Euclid: The reduced shear approximation and magnification bias for Stage IV cosmic shear experiments^⋆

¹ Mullard Space Science Laboratory, University College London, Holmbury St Mary, Dorking, Surrey RH5 6NT, UK
e-mail: anurag.deshpande.18@ucl.ac.uk
² I.N.F.N.–Sezione di Roma Piazzale Aldo Moro, 2 – c/o Dipartimento di Fisica, Edificio G. Marconi, 00185 Roma, Italy
³ INAF-Osservatorio Astronomico di Roma, Via Frascati 33, 00078 Monteporzio Catone, Italy
⁴ Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA
⁵ AIM, CEA, CNRS, Université Paris-Saclay, Université Paris Diderot, Sorbonne Paris Cité, 91191 Gif-sur-Yvette, France
⁶ INFN-Sezione di Torino, Via P. Giuria 1, 10125 Torino, Italy
⁷ Dipartimento di Fisica, Universitá degli Studi di Torino, Via P. Giuria 1, 10125 Torino, Italy
⁸ INAF-Osservatorio Astrofisico di Torino, Via Osservatorio 20, 10025 Pino Torinese, TO, Italy
⁹ INFN-Sezione di Milano, Via Celoria 16, 20133 Milano, Italy
¹⁰ INAF-IASF Milano, Via Alfonso Corti 12, 20133 Milano, Italy
¹¹ Institut d’Astrophysique de Paris, 98bis Boulevard Arago, 75014 Paris, France
¹² Université St Joseph, UR EGFEM, Faculty of Sciences, Beirut, Lebanon
¹³ Institut de Recherche en Astrophysique et Planétologie (IRAP), Université de Toulouse, CNRS, UPS, CNES, 14 Av. Edouard Belin, 31400 Toulouse, France
¹⁴ Departamento de Física, FCFM, Universidad de Chile, Blanco Encalada 2008, Santiago, Chile
¹⁵ Institute of Space Sciences (ICE, CSIC), Campus UAB, Carrer de Can Magrans, s/n, 08193 Barcelona, Spain
¹⁶ Institut d’Estudis Espacials de Catalunya (IEEC), 08034 Barcelona, Spain
¹⁷ INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy
¹⁸ Max Planck Institute for Extraterrestrial Physics, Giessenbachstr. 1, 85748 Garching, Germany
¹⁹ INAF-Osservatorio Astronomico di Capodimonte, Via Moiariello 16, 80131 Napoli, Italy
²⁰ Institut de Física d’Altes Energies IFAE, 08193 Bellaterra, Barcelona, Spain
²¹ Department of Physics “E. Pancini”, University Federico II, Via Cinthia 6, 80126 Napoli, Italy
²² INFN section of Naples, Via Cinthia 6, 80126 Napoli, Italy
²³ Centre National d’Etudes Spatiales, Toulouse, France
²⁴ Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ, UK
²⁵ ESAC/ESA, Camino Bajo del Castillo, s/n., Urb. Villafranca del Castillo, 28692 Villanueva de la Cañada, Madrid, Spain
²⁶ Department of Astronomy, University of Geneva, ch. d’Écogia 16, 1290 Versoix, Switzerland
²⁷ INFN-Padova, Via Marzolo 8, 35131 Padova, Italy
²⁸ Department of Physics & Astronomy, University of Sussex, Brighton BN1 9QH, UK
²⁹ Leiden Observatory, Leiden University, Niels Bohrweg 2, 2333 CA Leiden, The Netherlands
³⁰ von Hoerner & Sulger GmbH, SchloßPlatz 8, 68723 Schwetzingen, Germany
³¹ Universitäts-Sternwarte München, Fakultät für Physik, Ludwig-Maximilians-Universität München, Scheinerstrasse 1, 81679 München, Germany
³² Max-Planck-Institut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany
³³ Aix-Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France
³⁴ Univ Lyon, Univ Claude Bernard Lyon 1, CNRS/IN2P3, IP2I Lyon, UMR 5822, 69622 Villeurbanne, France
³⁵ Université de Genève, Département de Physique Théorique and Centre for Astroparticle Physics, 24 quai Ernest-Ansermet, 1211 Genève 4, Switzerland
³⁶ Institut d’Astrophysique Spatiale (IAS), Bâtiment 121, Université Paris-Sud 11 and CNRS, UMR 8617, 91405 Orsay, France
³⁷ Institute of Theoretical Astrophysics, University of Oslo, PO Box 1029 Blindern, 0315 Oslo, Norway
³⁸ Argelander-Institut für Astronomie, Universität Bonn, Auf dem Hügel 71, 53121 Bonn, Germany
³⁹ Institute for Computational Cosmology, Department of Physics, Durham University, South Road, Durham DH1 3LE, UK
⁴⁰ Université de Paris, 75013 Paris, France
⁴¹ LERMA, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Université, 75014 Paris, France
⁴² Observatoire de Sauverny, Ecole Polytechnique Fédérale de Lau- sanne, 1290 Versoix, Switzerland
⁴³ Dipartimento di Fisica e Astronomia, Universitá di Bologna, Via Gobetti 93/2, 40129 Bologna, Italy
⁴⁴ INFN-Bologna, Via Irnerio 46, 40126 Bologna, Italy
⁴⁵ INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34131 Trieste, Italy
⁴⁶ Space Science Data Center, Italian Space Agency, via del Politecnico snc, 00133 Roma, Italy
⁴⁷ Institute of Space Sciences (IEEC-CSIC), c/Can Magrans s/n, 08193 Cerdanyola del Vallés, Barcelona, Spain
⁴⁸ INFN-Sezione di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy
⁴⁹ Instituto de Astrofísica e Ciências do Espaço, Faculdade de Ciências, Universidade de Lisboa, Tapada da Ajuda, 1349-018 Lisboa, Portugal
⁵⁰ Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, Edifício C8, Campo Grande, PT1749-016 Lisboa, Portugal
⁵¹ Universidad Politécnica de Cartagena, Departamento de Electrónica y Tecnología de Computadoras, 30202 Cartagena, Spain
⁵² Infrared Processing and Analysis Center, California Institute of Technology, Pasadena, CA 91125, USA

