Euclid preparation

IV. Impact of undetected galaxies on weak-lensing shear measurements^⋆

¹ Argelander-Institut für Astronomie, Universität Bonn, Auf dem Hügel 71, 53121 Bonn, Germany
² Aix-Marseille Univ., CNRS, CNES, LAM, Marseille, France
e-mail: nicolas.martinet@lam.fr
³ Leiden Observatory, Leiden University, Niels Bohrweg 2, 2333 CA Leiden, The Netherlands
⁴ Department of Physics and Astronomy, Stony Brook University, Stony Brook, NY 11794, USA
⁵ Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ, UK
⁶ Instituto de Astrofísica e Ciências do Espaço, Universidade do Porto, CAUP, Rua das Estrelas, 4150-762 Porto, Portugal
⁷ Instituto de Astrofísica e Ciências do Espaço, Faculdade de Ciências, Universidade de Lisboa, Tapada da Ajuda, 1349-018 Lisboa, Portugal
⁸ INAF-Osservatorio Astronomico di Roma, Via Frascati 33, 00078 Monteporzio Catone, Italy
⁹ Universitäts-Sternwarte München, Fakultät für Physik, Ludwig-Maximilians-Universität München, Scheinerstrasse 1, 81679 München, Germany
¹⁰ INAF-Osservatorio Astrofisico di Torino, Via Osservatorio 20, 10025 Pino Torinese (TO), Italy
¹¹ Institute of Theoretical Astrophysics, University of Oslo, PO Box 1029, Blindern 0315 Oslo, Norway
¹² Institut de Física d’Altes Energies IFAE, 08193 Bellaterra, Barcelona, Spain
¹³ Université Paris Diderot, AIM, Sorbonne Paris Cité, CEA, CNRS, 91191 Gif-sur-Yvette Cedex, France
¹⁴ IRFU, CEA, Université Paris-Saclay, 91191 Gif-sur-Yvette Cedex, France
¹⁵ Departement of Physics and Astronomy, University of British Columbia, Vancouver, BC V6T 1Z1, Canada
¹⁶ Depto. de Electrónica y Tecnología de Computadoras Universidad Politécnica de Cartagena, 30202 Cartagena, Spain

Received: 1 February 2019
Accepted: 26 May 2019

Abstract

In modern weak-lensing surveys, the common approach to correct for residual systematic biases in the shear is to calibrate shape measurement algorithms using simulations. These simulations must fully capture the complexity of the observations to avoid introducing any additional bias. In this paper we study the importance of faint galaxies below the observational detection limit of a survey. We simulate simplified Euclid VIS images including and excluding this faint population, and measure the shift in the multiplicative shear bias between the two sets of simulations. We measure the shear with three different algorithms: a moment-based approach, model fitting, and machine learning. We find that for all methods, a spatially uniform random distribution of faint galaxies introduces a shear multiplicative bias of the order of a few times 10⁻³. This value increases to the order of 10⁻² when including the clustering of the faint galaxies, as measured in the Hubble Space Telescope Ultra-Deep Field. The magnification of the faint background galaxies due to the brighter galaxies along the line of sight is found to have a negligible impact on the multiplicative bias. We conclude that the undetected galaxies must be included in the calibration simulations with proper clustering properties down to magnitude 28 in order to reach a residual uncertainty on the multiplicative shear bias calibration of a few times 10⁻⁴, in line with the 2 × 10⁻³ total accuracy budget required by the scientific objectives of the Euclid survey. We propose two complementary methods for including faint galaxy clustering in the calibration simulations.