Euclid preparation

L. Calibration of the halo linear bias in Λ(v)CDM cosmologies

¹ INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34143 Trieste, Italy
² INFN, Sezione di Trieste, Via Valerio 2, 34127 Trieste TS, Italy
³ IFPU, Institute for Fundamental Physics of the Universe, via Beirut 2, 34151 Trieste, Italy
⁴ ICSC – Centro Nazionale di Ricerca in High Performance Computing, Big Data e Quantum Computing, Via Magnanelli 2, Bologna, Italy
⁵ Ludwig-Maximilians-University, Schellingstrasse 4, 80799 Munich, Germany
⁶ Donostia International Physics Center (DIPC), Paseo Manuel de Lardizabal, 4, 20018 Donostia-San Sebastián, Guipuzkoa, Spain
⁷ IKERBASQUE, Basque Foundation for Science, 48013 Bilbao, Spain
⁸ Universitäts-Sternwarte München, Fakultät für Physik, Ludwig-Maximilians-Universität München, Scheinerstrasse 1, 81679 München, Germany
⁹ Dipartimento di Fisica – Sezione di Astronomia, Università di Trieste, Via Tiepolo 11, 34131 Trieste, Italy
¹⁰ Department of Astrophysics, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland
¹¹ Université Paris-Saclay, CNRS, Institut d’astrophysique spatiale, 91405 Orsay, France
¹² Institut für Theoretische Physik, University of Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany
¹³ INAF-Osservatorio Astronomico di Brera, Via Brera 28, 20122 Milano, Italy
¹⁴ SISSA, International School for Advanced Studies, Via Bonomea 265, 34136 Trieste TS, Italy
¹⁵ Dipartimento di Fisica e Astronomia, Università di Bologna, Via Gobetti 93/2, 40129 Bologna, Italy
¹⁶ INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy
¹⁷ INFN-Sezione di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy
¹⁸ Max Planck Institute for Extraterrestrial Physics, Giessenbachstr. 1, 85748 Garching, Germany
¹⁹ INAF-Osservatorio Astrofisico di Torino, Via Osservatorio 20, 10025 Pino Torinese (TO), Italy
²⁰ Dipartimento di Fisica, Università di Genova, Via Dodecaneso 33, 16146, Genova, Italy
²¹ INFN-Sezione di Genova, Via Dodecaneso 33, 16146 Genova, Italy
²² Department of Physics “E. Pancini”, University Federico II, Via Cinthia 6, 80126, Napoli, Italy
²³ INAF-Osservatorio Astronomico di Capodimonte, Via Moiariello 16, 80131 Napoli, Italy
²⁴ INFN section of Naples, Via Cinthia 6, 80126 Napoli, Italy
²⁵ Aix-Marseille Université, CNRS, CNES, LAM, Marseille, France
²⁶ Dipartimento di Fisica, Università degli Studi di Torino, Via P. Giuria 1, 10125 Torino, Italy
²⁷ INFN-Sezione di Torino, Via P. Giuria 1, 10125 Torino, Italy
²⁸ INAF – IASF Milano, Via Alfonso Corti 12, 20133 Milano, 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 Institute for Theoretical Particle Physics and Cosmology (TTK), RWTH Aachen University, 52056 Aachen, Germany
³² INAF-Osservatorio Astronomico di Roma, Via Frascati 33, 00078 Monteporzio Catone, Italy
³³ Dipartimento di Fisica e Astronomia “Augusto Righi” – Alma Mater Studiorum Università di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy
³⁴ Instituto de Astrofísica de Canarias, Calle Vía Láctea s/n, 38204 San Cristóbal de La Laguna, Tenerife, Spain
³⁵ Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ, UK
³⁶ Jodrell Bank Centre for Astrophysics, Department of Physics and Astronomy, University of Manchester, Oxford Road, Manchester M13 9PL, UK
