Euclid preparation

LXXXIX. Accurate and precise data-driven angular power spectrum covariances

¹ Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK
² Institute of Cosmology and Gravitation, University of Portsmouth, Portsmouth PO1 3FX, UK
³ Oskar Klein Centre for Cosmoparticle Physics, Department of Physics, Stockholm University, Stockholm SE-106 91, Sweden
⁴ Astrophysics Group, Blackett Laboratory, Imperial College London, London SW7 2AZ, UK
⁵ Université Paris-Saclay, CNRS, Institut d’astrophysique spatiale, 91405 Orsay, France
⁶ ESAC/ESA, Camino Bajo del Castillo, s/n., Urb. Villafranca del Castillo, 28692 Villanueva de la Cañada, Madrid, Spain
⁷ School of Mathematics and Physics, University of Surrey, Guildford, Surrey GU2 7XH, UK
⁸ Institut für Theoretische Physik, University of Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany
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 IFPU, Institute for Fundamental Physics of the Universe, via Beirut 2, 34151 Trieste, Italy
¹² INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34143 Trieste, Italy
¹³ INFN, Sezione di Trieste, Via Valerio 2, 34127 Trieste TS, Italy
¹⁴ SISSA, International School for Advanced Studies, Via Bonomea 265, 34136 Trieste TS, Italy
¹⁵ Centre National d’Etudes Spatiales – Centre spatial de Toulouse, 18 avenue Edouard Belin, 31401 Toulouse Cedex 9, France
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 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 Dipartimento di Fisica, Università degli Studi di Torino, Via P. Giuria 1, 10125 Torino, Italy
²³ INFN-Sezione di Torino, Via P. Giuria 1, 10125 Torino, Italy
²⁴ INAF-Osservatorio Astrofisico di Torino, Via Osservatorio 20, 10025 Pino Torinese (TO), Italy
²⁵ INAF-IASF Milano, Via Alfonso Corti 12, 20133 Milano, Italy
²⁶ INAF-Osservatorio Astronomico di Roma, Via Frascati 33, 00078 Monteporzio Catone, Italy
²⁷ INFN-Sezione di Roma, Piazzale Aldo Moro, 2 – c/o Dipartimento di Fisica, Edificio G. Marconi, 00185 Roma, Italy
²⁸ Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas (CIEMAT), Avenida Complutense 40, 28040 Madrid, Spain
²⁹ Port d’Informació Científica, Campus UAB, C. Albareda s/n, 08193 Bellaterra (Barcelona), Spain
³⁰ INFN section of Naples, Via Cinthia 6, 80126 Napoli, Italy
³¹ Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu, HI 96822, USA
³² Dipartimento di Fisica e Astronomia “Augusto Righi” – Alma Mater Studiorum Università di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy
³³ Instituto de Astrofísica de Canarias, Vía Láctea, 38205 La Laguna, Tenerife, Spain
³⁴ Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ, UK
³⁵ European Space Agency/ESRIN, Largo Galileo Galilei 1, 00044 Frascati, Roma, Italy
³⁶ Université Claude Bernard Lyon 1, CNRS/IN2P3, IP2I Lyon, UMR 5822, Villeurbanne F-69100, France
³⁷ Institut de Ciències del Cosmos (ICCUB), Universitat de Barcelona (IEEC-UB), Martí i Franquès 1, 08028 Barcelona, Spain
³⁸ Institució Catalana de Recerca i Estudis Avançats (ICREA), Passeig de Lluís Companys 23, 08010 Barcelona, Spain
³⁹ UCB Lyon 1, CNRS/IN2P3, IUF, IP2I Lyon, 4 rue Enrico Fermi, 69622 Villeurbanne, France
⁴⁰ Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, Edifício C8, Campo Grande, PT1749-016 Lisboa, Portugal
