Euclid preparation

LIX. Angular power spectra from discrete observations

¹ Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK
² Oskar Klein Centre for Cosmoparticle Physics, Department of Physics, Stockholm University, Stockholm SE-106 91, Sweden
³ Astrophysics Group, Blackett Laboratory, Imperial College London, London SW7 2AZ, UK
⁴ Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ, UK
⁵ European Space Agency/ESTEC, Keplerlaan 1, 2201 AZ Noordwijk, The Netherlands
⁶ Institute Lorentz, Leiden University, Niels Bohrweg 2, 2333 CA Leiden, The Netherlands
⁷ Institut de Recherche en Astrophysique et Planétologie (IRAP), Université de Toulouse, CNRS, UPS, CNES, 14 Av. Edouard Belin, 31400 Toulouse, France
⁸ Mullard Space Science Laboratory, University College London, Holmbury St Mary, Dorking, Surrey RH5 6NT, UK
⁹ School of Mathematics and Physics, University of Surrey, Guildford, Surrey GU2 7XH, UK
¹⁰ INAF-Osservatorio Astronomico di Brera, Via Brera 28, 20122 Milano, Italy
¹¹ INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy
¹² IFPU, Institute for Fundamental Physics of the Universe, Via Beirut 2, 34151 Trieste, Italy
¹³ INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34143 Trieste, Italy
¹⁴ INFN, Sezione di Trieste, Via Valerio 2, 34127 Trieste, TS, Italy
¹⁵ SISSA, International School for Advanced Studies, Via Bonomea 265, 34136 Trieste, TS, Italy
¹⁶ Dipartimento di Fisica e Astronomia, Università di Bologna, Via Gobetti 93/2, 40129 Bologna, Italy
¹⁷ INFN-Sezione di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy
¹⁸ Institut de Physique Théorique, CEA, CNRS, Université Paris-Saclay, 91191 Gif-sur-Yvette Cedex, France
¹⁹ Institut d’Astrophysique de Paris, UMR 7095, CNRS, and Sorbonne Université, 98 bis Boulevard Arago, 75014 Paris, France
²⁰ INAF-Osservatorio Astrofisico di Torino, Via Osservatorio 20, 10025 Pino Torinese, TO, Italy
²¹ Dipartimento di Fisica, Università di Genova, Via Dodecaneso 33, 16146 Genova, Italy
²² INFN-Sezione di Genova, Via Dodecaneso 33, 16146 Genova, Italy
²³ Department of Physics “E. Pancini”, University Federico II, Via Cinthia 6, 80126 Napoli, Italy
²⁴ INAF-Osservatorio Astronomico di Capodimonte, Via Moiariello 16, 80131 Napoli, Italy
²⁵ INFN Section of Naples, Via Cinthia 6, 80126 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 Aix-Marseille Université, CNRS, CNES, LAM, Marseille, France
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-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 Institute for Theoretical Particle Physics and Cosmology (TTK), RWTH Aachen University, 52056 Aachen, Germany
³⁷ Institute of Cosmology and Gravitation, University of Portsmouth, Portsmouth PO1 3FX, UK
³⁸ Dipartimento di Fisica e Astronomia “Augusto Righi” – Alma Mater Studiorum Università di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy
³⁹ Instituto de Astrofísica de Canarias, Calle Vía Láctea s/n, 38204 San Cristóbal de La Laguna, Tenerife, Spain
⁴⁰ Jodrell Bank Centre for Astrophysics, Department of Physics and Astronomy, University of Manchester, Oxford Road, Manchester M13 9PL, UK
⁴¹ European Space Agency/ESRIN, Largo Galileo Galilei 1, 00044 Frascati, Roma, Italy
⁴² ESAC/ESA, Camino Bajo del Castillo, s/n, Urb. Villafranca del Castillo, 28692 Villanueva de la Cañada, Madrid, Spain
⁴³ Université Claude Bernard Lyon 1, CNRS/IN2P3, IP2I Lyon, UMR 5822, Villeurbanne F-69100, France
⁴⁴ Institute of Physics, Laboratory of Astrophysics, Ecole Polytechnique Fédérale de Lausanne (EPFL), Observatoire de Sauverny, 1290 Versoix, Switzerland
⁴⁵ Institut de Ciències del Cosmos (ICCUB), Universitat de Barcelona (IEEC-UB), Martí i Franquès 1, 08028 Barcelona, Spain
⁴⁶ Institució Catalana de Recerca i Estudis Avançats (ICREA), Passeig de Lluís Companys 23, 08010 Barcelona, Spain
⁴⁷ UCB Lyon 1, CNRS/IN2P3, IUF, IP2I Lyon, 4 Rue Enrico Fermi, 69622 Villeurbanne, France