³⁷ European Space Agency/ESRIN, Largo Galileo Galilei 1, 00044 Frascati, Roma, Italy
³⁸ ESAC/ESA, Camino Bajo del Castillo, s/n., Urb. Villafranca del Castillo, 28692 Villanueva de la Cañada, Madrid, Spain
³⁹ Université Claude Bernard Lyon 1, CNRS/IN2P3, IP2I Lyon, UMR 5822, Villeurbanne 69100, France
⁴⁰ Institute of Physics, Laboratory of Astrophysics, Ecole Polytechnique Fédérale de Lausanne (EPFL), Observatoire de Sauverny, 1290 Versoix, Switzerland
⁴¹ UCB Lyon 1, CNRS/IN2P3, IUF, IP2I Lyon, 4 rue Enrico Fermi, 69622 Villeurbanne, France
⁴² Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, Edifício C8, Campo Grande, 1749-016 Lisboa, Portugal
⁴³ Instituto de Astrofísica e Ciências do Espaço, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, 1749-016 Lisboa, Portugal
⁴⁴ Department of Astronomy, University of Geneva, ch. d’Ecogia 16, 1290 Versoix, Switzerland
⁴⁵ INAF-Istituto di Astrofisica e Planetologia Spaziali, via del Fosso del Cavaliere, 100, 00100 Roma, Italy
⁴⁶ INFN-Padova, Via Marzolo 8, 35131 Padova, Italy
⁴⁷ Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM, 91191 Gif-sur-Yvette, France
⁴⁸ Institut d’Estudis Espacials de Catalunya (IEEC), Edifici RDIT, Campus UPC, 08860 Castelldefels, Barcelona, Spain
⁴⁹ Institute of Space Sciences (ICE, CSIC), Campus UAB, Carrer de Can Magrans, s/n, 08193 Barcelona, Spain
⁵⁰ Istituto Nazionale di Fisica Nucleare, Sezione di Bologna, Via Irnerio 46, 40126 Bologna, Italy
⁵¹ FRACTAL S.L.N.E., calle Tulipán 2, Portal 13 1A, 28231 Las Rozas de Madrid, Spain
⁵² INAF-Osservatorio Astronomico di Padova, Via dell’Osservatorio 5, 35122 Padova, Italy
⁵³ Dipartimento di Fisica “Aldo Pontremoli”, Università degli Studi di Milano, Via Celoria 16, 20133 Milano, Italy
⁵⁴ Institute of Theoretical Astrophysics, University of Oslo, PO Box 1029 Blindern, 0315 Oslo, Norway
⁵⁵ Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA
⁵⁶ Felix Hormuth Engineering, Goethestr. 17, 69181 Leimen, Germany
⁵⁷ Technical University of Denmark, Elektrovej 327, 2800 Kgs. Lyngby, Denmark
⁵⁸ Cosmic Dawn Center (DAWN), Denmark
⁵⁹ Université Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France
⁶⁰ Institut de Recherche en Astrophysique et Planétologie (IRAP), Université de Toulouse, CNRS, UPS, CNES, 14 Av. Edouard Belin, 31400 Toulouse, France
⁶¹ Max-Planck-Institut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany
⁶² NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA
⁶³ Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK
⁶⁴ Department of Physics and Helsinki Institute of Physics, Gustaf Hällströmin katu 2, 00014 University of Helsinki, Finland
⁶⁵ Aix-Marseille Université, CNRS/IN2P3, CPPM, Marseille, France
⁶⁶ Université de Genève, Département de Physique Théorique and Centre for Astroparticle Physics, 24 quai Ernest-Ansermet, 1211 Genève 4, Switzerland
⁶⁷ Department of Physics, PO Box 64, 00014 University of Helsinki, Finland
⁶⁸ Helsinki Institute of Physics, Gustaf Hällströmin katu 2, University of Helsinki, Helsinki, Finland
⁶⁹ NOVA optical infrared instrumentation group at ASTRON, Oude Hoogeveensedijk 4, 7991PD, Dwingeloo, The Netherlands
⁷⁰ Universität Bonn, Argelander-Institut für Astronomie, Auf dem Hügel 71, 53121 Bonn, Germany
⁷¹ INFN-Sezione di Roma, Piazzale Aldo Moro 2, c/o Dipartimento di Fisica, Edificio G. Marconi, 00185 Roma, Italy