⁴¹ Instituto de Astrofísica e Ciências do Espaço, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, 1749-016 Lisboa, Portugal
⁴² Department of Astronomy, University of Geneva, ch. d’Ecogia 16, 1290 Versoix, Switzerland
⁴³ INFN-Padova, Via Marzolo 8, 35131 Padova, Italy
⁴⁴ Aix-Marseille Université, CNRS/IN2P3, CPPM, Marseille, France
⁴⁵ INAF-Istituto di Astrofisica e Planetologia Spaziali, via del Fosso del Cavaliere, 100, 00100 Roma, Italy
⁴⁶ Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM, 91191 Gif-sur-Yvette, France
⁴⁷ Space Science Data Center, Italian Space Agency, via del Politecnico snc, 00133 Roma, Italy
⁴⁸ INFN-Bologna, Via Irnerio 46, 40126 Bologna, Italy
⁴⁹ Institut d’Estudis Espacials de Catalunya (IEEC), Edifici RDIT, Campus UPC, 08860 Castelldefels, Barcelona, Spain
⁵⁰ Institute of Space Sciences (ICE, CSIC), Campus UAB, Carrer de Can Magrans, s/n, 08193 Barcelona, Spain
⁵¹ Universitäts-Sternwarte München, Fakultät für Physik, Ludwig-Maximilians-Universität München, Scheinerstrasse 1, 81679 München, Germany
⁵² Max Planck Institute for Extraterrestrial Physics, Giessenbachstr. 1, 85748 Garching, Germany
⁵³ INAF-Osservatorio Astronomico di Padova, Via dell’Osservatorio 5, 35122 Padova, Italy
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), 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 Helsinki Institute of Physics, Gustaf Hällströmin katu 2, 00014 University of Helsinki, Helsinki, Finland
⁶¹ Université de Genève, Département de Physique Théorique and Centre for Astroparticle Physics, 24 quai Ernest-Ansermet, CH-1211 Genève 4, Switzerland
⁶² Department of Physics, P.O. Box 64, 00014 University of Helsinki, Helsinki, Finland
⁶³ Helsinki Institute of Physics, Gustaf Hällströmin katu 2, University of Helsinki, Helsinki, Finland
⁶⁴ Laboratoire d’etude de l’Univers et des phenomenes eXtremes, Observatoire de Paris, Université PSL, Sorbonne Université, CNRS, 92190 Meudon, France
⁶⁵ Institute of Theoretical Astrophysics, University of Oslo, P.O. Box 1029, Blindern, 0315 Oslo, Norway
⁶⁶ SKA Observatory, Jodrell Bank, Lower Withington, Macclesfield, Cheshire SK11 9FT, UK
⁶⁷ Centre de Calcul de l’IN2P3/CNRS, 21 avenue Pierre de Coubertin, 69627 Villeurbanne Cedex, France
⁶⁸ Dipartimento di Fisica “Aldo Pontremoli”, Università degli Studi di Milano, Via Celoria 16, 20133 Milano, Italy
⁶⁹ INFN-Sezione di Milano, Via Celoria 16, 20133 Milano, Italy
⁷⁰ University of Applied Sciences and Arts of Northwestern Switzerland, School of Computer Science, 5210 Windisch, Switzerland
⁷¹ Universität Bonn, Argelander-Institut für Astronomie, Auf dem Hügel 71, 53121 Bonn, Germany
⁷² Aix-Marseille Université, CNRS, CNES, LAM, Marseille, France
⁷³ Dipartimento di Fisica e Astronomia “Augusto Righi” – Alma Mater Studiorum Università di Bologna, via Piero Gobetti 93/2, 40129 Bologna, Italy
⁷⁴ Department of Physics, Institute for Computational Cosmology, Durham University, South Road, Durham DH1 3LE, UK
⁷⁵ Université Paris Cité, CNRS, Astroparticule et Cosmologie, 75013 Paris, France
⁷⁶ CNRS-UCB International Research Laboratory, Centre Pierre Binétruy, IRL2007, CPB-IN2P3, Berkeley, USA
⁷⁷ Institut d’Astrophysique de Paris, 98bis Boulevard Arago, 75014 Paris, France
⁷⁸ Institut d’Astrophysique de Paris, UMR 7095, CNRS, and Sorbonne Université, 98 bis boulevard Arago, 75014 Paris, France