Received: 16 December 2019
Accepted: 4 March 2020

Abstract

Context. Stage IV weak lensing experiments will offer more than an order of magnitude leap in precision. We must therefore ensure that our analyses remain accurate in this new era. Accordingly, previously ignored systematic effects must be addressed.

Aims. In this work, we evaluate the impact of the reduced shear approximation and magnification bias on information obtained from the angular power spectrum. To first-order, the statistics of reduced shear, a combination of shear and convergence, are taken to be equal to those of shear. However, this approximation can induce a bias in the cosmological parameters that can no longer be neglected. A separate bias arises from the statistics of shear being altered by the preferential selection of galaxies and the dilution of their surface densities in high-magnification regions.

Methods. The corrections for these systematic effects take similar forms, allowing them to be treated together. We calculated the impact of neglecting these effects on the cosmological parameters that would be determined from Euclid, using cosmic shear tomography. To do so, we employed the Fisher matrix formalism, and included the impact of the super-sample covariance. We also demonstrate how the reduced shear correction can be calculated using a lognormal field forward modelling approach.

Results. These effects cause significant biases in Ω_m, σ₈, n_s, Ω_DE, w₀, and w_a of −0.53σ, 0.43σ, −0.34σ, 1.36σ, −0.68σ, and 1.21σ, respectively. We then show that these lensing biases interact with another systematic effect: the intrinsic alignment of galaxies. Accordingly, we have developed the formalism for an intrinsic alignment-enhanced lensing bias correction. Applying this to Euclid, we find that the additional terms introduced by this correction are sub-dominant.