ciências do Espaço, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, 1749-016 Lisboa, Portugal
⁴⁵ Department of Astronomy, University of Geneva, ch. d’Ecogia 16, 1290 Versoix, Switzerland
⁴⁶ INAF-Istituto di Astrofisica e Planetologia Spaziali, Via del Fosso del Cavaliere, 100, 00100 Roma, Italy
⁴⁷ Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM, 91191 Gif-sur-Yvette, France
⁴⁸ Institut de Ciencies de l’Espai (IEEC-CSIC), Campus UAB, Carrer de Can Magrans, s/n Cerdanyola del Vallés, 08193 Barcelona, Spain
⁴⁹ Istituto Nazionale di Fisica Nucleare, Sezione di Bologna, Via Irnerio 46, 40126 Bologna, Italy
⁵⁰ FRACTAL S.L.N.E., calle Tulipán 2, Portal 13 1A, 28231 Las Rozas de Madrid, Spain
⁵¹ Universitäts-Sternwarte München, Fakultät für Physik, Ludwig-Maximilians-Universität München, Scheinerstrasse 1, 81679 München, Germany
⁵² Dipartimento di Fisica “Aldo Pontremoli”, Università degli Studi di Milano, Via Celoria 16, 20133 Milano, Italy
⁵³ Institute of Theoretical Astrophysics, University of Oslo, PO Box 1029 Blindern 0315 Oslo, Norway
⁵⁴ Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA
⁵⁵ Felix Hormuth Engineering, Goethestr. 17, 69181 Leimen, Germany
⁵⁶ Technical University of Denmark, Elektrovej 327, 2800 Kgs. Lyngby, Denmark
⁵⁷ Cosmic Dawn Center (DAWN), Copenhagen N, Denmark
⁵⁸ Max-Planck-Institut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany
⁵⁹ NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA
⁶⁰ Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK
⁶¹ Department of Physics and Helsinki Institute of Physics, Gustaf Hällströmin katu 2, 00014 University of Helsinki, Finland
⁶² Aix-Marseille Université, CNRS/IN2P3, CPPM, Marseille, France
⁶³ Mullard Space Science Laboratory, University College London, Holmbury St Mary, Dorking, Surrey RH5 6NT, UK
⁶⁴ Leiden Observatory, Leiden University, Einsteinweg 55, 2333 CC Leiden, The Netherlands
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, PO Box 64 00014 University of Helsinki, Finland
⁶⁷ Helsinki Institute of Physics, Gustaf Hällströmin katu 2, University of Helsinki, Helsinki, Finland
⁶⁸ NOVA optical infrared instrumentation group at ASTRON, Oude Hoogeveensedijk 4, 7991 PD Dwingeloo, The Netherlands
⁶⁹ Centre de Calcul de l’IN2P3/CNRS, 21 avenue Pierre de Coubertin, 69627 Villeurbanne Cedex, France
⁷⁰ Aix-Marseille Université, CNRS, CNES, LAM, Marseille, France
⁷¹ Dipartimento di Fisica e Astronomia “Augusto Righi” – Alma Mater Studiorum Università di Bologna, Via Piero Gobetti 93/2, 40129 Bologna, Italy
⁷² Department of Physics, Institute for Computational Cosmology, Durham University, South Road, DH1 3LE Durham, UK
⁷³ Université Paris Cité, CNRS, Astroparticule et Cosmologie, 75013 Paris, France
⁷⁴ Institut d’Astrophysique de Paris, 98bis Boulevard Arago, 75014 Paris, France
⁷⁵ Institut d’Astrophysique de Paris, UMR 7095, CNRS, and Sorbonne Université, 98 bis boulevard Arago, 75014 Paris, France
⁷⁶ European Space Agency/ESTEC, Keplerlaan 1, 2201 AZ Noordwijk, The Netherlands
⁷⁷ Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Campus UAB, 08193 Bellaterra, (Barcelona), Spain
⁷⁸ Department of Physics and Astronomy, University of Aarhus, Ny Munkegade 120, DK-8000 Aarhus C, Denmark
⁷⁹ Space Science Data Center, Italian Space Agency, Via del Politecnico snc, 00133 Roma, Italy
⁸⁰ Centre National d’Etudes Spatiales – Centre spatial de Toulouse, 18 avenue Edouard Belin, 31401 Toulouse Cedex 9, France
⁸¹ Institute of Space Science, Str. Atomistilor, nr. 409 Măgurele, Ilfov 077125, Romania
⁸² Departamento de Astrofísica, Universidad de La Laguna, 38206 La Laguna, Tenerife, Spain
⁸³ Institut für Theoretische Physik, University of Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany
⁸⁴ Institut de Recherche en Astrophysique et Planétologie (IRAP), Université de Toulouse, CNRS, UPS, CNES, 14 Av. Edouard Belin, 31400 Toulouse, France
⁸⁵ Université St Joseph; Faculty of Sciences, Beirut, Lebanon
⁸⁶ Departamento de Física, FCFM, Universidad de Chile, Blanco Encalada 2008, Santiago, Chile
⁸⁷ Universität Innsbruck, Institut für Astro- und Teilchenphysik, Technikerstr. 25/8, 6020 Innsbruck, Austria