⁷² Dipartimento di Fisica e Astronomia “Augusto Righi” – Alma Mater Studiorum Università di Bologna, via Piero Gobetti 93/2, 40129 Bologna, Italy
⁷³ Department of Physics, Institute for Computational Cosmology, Durham University, South Road DH1 3LE, UK
⁷⁴ Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS, Laboratoire Lagrange, Bd de l’Observatoire, CS 34229, 06304 Nice cedex 4, France
⁷⁵ University of Applied Sciences and Arts of Northwestern Switzerland, School of Engineering, 5210 Windisch, Switzerland
⁷⁶ Institut d’Astrophysique de Paris, 98bis Boulevard Arago, 75014 Paris, France
⁷⁷ Institut d’Astrophysique de Paris, UMR 7095, CNRS, and Sorbonne Université, 98 bis boulevard Arago, 75014 Paris, France
⁷⁸ European Space Agency/ESTEC, Keplerlaan 1, 2201 AZ Noordwijk, The Netherlands
⁷⁹ Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Campus UAB, 08193 Bellaterra (Barcelona), Spain
⁸⁰ DARK, Niels Bohr Institute, University of Copenhagen, Jagtvej 155, 2200 Copenhagen, Denmark
⁸¹ Waterloo Centre for Astrophysics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
⁸² Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
⁸³ Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada
⁸⁴ Space Science Data Center, Italian Space Agency, via del Politecnico snc, 00133 Roma, Italy
⁸⁵ Centre National d’Etudes Spatiales – Centre spatial de Toulouse, 18 avenue Edouard Belin, 31401 Toulouse Cedex 9, France
⁸⁶ Institute of Space Science, Str. Atomistilor, nr. 409 Măgurele, Ilfov 077125, Romania
⁸⁷ Dipartimento di Fisica e Astronomia “G. Galilei”, Università di Padova, Via Marzolo 8, 35131 Padova, Italy
⁸⁸ Université St Joseph; Faculty of Sciences, Beirut, Lebanon
⁸⁹ Departamento de Física, FCFM, Universidad de Chile, Blanco Encalada 2008, Santiago, Chile
⁹⁰ Satlantis, University Science Park, Sede Bld 48940, Leioa-Bilbao, Spain
⁹¹ Instituto de Astrofísica e Ciências do Espaço, Faculdade de Ciências, Universidade de Lisboa, Tapada da Ajuda, 1349-018 Lisboa, Portugal
⁹² Universidad Politécnica de Cartagena, Departamento de Electrónica y Tecnología de Computadoras, Plaza del Hospital 1, 30202 Cartagena, Spain
⁹³ INFN-Bologna, Via Irnerio 46, 40126 Bologna, Italy
⁹⁴ Kapteyn Astronomical Institute, University of Groningen, PO Box 800, 9700 AV Groningen, The Netherlands
⁹⁵ Infrared Processing and Analysis Center, California Institute of Technology, Pasadena, CA 91125, USA
⁹⁶ INAF, Istituto di Radioastronomia, Via Piero Gobetti 101, 40129 Bologna, Italy
⁹⁷ Astronomical Observatory of the Autonomous Region of the Aosta Valley (OAVdA), Loc. Lignan 39, 11020 Nus (Aosta Valley), Italy
⁹⁸ Junia, EPA department, 41 Bd Vauban, 59800 Lille, France
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 INFN – Sezione di Milano, Via Celoria 16, 20133 Milano, Italy
¹⁰³ Departamento de Física Fundamental. Universidad de Salamanca. Plaza de la Merced s/n., 37008 Salamanca, Spain
¹⁰⁴ Departamento de Astrofísica, Universidad de La Laguna, 38206, La Laguna, Tenerife, Spain
¹⁰⁵ Dipartimento di Fisica e Scienze della Terra, Università degli Studi di Ferrara, Via Giuseppe Saragat 1, 44122 Ferrara, Italy
¹⁰⁶ Istituto Nazionale di Fisica Nucleare, Sezione di Ferrara, Via Giuseppe Saragat 1, 44122 Ferrara, Italy
