Euclid : Effects of sample covariance on the number counts of galaxy clusters^⋆

¹ IFPU, Institute for Fundamental Physics of the Universe, Via Beirut 2, 34151 Trieste, Italy
e-mail: alessandra.fumagalli@inaf.it
² Dipartimento di Fisica – Sezione di Astronomia, Universitá di Trieste, Via Tiepolo 11, 34131 Trieste, Italy
³ INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34131 Trieste, Italy
⁴ INFN, Sezione di Trieste, Via Valerio 2, 34127 Trieste TS, Italy
⁵ Institute of Cosmology and Gravitation, University of Portsmouth, Portsmouth PO1 3FX, UK
⁶ INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy
⁷ INAF-Osservatorio Astronomico di Padova, Via dell’Osservatorio 5, 35122 Padova, Italy
⁸ Max Planck Institute for Extraterrestrial Physics, Giessenbachstr. 1, 85748 Garching, Germany
⁹ INAF-Osservatorio Astrofisico di Torino, Via Osservatorio 20, 10025 Pino Torinese (TO), Italy
¹⁰ INFN-Sezione di Roma Tre, Via della Vasca Navale 84, 00146 Roma, Italy
¹¹ Department of Mathematics and Physics, Roma Tre University, Via della Vasca Navale 84, 00146 Rome, Italy
¹² INAF-Osservatorio Astronomico di Roma, Via Frascati 33, 00078 Monteporzio Catone, Italy
¹³ Centro de Astrofísica da Universidade do Porto, Rua das Estrelas, 4150-762 Porto, Portugal
¹⁴ Instituto de Astrofísica e Ciências do Espaço, Universidade do Porto, CAUP, Rua das Estrelas, 4150-762 Porto, Portugal
¹⁵ INAF-IASF Milano, Via Alfonso Corti 12, 20133 Milano, Italy
¹⁶ Department of Physics “E. Pancini”, University Federico II, Via Cinthia 6, 80126 Napoli, Italy
¹⁷ INFN section of Naples, Via Cinthia 6, 80126 Napoli, Italy
¹⁸ INAF-Osservatorio Astronomico di Capodimonte, Via Moiariello 16, 80131 Napoli, Italy
¹⁹ INAF-Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, 50125 Firenze, Italy
²⁰ Dipartimento di Fisica e Astronomia, Universitá di Bologna, Via Gobetti 93/2, 40129 Bologna, Italy
²¹ Institut national de physique nucléaire et de physique des particules, 3 rue Michel-Ange, 75794 Paris Cedex 16, France
²² Centre National d’Etudes Spatiales, Toulouse, France
²³ Jodrell Bank Centre for Astrophysics, School of Physics and Astronomy, University of Manchester, Oxford Road, Manchester M13 9PL, UK
²⁴ Aix-Marseille Univ, CNRS, CNES, LAM, Marseille, France
²⁵ Mullard Space Science Laboratory, University College London, Holmbury St Mary, Dorking, Surrey RH5 6NT, UK
²⁶ Department of Astronomy, University of Geneva, ch. d’Écogia 16, 1290 Versoix, Switzerland
²⁷ Université Paris-Saclay, CNRS, Institut d’astrophysique spatiale, 91405 Orsay, France
²⁸ INFN-Padova, Via Marzolo 8, 35131 Padova, Italy
²⁹ Univ Lyon, Univ Claude Bernard Lyon 1, CNRS/IN2P3, IP2I Lyon, UMR 5822, 69622 Villeurbanne, France
³⁰ Institute of Space Sciences (ICE, CSIC), Campus UAB, Carrer de Can Magrans, s/n, 08193 Barcelona, Spain
³¹ Institut d’Estudis Espacials de Catalunya (IEEC), Carrer Gran Capitá 2-4, 08034 Barcelona, Spain
³² INFN-Sezione di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy
³³ Universitäts-Sternwarte München, Fakultät für Physik, Ludwig-Maximilians-Universität München, Scheinerstrasse 1, 81679 München, Germany
³⁴ Dipartimento di Fisica “Aldo Pontremoli”, Universitá degli Studi di Milano, Via Celoria 16, 20133 Milano, Italy
³⁵ INFN-Sezione di Milano, Via Celoria 16, 20133 Milano, Italy
³⁶ INAF-Osservatorio Astronomico di Brera, Via Brera 28, 20122 Milano, Italy
³⁷ Institute of Theoretical Astrophysics, University of Oslo, PO Box 1029 Blindern, 0315 Oslo, Norway
³⁸ Leiden Observatory, Leiden University, Niels Bohrweg 2, 2333 CA Leiden, The Netherlands
³⁹ Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA
⁴⁰ von Hoerner & Sulger GmbH, SchloßPlatz 8, 68723 Schwetzingen, Germany
⁴¹ Max-Planck-Institut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany
⁴² AIM, CEA, CNRS, Université Paris-Saclay, Université Paris Diderot, Sorbonne Paris Cité, 91191 Gif-sur-Yvette, France