⁸⁸ Satlantis, University Science Park, Sede Bld 48940, Leioa-Bilbao, Spain
⁸⁹ Instituto de Astrofísica e Ciências do Espaço, Faculdade de Ciências, Universidade de Lisboa, Tapada da Ajuda, 1349-018 Lisboa, Portugal
⁹⁰ Universidad Politécnica de Cartagena, Departamento de Electrónica y Tecnología de Computadoras, Plaza del Hospital 1, 30202 Cartagena, Spain
⁹¹ INFN-Bologna, Via Irnerio 46, 40126 Bologna, Italy
⁹² Kapteyn Astronomical Institute, University of Groningen, PO Box 800 9700 AV Groningen, The Netherlands
⁹³ Dipartimento di Fisica, Università degli studi di Genova, and INFN-Sezione di Genova, Via Dodecaneso 33, 16146 Genova, Italy
⁹⁴ Infrared Processing and Analysis Center, California Institute of Technology, Pasadena, CA 91125, USA
⁹⁵ INAF, Istituto di Radioastronomia, Via Piero Gobetti 101, 40129 Bologna, Italy
⁹⁶ Astronomical Observatory of the Autonomous Region of the Aosta Valley (OAVdA), Loc. Lignan 39, I-11020 Nus (Aosta Valley), Italy
⁹⁷ Junia, EPA department, 41 Bd Vauban, 59800 Lille, France
⁹⁸ ICSC – Centro Nazionale di Ricerca in High Performance Computing, Big Data e Quantum Computing, Via Magnanelli 2, Bologna, Italy
⁹⁹ Instituto de Física Teórica UAM-CSIC, Campus de Cantoblanco, 28049 Madrid, Spain
¹⁰⁰ CERCA/ISO, Department of Physics, Case Western Reserve University, 10900 Euclid Avenue, Cleveland, OH 44106, USA
¹⁰¹ Laboratoire Univers et Théorie, Observatoire de Paris, Université PSL, Université Paris Cité, CNRS, 92190 Meudon, France
¹⁰² Dipartimento di Fisica e Scienze della Terra, Università degli Studi di Ferrara, Via Giuseppe Saragat 1, 44122 Ferrara, Italy
¹⁰³ Istituto Nazionale di Fisica Nucleare, Sezione di Ferrara, Via Giuseppe Saragat 1, 44122 Ferrara, Italy
¹⁰⁴ Kavli Institute for the Physics and Mathematics of the Universe (WPI), University of Tokyo, Kashiwa, Chiba 277-8583, Japan
¹⁰⁵ Ludwig-Maximilians-University, Schellingstrasse 4, 80799 Munich, Germany
¹⁰⁶ Max-Planck-Institut für Physik, Boltzmannstr. 8, 85748 Garching, Germany
¹⁰⁷ Minnesota Institute for Astrophysics, University of Minnesota, 116 Church St SE, Minneapolis, MN 55455, USA
¹⁰⁸ Institute Lorentz, Leiden University, Niels Bohrweg 2, 2333 CA Leiden, The Netherlands
¹⁰⁹ Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS, Laboratoire Lagrange, Bd de l’Observatoire, CS 34229, 06304 Nice cedex 4, France
¹¹⁰ Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu, HI 96822, USA
¹¹¹ Department of Physics & Astronomy, University of California Irvine, Irvine, CA 92697, USA
¹¹² Department of Astronomy & Physics and Institute for Computational Astrophysics, Saint Mary’s University, 923 Robie Street, Halifax, Nova Scotia B3H 3C3, Canada
¹¹³ Departamento Física Aplicada, Universidad Politécnica de Cartagena, Campus Muralla del Mar, 30202 Cartagena, Murcia, Spain
¹¹⁴ Instituto de Astrofísica de Canarias (IAC); Departamento de Astrofísica, Universidad de La Laguna (ULL), 38200 La Laguna, Tenerife, Spain
¹¹⁵ Department of Physics, Oxford University, Keble Road, Oxford OX1 3RH, UK
¹¹⁶ Institute of Cosmology and Gravitation, University of Portsmouth, Portsmouth PO1 3FX, UK
¹¹⁷ Department of Computer Science, Aalto University, PO Box 15400, Espoo FI-00 076, Finland
¹¹⁸ Ruhr University Bochum, Faculty of Physics and Astronomy, Astronomical Institute (AIRUB), German Centre for Cosmological Lensing (GCCL), 44780 Bochum, Germany
¹¹⁹ DARK, Niels Bohr Institute, University of Copenhagen, Jagtvej 155, 2200 Copenhagen, Denmark
¹²⁰ Univ. Grenoble Alpes, CNRS, Grenoble INP, LPSC-IN2P3, 53, Avenue des Martyrs, 38000 Grenoble, France
¹²¹ Department of Physics and Astronomy, Vesilinnantie 5, 20014 University of Turku, Finland
¹²² Serco for European Space Agency (ESA), Camino bajo del Castillo, s/n, Urbanizacion Villafranca del Castillo, Villanueva de la Cañada, 28692 Madrid, Spain
¹²³ ARC Centre of Excellence for Dark Matter Particle Physics, Melbourne, Australia
¹²⁴ Centre for Astrophysics & Supercomputing, Swinburne University of Technology, Hawthorn, Victoria 3122, Australia
¹²⁵ School of Physics and Astronomy, Queen Mary University of London, Mile End Road, London E1 4NS, UK
