Cluster strong lensing with hierarchical inference

Formalism, functional tests, and public code release

¹ INAF – Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Gobetti 93/3, 40129 Bologna, Italy
² DARK, Niels Bohr Institute, University of Copenhagen, Jagtvej 128, 2200 Copenhagen Ø, Denmark
e-mail: adriano.agnello@nbi.ku.dk
³ Kapteyn Astronomical Institute, University of Groningen, Postbus 800, 9700 AV Groningen, The Netherlands
⁴ Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85748 Garching, Germany

Received: 18 November 2019
Accepted: 9 November 2020

Abstract

Context. Lensing by galaxy clusters is a versatile probe of cosmology and extragalactic astrophysics, but the accuracy of some of its predictions is limited by the simplified models adopted to reduce the (otherwise intractable) number of degrees of freedom.

Aims. We aim to explore cluster lensing models in which the parameters of all cluster member galaxies are free to vary around some common scaling relations with non-zero scatter and deviate significantly from these relations if, and only if, the data require this.

Methods. We devised a Bayesian hierarchical inference framework that enables the determination of all lensing parameters and the scaling relation hyperparameters, including intrinsic scatter, from lensing constraints and (if given) stellar kinematic measurements. We achieve this through BAYESLENS, a purpose-built wrapper around common parametric lensing codes that can sample the full posterior on parameters and hyperparameters; we release BAYESLENS with this paper.

Results. We ran functional tests of our code against simple mock cluster lensing datasets with realistic uncertainties. The parameters and hyperparameters are recovered within their 68% credibility ranges and the positions of all the “observed” multiple images are accurately reproduced by the BAYELENS best-fit model, without over-fitting.

Conclusions. We have shown that an accurate description of cluster member galaxies is attainable, despite a large number of degrees of freedom, through fast and tractable inference. This extends beyond the most updated cluster lensing models. The precise impact on studies of cosmography, galaxy evolution, and high-redshift galaxy populations can then be quantified on real galaxy clusters. While other sources of systematics exist and may be significant in real clusters, our results show that the contribution of intrinsic scatter in cluster member populations can now be controlled.