¹⁰⁷ Université de Strasbourg, CNRS, Observatoire astronomique de Strasbourg, UMR 7550, 67000 Strasbourg, France
¹⁰⁸ Center for Data-Driven Discovery, Kavli IPMU (WPI), UTIAS, The University of Tokyo, Kashiwa, Chiba 277-8583, Japan
¹⁰⁹ Max-Planck-Institut für Physik, Boltzmannstr. 8, 85748 Garching, Germany
¹¹⁰ Minnesota Institute for Astrophysics, University of Minnesota, 116 Church St SE, Minneapolis, MN 55455, USA
¹¹¹ Institute Lorentz, Leiden University, Niels Bohrweg 2, 2333 CA Leiden, The Netherlands
¹¹² Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu, HI 96822, USA
¹¹³ Department of Physics & Astronomy, University of California Irvine, Irvine, CA 92697, USA
¹¹⁴ Department of Astronomy & Physics and Institute for Computational Astrophysics, Saint Mary’s University, 923 Robie Street, Halifax, Nova Scotia B3H 3C3, Canada
¹¹⁵ Departamento Física Aplicada, Universidad Politécnica de Cartagena, Campus Muralla del Mar, 30202 Cartagena, Murcia, Spain
¹¹⁶ Instituto de Astrofísica de Canarias (IAC); Departamento de Astrofísica, Universidad de La Laguna (ULL), 38200 La Laguna, Tenerife, Spain
¹¹⁷ Department of Physics, Oxford University, Keble Road, Oxford OX1 3RH, UK
¹¹⁸ Université Paris Cité, CNRS, Astroparticule et Cosmologie, 75013 Paris, France
¹¹⁹ CEA Saclay, DFR/IRFU, Service d’Astrophysique, Bat. 709, 91191 Gif-sur-Yvette, France
¹²⁰ Institute of Cosmology and Gravitation, University of Portsmouth, Portsmouth PO1 3FX, UK
¹²¹ Department of Computer Science, Aalto University, PO Box 15400, Espoo 00 076, Finland
¹²² 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
¹²³ Ruhr University Bochum, Faculty of Physics and Astronomy, Astronomical Institute (AIRUB), German Centre for Cosmological Lensing (GCCL), 44780 Bochum, Germany
¹²⁴ Univ. Grenoble Alpes, CNRS, Grenoble INP, LPSC-IN2P3, 53, Avenue des Martyrs, 38000 Grenoble, France
¹²⁵ Department of Physics and Astronomy, Vesilinnantie 5, 20014 University of Turku, Finland
¹²⁶ Serco for European Space Agency (ESA), Camino bajo del Castillo, s/n, Urbanizacion Villafranca del Castillo, Villanueva de la Cañada, 28692 Madrid, Spain
¹²⁷ ARC Centre of Excellence for Dark Matter Particle Physics, Melbourne, Australia
¹²⁸ Centre for Astrophysics & Supercomputing, Swinburne University of Technology, Hawthorn, Victoria 3122, Australia
¹²⁹ School of Physics and Astronomy, Queen Mary University of London, Mile End Road, London E1 4NS, UK
¹³⁰ Department of Physics and Astronomy, University of the Western Cape, Bellville, Cape Town 7535, South Africa
¹³¹ ICTP South American Institute for Fundamental Research, Instituto de Física Teórica, Universidade Estadual Paulista, São Paulo, Brazil
¹³² IRFU, CEA, Université Paris-Saclay 91191 Gif-sur-Yvette Cedex, France
¹³³ Oskar Klein Centre for Cosmoparticle Physics, Department of Physics, Stockholm University, Stockholm 106 91, Sweden
¹³⁴ Astrophysics Group, Blackett Laboratory, Imperial College London, London SW7 2AZ, UK
¹³⁵ INAF-Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, 50125 Firenze, Italy
¹³⁶ Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 2, 00185 Roma, Italy
¹³⁷ Centro de Astrofísica da Universidade do Porto, Rua das Estrelas, 4150-762 Porto, Portugal
¹³⁸ Instituto de Astrofísica e Ciências do Espaço, Universidade do Porto, CAUP, Rua das Estrelas, 4150-762 Porto, Portugal