¹²⁶ Department of Physics and Astronomy, University of the Western Cape, Bellville, Cape Town 7535, South Africa
¹²⁷ Université Libre de Bruxelles (ULB), Service de Physique Théorique CP225, Boulevard du Triophe, 1050 Bruxelles, Belgium
¹²⁸ ICTP South American Institute for Fundamental Research, Instituto de Física Teórica, Universidade Estadual Paulista, São Paulo, Brazil
¹²⁹ Oskar Klein Centre for Cosmoparticle Physics, Department of Physics, Stockholm University, Stockholm SE-106 91, Sweden
¹³⁰ Astrophysics Group, Blackett Laboratory, Imperial College London, London SW7 2AZ, UK
¹³¹ INAF-Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, 50125 Firenze, Italy
¹³² Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 2, 00185 Roma, Italy
¹³³ Centro de Astrofísica da Universidade do Porto, Rua das Estrelas, 4150-762 Porto, Portugal
¹³⁴ Dipartimento di Fisica, Università di Roma Tor Vergata, Via della Ricerca Scientifica 1, Roma, Italy
¹³⁵ INFN, Sezione di Roma 2, Via della Ricerca Scientifica 1, Roma, Italy
¹³⁶ Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK
¹³⁷ Department of Astrophysics, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland
¹³⁸ Theoretical astrophysics, Department of Physics and Astronomy, Uppsala University, Box 515 751 20 Uppsala, Sweden
¹³⁹ Department of Physics, Royal Holloway, University of London, Surrey TW20 0EX, UK
¹⁴⁰ Department of Astrophysical Sciences, Peyton Hall, Princeton University, Princeton, NJ 08544, USA
¹⁴¹ Niels Bohr Institute, University of Copenhagen, Jagtvej 128, 2200 Copenhagen, Denmark
¹⁴² Institut de Physique Théorique, CEA, CNRS, Université Paris-Saclay, 91191 Gif-sur-Yvette Cedex, France
¹⁴³ Center for Cosmology and Particle Physics, Department of Physics, New York University, New York, NY 10003, USA
¹⁴⁴ Center for Computational Astrophysics, Flatiron Institute, 162 5th Avenue, 10010 New York, NY, USA

^⋆ Corresponding author: mohamed.elkhashab@inaf.it

Received: 4 October 2024
Accepted: 28 February 2025

Abstract

Measurements of galaxy clustering are affected by redshift-space distortions (RSDs). Peculiar velocities, gravitational lensing, and other light-cone projection effects modify the observed redshifts, fluxes, and sky positions of distant light sources. We determined which of these effects leave a detectable imprint on several two-point clustering statistics to be extracted from the Euclid wide spectroscopic survey (EWSS) on large scales. We generated 140 mock galaxy catalogues with the survey geometry and selection function of the EWSS and made use of the LIGER (LIght cones with GEneral Relativity) method to account for a variable number of relativistic RSDs to linear order in the cosmological perturbations. We estimated different two-point clustering statistics from the mocks and used the likelihood-ratio test to calculate the statistical significance with which the EWSS could reject the null hypothesis that certain relativistic projection effects can be neglected in the theoretical models. We find that the combined effects of lensing magnification and convergence imprint characteristic signatures on several clustering observables. Their signal-to-noise ratio (S/N) ranges between 2.5 and 6 (depending on the adopted summary statistic) for the highest-redshift galaxies in the EWSS. The corresponding feature due to the peculiar velocity of the Sun is measured with a S/N of order one or two. The multipoles of the power spectrum from the catalogues that include all relativistic effects reject the null hypothesis that RSDs are only generated by the variation in the peculiar velocity along the line of sight with a significance of 2.9 standard deviations. As a by-product of our study, we demonstrate that the mixing-matrix formalism to model finite-volume effects in the multipole moments of the power spectrum can be robustly applied to surveys made of several disconnected patches. Our results indicate that relativistic RSDs, in particular the contribution from weak gravitational lensing, cannot be disregarded when modelling two-point clustering statistics extracted from the EWSS.