⁴³ Université de Genève, Département de Physique Théorique and Centre for Astroparticle Physics, 24 quai Ernest-Ansermet, 1211 Genève 4, Switzerland
⁴⁴ Department of Physics and Helsinki Institute of Physics, Gustaf Hällströmin katu 2, 00014 University of Helsinki, Finland
⁴⁵ European Space Agency/ESTEC, Keplerlaan 1, 2201 AZ Noordwijk, The Netherlands
⁴⁶ NOVA optical infrared instrumentation group at ASTRON, Oude Hoogeveensedijk 4, 7991 PD Dwingeloo, The Netherlands
⁴⁷ Argelander-Institut für Astronomie, Universität Bonn, Auf dem Hügel 71, 53121 Bonn, Germany
⁴⁸ Institute for Computational Cosmology, Department of Physics, Durham University, South Road, Durham DH1 3LE, UK
⁴⁹ California institute of Technology, 1200 E California Blvd, Pasadena, CA 91125, USA
⁵⁰ Observatoire de Sauverny, Ecole Polytechnique Fédérale de Lau- sanne, 1290 Versoix, Switzerland
⁵¹ INFN-Bologna, Via Irnerio 46, 40126 Bologna, Italy
⁵² Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Campus UAB, 08193 Bellaterra, (Barcelona), Spain
⁵³ Department of Physics and Astronomy, University of Aarhus, Ny Munkegade 120, 8000 Aarhus C, Denmark
⁵⁴ Institute of Space Science, Bucharest 077125, Romania
⁵⁵ I.N.F.N.-Sezione di Roma Piazzale Aldo Moro, 2 – c/o Dipartimento di Fisica, Edificio G. Marconi, 00185 Roma, Italy
⁵⁶ Aix-Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France
⁵⁷ Dipartimento di Fisica e Astronomia “G. Galilei”, Universitá di Padova, Via Marzolo 8, 35131 Padova, Italy
⁵⁸ Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ, UK
⁵⁹ Instituto de Astrofísica e Ciências do Espaço, Faculdade de Ciências, Universidade de Lisboa, Tapada da Ajuda, 1349-018 Lisboa, Portugal
⁶⁰ Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, Edifício C8, Campo Grande, 1749-016 Lisboa, Portugal
⁶¹ Universidad Politécnica de Cartagena, Departamento de Electrónica y Tecnología de Computadoras, 30202 Cartagena, Spain
⁶² Kapteyn Astronomical Institute, University of Groningen, PO Box 800 9700 AV Groningen, The Netherlands
⁶³ Infrared Processing and Analysis Center, California Institute of Technology, Pasadena, CA 91125, USA
⁶⁴ European Space Agency/ESRIN, Largo Galileo Galilei 1, 00044 Frascati, Roma, Italy
⁶⁵ ESAC/ESA, Camino Bajo del Castillo, s/n., Urb. Villafranca del Castillo, 28692 Villanueva de la Cañada, Madrid, Spain
⁶⁶ APC, AstroParticule et Cosmologie, Université Paris Diderot, CNRS/IN2P3, CEA/lrfu, Observatoire de Paris, Sorbonne Paris Cité, 10 rue Alice Domon et Léonie Duquet, 75205 Paris Cedex 13, France

Received: 17 February 2021
Accepted: 9 April 2021

Abstract

Aims. We investigate the contribution of shot-noise and sample variance to uncertainties in the cosmological parameter constraints inferred from cluster number counts, in the context of the Euclid survey.

Methods. By analysing 1000 Euclid-like light cones, produced with the PINOCCHIO approximate method, we validated the analytical model of Hu & Kravtsov (2003, ApJ, 584, 702) for the covariance matrix, which takes into account both sources of statistical error. Then, we used such a covariance to define the likelihood function that is better equipped to extract cosmological information from cluster number counts at the level of precision that will be reached by the future Euclid photometric catalogs of galaxy clusters. We also studied the impact of the cosmology dependence of the covariance matrix on the parameter constraints.

Results. The analytical covariance matrix reproduces the variance measured from simulations within the 10 percent; such a difference has no sizeable effect on the error of cosmological parameter constraints at this level of statistics. Also, we find that the Gaussian likelihood with full covariance is the only model that provides an unbiased inference of cosmological parameters without underestimating the errors, and that the cosmology-dependence of the covariance must be taken into account.