⁷⁹ Institute of Physics, Laboratory of Astrophysics, Ecole Polytechnique Fédérale de Lausanne (EPFL), Observatoire de Sauverny, 1290 Versoix, Switzerland
⁸⁰ 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
⁸¹ Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Campus UAB, 08193 Bellaterra (Barcelona), Spain
⁸² European Space Agency/ESTEC, Keplerlaan 1, 2201 AZ, Noordwijk, The Netherlands
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 Institute of Space Science, Str. Atomistilor, nr. 409 Măgurele, Ilfov 077125, Romania
⁸⁸ Consejo Superior de Investigaciones Cientificas, Calle Serrano 117, 28006 Madrid, Spain
⁸⁹ Universidad de La Laguna, Departamento de Astrofísica, 38206 La Laguna, Tenerife, Spain
⁹⁰ Dipartimento di Fisica e Astronomia “G. Galilei”, Università di Padova, Via Marzolo 8, 35131 Padova, Italy
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 Department of Physics, Royal Holloway, University of London, TW20 0EX, Egham, UK
⁹⁷ Instituto de Astrofísica e Ciências do Espaço, Faculdade de Ciências, Universidade de Lisboa, Tapada da Ajuda, 1349-018 Lisboa, Portugal
⁹⁸ Cosmic Dawn Center (DAWN)
⁹⁹ Niels Bohr Institute, University of Copenhagen, Jagtvej 128, 2200 Copenhagen, Denmark
¹⁰⁰ Universidad Politécnica de Cartagena, Departamento de Electrónica y Tecnología de Computadoras, Plaza del Hospital 1, 30202 Cartagena, Spain
¹⁰¹ Kapteyn Astronomical Institute, University of Groningen, PO Box 800, 9700 AV, Groningen, The Netherlands
¹⁰² Infrared Processing and Analysis Center, California Institute of Technology, Pasadena, CA 91125, USA
¹⁰³ Dipartimento di Fisica e Scienze della Terra, Università degli Studi di Ferrara, Via Giuseppe Saragat 1, 44122 Ferrara, Italy
¹⁰⁴ Istituto Nazionale di Fisica Nucleare, Sezione di Ferrara, Via Giuseppe Saragat 1, 44122 Ferrara, Italy
¹⁰⁵ INAF, Istituto di Radioastronomia, Via Piero Gobetti 101, 40129 Bologna, Italy
¹⁰⁶ Astronomical Observatory of the Autonomous Region of the Aosta Valley (OAVdA), Loc. Lignan 39, I-11020 Nus (Aosta Valley), Italy
¹⁰⁷ Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS, Laboratoire Lagrange, Bd de l’Observatoire, CS 34229, 06304 Nice cedex 4, France
¹⁰⁸ Department of Physics, Oxford University, Keble Road, Oxford OX1 3RH, UK
¹⁰⁹ Aurora Technology for European Space Agency (ESA), Camino bajo del Castillo, s/n, Urbanizacion Villafranca del Castillo, Villanueva de la Cañada, 28692 Madrid, Spain
¹¹⁰ INAF – Osservatorio Astronomico di Brera, via Emilio Bianchi 46, 23807 Merate, Italy
¹¹¹ INAF-Osservatorio Astronomico di Brera, Via Brera 28, 20122 Milano, Italy, and INFN-Sezione di Genova, Via Dodecaneso 33, 16146 Genova, Italy
¹¹² ICL, Junia, Université Catholique de Lille, LITL, 59000 Lille, France
¹¹³ ICSC – Centro Nazionale di Ricerca in High Performance Computing, Big Data e Quantum Computing, Via Magnanelli 2, Bologna, Italy
¹¹⁴ Instituto de Física Teórica UAM-CSIC, Campus de Cantoblanco, 28049 Madrid, Spain
¹¹⁵ CERCA/ISO, Department of Physics, Case Western Reserve University, 10900 Euclid Avenue, Cleveland, OH 44106, USA
¹¹⁶ Technical University of Munich, TUM School of Natural Sciences, Physics Department, James-Franck-Str. 1, 85748 Garching, Germany
¹¹⁷ Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85748 Garching, Germany