⁴⁸ Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, Edifício C8, Campo Grande, PT1749-016 Lisboa, Portugal
⁴⁹ Instituto de Astrofísica e Ciências do Espaço, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, 1749-016 Lisboa, Portugal
⁵⁰ Department of Astronomy, University of Geneva, Ch. d’Ecogia 16, 1290 Versoix, Switzerland
⁵¹ INFN-Padova, Via Marzolo 8, 35131 Padova, Italy
⁵² INAF-Istituto di Astrofisica e Planetologia Spaziali, Via del Fosso del Cavaliere, 100, 00100 Roma, Italy
⁵³ Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM, 91191 Gif-sur-Yvette, France
⁵⁴ Space Science Data Center, Italian Space Agency, Via del Politecnico snc, 00133 Roma, Italy
⁵⁵ Aix-Marseille Université, CNRS/IN2P3, CPPM, Marseille, France
⁵⁶ Istituto Nazionale di Fisica Nucleare, Sezione di Bologna, Via Irnerio 46, 40126 Bologna, Italy
⁵⁷ FRACTAL S.L.N.E., Calle Tulipán 2, Portal 13 1A, 28231 Las Rozas de Madrid, Spain
⁵⁸ INAF-Osservatorio Astronomico di Padova, Via dell’Osservatorio 5, 35122 Padova, Italy
⁵⁹ Max Planck Institute for Extraterrestrial Physics, Giessenbachstr. 1, 85748 Garching, Germany
⁶⁰ Universitäts-Sternwarte München, Fakultät für Physik, Ludwig-Maximilians-Universität München, Scheinerstrasse 1, 81679 München, Germany
⁶¹ Dipartimento di Fisica “Aldo Pontremoli”, Università degli Studi di Milano, Via Celoria 16, 20133 Milano, Italy
⁶² Institute of Theoretical Astrophysics, University of Oslo, PO Box 1029 Blindern, 0315 Oslo, Norway
⁶³ Leiden Observatory, Leiden University, Einsteinweg 55, 2333 CC Leiden, The Netherlands
⁶⁴ Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA
⁶⁵ Felix Hormuth Engineering, Goethestr. 17, 69181 Leimen, Germany
⁶⁶ Technical University of Denmark, Elektrovej 327, 2800 Kgs. Lyngby, Denmark
⁶⁷ Cosmic Dawn Center (DAWN), Denmark
⁶⁸ Max-Planck-Institut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany
⁶⁹ NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA
⁷⁰ Department of Physics and Helsinki Institute of Physics, Gustaf Hällströmin katu 2, 00014 University of Helsinki, Finland
⁷¹ Université de Genève, Département de Physique Théorique and Centre for Astroparticle Physics, 24 Quai Ernest-Ansermet, CH-1211 Genève 4, Switzerland
⁷² Department of Physics, PO Box 64 00014 University of Helsinki, Finland
⁷³ Helsinki Institute of Physics, Gustaf Hällströmin katu 2, University of Helsinki, Helsinki, Finland
⁷⁴ NOVA Optical Infrared Instrumentation Group at ASTRON, Oude Hoogeveensedijk 4, 7991 PD Dwingeloo, The Netherlands
⁷⁵ Centre de Calcul de l’IN2P3/CNRS, 21 Avenue Pierre de Coubertin, 69627 Villeurbanne Cedex, France
⁷⁶ Universität Bonn, Argelander-Institut für Astronomie, Auf dem Hügel 71, 53121 Bonn, Germany
⁷⁷ Dipartimento di Fisica e Astronomia “Augusto Righi” – Alma Mater Studiorum Università di Bologna, Via Piero Gobetti 93/2, 40129 Bologna, Italy
⁷⁸ Department of Physics, Institute for Computational Cosmology, Durham University, South Road DH1 3LE, UK
⁷⁹ Université Paris Cité, CNRS, Astroparticule et Cosmologie, 75013 Paris, France
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 Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Campus UAB, 08193 Bellaterra, (Barcelona), Spain
⁸³ DARK, Niels Bohr Institute, University of Copenhagen, Jagtvej 155, 2200 Copenhagen, Denmark
⁸⁴ Waterloo Centre for Astrophysics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
⁸⁵ Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
⁸⁶ Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada
⁸⁷ Centre National d’Etudes Spatiales – Centre Spatial de Toulouse, 18 Avenue Edouard Belin, 31401 Toulouse Cedex 9, France
⁸⁸ Institute of Space Science, Str. Atomistilor, Nr. 409 Măgurele, Ilfov 077125, Romania
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 Université St Joseph; Faculty of Sciences, Beirut, Lebanon
⁹² Departamento de Física, FCFM, Universidad de Chile, Blanco Encalada 2008, Santiago, Chile
