2023A&A...679A.124G

Context. Several recent studies have highlighted a discrepancy between the strong lensing (SL) properties of observed cluster galaxies and the predictions of Λ cold dark matter (CDM) cosmological hydrodynamical simulations. This discrepancy can be interpreted as the result of observed cluster members being more compact than their simulated counterparts.
Aims. In this work, we aim at a direct measurement of the compactness of a few selected galaxy-scale lenses in massive clusters, testing the accuracy of the scaling laws adopted to describe the members in SL models of galaxy clusters.
Methods. We selected the multiply imaged sources MACS J0416.1-2403 ID14 (z = 3.221), MACS J0416.1-2403 ID16 (z = 2.095), and MACS J1206.2-0847 ID14 (z = 3.753). Eight multiple images were observed for the first SL system, and six for the latter two. We focused on the main deflector of each galaxy-scale SL system (identified as members 8971, 8785, and 3910, respectively), and modelled its total mass distribution with a truncated isothermal sphere. To account for the lensing effects of the remaining components of the cluster, we took the most accurate SL model of its mass distribution available. To include the uncertainty and the systematics affecting the cluster-scale mass models, we explored the posterior probability distribution of its parameters and extracted 100 cluster mass distributions. For each of them, we optimised the mass parameters of the galaxy-scale lens: the bootstrapping procedure allowed us to obtain a realistic estimate of the uncertainty on their values.
Results. We measured a truncation radius value of $ 6.1^{+2.3}_{-1.1}\,\mathrm{kpc} $, $ 4.0^{+0.6}_{-0.4}\,\mathrm{kpc} $, and $ 5.2^{+1.3}_{-1.1}\,\mathrm{kpc} $ for members 8971, 8785, and 3910, corresponding to total mass values of $ M=1.2^{+0.3}_{-0.1}\times10^{11}\, M_\odot $, $ M=1.0^{+0.2}_{-0.1} \times 10^{10}\, M_\odot $, and $ M=6.3^{+1.0}_{-1.1} \times 10^{10}\, M_\odot $, respectively. Alternative non-truncated models with a higher number of free parameters do not lead to an improved description of the SL system and show some parametric degeneracies. We measured the stellar-to-total mass fraction within the effective radius for the three cluster members, finding 0.51 ± 0.21, 1.0 ± 0.4, and 0.39 ± 0.16, respectively.
Conclusions. We find that a parameterisation of the physical properties of cluster galaxies in SL models based on power-law scaling relations with respect to the observed total luminosity cannot accurately describe the compactness of the members over their full total mass range. Our results, instead, agree with recent modelling of the cluster members based on the Fundamental Plane relation. Finally, we report good agreement between our predicted values of the stellar-to-total mass fraction within the effective radius and those of early-type galaxies from the Sloan Lens ACS Survey. Our work significantly extends the regimes of the current samples of lens galaxies, towards the mass range that will be probed by the Euclid, Rubin, and James Webb Telescopes.