¹¹⁸ Laboratoire Univers et Théorie, Observatoire de Paris, Université PSL, Université Paris Cité, CNRS, 92190 Meudon, France
¹¹⁹ Departamento de Física Fundamental. Universidad de Salamanca, Plaza de la Merced s/n., 37008 Salamanca, Spain
¹²⁰ Instituto de Astrofísica de Canarias (IAC); Departamento de Astrofísica, Universidad de La Laguna (ULL), 38200 La Laguna, Tenerife, Spain
¹²¹ Université de Strasbourg, CNRS, Observatoire astronomique de Strasbourg, UMR 7550, 67000 Strasbourg, France
¹²² Center for Data-Driven Discovery, Kavli IPMU (WPI), UTIAS, The University of Tokyo, Kashiwa, Chiba 277-8583, Japan
¹²³ Dipartimento di Fisica – Sezione di Astronomia, Università di Trieste, Via Tiepolo 11, 34131 Trieste, Italy
¹²⁴ Jodrell Bank Centre for Astrophysics, Department of Physics and Astronomy, University of Manchester, Oxford Road, Manchester M13 9PL, UK
¹²⁵ California Institute of Technology, 1200 E California Blvd, Pasadena, CA 91125, USA
¹²⁶ Department of Physics & Astronomy, University of California Irvine, Irvine, CA 92697, USA
¹²⁷ Departamento Física Aplicada, Universidad Politécnica de Cartagena, Campus Muralla del Mar, 30202 Cartagena, Murcia, Spain
¹²⁸ Instituto de Física de Cantabria, Edificio Juan Jordá, Avenida de los Castros, 39005 Santander, Spain
¹²⁹ Observatorio Nacional, Rua General Jose Cristino, 77-Bairro Imperial de Sao Cristovao, Rio de Janeiro, 20921-400, Brazil
¹³⁰ INFN, Sezione di Lecce, Via per Arnesano, CP-193, 73100 Lecce, Italy
¹³¹ Department of Mathematics and Physics E. De Giorgi, University of Salento, Via per Arnesano, CP-I93, 73100 Lecce, Italy
¹³² INAF-Sezione di Lecce, c/o Dipartimento Matematica e Fisica, Via per Arnesano, 73100 Lecce, Italy
¹³³ CEA Saclay, DFR/IRFU, Service d’Astrophysique, Bat. 709, 91191 Gif-sur-Yvette, France
¹³⁴ Department of Computer Science, Aalto University, PO Box 15400 Espoo FI-00 076, Finland
¹³⁵ Instituto de Astrofísica de Canarias, c/ Via Lactea s/n, La Laguna 38200, Spain. Departamento de Astrofísica de la Universidad de La Laguna, Avda. Francisco Sanchez, La Laguna, 38200, Spain
¹³⁶ Ruhr University Bochum, Faculty of Physics and Astronomy, Astronomical Institute (AIRUB), German Centre for Cosmological Lensing (GCCL), 44780 Bochum, Germany
¹³⁷ Department of Physics and Astronomy, Vesilinnantie 5, 20014 University of Turku, Turku, Finland
¹³⁸ Serco for European Space Agency (ESA), Camino bajo del Castillo, s/n, Urbanizacion Villafranca del Castillo, Villanueva de la Cañada, 28692 Madrid, Spain
¹³⁹ ARC Centre of Excellence for Dark Matter Particle Physics, Melbourne, Australia
¹⁴⁰ Centre for Astrophysics & Supercomputing, Swinburne University of Technology, Hawthorn, Victoria 3122, Australia
¹⁴¹ Department of Physics and Astronomy, University of the Western Cape, Bellville, Cape Town, 7535, South Africa
¹⁴² DAMTP, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, UK
¹⁴³ Kavli Institute for Cosmology Cambridge, Madingley Road, Cambridge CB3 0HA, UK
¹⁴⁴ Department of Astrophysics, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland
¹⁴⁵ Department of Physics, Centre for Extragalactic Astronomy, Durham University, South Road, Durham DH1 3LE, UK
¹⁴⁶ Institute for Theoretical Particle Physics and Cosmology (TTK), RWTH Aachen University, 52056 Aachen, Germany