⁹³ Universität Innsbruck, Institut für Astro- und Teilchenphysik, Technikerstr. 25/8, 6020 Innsbruck, Austria
⁹⁴ Institut d’Estudis Espacials de Catalunya (IEEC), Edifici RDIT, Campus UPC, 08860 Castelldefels, Barcelona, Spain
⁹⁵ Satlantis, University Science Park, Sede Bld 48940, Leioa-Bilbao, Spain
⁹⁶ Institute of Space Sciences (ICE, CSIC), Campus UAB, Carrer de Can Magrans, s/n, 08193 Barcelona, Spain
⁹⁷ Instituto de Astrofísica e Ciências do Espaço, Faculdade de Ciências, Universidade de Lisboa, Tapada da Ajuda, 1349-018 Lisboa, Portugal
⁹⁸ Universidad Politécnica de Cartagena, Departamento de Electrónica y Tecnología de Computadoras, Plaza del Hospital 1, 30202 Cartagena, Spain
⁹⁹ INFN-Bologna, Via Irnerio 46, 40126 Bologna, Italy
¹⁰⁰ Infrared Processing and Analysis Center, California Institute of Technology, Pasadena, CA 91125, USA
¹⁰¹ INAF, Istituto di Radioastronomia, Via Piero Gobetti 101, 40129 Bologna, Italy
¹⁰² Astronomical Observatory of the Autonomous Region of the Aosta Valley (OAVdA), Loc. Lignan 39, I-11020 Nus, (Aosta Valley), Italy
¹⁰³ Junia, EPA Department, 41 Bd Vauban, 59800 Lille, France
¹⁰⁴ Department of Physics, Royal Holloway, University of London, London TW20 0EX, UK
¹⁰⁵ ICSC – Centro Nazionale di Ricerca in High Performance Computing, Big Data e Quantum Computing, Via Magnanelli 2, Bologna, Italy
¹⁰⁶ Instituto de Física Teórica UAM-CSIC, Campus de Cantoblanco, 28049 Madrid, Spain
¹⁰⁷ CERCA/ISO, Department of Physics, Case Western Reserve University, 10900 Euclid Avenue, Cleveland, OH 44106, USA
¹⁰⁸ Laboratoire Univers et Théorie, Observatoire de Paris, Université PSL, Université Paris Cité, CNRS, 92190 Meudon, France
¹⁰⁹ INFN-Sezione di Milano, Via Celoria 16, 20133 Milano, Italy
¹¹⁰ Departamento de Física Fundamental, Universidad de Salamanca, Plaza de la Merced s/n, 37008 Salamanca, Spain
¹¹¹ Departamento de Astrofísica, Universidad de La Laguna, 38206 La Laguna, Tenerife, Spain
¹¹² Dipartimento di Fisica e Scienze della Terra, Università degli Studi di Ferrara, Via Giuseppe Saragat 1, 44122 Ferrara, Italy
¹¹³ Istituto Nazionale di Fisica Nucleare, Sezione di Ferrara, Via Giuseppe Saragat 1, 44122 Ferrara, Italy
¹¹⁴ Center for Data-Driven Discovery, Kavli IPMU (WPI), UTIAS, The University of Tokyo, Kashiwa, Chiba 277-8583, Japan
¹¹⁵ Ludwig-Maximilians-University, Schellingstrasse 4, 80799 Munich, Germany
¹¹⁶ Max-Planck-Institut für Physik, Boltzmannstr. 8, 85748 Garching, Germany
¹¹⁷ Dipartimento di Fisica – Sezione di Astronomia, Università di Trieste, Via Tiepolo 11, 34131 Trieste, Italy
¹¹⁸ Minnesota Institute for Astrophysics, University of Minnesota, 116 Church St SE, Minneapolis, MN 55455, USA
¹¹⁹ Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS, Laboratoire Lagrange, Bd de l’Observatoire, CS 34229, 06304 Nice Cedex 4, France
¹²⁰ Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu, HI 96822, USA
¹²¹ Department of Physics & Astronomy, University of California Irvine, Irvine, CA 92697, USA
¹²² Department of Astronomy & Physics and Institute for Computational Astrophysics, Saint Mary’s University, 923 Robie Street, Halifax, Nova Scotia B3H 3C3, Canada
¹²³ Departamento Física Aplicada, Universidad Politécnica de Cartagena, Campus Muralla del Mar, 30202 Cartagena, Murcia, Spain
¹²⁴ Université Paris-Saclay, CNRS, Institut d’Astrophysique Spatiale, 91405, Orsay, France
¹²⁵ Department of Physics, Oxford University, Keble Road, Oxford OX1 3RH, UK
¹²⁶ Department of Computer Science, Aalto University, PO Box 15400 Espoo FI-00 076, Finland
¹²⁷ Instituto de Astrofísica de Canarias, c/ Via Lactea s/n, La Laguna E-38200, Spain
¹²⁸ Departamento de Astrofísica de la Universidad de La Laguna, Avda. Francisco Sanchez, La Laguna E-38200, Spain
¹²⁹ Ruhr University Bochum, Faculty of Physics and Astronomy, Astronomical Institute (AIRUB), German Centre for Cosmological Lensing (GCCL), 44780 Bochum, Germany