¹³⁹ HE Space for European Space Agency (ESA), Camino bajo del Castillo, s/n, Urbanizacion Villafranca del Castillo, Villanueva de la Cañada, 28692 Madrid, Spain
¹⁴⁰ Aurora Technology for European Space Agency (ESA), Camino bajo del Castillo, s/n, Urbanizacion Villafranca del Castillo, Villanueva de la Cañada, 28692 Madrid, Spain
¹⁴¹ Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK
¹⁴² Dipartimento di Fisica, Università degli studi di Genova, and INFN-Sezione di Genova, via Dodecaneso 33, 16146 Genova, Italy
¹⁴³ Theoretical astrophysics, Department of Physics and Astronomy, Uppsala University, Box 515, 751 20 Uppsala, Sweden
¹⁴⁴ Department of Physics, Royal Holloway, University of London, TW20 0EX, UK
¹⁴⁵ Mullard Space Science Laboratory, University College London, Holmbury St Mary, Dorking, Surrey RH5 6NT, UK
¹⁴⁶ Department of Astrophysical Sciences, Peyton Hall, Princeton University, Princeton, NJ 08544, USA
¹⁴⁷ Niels Bohr Institute, University of Copenhagen, Jagtvej 128, 2200 Copenhagen, Denmark
¹⁴⁸ Center for Cosmology and Particle Physics, Department of Physics, New York University, New York, NY 10003, USA
¹⁴⁹ Center for Computational Astrophysics, Flatiron Institute, 162 5th Avenue, New York, NY 10010, USA

^★ Corresponding author; tiago.batalha@inaf.it

Received: 24 June 2024
Accepted: 2 September 2024

Abstract

The Euclid mission, designed to map the geometry of the dark Universe, presents an unprecedented opportunity for advancing our understanding of the cosmos through its photometric galaxy cluster survey. Central to this endeavor is the accurate calibration of the mass- and redshift-dependent halo bias (HB), which is the focus of this paper. Our aim is to enhance the precision of HB predictions, which is crucial for deriving cosmological constraints from the clustering of galaxy clusters. Our study is based on the peak-background split (PBS) model linked to the halo mass function (HMF), and it extends it with a parametric correction to precisely align with results from an extended set of N-body simulations carried out with the OpenGADGET3 code. Employing simulations with fixed and paired initial conditions, we meticulously analyzed the matter-halo cross-spectrum and modeled its covariance using a large number of mock catalogs generated with Lagrangian perturbation theory simulations with the PINOCCHIO code. This ensures a comprehensive understanding of the uncertainties in our HB calibration. Our findings indicate that the calibrated HB model is remarkably resilient against changes in cosmological parameters, including those involving massive neutrinos. The robustness and adaptability of our calibrated HB model provide an important contribution to the cosmological exploitation of the cluster surveys to be provided by the Euclid mission. This study highlights the necessity of continuously refining the calibration of cosmological tools such as the HB to match the advancing quality of observational data. As we project the impact of our calibrated model on cosmological constraints, we find that given the sensitivity of the Euclid survey, a miscalibration of the HB could introduce biases in cluster cosmology analysis. Our work fills this critical gap, ensuring the HB calibration matches the expected precision of the Euclid survey.