¹⁴⁷ IRFU, CEA, Université Paris-Saclay, 91191 Gif-sur-Yvette Cedex, France
¹⁴⁸ Univ. Grenoble Alpes, CNRS, Grenoble INP, LPSC-IN2P3, 53, Avenue des Martyrs, 38000 Grenoble, France
¹⁴⁹ INAF-Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, 50125 Firenze, Italy
¹⁵⁰ Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 2, 00185 Roma, Italy
¹⁵¹ Centro de Astrofísica da Universidade do Porto, Rua das Estrelas, 4150-762 Porto, Portugal
¹⁵² Instituto de Astrofísica e Ciências do Espaço, Universidade do Porto, CAUP, Rua das Estrelas, PT4150-762 Porto, Portugal
¹⁵³ HE Space for European Space Agency (ESA), Camino bajo del Castillo, s/n, Urbanizacion Villafranca del Castillo, Villanueva de la Cañada, 28692 Madrid, Spain
¹⁵⁴ Theoretical astrophysics, Department of Physics and Astronomy, Uppsala University, Box 516, 751 37 Uppsala, Sweden
¹⁵⁵ Mathematical Institute, University of Leiden, Einsteinweg 55, 2333 CA, Leiden, The Netherlands
¹⁵⁶ Leiden Observatory, Leiden University, Einsteinweg 55, 2333 CC, Leiden, The Netherlands
¹⁵⁷ Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK
¹⁵⁸ Department of Astrophysical Sciences, Peyton Hall, Princeton University, Princeton, NJ 08544, USA
¹⁵⁹ Space physics and astronomy research unit, University of Oulu, Pentti Kaiteran katu 1, FI-90014 Oulu, Finland
¹⁶⁰ Center for Computational Astrophysics, Flatiron Institute, 162 5th Avenue, 10010 New York, NY, USA

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Received: 10 June 2025
Accepted: 1 February 2026

Abstract

We develop techniques for generating accurate and precise internal covariances for measurements of clustering and weak-lensing angular power spectra. These methods have been designed to produce non-singular and unbiased covariances for Euclid’s large anticipated data vector and will be critical for validation against observational systematic effects. We constructed jackknife segments that are equal in area to a high precision by adapting the binary space partition algorithm to work on arbitrarily shaped regions on the unit sphere. Jackknife estimates of the covariances are internally derived and require no assumptions about cosmology or galaxy population and bias. Our covariance estimation, called DICES (Debiased Internal Covariance Estimation with Shrinkage), first estimated a noisy covariance through conventional delete-1 jackknife resampling. This was followed by linear shrinkage of the empirical correlation matrix towards the Gaussian prediction, rather than linear shrinkage of the covariance matrix. Shrinkage ensures the covariance is non-singular and therefore invertible, which is critical for the estimation of likelihoods and validation. We then applied a delete-2 jackknife bias correction to the diagonal components of the jackknife covariance that removed the general tendency for jackknife error estimates to be biased high. We validated internally derived covariances, which used the jackknife resampling technique, on synthetic Euclid-like lognormal catalogues. We demonstrate that DICES produces accurate, non-singular covariance estimates, with the relative error improving by 33% for the covariance and 48% for the correlation structure in comparison to jackknife estimates. These estimates can be used for highly accurate regression and inference.