¹³⁰ Univ. Grenoble Alpes, CNRS, Grenoble INP, LPSC-IN2P3, 53, Avenue des Martyrs, 38000 Grenoble, France
¹³¹ Department of Physics and Astronomy, Vesilinnantie 5, 20014 University of Turku, Finland
¹³² Serco for European Space Agency (ESA), Camino bajo del Castillo, s/n, Urbanizacion Villafranca del Castillo, Villanueva de la Cañada, 28692 Madrid, Spain
¹³³ ARC Centre of Excellence for Dark Matter Particle Physics, Melbourne, Australia
¹³⁴ Centre for Astrophysics & Supercomputing, Swinburne University of Technology, Hawthorn, Victoria 3122, Australia
¹³⁵ School of Physics and Astronomy, Queen Mary University of London, Mile End Road, London E1 4NS, UK
¹³⁶ Department of Physics and Astronomy, University of the Western Cape, Bellville, Cape Town 7535, South Africa
¹³⁷ Université Libre de Bruxelles (ULB), Service de Physique Théorique CP225, Boulevard du Triophe, 1050 Bruxelles, Belgium
¹³⁸ ICTP South American Institute for Fundamental Research, Instituto de Física Teórica, Universidade Estadual Paulista, São Paulo, Brazil
¹³⁹ IRFU, CEA, Université Paris-Saclay, 91191 Gif-sur-Yvette Cedex, France
¹⁴⁰ INAF-Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, 50125 Firenze, Italy
¹⁴¹ Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 2, 00185 Roma, Italy
¹⁴² Aurora Technology for European Space Agency (ESA), Camino Bajo del Castillo, s/n, Urbanizacion Villafranca del Castillo, Villanueva de la Cañada, 28692 Madrid, Spain
¹⁴³ Centro de Astrofísica da Universidade do Porto, Rua das Estrelas, 4150-762 Porto, Portugal
¹⁴⁴ HE Space for European Space Agency (ESA), Camino bajo del Castillo, s/n, Urbanizacion Villafranca del Castillo, Villanueva de la Cañada, 28692 Madrid, Spain
¹⁴⁵ Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK
¹⁴⁶ Department of Astrophysics, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland
¹⁴⁷ INAF-Osservatorio Astronomico di Brera, Via Brera 28, 20122 Milano, Italy
¹⁴⁸ INFN-Sezione di Genova, Via Dodecaneso 33, 16146 Genova, Italy
¹⁴⁹ Theoretical Astrophysics, Department of Physics and Astronomy, Uppsala University, Box 515, 751 20 Uppsala, Sweden
¹⁵⁰ Department of Astrophysical Sciences, Peyton Hall, Princeton University, Princeton, NJ 08544, USA
¹⁵¹ Niels Bohr Institute, University of Copenhagen, Jagtvej 128, 2200 Copenhagen, Denmark
¹⁵² Center for Cosmology and Particle Physics, Department of Physics, New York University, New York, NY 10003, USA
¹⁵³ Center for Computational Astrophysics, Flatiron Institute, 162 5th Avenue, 10010 New York, NY, USA
¹⁵⁴ Mathematical Institute, University of Leiden, Niels Bohrweg 1, 2333 CA Leiden, The Netherlands

^⋆ Corresponding author; n.tessore@ucl.ac.uk

Received: 27 August 2024
Accepted: 8 November 2024

Abstract

In this paper we present the framework for measuring angular power spectra in the Euclid mission. The observables in galaxy surveys, such as galaxy clustering and cosmic shear, are not continuous fields, but discrete sets of data, obtained only at the positions of galaxies. We show how to compute the angular power spectra of such discrete data sets, without treating observations as maps of an underlying continuous field that is overlaid with a noise component. This formalism allows us to compute the exact theoretical expectations for our measured spectra, under a number of assumptions that we track explicitly. In particular, we obtain exact expressions for the additive biases (‘shot noise’) in angular galaxy clustering and cosmic shear. For efficient practical computations, we introduce a spin-weighted spherical convolution with a well-defined convolution theorem, which allows us to apply exact theoretical predictions to finite-resolution maps, including HEALPix. When validating our methodology, we find that our measurements are biased by less than 1% of their statistical uncertainty in simulations of Euclid’s first data release.