Strong lensing selection effects

¹ Department of Astronomy, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, PR China
e-mail: sonnenfeld@sjtu.edu.cn
² Leiden Observatory, Leiden University, PO Box 9513 2300 RA Leiden, The Netherlands
³ Alma Mater Studiorum – Università di Bologna, Dipartimento di Fisica e Astronomia “Augusto Righi”, Via Gobetti 93/2, Bologna, Italy
⁴ CNRS and CNES, Laboratoire d’Astrophysique de Marseille, Aix-Marseille Université, 38 Rue Frédéric Joliot-Curie, 13388 Marseille, France
⁵ Department of Astronomy & Astrophysics, University of Chicago, Chicago, IL 60637, USA
⁶ Kavli Institute for Cosmological Physics, University of Chicago, Chicago, IL 60637, USA
⁷ Centre for Astrophysics and Supercomputing, Swinburne University of Technology, Hawthorn 3122, Australia

Received: 30 January 2023
Accepted: 18 July 2023

Abstract

Contact. Strong lenses are a biased subset of the general population of galaxies.

Aims. The goal of this work is to quantify how lens galaxies and lensed sources differ from their parent distribution, namely the strong lensing bias.

Methods. We first studied how the strong lensing cross-section varies as a function of lens and source properties. Then, we simulated strong lensing surveys with data similar to that expected for Euclid and measured the strong lensing bias in different scenarios. We focused particularly on two quantities: the stellar population synthesis mismatch parameter, α_sps, defined as the ratio between the true stellar mass of a galaxy and the stellar mass obtained from photometry, and the central dark matter mass at fixed stellar mass and size.

Results. Strong lens galaxies are biased towards higher stellar masses, smaller half-mass radii, and higher dark matter masses. The amplitude of the bias depends on the intrinsic scatter in the mass-related parameters of the galaxy population and on the completeness in Einstein radius of the lens sample. For values of the scatter that are consistent with observed scaling relations and a minimum detectable Einstein radius of 0.5″, the strong lensing bias in α_sps is 10%, while that in the central dark matter mass is 5%. The bias has little dependence on the properties of the source population: samples of galaxy-galaxy lenses and galaxy-quasar lenses that probe the same Einstein radius distribution are biased in a very similar way.

Conclusions. Given current uncertainties, strong lensing observations can be used directly to improve our current knowledge of the inner structure of galaxies, without the need to correct for selection effects. Time-delay measurements of H₀ from lensed quasars can take advantage of prior information obtained from galaxy-galaxy lenses with similar Einstein radii.